diff --git a/C/convexhull.c b/C/convexhull.c deleted file mode 100644 --- a/C/convexhull.c +++ /dev/null @@ -1,714 +0,0 @@ -#define qh_QHimport -#include "qhull_ra.h" -#include "convexhull.h" -#include "utils.h" - -// to use the qsort function - sort vertices according to their ids -int cmpvertices (const void * a, const void * b) { - return ( (*((VertexT*)a)).id - (*((VertexT*)b)).id ); -} -// - sort full vertices -int cmpfullvertices (const void * a, const void * b) { - return ( (*((FullVertexT*)a)).id - (*((FullVertexT*)b)).id ); -} -// - sort edges -int cmpedges (const void * a, const void * b) { - if((*(unsigned**)a)[0] > (*(unsigned**)b)[0]){ - return 1; - }else if((*(unsigned**)a)[0] == (*(unsigned**)b)[0]){ - return (*(unsigned**)a)[1] - (*(unsigned**)b)[1]; - }else{ - return -1; - } -} - -/* test equality of two _sorted_ arrays */ -unsigned equalarraysu(unsigned* array1, unsigned* array2, unsigned length){ - unsigned i; - for(i=0; i < length; i++){ - if(array1[i] != array2[i]){ - break; - } - } - return i == length; -} - -/* return ids of a vector of VertexT */ -unsigned* map_vertexid(VertexT* vertices, unsigned nvertices){ - unsigned* ids = malloc(nvertices * sizeof(unsigned)); - for(unsigned v=0; v < nvertices; v++){ - ids[v] = vertices[v].id; - } - return ids; -} - -/* return ids of a vector of RidgeT */ -unsigned* map_ridgeid(RidgeT* ridges, unsigned nridges){ - unsigned* ids = malloc(nridges * sizeof(unsigned)); - for(unsigned r=0; r < nridges; r++){ - ids[r] = ridges[r].id; - } - return ids; -} - -// void deepCopyRidge(RidgeT* src, RidgeT* dest) { et dim ! -// dest = malloc(sizeof(RidgeT)); -// *dest = *src; -// dest->vertices = malloc(src->nvertices * sizeof(VertexT)); -// for(unsigned v=0; vnvertices; v++){ -// dest->vertices[v].id = src.vertices[v].id; -// memcpy(dest->vertices[v].point, dest->vertices[v].point, dim * sizeof(double)); -// } -// } - -/* deep copy of a ridge */ -RidgeT copyRidge(RidgeT ridge, unsigned dim){ - RidgeT out; - out.ridgeOf1 = ridge.ridgeOf1; - out.ridgeOf2 = ridge.ridgeOf2; - out.nvertices = ridge.nvertices; - out.nedges = ridge.nedges; - out.vertices = malloc(out.nvertices * sizeof(VertexT)); - for(unsigned v=0; v < out.nvertices; v++){ - out.vertices[v].id = ridge.vertices[v].id; - out.vertices[v].point = malloc(dim * sizeof(double)); - for(unsigned i=0; i < dim; i++){ - out.vertices[v].point[i] = ridge.vertices[v].point[i]; - } - } - // out.edges = malloc(out.nedges * sizeof(unsigned*)); - // for(unsigned e=0; e < out.nedges; e++){ - // out.edges[e] = malloc(2 * sizeof(unsigned)); - // out.edges[e][0] = ridge.edges[e][0]; - // out.edges[e][1] = ridge.edges[e][1]; - // } - return out; -} - -/* append to a vector of VertexT */ -void appendv(VertexT x, VertexT** array, unsigned length, unsigned* flag){ - *flag = 1; - for(unsigned i=0; i < length; i++){ - if(x.id == (*(*array + i)).id){ - *flag = 0; - break; - } - } - if(*flag == 1){ - *array = realloc(*array, (length+1) * sizeof(VertexT)); - if(*array == NULL){ - printf("realloc failure - exiting\n"); - exit(1); - } - *(*array + length) = x; - } -} - -/* union of two vectors of VertexT */ -void unionv(VertexT** vs1, VertexT* vs2, unsigned l1, unsigned l2, unsigned* l){ - *l = l1; - for(unsigned v=0; v < l2; v++){ - unsigned pushed; - appendv(vs2[v], vs1, *l, &pushed); - if(pushed){ - (*l)++; - } - } - /* sort vertices according to their ids */ - qsort(*vs1, *l, sizeof(VertexT), cmpvertices); -} - -/* merge ridges with same ridgeOf's */ -RidgeT* mergeRidges(RidgeT* ridges, unsigned nridges, unsigned* newlength){ - // http://www.c4learn.com/c-programs/to-delete-duplicate-elements-in-array.html - *newlength = nridges; - unsigned i,j,k; - for(i = 0; i < nridges; i++){ - for(j = i+1; j < nridges; ){ - if(ridges[i].ridgeOf1 == ridges[j].ridgeOf1 && - ridges[i].ridgeOf2 == ridges[j].ridgeOf2) - { - unsigned l; - unionv(&(ridges[i].vertices), ridges[j].vertices, - ridges[i].nvertices, ridges[j].nvertices, &l); - ridges[i].nvertices = l; - (*newlength)--; - for(k = j; k+1 < nridges; k++){ - ridges[k] = ridges[k+1]; - } - nridges--; - }else{ - j++; - } - } - } - RidgeT* out = malloc(*newlength * sizeof(RidgeT)); - for(unsigned r=0; r < *newlength; r++){ - out[r] = ridges[r]; - } - return out; -} - -/* all ridges from the ridges stored in the faces */ -RidgeT* allRidges(FaceT *faces, unsigned nfaces, unsigned dim, unsigned* length){ - RidgeT* out = malloc(faces[0].nridges * sizeof(RidgeT)); - for(unsigned i=0; i < faces[0].nridges; i++){ - out[i] = copyRidge(faces[0].ridges[i], dim); - out[i].id = i; - out[i].nedges = 0; - // RidgeT out[i]; - // deepCopyRidge(&(faces[0].ridges[i]), &(out[i])); - } - *length = faces[0].nridges; - unsigned n = faces[0].nridges; - for(unsigned f=1; f < nfaces; f++){ - for(unsigned j=0; j < faces[f].nridges; j++){ - unsigned count = 0; - for(unsigned i=0; i < n; i++){ - unsigned flag = 0; - for(unsigned v=0; v < faces[f].ridges[j].nvertices; v++){ - if(faces[f].ridges[j].vertices[v].id != out[i].vertices[v].id){ - flag = 1; - break; - } - } - if(flag){ - count++; - }else{ - break; - } - } - if(count == n){ - out = realloc(out, (*length+1) * sizeof(RidgeT)); - if(out == NULL){ - printf("realloc failure - exiting\n"); - exit(1); - } - out[*length] = copyRidge(faces[f].ridges[j], dim); - out[*length].id = *length; - out[*length].nedges = 0; - // RidgeT out[*length]; - // deepCopyRidge(&(faces[f].ridges[j]), &(out[*length])); - (*length)++; - } - } - n = *length; - } - return out; -} - -/* assign ids to the ridges stored in the faces */ -void assignRidgesIds(FaceT** faces, unsigned nfaces, RidgeT* allridges, - unsigned nallridges) -{ - for(unsigned f=0; f < nfaces; f++){ - for(unsigned fr=0; fr < (*(*faces + f)).nridges; fr++){ - for(unsigned r=0; r < nallridges; r++){ - if((allridges[r].nvertices == (*(*faces + f)).ridges[fr].nvertices) && - equalarraysu(map_vertexid(allridges[r].vertices, - allridges[r].nvertices), - map_vertexid((*(*faces + f)).ridges[fr].vertices, - allridges[r].nvertices), - allridges[r].nvertices)) - { - (*(*faces + f)).ridges[fr].id = allridges[r].id; - break; - } - } - } - } -} - -// double* ridgeCentroid(RidgeT ridge, unsigned dim){ -// double* out = malloc(dim * sizeof(double)); -// for(unsigned i=0; i2 */ -unsigned* neighVertices(unsigned id, RidgeT* allridges, unsigned nridges, - unsigned dim, unsigned triangulate, unsigned* lengthout) -{ - unsigned* neighs = malloc(0); - *lengthout = 0; - for(unsigned e=0; e < nridges; e++){ - for(unsigned v=0; v < allridges[e].nvertices; v++){ - if(id == allridges[e].vertices[v].id){ - for(unsigned w=0; w < allridges[e].nvertices; w++){ - if(w != v && (triangulate || dim == 3 || // dim3 pas besoin de tester la distance: il n'y a que deux vertices connectés - squaredDistance(allridges[e].vertices[w].point, - allridges[e].vertices[v].point, dim) <= - ridgeMaxDistance(allridges[e], v, dim))) - { - unsigned pushed; - appendu(allridges[e].vertices[w].id, &neighs, *lengthout, &pushed); - if(pushed){ - (*lengthout)++; - } - } - } - break; - } - } - } - return neighs; -} - -/* neighbor ridges of a vertex */ -unsigned* neighRidges(unsigned id, RidgeT* allridges, unsigned nridges, - unsigned* length) -{ - unsigned* neighs = malloc(0); - *length = 0; - for(unsigned e=0; e < nridges; e++){ - unsigned flag = 0; - for(unsigned v=0; v < allridges[e].nvertices; v++){ - if(id == allridges[e].vertices[v].id){ - flag = 1; - break; - } - } - if(flag){ - neighs = realloc(neighs, (*length+1)*sizeof(unsigned)); - if(neighs == NULL){ - printf("realloc failure - exiting\n"); - exit(1); - } - neighs[*length] = e; - (*length)++; - } - } - return neighs; -} - -/* whether distinct x1 and x2 belong to array of distinct values */ -unsigned areElementsOf(unsigned x1, unsigned x2, unsigned* array, - unsigned length) -{ - unsigned count = 0; - for(unsigned i=0; (i < length) && (count < 2); i++){ - if(x1 == array[i] || x2 == array[i]){ - count++; - } - } - return count==2; -} - -/* make face/ridge edges from all edges */ -unsigned** makeEdges(SetOfVerticesT face, unsigned** alledges, - unsigned nalledges, unsigned* lengthout) -{ - *lengthout = 0; - unsigned* faceverticesids = map_vertexid(face.vertices, face.nvertices); - unsigned flags[nalledges]; - for(unsigned e=0; e < nalledges; e++){ - if(areElementsOf(alledges[e][0], alledges[e][1], faceverticesids, - face.nvertices)) - { - flags[e] = 1; - (*lengthout)++; - }else{ - flags[e] = 0; - } - } - unsigned** out = malloc(*lengthout * sizeof(unsigned*)); - unsigned count = 0; - for(unsigned e=0; e < nalledges; e++){ - if(flags[e] == 1){ - out[count] = alledges[e]; - count++; - } - } - return out; -} - -/* all edges from all vertices */ -unsigned** allEdges(FullVertexT* vertices, unsigned nvertices, - unsigned outlength) -{ - unsigned** out = malloc(outlength * sizeof(unsigned*)); - for(unsigned i=0; i < vertices[0].nneighsvertices; i++){ - out[i] = malloc(2 * sizeof(unsigned)); - out[i][0] = vertices[0].id; - out[i][1] = vertices[0].neighvertices[i]; - qsortu(out[i], 2); - } - unsigned n = vertices[0].nneighsvertices; - for(unsigned v=1; v < nvertices; v++){ - unsigned ids[2]; - for(unsigned i=0; i < vertices[v].nneighsvertices; i++){ - ids[0] = vertices[v].id; - ids[1] = vertices[v].neighvertices[i]; - qsortu(ids, 2); - unsigned j; - for(j=0; j < n; j++){ - if(ids[0] == out[j][0] && ids[1] == out[j][1]){ - break; - } - } - if(j == n){ - out[n] = malloc(2 * sizeof(unsigned)); - out[n][0] = ids[0]; out[n][1] = ids[1]; - n++; - } - if(n == outlength){ - break; - } - } - if(n == outlength){ - break; - } - } - return out; -} - -// ATTENTION avec Qt le center dans facet->center est le centre de l'union des triangles, -// (ainsi que normal et offset mais ça ok) - -// un ridge est simplicial ; pour l'hypercube il y a 2 ridges entre 2 faces, -// ils forment le carré à l'intersection - -/* main function */ -ConvexHullT* convexHull( - double* points, - unsigned dim, - unsigned n, - unsigned triangulate, - unsigned print, - char* summaryFile, - unsigned* exitcode -) -{ - char opts[250]; /* option flags for qhull, see qh_opt.htm */ - sprintf(opts, "qhull s FF %s", triangulate ? "Qt" : ""); - qhT qh_qh; /* Qhull's data structure */ - qhT *qh= &qh_qh; - QHULL_LIB_CHECK - qh_meminit(qh, stderr); - boolT ismalloc = False; /* True if qhull should free points in qh_freeqhull() or reallocation */ - FILE *errfile = NULL; - FILE* outfile; - if(print){ - outfile = stdout; - }else{ - outfile = NULL; - } - qh_zero(qh, errfile); - exitcode[0] = qh_new_qhull(qh, dim, n, points, ismalloc, opts, outfile, - errfile); - //fclose(tmpstdout); - printf("exitcode: %u\n", exitcode[0]); - - ConvexHullT* out = malloc(sizeof(ConvexHullT)); - - if (!exitcode[0]) { /* 0 if no error from qhull */ - - /* print summary to file */ - if(*summaryFile != 0){ - FILE* sfile = fopen(summaryFile, "w"); - qh_printsummary(qh, sfile); - fclose(sfile); - } - - //qh_getarea(qh, qh->facet_list); // no triowner if I do that; do qh_facetarea, not facet->f.area - - unsigned nfaces = qh->num_facets; - FaceT* faces = malloc(nfaces * sizeof(FaceT)); - { - facetT *facet; unsigned i_facet = 0; - FORALLfacets{ - facet->id = i_facet; /* for neighbors and ridgeOf */ - faces[i_facet].area = qh_facetarea(qh, facet); - double* center = qh_getcenter(qh, facet->vertices); - faces[i_facet].center = malloc(dim * sizeof(double)); - for(unsigned i=0; i < dim; i++){ - faces[i_facet].center[i] = center[i]; - } - double* normal = facet->normal; - faces[i_facet].normal = malloc(dim * sizeof(double)); - for(unsigned i=0; i < dim; i++){ - faces[i_facet].normal[i] = normal[i]; - } - faces[i_facet].offset = facet->offset; - faces[i_facet].nvertices = (unsigned) qh_setsize(qh, facet->vertices); - { /* face vertices */ - faces[i_facet].vertices = - (VertexT*) malloc(faces[i_facet].nvertices * sizeof(VertexT)); - vertexT *vertex, **vertexp; - unsigned i_vertex = 0; - FOREACHvertex_(facet->vertices){ - faces[i_facet].vertices[i_vertex].id = - (unsigned) qh_pointid(qh, vertex->point); - faces[i_facet].vertices[i_vertex].point = - malloc(dim * sizeof(double)); - faces[i_facet].vertices[i_vertex].point = - getpoint(points, dim, faces[i_facet].vertices[i_vertex].id); - // plante dans Haskell: (faces[i_facet].vertices)[i_vertex].point = vertex->point; - i_vertex++; - } - qsort(faces[i_facet].vertices, faces[i_facet].nvertices, - sizeof(VertexT), cmpvertices); - } - if(dim == 3){ /* orientation of the normals */ - pointT* onepoint = ((vertexT*)facet->vertices->e[0].p)->point; - double thepoint[dim]; /* onepoint+normal */ - for(unsigned i=0; i < dim; i++){ - thepoint[i] = onepoint[i] + faces[i_facet].normal[i]; - } - /* we check that these two points are on the same side of the ridge */ - double h1 = dotproduct(qh->interior_point, - faces[i_facet].normal, dim) + - faces[i_facet].offset; - double h2 = dotproduct(thepoint, faces[i_facet].normal, dim) + - faces[i_facet].offset; - if(h1*h2 > 0){ - for(unsigned i=0; i < dim; i++){ - faces[i_facet].normal[i] *= -1; - } - printf("change sign\n"); // seems to never occur - }else{ - printf("not change sign\n"); - } - } - /**/ - i_facet++; - } - } - - { /* neighbor faces, faces families, and ridges */ - facetT *facet; - unsigned i_facet = 0; - FORALLfacets{ - { - faces[i_facet].neighborsize = qh_setsize(qh, facet->neighbors); - faces[i_facet].neighbors = - malloc(faces[i_facet].neighborsize * sizeof(unsigned)); - unsigned i_neighbor = 0; - facetT *neighbor, **neighborp; - FOREACHneighbor_(facet){ - faces[i_facet].neighbors[i_neighbor] = (unsigned) neighbor->id; - i_neighbor++; - } - qsortu(faces[i_facet].neighbors, faces[i_facet].neighborsize); - } - { /* face family, when option Qt */ - if(facet->tricoplanar){ - faces[i_facet].family = facet->f.triowner->id; - }else{ - faces[i_facet].family = -1; - } - } - { /* face ridges */ - qh_makeridges(qh, facet); - unsigned nridges = qh_setsize(qh, facet->ridges); - RidgeT* ridges = malloc(nridges * sizeof(RidgeT)); - ridgeT *ridge, **ridgep; - unsigned i_ridge = 0; - FOREACHridge_(facet->ridges){ - ridges[i_ridge].nedges = 0; - unsigned ridgeSize = qh_setsize(qh, ridge->vertices); // dim-1 -// printf("ridge size: %u\n", ridgeSize); - ridges[i_ridge].nvertices = ridgeSize; - unsigned ids[ridgeSize]; - for(unsigned v=0; v < ridgeSize; v++){ - ids[v] = - qh_pointid(qh, ((vertexT*)ridge->vertices->e[v].p)->point); - } - qsortu(ids, ridgeSize); - ridges[i_ridge].vertices = malloc(ridgeSize * sizeof(VertexT)); - for(unsigned v=0; v < ridgeSize; v++){ - ridges[i_ridge].vertices[v].id = ids[v]; - ridges[i_ridge].vertices[v].point = getpoint(points, dim, ids[v]); - } - unsigned ridgeofs[2]; - ridgeofs[0] = ridge->bottom->id; - ridgeofs[1] = ridge->top->id; - qsortu(ridgeofs, 2); - ridges[i_ridge].ridgeOf1 = ridgeofs[0]; - ridges[i_ridge].ridgeOf2 = ridgeofs[1]; - /**/ - i_ridge++; - } - /* merge triangulated ridges */ - if(dim > 3 && !triangulate){ - unsigned l; - faces[i_facet].ridges = mergeRidges(ridges, nridges, &l); - faces[i_facet].nridges = l; - }else{ /* dim 2 or 3, or triangulate option */ - faces[i_facet].ridges = ridges; - faces[i_facet].nridges = nridges; - } - } - /**/ - i_facet++; - } - } - - /* make unique ridges */ - unsigned n_allridges; - RidgeT* allridges = allRidges(faces, nfaces, dim, &n_allridges); -// printf("nallridges: %u\n", n_allridges); - - /* assign ridges ids to the ridges stored in the faces */ - assignRidgesIds(&faces, nfaces, allridges, n_allridges); - - /* all vertices */ - unsigned nvertices = qh->num_vertices; - FullVertexT* vertices = malloc(nvertices * sizeof(FullVertexT)); - { - qh_vertexneighbors(qh); /* make the neighbor facets of the vertices */ - vertexT *vertex; - unsigned i_vertex=0; - FORALLvertices{ - /* vertex id and coordinates */ - vertices[i_vertex].id = (unsigned) qh_pointid(qh, vertex->point); - vertices[i_vertex].point = getpoint(points, dim, vertices[i_vertex].id); - - /* neighbor facets of the vertex */ - vertices[i_vertex].nneighfacets = qh_setsize(qh, vertex->neighbors); - vertices[i_vertex].neighfacets = - malloc(vertices[i_vertex].nneighfacets * sizeof(unsigned)); - facetT *neighbor, **neighborp; - unsigned i_neighbor = 0; - FOREACHneighbor_(vertex){ - vertices[i_vertex].neighfacets[i_neighbor] = neighbor->id; - i_neighbor++; - } - qsortu(vertices[i_vertex].neighfacets, vertices[i_vertex].nneighfacets); - - /* neighbor vertices of the vertex */ - if(dim > 2){ - unsigned nneighsvertices; - vertices[i_vertex].neighvertices = - neighVertices(vertices[i_vertex].id, allridges, n_allridges, - dim, triangulate, &nneighsvertices); - vertices[i_vertex].nneighsvertices = nneighsvertices; - }else{ /* dim=2 */ - vertices[i_vertex].nneighsvertices = 2; - vertices[i_vertex].neighvertices = malloc(2 * sizeof(unsigned)); - unsigned count = 0; - for(unsigned f=0; f < nfaces; f++){ - for(unsigned i=0; i < 2; i++){ - if(faces[f].vertices[i].id == vertices[i_vertex].id){ - vertices[i_vertex].neighvertices[count] = - faces[f].vertices[1-i].id; - count++; - break; - } - } - if(count == 2){ - break; - } - } - } - qsortu(vertices[i_vertex].neighvertices, - vertices[i_vertex].nneighsvertices); - - /* neighbor ridges of the vertex */ - if(dim > 2){ - unsigned nneighridges; - vertices[i_vertex].neighridges = - neighRidges(vertices[i_vertex].id, allridges, n_allridges, - &nneighridges); - qsortu(vertices[i_vertex].neighridges, nneighridges); - vertices[i_vertex].nneighridges = nneighridges; - }else{ /* dim=2 */ - vertices[i_vertex].nneighridges = 0; /* ridge = vertex singleton */ - } - /**/ - i_vertex++; - } - /* sort vertices according to their ids */ - qsort(vertices, nvertices, sizeof(FullVertexT), cmpfullvertices); - } - - /* all edges */ - unsigned nalledges = 0; - for(unsigned v=0; v < nvertices; v++){ - nalledges += vertices[v].nneighsvertices; - } - nalledges /= 2; - unsigned** alledges = allEdges(vertices, nvertices, nalledges); - qsort(alledges, nalledges, sizeof(unsigned*), cmpedges); - - { /* faces edges and ridges ids */ - facetT *facet; unsigned i_facet=0; - FORALLfacets{ - /* facet ridges ids */ - faces[i_facet].ridgesids = - map_ridgeid(faces[i_facet].ridges, faces[i_facet].nridges); - qsortu(faces[i_facet].ridgesids, faces[i_facet].nridges); - /* facet edges */ - SetOfVerticesT facet_vset = {.vertices = faces[i_facet].vertices, - .nvertices = faces[i_facet].nvertices}; - unsigned nfaceedges; - faces[i_facet].edges = - makeEdges(facet_vset, alledges, nalledges, &nfaceedges); - //qsort(faces[i_facet].edges, nfaceedges, sizeof(unsigned*), cmpedges); useless, I think - faces[i_facet].nedges = nfaceedges; - /**/ - i_facet++; - } - } - - /* ridges edges */ - if(dim > 3){ - for(unsigned r=0; r < n_allridges; r++){ - unsigned facetid = allridges[r].ridgeOf1; - SetOfVerticesT vset = {.vertices = allridges[r].vertices, - .nvertices = allridges[r].nvertices}; - unsigned nedges; - allridges[r].edges = - makeEdges(vset, faces[facetid].edges, faces[facetid].nedges, &nedges); - allridges[r].nedges = nedges; - } - } - - /* output */ - out->dim = dim; - out->vertices = vertices; - out->nvertices = nvertices; - out->faces = faces; - out->nfaces = nfaces; - out->ridges = allridges; - out->nridges = n_allridges; - out->edges = alledges; - out->nedges = nalledges; - - } // end if exitcode - - /* Do cleanup regardless of whether there is an error */ - int curlong, totlong; - qh_freeqhull(qh, !qh_ALL); /* free long memory */ - qh_memfreeshort(qh, &curlong, &totlong); /* free short memory and memory allocator */ - - printf("RETURN\n"); - if(*exitcode){ - free(out); - return 0; - }else{ - return out; - } - -} diff --git a/C/delaunay.c b/C/delaunay.c deleted file mode 100644 --- a/C/delaunay.c +++ /dev/null @@ -1,577 +0,0 @@ -#define qh_QHimport -#include "qhull_ra.h" -#include "delaunay.h" -#include "utils.h" -#include /* to use NAN */ - -// void printfacet(qhT* qh, facetT* facet){ -// vertexT *vertex, **vertexp; -// FOREACHvertex_(facet->vertices){ -// printf("facetid: %d, pointid: %d ", facet->id, qh_pointid(qh, vertex->point)); -// } -// } - -unsigned facetOK_(facetT* facet, unsigned degenerate){ - return !facet->upperdelaunay && (degenerate || !facet->degenerate); -} // && simplicial, && !facet->redundant - pas de simplicial avec Qt - - - -TesselationT* tesselation( - double* sites, - unsigned dim, - unsigned n, - unsigned atinfinity, - unsigned degenerate, - double vthreshold, - unsigned* exitcode -) -{ - char opts[50]; /* option flags for qhull, see qh_opt.htm */ - sprintf(opts, "qhull d Qt Qbb%s%s", - atinfinity ? " Qz" : "", dim>3 ? " Qx" : ""); - qhT qh_qh; /* Qhull's data structure */ - qhT *qh= &qh_qh; - QHULL_LIB_CHECK - qh_meminit(qh, stderr); - boolT ismalloc = False; /* True if qhull should free points in qh_freeqhull() or reallocation */ - FILE *errfile = NULL; - FILE* outfile = NULL; - qh_zero(qh, errfile); - *exitcode = qh_new_qhull(qh, dim, n, sites, ismalloc, opts, outfile, errfile); - //fclose(tmpstdout); - printf("exitcode: %u\n", *exitcode); - - TesselationT* out = malloc(sizeof(TesselationT)); /* output */ - - if (!(*exitcode)) { /* 0 if no error from qhull */ - - /* Count the number of facets we keep */ - unsigned nfacets = 0; /* to store the number of facets */ - { - facetT *facet; /* set by FORALLfacets */ - FORALLfacets { - if(facetOK_(facet, degenerate)){ - facet->id = nfacets; - nfacets++; - }else{ - qh_removefacet(qh, facet); - } - } - } - - /* Initialize the tiles */ - TileT* allfacets = malloc(nfacets * sizeof(TileT)); - - { /* tiles families and volumes, and centers of tiles with >0 volume */ - facetT* facet; - unsigned i_facet = 0; - FORALLfacets{ - if(facet->tricoplanar){ - allfacets[i_facet].family = facet->f.triowner->id; - // if(!facet->degenerate){ - // if(i_facet == 392){ - // printf("area: %f", qh_facetarea(qh, facet)); - // } - // allfacets[i_facet].simplex.center = - // qh_facetcenter(qh, facet->vertices); - // }else{ - // facetT *neighbor, **neighborp; - // FOREACHneighbor_(facet){ - // if(facetOK_(neighbor,0) && neighbor->f.triowner->id == facet->f.triowner->id){ - // allfacets[i_facet].simplex.center = - // qh_facetcenter(qh, neighbor->vertices); - // break; - // } - // } - // } - }else{ - allfacets[i_facet].family = -1; - } - if(facet->degenerate){ // ? - allfacets[i_facet].simplex.volume = 0; - }else{ - allfacets[i_facet].simplex.volume = fmax(0, qh_facetarea(qh, facet)); - } - if(allfacets[i_facet].simplex.volume > vthreshold){ - allfacets[i_facet].simplex.center = malloc(dim * sizeof(double)); - double* center = qh_facetcenter(qh, facet->vertices); - for(unsigned i=0; i < dim; i++){ - allfacets[i_facet].simplex.center[i] = center[i]; - } - } - i_facet++; - } - } - - { /* facets ids, orientations, centers, sites ids, neighbors */ - facetT* facet; - unsigned i_facet = 0; /* facet counter */ - FORALLfacets { - allfacets[i_facet].id = facet->id; - allfacets[i_facet].orientation = facet->toporient ? 1 : -1; - /* center and circumradius */ - if(allfacets[i_facet].simplex.volume <= vthreshold){ - if(facet->tricoplanar){ - unsigned ok = 0; - vertexT* apex = (vertexT*)facet->vertices->e[0].p; - facetT *neighbor, **neighborp; - FOREACHneighbor_(apex){ - if(facetOK_(neighbor,degenerate) && - allfacets[neighbor->id].family == allfacets[i_facet].family && - allfacets[neighbor->id].simplex.volume > vthreshold) - { - allfacets[i_facet].simplex.center = - allfacets[neighbor->id].simplex.center; - ok = 1; - break; - } - } - if(!ok){ /* should not happen */ - allfacets[i_facet].simplex.center = nanvector(dim); - } - }else{ /* should not happen */ - allfacets[i_facet].simplex.center = nanvector(dim); - } - } -// printf("center facet %u: %f %f %f\n", i_facet, allfacets[i_facet].simplex.center[0], allfacets[i_facet].simplex.center[1], allfacets[i_facet].simplex.center[2]); - allfacets[i_facet].simplex.radius = - sqrt(squaredDistance(((vertexT*)facet->vertices->e[0].p)->point, - allfacets[i_facet].simplex.center, dim)); - // allfacets[i_facet].simplex.center = - // facet->degenerate ? nanvector(dim) - // : qh_facetcenter(qh, facet->vertices); - // if(!facet->degenerate){ - // allfacets[i_facet].simplex.center = //facet->center; - // qh_facetcenter(qh, facet->vertices); - // // faire une première passe : calculer les centres des triowner - // // pour ne pas les calculer pour les facets de la même famille - // printf("center1: %f %f %f\n", facet->center[0], facet->center[1], facet->center[2]); - // printf("center2: %f %f %f\n", allfacets[i_facet].simplex.center[0], allfacets[i_facet].simplex.center[1], allfacets[i_facet].simplex.center[2]); - // pointT* point = ((vertexT*)facet->vertices->e[0].p)->point; - // allfacets[i_facet].simplex.radius = - // sqrt(squaredDistance(point, allfacets[i_facet].simplex.center, - // dim)); - // }// }else{ - // // allfacets[i_facet].simplex.radius = NAN; - // // } - - { /* vertices ids of the facet */ - allfacets[i_facet].simplex.sitesids = - malloc((dim+1) * sizeof(unsigned)); - vertexT *vertex, **vertexp; - unsigned i_vertex = 0; - FOREACHvertex_(facet->vertices) { - allfacets[i_facet].simplex.sitesids[i_vertex] = - qh_pointid(qh, vertex->point); - i_vertex++; - } - qsortu(allfacets[i_facet].simplex.sitesids, dim+1); - } - - { /* neighbors facets of the facet */ - facetT *neighbor, **neighborp; - unsigned flag[dim+1]; - allfacets[i_facet].nneighbors = 0; - unsigned i_neighbor = 0; - FOREACHneighbor_(facet) { - if(flag[i_neighbor] = facetOK_(neighbor, degenerate)){ - allfacets[i_facet].nneighbors++; - } - i_neighbor++; - } - allfacets[i_facet].neighbors = - malloc(allfacets[i_facet].nneighbors * sizeof(unsigned)); - unsigned countok = 0; - i_neighbor = 0; - FOREACHneighbor_(facet) { - if(flag[i_neighbor]){ - allfacets[i_facet].neighbors[countok] = neighbor->id; - countok++; - } - i_neighbor++; - } - } - - // /* facet family */ - // if(facet->tricoplanar){ - // allfacets[i_facet].family = facet->f.triowner->id; - // }else{ - // allfacets[i_facet].family = -1; - // } - - /**/ - i_facet++; - } - } - - // /* for degenerate facets, take the center of the owner */ - // if(degenerate){ - // facetT *facet; - // unsigned i_facet = 0; - // FORALLfacets{ - // if(facet->degenerate){ - // allfacets[i_facet].simplex.center = - // allfacets[allfacets[i_facet].family].simplex.center; - // pointT* point = ((vertexT*)facet->vertices->e[0].p)->point; - // allfacets[i_facet].simplex.radius = - // sqrt(squaredDistance(point, allfacets[i_facet].simplex.center, - // dim)); - // } - // i_facet++; - // } - // } - - /* neighbor facets and neighbor vertices per vertex */ - /* --- we will use the following combinations, also used later */ - /* --- combinations[m] contains all k between 0 and dim but m */ - unsigned combinations[dim+1][dim]; - for(unsigned m=0; m < dim+1; m++){ - unsigned kk=0; - for(unsigned k=0; k < dim+1; k++){ - if(k != m){ - combinations[m][kk] = k; - kk++; - } - } - } - /* --- initialize the sites */ - SiteT* allsites = malloc(n * sizeof(SiteT)); - /* --- array to flag neighbors - 0/1 if not neighbour/neighbour */ - unsigned** verticesFacetsNeighbours = malloc(n * sizeof(unsigned*)); - /* unsigned verticesFacetsNeighbours[n][nfacets] => stackoverflow */ - for(unsigned v=0; v < n; v++){ - allsites[v].id = v; - allsites[v].nneighsites = 0; - allsites[v].neighsites = malloc(0); /* will be filled by appending */ - allsites[v].nneighridges = 0; - allsites[v].nneightiles = 0; - verticesFacetsNeighbours[v] = uzeros(nfacets); - } - /* --- fill verticesFacetsNeighbours, derive number of neighbor facets */ - /* --- and derive neighbor sites */ - for(unsigned i_facet=0; i_facet < nfacets; i_facet++){ - for(unsigned j=0; j < dim+1; j++){ - unsigned vertexid = allfacets[i_facet].simplex.sitesids[j]; - if(verticesFacetsNeighbours[vertexid][i_facet] == 0){ - verticesFacetsNeighbours[vertexid][i_facet] = 1; - allsites[vertexid].nneightiles++; - } - for(unsigned k=0; k < dim; k++){ - unsigned vertexid2 = - allfacets[i_facet].simplex.sitesids[combinations[j][k]]; - unsigned pushed; - appendu(vertexid2, &allsites[vertexid].neighsites, - allsites[vertexid].nneighsites, &pushed); - if(pushed){ - allsites[vertexid].nneighsites++; - } - } - } - } - - /************************************************************/ - /* second pass on facets: ridges and facet volumes */ - unsigned n_ridges_dup = nfacets * (dim+1); /* number of ridges with duplicates */ - SubTileT* allridges_dup = malloc(n_ridges_dup * sizeof(SubTileT)); - for(unsigned r=0; r < n_ridges_dup; r++){ - allridges_dup[r].simplex.sitesids = malloc(dim * sizeof(unsigned)); - allridges_dup[r].flag = 0; - } -// qh_getarea(qh, qh->facet_list); /* make facets volumes, available in facet->f.area */ - unsigned n_ridges = 0; /* count distinct ridges */ - - { /* loop on facets */ - facetT *facet; - unsigned i_ridge_dup = 0; /* ridge counter */ - unsigned i_facet = 0; /* facet counter */ - FORALLfacets { - -// allfacets[i_facet].simplex.volume = facet->f.area; - allfacets[i_facet].nridges = dim+1; - allfacets[i_facet].ridgesids = malloc((dim+1) * sizeof(unsigned)); - - /* loop on the combinations - it increments i_ridge_dup */ - for(unsigned m=0; m < dim+1; m++){ - allridges_dup[i_ridge_dup].ridgeOf1 = facet->id; - allridges_dup[i_ridge_dup].ridgeOf2 = -1; /* this means "nothing" */ - unsigned ids[dim]; - for(unsigned i=0; i < dim; i++){ - ids[i] = allfacets[i_facet].simplex.sitesids[combinations[m][i]]; - } - unsigned done = 0; /* flag ridge is already done */ - for(unsigned r=0; r < i_ridge_dup; r++){ - if(allridges_dup[r].ridgeOf2 == (int) facet->id && - allridges_dup[r].flag==1) - { - unsigned ids2[dim]; - unsigned i; - for(i=0; i < dim; i++){ - ids2[i] = allridges_dup[r].simplex.sitesids[i]; - if(ids2[i] != ids[i]){ - break; - } - } - if(i == dim){ - allfacets[i_facet].ridgesids[m] = allridges_dup[r].id; - done = 1; - break; - } - } - } - if(done == 0){ /* => then do the ridge */ - allridges_dup[i_ridge_dup].flag = 1; - allridges_dup[i_ridge_dup].id = n_ridges; - allfacets[i_facet].ridgesids[m] = n_ridges; - n_ridges++; - for(unsigned i=0; i < dim; i++){ - allridges_dup[i_ridge_dup].simplex.sitesids[i] = ids[i]; - allsites[ids[i]].nneighridges++; - } - - { /* loop on facet neighbors to find ridgeOf2 */ - facetT *neighbor, **neighborp; - FOREACHneighbor_(facet){ - if(facetOK_(neighbor, degenerate)){ - unsigned fnid = neighbor->id; - unsigned ok; - for(unsigned mm=0; mm < dim+1; mm++){ - ok = 0; - for(unsigned i=0; i < dim; i++){ - if(allfacets[fnid].simplex.sitesids[combinations[mm][i]] - != ids[i]) - { - break; - }else{ - ok++; - } - } - if(ok==dim){ - break; - } - } - if(ok==dim){ - allridges_dup[i_ridge_dup].ridgeOf2 = (int) fnid; - break; - } - } - } /* end FOREACHneighbor_(facet) */ - } - - pointT* points[dim]; /* the points corresponding to the combination */ - for(unsigned i=0; i < dim; i++){ - points[i] = getpoint(sites, dim, ids[i]); - } - double normal[dim]; /* to store the ridge normal */ - if(dim == 2){ - double u1 = points[1][0] - points[0][0]; - double v1 = points[1][1] - points[0][1]; - allridges_dup[i_ridge_dup].simplex.volume = - sqrt(square(u1)+square(v1)); - allridges_dup[i_ridge_dup].simplex.center = - middle(points[0], points[1], dim); - allridges_dup[i_ridge_dup].simplex.radius = - sqrt(squaredDistance(allridges_dup[i_ridge_dup].simplex.center, - points[0], dim)); - normal[0] = v1; normal[1] = -u1; - }else{ - int parity=1; - double squaredNorm = 0; - for(unsigned i=0; i < dim; i++){ - double** rows = malloc((dim-1) * sizeof(double*)); - for(unsigned j=0; j < dim-1; j++){ - rows[j] = (double*) malloc((dim-1) * sizeof(double)); - for(unsigned k=0; k < dim-1; k++){ - unsigned kk = k 2){ /* ridge center is already done if dim 2 */ - // if(facet->degenerate){ - // allridges_dup[i_ridge_dup].simplex.center = nanvector(dim); - // allridges_dup[i_ridge_dup].simplex.radius = NAN; - // }else{ - allridges_dup[i_ridge_dup].simplex.center = - malloc(dim * sizeof(double)); - double scal = 0; - for(unsigned i=0; i < dim; i++){ - scal += (points[0][i]-allfacets[i_facet].simplex.center[i]) * - normal[i]; - } - for(unsigned i=0; i < dim; i++){ - allridges_dup[i_ridge_dup].simplex.center[i] = - allfacets[i_facet].simplex.center[i] + scal*normal[i]; - } - allridges_dup[i_ridge_dup].simplex.radius = - sqrt(squaredDistance( - allridges_dup[i_ridge_dup].simplex.center, - points[0], dim)); -// } - } - /* orient the normal (used for plotting unbounded Voronoi cells) */ - if(allridges_dup[i_ridge_dup].ridgeOf2 == -1) - //&& (!facet->degenerate || dim==2)) - { - pointT* otherpoint = /* the remaining vertex of the facet (the one not in the ridge) */ - qh->interior_point; // getpoint(sites, dim, allfacets[facet->id].simplex.sitesids[m]); - double thepoint[dim]; /* the point center+normal */ - for(unsigned i=0; i < dim; i++){ - thepoint[i] = allridges_dup[i_ridge_dup].simplex.center[i] + - allridges_dup[i_ridge_dup].normal[i]; - } - /* we check that these two points are on the same side of the ridge */ - double h1 = dotproduct(otherpoint, - allridges_dup[i_ridge_dup].normal, dim) + - allridges_dup[i_ridge_dup].offset; - double h2 = dotproduct(thepoint, - allridges_dup[i_ridge_dup].normal, dim) + - allridges_dup[i_ridge_dup].offset; - // printf("deg: %u, h1: %f, h2: %f\n", facet->degenerate, h1, h2); - // printf("offset: %f\n", allridges_dup[i_ridge_dup].offset); - // printf("normal: %f %f %f\n", allridges_dup[i_ridge_dup].normal[0], allridges_dup[i_ridge_dup].normal[1], allridges_dup[i_ridge_dup].normal[2]); - if(h1*h2 >= 0){ - for(unsigned i=0; i < dim; i++){ - allridges_dup[i_ridge_dup].normal[i] *= -1; - } - } - } - for(unsigned i=0; i < dim; i++){ - free(points[i]); - } - } - i_ridge_dup++; - } // end loop combinations (m) - qsortu(allfacets[i_facet].ridgesids, dim+1); - /**/ - i_facet++; - } // end FORALLfacets - } - - /* extract unique ridges */ - SubTileT* allridges = malloc(n_ridges * sizeof(SubTileT)); - unsigned inc_ridge = 0; - for(unsigned l=0; l < n_ridges_dup; l++){ - if(allridges_dup[l].flag){ - allridges[inc_ridge] = allridges_dup[l]; - inc_ridge++; - } - } - - /* make neighbor ridges per vertex */ - unsigned* i_ridges_per_vertex = uzeros(n); - for(unsigned v=0; v < n; v++){ - allsites[v].neighridgesids = - malloc(allsites[v].nneighridges * sizeof(unsigned)); - } - for(unsigned l=0; l < n_ridges_dup; l++){ - if(allridges_dup[l].flag){ - for(unsigned i=0; i < dim; i++){ - unsigned v = allridges_dup[l].simplex.sitesids[i]; - allsites[v].neighridgesids[i_ridges_per_vertex[v]] = - allridges_dup[l].id; - i_ridges_per_vertex[v]++; - } - } - } - - /* order vertices neighbor sites and make neighbor tiles per vertex */ - for(unsigned v=0; v < n; v++){ - qsortu(allsites[v].neighsites, allsites[v].nneighsites); - allsites[v].neightiles = - malloc(allsites[v].nneightiles * sizeof(unsigned)); - unsigned inc_facet = 0; unsigned inc_vfn = 0; - while(inc_vfn < allsites[v].nneightiles){ - if(verticesFacetsNeighbours[v][inc_facet] == 1){ - allsites[v].neightiles[inc_vfn] = inc_facet; - inc_vfn++; - } - inc_facet++; - } - } - - /* make the output */ - out->sites = allsites; - out->tiles = allfacets; - out->ntiles = nfacets; - out->subtiles = allridges; - out->nsubtiles = n_ridges; - - free(allridges_dup); - free(i_ridges_per_vertex); - free(verticesFacetsNeighbours); - - } - - /* Do cleanup regardless of whether there is an error */ - int curlong, totlong; - qh_freeqhull(qh, !qh_ALL); /* free long memory */ - qh_memfreeshort(qh, &curlong, &totlong); /* free short memory and memory allocator */ - - printf("RETURN\n"); - if(*exitcode){ - free(out); - return 0; - }else{ - return out; - } - -} - - -void testdel2(){ - double sites[27] = {0,0,0, 0,0,1, 0,1,0, 0,1,1, 1,0,0, 1,0,1, 1,1,0, 1,1,1, 0.5,0.5,0.5}; - unsigned exitcode; - unsigned dim = 3; - TesselationT* x = tesselation(sites, dim, 9, 0, 0, 0, &exitcode); - printf("TESTDEL2 - nfacets:%u\n", x->ntiles); - for(unsigned f=0; f < x->ntiles; f++){ - printf("facet %u - sites:\n", f); - for(unsigned i=0; i < dim+1; i++){ - printf("%u - ", x->tiles[f].simplex.sitesids[i]); - } - printf("\n"); - printf("facet %u - ridges:\n", f); - for(unsigned i=0; i < dim+1; i++){ - printf("%u - ", x->tiles[f].ridgesids[i]); - } - printf("\n"); - printf("facet %u - neighbors:\n", f); - for(unsigned i=0; i < x->tiles[f].nneighbors; i++){ - printf("%u - ", x->tiles[f].neighbors[i]); - } - printf("\n"); - } - printf("nallridges:%u\n", x->nsubtiles); - for(unsigned r=0; r < x->nsubtiles; r++){ - printf("ridge %u - id %u:\n", r, x->subtiles[r].id); - for(unsigned i=0; i < dim; i++){ - printf("%u - ", x->subtiles[r].simplex.sitesids[i]); - } - printf("ridgeOf: %u %d", x->subtiles[r].ridgeOf1, x->subtiles[r].ridgeOf2); - printf("\n"); - } - free(x); -} diff --git a/C/geom2_r.c b/C/geom2_r.c deleted file mode 100644 --- a/C/geom2_r.c +++ /dev/null @@ -1,2096 +0,0 @@ -/*
  ---------------------------------
-
-
-   geom2_r.c
-   infrequently used geometric routines of qhull
-
-   see qh-geom_r.htm and geom_r.h
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull_r/geom2_r.c#6 $$Change: 2065 $
-   $DateTime: 2016/01/18 13:51:04 $$Author: bbarber $
-
-   frequently used code goes into geom_r.c
-*/
-
-#include "qhull_ra.h"
-
-/*================== functions in alphabetic order ============*/
-
-/*---------------------------------
-
-  qh_copypoints(qh, points, numpoints, dimension)
-    return qh_malloc'd copy of points
-  
-  notes:
-    qh_free the returned points to avoid a memory leak
-*/
-coordT *qh_copypoints(qhT *qh, coordT *points, int numpoints, int dimension) {
-  int size;
-  coordT *newpoints;
-
-  size= numpoints * dimension * (int)sizeof(coordT);
-  if (!(newpoints= (coordT*)qh_malloc((size_t)size))) {
-    qh_fprintf(qh, qh->ferr, 6004, "qhull error: insufficient memory to copy %d points\n",
-        numpoints);
-    qh_errexit(qh, qh_ERRmem, NULL, NULL);
-  }
-  memcpy((char *)newpoints, (char *)points, (size_t)size); /* newpoints!=0 by QH6004 */
-  return newpoints;
-} /* copypoints */
-
-/*---------------------------------
-
-  qh_crossproduct( dim, vecA, vecB, vecC )
-    crossproduct of 2 dim vectors
-    C= A x B
-
-  notes:
-    from Glasner, Graphics Gems I, p. 639
-    only defined for dim==3
-*/
-void qh_crossproduct(int dim, realT vecA[3], realT vecB[3], realT vecC[3]){
-
-  if (dim == 3) {
-    vecC[0]=   det2_(vecA[1], vecA[2],
-                     vecB[1], vecB[2]);
-    vecC[1]= - det2_(vecA[0], vecA[2],
-                     vecB[0], vecB[2]);
-    vecC[2]=   det2_(vecA[0], vecA[1],
-                     vecB[0], vecB[1]);
-  }
-} /* vcross */
-
-/*---------------------------------
-
-  qh_determinant(qh, rows, dim, nearzero )
-    compute signed determinant of a square matrix
-    uses qh.NEARzero to test for degenerate matrices
-
-  returns:
-    determinant
-    overwrites rows and the matrix
-    if dim == 2 or 3
-      nearzero iff determinant < qh->NEARzero[dim-1]
-      (!quite correct, not critical)
-    if dim >= 4
-      nearzero iff diagonal[k] < qh->NEARzero[k]
-*/
-realT qh_determinant(qhT *qh, realT **rows, int dim, boolT *nearzero) {
-  realT det=0;
-  int i;
-  boolT sign= False;
-
-  *nearzero= False;
-  if (dim < 2) {
-    qh_fprintf(qh, qh->ferr, 6005, "qhull internal error (qh_determinate): only implemented for dimension >= 2\n");
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }else if (dim == 2) {
-    det= det2_(rows[0][0], rows[0][1],
-                 rows[1][0], rows[1][1]);
-    if (fabs_(det) < 10*qh->NEARzero[1])  /* not really correct, what should this be? */
-      *nearzero= True;
-  }else if (dim == 3) {
-    det= det3_(rows[0][0], rows[0][1], rows[0][2],
-                 rows[1][0], rows[1][1], rows[1][2],
-                 rows[2][0], rows[2][1], rows[2][2]);
-    if (fabs_(det) < 10*qh->NEARzero[2])  /* what should this be?  det 5.5e-12 was flat for qh_maxsimplex of qdelaunay 0,0 27,27 -36,36 -9,63 */
-      *nearzero= True;
-  }else {
-    qh_gausselim(qh, rows, dim, dim, &sign, nearzero);  /* if nearzero, diagonal still ok*/
-    det= 1.0;
-    for (i=dim; i--; )
-      det *= (rows[i])[i];
-    if (sign)
-      det= -det;
-  }
-  return det;
-} /* determinant */
-
-/*---------------------------------
-
-  qh_detjoggle(qh, points, numpoints, dimension )
-    determine default max joggle for point array
-      as qh_distround * qh_JOGGLEdefault
-
-  returns:
-    initial value for JOGGLEmax from points and REALepsilon
-
-  notes:
-    computes DISTround since qh_maxmin not called yet
-    if qh->SCALElast, last dimension will be scaled later to MAXwidth
-
-    loop duplicated from qh_maxmin
-*/
-realT qh_detjoggle(qhT *qh, pointT *points, int numpoints, int dimension) {
-  realT abscoord, distround, joggle, maxcoord, mincoord;
-  pointT *point, *pointtemp;
-  realT maxabs= -REALmax;
-  realT sumabs= 0;
-  realT maxwidth= 0;
-  int k;
-
-  for (k=0; k < dimension; k++) {
-    if (qh->SCALElast && k == dimension-1)
-      abscoord= maxwidth;
-    else if (qh->DELAUNAY && k == dimension-1) /* will qh_setdelaunay() */
-      abscoord= 2 * maxabs * maxabs;  /* may be low by qh->hull_dim/2 */
-    else {
-      maxcoord= -REALmax;
-      mincoord= REALmax;
-      FORALLpoint_(qh, points, numpoints) {
-        maximize_(maxcoord, point[k]);
-        minimize_(mincoord, point[k]);
-      }
-      maximize_(maxwidth, maxcoord-mincoord);
-      abscoord= fmax_(maxcoord, -mincoord);
-    }
-    sumabs += abscoord;
-    maximize_(maxabs, abscoord);
-  } /* for k */
-  distround= qh_distround(qh, qh->hull_dim, maxabs, sumabs);
-  joggle= distround * qh_JOGGLEdefault;
-  maximize_(joggle, REALepsilon * qh_JOGGLEdefault);
-  trace2((qh, qh->ferr, 2001, "qh_detjoggle: joggle=%2.2g maxwidth=%2.2g\n", joggle, maxwidth));
-  return joggle;
-} /* detjoggle */
-
-/*---------------------------------
-
-  qh_detroundoff(qh)
-    determine maximum roundoff errors from
-      REALepsilon, REALmax, REALmin, qh.hull_dim, qh.MAXabs_coord,
-      qh.MAXsumcoord, qh.MAXwidth, qh.MINdenom_1
-
-    accounts for qh.SETroundoff, qh.RANDOMdist, qh->MERGEexact
-      qh.premerge_cos, qh.postmerge_cos, qh.premerge_centrum,
-      qh.postmerge_centrum, qh.MINoutside,
-      qh_RATIOnearinside, qh_COPLANARratio, qh_WIDEcoplanar
-
-  returns:
-    sets qh.DISTround, etc. (see below)
-    appends precision constants to qh.qhull_options
-
-  see:
-    qh_maxmin() for qh.NEARzero
-
-  design:
-    determine qh.DISTround for distance computations
-    determine minimum denominators for qh_divzero
-    determine qh.ANGLEround for angle computations
-    adjust qh.premerge_cos,... for roundoff error
-    determine qh.ONEmerge for maximum error due to a single merge
-    determine qh.NEARinside, qh.MAXcoplanar, qh.MINvisible,
-      qh.MINoutside, qh.WIDEfacet
-    initialize qh.max_vertex and qh.minvertex
-*/
-void qh_detroundoff(qhT *qh) {
-
-  qh_option(qh, "_max-width", NULL, &qh->MAXwidth);
-  if (!qh->SETroundoff) {
-    qh->DISTround= qh_distround(qh, qh->hull_dim, qh->MAXabs_coord, qh->MAXsumcoord);
-    if (qh->RANDOMdist)
-      qh->DISTround += qh->RANDOMfactor * qh->MAXabs_coord;
-    qh_option(qh, "Error-roundoff", NULL, &qh->DISTround);
-  }
-  qh->MINdenom= qh->MINdenom_1 * qh->MAXabs_coord;
-  qh->MINdenom_1_2= sqrt(qh->MINdenom_1 * qh->hull_dim) ;  /* if will be normalized */
-  qh->MINdenom_2= qh->MINdenom_1_2 * qh->MAXabs_coord;
-                                              /* for inner product */
-  qh->ANGLEround= 1.01 * qh->hull_dim * REALepsilon;
-  if (qh->RANDOMdist)
-    qh->ANGLEround += qh->RANDOMfactor;
-  if (qh->premerge_cos < REALmax/2) {
-    qh->premerge_cos -= qh->ANGLEround;
-    if (qh->RANDOMdist)
-      qh_option(qh, "Angle-premerge-with-random", NULL, &qh->premerge_cos);
-  }
-  if (qh->postmerge_cos < REALmax/2) {
-    qh->postmerge_cos -= qh->ANGLEround;
-    if (qh->RANDOMdist)
-      qh_option(qh, "Angle-postmerge-with-random", NULL, &qh->postmerge_cos);
-  }
-  qh->premerge_centrum += 2 * qh->DISTround;    /*2 for centrum and distplane()*/
-  qh->postmerge_centrum += 2 * qh->DISTround;
-  if (qh->RANDOMdist && (qh->MERGEexact || qh->PREmerge))
-    qh_option(qh, "Centrum-premerge-with-random", NULL, &qh->premerge_centrum);
-  if (qh->RANDOMdist && qh->POSTmerge)
-    qh_option(qh, "Centrum-postmerge-with-random", NULL, &qh->postmerge_centrum);
-  { /* compute ONEmerge, max vertex offset for merging simplicial facets */
-    realT maxangle= 1.0, maxrho;
-
-    minimize_(maxangle, qh->premerge_cos);
-    minimize_(maxangle, qh->postmerge_cos);
-    /* max diameter * sin theta + DISTround for vertex to its hyperplane */
-    qh->ONEmerge= sqrt((realT)qh->hull_dim) * qh->MAXwidth *
-      sqrt(1.0 - maxangle * maxangle) + qh->DISTround;
-    maxrho= qh->hull_dim * qh->premerge_centrum + qh->DISTround;
-    maximize_(qh->ONEmerge, maxrho);
-    maxrho= qh->hull_dim * qh->postmerge_centrum + qh->DISTround;
-    maximize_(qh->ONEmerge, maxrho);
-    if (qh->MERGING)
-      qh_option(qh, "_one-merge", NULL, &qh->ONEmerge);
-  }
-  qh->NEARinside= qh->ONEmerge * qh_RATIOnearinside; /* only used if qh->KEEPnearinside */
-  if (qh->JOGGLEmax < REALmax/2 && (qh->KEEPcoplanar || qh->KEEPinside)) {
-    realT maxdist;             /* adjust qh.NEARinside for joggle */
-    qh->KEEPnearinside= True;
-    maxdist= sqrt((realT)qh->hull_dim) * qh->JOGGLEmax + qh->DISTround;
-    maxdist= 2*maxdist;        /* vertex and coplanar point can joggle in opposite directions */
-    maximize_(qh->NEARinside, maxdist);  /* must agree with qh_nearcoplanar() */
-  }
-  if (qh->KEEPnearinside)
-    qh_option(qh, "_near-inside", NULL, &qh->NEARinside);
-  if (qh->JOGGLEmax < qh->DISTround) {
-    qh_fprintf(qh, qh->ferr, 6006, "qhull error: the joggle for 'QJn', %.2g, is below roundoff for distance computations, %.2g\n",
-         qh->JOGGLEmax, qh->DISTround);
-    qh_errexit(qh, qh_ERRinput, NULL, NULL);
-  }
-  if (qh->MINvisible > REALmax/2) {
-    if (!qh->MERGING)
-      qh->MINvisible= qh->DISTround;
-    else if (qh->hull_dim <= 3)
-      qh->MINvisible= qh->premerge_centrum;
-    else
-      qh->MINvisible= qh_COPLANARratio * qh->premerge_centrum;
-    if (qh->APPROXhull && qh->MINvisible > qh->MINoutside)
-      qh->MINvisible= qh->MINoutside;
-    qh_option(qh, "Visible-distance", NULL, &qh->MINvisible);
-  }
-  if (qh->MAXcoplanar > REALmax/2) {
-    qh->MAXcoplanar= qh->MINvisible;
-    qh_option(qh, "U-coplanar-distance", NULL, &qh->MAXcoplanar);
-  }
-  if (!qh->APPROXhull) {             /* user may specify qh->MINoutside */
-    qh->MINoutside= 2 * qh->MINvisible;
-    if (qh->premerge_cos < REALmax/2)
-      maximize_(qh->MINoutside, (1- qh->premerge_cos) * qh->MAXabs_coord);
-    qh_option(qh, "Width-outside", NULL, &qh->MINoutside);
-  }
-  qh->WIDEfacet= qh->MINoutside;
-  maximize_(qh->WIDEfacet, qh_WIDEcoplanar * qh->MAXcoplanar);
-  maximize_(qh->WIDEfacet, qh_WIDEcoplanar * qh->MINvisible);
-  qh_option(qh, "_wide-facet", NULL, &qh->WIDEfacet);
-  if (qh->MINvisible > qh->MINoutside + 3 * REALepsilon
-  && !qh->BESToutside && !qh->FORCEoutput)
-    qh_fprintf(qh, qh->ferr, 7001, "qhull input warning: minimum visibility V%.2g is greater than \nminimum outside W%.2g.  Flipped facets are likely.\n",
-             qh->MINvisible, qh->MINoutside);
-  qh->max_vertex= qh->DISTround;
-  qh->min_vertex= -qh->DISTround;
-  /* numeric constants reported in printsummary */
-} /* detroundoff */
-
-/*---------------------------------
-
-  qh_detsimplex(qh, apex, points, dim, nearzero )
-    compute determinant of a simplex with point apex and base points
-
-  returns:
-     signed determinant and nearzero from qh_determinant
-
-  notes:
-     uses qh.gm_matrix/qh.gm_row (assumes they're big enough)
-
-  design:
-    construct qm_matrix by subtracting apex from points
-    compute determinate
-*/
-realT qh_detsimplex(qhT *qh, pointT *apex, setT *points, int dim, boolT *nearzero) {
-  pointT *coorda, *coordp, *gmcoord, *point, **pointp;
-  coordT **rows;
-  int k,  i=0;
-  realT det;
-
-  zinc_(Zdetsimplex);
-  gmcoord= qh->gm_matrix;
-  rows= qh->gm_row;
-  FOREACHpoint_(points) {
-    if (i == dim)
-      break;
-    rows[i++]= gmcoord;
-    coordp= point;
-    coorda= apex;
-    for (k=dim; k--; )
-      *(gmcoord++)= *coordp++ - *coorda++;
-  }
-  if (i < dim) {
-    qh_fprintf(qh, qh->ferr, 6007, "qhull internal error (qh_detsimplex): #points %d < dimension %d\n",
-               i, dim);
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }
-  det= qh_determinant(qh, rows, dim, nearzero);
-  trace2((qh, qh->ferr, 2002, "qh_detsimplex: det=%2.2g for point p%d, dim %d, nearzero? %d\n",
-          det, qh_pointid(qh, apex), dim, *nearzero));
-  return det;
-} /* detsimplex */
-
-/*---------------------------------
-
-  qh_distnorm( dim, point, normal, offset )
-    return distance from point to hyperplane at normal/offset
-
-  returns:
-    dist
-
-  notes:
-    dist > 0 if point is outside of hyperplane
-
-  see:
-    qh_distplane in geom_r.c
-*/
-realT qh_distnorm(int dim, pointT *point, pointT *normal, realT *offsetp) {
-  coordT *normalp= normal, *coordp= point;
-  realT dist;
-  int k;
-
-  dist= *offsetp;
-  for (k=dim; k--; )
-    dist += *(coordp++) * *(normalp++);
-  return dist;
-} /* distnorm */
-
-/*---------------------------------
-
-  qh_distround(qh, dimension, maxabs, maxsumabs )
-    compute maximum round-off error for a distance computation
-      to a normalized hyperplane
-    maxabs is the maximum absolute value of a coordinate
-    maxsumabs is the maximum possible sum of absolute coordinate values
-
-  returns:
-    max dist round for REALepsilon
-
-  notes:
-    calculate roundoff error according to Golub & van Loan, 1983, Lemma 3.2-1, "Rounding Errors"
-    use sqrt(dim) since one vector is normalized
-      or use maxsumabs since one vector is < 1
-*/
-realT qh_distround(qhT *qh, int dimension, realT maxabs, realT maxsumabs) {
-  realT maxdistsum, maxround;
-
-  maxdistsum= sqrt((realT)dimension) * maxabs;
-  minimize_( maxdistsum, maxsumabs);
-  maxround= REALepsilon * (dimension * maxdistsum * 1.01 + maxabs);
-              /* adds maxabs for offset */
-  trace4((qh, qh->ferr, 4008, "qh_distround: %2.2g maxabs %2.2g maxsumabs %2.2g maxdistsum %2.2g\n",
-                 maxround, maxabs, maxsumabs, maxdistsum));
-  return maxround;
-} /* distround */
-
-/*---------------------------------
-
-  qh_divzero( numer, denom, mindenom1, zerodiv )
-    divide by a number that's nearly zero
-    mindenom1= minimum denominator for dividing into 1.0
-
-  returns:
-    quotient
-    sets zerodiv and returns 0.0 if it would overflow
-
-  design:
-    if numer is nearly zero and abs(numer) < abs(denom)
-      return numer/denom
-    else if numer is nearly zero
-      return 0 and zerodiv
-    else if denom/numer non-zero
-      return numer/denom
-    else
-      return 0 and zerodiv
-*/
-realT qh_divzero(realT numer, realT denom, realT mindenom1, boolT *zerodiv) {
-  realT temp, numerx, denomx;
-
-
-  if (numer < mindenom1 && numer > -mindenom1) {
-    numerx= fabs_(numer);
-    denomx= fabs_(denom);
-    if (numerx < denomx) {
-      *zerodiv= False;
-      return numer/denom;
-    }else {
-      *zerodiv= True;
-      return 0.0;
-    }
-  }
-  temp= denom/numer;
-  if (temp > mindenom1 || temp < -mindenom1) {
-    *zerodiv= False;
-    return numer/denom;
-  }else {
-    *zerodiv= True;
-    return 0.0;
-  }
-} /* divzero */
-
-
-/*---------------------------------
-
-  qh_facetarea(qh, facet )
-    return area for a facet
-
-  notes:
-    if non-simplicial,
-      uses centrum to triangulate facet and sums the projected areas.
-    if (qh->DELAUNAY),
-      computes projected area instead for last coordinate
-    assumes facet->normal exists
-    projecting tricoplanar facets to the hyperplane does not appear to make a difference
-
-  design:
-    if simplicial
-      compute area
-    else
-      for each ridge
-        compute area from centrum to ridge
-    negate area if upper Delaunay facet
-*/
-realT qh_facetarea(qhT *qh, facetT *facet) {
-  vertexT *apex;
-  pointT *centrum;
-  realT area= 0.0;
-  ridgeT *ridge, **ridgep;
-
-  if (facet->simplicial) {
-    apex= SETfirstt_(facet->vertices, vertexT);
-    area= qh_facetarea_simplex(qh, qh->hull_dim, apex->point, facet->vertices,
-                    apex, facet->toporient, facet->normal, &facet->offset);
-  }else {
-    if (qh->CENTERtype == qh_AScentrum)
-      centrum= facet->center;
-    else
-      centrum= qh_getcentrum(qh, facet);
-    FOREACHridge_(facet->ridges)
-      area += qh_facetarea_simplex(qh, qh->hull_dim, centrum, ridge->vertices,
-                 NULL, (boolT)(ridge->top == facet),  facet->normal, &facet->offset);
-    if (qh->CENTERtype != qh_AScentrum)
-      qh_memfree(qh, centrum, qh->normal_size);
-  }
-  if (facet->upperdelaunay && qh->DELAUNAY)
-    area= -area;  /* the normal should be [0,...,1] */
-  trace4((qh, qh->ferr, 4009, "qh_facetarea: f%d area %2.2g\n", facet->id, area));
-  return area;
-} /* facetarea */
-
-/*---------------------------------
-
-  qh_facetarea_simplex(qh, dim, apex, vertices, notvertex, toporient, normal, offset )
-    return area for a simplex defined by
-      an apex, a base of vertices, an orientation, and a unit normal
-    if simplicial or tricoplanar facet,
-      notvertex is defined and it is skipped in vertices
-
-  returns:
-    computes area of simplex projected to plane [normal,offset]
-    returns 0 if vertex too far below plane (qh->WIDEfacet)
-      vertex can't be apex of tricoplanar facet
-
-  notes:
-    if (qh->DELAUNAY),
-      computes projected area instead for last coordinate
-    uses qh->gm_matrix/gm_row and qh->hull_dim
-    helper function for qh_facetarea
-
-  design:
-    if Notvertex
-      translate simplex to apex
-    else
-      project simplex to normal/offset
-      translate simplex to apex
-    if Delaunay
-      set last row/column to 0 with -1 on diagonal
-    else
-      set last row to Normal
-    compute determinate
-    scale and flip sign for area
-*/
-realT qh_facetarea_simplex(qhT *qh, int dim, coordT *apex, setT *vertices,
-        vertexT *notvertex,  boolT toporient, coordT *normal, realT *offset) {
-  pointT *coorda, *coordp, *gmcoord;
-  coordT **rows, *normalp;
-  int k,  i=0;
-  realT area, dist;
-  vertexT *vertex, **vertexp;
-  boolT nearzero;
-
-  gmcoord= qh->gm_matrix;
-  rows= qh->gm_row;
-  FOREACHvertex_(vertices) {
-    if (vertex == notvertex)
-      continue;
-    rows[i++]= gmcoord;
-    coorda= apex;
-    coordp= vertex->point;
-    normalp= normal;
-    if (notvertex) {
-      for (k=dim; k--; )
-        *(gmcoord++)= *coordp++ - *coorda++;
-    }else {
-      dist= *offset;
-      for (k=dim; k--; )
-        dist += *coordp++ * *normalp++;
-      if (dist < -qh->WIDEfacet) {
-        zinc_(Znoarea);
-        return 0.0;
-      }
-      coordp= vertex->point;
-      normalp= normal;
-      for (k=dim; k--; )
-        *(gmcoord++)= (*coordp++ - dist * *normalp++) - *coorda++;
-    }
-  }
-  if (i != dim-1) {
-    qh_fprintf(qh, qh->ferr, 6008, "qhull internal error (qh_facetarea_simplex): #points %d != dim %d -1\n",
-               i, dim);
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }
-  rows[i]= gmcoord;
-  if (qh->DELAUNAY) {
-    for (i=0; i < dim-1; i++)
-      rows[i][dim-1]= 0.0;
-    for (k=dim; k--; )
-      *(gmcoord++)= 0.0;
-    rows[dim-1][dim-1]= -1.0;
-  }else {
-    normalp= normal;
-    for (k=dim; k--; )
-      *(gmcoord++)= *normalp++;
-  }
-  zinc_(Zdetsimplex);
-  area= qh_determinant(qh, rows, dim, &nearzero);
-  if (toporient)
-    area= -area;
-  area *= qh->AREAfactor;
-  trace4((qh, qh->ferr, 4010, "qh_facetarea_simplex: area=%2.2g for point p%d, toporient %d, nearzero? %d\n",
-          area, qh_pointid(qh, apex), toporient, nearzero));
-  return area;
-} /* facetarea_simplex */
-
-/*---------------------------------
-
-  qh_facetcenter(qh, vertices )
-    return Voronoi center (Voronoi vertex) for a facet's vertices
-
-  returns:
-    return temporary point equal to the center
-
-  see:
-    qh_voronoi_center()
-*/
-pointT *qh_facetcenter(qhT *qh, setT *vertices) {
-  setT *points= qh_settemp(qh, qh_setsize(qh, vertices));
-  vertexT *vertex, **vertexp;
-  pointT *center;
-
-  FOREACHvertex_(vertices)
-    qh_setappend(qh, &points, vertex->point);
-  center= qh_voronoi_center(qh, qh->hull_dim-1, points);
-  qh_settempfree(qh, &points);
-  return center;
-} /* facetcenter */
-
-/*---------------------------------
-
-  qh_findgooddist(qh, point, facetA, dist, facetlist )
-    find best good facet visible for point from facetA
-    assumes facetA is visible from point
-
-  returns:
-    best facet, i.e., good facet that is furthest from point
-      distance to best facet
-      NULL if none
-
-    moves good, visible facets (and some other visible facets)
-      to end of qh->facet_list
-
-  notes:
-    uses qh->visit_id
-
-  design:
-    initialize bestfacet if facetA is good
-    move facetA to end of facetlist
-    for each facet on facetlist
-      for each unvisited neighbor of facet
-        move visible neighbors to end of facetlist
-        update best good neighbor
-        if no good neighbors, update best facet
-*/
-facetT *qh_findgooddist(qhT *qh, pointT *point, facetT *facetA, realT *distp,
-               facetT **facetlist) {
-  realT bestdist= -REALmax, dist;
-  facetT *neighbor, **neighborp, *bestfacet=NULL, *facet;
-  boolT goodseen= False;
-
-  if (facetA->good) {
-    zzinc_(Zcheckpart);  /* calls from check_bestdist occur after print stats */
-    qh_distplane(qh, point, facetA, &bestdist);
-    bestfacet= facetA;
-    goodseen= True;
-  }
-  qh_removefacet(qh, facetA);
-  qh_appendfacet(qh, facetA);
-  *facetlist= facetA;
-  facetA->visitid= ++qh->visit_id;
-  FORALLfacet_(*facetlist) {
-    FOREACHneighbor_(facet) {
-      if (neighbor->visitid == qh->visit_id)
-        continue;
-      neighbor->visitid= qh->visit_id;
-      if (goodseen && !neighbor->good)
-        continue;
-      zzinc_(Zcheckpart);
-      qh_distplane(qh, point, neighbor, &dist);
-      if (dist > 0) {
-        qh_removefacet(qh, neighbor);
-        qh_appendfacet(qh, neighbor);
-        if (neighbor->good) {
-          goodseen= True;
-          if (dist > bestdist) {
-            bestdist= dist;
-            bestfacet= neighbor;
-          }
-        }
-      }
-    }
-  }
-  if (bestfacet) {
-    *distp= bestdist;
-    trace2((qh, qh->ferr, 2003, "qh_findgooddist: p%d is %2.2g above good facet f%d\n",
-      qh_pointid(qh, point), bestdist, bestfacet->id));
-    return bestfacet;
-  }
-  trace4((qh, qh->ferr, 4011, "qh_findgooddist: no good facet for p%d above f%d\n",
-      qh_pointid(qh, point), facetA->id));
-  return NULL;
-}  /* findgooddist */
-
-/*---------------------------------
-
-  qh_getarea(qh, facetlist )
-    set area of all facets in facetlist
-    collect statistics
-    nop if hasAreaVolume
-
-  returns:
-    sets qh->totarea/totvol to total area and volume of convex hull
-    for Delaunay triangulation, computes projected area of the lower or upper hull
-      ignores upper hull if qh->ATinfinity
-
-  notes:
-    could compute outer volume by expanding facet area by rays from interior
-    the following attempt at perpendicular projection underestimated badly:
-      qh.totoutvol += (-dist + facet->maxoutside + qh->DISTround)
-                            * area/ qh->hull_dim;
-  design:
-    for each facet on facetlist
-      compute facet->area
-      update qh.totarea and qh.totvol
-*/
-void qh_getarea(qhT *qh, facetT *facetlist) {
-  realT area;
-  realT dist;
-  facetT *facet;
-
-  if (qh->hasAreaVolume)
-    return;
-  if (qh->REPORTfreq)
-    qh_fprintf(qh, qh->ferr, 8020, "computing area of each facet and volume of the convex hull\n");
-  else
-    trace1((qh, qh->ferr, 1001, "qh_getarea: computing volume and area for each facet\n"));
-  qh->totarea= qh->totvol= 0.0;
-  FORALLfacet_(facetlist) {
-    if (!facet->normal)
-      continue;
-    if (facet->upperdelaunay && qh->ATinfinity)
-      continue;
-    if (!facet->isarea) {
-      facet->f.area= qh_facetarea(qh, facet);
-      facet->isarea= True;
-    }
-    area= facet->f.area;
-    if (qh->DELAUNAY) {
-      if (facet->upperdelaunay == qh->UPPERdelaunay)
-        qh->totarea += area;
-    }else {
-      qh->totarea += area;
-      qh_distplane(qh, qh->interior_point, facet, &dist);
-      qh->totvol += -dist * area/ qh->hull_dim;
-    }
-    if (qh->PRINTstatistics) {
-      wadd_(Wareatot, area);
-      wmax_(Wareamax, area);
-      wmin_(Wareamin, area);
-    }
-  }
-  qh->hasAreaVolume= True;
-} /* getarea */
-
-/*---------------------------------
-
-  qh_gram_schmidt(qh, dim, row )
-    implements Gram-Schmidt orthogonalization by rows
-
-  returns:
-    false if zero norm
-    overwrites rows[dim][dim]
-
-  notes:
-    see Golub & van Loan, 1983, Algorithm 6.2-2, "Modified Gram-Schmidt"
-    overflow due to small divisors not handled
-
-  design:
-    for each row
-      compute norm for row
-      if non-zero, normalize row
-      for each remaining rowA
-        compute inner product of row and rowA
-        reduce rowA by row * inner product
-*/
-boolT qh_gram_schmidt(qhT *qh, int dim, realT **row) {
-  realT *rowi, *rowj, norm;
-  int i, j, k;
-
-  for (i=0; i < dim; i++) {
-    rowi= row[i];
-    for (norm= 0.0, k= dim; k--; rowi++)
-      norm += *rowi * *rowi;
-    norm= sqrt(norm);
-    wmin_(Wmindenom, norm);
-    if (norm == 0.0)  /* either 0 or overflow due to sqrt */
-      return False;
-    for (k=dim; k--; )
-      *(--rowi) /= norm;
-    for (j=i+1; j < dim; j++) {
-      rowj= row[j];
-      for (norm= 0.0, k=dim; k--; )
-        norm += *rowi++ * *rowj++;
-      for (k=dim; k--; )
-        *(--rowj) -= *(--rowi) * norm;
-    }
-  }
-  return True;
-} /* gram_schmidt */
-
-
-/*---------------------------------
-
-  qh_inthresholds(qh, normal, angle )
-    return True if normal within qh.lower_/upper_threshold
-
-  returns:
-    estimate of angle by summing of threshold diffs
-      angle may be NULL
-      smaller "angle" is better
-
-  notes:
-    invalid if qh.SPLITthresholds
-
-  see:
-    qh.lower_threshold in qh_initbuild()
-    qh_initthresholds()
-
-  design:
-    for each dimension
-      test threshold
-*/
-boolT qh_inthresholds(qhT *qh, coordT *normal, realT *angle) {
-  boolT within= True;
-  int k;
-  realT threshold;
-
-  if (angle)
-    *angle= 0.0;
-  for (k=0; k < qh->hull_dim; k++) {
-    threshold= qh->lower_threshold[k];
-    if (threshold > -REALmax/2) {
-      if (normal[k] < threshold)
-        within= False;
-      if (angle) {
-        threshold -= normal[k];
-        *angle += fabs_(threshold);
-      }
-    }
-    if (qh->upper_threshold[k] < REALmax/2) {
-      threshold= qh->upper_threshold[k];
-      if (normal[k] > threshold)
-        within= False;
-      if (angle) {
-        threshold -= normal[k];
-        *angle += fabs_(threshold);
-      }
-    }
-  }
-  return within;
-} /* inthresholds */
-
-
-/*---------------------------------
-
-  qh_joggleinput(qh)
-    randomly joggle input to Qhull by qh.JOGGLEmax
-    initial input is qh.first_point/qh.num_points of qh.hull_dim
-      repeated calls use qh.input_points/qh.num_points
-
-  returns:
-    joggles points at qh.first_point/qh.num_points
-    copies data to qh.input_points/qh.input_malloc if first time
-    determines qh.JOGGLEmax if it was zero
-    if qh.DELAUNAY
-      computes the Delaunay projection of the joggled points
-
-  notes:
-    if qh.DELAUNAY, unnecessarily joggles the last coordinate
-    the initial 'QJn' may be set larger than qh_JOGGLEmaxincrease
-
-  design:
-    if qh.DELAUNAY
-      set qh.SCALElast for reduced precision errors
-    if first call
-      initialize qh.input_points to the original input points
-      if qh.JOGGLEmax == 0
-        determine default qh.JOGGLEmax
-    else
-      increase qh.JOGGLEmax according to qh.build_cnt
-    joggle the input by adding a random number in [-qh.JOGGLEmax,qh.JOGGLEmax]
-    if qh.DELAUNAY
-      sets the Delaunay projection
-*/
-void qh_joggleinput(qhT *qh) {
-  int i, seed, size;
-  coordT *coordp, *inputp;
-  realT randr, randa, randb;
-
-  if (!qh->input_points) { /* first call */
-    qh->input_points= qh->first_point;
-    qh->input_malloc= qh->POINTSmalloc;
-    size= qh->num_points * qh->hull_dim * sizeof(coordT);
-    if (!(qh->first_point=(coordT*)qh_malloc((size_t)size))) {
-      qh_fprintf(qh, qh->ferr, 6009, "qhull error: insufficient memory to joggle %d points\n",
-          qh->num_points);
-      qh_errexit(qh, qh_ERRmem, NULL, NULL);
-    }
-    qh->POINTSmalloc= True;
-    if (qh->JOGGLEmax == 0.0) {
-      qh->JOGGLEmax= qh_detjoggle(qh, qh->input_points, qh->num_points, qh->hull_dim);
-      qh_option(qh, "QJoggle", NULL, &qh->JOGGLEmax);
-    }
-  }else {                 /* repeated call */
-    if (!qh->RERUN && qh->build_cnt > qh_JOGGLEretry) {
-      if (((qh->build_cnt-qh_JOGGLEretry-1) % qh_JOGGLEagain) == 0) {
-        realT maxjoggle= qh->MAXwidth * qh_JOGGLEmaxincrease;
-        if (qh->JOGGLEmax < maxjoggle) {
-          qh->JOGGLEmax *= qh_JOGGLEincrease;
-          minimize_(qh->JOGGLEmax, maxjoggle);
-        }
-      }
-    }
-    qh_option(qh, "QJoggle", NULL, &qh->JOGGLEmax);
-  }
-  if (qh->build_cnt > 1 && qh->JOGGLEmax > fmax_(qh->MAXwidth/4, 0.1)) {
-      qh_fprintf(qh, qh->ferr, 6010, "qhull error: the current joggle for 'QJn', %.2g, is too large for the width\nof the input.  If possible, recompile Qhull with higher-precision reals.\n",
-                qh->JOGGLEmax);
-      qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }
-  /* for some reason, using qh->ROTATErandom and qh_RANDOMseed does not repeat the run. Use 'TRn' instead */
-  seed= qh_RANDOMint;
-  qh_option(qh, "_joggle-seed", &seed, NULL);
-  trace0((qh, qh->ferr, 6, "qh_joggleinput: joggle input by %2.2g with seed %d\n",
-    qh->JOGGLEmax, seed));
-  inputp= qh->input_points;
-  coordp= qh->first_point;
-  randa= 2.0 * qh->JOGGLEmax/qh_RANDOMmax;
-  randb= -qh->JOGGLEmax;
-  size= qh->num_points * qh->hull_dim;
-  for (i=size; i--; ) {
-    randr= qh_RANDOMint;
-    *(coordp++)= *(inputp++) + (randr * randa + randb);
-  }
-  if (qh->DELAUNAY) {
-    qh->last_low= qh->last_high= qh->last_newhigh= REALmax;
-    qh_setdelaunay(qh, qh->hull_dim, qh->num_points, qh->first_point);
-  }
-} /* joggleinput */
-
-/*---------------------------------
-
-  qh_maxabsval( normal, dim )
-    return pointer to maximum absolute value of a dim vector
-    returns NULL if dim=0
-*/
-realT *qh_maxabsval(realT *normal, int dim) {
-  realT maxval= -REALmax;
-  realT *maxp= NULL, *colp, absval;
-  int k;
-
-  for (k=dim, colp= normal; k--; colp++) {
-    absval= fabs_(*colp);
-    if (absval > maxval) {
-      maxval= absval;
-      maxp= colp;
-    }
-  }
-  return maxp;
-} /* maxabsval */
-
-
-/*---------------------------------
-
-  qh_maxmin(qh, points, numpoints, dimension )
-    return max/min points for each dimension
-    determine max and min coordinates
-
-  returns:
-    returns a temporary set of max and min points
-      may include duplicate points. Does not include qh.GOODpoint
-    sets qh.NEARzero, qh.MAXabs_coord, qh.MAXsumcoord, qh.MAXwidth
-         qh.MAXlastcoord, qh.MINlastcoord
-    initializes qh.max_outside, qh.min_vertex, qh.WAScoplanar, qh.ZEROall_ok
-
-  notes:
-    loop duplicated in qh_detjoggle()
-
-  design:
-    initialize global precision variables
-    checks definition of REAL...
-    for each dimension
-      for each point
-        collect maximum and minimum point
-      collect maximum of maximums and minimum of minimums
-      determine qh.NEARzero for Gaussian Elimination
-*/
-setT *qh_maxmin(qhT *qh, pointT *points, int numpoints, int dimension) {
-  int k;
-  realT maxcoord, temp;
-  pointT *minimum, *maximum, *point, *pointtemp;
-  setT *set;
-
-  qh->max_outside= 0.0;
-  qh->MAXabs_coord= 0.0;
-  qh->MAXwidth= -REALmax;
-  qh->MAXsumcoord= 0.0;
-  qh->min_vertex= 0.0;
-  qh->WAScoplanar= False;
-  if (qh->ZEROcentrum)
-    qh->ZEROall_ok= True;
-  if (REALmin < REALepsilon && REALmin < REALmax && REALmin > -REALmax
-  && REALmax > 0.0 && -REALmax < 0.0)
-    ; /* all ok */
-  else {
-    qh_fprintf(qh, qh->ferr, 6011, "qhull error: floating point constants in user.h are wrong\n\
-REALepsilon %g REALmin %g REALmax %g -REALmax %g\n",
-             REALepsilon, REALmin, REALmax, -REALmax);
-    qh_errexit(qh, qh_ERRinput, NULL, NULL);
-  }
-  set= qh_settemp(qh, 2*dimension);
-  for (k=0; k < dimension; k++) {
-    if (points == qh->GOODpointp)
-      minimum= maximum= points + dimension;
-    else
-      minimum= maximum= points;
-    FORALLpoint_(qh, points, numpoints) {
-      if (point == qh->GOODpointp)
-        continue;
-      if (maximum[k] < point[k])
-        maximum= point;
-      else if (minimum[k] > point[k])
-        minimum= point;
-    }
-    if (k == dimension-1) {
-      qh->MINlastcoord= minimum[k];
-      qh->MAXlastcoord= maximum[k];
-    }
-    if (qh->SCALElast && k == dimension-1)
-      maxcoord= qh->MAXwidth;
-    else {
-      maxcoord= fmax_(maximum[k], -minimum[k]);
-      if (qh->GOODpointp) {
-        temp= fmax_(qh->GOODpointp[k], -qh->GOODpointp[k]);
-        maximize_(maxcoord, temp);
-      }
-      temp= maximum[k] - minimum[k];
-      maximize_(qh->MAXwidth, temp);
-    }
-    maximize_(qh->MAXabs_coord, maxcoord);
-    qh->MAXsumcoord += maxcoord;
-    qh_setappend(qh, &set, maximum);
-    qh_setappend(qh, &set, minimum);
-    /* calculation of qh NEARzero is based on Golub & van Loan, 1983,
-       Eq. 4.4-13 for "Gaussian elimination with complete pivoting".
-       Golub & van Loan say that n^3 can be ignored and 10 be used in
-       place of rho */
-    qh->NEARzero[k]= 80 * qh->MAXsumcoord * REALepsilon;
-  }
-  if (qh->IStracing >=1)
-    qh_printpoints(qh, qh->ferr, "qh_maxmin: found the max and min points(by dim):", set);
-  return(set);
-} /* maxmin */
-
-/*---------------------------------
-
-  qh_maxouter(qh)
-    return maximum distance from facet to outer plane
-    normally this is qh.max_outside+qh.DISTround
-    does not include qh.JOGGLEmax
-
-  see:
-    qh_outerinner()
-
-  notes:
-    need to add another qh.DISTround if testing actual point with computation
-
-  for joggle:
-    qh_setfacetplane() updated qh.max_outer for Wnewvertexmax (max distance to vertex)
-    need to use Wnewvertexmax since could have a coplanar point for a high
-      facet that is replaced by a low facet
-    need to add qh.JOGGLEmax if testing input points
-*/
-realT qh_maxouter(qhT *qh) {
-  realT dist;
-
-  dist= fmax_(qh->max_outside, qh->DISTround);
-  dist += qh->DISTround;
-  trace4((qh, qh->ferr, 4012, "qh_maxouter: max distance from facet to outer plane is %2.2g max_outside is %2.2g\n", dist, qh->max_outside));
-  return dist;
-} /* maxouter */
-
-/*---------------------------------
-
-  qh_maxsimplex(qh, dim, maxpoints, points, numpoints, simplex )
-    determines maximum simplex for a set of points
-    starts from points already in simplex
-    skips qh.GOODpointp (assumes that it isn't in maxpoints)
-
-  returns:
-    simplex with dim+1 points
-
-  notes:
-    assumes at least pointsneeded points in points
-    maximizes determinate for x,y,z,w, etc.
-    uses maxpoints as long as determinate is clearly non-zero
-
-  design:
-    initialize simplex with at least two points
-      (find points with max or min x coordinate)
-    for each remaining dimension
-      add point that maximizes the determinate
-        (use points from maxpoints first)
-*/
-void qh_maxsimplex(qhT *qh, int dim, setT *maxpoints, pointT *points, int numpoints, setT **simplex) {
-  pointT *point, **pointp, *pointtemp, *maxpoint, *minx=NULL, *maxx=NULL;
-  boolT nearzero, maxnearzero= False;
-  int k, sizinit;
-  realT maxdet= -REALmax, det, mincoord= REALmax, maxcoord= -REALmax;
-
-  sizinit= qh_setsize(qh, *simplex);
-  if (sizinit < 2) {
-    if (qh_setsize(qh, maxpoints) >= 2) {
-      FOREACHpoint_(maxpoints) {
-        if (maxcoord < point[0]) {
-          maxcoord= point[0];
-          maxx= point;
-        }
-        if (mincoord > point[0]) {
-          mincoord= point[0];
-          minx= point;
-        }
-      }
-    }else {
-      FORALLpoint_(qh, points, numpoints) {
-        if (point == qh->GOODpointp)
-          continue;
-        if (maxcoord < point[0]) {
-          maxcoord= point[0];
-          maxx= point;
-        }
-        if (mincoord > point[0]) {
-          mincoord= point[0];
-          minx= point;
-        }
-      }
-    }
-    qh_setunique(qh, simplex, minx);
-    if (qh_setsize(qh, *simplex) < 2)
-      qh_setunique(qh, simplex, maxx);
-    sizinit= qh_setsize(qh, *simplex);
-    if (sizinit < 2) {
-      qh_precision(qh, "input has same x coordinate");
-      if (zzval_(Zsetplane) > qh->hull_dim+1) {
-        qh_fprintf(qh, qh->ferr, 6012, "qhull precision error (qh_maxsimplex for voronoi_center):\n%d points with the same x coordinate.\n",
-                 qh_setsize(qh, maxpoints)+numpoints);
-        qh_errexit(qh, qh_ERRprec, NULL, NULL);
-      }else {
-        qh_fprintf(qh, qh->ferr, 6013, "qhull input error: input is less than %d-dimensional since it has the same x coordinate\n", qh->hull_dim);
-        qh_errexit(qh, qh_ERRinput, NULL, NULL);
-      }
-    }
-  }
-  for (k=sizinit; k < dim+1; k++) {
-    maxpoint= NULL;
-    maxdet= -REALmax;
-    FOREACHpoint_(maxpoints) {
-      if (!qh_setin(*simplex, point)) {
-        det= qh_detsimplex(qh, point, *simplex, k, &nearzero);
-        if ((det= fabs_(det)) > maxdet) {
-          maxdet= det;
-          maxpoint= point;
-          maxnearzero= nearzero;
-        }
-      }
-    }
-    if (!maxpoint || maxnearzero) {
-      zinc_(Zsearchpoints);
-      if (!maxpoint) {
-        trace0((qh, qh->ferr, 7, "qh_maxsimplex: searching all points for %d-th initial vertex.\n", k+1));
-      }else {
-        trace0((qh, qh->ferr, 8, "qh_maxsimplex: searching all points for %d-th initial vertex, better than p%d det %2.2g\n",
-                k+1, qh_pointid(qh, maxpoint), maxdet));
-      }
-      FORALLpoint_(qh, points, numpoints) {
-        if (point == qh->GOODpointp)
-          continue;
-        if (!qh_setin(*simplex, point)) {
-          det= qh_detsimplex(qh, point, *simplex, k, &nearzero);
-          if ((det= fabs_(det)) > maxdet) {
-            maxdet= det;
-            maxpoint= point;
-            maxnearzero= nearzero;
-          }
-        }
-      }
-    } /* !maxpoint */
-    if (!maxpoint) {
-      qh_fprintf(qh, qh->ferr, 6014, "qhull internal error (qh_maxsimplex): not enough points available\n");
-      qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-    }
-    qh_setappend(qh, simplex, maxpoint);
-    trace1((qh, qh->ferr, 1002, "qh_maxsimplex: selected point p%d for %d`th initial vertex, det=%2.2g\n",
-            qh_pointid(qh, maxpoint), k+1, maxdet));
-  } /* k */
-} /* maxsimplex */
-
-/*---------------------------------
-
-  qh_minabsval( normal, dim )
-    return minimum absolute value of a dim vector
-*/
-realT qh_minabsval(realT *normal, int dim) {
-  realT minval= 0;
-  realT maxval= 0;
-  realT *colp;
-  int k;
-
-  for (k=dim, colp=normal; k--; colp++) {
-    maximize_(maxval, *colp);
-    minimize_(minval, *colp);
-  }
-  return fmax_(maxval, -minval);
-} /* minabsval */
-
-
-/*---------------------------------
-
-  qh_mindif(qh, vecA, vecB, dim )
-    return index of min abs. difference of two vectors
-*/
-int qh_mindiff(realT *vecA, realT *vecB, int dim) {
-  realT mindiff= REALmax, diff;
-  realT *vecAp= vecA, *vecBp= vecB;
-  int k, mink= 0;
-
-  for (k=0; k < dim; k++) {
-    diff= *vecAp++ - *vecBp++;
-    diff= fabs_(diff);
-    if (diff < mindiff) {
-      mindiff= diff;
-      mink= k;
-    }
-  }
-  return mink;
-} /* mindiff */
-
-
-
-/*---------------------------------
-
-  qh_orientoutside(qh, facet  )
-    make facet outside oriented via qh.interior_point
-
-  returns:
-    True if facet reversed orientation.
-*/
-boolT qh_orientoutside(qhT *qh, facetT *facet) {
-  int k;
-  realT dist;
-
-  qh_distplane(qh, qh->interior_point, facet, &dist);
-  if (dist > 0) {
-    for (k=qh->hull_dim; k--; )
-      facet->normal[k]= -facet->normal[k];
-    facet->offset= -facet->offset;
-    return True;
-  }
-  return False;
-} /* orientoutside */
-
-/*---------------------------------
-
-  qh_outerinner(qh, facet, outerplane, innerplane  )
-    if facet and qh.maxoutdone (i.e., qh_check_maxout)
-      returns outer and inner plane for facet
-    else
-      returns maximum outer and inner plane
-    accounts for qh.JOGGLEmax
-
-  see:
-    qh_maxouter(qh), qh_check_bestdist(), qh_check_points()
-
-  notes:
-    outerplaner or innerplane may be NULL
-    facet is const
-    Does not error (QhullFacet)
-
-    includes qh.DISTround for actual points
-    adds another qh.DISTround if testing with floating point arithmetic
-*/
-void qh_outerinner(qhT *qh, facetT *facet, realT *outerplane, realT *innerplane) {
-  realT dist, mindist;
-  vertexT *vertex, **vertexp;
-
-  if (outerplane) {
-    if (!qh_MAXoutside || !facet || !qh->maxoutdone) {
-      *outerplane= qh_maxouter(qh);       /* includes qh.DISTround */
-    }else { /* qh_MAXoutside ... */
-#if qh_MAXoutside
-      *outerplane= facet->maxoutside + qh->DISTround;
-#endif
-
-    }
-    if (qh->JOGGLEmax < REALmax/2)
-      *outerplane += qh->JOGGLEmax * sqrt((realT)qh->hull_dim);
-  }
-  if (innerplane) {
-    if (facet) {
-      mindist= REALmax;
-      FOREACHvertex_(facet->vertices) {
-        zinc_(Zdistio);
-        qh_distplane(qh, vertex->point, facet, &dist);
-        minimize_(mindist, dist);
-      }
-      *innerplane= mindist - qh->DISTround;
-    }else
-      *innerplane= qh->min_vertex - qh->DISTround;
-    if (qh->JOGGLEmax < REALmax/2)
-      *innerplane -= qh->JOGGLEmax * sqrt((realT)qh->hull_dim);
-  }
-} /* outerinner */
-
-/*---------------------------------
-
-  qh_pointdist( point1, point2, dim )
-    return distance between two points
-
-  notes:
-    returns distance squared if 'dim' is negative
-*/
-coordT qh_pointdist(pointT *point1, pointT *point2, int dim) {
-  coordT dist, diff;
-  int k;
-
-  dist= 0.0;
-  for (k= (dim > 0 ? dim : -dim); k--; ) {
-    diff= *point1++ - *point2++;
-    dist += diff * diff;
-  }
-  if (dim > 0)
-    return(sqrt(dist));
-  return dist;
-} /* pointdist */
-
-
-/*---------------------------------
-
-  qh_printmatrix(qh, fp, string, rows, numrow, numcol )
-    print matrix to fp given by row vectors
-    print string as header
-    qh may be NULL if fp is defined
-
-  notes:
-    print a vector by qh_printmatrix(qh, fp, "", &vect, 1, len)
-*/
-void qh_printmatrix(qhT *qh, FILE *fp, const char *string, realT **rows, int numrow, int numcol) {
-  realT *rowp;
-  realT r; /*bug fix*/
-  int i,k;
-
-  qh_fprintf(qh, fp, 9001, "%s\n", string);
-  for (i=0; i < numrow; i++) {
-    rowp= rows[i];
-    for (k=0; k < numcol; k++) {
-      r= *rowp++;
-      qh_fprintf(qh, fp, 9002, "%6.3g ", r);
-    }
-    qh_fprintf(qh, fp, 9003, "\n");
-  }
-} /* printmatrix */
-
-
-/*---------------------------------
-
-  qh_printpoints(qh, fp, string, points )
-    print pointids to fp for a set of points
-    if string, prints string and 'p' point ids
-*/
-void qh_printpoints(qhT *qh, FILE *fp, const char *string, setT *points) {
-  pointT *point, **pointp;
-
-  if (string) {
-    qh_fprintf(qh, fp, 9004, "%s", string);
-    FOREACHpoint_(points)
-      qh_fprintf(qh, fp, 9005, " p%d", qh_pointid(qh, point));
-    qh_fprintf(qh, fp, 9006, "\n");
-  }else {
-    FOREACHpoint_(points)
-      qh_fprintf(qh, fp, 9007, " %d", qh_pointid(qh, point));
-    qh_fprintf(qh, fp, 9008, "\n");
-  }
-} /* printpoints */
-
-
-/*---------------------------------
-
-  qh_projectinput(qh)
-    project input points using qh.lower_bound/upper_bound and qh->DELAUNAY
-    if qh.lower_bound[k]=qh.upper_bound[k]= 0,
-      removes dimension k
-    if halfspace intersection
-      removes dimension k from qh.feasible_point
-    input points in qh->first_point, num_points, input_dim
-
-  returns:
-    new point array in qh->first_point of qh->hull_dim coordinates
-    sets qh->POINTSmalloc
-    if qh->DELAUNAY
-      projects points to paraboloid
-      lowbound/highbound is also projected
-    if qh->ATinfinity
-      adds point "at-infinity"
-    if qh->POINTSmalloc
-      frees old point array
-
-  notes:
-    checks that qh.hull_dim agrees with qh.input_dim, PROJECTinput, and DELAUNAY
-
-
-  design:
-    sets project[k] to -1 (delete), 0 (keep), 1 (add for Delaunay)
-    determines newdim and newnum for qh->hull_dim and qh->num_points
-    projects points to newpoints
-    projects qh.lower_bound to itself
-    projects qh.upper_bound to itself
-    if qh->DELAUNAY
-      if qh->ATINFINITY
-        projects points to paraboloid
-        computes "infinity" point as vertex average and 10% above all points
-      else
-        uses qh_setdelaunay to project points to paraboloid
-*/
-void qh_projectinput(qhT *qh) {
-  int k,i;
-  int newdim= qh->input_dim, newnum= qh->num_points;
-  signed char *project;
-  int projectsize= (qh->input_dim+1)*sizeof(*project);
-  pointT *newpoints, *coord, *infinity;
-  realT paraboloid, maxboloid= 0;
-
-  project= (signed char*)qh_memalloc(qh, projectsize);
-  memset((char*)project, 0, (size_t)projectsize);
-  for (k=0; k < qh->input_dim; k++) {   /* skip Delaunay bound */
-    if (qh->lower_bound[k] == 0 && qh->upper_bound[k] == 0) {
-      project[k]= -1;
-      newdim--;
-    }
-  }
-  if (qh->DELAUNAY) {
-    project[k]= 1;
-    newdim++;
-    if (qh->ATinfinity)
-      newnum++;
-  }
-  if (newdim != qh->hull_dim) {
-    qh_memfree(qh, project, projectsize);
-    qh_fprintf(qh, qh->ferr, 6015, "qhull internal error (qh_projectinput): dimension after projection %d != hull_dim %d\n", newdim, qh->hull_dim);
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }
-  if (!(newpoints= qh->temp_malloc= (coordT*)qh_malloc(newnum*newdim*sizeof(coordT)))){
-    qh_memfree(qh, project, projectsize);
-    qh_fprintf(qh, qh->ferr, 6016, "qhull error: insufficient memory to project %d points\n",
-           qh->num_points);
-    qh_errexit(qh, qh_ERRmem, NULL, NULL);
-  }
-  /* qh_projectpoints throws error if mismatched dimensions */
-  qh_projectpoints(qh, project, qh->input_dim+1, qh->first_point,
-                    qh->num_points, qh->input_dim, newpoints, newdim);
-  trace1((qh, qh->ferr, 1003, "qh_projectinput: updating lower and upper_bound\n"));
-  qh_projectpoints(qh, project, qh->input_dim+1, qh->lower_bound,
-                    1, qh->input_dim+1, qh->lower_bound, newdim+1);
-  qh_projectpoints(qh, project, qh->input_dim+1, qh->upper_bound,
-                    1, qh->input_dim+1, qh->upper_bound, newdim+1);
-  if (qh->HALFspace) {
-    if (!qh->feasible_point) {
-      qh_memfree(qh, project, projectsize);
-      qh_fprintf(qh, qh->ferr, 6017, "qhull internal error (qh_projectinput): HALFspace defined without qh.feasible_point\n");
-      qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-    }
-    qh_projectpoints(qh, project, qh->input_dim, qh->feasible_point,
-                      1, qh->input_dim, qh->feasible_point, newdim);
-  }
-  qh_memfree(qh, project, projectsize);
-  if (qh->POINTSmalloc)
-    qh_free(qh->first_point);
-  qh->first_point= newpoints;
-  qh->POINTSmalloc= True;
-  qh->temp_malloc= NULL;
-  if (qh->DELAUNAY && qh->ATinfinity) {
-    coord= qh->first_point;
-    infinity= qh->first_point + qh->hull_dim * qh->num_points;
-    for (k=qh->hull_dim-1; k--; )
-      infinity[k]= 0.0;
-    for (i=qh->num_points; i--; ) {
-      paraboloid= 0.0;
-      for (k=0; k < qh->hull_dim-1; k++) {
-        paraboloid += *coord * *coord;
-        infinity[k] += *coord;
-        coord++;
-      }
-      *(coord++)= paraboloid;
-      maximize_(maxboloid, paraboloid);
-    }
-    /* coord == infinity */
-    for (k=qh->hull_dim-1; k--; )
-      *(coord++) /= qh->num_points;
-    *(coord++)= maxboloid * 1.1;
-    qh->num_points++;
-    trace0((qh, qh->ferr, 9, "qh_projectinput: projected points to paraboloid for Delaunay\n"));
-  }else if (qh->DELAUNAY)  /* !qh->ATinfinity */
-    qh_setdelaunay(qh, qh->hull_dim, qh->num_points, qh->first_point);
-} /* projectinput */
-
-
-/*---------------------------------
-
-  qh_projectpoints(qh, project, n, points, numpoints, dim, newpoints, newdim )
-    project points/numpoints/dim to newpoints/newdim
-    if project[k] == -1
-      delete dimension k
-    if project[k] == 1
-      add dimension k by duplicating previous column
-    n is size of project
-
-  notes:
-    newpoints may be points if only adding dimension at end
-
-  design:
-    check that 'project' and 'newdim' agree
-    for each dimension
-      if project == -1
-        skip dimension
-      else
-        determine start of column in newpoints
-        determine start of column in points
-          if project == +1, duplicate previous column
-        copy dimension (column) from points to newpoints
-*/
-void qh_projectpoints(qhT *qh, signed char *project, int n, realT *points,
-        int numpoints, int dim, realT *newpoints, int newdim) {
-  int testdim= dim, oldk=0, newk=0, i,j=0,k;
-  realT *newp, *oldp;
-
-  for (k=0; k < n; k++)
-    testdim += project[k];
-  if (testdim != newdim) {
-    qh_fprintf(qh, qh->ferr, 6018, "qhull internal error (qh_projectpoints): newdim %d should be %d after projection\n",
-      newdim, testdim);
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }
-  for (j=0; j= dim)
-          continue;
-        oldp= points+oldk;
-      }else
-        oldp= points+oldk++;
-      for (i=numpoints; i--; ) {
-        *newp= *oldp;
-        newp += newdim;
-        oldp += dim;
-      }
-    }
-    if (oldk >= dim)
-      break;
-  }
-  trace1((qh, qh->ferr, 1004, "qh_projectpoints: projected %d points from dim %d to dim %d\n",
-    numpoints, dim, newdim));
-} /* projectpoints */
-
-
-/*---------------------------------
-
-  qh_rotateinput(qh, rows )
-    rotate input using row matrix
-    input points given by qh->first_point, num_points, hull_dim
-    assumes rows[dim] is a scratch buffer
-    if qh->POINTSmalloc, overwrites input points, else mallocs a new array
-
-  returns:
-    rotated input
-    sets qh->POINTSmalloc
-
-  design:
-    see qh_rotatepoints
-*/
-void qh_rotateinput(qhT *qh, realT **rows) {
-
-  if (!qh->POINTSmalloc) {
-    qh->first_point= qh_copypoints(qh, qh->first_point, qh->num_points, qh->hull_dim);
-    qh->POINTSmalloc= True;
-  }
-  qh_rotatepoints(qh, qh->first_point, qh->num_points, qh->hull_dim, rows);
-}  /* rotateinput */
-
-/*---------------------------------
-
-  qh_rotatepoints(qh, points, numpoints, dim, row )
-    rotate numpoints points by a d-dim row matrix
-    assumes rows[dim] is a scratch buffer
-
-  returns:
-    rotated points in place
-
-  design:
-    for each point
-      for each coordinate
-        use row[dim] to compute partial inner product
-      for each coordinate
-        rotate by partial inner product
-*/
-void qh_rotatepoints(qhT *qh, realT *points, int numpoints, int dim, realT **row) {
-  realT *point, *rowi, *coord= NULL, sum, *newval;
-  int i,j,k;
-
-  if (qh->IStracing >= 1)
-    qh_printmatrix(qh, qh->ferr, "qh_rotatepoints: rotate points by", row, dim, dim);
-  for (point= points, j= numpoints; j--; point += dim) {
-    newval= row[dim];
-    for (i=0; i < dim; i++) {
-      rowi= row[i];
-      coord= point;
-      for (sum= 0.0, k= dim; k--; )
-        sum += *rowi++ * *coord++;
-      *(newval++)= sum;
-    }
-    for (k=dim; k--; )
-      *(--coord)= *(--newval);
-  }
-} /* rotatepoints */
-
-
-/*---------------------------------
-
-  qh_scaleinput(qh)
-    scale input points using qh->low_bound/high_bound
-    input points given by qh->first_point, num_points, hull_dim
-    if qh->POINTSmalloc, overwrites input points, else mallocs a new array
-
-  returns:
-    scales coordinates of points to low_bound[k], high_bound[k]
-    sets qh->POINTSmalloc
-
-  design:
-    see qh_scalepoints
-*/
-void qh_scaleinput(qhT *qh) {
-
-  if (!qh->POINTSmalloc) {
-    qh->first_point= qh_copypoints(qh, qh->first_point, qh->num_points, qh->hull_dim);
-    qh->POINTSmalloc= True;
-  }
-  qh_scalepoints(qh, qh->first_point, qh->num_points, qh->hull_dim,
-       qh->lower_bound, qh->upper_bound);
-}  /* scaleinput */
-
-/*---------------------------------
-
-  qh_scalelast(qh, points, numpoints, dim, low, high, newhigh )
-    scale last coordinate to [0,m] for Delaunay triangulations
-    input points given by points, numpoints, dim
-
-  returns:
-    changes scale of last coordinate from [low, high] to [0, newhigh]
-    overwrites last coordinate of each point
-    saves low/high/newhigh in qh.last_low, etc. for qh_setdelaunay()
-
-  notes:
-    when called by qh_setdelaunay, low/high may not match actual data
-
-  design:
-    compute scale and shift factors
-    apply to last coordinate of each point
-*/
-void qh_scalelast(qhT *qh, coordT *points, int numpoints, int dim, coordT low,
-                   coordT high, coordT newhigh) {
-  realT scale, shift;
-  coordT *coord;
-  int i;
-  boolT nearzero= False;
-
-  trace4((qh, qh->ferr, 4013, "qh_scalelast: scale last coordinate from [%2.2g, %2.2g] to [0,%2.2g]\n",
-    low, high, newhigh));
-  qh->last_low= low;
-  qh->last_high= high;
-  qh->last_newhigh= newhigh;
-  scale= qh_divzero(newhigh, high - low,
-                  qh->MINdenom_1, &nearzero);
-  if (nearzero) {
-    if (qh->DELAUNAY)
-      qh_fprintf(qh, qh->ferr, 6019, "qhull input error: can not scale last coordinate.  Input is cocircular\n   or cospherical.   Use option 'Qz' to add a point at infinity.\n");
-    else
-      qh_fprintf(qh, qh->ferr, 6020, "qhull input error: can not scale last coordinate.  New bounds [0, %2.2g] are too wide for\nexisting bounds [%2.2g, %2.2g] (width %2.2g)\n",
-                newhigh, low, high, high-low);
-    qh_errexit(qh, qh_ERRinput, NULL, NULL);
-  }
-  shift= - low * newhigh / (high-low);
-  coord= points + dim - 1;
-  for (i=numpoints; i--; coord += dim)
-    *coord= *coord * scale + shift;
-} /* scalelast */
-
-/*---------------------------------
-
-  qh_scalepoints(qh, points, numpoints, dim, newlows, newhighs )
-    scale points to new lowbound and highbound
-    retains old bound when newlow= -REALmax or newhigh= +REALmax
-
-  returns:
-    scaled points
-    overwrites old points
-
-  design:
-    for each coordinate
-      compute current low and high bound
-      compute scale and shift factors
-      scale all points
-      enforce new low and high bound for all points
-*/
-void qh_scalepoints(qhT *qh, pointT *points, int numpoints, int dim,
-        realT *newlows, realT *newhighs) {
-  int i,k;
-  realT shift, scale, *coord, low, high, newlow, newhigh, mincoord, maxcoord;
-  boolT nearzero= False;
-
-  for (k=0; k < dim; k++) {
-    newhigh= newhighs[k];
-    newlow= newlows[k];
-    if (newhigh > REALmax/2 && newlow < -REALmax/2)
-      continue;
-    low= REALmax;
-    high= -REALmax;
-    for (i=numpoints, coord=points+k; i--; coord += dim) {
-      minimize_(low, *coord);
-      maximize_(high, *coord);
-    }
-    if (newhigh > REALmax/2)
-      newhigh= high;
-    if (newlow < -REALmax/2)
-      newlow= low;
-    if (qh->DELAUNAY && k == dim-1 && newhigh < newlow) {
-      qh_fprintf(qh, qh->ferr, 6021, "qhull input error: 'Qb%d' or 'QB%d' inverts paraboloid since high bound %.2g < low bound %.2g\n",
-               k, k, newhigh, newlow);
-      qh_errexit(qh, qh_ERRinput, NULL, NULL);
-    }
-    scale= qh_divzero(newhigh - newlow, high - low,
-                  qh->MINdenom_1, &nearzero);
-    if (nearzero) {
-      qh_fprintf(qh, qh->ferr, 6022, "qhull input error: %d'th dimension's new bounds [%2.2g, %2.2g] too wide for\nexisting bounds [%2.2g, %2.2g]\n",
-              k, newlow, newhigh, low, high);
-      qh_errexit(qh, qh_ERRinput, NULL, NULL);
-    }
-    shift= (newlow * high - low * newhigh)/(high-low);
-    coord= points+k;
-    for (i=numpoints; i--; coord += dim)
-      *coord= *coord * scale + shift;
-    coord= points+k;
-    if (newlow < newhigh) {
-      mincoord= newlow;
-      maxcoord= newhigh;
-    }else {
-      mincoord= newhigh;
-      maxcoord= newlow;
-    }
-    for (i=numpoints; i--; coord += dim) {
-      minimize_(*coord, maxcoord);  /* because of roundoff error */
-      maximize_(*coord, mincoord);
-    }
-    trace0((qh, qh->ferr, 10, "qh_scalepoints: scaled %d'th coordinate [%2.2g, %2.2g] to [%.2g, %.2g] for %d points by %2.2g and shifted %2.2g\n",
-      k, low, high, newlow, newhigh, numpoints, scale, shift));
-  }
-} /* scalepoints */
-
-
-/*---------------------------------
-
-  qh_setdelaunay(qh, dim, count, points )
-    project count points to dim-d paraboloid for Delaunay triangulation
-
-    dim is one more than the dimension of the input set
-    assumes dim is at least 3 (i.e., at least a 2-d Delaunay triangulation)
-
-    points is a dim*count realT array.  The first dim-1 coordinates
-    are the coordinates of the first input point.  array[dim] is
-    the first coordinate of the second input point.  array[2*dim] is
-    the first coordinate of the third input point.
-
-    if qh.last_low defined (i.e., 'Qbb' called qh_scalelast)
-      calls qh_scalelast to scale the last coordinate the same as the other points
-
-  returns:
-    for each point
-      sets point[dim-1] to sum of squares of coordinates
-    scale points to 'Qbb' if needed
-
-  notes:
-    to project one point, use
-      qh_setdelaunay(qh, qh->hull_dim, 1, point)
-
-    Do not use options 'Qbk', 'QBk', or 'QbB' since they scale
-    the coordinates after the original projection.
-
-*/
-void qh_setdelaunay(qhT *qh, int dim, int count, pointT *points) {
-  int i, k;
-  coordT *coordp, coord;
-  realT paraboloid;
-
-  trace0((qh, qh->ferr, 11, "qh_setdelaunay: project %d points to paraboloid for Delaunay triangulation\n", count));
-  coordp= points;
-  for (i=0; i < count; i++) {
-    coord= *coordp++;
-    paraboloid= coord*coord;
-    for (k=dim-2; k--; ) {
-      coord= *coordp++;
-      paraboloid += coord*coord;
-    }
-    *coordp++ = paraboloid;
-  }
-  if (qh->last_low < REALmax/2)
-    qh_scalelast(qh, points, count, dim, qh->last_low, qh->last_high, qh->last_newhigh);
-} /* setdelaunay */
-
-
-/*---------------------------------
-
-  qh_sethalfspace(qh, dim, coords, nextp, normal, offset, feasible )
-    set point to dual of halfspace relative to feasible point
-    halfspace is normal coefficients and offset.
-
-  returns:
-    false and prints error if feasible point is outside of hull
-    overwrites coordinates for point at dim coords
-    nextp= next point (coords)
-    does not call qh_errexit
-
-  design:
-    compute distance from feasible point to halfspace
-    divide each normal coefficient by -dist
-*/
-boolT qh_sethalfspace(qhT *qh, int dim, coordT *coords, coordT **nextp,
-         coordT *normal, coordT *offset, coordT *feasible) {
-  coordT *normp= normal, *feasiblep= feasible, *coordp= coords;
-  realT dist;
-  realT r; /*bug fix*/
-  int k;
-  boolT zerodiv;
-
-  dist= *offset;
-  for (k=dim; k--; )
-    dist += *(normp++) * *(feasiblep++);
-  if (dist > 0)
-    goto LABELerroroutside;
-  normp= normal;
-  if (dist < -qh->MINdenom) {
-    for (k=dim; k--; )
-      *(coordp++)= *(normp++) / -dist;
-  }else {
-    for (k=dim; k--; ) {
-      *(coordp++)= qh_divzero(*(normp++), -dist, qh->MINdenom_1, &zerodiv);
-      if (zerodiv)
-        goto LABELerroroutside;
-    }
-  }
-  *nextp= coordp;
-  if (qh->IStracing >= 4) {
-    qh_fprintf(qh, qh->ferr, 8021, "qh_sethalfspace: halfspace at offset %6.2g to point: ", *offset);
-    for (k=dim, coordp=coords; k--; ) {
-      r= *coordp++;
-      qh_fprintf(qh, qh->ferr, 8022, " %6.2g", r);
-    }
-    qh_fprintf(qh, qh->ferr, 8023, "\n");
-  }
-  return True;
-LABELerroroutside:
-  feasiblep= feasible;
-  normp= normal;
-  qh_fprintf(qh, qh->ferr, 6023, "qhull input error: feasible point is not clearly inside halfspace\nfeasible point: ");
-  for (k=dim; k--; )
-    qh_fprintf(qh, qh->ferr, 8024, qh_REAL_1, r=*(feasiblep++));
-  qh_fprintf(qh, qh->ferr, 8025, "\n     halfspace: ");
-  for (k=dim; k--; )
-    qh_fprintf(qh, qh->ferr, 8026, qh_REAL_1, r=*(normp++));
-  qh_fprintf(qh, qh->ferr, 8027, "\n     at offset: ");
-  qh_fprintf(qh, qh->ferr, 8028, qh_REAL_1, *offset);
-  qh_fprintf(qh, qh->ferr, 8029, " and distance: ");
-  qh_fprintf(qh, qh->ferr, 8030, qh_REAL_1, dist);
-  qh_fprintf(qh, qh->ferr, 8031, "\n");
-  return False;
-} /* sethalfspace */
-
-/*---------------------------------
-
-  qh_sethalfspace_all(qh, dim, count, halfspaces, feasible )
-    generate dual for halfspace intersection with feasible point
-    array of count halfspaces
-      each halfspace is normal coefficients followed by offset
-      the origin is inside the halfspace if the offset is negative
-    feasible is a point inside all halfspaces (http://www.qhull.org/html/qhalf.htm#notes)
-
-  returns:
-    malloc'd array of count X dim-1 points
-
-  notes:
-    call before qh_init_B or qh_initqhull_globals
-    free memory when done
-    unused/untested code: please email bradb@shore.net if this works ok for you
-    if using option 'Fp', qh->feasible_point must be set (e.g., to 'feasible')
-    qh->feasible_point is a malloc'd array that is freed by qh_freebuffers.
-
-  design:
-    see qh_sethalfspace
-*/
-coordT *qh_sethalfspace_all(qhT *qh, int dim, int count, coordT *halfspaces, pointT *feasible) {
-  int i, newdim;
-  pointT *newpoints;
-  coordT *coordp, *normalp, *offsetp;
-
-  trace0((qh, qh->ferr, 12, "qh_sethalfspace_all: compute dual for halfspace intersection\n"));
-  newdim= dim - 1;
-  if (!(newpoints=(coordT*)qh_malloc(count*newdim*sizeof(coordT)))){
-    qh_fprintf(qh, qh->ferr, 6024, "qhull error: insufficient memory to compute dual of %d halfspaces\n",
-          count);
-    qh_errexit(qh, qh_ERRmem, NULL, NULL);
-  }
-  coordp= newpoints;
-  normalp= halfspaces;
-  for (i=0; i < count; i++) {
-    offsetp= normalp + newdim;
-    if (!qh_sethalfspace(qh, newdim, coordp, &coordp, normalp, offsetp, feasible)) {
-      qh_free(newpoints);  /* feasible is not inside halfspace as reported by qh_sethalfspace */
-      qh_fprintf(qh, qh->ferr, 8032, "The halfspace was at index %d\n", i);
-      qh_errexit(qh, qh_ERRinput, NULL, NULL);
-    }
-    normalp= offsetp + 1;
-  }
-  return newpoints;
-} /* sethalfspace_all */
-
-
-/*---------------------------------
-
-  qh_sharpnewfacets(qh)
-
-  returns:
-    true if could be an acute angle (facets in different quadrants)
-
-  notes:
-    for qh_findbest
-
-  design:
-    for all facets on qh.newfacet_list
-      if two facets are in different quadrants
-        set issharp
-*/
-boolT qh_sharpnewfacets(qhT *qh) {
-  facetT *facet;
-  boolT issharp = False;
-  int *quadrant, k;
-
-  quadrant= (int*)qh_memalloc(qh, qh->hull_dim * sizeof(int));
-  FORALLfacet_(qh->newfacet_list) {
-    if (facet == qh->newfacet_list) {
-      for (k=qh->hull_dim; k--; )
-        quadrant[ k]= (facet->normal[ k] > 0);
-    }else {
-      for (k=qh->hull_dim; k--; ) {
-        if (quadrant[ k] != (facet->normal[ k] > 0)) {
-          issharp= True;
-          break;
-        }
-      }
-    }
-    if (issharp)
-      break;
-  }
-  qh_memfree(qh, quadrant, qh->hull_dim * sizeof(int));
-  trace3((qh, qh->ferr, 3001, "qh_sharpnewfacets: %d\n", issharp));
-  return issharp;
-} /* sharpnewfacets */
-
-/*---------------------------------
-
-  qh_voronoi_center(qh, dim, points )
-    return Voronoi center for a set of points
-    dim is the orginal dimension of the points
-    gh.gm_matrix/qh.gm_row are scratch buffers
-
-  returns:
-    center as a temporary point (qh_memalloc)
-    if non-simplicial,
-      returns center for max simplex of points
-
-  notes:
-    only called by qh_facetcenter
-    from Bowyer & Woodwark, A Programmer's Geometry, 1983, p. 65
-
-  design:
-    if non-simplicial
-      determine max simplex for points
-    translate point0 of simplex to origin
-    compute sum of squares of diagonal
-    compute determinate
-    compute Voronoi center (see Bowyer & Woodwark)
-*/
-pointT *qh_voronoi_center(qhT *qh, int dim, setT *points) {
-  pointT *point, **pointp, *point0;
-  pointT *center= (pointT*)qh_memalloc(qh, qh->center_size);
-  setT *simplex;
-  int i, j, k, size= qh_setsize(qh, points);
-  coordT *gmcoord;
-  realT *diffp, sum2, *sum2row, *sum2p, det, factor;
-  boolT nearzero, infinite;
-
-  if (size == dim+1)
-    simplex= points;
-  else if (size < dim+1) {
-    qh_memfree(qh, center, qh->center_size);
-    qh_fprintf(qh, qh->ferr, 6025, "qhull internal error (qh_voronoi_center):\n  need at least %d points to construct a Voronoi center\n",
-             dim+1);
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-    simplex= points;  /* never executed -- avoids warning */
-  }else {
-    simplex= qh_settemp(qh, dim+1);
-    qh_maxsimplex(qh, dim, points, NULL, 0, &simplex);
-  }
-  point0= SETfirstt_(simplex, pointT);
-  gmcoord= qh->gm_matrix;
-  for (k=0; k < dim; k++) {
-    qh->gm_row[k]= gmcoord;
-    FOREACHpoint_(simplex) {
-      if (point != point0)
-        *(gmcoord++)= point[k] - point0[k];
-    }
-  }
-  sum2row= gmcoord;
-  for (i=0; i < dim; i++) {
-    sum2= 0.0;
-    for (k=0; k < dim; k++) {
-      diffp= qh->gm_row[k] + i;
-      sum2 += *diffp * *diffp;
-    }
-    *(gmcoord++)= sum2;
-  }
-  det= qh_determinant(qh, qh->gm_row, dim, &nearzero);
-  factor= qh_divzero(0.5, det, qh->MINdenom, &infinite);
-  if (infinite) {
-    for (k=dim; k--; )
-      center[k]= qh_INFINITE;
-    if (qh->IStracing)
-      qh_printpoints(qh, qh->ferr, "qh_voronoi_center: at infinity for ", simplex);
-  }else {
-    for (i=0; i < dim; i++) {
-      gmcoord= qh->gm_matrix;
-      sum2p= sum2row;
-      for (k=0; k < dim; k++) {
-        qh->gm_row[k]= gmcoord;
-        if (k == i) {
-          for (j=dim; j--; )
-            *(gmcoord++)= *sum2p++;
-        }else {
-          FOREACHpoint_(simplex) {
-            if (point != point0)
-              *(gmcoord++)= point[k] - point0[k];
-          }
-        }
-      }
-      center[i]= qh_determinant(qh, qh->gm_row, dim, &nearzero)*factor + point0[i];
-    }
-#ifndef qh_NOtrace
-    if (qh->IStracing >= 3) {
-      qh_fprintf(qh, qh->ferr, 8033, "qh_voronoi_center: det %2.2g factor %2.2g ", det, factor);
-      qh_printmatrix(qh, qh->ferr, "center:", ¢er, 1, dim);
-      if (qh->IStracing >= 5) {
-        qh_printpoints(qh, qh->ferr, "points", simplex);
-        FOREACHpoint_(simplex)
-          qh_fprintf(qh, qh->ferr, 8034, "p%d dist %.2g, ", qh_pointid(qh, point),
-                   qh_pointdist(point, center, dim));
-        qh_fprintf(qh, qh->ferr, 8035, "\n");
-      }
-    }
-#endif
-  }
-  if (simplex != points)
-    qh_settempfree(qh, &simplex);
-  return center;
-} /* voronoi_center */
-
diff --git a/C/geom_r.c b/C/geom_r.c
deleted file mode 100644
--- a/C/geom_r.c
+++ /dev/null
@@ -1,1234 +0,0 @@
-/*
  ---------------------------------
-
-   geom_r.c
-   geometric routines of qhull
-
-   see qh-geom_r.htm and geom_r.h
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull_r/geom_r.c#2 $$Change: 1995 $
-   $DateTime: 2015/10/13 21:59:42 $$Author: bbarber $
-
-   infrequent code goes into geom2_r.c
-*/
-
-#include "qhull_ra.h"
-
-/*---------------------------------
-
-  qh_distplane(qh, point, facet, dist )
-    return distance from point to facet
-
-  returns:
-    dist
-    if qh.RANDOMdist, joggles result
-
-  notes:
-    dist > 0 if point is above facet (i.e., outside)
-    does not error (for qh_sortfacets, qh_outerinner)
-
-  see:
-    qh_distnorm in geom2_r.c
-    qh_distplane [geom_r.c], QhullFacet::distance, and QhullHyperplane::distance are copies
-*/
-void qh_distplane(qhT *qh, pointT *point, facetT *facet, realT *dist) {
-  coordT *normal= facet->normal, *coordp, randr;
-  int k;
-
-  switch (qh->hull_dim){
-  case 2:
-    *dist= facet->offset + point[0] * normal[0] + point[1] * normal[1];
-    break;
-  case 3:
-    *dist= facet->offset + point[0] * normal[0] + point[1] * normal[1] + point[2] * normal[2];
-    break;
-  case 4:
-    *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3];
-    break;
-  case 5:
-    *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4];
-    break;
-  case 6:
-    *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5];
-    break;
-  case 7:
-    *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5]+point[6]*normal[6];
-    break;
-  case 8:
-    *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5]+point[6]*normal[6]+point[7]*normal[7];
-    break;
-  default:
-    *dist= facet->offset;
-    coordp= point;
-    for (k=qh->hull_dim; k--; )
-      *dist += *coordp++ * *normal++;
-    break;
-  }
-  zinc_(Zdistplane);
-  if (!qh->RANDOMdist && qh->IStracing < 4)
-    return;
-  if (qh->RANDOMdist) {
-    randr= qh_RANDOMint;
-    *dist += (2.0 * randr / qh_RANDOMmax - 1.0) *
-      qh->RANDOMfactor * qh->MAXabs_coord;
-  }
-  if (qh->IStracing >= 4) {
-    qh_fprintf(qh, qh->ferr, 8001, "qh_distplane: ");
-    qh_fprintf(qh, qh->ferr, 8002, qh_REAL_1, *dist);
-    qh_fprintf(qh, qh->ferr, 8003, "from p%d to f%d\n", qh_pointid(qh, point), facet->id);
-  }
-  return;
-} /* distplane */
-
-
-/*---------------------------------
-
-  qh_findbest(qh, point, startfacet, bestoutside, qh_ISnewfacets, qh_NOupper, dist, isoutside, numpart )
-    find facet that is furthest below a point
-    for upperDelaunay facets
-      returns facet only if !qh_NOupper and clearly above
-
-  input:
-    starts search at 'startfacet' (can not be flipped)
-    if !bestoutside(qh_ALL), stops at qh.MINoutside
-
-  returns:
-    best facet (reports error if NULL)
-    early out if isoutside defined and bestdist > qh.MINoutside
-    dist is distance to facet
-    isoutside is true if point is outside of facet
-    numpart counts the number of distance tests
-
-  see also:
-    qh_findbestnew()
-
-  notes:
-    If merging (testhorizon), searches horizon facets of coplanar best facets because
-    after qh_distplane, this and qh_partitionpoint are the most expensive in 3-d
-      avoid calls to distplane, function calls, and real number operations.
-    caller traces result
-    Optimized for outside points.   Tried recording a search set for qh_findhorizon.
-    Made code more complicated.
-
-  when called by qh_partitionvisible():
-    indicated by qh_ISnewfacets
-    qh.newfacet_list is list of simplicial, new facets
-    qh_findbestnew set if qh_sharpnewfacets returns True (to use qh_findbestnew)
-    qh.bestfacet_notsharp set if qh_sharpnewfacets returns False
-
-  when called by qh_findfacet(), qh_partitionpoint(), qh_partitioncoplanar(),
-                 qh_check_bestdist(), qh_addpoint()
-    indicated by !qh_ISnewfacets
-    returns best facet in neighborhood of given facet
-      this is best facet overall if dist > -   qh.MAXcoplanar
-        or hull has at least a "spherical" curvature
-
-  design:
-    initialize and test for early exit
-    repeat while there are better facets
-      for each neighbor of facet
-        exit if outside facet found
-        test for better facet
-    if point is inside and partitioning
-      test for new facets with a "sharp" intersection
-      if so, future calls go to qh_findbestnew()
-    test horizon facets
-*/
-facetT *qh_findbest(qhT *qh, pointT *point, facetT *startfacet,
-                     boolT bestoutside, boolT isnewfacets, boolT noupper,
-                     realT *dist, boolT *isoutside, int *numpart) {
-  realT bestdist= -REALmax/2 /* avoid underflow */;
-  facetT *facet, *neighbor, **neighborp;
-  facetT *bestfacet= NULL, *lastfacet= NULL;
-  int oldtrace= qh->IStracing;
-  unsigned int visitid= ++qh->visit_id;
-  int numpartnew=0;
-  boolT testhorizon = True; /* needed if precise, e.g., rbox c D6 | qhull Q0 Tv */
-
-  zinc_(Zfindbest);
-  if (qh->IStracing >= 3 || (qh->TRACElevel && qh->TRACEpoint >= 0 && qh->TRACEpoint == qh_pointid(qh, point))) {
-    if (qh->TRACElevel > qh->IStracing)
-      qh->IStracing= qh->TRACElevel;
-    qh_fprintf(qh, qh->ferr, 8004, "qh_findbest: point p%d starting at f%d isnewfacets? %d, unless %d exit if > %2.2g\n",
-             qh_pointid(qh, point), startfacet->id, isnewfacets, bestoutside, qh->MINoutside);
-    qh_fprintf(qh, qh->ferr, 8005, "  testhorizon? %d noupper? %d", testhorizon, noupper);
-    qh_fprintf(qh, qh->ferr, 8006, "  Last point added was p%d.", qh->furthest_id);
-    qh_fprintf(qh, qh->ferr, 8007, "  Last merge was #%d.  max_outside %2.2g\n", zzval_(Ztotmerge), qh->max_outside);
-  }
-  if (isoutside)
-    *isoutside= True;
-  if (!startfacet->flipped) {  /* test startfacet */
-    *numpart= 1;
-    qh_distplane(qh, point, startfacet, dist);  /* this code is duplicated below */
-    if (!bestoutside && *dist >= qh->MINoutside
-    && (!startfacet->upperdelaunay || !noupper)) {
-      bestfacet= startfacet;
-      goto LABELreturn_best;
-    }
-    bestdist= *dist;
-    if (!startfacet->upperdelaunay) {
-      bestfacet= startfacet;
-    }
-  }else
-    *numpart= 0;
-  startfacet->visitid= visitid;
-  facet= startfacet;
-  while (facet) {
-    trace4((qh, qh->ferr, 4001, "qh_findbest: neighbors of f%d, bestdist %2.2g f%d\n",
-                facet->id, bestdist, getid_(bestfacet)));
-    lastfacet= facet;
-    FOREACHneighbor_(facet) {
-      if (!neighbor->newfacet && isnewfacets)
-        continue;
-      if (neighbor->visitid == visitid)
-        continue;
-      neighbor->visitid= visitid;
-      if (!neighbor->flipped) {  /* code duplicated above */
-        (*numpart)++;
-        qh_distplane(qh, point, neighbor, dist);
-        if (*dist > bestdist) {
-          if (!bestoutside && *dist >= qh->MINoutside
-          && (!neighbor->upperdelaunay || !noupper)) {
-            bestfacet= neighbor;
-            goto LABELreturn_best;
-          }
-          if (!neighbor->upperdelaunay) {
-            bestfacet= neighbor;
-            bestdist= *dist;
-            break; /* switch to neighbor */
-          }else if (!bestfacet) {
-            bestdist= *dist;
-            break; /* switch to neighbor */
-          }
-        } /* end of *dist>bestdist */
-      } /* end of !flipped */
-    } /* end of FOREACHneighbor */
-    facet= neighbor;  /* non-NULL only if *dist>bestdist */
-  } /* end of while facet (directed search) */
-  if (isnewfacets) {
-    if (!bestfacet) {
-      bestdist= -REALmax/2;
-      bestfacet= qh_findbestnew(qh, point, startfacet->next, &bestdist, bestoutside, isoutside, &numpartnew);
-      testhorizon= False; /* qh_findbestnew calls qh_findbesthorizon */
-    }else if (!qh->findbest_notsharp && bestdist < - qh->DISTround) {
-      if (qh_sharpnewfacets(qh)) {
-        /* seldom used, qh_findbestnew will retest all facets */
-        zinc_(Zfindnewsharp);
-        bestfacet= qh_findbestnew(qh, point, bestfacet, &bestdist, bestoutside, isoutside, &numpartnew);
-        testhorizon= False; /* qh_findbestnew calls qh_findbesthorizon */
-        qh->findbestnew= True;
-      }else
-        qh->findbest_notsharp= True;
-    }
-  }
-  if (!bestfacet)
-    bestfacet= qh_findbestlower(qh, lastfacet, point, &bestdist, numpart);
-  if (testhorizon)
-    bestfacet= qh_findbesthorizon(qh, !qh_IScheckmax, point, bestfacet, noupper, &bestdist, &numpartnew);
-  *dist= bestdist;
-  if (isoutside && bestdist < qh->MINoutside)
-    *isoutside= False;
-LABELreturn_best:
-  zadd_(Zfindbesttot, *numpart);
-  zmax_(Zfindbestmax, *numpart);
-  (*numpart) += numpartnew;
-  qh->IStracing= oldtrace;
-  return bestfacet;
-}  /* findbest */
-
-
-/*---------------------------------
-
-  qh_findbesthorizon(qh, qh_IScheckmax, point, startfacet, qh_NOupper, &bestdist, &numpart )
-    search coplanar and better horizon facets from startfacet/bestdist
-    ischeckmax turns off statistics and minsearch update
-    all arguments must be initialized
-  returns(ischeckmax):
-    best facet
-  returns(!ischeckmax):
-    best facet that is not upperdelaunay
-    allows upperdelaunay that is clearly outside
-  returns:
-    bestdist is distance to bestfacet
-    numpart -- updates number of distance tests
-
-  notes:
-    no early out -- use qh_findbest() or qh_findbestnew()
-    Searches coplanar or better horizon facets
-
-  when called by qh_check_maxout() (qh_IScheckmax)
-    startfacet must be closest to the point
-      Otherwise, if point is beyond and below startfacet, startfacet may be a local minimum
-      even though other facets are below the point.
-    updates facet->maxoutside for good, visited facets
-    may return NULL
-
-    searchdist is qh.max_outside + 2 * DISTround
-      + max( MINvisible('Vn'), MAXcoplanar('Un'));
-    This setting is a guess.  It must be at least max_outside + 2*DISTround
-    because a facet may have a geometric neighbor across a vertex
-
-  design:
-    for each horizon facet of coplanar best facets
-      continue if clearly inside
-      unless upperdelaunay or clearly outside
-         update best facet
-*/
-facetT *qh_findbesthorizon(qhT *qh, boolT ischeckmax, pointT* point, facetT *startfacet, boolT noupper, realT *bestdist, int *numpart) {
-  facetT *bestfacet= startfacet;
-  realT dist;
-  facetT *neighbor, **neighborp, *facet;
-  facetT *nextfacet= NULL; /* optimize last facet of coplanarfacetset */
-  int numpartinit= *numpart, coplanarfacetset_size;
-  unsigned int visitid= ++qh->visit_id;
-  boolT newbest= False; /* for tracing */
-  realT minsearch, searchdist;  /* skip facets that are too far from point */
-
-  if (!ischeckmax) {
-    zinc_(Zfindhorizon);
-  }else {
-#if qh_MAXoutside
-    if ((!qh->ONLYgood || startfacet->good) && *bestdist > startfacet->maxoutside)
-      startfacet->maxoutside= *bestdist;
-#endif
-  }
-  searchdist= qh_SEARCHdist; /* multiple of qh.max_outside and precision constants */
-  minsearch= *bestdist - searchdist;
-  if (ischeckmax) {
-    /* Always check coplanar facets.  Needed for RBOX 1000 s Z1 G1e-13 t996564279 | QHULL Tv */
-    minimize_(minsearch, -searchdist);
-  }
-  coplanarfacetset_size= 0;
-  facet= startfacet;
-  while (True) {
-    trace4((qh, qh->ferr, 4002, "qh_findbesthorizon: neighbors of f%d bestdist %2.2g f%d ischeckmax? %d noupper? %d minsearch %2.2g searchdist %2.2g\n",
-                facet->id, *bestdist, getid_(bestfacet), ischeckmax, noupper,
-                minsearch, searchdist));
-    FOREACHneighbor_(facet) {
-      if (neighbor->visitid == visitid)
-        continue;
-      neighbor->visitid= visitid;
-      if (!neighbor->flipped) {
-        qh_distplane(qh, point, neighbor, &dist);
-        (*numpart)++;
-        if (dist > *bestdist) {
-          if (!neighbor->upperdelaunay || ischeckmax || (!noupper && dist >= qh->MINoutside)) {
-            bestfacet= neighbor;
-            *bestdist= dist;
-            newbest= True;
-            if (!ischeckmax) {
-              minsearch= dist - searchdist;
-              if (dist > *bestdist + searchdist) {
-                zinc_(Zfindjump);  /* everything in qh.coplanarfacetset at least searchdist below */
-                coplanarfacetset_size= 0;
-              }
-            }
-          }
-        }else if (dist < minsearch)
-          continue;  /* if ischeckmax, dist can't be positive */
-#if qh_MAXoutside
-        if (ischeckmax && dist > neighbor->maxoutside)
-          neighbor->maxoutside= dist;
-#endif
-      } /* end of !flipped */
-      if (nextfacet) {
-        if (!coplanarfacetset_size++) {
-          SETfirst_(qh->coplanarfacetset)= nextfacet;
-          SETtruncate_(qh->coplanarfacetset, 1);
-        }else
-          qh_setappend(qh, &qh->coplanarfacetset, nextfacet); /* Was needed for RBOX 1000 s W1e-13 P0 t996547055 | QHULL d Qbb Qc Tv
-                                                 and RBOX 1000 s Z1 G1e-13 t996564279 | qhull Tv  */
-      }
-      nextfacet= neighbor;
-    } /* end of EACHneighbor */
-    facet= nextfacet;
-    if (facet)
-      nextfacet= NULL;
-    else if (!coplanarfacetset_size)
-      break;
-    else if (!--coplanarfacetset_size) {
-      facet= SETfirstt_(qh->coplanarfacetset, facetT);
-      SETtruncate_(qh->coplanarfacetset, 0);
-    }else
-      facet= (facetT*)qh_setdellast(qh->coplanarfacetset);
-  } /* while True, for each facet in qh.coplanarfacetset */
-  if (!ischeckmax) {
-    zadd_(Zfindhorizontot, *numpart - numpartinit);
-    zmax_(Zfindhorizonmax, *numpart - numpartinit);
-    if (newbest)
-      zinc_(Zparthorizon);
-  }
-  trace4((qh, qh->ferr, 4003, "qh_findbesthorizon: newbest? %d bestfacet f%d bestdist %2.2g\n", newbest, getid_(bestfacet), *bestdist));
-  return bestfacet;
-}  /* findbesthorizon */
-
-/*---------------------------------
-
-  qh_findbestnew(qh, point, startfacet, dist, isoutside, numpart )
-    find best newfacet for point
-    searches all of qh.newfacet_list starting at startfacet
-    searches horizon facets of coplanar best newfacets
-    searches all facets if startfacet == qh.facet_list
-  returns:
-    best new or horizon facet that is not upperdelaunay
-    early out if isoutside and not 'Qf'
-    dist is distance to facet
-    isoutside is true if point is outside of facet
-    numpart is number of distance tests
-
-  notes:
-    Always used for merged new facets (see qh_USEfindbestnew)
-    Avoids upperdelaunay facet unless (isoutside and outside)
-
-    Uses qh.visit_id, qh.coplanarfacetset.
-    If share visit_id with qh_findbest, coplanarfacetset is incorrect.
-
-    If merging (testhorizon), searches horizon facets of coplanar best facets because
-    a point maybe coplanar to the bestfacet, below its horizon facet,
-    and above a horizon facet of a coplanar newfacet.  For example,
-      rbox 1000 s Z1 G1e-13 | qhull
-      rbox 1000 s W1e-13 P0 t992110337 | QHULL d Qbb Qc
-
-    qh_findbestnew() used if
-       qh_sharpnewfacets -- newfacets contains a sharp angle
-       if many merges, qh_premerge found a merge, or 'Qf' (qh.findbestnew)
-
-  see also:
-    qh_partitionall() and qh_findbest()
-
-  design:
-    for each new facet starting from startfacet
-      test distance from point to facet
-      return facet if clearly outside
-      unless upperdelaunay and a lowerdelaunay exists
-         update best facet
-    test horizon facets
-*/
-facetT *qh_findbestnew(qhT *qh, pointT *point, facetT *startfacet,
-           realT *dist, boolT bestoutside, boolT *isoutside, int *numpart) {
-  realT bestdist= -REALmax/2;
-  facetT *bestfacet= NULL, *facet;
-  int oldtrace= qh->IStracing, i;
-  unsigned int visitid= ++qh->visit_id;
-  realT distoutside= 0.0;
-  boolT isdistoutside; /* True if distoutside is defined */
-  boolT testhorizon = True; /* needed if precise, e.g., rbox c D6 | qhull Q0 Tv */
-
-  if (!startfacet) {
-    if (qh->MERGING)
-      qh_fprintf(qh, qh->ferr, 6001, "qhull precision error (qh_findbestnew): merging has formed and deleted a cone of new facets.  Can not continue.\n");
-    else
-      qh_fprintf(qh, qh->ferr, 6002, "qhull internal error (qh_findbestnew): no new facets for point p%d\n",
-              qh->furthest_id);
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }
-  zinc_(Zfindnew);
-  if (qh->BESToutside || bestoutside)
-    isdistoutside= False;
-  else {
-    isdistoutside= True;
-    distoutside= qh_DISToutside; /* multiple of qh.MINoutside & qh.max_outside, see user.h */
-  }
-  if (isoutside)
-    *isoutside= True;
-  *numpart= 0;
-  if (qh->IStracing >= 3 || (qh->TRACElevel && qh->TRACEpoint >= 0 && qh->TRACEpoint == qh_pointid(qh, point))) {
-    if (qh->TRACElevel > qh->IStracing)
-      qh->IStracing= qh->TRACElevel;
-    qh_fprintf(qh, qh->ferr, 8008, "qh_findbestnew: point p%d facet f%d. Stop? %d if dist > %2.2g\n",
-             qh_pointid(qh, point), startfacet->id, isdistoutside, distoutside);
-    qh_fprintf(qh, qh->ferr, 8009, "  Last point added p%d visitid %d.",  qh->furthest_id, visitid);
-    qh_fprintf(qh, qh->ferr, 8010, "  Last merge was #%d.\n", zzval_(Ztotmerge));
-  }
-  /* visit all new facets starting with startfacet, maybe qh->facet_list */
-  for (i=0, facet=startfacet; i < 2; i++, facet= qh->newfacet_list) {
-    FORALLfacet_(facet) {
-      if (facet == startfacet && i)
-        break;
-      facet->visitid= visitid;
-      if (!facet->flipped) {
-        qh_distplane(qh, point, facet, dist);
-        (*numpart)++;
-        if (*dist > bestdist) {
-          if (!facet->upperdelaunay || *dist >= qh->MINoutside) {
-            bestfacet= facet;
-            if (isdistoutside && *dist >= distoutside)
-              goto LABELreturn_bestnew;
-            bestdist= *dist;
-          }
-        }
-      } /* end of !flipped */
-    } /* FORALLfacet from startfacet or qh->newfacet_list */
-  }
-  if (testhorizon || !bestfacet) /* testhorizon is always True.  Keep the same code as qh_findbest */
-    bestfacet= qh_findbesthorizon(qh, !qh_IScheckmax, point, bestfacet ? bestfacet : startfacet,
-                                        !qh_NOupper, &bestdist, numpart);
-  *dist= bestdist;
-  if (isoutside && *dist < qh->MINoutside)
-    *isoutside= False;
-LABELreturn_bestnew:
-  zadd_(Zfindnewtot, *numpart);
-  zmax_(Zfindnewmax, *numpart);
-  trace4((qh, qh->ferr, 4004, "qh_findbestnew: bestfacet f%d bestdist %2.2g\n", getid_(bestfacet), *dist));
-  qh->IStracing= oldtrace;
-  return bestfacet;
-}  /* findbestnew */
-
-/* ============ hyperplane functions -- keep code together [?] ============ */
-
-/*---------------------------------
-
-  qh_backnormal(qh, rows, numrow, numcol, sign, normal, nearzero )
-    given an upper-triangular rows array and a sign,
-    solve for normal equation x using back substitution over rows U
-
-  returns:
-     normal= x
-
-     if will not be able to divzero() when normalized(qh.MINdenom_2 and qh.MINdenom_1_2),
-       if fails on last row
-         this means that the hyperplane intersects [0,..,1]
-         sets last coordinate of normal to sign
-       otherwise
-         sets tail of normal to [...,sign,0,...], i.e., solves for b= [0...0]
-         sets nearzero
-
-  notes:
-     assumes numrow == numcol-1
-
-     see Golub & van Loan, 1983, Eq. 4.4-9 for "Gaussian elimination with complete pivoting"
-
-     solves Ux=b where Ax=b and PA=LU
-     b= [0,...,0,sign or 0]  (sign is either -1 or +1)
-     last row of A= [0,...,0,1]
-
-     1) Ly=Pb == y=b since P only permutes the 0's of   b
-
-  design:
-    for each row from end
-      perform back substitution
-      if near zero
-        use qh_divzero for division
-        if zero divide and not last row
-          set tail of normal to 0
-*/
-void qh_backnormal(qhT *qh, realT **rows, int numrow, int numcol, boolT sign,
-        coordT *normal, boolT *nearzero) {
-  int i, j;
-  coordT *normalp, *normal_tail, *ai, *ak;
-  realT diagonal;
-  boolT waszero;
-  int zerocol= -1;
-
-  normalp= normal + numcol - 1;
-  *normalp--= (sign ? -1.0 : 1.0);
-  for (i=numrow; i--; ) {
-    *normalp= 0.0;
-    ai= rows[i] + i + 1;
-    ak= normalp+1;
-    for (j=i+1; j < numcol; j++)
-      *normalp -= *ai++ * *ak++;
-    diagonal= (rows[i])[i];
-    if (fabs_(diagonal) > qh->MINdenom_2)
-      *(normalp--) /= diagonal;
-    else {
-      waszero= False;
-      *normalp= qh_divzero(*normalp, diagonal, qh->MINdenom_1_2, &waszero);
-      if (waszero) {
-        zerocol= i;
-        *(normalp--)= (sign ? -1.0 : 1.0);
-        for (normal_tail= normalp+2; normal_tail < normal + numcol; normal_tail++)
-          *normal_tail= 0.0;
-      }else
-        normalp--;
-    }
-  }
-  if (zerocol != -1) {
-    zzinc_(Zback0);
-    *nearzero= True;
-    trace4((qh, qh->ferr, 4005, "qh_backnormal: zero diagonal at column %d.\n", i));
-    qh_precision(qh, "zero diagonal on back substitution");
-  }
-} /* backnormal */
-
-/*---------------------------------
-
-  qh_gausselim(qh, rows, numrow, numcol, sign )
-    Gaussian elimination with partial pivoting
-
-  returns:
-    rows is upper triangular (includes row exchanges)
-    flips sign for each row exchange
-    sets nearzero if pivot[k] < qh.NEARzero[k], else clears it
-
-  notes:
-    if nearzero, the determinant's sign may be incorrect.
-    assumes numrow <= numcol
-
-  design:
-    for each row
-      determine pivot and exchange rows if necessary
-      test for near zero
-      perform gaussian elimination step
-*/
-void qh_gausselim(qhT *qh, realT **rows, int numrow, int numcol, boolT *sign, boolT *nearzero) {
-  realT *ai, *ak, *rowp, *pivotrow;
-  realT n, pivot, pivot_abs= 0.0, temp;
-  int i, j, k, pivoti, flip=0;
-
-  *nearzero= False;
-  for (k=0; k < numrow; k++) {
-    pivot_abs= fabs_((rows[k])[k]);
-    pivoti= k;
-    for (i=k+1; i < numrow; i++) {
-      if ((temp= fabs_((rows[i])[k])) > pivot_abs) {
-        pivot_abs= temp;
-        pivoti= i;
-      }
-    }
-    if (pivoti != k) {
-      rowp= rows[pivoti];
-      rows[pivoti]= rows[k];
-      rows[k]= rowp;
-      *sign ^= 1;
-      flip ^= 1;
-    }
-    if (pivot_abs <= qh->NEARzero[k]) {
-      *nearzero= True;
-      if (pivot_abs == 0.0) {   /* remainder of column == 0 */
-        if (qh->IStracing >= 4) {
-          qh_fprintf(qh, qh->ferr, 8011, "qh_gausselim: 0 pivot at column %d. (%2.2g < %2.2g)\n", k, pivot_abs, qh->DISTround);
-          qh_printmatrix(qh, qh->ferr, "Matrix:", rows, numrow, numcol);
-        }
-        zzinc_(Zgauss0);
-        qh_precision(qh, "zero pivot for Gaussian elimination");
-        goto LABELnextcol;
-      }
-    }
-    pivotrow= rows[k] + k;
-    pivot= *pivotrow++;  /* signed value of pivot, and remainder of row */
-    for (i=k+1; i < numrow; i++) {
-      ai= rows[i] + k;
-      ak= pivotrow;
-      n= (*ai++)/pivot;   /* divzero() not needed since |pivot| >= |*ai| */
-      for (j= numcol - (k+1); j--; )
-        *ai++ -= n * *ak++;
-    }
-  LABELnextcol:
-    ;
-  }
-  wmin_(Wmindenom, pivot_abs);  /* last pivot element */
-  if (qh->IStracing >= 5)
-    qh_printmatrix(qh, qh->ferr, "qh_gausselem: result", rows, numrow, numcol);
-} /* gausselim */
-
-
-/*---------------------------------
-
-  qh_getangle(qh, vect1, vect2 )
-    returns the dot product of two vectors
-    if qh.RANDOMdist, joggles result
-
-  notes:
-    the angle may be > 1.0 or < -1.0 because of roundoff errors
-
-*/
-realT qh_getangle(qhT *qh, pointT *vect1, pointT *vect2) {
-  realT angle= 0, randr;
-  int k;
-
-  for (k=qh->hull_dim; k--; )
-    angle += *vect1++ * *vect2++;
-  if (qh->RANDOMdist) {
-    randr= qh_RANDOMint;
-    angle += (2.0 * randr / qh_RANDOMmax - 1.0) *
-      qh->RANDOMfactor;
-  }
-  trace4((qh, qh->ferr, 4006, "qh_getangle: %2.2g\n", angle));
-  return(angle);
-} /* getangle */
-
-
-/*---------------------------------
-
-  qh_getcenter(qh, vertices )
-    returns arithmetic center of a set of vertices as a new point
-
-  notes:
-    allocates point array for center
-*/
-pointT *qh_getcenter(qhT *qh, setT *vertices) {
-  int k;
-  pointT *center, *coord;
-  vertexT *vertex, **vertexp;
-  int count= qh_setsize(qh, vertices);
-
-  if (count < 2) {
-    qh_fprintf(qh, qh->ferr, 6003, "qhull internal error (qh_getcenter): not defined for %d points\n", count);
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }
-  center= (pointT *)qh_memalloc(qh, qh->normal_size);
-  for (k=0; k < qh->hull_dim; k++) {
-    coord= center+k;
-    *coord= 0.0;
-    FOREACHvertex_(vertices)
-      *coord += vertex->point[k];
-    *coord /= count;  /* count>=2 by QH6003 */
-  }
-  return(center);
-} /* getcenter */
-
-
-/*---------------------------------
-
-  qh_getcentrum(qh, facet )
-    returns the centrum for a facet as a new point
-
-  notes:
-    allocates the centrum
-*/
-pointT *qh_getcentrum(qhT *qh, facetT *facet) {
-  realT dist;
-  pointT *centrum, *point;
-
-  point= qh_getcenter(qh, facet->vertices);
-  zzinc_(Zcentrumtests);
-  qh_distplane(qh, point, facet, &dist);
-  centrum= qh_projectpoint(qh, point, facet, dist);
-  qh_memfree(qh, point, qh->normal_size);
-  trace4((qh, qh->ferr, 4007, "qh_getcentrum: for f%d, %d vertices dist= %2.2g\n",
-          facet->id, qh_setsize(qh, facet->vertices), dist));
-  return centrum;
-} /* getcentrum */
-
-
-/*---------------------------------
-
-  qh_getdistance(qh, facet, neighbor, mindist, maxdist )
-    returns the maxdist and mindist distance of any vertex from neighbor
-
-  returns:
-    the max absolute value
-
-  design:
-    for each vertex of facet that is not in neighbor
-      test the distance from vertex to neighbor
-*/
-realT qh_getdistance(qhT *qh, facetT *facet, facetT *neighbor, realT *mindist, realT *maxdist) {
-  vertexT *vertex, **vertexp;
-  realT dist, maxd, mind;
-
-  FOREACHvertex_(facet->vertices)
-    vertex->seen= False;
-  FOREACHvertex_(neighbor->vertices)
-    vertex->seen= True;
-  mind= 0.0;
-  maxd= 0.0;
-  FOREACHvertex_(facet->vertices) {
-    if (!vertex->seen) {
-      zzinc_(Zbestdist);
-      qh_distplane(qh, vertex->point, neighbor, &dist);
-      if (dist < mind)
-        mind= dist;
-      else if (dist > maxd)
-        maxd= dist;
-    }
-  }
-  *mindist= mind;
-  *maxdist= maxd;
-  mind= -mind;
-  if (maxd > mind)
-    return maxd;
-  else
-    return mind;
-} /* getdistance */
-
-
-/*---------------------------------
-
-  qh_normalize(qh, normal, dim, toporient )
-    normalize a vector and report if too small
-    does not use min norm
-
-  see:
-    qh_normalize2
-*/
-void qh_normalize(qhT *qh, coordT *normal, int dim, boolT toporient) {
-  qh_normalize2(qh, normal, dim, toporient, NULL, NULL);
-} /* normalize */
-
-/*---------------------------------
-
-  qh_normalize2(qh, normal, dim, toporient, minnorm, ismin )
-    normalize a vector and report if too small
-    qh.MINdenom/MINdenom1 are the upper limits for divide overflow
-
-  returns:
-    normalized vector
-    flips sign if !toporient
-    if minnorm non-NULL,
-      sets ismin if normal < minnorm
-
-  notes:
-    if zero norm
-       sets all elements to sqrt(1.0/dim)
-    if divide by zero (divzero())
-       sets largest element to   +/-1
-       bumps Znearlysingular
-
-  design:
-    computes norm
-    test for minnorm
-    if not near zero
-      normalizes normal
-    else if zero norm
-      sets normal to standard value
-    else
-      uses qh_divzero to normalize
-      if nearzero
-        sets norm to direction of maximum value
-*/
-void qh_normalize2(qhT *qh, coordT *normal, int dim, boolT toporient,
-            realT *minnorm, boolT *ismin) {
-  int k;
-  realT *colp, *maxp, norm= 0, temp, *norm1, *norm2, *norm3;
-  boolT zerodiv;
-
-  norm1= normal+1;
-  norm2= normal+2;
-  norm3= normal+3;
-  if (dim == 2)
-    norm= sqrt((*normal)*(*normal) + (*norm1)*(*norm1));
-  else if (dim == 3)
-    norm= sqrt((*normal)*(*normal) + (*norm1)*(*norm1) + (*norm2)*(*norm2));
-  else if (dim == 4) {
-    norm= sqrt((*normal)*(*normal) + (*norm1)*(*norm1) + (*norm2)*(*norm2)
-               + (*norm3)*(*norm3));
-  }else if (dim > 4) {
-    norm= (*normal)*(*normal) + (*norm1)*(*norm1) + (*norm2)*(*norm2)
-               + (*norm3)*(*norm3);
-    for (k=dim-4, colp=normal+4; k--; colp++)
-      norm += (*colp) * (*colp);
-    norm= sqrt(norm);
-  }
-  if (minnorm) {
-    if (norm < *minnorm)
-      *ismin= True;
-    else
-      *ismin= False;
-  }
-  wmin_(Wmindenom, norm);
-  if (norm > qh->MINdenom) {
-    if (!toporient)
-      norm= -norm;
-    *normal /= norm;
-    *norm1 /= norm;
-    if (dim == 2)
-      ; /* all done */
-    else if (dim == 3)
-      *norm2 /= norm;
-    else if (dim == 4) {
-      *norm2 /= norm;
-      *norm3 /= norm;
-    }else if (dim >4) {
-      *norm2 /= norm;
-      *norm3 /= norm;
-      for (k=dim-4, colp=normal+4; k--; )
-        *colp++ /= norm;
-    }
-  }else if (norm == 0.0) {
-    temp= sqrt(1.0/dim);
-    for (k=dim, colp=normal; k--; )
-      *colp++ = temp;
-  }else {
-    if (!toporient)
-      norm= -norm;
-    for (k=dim, colp=normal; k--; colp++) { /* k used below */
-      temp= qh_divzero(*colp, norm, qh->MINdenom_1, &zerodiv);
-      if (!zerodiv)
-        *colp= temp;
-      else {
-        maxp= qh_maxabsval(normal, dim);
-        temp= ((*maxp * norm >= 0.0) ? 1.0 : -1.0);
-        for (k=dim, colp=normal; k--; colp++)
-          *colp= 0.0;
-        *maxp= temp;
-        zzinc_(Znearlysingular);
-        trace0((qh, qh->ferr, 1, "qh_normalize: norm=%2.2g too small during p%d\n",
-               norm, qh->furthest_id));
-        return;
-      }
-    }
-  }
-} /* normalize */
-
-
-/*---------------------------------
-
-  qh_projectpoint(qh, point, facet, dist )
-    project point onto a facet by dist
-
-  returns:
-    returns a new point
-
-  notes:
-    if dist= distplane(point,facet)
-      this projects point to hyperplane
-    assumes qh_memfree_() is valid for normal_size
-*/
-pointT *qh_projectpoint(qhT *qh, pointT *point, facetT *facet, realT dist) {
-  pointT *newpoint, *np, *normal;
-  int normsize= qh->normal_size;
-  int k;
-  void **freelistp; /* used if !qh_NOmem by qh_memalloc_() */
-
-  qh_memalloc_(qh, normsize, freelistp, newpoint, pointT);
-  np= newpoint;
-  normal= facet->normal;
-  for (k=qh->hull_dim; k--; )
-    *(np++)= *point++ - dist * *normal++;
-  return(newpoint);
-} /* projectpoint */
-
-
-/*---------------------------------
-
-  qh_setfacetplane(qh, facet )
-    sets the hyperplane for a facet
-    if qh.RANDOMdist, joggles hyperplane
-
-  notes:
-    uses global buffers qh.gm_matrix and qh.gm_row
-    overwrites facet->normal if already defined
-    updates Wnewvertex if PRINTstatistics
-    sets facet->upperdelaunay if upper envelope of Delaunay triangulation
-
-  design:
-    copy vertex coordinates to qh.gm_matrix/gm_row
-    compute determinate
-    if nearzero
-      recompute determinate with gaussian elimination
-      if nearzero
-        force outside orientation by testing interior point
-*/
-void qh_setfacetplane(qhT *qh, facetT *facet) {
-  pointT *point;
-  vertexT *vertex, **vertexp;
-  int normsize= qh->normal_size;
-  int k,i, oldtrace= 0;
-  realT dist;
-  void **freelistp; /* used if !qh_NOmem by qh_memalloc_() */
-  coordT *coord, *gmcoord;
-  pointT *point0= SETfirstt_(facet->vertices, vertexT)->point;
-  boolT nearzero= False;
-
-  zzinc_(Zsetplane);
-  if (!facet->normal)
-    qh_memalloc_(qh, normsize, freelistp, facet->normal, coordT);
-  if (facet == qh->tracefacet) {
-    oldtrace= qh->IStracing;
-    qh->IStracing= 5;
-    qh_fprintf(qh, qh->ferr, 8012, "qh_setfacetplane: facet f%d created.\n", facet->id);
-    qh_fprintf(qh, qh->ferr, 8013, "  Last point added to hull was p%d.", qh->furthest_id);
-    if (zzval_(Ztotmerge))
-      qh_fprintf(qh, qh->ferr, 8014, "  Last merge was #%d.", zzval_(Ztotmerge));
-    qh_fprintf(qh, qh->ferr, 8015, "\n\nCurrent summary is:\n");
-      qh_printsummary(qh, qh->ferr);
-  }
-  if (qh->hull_dim <= 4) {
-    i= 0;
-    if (qh->RANDOMdist) {
-      gmcoord= qh->gm_matrix;
-      FOREACHvertex_(facet->vertices) {
-        qh->gm_row[i++]= gmcoord;
-        coord= vertex->point;
-        for (k=qh->hull_dim; k--; )
-          *(gmcoord++)= *coord++ * qh_randomfactor(qh, qh->RANDOMa, qh->RANDOMb);
-      }
-    }else {
-      FOREACHvertex_(facet->vertices)
-       qh->gm_row[i++]= vertex->point;
-    }
-    qh_sethyperplane_det(qh, qh->hull_dim, qh->gm_row, point0, facet->toporient,
-                facet->normal, &facet->offset, &nearzero);
-  }
-  if (qh->hull_dim > 4 || nearzero) {
-    i= 0;
-    gmcoord= qh->gm_matrix;
-    FOREACHvertex_(facet->vertices) {
-      if (vertex->point != point0) {
-        qh->gm_row[i++]= gmcoord;
-        coord= vertex->point;
-        point= point0;
-        for (k=qh->hull_dim; k--; )
-          *(gmcoord++)= *coord++ - *point++;
-      }
-    }
-    qh->gm_row[i]= gmcoord;  /* for areasimplex */
-    if (qh->RANDOMdist) {
-      gmcoord= qh->gm_matrix;
-      for (i=qh->hull_dim-1; i--; ) {
-        for (k=qh->hull_dim; k--; )
-          *(gmcoord++) *= qh_randomfactor(qh, qh->RANDOMa, qh->RANDOMb);
-      }
-    }
-    qh_sethyperplane_gauss(qh, qh->hull_dim, qh->gm_row, point0, facet->toporient,
-                facet->normal, &facet->offset, &nearzero);
-    if (nearzero) {
-      if (qh_orientoutside(qh, facet)) {
-        trace0((qh, qh->ferr, 2, "qh_setfacetplane: flipped orientation after testing interior_point during p%d\n", qh->furthest_id));
-      /* this is part of using Gaussian Elimination.  For example in 5-d
-           1 1 1 1 0
-           1 1 1 1 1
-           0 0 0 1 0
-           0 1 0 0 0
-           1 0 0 0 0
-           norm= 0.38 0.38 -0.76 0.38 0
-         has a determinate of 1, but g.e. after subtracting pt. 0 has
-         0's in the diagonal, even with full pivoting.  It does work
-         if you subtract pt. 4 instead. */
-      }
-    }
-  }
-  facet->upperdelaunay= False;
-  if (qh->DELAUNAY) {
-    if (qh->UPPERdelaunay) {     /* matches qh_triangulate_facet and qh.lower_threshold in qh_initbuild */
-      if (facet->normal[qh->hull_dim -1] >= qh->ANGLEround * qh_ZEROdelaunay)
-        facet->upperdelaunay= True;
-    }else {
-      if (facet->normal[qh->hull_dim -1] > -qh->ANGLEround * qh_ZEROdelaunay)
-        facet->upperdelaunay= True;
-    }
-  }
-  if (qh->PRINTstatistics || qh->IStracing || qh->TRACElevel || qh->JOGGLEmax < REALmax) {
-    qh->old_randomdist= qh->RANDOMdist;
-    qh->RANDOMdist= False;
-    FOREACHvertex_(facet->vertices) {
-      if (vertex->point != point0) {
-        boolT istrace= False;
-        zinc_(Zdiststat);
-        qh_distplane(qh, vertex->point, facet, &dist);
-        dist= fabs_(dist);
-        zinc_(Znewvertex);
-        wadd_(Wnewvertex, dist);
-        if (dist > wwval_(Wnewvertexmax)) {
-          wwval_(Wnewvertexmax)= dist;
-          if (dist > qh->max_outside) {
-            qh->max_outside= dist;  /* used by qh_maxouter(qh) */
-            if (dist > qh->TRACEdist)
-              istrace= True;
-          }
-        }else if (-dist > qh->TRACEdist)
-          istrace= True;
-        if (istrace) {
-          qh_fprintf(qh, qh->ferr, 8016, "qh_setfacetplane: ====== vertex p%d(v%d) increases max_outside to %2.2g for new facet f%d last p%d\n",
-                qh_pointid(qh, vertex->point), vertex->id, dist, facet->id, qh->furthest_id);
-          qh_errprint(qh, "DISTANT", facet, NULL, NULL, NULL);
-        }
-      }
-    }
-    qh->RANDOMdist= qh->old_randomdist;
-  }
-  if (qh->IStracing >= 3) {
-    qh_fprintf(qh, qh->ferr, 8017, "qh_setfacetplane: f%d offset %2.2g normal: ",
-             facet->id, facet->offset);
-    for (k=0; k < qh->hull_dim; k++)
-      qh_fprintf(qh, qh->ferr, 8018, "%2.2g ", facet->normal[k]);
-    qh_fprintf(qh, qh->ferr, 8019, "\n");
-  }
-  if (facet == qh->tracefacet)
-    qh->IStracing= oldtrace;
-} /* setfacetplane */
-
-
-/*---------------------------------
-
-  qh_sethyperplane_det(qh, dim, rows, point0, toporient, normal, offset, nearzero )
-    given dim X dim array indexed by rows[], one row per point,
-        toporient(flips all signs),
-        and point0 (any row)
-    set normalized hyperplane equation from oriented simplex
-
-  returns:
-    normal (normalized)
-    offset (places point0 on the hyperplane)
-    sets nearzero if hyperplane not through points
-
-  notes:
-    only defined for dim == 2..4
-    rows[] is not modified
-    solves det(P-V_0, V_n-V_0, ..., V_1-V_0)=0, i.e. every point is on hyperplane
-    see Bower & Woodworth, A programmer's geometry, Butterworths 1983.
-
-  derivation of 3-d minnorm
-    Goal: all vertices V_i within qh.one_merge of hyperplane
-    Plan: exactly translate the facet so that V_0 is the origin
-          exactly rotate the facet so that V_1 is on the x-axis and y_2=0.
-          exactly rotate the effective perturbation to only effect n_0
-             this introduces a factor of sqrt(3)
-    n_0 = ((y_2-y_0)*(z_1-z_0) - (z_2-z_0)*(y_1-y_0)) / norm
-    Let M_d be the max coordinate difference
-    Let M_a be the greater of M_d and the max abs. coordinate
-    Let u be machine roundoff and distround be max error for distance computation
-    The max error for n_0 is sqrt(3) u M_a M_d / norm.  n_1 is approx. 1 and n_2 is approx. 0
-    The max error for distance of V_1 is sqrt(3) u M_a M_d M_d / norm.  Offset=0 at origin
-    Then minnorm = 1.8 u M_a M_d M_d / qh.ONEmerge
-    Note that qh.one_merge is approx. 45.5 u M_a and norm is usually about M_d M_d
-
-  derivation of 4-d minnorm
-    same as above except rotate the facet so that V_1 on x-axis and w_2, y_3, w_3=0
-     [if two vertices fixed on x-axis, can rotate the other two in yzw.]
-    n_0 = det3_(...) = y_2 det2_(z_1, w_1, z_3, w_3) = - y_2 w_1 z_3
-     [all other terms contain at least two factors nearly zero.]
-    The max error for n_0 is sqrt(4) u M_a M_d M_d / norm
-    Then minnorm = 2 u M_a M_d M_d M_d / qh.ONEmerge
-    Note that qh.one_merge is approx. 82 u M_a and norm is usually about M_d M_d M_d
-*/
-void qh_sethyperplane_det(qhT *qh, int dim, coordT **rows, coordT *point0,
-          boolT toporient, coordT *normal, realT *offset, boolT *nearzero) {
-  realT maxround, dist;
-  int i;
-  pointT *point;
-
-
-  if (dim == 2) {
-    normal[0]= dY(1,0);
-    normal[1]= dX(0,1);
-    qh_normalize2(qh, normal, dim, toporient, NULL, NULL);
-    *offset= -(point0[0]*normal[0]+point0[1]*normal[1]);
-    *nearzero= False;  /* since nearzero norm => incident points */
-  }else if (dim == 3) {
-    normal[0]= det2_(dY(2,0), dZ(2,0),
-                     dY(1,0), dZ(1,0));
-    normal[1]= det2_(dX(1,0), dZ(1,0),
-                     dX(2,0), dZ(2,0));
-    normal[2]= det2_(dX(2,0), dY(2,0),
-                     dX(1,0), dY(1,0));
-    qh_normalize2(qh, normal, dim, toporient, NULL, NULL);
-    *offset= -(point0[0]*normal[0] + point0[1]*normal[1]
-               + point0[2]*normal[2]);
-    maxround= qh->DISTround;
-    for (i=dim; i--; ) {
-      point= rows[i];
-      if (point != point0) {
-        dist= *offset + (point[0]*normal[0] + point[1]*normal[1]
-               + point[2]*normal[2]);
-        if (dist > maxround || dist < -maxround) {
-          *nearzero= True;
-          break;
-        }
-      }
-    }
-  }else if (dim == 4) {
-    normal[0]= - det3_(dY(2,0), dZ(2,0), dW(2,0),
-                        dY(1,0), dZ(1,0), dW(1,0),
-                        dY(3,0), dZ(3,0), dW(3,0));
-    normal[1]=   det3_(dX(2,0), dZ(2,0), dW(2,0),
-                        dX(1,0), dZ(1,0), dW(1,0),
-                        dX(3,0), dZ(3,0), dW(3,0));
-    normal[2]= - det3_(dX(2,0), dY(2,0), dW(2,0),
-                        dX(1,0), dY(1,0), dW(1,0),
-                        dX(3,0), dY(3,0), dW(3,0));
-    normal[3]=   det3_(dX(2,0), dY(2,0), dZ(2,0),
-                        dX(1,0), dY(1,0), dZ(1,0),
-                        dX(3,0), dY(3,0), dZ(3,0));
-    qh_normalize2(qh, normal, dim, toporient, NULL, NULL);
-    *offset= -(point0[0]*normal[0] + point0[1]*normal[1]
-               + point0[2]*normal[2] + point0[3]*normal[3]);
-    maxround= qh->DISTround;
-    for (i=dim; i--; ) {
-      point= rows[i];
-      if (point != point0) {
-        dist= *offset + (point[0]*normal[0] + point[1]*normal[1]
-               + point[2]*normal[2] + point[3]*normal[3]);
-        if (dist > maxround || dist < -maxround) {
-          *nearzero= True;
-          break;
-        }
-      }
-    }
-  }
-  if (*nearzero) {
-    zzinc_(Zminnorm);
-    trace0((qh, qh->ferr, 3, "qh_sethyperplane_det: degenerate norm during p%d.\n", qh->furthest_id));
-    zzinc_(Znearlysingular);
-  }
-} /* sethyperplane_det */
-
-
-/*---------------------------------
-
-  qh_sethyperplane_gauss(qh, dim, rows, point0, toporient, normal, offset, nearzero )
-    given(dim-1) X dim array of rows[i]= V_{i+1} - V_0 (point0)
-    set normalized hyperplane equation from oriented simplex
-
-  returns:
-    normal (normalized)
-    offset (places point0 on the hyperplane)
-
-  notes:
-    if nearzero
-      orientation may be incorrect because of incorrect sign flips in gausselim
-    solves [V_n-V_0,...,V_1-V_0, 0 .. 0 1] * N == [0 .. 0 1]
-        or [V_n-V_0,...,V_1-V_0, 0 .. 0 1] * N == [0]
-    i.e., N is normal to the hyperplane, and the unnormalized
-        distance to [0 .. 1] is either 1 or   0
-
-  design:
-    perform gaussian elimination
-    flip sign for negative values
-    perform back substitution
-    normalize result
-    compute offset
-*/
-void qh_sethyperplane_gauss(qhT *qh, int dim, coordT **rows, pointT *point0,
-                boolT toporient, coordT *normal, coordT *offset, boolT *nearzero) {
-  coordT *pointcoord, *normalcoef;
-  int k;
-  boolT sign= toporient, nearzero2= False;
-
-  qh_gausselim(qh, rows, dim-1, dim, &sign, nearzero);
-  for (k=dim-1; k--; ) {
-    if ((rows[k])[k] < 0)
-      sign ^= 1;
-  }
-  if (*nearzero) {
-    zzinc_(Znearlysingular);
-    trace0((qh, qh->ferr, 4, "qh_sethyperplane_gauss: nearly singular or axis parallel hyperplane during p%d.\n", qh->furthest_id));
-    qh_backnormal(qh, rows, dim-1, dim, sign, normal, &nearzero2);
-  }else {
-    qh_backnormal(qh, rows, dim-1, dim, sign, normal, &nearzero2);
-    if (nearzero2) {
-      zzinc_(Znearlysingular);
-      trace0((qh, qh->ferr, 5, "qh_sethyperplane_gauss: singular or axis parallel hyperplane at normalization during p%d.\n", qh->furthest_id));
-    }
-  }
-  if (nearzero2)
-    *nearzero= True;
-  qh_normalize2(qh, normal, dim, True, NULL, NULL);
-  pointcoord= point0;
-  normalcoef= normal;
-  *offset= -(*pointcoord++ * *normalcoef++);
-  for (k=dim-1; k--; )
-    *offset -= *pointcoord++ * *normalcoef++;
-} /* sethyperplane_gauss */
-
-
-
diff --git a/C/global_r.c b/C/global_r.c
deleted file mode 100644
--- a/C/global_r.c
+++ /dev/null
@@ -1,2100 +0,0 @@
-
-/*
  ---------------------------------
-
-   global_r.c
-   initializes all the globals of the qhull application
-
-   see README
-
-   see libqhull_r.h for qh.globals and function prototypes
-
-   see qhull_ra.h for internal functions
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull_r/global_r.c#16 $$Change: 2066 $
-   $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
- */
-
-#include "qhull_ra.h"
-
-/*========= qh->definition -- globals defined in libqhull_r.h =======================*/
-
-/*----------------------------------
-
-  qh_version
-    version string by year and date
-    qh_version2 for Unix users and -V
-
-    the revision increases on code changes only
-
-  notes:
-    change date:    Changes.txt, Announce.txt, index.htm, README.txt,
-                    qhull-news.html, Eudora signatures, CMakeLists.txt
-    change version: README.txt, qh-get.htm, File_id.diz, Makefile.txt, CMakeLists.txt
-    check that CmakeLists @version is the same as qh_version2
-    change year:    Copying.txt
-    check download size
-    recompile user_eg_r.c, rbox_r.c, libqhull_r.c, qconvex_r.c, qdelaun_r.c qvoronoi_r.c, qhalf_r.c, testqset_r.c
-*/
-
-const char qh_version[]= "2015.2.r 2016/01/18";
-const char qh_version2[]= "qhull_r 7.2.0 (2015.2.r 2016/01/18)";
-
-/*---------------------------------
-
-  qh_appendprint(qh, printFormat )
-    append printFormat to qh.PRINTout unless already defined
-*/
-void qh_appendprint(qhT *qh, qh_PRINT format) {
-  int i;
-
-  for (i=0; i < qh_PRINTEND; i++) {
-    if (qh->PRINTout[i] == format && format != qh_PRINTqhull)
-      break;
-    if (!qh->PRINTout[i]) {
-      qh->PRINTout[i]= format;
-      break;
-    }
-  }
-} /* appendprint */
-
-/*---------------------------------
-
-  qh_checkflags(qh, commandStr, hiddenFlags )
-    errors if commandStr contains hiddenFlags
-    hiddenFlags starts and ends with a space and is space delimited (checked)
-
-  notes:
-    ignores first word (e.g., "qconvex i")
-    use qh_strtol/strtod since strtol/strtod may or may not skip trailing spaces
-
-  see:
-    qh_initflags() initializes Qhull according to commandStr
-*/
-void qh_checkflags(qhT *qh, char *command, char *hiddenflags) {
-  char *s= command, *t, *chkerr; /* qh_skipfilename is non-const */
-  char key, opt, prevopt;
-  char chkkey[]= "   ";
-  char chkopt[]=  "    ";
-  char chkopt2[]= "     ";
-  boolT waserr= False;
-
-  if (*hiddenflags != ' ' || hiddenflags[strlen(hiddenflags)-1] != ' ') {
-    qh_fprintf(qh, qh->ferr, 6026, "qhull error (qh_checkflags): hiddenflags must start and end with a space: \"%s\"", hiddenflags);
-    qh_errexit(qh, qh_ERRinput, NULL, NULL);
-  }
-  if (strpbrk(hiddenflags, ",\n\r\t")) {
-    qh_fprintf(qh, qh->ferr, 6027, "qhull error (qh_checkflags): hiddenflags contains commas, newlines, or tabs: \"%s\"", hiddenflags);
-    qh_errexit(qh, qh_ERRinput, NULL, NULL);
-  }
-  while (*s && !isspace(*s))  /* skip program name */
-    s++;
-  while (*s) {
-    while (*s && isspace(*s))
-      s++;
-    if (*s == '-')
-      s++;
-    if (!*s)
-      break;
-    key = *s++;
-    chkerr = NULL;
-    if (key == 'T' && (*s == 'I' || *s == 'O')) {  /* TI or TO 'file name' */
-      s= qh_skipfilename(qh, ++s);
-      continue;
-    }
-    chkkey[1]= key;
-    if (strstr(hiddenflags, chkkey)) {
-      chkerr= chkkey;
-    }else if (isupper(key)) {
-      opt= ' ';
-      prevopt= ' ';
-      chkopt[1]= key;
-      chkopt2[1]= key;
-      while (!chkerr && *s && !isspace(*s)) {
-        opt= *s++;
-        if (isalpha(opt)) {
-          chkopt[2]= opt;
-          if (strstr(hiddenflags, chkopt))
-            chkerr= chkopt;
-          if (prevopt != ' ') {
-            chkopt2[2]= prevopt;
-            chkopt2[3]= opt;
-            if (strstr(hiddenflags, chkopt2))
-              chkerr= chkopt2;
-          }
-        }else if (key == 'Q' && isdigit(opt) && prevopt != 'b'
-              && (prevopt == ' ' || islower(prevopt))) {
-            chkopt[2]= opt;
-            if (strstr(hiddenflags, chkopt))
-              chkerr= chkopt;
-        }else {
-          qh_strtod(s-1, &t);
-          if (s < t)
-            s= t;
-        }
-        prevopt= opt;
-      }
-    }
-    if (chkerr) {
-      *chkerr= '\'';
-      chkerr[strlen(chkerr)-1]=  '\'';
-      qh_fprintf(qh, qh->ferr, 6029, "qhull error: option %s is not used with this program.\n             It may be used with qhull.\n", chkerr);
-      waserr= True;
-    }
-  }
-  if (waserr)
-    qh_errexit(qh, qh_ERRinput, NULL, NULL);
-} /* checkflags */
-
-/*---------------------------------
-
-  qh_clear_outputflags(qh)
-    Clear output flags for QhullPoints
-*/
-void qh_clear_outputflags(qhT *qh) {
-  int i,k;
-
-  qh->ANNOTATEoutput= False;
-  qh->DOintersections= False;
-  qh->DROPdim= -1;
-  qh->FORCEoutput= False;
-  qh->GETarea= False;
-  qh->GOODpoint= 0;
-  qh->GOODpointp= NULL;
-  qh->GOODthreshold= False;
-  qh->GOODvertex= 0;
-  qh->GOODvertexp= NULL;
-  qh->IStracing= 0;
-  qh->KEEParea= False;
-  qh->KEEPmerge= False;
-  qh->KEEPminArea= REALmax;
-  qh->PRINTcentrums= False;
-  qh->PRINTcoplanar= False;
-  qh->PRINTdots= False;
-  qh->PRINTgood= False;
-  qh->PRINTinner= False;
-  qh->PRINTneighbors= False;
-  qh->PRINTnoplanes= False;
-  qh->PRINToptions1st= False;
-  qh->PRINTouter= False;
-  qh->PRINTprecision= True;
-  qh->PRINTridges= False;
-  qh->PRINTspheres= False;
-  qh->PRINTstatistics= False;
-  qh->PRINTsummary= False;
-  qh->PRINTtransparent= False;
-  qh->SPLITthresholds= False;
-  qh->TRACElevel= 0;
-  qh->TRInormals= False;
-  qh->USEstdout= False;
-  qh->VERIFYoutput= False;
-  for (k=qh->input_dim+1; k--; ) {  /* duplicated in qh_initqhull_buffers and qh_clear_outputflags */
-    qh->lower_threshold[k]= -REALmax;
-    qh->upper_threshold[k]= REALmax;
-    qh->lower_bound[k]= -REALmax;
-    qh->upper_bound[k]= REALmax;
-  }
-
-  for (i=0; i < qh_PRINTEND; i++) {
-    qh->PRINTout[i]= qh_PRINTnone;
-  }
-
-  if (!qh->qhull_commandsiz2)
-      qh->qhull_commandsiz2= (int)strlen(qh->qhull_command); /* WARN64 */
-  else {
-      qh->qhull_command[qh->qhull_commandsiz2]= '\0';
-  }
-  if (!qh->qhull_optionsiz2)
-    qh->qhull_optionsiz2= (int)strlen(qh->qhull_options);  /* WARN64 */
-  else {
-    qh->qhull_options[qh->qhull_optionsiz2]= '\0';
-    qh->qhull_optionlen= qh_OPTIONline;  /* start a new line */
-  }
-} /* clear_outputflags */
-
-/*---------------------------------
-
-  qh_clock()
-    return user CPU time in 100ths (qh_SECtick)
-    only defined for qh_CLOCKtype == 2
-
-  notes:
-    use first value to determine time 0
-    from Stevens '92 8.15
-*/
-unsigned long qh_clock(qhT *qh) {
-
-#if (qh_CLOCKtype == 2)
-  struct tms time;
-  static long clktck;  /* initialized first call and never updated */
-  double ratio, cpu;
-  unsigned long ticks;
-
-  if (!clktck) {
-    if ((clktck= sysconf(_SC_CLK_TCK)) < 0) {
-      qh_fprintf(qh, qh->ferr, 6030, "qhull internal error (qh_clock): sysconf() failed.  Use qh_CLOCKtype 1 in user.h\n");
-      qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-    }
-  }
-  if (times(&time) == -1) {
-    qh_fprintf(qh, qh->ferr, 6031, "qhull internal error (qh_clock): times() failed.  Use qh_CLOCKtype 1 in user.h\n");
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }
-  ratio= qh_SECticks / (double)clktck;
-  ticks= time.tms_utime * ratio;
-  return ticks;
-#else
-  qh_fprintf(qh, qh->ferr, 6032, "qhull internal error (qh_clock): use qh_CLOCKtype 2 in user.h\n");
-  qh_errexit(qh, qh_ERRqhull, NULL, NULL); /* never returns */
-  return 0;
-#endif
-} /* clock */
-
-/*---------------------------------
-
-  qh_freebuffers()
-    free up global memory buffers
-
-  notes:
-    must match qh_initbuffers()
-*/
-void qh_freebuffers(qhT *qh) {
-
-  trace5((qh, qh->ferr, 5001, "qh_freebuffers: freeing up global memory buffers\n"));
-  /* allocated by qh_initqhull_buffers */
-  qh_memfree(qh, qh->NEARzero, qh->hull_dim * sizeof(realT));
-  qh_memfree(qh, qh->lower_threshold, (qh->input_dim+1) * sizeof(realT));
-  qh_memfree(qh, qh->upper_threshold, (qh->input_dim+1) * sizeof(realT));
-  qh_memfree(qh, qh->lower_bound, (qh->input_dim+1) * sizeof(realT));
-  qh_memfree(qh, qh->upper_bound, (qh->input_dim+1) * sizeof(realT));
-  qh_memfree(qh, qh->gm_matrix, (qh->hull_dim+1) * qh->hull_dim * sizeof(coordT));
-  qh_memfree(qh, qh->gm_row, (qh->hull_dim+1) * sizeof(coordT *));
-  qh->NEARzero= qh->lower_threshold= qh->upper_threshold= NULL;
-  qh->lower_bound= qh->upper_bound= NULL;
-  qh->gm_matrix= NULL;
-  qh->gm_row= NULL;
-  qh_setfree(qh, &qh->other_points);
-  qh_setfree(qh, &qh->del_vertices);
-  qh_setfree(qh, &qh->coplanarfacetset);
-  if (qh->line)                /* allocated by qh_readinput, freed if no error */
-    qh_free(qh->line);
-  if (qh->half_space)
-    qh_free(qh->half_space);
-  if (qh->temp_malloc)
-    qh_free(qh->temp_malloc);
-  if (qh->feasible_point)      /* allocated by qh_readfeasible */
-    qh_free(qh->feasible_point);
-  if (qh->feasible_string)     /* allocated by qh_initflags */
-    qh_free(qh->feasible_string);
-  qh->line= qh->feasible_string= NULL;
-  qh->half_space= qh->feasible_point= qh->temp_malloc= NULL;
-  /* usually allocated by qh_readinput */
-  if (qh->first_point && qh->POINTSmalloc) {
-    qh_free(qh->first_point);
-    qh->first_point= NULL;
-  }
-  if (qh->input_points && qh->input_malloc) { /* set by qh_joggleinput */
-    qh_free(qh->input_points);
-    qh->input_points= NULL;
-  }
-  trace5((qh, qh->ferr, 5002, "qh_freebuffers: finished\n"));
-} /* freebuffers */
-
-
-/*---------------------------------
-
-  qh_freebuild(qh, allmem )
-    free global memory used by qh_initbuild and qh_buildhull
-    if !allmem,
-      does not free short memory (e.g., facetT, freed by qh_memfreeshort)
-
-  design:
-    free centrums
-    free each vertex
-    mark unattached ridges
-    for each facet
-      free ridges
-      free outside set, coplanar set, neighbor set, ridge set, vertex set
-      free facet
-    free hash table
-    free interior point
-    free merge set
-    free temporary sets
-*/
-void qh_freebuild(qhT *qh, boolT allmem) {
-  facetT *facet;
-  vertexT *vertex;
-  ridgeT *ridge, **ridgep;
-  mergeT *merge, **mergep;
-
-  trace1((qh, qh->ferr, 1005, "qh_freebuild: free memory from qh_inithull and qh_buildhull\n"));
-  if (qh->del_vertices)
-    qh_settruncate(qh, qh->del_vertices, 0);
-  if (allmem) {
-    while ((vertex= qh->vertex_list)) {
-      if (vertex->next)
-        qh_delvertex(qh, vertex);
-      else {
-        qh_memfree(qh, vertex, (int)sizeof(vertexT));
-        qh->newvertex_list= qh->vertex_list= NULL;
-      }
-    }
-  }else if (qh->VERTEXneighbors) {
-    FORALLvertices
-      qh_setfreelong(qh, &(vertex->neighbors));
-  }
-  qh->VERTEXneighbors= False;
-  qh->GOODclosest= NULL;
-  if (allmem) {
-    FORALLfacets {
-      FOREACHridge_(facet->ridges)
-        ridge->seen= False;
-    }
-    FORALLfacets {
-      if (facet->visible) {
-        FOREACHridge_(facet->ridges) {
-          if (!otherfacet_(ridge, facet)->visible)
-            ridge->seen= True;  /* an unattached ridge */
-        }
-      }
-    }
-    while ((facet= qh->facet_list)) {
-      FOREACHridge_(facet->ridges) {
-        if (ridge->seen) {
-          qh_setfree(qh, &(ridge->vertices));
-          qh_memfree(qh, ridge, (int)sizeof(ridgeT));
-        }else
-          ridge->seen= True;
-      }
-      qh_setfree(qh, &(facet->outsideset));
-      qh_setfree(qh, &(facet->coplanarset));
-      qh_setfree(qh, &(facet->neighbors));
-      qh_setfree(qh, &(facet->ridges));
-      qh_setfree(qh, &(facet->vertices));
-      if (facet->next)
-        qh_delfacet(qh, facet);
-      else {
-        qh_memfree(qh, facet, (int)sizeof(facetT));
-        qh->visible_list= qh->newfacet_list= qh->facet_list= NULL;
-      }
-    }
-  }else {
-    FORALLfacets {
-      qh_setfreelong(qh, &(facet->outsideset));
-      qh_setfreelong(qh, &(facet->coplanarset));
-      if (!facet->simplicial) {
-        qh_setfreelong(qh, &(facet->neighbors));
-        qh_setfreelong(qh, &(facet->ridges));
-        qh_setfreelong(qh, &(facet->vertices));
-      }
-    }
-  }
-  qh_setfree(qh, &(qh->hash_table));
-  qh_memfree(qh, qh->interior_point, qh->normal_size);
-  qh->interior_point= NULL;
-  FOREACHmerge_(qh->facet_mergeset)  /* usually empty */
-    qh_memfree(qh, merge, (int)sizeof(mergeT));
-  qh->facet_mergeset= NULL;  /* temp set */
-  qh->degen_mergeset= NULL;  /* temp set */
-  qh_settempfree_all(qh);
-} /* freebuild */
-
-/*---------------------------------
-
-  qh_freeqhull(qh, allmem )
-
-  free global memory and set qhT to 0
-  if !allmem,
-    does not free short memory (freed by qh_memfreeshort unless qh_NOmem)
-
-notes:
-  sets qh.NOerrexit in case caller forgets to
-  Does not throw errors
-
-see:
-  see qh_initqhull_start2()
-  For libqhull_r, qhstatT is part of qhT
-
-design:
-  free global and temporary memory from qh_initbuild and qh_buildhull
-  free buffers
-*/
-void qh_freeqhull(qhT *qh, boolT allmem) {
-
-  qh->NOerrexit= True;  /* no more setjmp since called at exit and ~QhullQh */
-  trace1((qh, qh->ferr, 1006, "qh_freeqhull: free global memory\n"));
-  qh_freebuild(qh, allmem);
-  qh_freebuffers(qh);
-  /* memset is the same in qh_freeqhull() and qh_initqhull_start2() */
-  memset((char *)qh, 0, sizeof(qhT)-sizeof(qhmemT)-sizeof(qhstatT));
-  qh->NOerrexit= True;
-} /* freeqhull2 */
-
-/*---------------------------------
-
-  qh_init_A(qh, infile, outfile, errfile, argc, argv )
-    initialize memory and stdio files
-    convert input options to option string (qh.qhull_command)
-
-  notes:
-    infile may be NULL if qh_readpoints() is not called
-
-    errfile should always be defined.  It is used for reporting
-    errors.  outfile is used for output and format options.
-
-    argc/argv may be 0/NULL
-
-    called before error handling initialized
-    qh_errexit() may not be used
-*/
-void qh_init_A(qhT *qh, FILE *infile, FILE *outfile, FILE *errfile, int argc, char *argv[]) {
-  qh_meminit(qh, errfile);
-  qh_initqhull_start(qh, infile, outfile, errfile);
-  qh_init_qhull_command(qh, argc, argv);
-} /* init_A */
-
-/*---------------------------------
-
-  qh_init_B(qh, points, numpoints, dim, ismalloc )
-    initialize globals for points array
-
-    points has numpoints dim-dimensional points
-      points[0] is the first coordinate of the first point
-      points[1] is the second coordinate of the first point
-      points[dim] is the first coordinate of the second point
-
-    ismalloc=True
-      Qhull will call qh_free(points) on exit or input transformation
-    ismalloc=False
-      Qhull will allocate a new point array if needed for input transformation
-
-    qh.qhull_command
-      is the option string.
-      It is defined by qh_init_B(), qh_qhull_command(), or qh_initflags
-
-  returns:
-    if qh.PROJECTinput or (qh.DELAUNAY and qh.PROJECTdelaunay)
-      projects the input to a new point array
-
-        if qh.DELAUNAY,
-          qh.hull_dim is increased by one
-        if qh.ATinfinity,
-          qh_projectinput adds point-at-infinity for Delaunay tri.
-
-    if qh.SCALEinput
-      changes the upper and lower bounds of the input, see qh_scaleinput(qh)
-
-    if qh.ROTATEinput
-      rotates the input by a random rotation, see qh_rotateinput()
-      if qh.DELAUNAY
-        rotates about the last coordinate
-
-  notes:
-    called after points are defined
-    qh_errexit() may be used
-*/
-void qh_init_B(qhT *qh, coordT *points, int numpoints, int dim, boolT ismalloc) {
-  qh_initqhull_globals(qh, points, numpoints, dim, ismalloc);
-  if (qh->qhmem.LASTsize == 0)
-    qh_initqhull_mem(qh);
-  /* mem_r.c and qset_r.c are initialized */
-  qh_initqhull_buffers(qh);
-  qh_initthresholds(qh, qh->qhull_command);
-  if (qh->PROJECTinput || (qh->DELAUNAY && qh->PROJECTdelaunay))
-    qh_projectinput(qh);
-  if (qh->SCALEinput)
-    qh_scaleinput(qh);
-  if (qh->ROTATErandom >= 0) {
-    qh_randommatrix(qh, qh->gm_matrix, qh->hull_dim, qh->gm_row);
-    if (qh->DELAUNAY) {
-      int k, lastk= qh->hull_dim-1;
-      for (k=0; k < lastk; k++) {
-        qh->gm_row[k][lastk]= 0.0;
-        qh->gm_row[lastk][k]= 0.0;
-      }
-      qh->gm_row[lastk][lastk]= 1.0;
-    }
-    qh_gram_schmidt(qh, qh->hull_dim, qh->gm_row);
-    qh_rotateinput(qh, qh->gm_row);
-  }
-} /* init_B */
-
-/*---------------------------------
-
-  qh_init_qhull_command(qh, argc, argv )
-    build qh.qhull_command from argc/argv
-    Calls qh_exit if qhull_command is too short
-
-  returns:
-    a space-delimited string of options (just as typed)
-
-  notes:
-    makes option string easy to input and output
-
-    argc/argv may be 0/NULL
-*/
-void qh_init_qhull_command(qhT *qh, int argc, char *argv[]) {
-
-  if (!qh_argv_to_command(argc, argv, qh->qhull_command, (int)sizeof(qh->qhull_command))){
-    /* Assumes qh.ferr is defined. */
-    qh_fprintf(qh, qh->ferr, 6033, "qhull input error: more than %d characters in command line.\n",
-          (int)sizeof(qh->qhull_command));
-    qh_exit(qh_ERRinput);  /* error reported, can not use qh_errexit */
-  }
-} /* init_qhull_command */
-
-/*---------------------------------
-
-  qh_initflags(qh, commandStr )
-    set flags and initialized constants from commandStr
-    calls qh_exit() if qh->NOerrexit
-
-  returns:
-    sets qh.qhull_command to command if needed
-
-  notes:
-    ignores first word (e.g., "qhull d")
-    use qh_strtol/strtod since strtol/strtod may or may not skip trailing spaces
-
-  see:
-    qh_initthresholds() continues processing of 'Pdn' and 'PDn'
-    'prompt' in unix_r.c for documentation
-
-  design:
-    for each space-delimited option group
-      if top-level option
-        check syntax
-        append appropriate option to option string
-        set appropriate global variable or append printFormat to print options
-      else
-        for each sub-option
-          check syntax
-          append appropriate option to option string
-          set appropriate global variable or append printFormat to print options
-*/
-void qh_initflags(qhT *qh, char *command) {
-  int k, i, lastproject;
-  char *s= command, *t, *prev_s, *start, key;
-  boolT isgeom= False, wasproject;
-  realT r;
-
-  if(qh->NOerrexit){
-    qh_fprintf(qh, qh->ferr, 6245, "qhull initflags error: qh.NOerrexit was not cleared before calling qh_initflags().  It should be cleared after setjmp().  Exit qhull.");
-    qh_exit(6245);
-  }
-  if (command <= &qh->qhull_command[0] || command > &qh->qhull_command[0] + sizeof(qh->qhull_command)) {
-    if (command != &qh->qhull_command[0]) {
-      *qh->qhull_command= '\0';
-      strncat(qh->qhull_command, command, sizeof(qh->qhull_command)-strlen(qh->qhull_command)-1);
-    }
-    while (*s && !isspace(*s))  /* skip program name */
-      s++;
-  }
-  while (*s) {
-    while (*s && isspace(*s))
-      s++;
-    if (*s == '-')
-      s++;
-    if (!*s)
-      break;
-    prev_s= s;
-    switch (*s++) {
-    case 'd':
-      qh_option(qh, "delaunay", NULL, NULL);
-      qh->DELAUNAY= True;
-      break;
-    case 'f':
-      qh_option(qh, "facets", NULL, NULL);
-      qh_appendprint(qh, qh_PRINTfacets);
-      break;
-    case 'i':
-      qh_option(qh, "incidence", NULL, NULL);
-      qh_appendprint(qh, qh_PRINTincidences);
-      break;
-    case 'm':
-      qh_option(qh, "mathematica", NULL, NULL);
-      qh_appendprint(qh, qh_PRINTmathematica);
-      break;
-    case 'n':
-      qh_option(qh, "normals", NULL, NULL);
-      qh_appendprint(qh, qh_PRINTnormals);
-      break;
-    case 'o':
-      qh_option(qh, "offFile", NULL, NULL);
-      qh_appendprint(qh, qh_PRINToff);
-      break;
-    case 'p':
-      qh_option(qh, "points", NULL, NULL);
-      qh_appendprint(qh, qh_PRINTpoints);
-      break;
-    case 's':
-      qh_option(qh, "summary", NULL, NULL);
-      qh->PRINTsummary= True;
-      break;
-    case 'v':
-      qh_option(qh, "voronoi", NULL, NULL);
-      qh->VORONOI= True;
-      qh->DELAUNAY= True;
-      break;
-    case 'A':
-      if (!isdigit(*s) && *s != '.' && *s != '-')
-        qh_fprintf(qh, qh->ferr, 7002, "qhull warning: no maximum cosine angle given for option 'An'.  Ignored.\n");
-      else {
-        if (*s == '-') {
-          qh->premerge_cos= -qh_strtod(s, &s);
-          qh_option(qh, "Angle-premerge-", NULL, &qh->premerge_cos);
-          qh->PREmerge= True;
-        }else {
-          qh->postmerge_cos= qh_strtod(s, &s);
-          qh_option(qh, "Angle-postmerge", NULL, &qh->postmerge_cos);
-          qh->POSTmerge= True;
-        }
-        qh->MERGING= True;
-      }
-      break;
-    case 'C':
-      if (!isdigit(*s) && *s != '.' && *s != '-')
-        qh_fprintf(qh, qh->ferr, 7003, "qhull warning: no centrum radius given for option 'Cn'.  Ignored.\n");
-      else {
-        if (*s == '-') {
-          qh->premerge_centrum= -qh_strtod(s, &s);
-          qh_option(qh, "Centrum-premerge-", NULL, &qh->premerge_centrum);
-          qh->PREmerge= True;
-        }else {
-          qh->postmerge_centrum= qh_strtod(s, &s);
-          qh_option(qh, "Centrum-postmerge", NULL, &qh->postmerge_centrum);
-          qh->POSTmerge= True;
-        }
-        qh->MERGING= True;
-      }
-      break;
-    case 'E':
-      if (*s == '-')
-        qh_fprintf(qh, qh->ferr, 7004, "qhull warning: negative maximum roundoff given for option 'An'.  Ignored.\n");
-      else if (!isdigit(*s))
-        qh_fprintf(qh, qh->ferr, 7005, "qhull warning: no maximum roundoff given for option 'En'.  Ignored.\n");
-      else {
-        qh->DISTround= qh_strtod(s, &s);
-        qh_option(qh, "Distance-roundoff", NULL, &qh->DISTround);
-        qh->SETroundoff= True;
-      }
-      break;
-    case 'H':
-      start= s;
-      qh->HALFspace= True;
-      qh_strtod(s, &t);
-      while (t > s)  {
-        if (*t && !isspace(*t)) {
-          if (*t == ',')
-            t++;
-          else
-            qh_fprintf(qh, qh->ferr, 7006, "qhull warning: origin for Halfspace intersection should be 'Hn,n,n,...'\n");
-        }
-        s= t;
-        qh_strtod(s, &t);
-      }
-      if (start < t) {
-        if (!(qh->feasible_string= (char*)calloc((size_t)(t-start+1), (size_t)1))) {
-          qh_fprintf(qh, qh->ferr, 6034, "qhull error: insufficient memory for 'Hn,n,n'\n");
-          qh_errexit(qh, qh_ERRmem, NULL, NULL);
-        }
-        strncpy(qh->feasible_string, start, (size_t)(t-start));
-        qh_option(qh, "Halfspace-about", NULL, NULL);
-        qh_option(qh, qh->feasible_string, NULL, NULL);
-      }else
-        qh_option(qh, "Halfspace", NULL, NULL);
-      break;
-    case 'R':
-      if (!isdigit(*s))
-        qh_fprintf(qh, qh->ferr, 7007, "qhull warning: missing random perturbation for option 'Rn'.  Ignored\n");
-      else {
-        qh->RANDOMfactor= qh_strtod(s, &s);
-        qh_option(qh, "Random_perturb", NULL, &qh->RANDOMfactor);
-        qh->RANDOMdist= True;
-      }
-      break;
-    case 'V':
-      if (!isdigit(*s) && *s != '-')
-        qh_fprintf(qh, qh->ferr, 7008, "qhull warning: missing visible distance for option 'Vn'.  Ignored\n");
-      else {
-        qh->MINvisible= qh_strtod(s, &s);
-        qh_option(qh, "Visible", NULL, &qh->MINvisible);
-      }
-      break;
-    case 'U':
-      if (!isdigit(*s) && *s != '-')
-        qh_fprintf(qh, qh->ferr, 7009, "qhull warning: missing coplanar distance for option 'Un'.  Ignored\n");
-      else {
-        qh->MAXcoplanar= qh_strtod(s, &s);
-        qh_option(qh, "U-coplanar", NULL, &qh->MAXcoplanar);
-      }
-      break;
-    case 'W':
-      if (*s == '-')
-        qh_fprintf(qh, qh->ferr, 7010, "qhull warning: negative outside width for option 'Wn'.  Ignored.\n");
-      else if (!isdigit(*s))
-        qh_fprintf(qh, qh->ferr, 7011, "qhull warning: missing outside width for option 'Wn'.  Ignored\n");
-      else {
-        qh->MINoutside= qh_strtod(s, &s);
-        qh_option(qh, "W-outside", NULL, &qh->MINoutside);
-        qh->APPROXhull= True;
-      }
-      break;
-    /************  sub menus ***************/
-    case 'F':
-      while (*s && !isspace(*s)) {
-        switch (*s++) {
-        case 'a':
-          qh_option(qh, "Farea", NULL, NULL);
-          qh_appendprint(qh, qh_PRINTarea);
-          qh->GETarea= True;
-          break;
-        case 'A':
-          qh_option(qh, "FArea-total", NULL, NULL);
-          qh->GETarea= True;
-          break;
-        case 'c':
-          qh_option(qh, "Fcoplanars", NULL, NULL);
-          qh_appendprint(qh, qh_PRINTcoplanars);
-          break;
-        case 'C':
-          qh_option(qh, "FCentrums", NULL, NULL);
-          qh_appendprint(qh, qh_PRINTcentrums);
-          break;
-        case 'd':
-          qh_option(qh, "Fd-cdd-in", NULL, NULL);
-          qh->CDDinput= True;
-          break;
-        case 'D':
-          qh_option(qh, "FD-cdd-out", NULL, NULL);
-          qh->CDDoutput= True;
-          break;
-        case 'F':
-          qh_option(qh, "FFacets-xridge", NULL, NULL);
-          qh_appendprint(qh, qh_PRINTfacets_xridge);
-          break;
-        case 'i':
-          qh_option(qh, "Finner", NULL, NULL);
-          qh_appendprint(qh, qh_PRINTinner);
-          break;
-        case 'I':
-          qh_option(qh, "FIDs", NULL, NULL);
-          qh_appendprint(qh, qh_PRINTids);
-          break;
-        case 'm':
-          qh_option(qh, "Fmerges", NULL, NULL);
-          qh_appendprint(qh, qh_PRINTmerges);
-          break;
-        case 'M':
-          qh_option(qh, "FMaple", NULL, NULL);
-          qh_appendprint(qh, qh_PRINTmaple);
-          break;
-        case 'n':
-          qh_option(qh, "Fneighbors", NULL, NULL);
-          qh_appendprint(qh, qh_PRINTneighbors);
-          break;
-        case 'N':
-          qh_option(qh, "FNeighbors-vertex", NULL, NULL);
-          qh_appendprint(qh, qh_PRINTvneighbors);
-          break;
-        case 'o':
-          qh_option(qh, "Fouter", NULL, NULL);
-          qh_appendprint(qh, qh_PRINTouter);
-          break;
-        case 'O':
-          if (qh->PRINToptions1st) {
-            qh_option(qh, "FOptions", NULL, NULL);
-            qh_appendprint(qh, qh_PRINToptions);
-          }else
-            qh->PRINToptions1st= True;
-          break;
-        case 'p':
-          qh_option(qh, "Fpoint-intersect", NULL, NULL);
-          qh_appendprint(qh, qh_PRINTpointintersect);
-          break;
-        case 'P':
-          qh_option(qh, "FPoint-nearest", NULL, NULL);
-          qh_appendprint(qh, qh_PRINTpointnearest);
-          break;
-        case 'Q':
-          qh_option(qh, "FQhull", NULL, NULL);
-          qh_appendprint(qh, qh_PRINTqhull);
-          break;
-        case 's':
-          qh_option(qh, "Fsummary", NULL, NULL);
-          qh_appendprint(qh, qh_PRINTsummary);
-          break;
-        case 'S':
-          qh_option(qh, "FSize", NULL, NULL);
-          qh_appendprint(qh, qh_PRINTsize);
-          qh->GETarea= True;
-          break;
-        case 't':
-          qh_option(qh, "Ftriangles", NULL, NULL);
-          qh_appendprint(qh, qh_PRINTtriangles);
-          break;
-        case 'v':
-          /* option set in qh_initqhull_globals */
-          qh_appendprint(qh, qh_PRINTvertices);
-          break;
-        case 'V':
-          qh_option(qh, "FVertex-average", NULL, NULL);
-          qh_appendprint(qh, qh_PRINTaverage);
-          break;
-        case 'x':
-          qh_option(qh, "Fxtremes", NULL, NULL);
-          qh_appendprint(qh, qh_PRINTextremes);
-          break;
-        default:
-          s--;
-          qh_fprintf(qh, qh->ferr, 7012, "qhull warning: unknown 'F' output option %c, rest ignored\n", (int)s[0]);
-          while (*++s && !isspace(*s));
-          break;
-        }
-      }
-      break;
-    case 'G':
-      isgeom= True;
-      qh_appendprint(qh, qh_PRINTgeom);
-      while (*s && !isspace(*s)) {
-        switch (*s++) {
-        case 'a':
-          qh_option(qh, "Gall-points", NULL, NULL);
-          qh->PRINTdots= True;
-          break;
-        case 'c':
-          qh_option(qh, "Gcentrums", NULL, NULL);
-          qh->PRINTcentrums= True;
-          break;
-        case 'h':
-          qh_option(qh, "Gintersections", NULL, NULL);
-          qh->DOintersections= True;
-          break;
-        case 'i':
-          qh_option(qh, "Ginner", NULL, NULL);
-          qh->PRINTinner= True;
-          break;
-        case 'n':
-          qh_option(qh, "Gno-planes", NULL, NULL);
-          qh->PRINTnoplanes= True;
-          break;
-        case 'o':
-          qh_option(qh, "Gouter", NULL, NULL);
-          qh->PRINTouter= True;
-          break;
-        case 'p':
-          qh_option(qh, "Gpoints", NULL, NULL);
-          qh->PRINTcoplanar= True;
-          break;
-        case 'r':
-          qh_option(qh, "Gridges", NULL, NULL);
-          qh->PRINTridges= True;
-          break;
-        case 't':
-          qh_option(qh, "Gtransparent", NULL, NULL);
-          qh->PRINTtransparent= True;
-          break;
-        case 'v':
-          qh_option(qh, "Gvertices", NULL, NULL);
-          qh->PRINTspheres= True;
-          break;
-        case 'D':
-          if (!isdigit(*s))
-            qh_fprintf(qh, qh->ferr, 6035, "qhull input error: missing dimension for option 'GDn'\n");
-          else {
-            if (qh->DROPdim >= 0)
-              qh_fprintf(qh, qh->ferr, 7013, "qhull warning: can only drop one dimension.  Previous 'GD%d' ignored\n",
-                   qh->DROPdim);
-            qh->DROPdim= qh_strtol(s, &s);
-            qh_option(qh, "GDrop-dim", &qh->DROPdim, NULL);
-          }
-          break;
-        default:
-          s--;
-          qh_fprintf(qh, qh->ferr, 7014, "qhull warning: unknown 'G' print option %c, rest ignored\n", (int)s[0]);
-          while (*++s && !isspace(*s));
-          break;
-        }
-      }
-      break;
-    case 'P':
-      while (*s && !isspace(*s)) {
-        switch (*s++) {
-        case 'd': case 'D':  /* see qh_initthresholds() */
-          key= s[-1];
-          i= qh_strtol(s, &s);
-          r= 0;
-          if (*s == ':') {
-            s++;
-            r= qh_strtod(s, &s);
-          }
-          if (key == 'd')
-            qh_option(qh, "Pdrop-facets-dim-less", &i, &r);
-          else
-            qh_option(qh, "PDrop-facets-dim-more", &i, &r);
-          break;
-        case 'g':
-          qh_option(qh, "Pgood-facets", NULL, NULL);
-          qh->PRINTgood= True;
-          break;
-        case 'G':
-          qh_option(qh, "PGood-facet-neighbors", NULL, NULL);
-          qh->PRINTneighbors= True;
-          break;
-        case 'o':
-          qh_option(qh, "Poutput-forced", NULL, NULL);
-          qh->FORCEoutput= True;
-          break;
-        case 'p':
-          qh_option(qh, "Pprecision-ignore", NULL, NULL);
-          qh->PRINTprecision= False;
-          break;
-        case 'A':
-          if (!isdigit(*s))
-            qh_fprintf(qh, qh->ferr, 6036, "qhull input error: missing facet count for keep area option 'PAn'\n");
-          else {
-            qh->KEEParea= qh_strtol(s, &s);
-            qh_option(qh, "PArea-keep", &qh->KEEParea, NULL);
-            qh->GETarea= True;
-          }
-          break;
-        case 'F':
-          if (!isdigit(*s))
-            qh_fprintf(qh, qh->ferr, 6037, "qhull input error: missing facet area for option 'PFn'\n");
-          else {
-            qh->KEEPminArea= qh_strtod(s, &s);
-            qh_option(qh, "PFacet-area-keep", NULL, &qh->KEEPminArea);
-            qh->GETarea= True;
-          }
-          break;
-        case 'M':
-          if (!isdigit(*s))
-            qh_fprintf(qh, qh->ferr, 6038, "qhull input error: missing merge count for option 'PMn'\n");
-          else {
-            qh->KEEPmerge= qh_strtol(s, &s);
-            qh_option(qh, "PMerge-keep", &qh->KEEPmerge, NULL);
-          }
-          break;
-        default:
-          s--;
-          qh_fprintf(qh, qh->ferr, 7015, "qhull warning: unknown 'P' print option %c, rest ignored\n", (int)s[0]);
-          while (*++s && !isspace(*s));
-          break;
-        }
-      }
-      break;
-    case 'Q':
-      lastproject= -1;
-      while (*s && !isspace(*s)) {
-        switch (*s++) {
-        case 'b': case 'B':  /* handled by qh_initthresholds */
-          key= s[-1];
-          if (key == 'b' && *s == 'B') {
-            s++;
-            r= qh_DEFAULTbox;
-            qh->SCALEinput= True;
-            qh_option(qh, "QbBound-unit-box", NULL, &r);
-            break;
-          }
-          if (key == 'b' && *s == 'b') {
-            s++;
-            qh->SCALElast= True;
-            qh_option(qh, "Qbbound-last", NULL, NULL);
-            break;
-          }
-          k= qh_strtol(s, &s);
-          r= 0.0;
-          wasproject= False;
-          if (*s == ':') {
-            s++;
-            if ((r= qh_strtod(s, &s)) == 0.0) {
-              t= s;            /* need true dimension for memory allocation */
-              while (*t && !isspace(*t)) {
-                if (toupper(*t++) == 'B'
-                 && k == qh_strtol(t, &t)
-                 && *t++ == ':'
-                 && qh_strtod(t, &t) == 0.0) {
-                  qh->PROJECTinput++;
-                  trace2((qh, qh->ferr, 2004, "qh_initflags: project dimension %d\n", k));
-                  qh_option(qh, "Qb-project-dim", &k, NULL);
-                  wasproject= True;
-                  lastproject= k;
-                  break;
-                }
-              }
-            }
-          }
-          if (!wasproject) {
-            if (lastproject == k && r == 0.0)
-              lastproject= -1;  /* doesn't catch all possible sequences */
-            else if (key == 'b') {
-              qh->SCALEinput= True;
-              if (r == 0.0)
-                r= -qh_DEFAULTbox;
-              qh_option(qh, "Qbound-dim-low", &k, &r);
-            }else {
-              qh->SCALEinput= True;
-              if (r == 0.0)
-                r= qh_DEFAULTbox;
-              qh_option(qh, "QBound-dim-high", &k, &r);
-            }
-          }
-          break;
-        case 'c':
-          qh_option(qh, "Qcoplanar-keep", NULL, NULL);
-          qh->KEEPcoplanar= True;
-          break;
-        case 'f':
-          qh_option(qh, "Qfurthest-outside", NULL, NULL);
-          qh->BESToutside= True;
-          break;
-        case 'g':
-          qh_option(qh, "Qgood-facets-only", NULL, NULL);
-          qh->ONLYgood= True;
-          break;
-        case 'i':
-          qh_option(qh, "Qinterior-keep", NULL, NULL);
-          qh->KEEPinside= True;
-          break;
-        case 'm':
-          qh_option(qh, "Qmax-outside-only", NULL, NULL);
-          qh->ONLYmax= True;
-          break;
-        case 'r':
-          qh_option(qh, "Qrandom-outside", NULL, NULL);
-          qh->RANDOMoutside= True;
-          break;
-        case 's':
-          qh_option(qh, "Qsearch-initial-simplex", NULL, NULL);
-          qh->ALLpoints= True;
-          break;
-        case 't':
-          qh_option(qh, "Qtriangulate", NULL, NULL);
-          qh->TRIangulate= True;
-          break;
-        case 'T':
-          qh_option(qh, "QTestPoints", NULL, NULL);
-          if (!isdigit(*s))
-            qh_fprintf(qh, qh->ferr, 6039, "qhull input error: missing number of test points for option 'QTn'\n");
-          else {
-            qh->TESTpoints= qh_strtol(s, &s);
-            qh_option(qh, "QTestPoints", &qh->TESTpoints, NULL);
-          }
-          break;
-        case 'u':
-          qh_option(qh, "QupperDelaunay", NULL, NULL);
-          qh->UPPERdelaunay= True;
-          break;
-        case 'v':
-          qh_option(qh, "Qvertex-neighbors-convex", NULL, NULL);
-          qh->TESTvneighbors= True;
-          break;
-        case 'x':
-          qh_option(qh, "Qxact-merge", NULL, NULL);
-          qh->MERGEexact= True;
-          break;
-        case 'z':
-          qh_option(qh, "Qz-infinity-point", NULL, NULL);
-          qh->ATinfinity= True;
-          break;
-        case '0':
-          qh_option(qh, "Q0-no-premerge", NULL, NULL);
-          qh->NOpremerge= True;
-          break;
-        case '1':
-          if (!isdigit(*s)) {
-            qh_option(qh, "Q1-no-angle-sort", NULL, NULL);
-            qh->ANGLEmerge= False;
-            break;
-          }
-          switch (*s++) {
-          case '0':
-            qh_option(qh, "Q10-no-narrow", NULL, NULL);
-            qh->NOnarrow= True;
-            break;
-          case '1':
-            qh_option(qh, "Q11-trinormals Qtriangulate", NULL, NULL);
-            qh->TRInormals= True;
-            qh->TRIangulate= True;
-            break;
-          case '2':
-              qh_option(qh, "Q12-no-wide-dup", NULL, NULL);
-              qh->NOwide= True;
-            break;
-          default:
-            s--;
-            qh_fprintf(qh, qh->ferr, 7016, "qhull warning: unknown 'Q' qhull option 1%c, rest ignored\n", (int)s[0]);
-            while (*++s && !isspace(*s));
-            break;
-          }
-          break;
-        case '2':
-          qh_option(qh, "Q2-no-merge-independent", NULL, NULL);
-          qh->MERGEindependent= False;
-          goto LABELcheckdigit;
-          break; /* no warnings */
-        case '3':
-          qh_option(qh, "Q3-no-merge-vertices", NULL, NULL);
-          qh->MERGEvertices= False;
-        LABELcheckdigit:
-          if (isdigit(*s))
-            qh_fprintf(qh, qh->ferr, 7017, "qhull warning: can not follow '1', '2', or '3' with a digit.  '%c' skipped.\n",
-                     *s++);
-          break;
-        case '4':
-          qh_option(qh, "Q4-avoid-old-into-new", NULL, NULL);
-          qh->AVOIDold= True;
-          break;
-        case '5':
-          qh_option(qh, "Q5-no-check-outer", NULL, NULL);
-          qh->SKIPcheckmax= True;
-          break;
-        case '6':
-          qh_option(qh, "Q6-no-concave-merge", NULL, NULL);
-          qh->SKIPconvex= True;
-          break;
-        case '7':
-          qh_option(qh, "Q7-no-breadth-first", NULL, NULL);
-          qh->VIRTUALmemory= True;
-          break;
-        case '8':
-          qh_option(qh, "Q8-no-near-inside", NULL, NULL);
-          qh->NOnearinside= True;
-          break;
-        case '9':
-          qh_option(qh, "Q9-pick-furthest", NULL, NULL);
-          qh->PICKfurthest= True;
-          break;
-        case 'G':
-          i= qh_strtol(s, &t);
-          if (qh->GOODpoint)
-            qh_fprintf(qh, qh->ferr, 7018, "qhull warning: good point already defined for option 'QGn'.  Ignored\n");
-          else if (s == t)
-            qh_fprintf(qh, qh->ferr, 7019, "qhull warning: missing good point id for option 'QGn'.  Ignored\n");
-          else if (i < 0 || *s == '-') {
-            qh->GOODpoint= i-1;
-            qh_option(qh, "QGood-if-dont-see-point", &i, NULL);
-          }else {
-            qh->GOODpoint= i+1;
-            qh_option(qh, "QGood-if-see-point", &i, NULL);
-          }
-          s= t;
-          break;
-        case 'J':
-          if (!isdigit(*s) && *s != '-')
-            qh->JOGGLEmax= 0.0;
-          else {
-            qh->JOGGLEmax= (realT) qh_strtod(s, &s);
-            qh_option(qh, "QJoggle", NULL, &qh->JOGGLEmax);
-          }
-          break;
-        case 'R':
-          if (!isdigit(*s) && *s != '-')
-            qh_fprintf(qh, qh->ferr, 7020, "qhull warning: missing random seed for option 'QRn'.  Ignored\n");
-          else {
-            qh->ROTATErandom= i= qh_strtol(s, &s);
-            if (i > 0)
-              qh_option(qh, "QRotate-id", &i, NULL );
-            else if (i < -1)
-              qh_option(qh, "QRandom-seed", &i, NULL );
-          }
-          break;
-        case 'V':
-          i= qh_strtol(s, &t);
-          if (qh->GOODvertex)
-            qh_fprintf(qh, qh->ferr, 7021, "qhull warning: good vertex already defined for option 'QVn'.  Ignored\n");
-          else if (s == t)
-            qh_fprintf(qh, qh->ferr, 7022, "qhull warning: no good point id given for option 'QVn'.  Ignored\n");
-          else if (i < 0) {
-            qh->GOODvertex= i - 1;
-            qh_option(qh, "QV-good-facets-not-point", &i, NULL);
-          }else {
-            qh_option(qh, "QV-good-facets-point", &i, NULL);
-            qh->GOODvertex= i + 1;
-          }
-          s= t;
-          break;
-        default:
-          s--;
-          qh_fprintf(qh, qh->ferr, 7023, "qhull warning: unknown 'Q' qhull option %c, rest ignored\n", (int)s[0]);
-          while (*++s && !isspace(*s));
-          break;
-        }
-      }
-      break;
-    case 'T':
-      while (*s && !isspace(*s)) {
-        if (isdigit(*s) || *s == '-')
-          qh->IStracing= qh_strtol(s, &s);
-        else switch (*s++) {
-        case 'a':
-          qh_option(qh, "Tannotate-output", NULL, NULL);
-          qh->ANNOTATEoutput= True;
-          break;
-        case 'c':
-          qh_option(qh, "Tcheck-frequently", NULL, NULL);
-          qh->CHECKfrequently= True;
-          break;
-        case 's':
-          qh_option(qh, "Tstatistics", NULL, NULL);
-          qh->PRINTstatistics= True;
-          break;
-        case 'v':
-          qh_option(qh, "Tverify", NULL, NULL);
-          qh->VERIFYoutput= True;
-          break;
-        case 'z':
-          if (qh->ferr == qh_FILEstderr) {
-            /* The C++ interface captures the output in qh_fprint_qhull() */
-            qh_option(qh, "Tz-stdout", NULL, NULL);
-            qh->USEstdout= True;
-          }else if (!qh->fout)
-            qh_fprintf(qh, qh->ferr, 7024, "qhull warning: output file undefined(stdout).  Option 'Tz' ignored.\n");
-          else {
-            qh_option(qh, "Tz-stdout", NULL, NULL);
-            qh->USEstdout= True;
-            qh->ferr= qh->fout;
-            qh->qhmem.ferr= qh->fout;
-          }
-          break;
-        case 'C':
-          if (!isdigit(*s))
-            qh_fprintf(qh, qh->ferr, 7025, "qhull warning: missing point id for cone for trace option 'TCn'.  Ignored\n");
-          else {
-            i= qh_strtol(s, &s);
-            qh_option(qh, "TCone-stop", &i, NULL);
-            qh->STOPcone= i + 1;
-          }
-          break;
-        case 'F':
-          if (!isdigit(*s))
-            qh_fprintf(qh, qh->ferr, 7026, "qhull warning: missing frequency count for trace option 'TFn'.  Ignored\n");
-          else {
-            qh->REPORTfreq= qh_strtol(s, &s);
-            qh_option(qh, "TFacet-log", &qh->REPORTfreq, NULL);
-            qh->REPORTfreq2= qh->REPORTfreq/2;  /* for tracemerging() */
-          }
-          break;
-        case 'I':
-          if (!isspace(*s))
-            qh_fprintf(qh, qh->ferr, 7027, "qhull warning: missing space between 'TI' and filename, %s\n", s);
-          while (isspace(*s))
-            s++;
-          t= qh_skipfilename(qh, s);
-          {
-            char filename[qh_FILENAMElen];
-
-            qh_copyfilename(qh, filename, (int)sizeof(filename), s, (int)(t-s));   /* WARN64 */
-            s= t;
-            if (!freopen(filename, "r", stdin)) {
-              qh_fprintf(qh, qh->ferr, 6041, "qhull error: could not open file \"%s\".", filename);
-              qh_errexit(qh, qh_ERRinput, NULL, NULL);
-            }else {
-              qh_option(qh, "TInput-file", NULL, NULL);
-              qh_option(qh, filename, NULL, NULL);
-            }
-          }
-          break;
-        case 'O':
-            if (!isspace(*s))
-                qh_fprintf(qh, qh->ferr, 7028, "qhull warning: missing space between 'TO' and filename, %s\n", s);
-            while (isspace(*s))
-                s++;
-            t= qh_skipfilename(qh, s);
-            {
-              char filename[qh_FILENAMElen];
-
-              qh_copyfilename(qh, filename, (int)sizeof(filename), s, (int)(t-s));  /* WARN64 */
-              s= t;
-              if (!qh->fout) {
-                qh_fprintf(qh, qh->ferr, 6266, "qhull input warning: qh.fout was not set by caller.  Cannot use option 'TO' to redirect output.  Ignoring option 'TO'\n");
-              }else if (!freopen(filename, "w", qh->fout)) {
-                qh_fprintf(qh, qh->ferr, 6044, "qhull error: could not open file \"%s\".", filename);
-                qh_errexit(qh, qh_ERRinput, NULL, NULL);
-              }else {
-                qh_option(qh, "TOutput-file", NULL, NULL);
-              qh_option(qh, filename, NULL, NULL);
-            }
-          }
-          break;
-        case 'P':
-          if (!isdigit(*s))
-            qh_fprintf(qh, qh->ferr, 7029, "qhull warning: missing point id for trace option 'TPn'.  Ignored\n");
-          else {
-            qh->TRACEpoint= qh_strtol(s, &s);
-            qh_option(qh, "Trace-point", &qh->TRACEpoint, NULL);
-          }
-          break;
-        case 'M':
-          if (!isdigit(*s))
-            qh_fprintf(qh, qh->ferr, 7030, "qhull warning: missing merge id for trace option 'TMn'.  Ignored\n");
-          else {
-            qh->TRACEmerge= qh_strtol(s, &s);
-            qh_option(qh, "Trace-merge", &qh->TRACEmerge, NULL);
-          }
-          break;
-        case 'R':
-          if (!isdigit(*s))
-            qh_fprintf(qh, qh->ferr, 7031, "qhull warning: missing rerun count for trace option 'TRn'.  Ignored\n");
-          else {
-            qh->RERUN= qh_strtol(s, &s);
-            qh_option(qh, "TRerun", &qh->RERUN, NULL);
-          }
-          break;
-        case 'V':
-          i= qh_strtol(s, &t);
-          if (s == t)
-            qh_fprintf(qh, qh->ferr, 7032, "qhull warning: missing furthest point id for trace option 'TVn'.  Ignored\n");
-          else if (i < 0) {
-            qh->STOPpoint= i - 1;
-            qh_option(qh, "TV-stop-before-point", &i, NULL);
-          }else {
-            qh->STOPpoint= i + 1;
-            qh_option(qh, "TV-stop-after-point", &i, NULL);
-          }
-          s= t;
-          break;
-        case 'W':
-          if (!isdigit(*s))
-            qh_fprintf(qh, qh->ferr, 7033, "qhull warning: missing max width for trace option 'TWn'.  Ignored\n");
-          else {
-            qh->TRACEdist= (realT) qh_strtod(s, &s);
-            qh_option(qh, "TWide-trace", NULL, &qh->TRACEdist);
-          }
-          break;
-        default:
-          s--;
-          qh_fprintf(qh, qh->ferr, 7034, "qhull warning: unknown 'T' trace option %c, rest ignored\n", (int)s[0]);
-          while (*++s && !isspace(*s));
-          break;
-        }
-      }
-      break;
-    default:
-      qh_fprintf(qh, qh->ferr, 7035, "qhull warning: unknown flag %c(%x)\n", (int)s[-1],
-               (int)s[-1]);
-      break;
-    }
-    if (s-1 == prev_s && *s && !isspace(*s)) {
-      qh_fprintf(qh, qh->ferr, 7036, "qhull warning: missing space after flag %c(%x); reserved for menu. Skipped.\n",
-               (int)*prev_s, (int)*prev_s);
-      while (*s && !isspace(*s))
-        s++;
-    }
-  }
-  if (qh->STOPcone && qh->JOGGLEmax < REALmax/2)
-    qh_fprintf(qh, qh->ferr, 7078, "qhull warning: 'TCn' (stopCone) ignored when used with 'QJn' (joggle)\n");
-  if (isgeom && !qh->FORCEoutput && qh->PRINTout[1])
-    qh_fprintf(qh, qh->ferr, 7037, "qhull warning: additional output formats are not compatible with Geomview\n");
-  /* set derived values in qh_initqhull_globals */
-} /* initflags */
-
-
-/*---------------------------------
-
-  qh_initqhull_buffers(qh)
-    initialize global memory buffers
-
-  notes:
-    must match qh_freebuffers()
-*/
-void qh_initqhull_buffers(qhT *qh) {
-  int k;
-
-  qh->TEMPsize= (qh->qhmem.LASTsize - sizeof(setT))/SETelemsize;
-  if (qh->TEMPsize <= 0 || qh->TEMPsize > qh->qhmem.LASTsize)
-    qh->TEMPsize= 8;  /* e.g., if qh_NOmem */
-  qh->other_points= qh_setnew(qh, qh->TEMPsize);
-  qh->del_vertices= qh_setnew(qh, qh->TEMPsize);
-  qh->coplanarfacetset= qh_setnew(qh, qh->TEMPsize);
-  qh->NEARzero= (realT *)qh_memalloc(qh, qh->hull_dim * sizeof(realT));
-  qh->lower_threshold= (realT *)qh_memalloc(qh, (qh->input_dim+1) * sizeof(realT));
-  qh->upper_threshold= (realT *)qh_memalloc(qh, (qh->input_dim+1) * sizeof(realT));
-  qh->lower_bound= (realT *)qh_memalloc(qh, (qh->input_dim+1) * sizeof(realT));
-  qh->upper_bound= (realT *)qh_memalloc(qh, (qh->input_dim+1) * sizeof(realT));
-  for (k=qh->input_dim+1; k--; ) {  /* duplicated in qh_initqhull_buffers and qh_clear_outputflags */
-    qh->lower_threshold[k]= -REALmax;
-    qh->upper_threshold[k]= REALmax;
-    qh->lower_bound[k]= -REALmax;
-    qh->upper_bound[k]= REALmax;
-  }
-  qh->gm_matrix= (coordT *)qh_memalloc(qh, (qh->hull_dim+1) * qh->hull_dim * sizeof(coordT));
-  qh->gm_row= (coordT **)qh_memalloc(qh, (qh->hull_dim+1) * sizeof(coordT *));
-} /* initqhull_buffers */
-
-/*---------------------------------
-
-  qh_initqhull_globals(qh, points, numpoints, dim, ismalloc )
-    initialize globals
-    if ismalloc
-      points were malloc'd and qhull should free at end
-
-  returns:
-    sets qh.first_point, num_points, input_dim, hull_dim and others
-    seeds random number generator (seed=1 if tracing)
-    modifies qh.hull_dim if ((qh.DELAUNAY and qh.PROJECTdelaunay) or qh.PROJECTinput)
-    adjust user flags as needed
-    also checks DIM3 dependencies and constants
-
-  notes:
-    do not use qh_point() since an input transformation may move them elsewhere
-
-  see:
-    qh_initqhull_start() sets default values for non-zero globals
-
-  design:
-    initialize points array from input arguments
-    test for qh.ZEROcentrum
-      (i.e., use opposite vertex instead of cetrum for convexity testing)
-    initialize qh.CENTERtype, qh.normal_size,
-      qh.center_size, qh.TRACEpoint/level,
-    initialize and test random numbers
-    qh_initqhull_outputflags() -- adjust and test output flags
-*/
-void qh_initqhull_globals(qhT *qh, coordT *points, int numpoints, int dim, boolT ismalloc) {
-  int seed, pointsneeded, extra= 0, i, randi, k;
-  realT randr;
-  realT factorial;
-
-  time_t timedata;
-
-  trace0((qh, qh->ferr, 13, "qh_initqhull_globals: for %s | %s\n", qh->rbox_command,
-      qh->qhull_command));
-  qh->POINTSmalloc= ismalloc;
-  qh->first_point= points;
-  qh->num_points= numpoints;
-  qh->hull_dim= qh->input_dim= dim;
-  if (!qh->NOpremerge && !qh->MERGEexact && !qh->PREmerge && qh->JOGGLEmax > REALmax/2) {
-    qh->MERGING= True;
-    if (qh->hull_dim <= 4) {
-      qh->PREmerge= True;
-      qh_option(qh, "_pre-merge", NULL, NULL);
-    }else {
-      qh->MERGEexact= True;
-      qh_option(qh, "Qxact_merge", NULL, NULL);
-    }
-  }else if (qh->MERGEexact)
-    qh->MERGING= True;
-  if (!qh->NOpremerge && qh->JOGGLEmax > REALmax/2) {
-#ifdef qh_NOmerge
-    qh->JOGGLEmax= 0.0;
-#endif
-  }
-  if (qh->TRIangulate && qh->JOGGLEmax < REALmax/2 && qh->PRINTprecision)
-    qh_fprintf(qh, qh->ferr, 7038, "qhull warning: joggle('QJ') always produces simplicial output.  Triangulated output('Qt') does nothing.\n");
-  if (qh->JOGGLEmax < REALmax/2 && qh->DELAUNAY && !qh->SCALEinput && !qh->SCALElast) {
-    qh->SCALElast= True;
-    qh_option(qh, "Qbbound-last-qj", NULL, NULL);
-  }
-  if (qh->MERGING && !qh->POSTmerge && qh->premerge_cos > REALmax/2
-  && qh->premerge_centrum == 0) {
-    qh->ZEROcentrum= True;
-    qh->ZEROall_ok= True;
-    qh_option(qh, "_zero-centrum", NULL, NULL);
-  }
-  if (qh->JOGGLEmax < REALmax/2 && REALepsilon > 2e-8 && qh->PRINTprecision)
-    qh_fprintf(qh, qh->ferr, 7039, "qhull warning: real epsilon, %2.2g, is probably too large for joggle('QJn')\nRecompile with double precision reals(see user.h).\n",
-          REALepsilon);
-#ifdef qh_NOmerge
-  if (qh->MERGING) {
-    qh_fprintf(qh, qh->ferr, 6045, "qhull input error: merging not installed(qh_NOmerge + 'Qx', 'Cn' or 'An')\n");
-    qh_errexit(qh, qh_ERRinput, NULL, NULL);
-  }
-#endif
-  if (qh->DELAUNAY && qh->KEEPcoplanar && !qh->KEEPinside) {
-    qh->KEEPinside= True;
-    qh_option(qh, "Qinterior-keep", NULL, NULL);
-  }
-  if (qh->DELAUNAY && qh->HALFspace) {
-    qh_fprintf(qh, qh->ferr, 6046, "qhull input error: can not use Delaunay('d') or Voronoi('v') with halfspace intersection('H')\n");
-    qh_errexit(qh, qh_ERRinput, NULL, NULL);
-  }
-  if (!qh->DELAUNAY && (qh->UPPERdelaunay || qh->ATinfinity)) {
-    qh_fprintf(qh, qh->ferr, 6047, "qhull input error: use upper-Delaunay('Qu') or infinity-point('Qz') with Delaunay('d') or Voronoi('v')\n");
-    qh_errexit(qh, qh_ERRinput, NULL, NULL);
-  }
-  if (qh->UPPERdelaunay && qh->ATinfinity) {
-    qh_fprintf(qh, qh->ferr, 6048, "qhull input error: can not use infinity-point('Qz') with upper-Delaunay('Qu')\n");
-    qh_errexit(qh, qh_ERRinput, NULL, NULL);
-  }
-  if (qh->SCALElast && !qh->DELAUNAY && qh->PRINTprecision)
-    qh_fprintf(qh, qh->ferr, 7040, "qhull input warning: option 'Qbb' (scale-last-coordinate) is normally used with 'd' or 'v'\n");
-  qh->DOcheckmax= (!qh->SKIPcheckmax && qh->MERGING );
-  qh->KEEPnearinside= (qh->DOcheckmax && !(qh->KEEPinside && qh->KEEPcoplanar)
-                          && !qh->NOnearinside);
-  if (qh->MERGING)
-    qh->CENTERtype= qh_AScentrum;
-  else if (qh->VORONOI)
-    qh->CENTERtype= qh_ASvoronoi;
-  if (qh->TESTvneighbors && !qh->MERGING) {
-    qh_fprintf(qh, qh->ferr, 6049, "qhull input error: test vertex neighbors('Qv') needs a merge option\n");
-    qh_errexit(qh, qh_ERRinput, NULL ,NULL);
-  }
-  if (qh->PROJECTinput || (qh->DELAUNAY && qh->PROJECTdelaunay)) {
-    qh->hull_dim -= qh->PROJECTinput;
-    if (qh->DELAUNAY) {
-      qh->hull_dim++;
-      if (qh->ATinfinity)
-        extra= 1;
-    }
-  }
-  if (qh->hull_dim <= 1) {
-    qh_fprintf(qh, qh->ferr, 6050, "qhull error: dimension %d must be > 1\n", qh->hull_dim);
-    qh_errexit(qh, qh_ERRinput, NULL, NULL);
-  }
-  for (k=2, factorial=1.0; k < qh->hull_dim; k++)
-    factorial *= k;
-  qh->AREAfactor= 1.0 / factorial;
-  trace2((qh, qh->ferr, 2005, "qh_initqhull_globals: initialize globals.  dim %d numpoints %d malloc? %d projected %d to hull_dim %d\n",
-        dim, numpoints, ismalloc, qh->PROJECTinput, qh->hull_dim));
-  qh->normal_size= qh->hull_dim * sizeof(coordT);
-  qh->center_size= qh->normal_size - sizeof(coordT);
-  pointsneeded= qh->hull_dim+1;
-  if (qh->hull_dim > qh_DIMmergeVertex) {
-    qh->MERGEvertices= False;
-    qh_option(qh, "Q3-no-merge-vertices-dim-high", NULL, NULL);
-  }
-  if (qh->GOODpoint)
-    pointsneeded++;
-#ifdef qh_NOtrace
-  if (qh->IStracing) {
-    qh_fprintf(qh, qh->ferr, 6051, "qhull input error: tracing is not installed(qh_NOtrace in user.h)");
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }
-#endif
-  if (qh->RERUN > 1) {
-    qh->TRACElastrun= qh->IStracing; /* qh_build_withrestart duplicates next conditional */
-    if (qh->IStracing != -1)
-      qh->IStracing= 0;
-  }else if (qh->TRACEpoint != qh_IDunknown || qh->TRACEdist < REALmax/2 || qh->TRACEmerge) {
-    qh->TRACElevel= (qh->IStracing? qh->IStracing : 3);
-    qh->IStracing= 0;
-  }
-  if (qh->ROTATErandom == 0 || qh->ROTATErandom == -1) {
-    seed= (int)time(&timedata);
-    if (qh->ROTATErandom  == -1) {
-      seed= -seed;
-      qh_option(qh, "QRandom-seed", &seed, NULL );
-    }else
-      qh_option(qh, "QRotate-random", &seed, NULL);
-    qh->ROTATErandom= seed;
-  }
-  seed= qh->ROTATErandom;
-  if (seed == INT_MIN)    /* default value */
-    seed= 1;
-  else if (seed < 0)
-    seed= -seed;
-  qh_RANDOMseed_(qh, seed);
-  randr= 0.0;
-  for (i=1000; i--; ) {
-    randi= qh_RANDOMint;
-    randr += randi;
-    if (randi > qh_RANDOMmax) {
-      qh_fprintf(qh, qh->ferr, 8036, "\
-qhull configuration error (qh_RANDOMmax in user.h):\n\
-   random integer %d > qh_RANDOMmax(qh, %.8g)\n",
-               randi, qh_RANDOMmax);
-      qh_errexit(qh, qh_ERRinput, NULL, NULL);
-    }
-  }
-  qh_RANDOMseed_(qh, seed);
-  randr = randr/1000;
-  if (randr < qh_RANDOMmax * 0.1
-  || randr > qh_RANDOMmax * 0.9)
-    qh_fprintf(qh, qh->ferr, 8037, "\
-qhull configuration warning (qh_RANDOMmax in user.h):\n\
-   average of 1000 random integers (%.2g) is much different than expected (%.2g).\n\
-   Is qh_RANDOMmax (%.2g) wrong?\n",
-             randr, qh_RANDOMmax * 0.5, qh_RANDOMmax);
-  qh->RANDOMa= 2.0 * qh->RANDOMfactor/qh_RANDOMmax;
-  qh->RANDOMb= 1.0 - qh->RANDOMfactor;
-  if (qh_HASHfactor < 1.1) {
-    qh_fprintf(qh, qh->ferr, 6052, "qhull internal error (qh_initqhull_globals): qh_HASHfactor %d must be at least 1.1.  Qhull uses linear hash probing\n",
-      qh_HASHfactor);
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }
-  if (numpoints+extra < pointsneeded) {
-    qh_fprintf(qh, qh->ferr, 6214, "qhull input error: not enough points(%d) to construct initial simplex (need %d)\n",
-            numpoints, pointsneeded);
-    qh_errexit(qh, qh_ERRinput, NULL, NULL);
-  }
-  qh_initqhull_outputflags(qh);
-} /* initqhull_globals */
-
-/*---------------------------------
-
-  qh_initqhull_mem(qh, )
-    initialize mem_r.c for qhull
-    qh.hull_dim and qh.normal_size determine some of the allocation sizes
-    if qh.MERGING,
-      includes ridgeT
-    calls qh_user_memsizes(qh) to add up to 10 additional sizes for quick allocation
-      (see numsizes below)
-
-  returns:
-    mem_r.c already for qh_memalloc/qh_memfree (errors if called beforehand)
-
-  notes:
-    qh_produceoutput() prints memsizes
-
-*/
-void qh_initqhull_mem(qhT *qh) {
-  int numsizes;
-  int i;
-
-  numsizes= 8+10;
-  qh_meminitbuffers(qh, qh->IStracing, qh_MEMalign, numsizes,
-                     qh_MEMbufsize, qh_MEMinitbuf);
-  qh_memsize(qh, (int)sizeof(vertexT));
-  if (qh->MERGING) {
-    qh_memsize(qh, (int)sizeof(ridgeT));
-    qh_memsize(qh, (int)sizeof(mergeT));
-  }
-  qh_memsize(qh, (int)sizeof(facetT));
-  i= sizeof(setT) + (qh->hull_dim - 1) * SETelemsize;  /* ridge.vertices */
-  qh_memsize(qh, i);
-  qh_memsize(qh, qh->normal_size);        /* normal */
-  i += SETelemsize;                 /* facet.vertices, .ridges, .neighbors */
-  qh_memsize(qh, i);
-  qh_user_memsizes(qh);
-  qh_memsetup(qh);
-} /* initqhull_mem */
-
-/*---------------------------------
-
-  qh_initqhull_outputflags
-    initialize flags concerned with output
-
-  returns:
-    adjust user flags as needed
-
-  see:
-    qh_clear_outputflags() resets the flags
-
-  design:
-    test for qh.PRINTgood (i.e., only print 'good' facets)
-    check for conflicting print output options
-*/
-void qh_initqhull_outputflags(qhT *qh) {
-  boolT printgeom= False, printmath= False, printcoplanar= False;
-  int i;
-
-  trace3((qh, qh->ferr, 3024, "qh_initqhull_outputflags: %s\n", qh->qhull_command));
-  if (!(qh->PRINTgood || qh->PRINTneighbors)) {
-    if (qh->KEEParea || qh->KEEPminArea < REALmax/2 || qh->KEEPmerge || qh->DELAUNAY
-        || (!qh->ONLYgood && (qh->GOODvertex || qh->GOODpoint))) {
-      qh->PRINTgood= True;
-      qh_option(qh, "Pgood", NULL, NULL);
-    }
-  }
-  if (qh->PRINTtransparent) {
-    if (qh->hull_dim != 4 || !qh->DELAUNAY || qh->VORONOI || qh->DROPdim >= 0) {
-      qh_fprintf(qh, qh->ferr, 6215, "qhull input error: transparent Delaunay('Gt') needs 3-d Delaunay('d') w/o 'GDn'\n");
-      qh_errexit(qh, qh_ERRinput, NULL, NULL);
-    }
-    qh->DROPdim = 3;
-    qh->PRINTridges = True;
-  }
-  for (i=qh_PRINTEND; i--; ) {
-    if (qh->PRINTout[i] == qh_PRINTgeom)
-      printgeom= True;
-    else if (qh->PRINTout[i] == qh_PRINTmathematica || qh->PRINTout[i] == qh_PRINTmaple)
-      printmath= True;
-    else if (qh->PRINTout[i] == qh_PRINTcoplanars)
-      printcoplanar= True;
-    else if (qh->PRINTout[i] == qh_PRINTpointnearest)
-      printcoplanar= True;
-    else if (qh->PRINTout[i] == qh_PRINTpointintersect && !qh->HALFspace) {
-      qh_fprintf(qh, qh->ferr, 6053, "qhull input error: option 'Fp' is only used for \nhalfspace intersection('Hn,n,n').\n");
-      qh_errexit(qh, qh_ERRinput, NULL, NULL);
-    }else if (qh->PRINTout[i] == qh_PRINTtriangles && (qh->HALFspace || qh->VORONOI)) {
-      qh_fprintf(qh, qh->ferr, 6054, "qhull input error: option 'Ft' is not available for Voronoi vertices or halfspace intersection\n");
-      qh_errexit(qh, qh_ERRinput, NULL, NULL);
-    }else if (qh->PRINTout[i] == qh_PRINTcentrums && qh->VORONOI) {
-      qh_fprintf(qh, qh->ferr, 6055, "qhull input error: option 'FC' is not available for Voronoi vertices('v')\n");
-      qh_errexit(qh, qh_ERRinput, NULL, NULL);
-    }else if (qh->PRINTout[i] == qh_PRINTvertices) {
-      if (qh->VORONOI)
-        qh_option(qh, "Fvoronoi", NULL, NULL);
-      else
-        qh_option(qh, "Fvertices", NULL, NULL);
-    }
-  }
-  if (printcoplanar && qh->DELAUNAY && qh->JOGGLEmax < REALmax/2) {
-    if (qh->PRINTprecision)
-      qh_fprintf(qh, qh->ferr, 7041, "qhull input warning: 'QJ' (joggle) will usually prevent coincident input sites for options 'Fc' and 'FP'\n");
-  }
-  if (printmath && (qh->hull_dim > 3 || qh->VORONOI)) {
-    qh_fprintf(qh, qh->ferr, 6056, "qhull input error: Mathematica and Maple output is only available for 2-d and 3-d convex hulls and 2-d Delaunay triangulations\n");
-    qh_errexit(qh, qh_ERRinput, NULL, NULL);
-  }
-  if (printgeom) {
-    if (qh->hull_dim > 4) {
-      qh_fprintf(qh, qh->ferr, 6057, "qhull input error: Geomview output is only available for 2-d, 3-d and 4-d\n");
-      qh_errexit(qh, qh_ERRinput, NULL, NULL);
-    }
-    if (qh->PRINTnoplanes && !(qh->PRINTcoplanar + qh->PRINTcentrums
-     + qh->PRINTdots + qh->PRINTspheres + qh->DOintersections + qh->PRINTridges)) {
-      qh_fprintf(qh, qh->ferr, 6058, "qhull input error: no output specified for Geomview\n");
-      qh_errexit(qh, qh_ERRinput, NULL, NULL);
-    }
-    if (qh->VORONOI && (qh->hull_dim > 3 || qh->DROPdim >= 0)) {
-      qh_fprintf(qh, qh->ferr, 6059, "qhull input error: Geomview output for Voronoi diagrams only for 2-d\n");
-      qh_errexit(qh, qh_ERRinput, NULL, NULL);
-    }
-    /* can not warn about furthest-site Geomview output: no lower_threshold */
-    if (qh->hull_dim == 4 && qh->DROPdim == -1 &&
-        (qh->PRINTcoplanar || qh->PRINTspheres || qh->PRINTcentrums)) {
-      qh_fprintf(qh, qh->ferr, 7042, "qhull input warning: coplanars, vertices, and centrums output not\n\
-available for 4-d output(ignored).  Could use 'GDn' instead.\n");
-      qh->PRINTcoplanar= qh->PRINTspheres= qh->PRINTcentrums= False;
-    }
-  }
-  if (!qh->KEEPcoplanar && !qh->KEEPinside && !qh->ONLYgood) {
-    if ((qh->PRINTcoplanar && qh->PRINTspheres) || printcoplanar) {
-      if (qh->QHULLfinished) {
-        qh_fprintf(qh, qh->ferr, 7072, "qhull output warning: ignoring coplanar points, option 'Qc' was not set for the first run of qhull.\n");
-      }else {
-        qh->KEEPcoplanar = True;
-        qh_option(qh, "Qcoplanar", NULL, NULL);
-      }
-    }
-  }
-  qh->PRINTdim= qh->hull_dim;
-  if (qh->DROPdim >=0) {    /* after Geomview checks */
-    if (qh->DROPdim < qh->hull_dim) {
-      qh->PRINTdim--;
-      if (!printgeom || qh->hull_dim < 3)
-        qh_fprintf(qh, qh->ferr, 7043, "qhull input warning: drop dimension 'GD%d' is only available for 3-d/4-d Geomview\n", qh->DROPdim);
-    }else
-      qh->DROPdim= -1;
-  }else if (qh->VORONOI) {
-    qh->DROPdim= qh->hull_dim-1;
-    qh->PRINTdim= qh->hull_dim-1;
-  }
-} /* qh_initqhull_outputflags */
-
-/*---------------------------------
-
-  qh_initqhull_start(qh, infile, outfile, errfile )
-    allocate memory if needed and call qh_initqhull_start2()
-*/
-void qh_initqhull_start(qhT *qh, FILE *infile, FILE *outfile, FILE *errfile) {
-
-  qh_initstatistics(qh);
-  qh_initqhull_start2(qh, infile, outfile, errfile);
-} /* initqhull_start */
-
-/*---------------------------------
-
-  qh_initqhull_start2(qh, infile, outfile, errfile )
-    start initialization of qhull
-    initialize statistics, stdio, default values for global variables
-    assumes qh is allocated
-  notes:
-    report errors elsewhere, error handling and g_qhull_output [Qhull.cpp, QhullQh()] not in initialized
-  see:
-    qh_maxmin() determines the precision constants
-    qh_freeqhull()
-*/
-void qh_initqhull_start2(qhT *qh, FILE *infile, FILE *outfile, FILE *errfile) {
-  time_t timedata;
-  int seed;
-
-  qh_CPUclock; /* start the clock(for qh_clock).  One-shot. */
-  /* memset is the same in qh_freeqhull() and qh_initqhull_start2() */
-  memset((char *)qh, 0, sizeof(qhT)-sizeof(qhmemT)-sizeof(qhstatT));   /* every field is 0, FALSE, NULL */
-  qh->NOerrexit= True;
-  qh->ANGLEmerge= True;
-  qh->DROPdim= -1;
-  qh->ferr= errfile;
-  qh->fin= infile;
-  qh->fout= outfile;
-  qh->furthest_id= qh_IDunknown;
-  qh->JOGGLEmax= REALmax;
-  qh->KEEPminArea = REALmax;
-  qh->last_low= REALmax;
-  qh->last_high= REALmax;
-  qh->last_newhigh= REALmax;
-  qh->last_random= 1;
-  qh->max_outside= 0.0;
-  qh->max_vertex= 0.0;
-  qh->MAXabs_coord= 0.0;
-  qh->MAXsumcoord= 0.0;
-  qh->MAXwidth= -REALmax;
-  qh->MERGEindependent= True;
-  qh->MINdenom_1= fmax_(1.0/REALmax, REALmin); /* used by qh_scalepoints */
-  qh->MINoutside= 0.0;
-  qh->MINvisible= REALmax;
-  qh->MAXcoplanar= REALmax;
-  qh->outside_err= REALmax;
-  qh->premerge_centrum= 0.0;
-  qh->premerge_cos= REALmax;
-  qh->PRINTprecision= True;
-  qh->PRINTradius= 0.0;
-  qh->postmerge_cos= REALmax;
-  qh->postmerge_centrum= 0.0;
-  qh->ROTATErandom= INT_MIN;
-  qh->MERGEvertices= True;
-  qh->totarea= 0.0;
-  qh->totvol= 0.0;
-  qh->TRACEdist= REALmax;
-  qh->TRACEpoint= qh_IDunknown; /* recompile or use 'TPn' */
-  qh->tracefacet_id= UINT_MAX;  /* recompile to trace a facet */
-  qh->tracevertex_id= UINT_MAX; /* recompile to trace a vertex */
-  seed= (int)time(&timedata);
-  qh_RANDOMseed_(qh, seed);
-  qh->run_id= qh_RANDOMint;
-  if(!qh->run_id)
-      qh->run_id++;  /* guarantee non-zero */
-  qh_option(qh, "run-id", &qh->run_id, NULL);
-  strcat(qh->qhull, "qhull");
-} /* initqhull_start2 */
-
-/*---------------------------------
-
-  qh_initthresholds(qh, commandString )
-    set thresholds for printing and scaling from commandString
-
-  returns:
-    sets qh.GOODthreshold or qh.SPLITthreshold if 'Pd0D1' used
-
-  see:
-    qh_initflags(), 'Qbk' 'QBk' 'Pdk' and 'PDk'
-    qh_inthresholds()
-
-  design:
-    for each 'Pdn' or 'PDn' option
-      check syntax
-      set qh.lower_threshold or qh.upper_threshold
-    set qh.GOODthreshold if an unbounded threshold is used
-    set qh.SPLITthreshold if a bounded threshold is used
-*/
-void qh_initthresholds(qhT *qh, char *command) {
-  realT value;
-  int idx, maxdim, k;
-  char *s= command; /* non-const due to strtol */
-  char key;
-
-  maxdim= qh->input_dim;
-  if (qh->DELAUNAY && (qh->PROJECTdelaunay || qh->PROJECTinput))
-    maxdim++;
-  while (*s) {
-    if (*s == '-')
-      s++;
-    if (*s == 'P') {
-      s++;
-      while (*s && !isspace(key= *s++)) {
-        if (key == 'd' || key == 'D') {
-          if (!isdigit(*s)) {
-            qh_fprintf(qh, qh->ferr, 7044, "qhull warning: no dimension given for Print option '%c' at: %s.  Ignored\n",
-                    key, s-1);
-            continue;
-          }
-          idx= qh_strtol(s, &s);
-          if (idx >= qh->hull_dim) {
-            qh_fprintf(qh, qh->ferr, 7045, "qhull warning: dimension %d for Print option '%c' is >= %d.  Ignored\n",
-                idx, key, qh->hull_dim);
-            continue;
-          }
-          if (*s == ':') {
-            s++;
-            value= qh_strtod(s, &s);
-            if (fabs((double)value) > 1.0) {
-              qh_fprintf(qh, qh->ferr, 7046, "qhull warning: value %2.4g for Print option %c is > +1 or < -1.  Ignored\n",
-                      value, key);
-              continue;
-            }
-          }else
-            value= 0.0;
-          if (key == 'd')
-            qh->lower_threshold[idx]= value;
-          else
-            qh->upper_threshold[idx]= value;
-        }
-      }
-    }else if (*s == 'Q') {
-      s++;
-      while (*s && !isspace(key= *s++)) {
-        if (key == 'b' && *s == 'B') {
-          s++;
-          for (k=maxdim; k--; ) {
-            qh->lower_bound[k]= -qh_DEFAULTbox;
-            qh->upper_bound[k]= qh_DEFAULTbox;
-          }
-        }else if (key == 'b' && *s == 'b')
-          s++;
-        else if (key == 'b' || key == 'B') {
-          if (!isdigit(*s)) {
-            qh_fprintf(qh, qh->ferr, 7047, "qhull warning: no dimension given for Qhull option %c.  Ignored\n",
-                    key);
-            continue;
-          }
-          idx= qh_strtol(s, &s);
-          if (idx >= maxdim) {
-            qh_fprintf(qh, qh->ferr, 7048, "qhull warning: dimension %d for Qhull option %c is >= %d.  Ignored\n",
-                idx, key, maxdim);
-            continue;
-          }
-          if (*s == ':') {
-            s++;
-            value= qh_strtod(s, &s);
-          }else if (key == 'b')
-            value= -qh_DEFAULTbox;
-          else
-            value= qh_DEFAULTbox;
-          if (key == 'b')
-            qh->lower_bound[idx]= value;
-          else
-            qh->upper_bound[idx]= value;
-        }
-      }
-    }else {
-      while (*s && !isspace(*s))
-        s++;
-    }
-    while (isspace(*s))
-      s++;
-  }
-  for (k=qh->hull_dim; k--; ) {
-    if (qh->lower_threshold[k] > -REALmax/2) {
-      qh->GOODthreshold= True;
-      if (qh->upper_threshold[k] < REALmax/2) {
-        qh->SPLITthresholds= True;
-        qh->GOODthreshold= False;
-        break;
-      }
-    }else if (qh->upper_threshold[k] < REALmax/2)
-      qh->GOODthreshold= True;
-  }
-} /* initthresholds */
-
-/*---------------------------------
-
-  qh_lib_check( qhullLibraryType, qhTsize, vertexTsize, ridgeTsize, facetTsize, setTsize, qhmemTsize )
-    Report error if library does not agree with caller
-
-  notes:
-    NOerrors -- qh_lib_check can not call qh_errexit()
-*/
-void qh_lib_check(int qhullLibraryType, int qhTsize, int vertexTsize, int ridgeTsize, int facetTsize, int setTsize, int qhmemTsize) {
-    boolT iserror= False;
-
-#if defined(_MSC_VER) && defined(_DEBUG) && defined(QHULL_CRTDBG)  /* user_r.h */
-    // _CrtSetBreakAlloc(744);  /* Break at memalloc {744}, or 'watch' _crtBreakAlloc */
-    _CrtSetDbgFlag( _CRTDBG_ALLOC_MEM_DF | _CRTDBG_DELAY_FREE_MEM_DF | _CRTDBG_LEAK_CHECK_DF | _CrtSetDbgFlag(_CRTDBG_REPORT_FLAG) );
-    _CrtSetReportMode( _CRT_ERROR, _CRTDBG_MODE_FILE | _CRTDBG_MODE_DEBUG );
-    _CrtSetReportFile( _CRT_ERROR, _CRTDBG_FILE_STDERR );
-    _CrtSetReportMode( _CRT_WARN, _CRTDBG_MODE_FILE | _CRTDBG_MODE_DEBUG );
-    _CrtSetReportFile( _CRT_WARN, _CRTDBG_FILE_STDERR );
-    _CrtSetReportMode( _CRT_ASSERT, _CRTDBG_MODE_FILE | _CRTDBG_MODE_DEBUG );
-    _CrtSetReportFile( _CRT_ASSERT, _CRTDBG_FILE_STDERR );
-#endif
-
-    if (qhullLibraryType==QHULL_NON_REENTRANT) { /* 0 */
-        qh_fprintf_stderr(6257, "qh_lib_check: Incorrect qhull library called.  Caller uses non-reentrant Qhull with a static qhT.  Library is reentrant.\n");
-        iserror= True;
-    }else if (qhullLibraryType==QHULL_QH_POINTER) { /* 1 */
-        qh_fprintf_stderr(6258, "qh_lib_check: Incorrect qhull library called.  Caller uses non-reentrant Qhull with a dynamic qhT via qh_QHpointer.  Library is reentrant.\n");
-        iserror= True;
-    }else if (qhullLibraryType!=QHULL_REENTRANT) { /* 2 */
-        qh_fprintf_stderr(6262, "qh_lib_check: Expecting qhullLibraryType QHULL_NON_REENTRANT(0), QHULL_QH_POINTER(1), or QHULL_REENTRANT(2).  Got %d\n", qhullLibraryType);
-        iserror= True;
-    }
-    if (qhTsize != sizeof(qhT)) {
-        qh_fprintf_stderr(6249, "qh_lib_check: Incorrect qhull library called.  Size of qhT for caller is %d, but for library is %d.\n", qhTsize, sizeof(qhT));
-        iserror= True;
-    }
-    if (vertexTsize != sizeof(vertexT)) {
-        qh_fprintf_stderr(6250, "qh_lib_check: Incorrect qhull library called.  Size of vertexT for caller is %d, but for library is %d.\n", vertexTsize, sizeof(vertexT));
-        iserror= True;
-    }
-    if (ridgeTsize != sizeof(ridgeT)) {
-        qh_fprintf_stderr(6251, "qh_lib_check: Incorrect qhull library called.  Size of ridgeT for caller is %d, but for library is %d.\n", ridgeTsize, sizeof(ridgeT));
-        iserror= True;
-    }
-    if (facetTsize != sizeof(facetT)) {
-        qh_fprintf_stderr(6252, "qh_lib_check: Incorrect qhull library called.  Size of facetT for caller is %d, but for library is %d.\n", facetTsize, sizeof(facetT));
-        iserror= True;
-    }
-    if (setTsize && setTsize != sizeof(setT)) {
-        qh_fprintf_stderr(6253, "qh_lib_check: Incorrect qhull library called.  Size of setT for caller is %d, but for library is %d.\n", setTsize, sizeof(setT));
-        iserror= True;
-    }
-    if (qhmemTsize && qhmemTsize != sizeof(qhmemT)) {
-        qh_fprintf_stderr(6254, "qh_lib_check: Incorrect qhull library called.  Size of qhmemT for caller is %d, but for library is %d.\n", qhmemTsize, sizeof(qhmemT));
-        iserror= True;
-    }
-    if (iserror) {
-        qh_fprintf_stderr(6259, "qh_lib_check: Cannot continue.  Library '%s' is reentrant (e.g., qhull_r.so)\n", qh_version2);
-        qh_exit(qh_ERRqhull);  /* can not use qh_errexit() */
-    }
-} /* lib_check */
-
-/*---------------------------------
-
-  qh_option(qh, option, intVal, realVal )
-    add an option description to qh.qhull_options
-
-  notes:
-    NOerrors -- qh_option can not call qh_errexit() [qh_initqhull_start2]
-    will be printed with statistics ('Ts') and errors
-    strlen(option) < 40
-*/
-void qh_option(qhT *qh, const char *option, int *i, realT *r) {
-  char buf[200];
-  int len, maxlen;
-
-  sprintf(buf, "  %s", option);
-  if (i)
-    sprintf(buf+strlen(buf), " %d", *i);
-  if (r)
-    sprintf(buf+strlen(buf), " %2.2g", *r);
-  len= (int)strlen(buf);  /* WARN64 */
-  qh->qhull_optionlen += len;
-  maxlen= sizeof(qh->qhull_options) - len -1;
-  maximize_(maxlen, 0);
-  if (qh->qhull_optionlen >= qh_OPTIONline && maxlen > 0) {
-    qh->qhull_optionlen= len;
-    strncat(qh->qhull_options, "\n", (size_t)(maxlen--));
-  }
-  strncat(qh->qhull_options, buf, (size_t)maxlen);
-} /* option */
-
-/*---------------------------------
-
-  qh_zero( qh, errfile )
-    Initialize and zero Qhull's memory for qh_new_qhull()
-
-  notes:
-    Not needed in global.c because static variables are initialized to zero
-*/
-void qh_zero(qhT *qh, FILE *errfile) {
-    memset((char *)qh, 0, sizeof(qhT));   /* every field is 0, FALSE, NULL */
-    qh->NOerrexit= True;
-    qh_meminit(qh, errfile);
-} /* zero */
-
diff --git a/C/halfspaces.c b/C/halfspaces.c
deleted file mode 100644
--- a/C/halfspaces.c
+++ /dev/null
@@ -1,68 +0,0 @@
-#define qh_QHimport
-#include "qhull_ra.h"
-
-double** intersections(
-  double*   halfspaces,
-  double*   interiorpoint,
-  unsigned  dim,
-  unsigned  n,
-  unsigned* nintersections,
-  unsigned* exitcode,
-  unsigned  print
-)
-{
-  char opts[250];
-  sprintf(opts, "qhull s Fp FF H H%f", interiorpoint[0]); //, interiorpoint[1] , interiorpoint[2]);
-  for(unsigned i=1; i < dim; i++){
-    char x[20];
-    sprintf(x, ",%f", interiorpoint[i]);
-    strcat(opts, x);
-  }
-  printf(opts); printf("\n");
-
-  qhT qh_qh; /* Qhull's data structure */
-  qhT* qh= &qh_qh;
-  QHULL_LIB_CHECK
-  qh_meminit(qh, stderr);
-  boolT ismalloc  = False; /* True if qhull should free points in qh_freeqhull() or reallocation */
-  FILE *errfile   = NULL;
-  FILE* outfile = print ? stdout : NULL;
-  qh_zero(qh, errfile);
-  *exitcode = qh_new_qhull(qh, dim+1, n, halfspaces, ismalloc, opts, outfile,
-                           errfile);
-  printf("exitcode: %u\n", *exitcode);
-
-  double** out;
-  if(!(*exitcode)){
-    *nintersections = qh->num_facets;
-    out = malloc(*nintersections * sizeof(double*));
-    facetT *facet;
-    unsigned i_facet = 0;
-    FORALLfacets{
-      if(facet->offset != 0){
-        out[i_facet] = malloc(dim * sizeof(double));
-        for(unsigned i=0; i < dim; i++){
-          out[i_facet][i] = - facet->normal[i] / facet->offset +
-                            qh->feasible_point[i]; // = interiorpoint ? yes
-        }
-        i_facet++;
-      }else{
-        (*nintersections)--;
-      }
-    }
-
-  }
-
-  /* Do cleanup regardless of whether there is an error */
-  int curlong, totlong;
-  qh_freeqhull(qh, !qh_ALL);                /* free long memory */
-  qh_memfreeshort(qh, &curlong, &totlong);  /* free short memory and memory allocator */
-
-  if(*exitcode){
-    free(out);
-    return 0;
-  }else{
-    return out;
-  }
-
-}
diff --git a/C/io_r.c b/C/io_r.c
deleted file mode 100644
--- a/C/io_r.c
+++ /dev/null
@@ -1,4062 +0,0 @@
-/*
  ---------------------------------
-
-   io_r.c
-   Input/Output routines of qhull application
-
-   see qh-io_r.htm and io_r.h
-
-   see user_r.c for qh_errprint and qh_printfacetlist
-
-   unix_r.c calls qh_readpoints and qh_produce_output
-
-   unix_r.c and user_r.c are the only callers of io_r.c functions
-   This allows the user to avoid loading io_r.o from qhull.a
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull_r/io_r.c#4 $$Change: 2064 $
-   $DateTime: 2016/01/18 12:36:08 $$Author: bbarber $
-*/
-
-#include "qhull_ra.h"
-
-/*========= -functions in alphabetical order after qh_produce_output(qh)  =====*/
-
-/*---------------------------------
-
-  qh_produce_output(qh)
-  qh_produce_output2(qh)
-    prints out the result of qhull in desired format
-    qh_produce_output2(qh) does not call qh_prepare_output(qh)
-    if qh.GETarea
-      computes and prints area and volume
-    qh.PRINTout[] is an array of output formats
-
-  notes:
-    prints output in qh.PRINTout order
-*/
-void qh_produce_output(qhT *qh) {
-    int tempsize= qh_setsize(qh, qh->qhmem.tempstack);
-
-    qh_prepare_output(qh);
-    qh_produce_output2(qh);
-    if (qh_setsize(qh, qh->qhmem.tempstack) != tempsize) {
-        qh_fprintf(qh, qh->ferr, 6206, "qhull internal error (qh_produce_output): temporary sets not empty(%d)\n",
-            qh_setsize(qh, qh->qhmem.tempstack));
-        qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-    }
-} /* produce_output */
-
-
-void qh_produce_output2(qhT *qh) {
-  int i, tempsize= qh_setsize(qh, qh->qhmem.tempstack), d_1;
-
-  if (qh->PRINTsummary)
-    qh_printsummary(qh, qh->ferr);
-  else if (qh->PRINTout[0] == qh_PRINTnone)
-    qh_printsummary(qh, qh->fout);
-  for (i=0; i < qh_PRINTEND; i++)
-    qh_printfacets(qh, qh->fout, qh->PRINTout[i], qh->facet_list, NULL, !qh_ALL);
-  qh_allstatistics(qh);
-  if (qh->PRINTprecision && !qh->MERGING && (qh->JOGGLEmax > REALmax/2 || qh->RERUN))
-    qh_printstats(qh, qh->ferr, qh->qhstat.precision, NULL);
-  if (qh->VERIFYoutput && (zzval_(Zridge) > 0 || zzval_(Zridgemid) > 0))
-    qh_printstats(qh, qh->ferr, qh->qhstat.vridges, NULL);
-  if (qh->PRINTstatistics) {
-    qh_printstatistics(qh, qh->ferr, "");
-    qh_memstatistics(qh, qh->ferr);
-    d_1= sizeof(setT) + (qh->hull_dim - 1) * SETelemsize;
-    qh_fprintf(qh, qh->ferr, 8040, "\
-    size in bytes: merge %d ridge %d vertex %d facet %d\n\
-         normal %d ridge vertices %d facet vertices or neighbors %d\n",
-            (int)sizeof(mergeT), (int)sizeof(ridgeT),
-            (int)sizeof(vertexT), (int)sizeof(facetT),
-            qh->normal_size, d_1, d_1 + SETelemsize);
-  }
-  if (qh_setsize(qh, qh->qhmem.tempstack) != tempsize) {
-    qh_fprintf(qh, qh->ferr, 6065, "qhull internal error (qh_produce_output2): temporary sets not empty(%d)\n",
-             qh_setsize(qh, qh->qhmem.tempstack));
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }
-} /* produce_output2 */
-
-/*---------------------------------
-
-  qh_dfacet(qh, id )
-    print facet by id, for debugging
-
-*/
-void qh_dfacet(qhT *qh, unsigned id) {
-  facetT *facet;
-
-  FORALLfacets {
-    if (facet->id == id) {
-      qh_printfacet(qh, qh->fout, facet);
-      break;
-    }
-  }
-} /* dfacet */
-
-
-/*---------------------------------
-
-  qh_dvertex(qh, id )
-    print vertex by id, for debugging
-*/
-void qh_dvertex(qhT *qh, unsigned id) {
-  vertexT *vertex;
-
-  FORALLvertices {
-    if (vertex->id == id) {
-      qh_printvertex(qh, qh->fout, vertex);
-      break;
-    }
-  }
-} /* dvertex */
-
-
-/*---------------------------------
-
-  qh_compare_facetarea(p1, p2 )
-    used by qsort() to order facets by area
-*/
-int qh_compare_facetarea(const void *p1, const void *p2) {
-  const facetT *a= *((facetT *const*)p1), *b= *((facetT *const*)p2);
-
-  if (!a->isarea)
-    return -1;
-  if (!b->isarea)
-    return 1;
-  if (a->f.area > b->f.area)
-    return 1;
-  else if (a->f.area == b->f.area)
-    return 0;
-  return -1;
-} /* compare_facetarea */
-
-/*---------------------------------
-
-  qh_compare_facetmerge(p1, p2 )
-    used by qsort() to order facets by number of merges
-*/
-int qh_compare_facetmerge(const void *p1, const void *p2) {
-  const facetT *a= *((facetT *const*)p1), *b= *((facetT *const*)p2);
-
-  return(a->nummerge - b->nummerge);
-} /* compare_facetvisit */
-
-/*---------------------------------
-
-  qh_compare_facetvisit(p1, p2 )
-    used by qsort() to order facets by visit id or id
-*/
-int qh_compare_facetvisit(const void *p1, const void *p2) {
-  const facetT *a= *((facetT *const*)p1), *b= *((facetT *const*)p2);
-  int i,j;
-
-  if (!(i= a->visitid))
-    i= 0 - a->id; /* do not convert to int, sign distinguishes id from visitid */
-  if (!(j= b->visitid))
-    j= 0 - b->id;
-  return(i - j);
-} /* compare_facetvisit */
-
-/*---------------------------------
-
-  qh_compare_vertexpoint( p1, p2 )
-    used by qsort() to order vertices by point id
-
-  Not usable in qhulllib_r since qh_pointid depends on qh
-
-  int qh_compare_vertexpoint(const void *p1, const void *p2) {
-  const vertexT *a= *((vertexT *const*)p1), *b= *((vertexT *const*)p2);
-
-  return((qh_pointid(qh, a->point) > qh_pointid(qh, b->point)?1:-1));
-}*/
-
-/*---------------------------------
-
-  qh_copyfilename(qh, dest, size, source, length )
-    copy filename identified by qh_skipfilename()
-
-  notes:
-    see qh_skipfilename() for syntax
-*/
-void qh_copyfilename(qhT *qh, char *filename, int size, const char* source, int length) {
-  char c= *source;
-
-  if (length > size + 1) {
-      qh_fprintf(qh, qh->ferr, 6040, "qhull error: filename is more than %d characters, %s\n",  size-1, source);
-      qh_errexit(qh, qh_ERRinput, NULL, NULL);
-  }
-  strncpy(filename, source, length);
-  filename[length]= '\0';
-  if (c == '\'' || c == '"') {
-    char *s= filename + 1;
-    char *t= filename;
-    while (*s) {
-      if (*s == c) {
-          if (s[-1] == '\\')
-              t[-1]= c;
-      }else
-          *t++= *s;
-      s++;
-    }
-    *t= '\0';
-  }
-} /* copyfilename */
-
-/*---------------------------------
-
-  qh_countfacets(qh, facetlist, facets, printall,
-          numfacets, numsimplicial, totneighbors, numridges, numcoplanar, numtricoplanars  )
-    count good facets for printing and set visitid
-    if allfacets, ignores qh_skipfacet()
-
-  notes:
-    qh_printsummary and qh_countfacets must match counts
-
-  returns:
-    numfacets, numsimplicial, total neighbors, numridges, coplanars
-    each facet with ->visitid indicating 1-relative position
-      ->visitid==0 indicates not good
-
-  notes
-    numfacets >= numsimplicial
-    if qh.NEWfacets,
-      does not count visible facets (matches qh_printafacet)
-
-  design:
-    for all facets on facetlist and in facets set
-      unless facet is skipped or visible (i.e., will be deleted)
-        mark facet->visitid
-        update counts
-*/
-void qh_countfacets(qhT *qh, facetT *facetlist, setT *facets, boolT printall,
-    int *numfacetsp, int *numsimplicialp, int *totneighborsp, int *numridgesp, int *numcoplanarsp, int *numtricoplanarsp) {
-  facetT *facet, **facetp;
-  int numfacets= 0, numsimplicial= 0, numridges= 0, totneighbors= 0, numcoplanars= 0, numtricoplanars= 0;
-
-  FORALLfacet_(facetlist) {
-    if ((facet->visible && qh->NEWfacets)
-    || (!printall && qh_skipfacet(qh, facet)))
-      facet->visitid= 0;
-    else {
-      facet->visitid= ++numfacets;
-      totneighbors += qh_setsize(qh, facet->neighbors);
-      if (facet->simplicial) {
-        numsimplicial++;
-        if (facet->keepcentrum && facet->tricoplanar)
-          numtricoplanars++;
-      }else
-        numridges += qh_setsize(qh, facet->ridges);
-      if (facet->coplanarset)
-        numcoplanars += qh_setsize(qh, facet->coplanarset);
-    }
-  }
-
-  FOREACHfacet_(facets) {
-    if ((facet->visible && qh->NEWfacets)
-    || (!printall && qh_skipfacet(qh, facet)))
-      facet->visitid= 0;
-    else {
-      facet->visitid= ++numfacets;
-      totneighbors += qh_setsize(qh, facet->neighbors);
-      if (facet->simplicial){
-        numsimplicial++;
-        if (facet->keepcentrum && facet->tricoplanar)
-          numtricoplanars++;
-      }else
-        numridges += qh_setsize(qh, facet->ridges);
-      if (facet->coplanarset)
-        numcoplanars += qh_setsize(qh, facet->coplanarset);
-    }
-  }
-  qh->visit_id += numfacets+1;
-  *numfacetsp= numfacets;
-  *numsimplicialp= numsimplicial;
-  *totneighborsp= totneighbors;
-  *numridgesp= numridges;
-  *numcoplanarsp= numcoplanars;
-  *numtricoplanarsp= numtricoplanars;
-} /* countfacets */
-
-/*---------------------------------
-
-  qh_detvnorm(qh, vertex, vertexA, centers, offset )
-    compute separating plane of the Voronoi diagram for a pair of input sites
-    centers= set of facets (i.e., Voronoi vertices)
-      facet->visitid= 0 iff vertex-at-infinity (i.e., unbounded)
-
-  assumes:
-    qh_ASvoronoi and qh_vertexneighbors() already set
-
-  returns:
-    norm
-      a pointer into qh.gm_matrix to qh.hull_dim-1 reals
-      copy the data before reusing qh.gm_matrix
-    offset
-      if 'QVn'
-        sign adjusted so that qh.GOODvertexp is inside
-      else
-        sign adjusted so that vertex is inside
-
-    qh.gm_matrix= simplex of points from centers relative to first center
-
-  notes:
-    in io_r.c so that code for 'v Tv' can be removed by removing io_r.c
-    returns pointer into qh.gm_matrix to avoid tracking of temporary memory
-
-  design:
-    determine midpoint of input sites
-    build points as the set of Voronoi vertices
-    select a simplex from points (if necessary)
-      include midpoint if the Voronoi region is unbounded
-    relocate the first vertex of the simplex to the origin
-    compute the normalized hyperplane through the simplex
-    orient the hyperplane toward 'QVn' or 'vertex'
-    if 'Tv' or 'Ts'
-      if bounded
-        test that hyperplane is the perpendicular bisector of the input sites
-      test that Voronoi vertices not in the simplex are still on the hyperplane
-    free up temporary memory
-*/
-pointT *qh_detvnorm(qhT *qh, vertexT *vertex, vertexT *vertexA, setT *centers, realT *offsetp) {
-  facetT *facet, **facetp;
-  int  i, k, pointid, pointidA, point_i, point_n;
-  setT *simplex= NULL;
-  pointT *point, **pointp, *point0, *midpoint, *normal, *inpoint;
-  coordT *coord, *gmcoord, *normalp;
-  setT *points= qh_settemp(qh, qh->TEMPsize);
-  boolT nearzero= False;
-  boolT unbounded= False;
-  int numcenters= 0;
-  int dim= qh->hull_dim - 1;
-  realT dist, offset, angle, zero= 0.0;
-
-  midpoint= qh->gm_matrix + qh->hull_dim * qh->hull_dim;  /* last row */
-  for (k=0; k < dim; k++)
-    midpoint[k]= (vertex->point[k] + vertexA->point[k])/2;
-  FOREACHfacet_(centers) {
-    numcenters++;
-    if (!facet->visitid)
-      unbounded= True;
-    else {
-      if (!facet->center)
-        facet->center= qh_facetcenter(qh, facet->vertices);
-      qh_setappend(qh, &points, facet->center);
-    }
-  }
-  if (numcenters > dim) {
-    simplex= qh_settemp(qh, qh->TEMPsize);
-    qh_setappend(qh, &simplex, vertex->point);
-    if (unbounded)
-      qh_setappend(qh, &simplex, midpoint);
-    qh_maxsimplex(qh, dim, points, NULL, 0, &simplex);
-    qh_setdelnth(qh, simplex, 0);
-  }else if (numcenters == dim) {
-    if (unbounded)
-      qh_setappend(qh, &points, midpoint);
-    simplex= points;
-  }else {
-    qh_fprintf(qh, qh->ferr, 6216, "qhull internal error (qh_detvnorm): too few points(%d) to compute separating plane\n", numcenters);
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }
-  i= 0;
-  gmcoord= qh->gm_matrix;
-  point0= SETfirstt_(simplex, pointT);
-  FOREACHpoint_(simplex) {
-    if (qh->IStracing >= 4)
-      qh_printmatrix(qh, qh->ferr, "qh_detvnorm: Voronoi vertex or midpoint",
-                              &point, 1, dim);
-    if (point != point0) {
-      qh->gm_row[i++]= gmcoord;
-      coord= point0;
-      for (k=dim; k--; )
-        *(gmcoord++)= *point++ - *coord++;
-    }
-  }
-  qh->gm_row[i]= gmcoord;  /* does not overlap midpoint, may be used later for qh_areasimplex */
-  normal= gmcoord;
-  qh_sethyperplane_gauss(qh, dim, qh->gm_row, point0, True,
-                normal, &offset, &nearzero);
-  if (qh->GOODvertexp == vertexA->point)
-    inpoint= vertexA->point;
-  else
-    inpoint= vertex->point;
-  zinc_(Zdistio);
-  dist= qh_distnorm(dim, inpoint, normal, &offset);
-  if (dist > 0) {
-    offset= -offset;
-    normalp= normal;
-    for (k=dim; k--; ) {
-      *normalp= -(*normalp);
-      normalp++;
-    }
-  }
-  if (qh->VERIFYoutput || qh->PRINTstatistics) {
-    pointid= qh_pointid(qh, vertex->point);
-    pointidA= qh_pointid(qh, vertexA->point);
-    if (!unbounded) {
-      zinc_(Zdiststat);
-      dist= qh_distnorm(dim, midpoint, normal, &offset);
-      if (dist < 0)
-        dist= -dist;
-      zzinc_(Zridgemid);
-      wwmax_(Wridgemidmax, dist);
-      wwadd_(Wridgemid, dist);
-      trace4((qh, qh->ferr, 4014, "qh_detvnorm: points %d %d midpoint dist %2.2g\n",
-                 pointid, pointidA, dist));
-      for (k=0; k < dim; k++)
-        midpoint[k]= vertexA->point[k] - vertex->point[k];  /* overwrites midpoint! */
-      qh_normalize(qh, midpoint, dim, False);
-      angle= qh_distnorm(dim, midpoint, normal, &zero); /* qh_detangle uses dim+1 */
-      if (angle < 0.0)
-        angle= angle + 1.0;
-      else
-        angle= angle - 1.0;
-      if (angle < 0.0)
-        angle -= angle;
-      trace4((qh, qh->ferr, 4015, "qh_detvnorm: points %d %d angle %2.2g nearzero %d\n",
-                 pointid, pointidA, angle, nearzero));
-      if (nearzero) {
-        zzinc_(Zridge0);
-        wwmax_(Wridge0max, angle);
-        wwadd_(Wridge0, angle);
-      }else {
-        zzinc_(Zridgeok)
-        wwmax_(Wridgeokmax, angle);
-        wwadd_(Wridgeok, angle);
-      }
-    }
-    if (simplex != points) {
-      FOREACHpoint_i_(qh, points) {
-        if (!qh_setin(simplex, point)) {
-          facet= SETelemt_(centers, point_i, facetT);
-          zinc_(Zdiststat);
-          dist= qh_distnorm(dim, point, normal, &offset);
-          if (dist < 0)
-            dist= -dist;
-          zzinc_(Zridge);
-          wwmax_(Wridgemax, dist);
-          wwadd_(Wridge, dist);
-          trace4((qh, qh->ferr, 4016, "qh_detvnorm: points %d %d Voronoi vertex %d dist %2.2g\n",
-                             pointid, pointidA, facet->visitid, dist));
-        }
-      }
-    }
-  }
-  *offsetp= offset;
-  if (simplex != points)
-    qh_settempfree(qh, &simplex);
-  qh_settempfree(qh, &points);
-  return normal;
-} /* detvnorm */
-
-/*---------------------------------
-
-  qh_detvridge(qh, vertexA )
-    determine Voronoi ridge from 'seen' neighbors of vertexA
-    include one vertex-at-infinite if an !neighbor->visitid
-
-  returns:
-    temporary set of centers (facets, i.e., Voronoi vertices)
-    sorted by center id
-*/
-setT *qh_detvridge(qhT *qh, vertexT *vertex) {
-  setT *centers= qh_settemp(qh, qh->TEMPsize);
-  setT *tricenters= qh_settemp(qh, qh->TEMPsize);
-  facetT *neighbor, **neighborp;
-  boolT firstinf= True;
-
-  FOREACHneighbor_(vertex) {
-    if (neighbor->seen) {
-      if (neighbor->visitid) {
-        if (!neighbor->tricoplanar || qh_setunique(qh, &tricenters, neighbor->center))
-          qh_setappend(qh, ¢ers, neighbor);
-      }else if (firstinf) {
-        firstinf= False;
-        qh_setappend(qh, ¢ers, neighbor);
-      }
-    }
-  }
-  qsort(SETaddr_(centers, facetT), (size_t)qh_setsize(qh, centers),
-             sizeof(facetT *), qh_compare_facetvisit);
-  qh_settempfree(qh, &tricenters);
-  return centers;
-} /* detvridge */
-
-/*---------------------------------
-
-  qh_detvridge3(qh, atvertex, vertex )
-    determine 3-d Voronoi ridge from 'seen' neighbors of atvertex and vertex
-    include one vertex-at-infinite for !neighbor->visitid
-    assumes all facet->seen2= True
-
-  returns:
-    temporary set of centers (facets, i.e., Voronoi vertices)
-    listed in adjacency order (!oriented)
-    all facet->seen2= True
-
-  design:
-    mark all neighbors of atvertex
-    for each adjacent neighbor of both atvertex and vertex
-      if neighbor selected
-        add neighbor to set of Voronoi vertices
-*/
-setT *qh_detvridge3(qhT *qh, vertexT *atvertex, vertexT *vertex) {
-  setT *centers= qh_settemp(qh, qh->TEMPsize);
-  setT *tricenters= qh_settemp(qh, qh->TEMPsize);
-  facetT *neighbor, **neighborp, *facet= NULL;
-  boolT firstinf= True;
-
-  FOREACHneighbor_(atvertex)
-    neighbor->seen2= False;
-  FOREACHneighbor_(vertex) {
-    if (!neighbor->seen2) {
-      facet= neighbor;
-      break;
-    }
-  }
-  while (facet) {
-    facet->seen2= True;
-    if (neighbor->seen) {
-      if (facet->visitid) {
-        if (!facet->tricoplanar || qh_setunique(qh, &tricenters, facet->center))
-          qh_setappend(qh, ¢ers, facet);
-      }else if (firstinf) {
-        firstinf= False;
-        qh_setappend(qh, ¢ers, facet);
-      }
-    }
-    FOREACHneighbor_(facet) {
-      if (!neighbor->seen2) {
-        if (qh_setin(vertex->neighbors, neighbor))
-          break;
-        else
-          neighbor->seen2= True;
-      }
-    }
-    facet= neighbor;
-  }
-  if (qh->CHECKfrequently) {
-    FOREACHneighbor_(vertex) {
-      if (!neighbor->seen2) {
-          qh_fprintf(qh, qh->ferr, 6217, "qhull internal error (qh_detvridge3): neighbors of vertex p%d are not connected at facet %d\n",
-                 qh_pointid(qh, vertex->point), neighbor->id);
-        qh_errexit(qh, qh_ERRqhull, neighbor, NULL);
-      }
-    }
-  }
-  FOREACHneighbor_(atvertex)
-    neighbor->seen2= True;
-  qh_settempfree(qh, &tricenters);
-  return centers;
-} /* detvridge3 */
-
-/*---------------------------------
-
-  qh_eachvoronoi(qh, fp, printvridge, vertex, visitall, innerouter, inorder )
-    if visitall,
-      visit all Voronoi ridges for vertex (i.e., an input site)
-    else
-      visit all unvisited Voronoi ridges for vertex
-      all vertex->seen= False if unvisited
-    assumes
-      all facet->seen= False
-      all facet->seen2= True (for qh_detvridge3)
-      all facet->visitid == 0 if vertex_at_infinity
-                         == index of Voronoi vertex
-                         >= qh.num_facets if ignored
-    innerouter:
-      qh_RIDGEall--  both inner (bounded) and outer(unbounded) ridges
-      qh_RIDGEinner- only inner
-      qh_RIDGEouter- only outer
-
-    if inorder
-      orders vertices for 3-d Voronoi diagrams
-
-  returns:
-    number of visited ridges (does not include previously visited ridges)
-
-    if printvridge,
-      calls printvridge( fp, vertex, vertexA, centers)
-        fp== any pointer (assumes FILE*)
-        vertex,vertexA= pair of input sites that define a Voronoi ridge
-        centers= set of facets (i.e., Voronoi vertices)
-                 ->visitid == index or 0 if vertex_at_infinity
-                 ordered for 3-d Voronoi diagram
-  notes:
-    uses qh.vertex_visit
-
-  see:
-    qh_eachvoronoi_all()
-
-  design:
-    mark selected neighbors of atvertex
-    for each selected neighbor (either Voronoi vertex or vertex-at-infinity)
-      for each unvisited vertex
-        if atvertex and vertex share more than d-1 neighbors
-          bump totalcount
-          if printvridge defined
-            build the set of shared neighbors (i.e., Voronoi vertices)
-            call printvridge
-*/
-int qh_eachvoronoi(qhT *qh, FILE *fp, printvridgeT printvridge, vertexT *atvertex, boolT visitall, qh_RIDGE innerouter, boolT inorder) {
-  boolT unbounded;
-  int count;
-  facetT *neighbor, **neighborp, *neighborA, **neighborAp;
-  setT *centers;
-  setT *tricenters= qh_settemp(qh, qh->TEMPsize);
-
-  vertexT *vertex, **vertexp;
-  boolT firstinf;
-  unsigned int numfacets= (unsigned int)qh->num_facets;
-  int totridges= 0;
-
-  qh->vertex_visit++;
-  atvertex->seen= True;
-  if (visitall) {
-    FORALLvertices
-      vertex->seen= False;
-  }
-  FOREACHneighbor_(atvertex) {
-    if (neighbor->visitid < numfacets)
-      neighbor->seen= True;
-  }
-  FOREACHneighbor_(atvertex) {
-    if (neighbor->seen) {
-      FOREACHvertex_(neighbor->vertices) {
-        if (vertex->visitid != qh->vertex_visit && !vertex->seen) {
-          vertex->visitid= qh->vertex_visit;
-          count= 0;
-          firstinf= True;
-          qh_settruncate(qh, tricenters, 0);
-          FOREACHneighborA_(vertex) {
-            if (neighborA->seen) {
-              if (neighborA->visitid) {
-                if (!neighborA->tricoplanar || qh_setunique(qh, &tricenters, neighborA->center))
-                  count++;
-              }else if (firstinf) {
-                count++;
-                firstinf= False;
-              }
-            }
-          }
-          if (count >= qh->hull_dim - 1) {  /* e.g., 3 for 3-d Voronoi */
-            if (firstinf) {
-              if (innerouter == qh_RIDGEouter)
-                continue;
-              unbounded= False;
-            }else {
-              if (innerouter == qh_RIDGEinner)
-                continue;
-              unbounded= True;
-            }
-            totridges++;
-            trace4((qh, qh->ferr, 4017, "qh_eachvoronoi: Voronoi ridge of %d vertices between sites %d and %d\n",
-                  count, qh_pointid(qh, atvertex->point), qh_pointid(qh, vertex->point)));
-            if (printvridge && fp) {
-              if (inorder && qh->hull_dim == 3+1) /* 3-d Voronoi diagram */
-                centers= qh_detvridge3(qh, atvertex, vertex);
-              else
-                centers= qh_detvridge(qh, vertex);
-              (*printvridge)(qh, fp, atvertex, vertex, centers, unbounded);
-              qh_settempfree(qh, ¢ers);
-            }
-          }
-        }
-      }
-    }
-  }
-  FOREACHneighbor_(atvertex)
-    neighbor->seen= False;
-  qh_settempfree(qh, &tricenters);
-  return totridges;
-} /* eachvoronoi */
-
-
-/*---------------------------------
-
-  qh_eachvoronoi_all(qh, fp, printvridge, isUpper, innerouter, inorder )
-    visit all Voronoi ridges
-
-    innerouter:
-      see qh_eachvoronoi()
-
-    if inorder
-      orders vertices for 3-d Voronoi diagrams
-
-  returns
-    total number of ridges
-
-    if isUpper == facet->upperdelaunay  (i.e., a Vornoi vertex)
-      facet->visitid= Voronoi vertex index(same as 'o' format)
-    else
-      facet->visitid= 0
-
-    if printvridge,
-      calls printvridge( fp, vertex, vertexA, centers)
-      [see qh_eachvoronoi]
-
-  notes:
-    Not used for qhull.exe
-    same effect as qh_printvdiagram but ridges not sorted by point id
-*/
-int qh_eachvoronoi_all(qhT *qh, FILE *fp, printvridgeT printvridge, boolT isUpper, qh_RIDGE innerouter, boolT inorder) {
-  facetT *facet;
-  vertexT *vertex;
-  int numcenters= 1;  /* vertex 0 is vertex-at-infinity */
-  int totridges= 0;
-
-  qh_clearcenters(qh, qh_ASvoronoi);
-  qh_vertexneighbors(qh);
-  maximize_(qh->visit_id, (unsigned) qh->num_facets);
-  FORALLfacets {
-    facet->visitid= 0;
-    facet->seen= False;
-    facet->seen2= True;
-  }
-  FORALLfacets {
-    if (facet->upperdelaunay == isUpper)
-      facet->visitid= numcenters++;
-  }
-  FORALLvertices
-    vertex->seen= False;
-  FORALLvertices {
-    if (qh->GOODvertex > 0 && qh_pointid(qh, vertex->point)+1 != qh->GOODvertex)
-      continue;
-    totridges += qh_eachvoronoi(qh, fp, printvridge, vertex,
-                   !qh_ALL, innerouter, inorder);
-  }
-  return totridges;
-} /* eachvoronoi_all */
-
-/*---------------------------------
-
-  qh_facet2point(qh, facet, point0, point1, mindist )
-    return two projected temporary vertices for a 2-d facet
-    may be non-simplicial
-
-  returns:
-    point0 and point1 oriented and projected to the facet
-    returns mindist (maximum distance below plane)
-*/
-void qh_facet2point(qhT *qh, facetT *facet, pointT **point0, pointT **point1, realT *mindist) {
-  vertexT *vertex0, *vertex1;
-  realT dist;
-
-  if (facet->toporient ^ qh_ORIENTclock) {
-    vertex0= SETfirstt_(facet->vertices, vertexT);
-    vertex1= SETsecondt_(facet->vertices, vertexT);
-  }else {
-    vertex1= SETfirstt_(facet->vertices, vertexT);
-    vertex0= SETsecondt_(facet->vertices, vertexT);
-  }
-  zadd_(Zdistio, 2);
-  qh_distplane(qh, vertex0->point, facet, &dist);
-  *mindist= dist;
-  *point0= qh_projectpoint(qh, vertex0->point, facet, dist);
-  qh_distplane(qh, vertex1->point, facet, &dist);
-  minimize_(*mindist, dist);
-  *point1= qh_projectpoint(qh, vertex1->point, facet, dist);
-} /* facet2point */
-
-
-/*---------------------------------
-
-  qh_facetvertices(qh, facetlist, facets, allfacets )
-    returns temporary set of vertices in a set and/or list of facets
-    if allfacets, ignores qh_skipfacet()
-
-  returns:
-    vertices with qh.vertex_visit
-
-  notes:
-    optimized for allfacets of facet_list
-
-  design:
-    if allfacets of facet_list
-      create vertex set from vertex_list
-    else
-      for each selected facet in facets or facetlist
-        append unvisited vertices to vertex set
-*/
-setT *qh_facetvertices(qhT *qh, facetT *facetlist, setT *facets, boolT allfacets) {
-  setT *vertices;
-  facetT *facet, **facetp;
-  vertexT *vertex, **vertexp;
-
-  qh->vertex_visit++;
-  if (facetlist == qh->facet_list && allfacets && !facets) {
-    vertices= qh_settemp(qh, qh->num_vertices);
-    FORALLvertices {
-      vertex->visitid= qh->vertex_visit;
-      qh_setappend(qh, &vertices, vertex);
-    }
-  }else {
-    vertices= qh_settemp(qh, qh->TEMPsize);
-    FORALLfacet_(facetlist) {
-      if (!allfacets && qh_skipfacet(qh, facet))
-        continue;
-      FOREACHvertex_(facet->vertices) {
-        if (vertex->visitid != qh->vertex_visit) {
-          vertex->visitid= qh->vertex_visit;
-          qh_setappend(qh, &vertices, vertex);
-        }
-      }
-    }
-  }
-  FOREACHfacet_(facets) {
-    if (!allfacets && qh_skipfacet(qh, facet))
-      continue;
-    FOREACHvertex_(facet->vertices) {
-      if (vertex->visitid != qh->vertex_visit) {
-        vertex->visitid= qh->vertex_visit;
-        qh_setappend(qh, &vertices, vertex);
-      }
-    }
-  }
-  return vertices;
-} /* facetvertices */
-
-/*---------------------------------
-
-  qh_geomplanes(qh, facet, outerplane, innerplane )
-    return outer and inner planes for Geomview
-    qh.PRINTradius is size of vertices and points (includes qh.JOGGLEmax)
-
-  notes:
-    assume precise calculations in io.c with roundoff covered by qh_GEOMepsilon
-*/
-void qh_geomplanes(qhT *qh, facetT *facet, realT *outerplane, realT *innerplane) {
-  realT radius;
-
-  if (qh->MERGING || qh->JOGGLEmax < REALmax/2) {
-    qh_outerinner(qh, facet, outerplane, innerplane);
-    radius= qh->PRINTradius;
-    if (qh->JOGGLEmax < REALmax/2)
-      radius -= qh->JOGGLEmax * sqrt((realT)qh->hull_dim);  /* already accounted for in qh_outerinner() */
-    *outerplane += radius;
-    *innerplane -= radius;
-    if (qh->PRINTcoplanar || qh->PRINTspheres) {
-      *outerplane += qh->MAXabs_coord * qh_GEOMepsilon;
-      *innerplane -= qh->MAXabs_coord * qh_GEOMepsilon;
-    }
-  }else
-    *innerplane= *outerplane= 0;
-} /* geomplanes */
-
-
-/*---------------------------------
-
-  qh_markkeep(qh, facetlist )
-    mark good facets that meet qh.KEEParea, qh.KEEPmerge, and qh.KEEPminArea
-    ignores visible facets (!part of convex hull)
-
-  returns:
-    may clear facet->good
-    recomputes qh.num_good
-
-  design:
-    get set of good facets
-    if qh.KEEParea
-      sort facets by area
-      clear facet->good for all but n largest facets
-    if qh.KEEPmerge
-      sort facets by merge count
-      clear facet->good for all but n most merged facets
-    if qh.KEEPminarea
-      clear facet->good if area too small
-    update qh.num_good
-*/
-void qh_markkeep(qhT *qh, facetT *facetlist) {
-  facetT *facet, **facetp;
-  setT *facets= qh_settemp(qh, qh->num_facets);
-  int size, count;
-
-  trace2((qh, qh->ferr, 2006, "qh_markkeep: only keep %d largest and/or %d most merged facets and/or min area %.2g\n",
-          qh->KEEParea, qh->KEEPmerge, qh->KEEPminArea));
-  FORALLfacet_(facetlist) {
-    if (!facet->visible && facet->good)
-      qh_setappend(qh, &facets, facet);
-  }
-  size= qh_setsize(qh, facets);
-  if (qh->KEEParea) {
-    qsort(SETaddr_(facets, facetT), (size_t)size,
-             sizeof(facetT *), qh_compare_facetarea);
-    if ((count= size - qh->KEEParea) > 0) {
-      FOREACHfacet_(facets) {
-        facet->good= False;
-        if (--count == 0)
-          break;
-      }
-    }
-  }
-  if (qh->KEEPmerge) {
-    qsort(SETaddr_(facets, facetT), (size_t)size,
-             sizeof(facetT *), qh_compare_facetmerge);
-    if ((count= size - qh->KEEPmerge) > 0) {
-      FOREACHfacet_(facets) {
-        facet->good= False;
-        if (--count == 0)
-          break;
-      }
-    }
-  }
-  if (qh->KEEPminArea < REALmax/2) {
-    FOREACHfacet_(facets) {
-      if (!facet->isarea || facet->f.area < qh->KEEPminArea)
-        facet->good= False;
-    }
-  }
-  qh_settempfree(qh, &facets);
-  count= 0;
-  FORALLfacet_(facetlist) {
-    if (facet->good)
-      count++;
-  }
-  qh->num_good= count;
-} /* markkeep */
-
-
-/*---------------------------------
-
-  qh_markvoronoi(qh, facetlist, facets, printall, isLower, numcenters )
-    mark voronoi vertices for printing by site pairs
-
-  returns:
-    temporary set of vertices indexed by pointid
-    isLower set if printing lower hull (i.e., at least one facet is lower hull)
-    numcenters= total number of Voronoi vertices
-    bumps qh.printoutnum for vertex-at-infinity
-    clears all facet->seen and sets facet->seen2
-
-    if selected
-      facet->visitid= Voronoi vertex id
-    else if upper hull (or 'Qu' and lower hull)
-      facet->visitid= 0
-    else
-      facet->visitid >= qh->num_facets
-
-  notes:
-    ignores qh.ATinfinity, if defined
-*/
-setT *qh_markvoronoi(qhT *qh, facetT *facetlist, setT *facets, boolT printall, boolT *isLowerp, int *numcentersp) {
-  int numcenters=0;
-  facetT *facet, **facetp;
-  setT *vertices;
-  boolT isLower= False;
-
-  qh->printoutnum++;
-  qh_clearcenters(qh, qh_ASvoronoi);  /* in case, qh_printvdiagram2 called by user */
-  qh_vertexneighbors(qh);
-  vertices= qh_pointvertex(qh);
-  if (qh->ATinfinity)
-    SETelem_(vertices, qh->num_points-1)= NULL;
-  qh->visit_id++;
-  maximize_(qh->visit_id, (unsigned) qh->num_facets);
-  FORALLfacet_(facetlist) {
-    if (printall || !qh_skipfacet(qh, facet)) {
-      if (!facet->upperdelaunay) {
-        isLower= True;
-        break;
-      }
-    }
-  }
-  FOREACHfacet_(facets) {
-    if (printall || !qh_skipfacet(qh, facet)) {
-      if (!facet->upperdelaunay) {
-        isLower= True;
-        break;
-      }
-    }
-  }
-  FORALLfacets {
-    if (facet->normal && (facet->upperdelaunay == isLower))
-      facet->visitid= 0;  /* facetlist or facets may overwrite */
-    else
-      facet->visitid= qh->visit_id;
-    facet->seen= False;
-    facet->seen2= True;
-  }
-  numcenters++;  /* qh_INFINITE */
-  FORALLfacet_(facetlist) {
-    if (printall || !qh_skipfacet(qh, facet))
-      facet->visitid= numcenters++;
-  }
-  FOREACHfacet_(facets) {
-    if (printall || !qh_skipfacet(qh, facet))
-      facet->visitid= numcenters++;
-  }
-  *isLowerp= isLower;
-  *numcentersp= numcenters;
-  trace2((qh, qh->ferr, 2007, "qh_markvoronoi: isLower %d numcenters %d\n", isLower, numcenters));
-  return vertices;
-} /* markvoronoi */
-
-/*---------------------------------
-
-  qh_order_vertexneighbors(qh, vertex )
-    order facet neighbors of a 2-d or 3-d vertex by adjacency
-
-  notes:
-    does not orient the neighbors
-
-  design:
-    initialize a new neighbor set with the first facet in vertex->neighbors
-    while vertex->neighbors non-empty
-      select next neighbor in the previous facet's neighbor set
-    set vertex->neighbors to the new neighbor set
-*/
-void qh_order_vertexneighbors(qhT *qh, vertexT *vertex) {
-  setT *newset;
-  facetT *facet, *neighbor, **neighborp;
-
-  trace4((qh, qh->ferr, 4018, "qh_order_vertexneighbors: order neighbors of v%d for 3-d\n", vertex->id));
-  newset= qh_settemp(qh, qh_setsize(qh, vertex->neighbors));
-  facet= (facetT*)qh_setdellast(vertex->neighbors);
-  qh_setappend(qh, &newset, facet);
-  while (qh_setsize(qh, vertex->neighbors)) {
-    FOREACHneighbor_(vertex) {
-      if (qh_setin(facet->neighbors, neighbor)) {
-        qh_setdel(vertex->neighbors, neighbor);
-        qh_setappend(qh, &newset, neighbor);
-        facet= neighbor;
-        break;
-      }
-    }
-    if (!neighbor) {
-      qh_fprintf(qh, qh->ferr, 6066, "qhull internal error (qh_order_vertexneighbors): no neighbor of v%d for f%d\n",
-        vertex->id, facet->id);
-      qh_errexit(qh, qh_ERRqhull, facet, NULL);
-    }
-  }
-  qh_setfree(qh, &vertex->neighbors);
-  qh_settemppop(qh);
-  vertex->neighbors= newset;
-} /* order_vertexneighbors */
-
-/*---------------------------------
-
-  qh_prepare_output(qh, )
-    prepare for qh_produce_output2(qh) according to
-      qh.KEEPminArea, KEEParea, KEEPmerge, GOODvertex, GOODthreshold, GOODpoint, ONLYgood, SPLITthresholds
-    does not reset facet->good
-
-  notes
-    except for PRINTstatistics, no-op if previously called with same options
-*/
-void qh_prepare_output(qhT *qh) {
-  if (qh->VORONOI) {
-    qh_clearcenters(qh, qh_ASvoronoi);  /* must be before qh_triangulate */
-    qh_vertexneighbors(qh);
-  }
-  if (qh->TRIangulate && !qh->hasTriangulation) {
-    qh_triangulate(qh);
-    if (qh->VERIFYoutput && !qh->CHECKfrequently)
-      qh_checkpolygon(qh, qh->facet_list);
-  }
-  qh_findgood_all(qh, qh->facet_list);
-  if (qh->GETarea)
-    qh_getarea(qh, qh->facet_list);
-  if (qh->KEEParea || qh->KEEPmerge || qh->KEEPminArea < REALmax/2)
-    qh_markkeep(qh, qh->facet_list);
-  if (qh->PRINTstatistics)
-    qh_collectstatistics(qh);
-}
-
-/*---------------------------------
-
-  qh_printafacet(qh, fp, format, facet, printall )
-    print facet to fp in given output format (see qh.PRINTout)
-
-  returns:
-    nop if !printall and qh_skipfacet()
-    nop if visible facet and NEWfacets and format != PRINTfacets
-    must match qh_countfacets
-
-  notes
-    preserves qh.visit_id
-    facet->normal may be null if PREmerge/MERGEexact and STOPcone before merge
-
-  see
-    qh_printbegin() and qh_printend()
-
-  design:
-    test for printing facet
-    call appropriate routine for format
-    or output results directly
-*/
-void qh_printafacet(qhT *qh, FILE *fp, qh_PRINT format, facetT *facet, boolT printall) {
-  realT color[4], offset, dist, outerplane, innerplane;
-  boolT zerodiv;
-  coordT *point, *normp, *coordp, **pointp, *feasiblep;
-  int k;
-  vertexT *vertex, **vertexp;
-  facetT *neighbor, **neighborp;
-
-  if (!printall && qh_skipfacet(qh, facet))
-    return;
-  if (facet->visible && qh->NEWfacets && format != qh_PRINTfacets)
-    return;
-  qh->printoutnum++;
-  switch (format) {
-  case qh_PRINTarea:
-    if (facet->isarea) {
-      qh_fprintf(qh, fp, 9009, qh_REAL_1, facet->f.area);
-      qh_fprintf(qh, fp, 9010, "\n");
-    }else
-      qh_fprintf(qh, fp, 9011, "0\n");
-    break;
-  case qh_PRINTcoplanars:
-    qh_fprintf(qh, fp, 9012, "%d", qh_setsize(qh, facet->coplanarset));
-    FOREACHpoint_(facet->coplanarset)
-      qh_fprintf(qh, fp, 9013, " %d", qh_pointid(qh, point));
-    qh_fprintf(qh, fp, 9014, "\n");
-    break;
-  case qh_PRINTcentrums:
-    qh_printcenter(qh, fp, format, NULL, facet);
-    break;
-  case qh_PRINTfacets:
-    qh_printfacet(qh, fp, facet);
-    break;
-  case qh_PRINTfacets_xridge:
-    qh_printfacetheader(qh, fp, facet);
-    break;
-  case qh_PRINTgeom:  /* either 2 , 3, or 4-d by qh_printbegin */
-    if (!facet->normal)
-      break;
-    for (k=qh->hull_dim; k--; ) {
-      color[k]= (facet->normal[k]+1.0)/2.0;
-      maximize_(color[k], -1.0);
-      minimize_(color[k], +1.0);
-    }
-    qh_projectdim3(qh, color, color);
-    if (qh->PRINTdim != qh->hull_dim)
-      qh_normalize2(qh, color, 3, True, NULL, NULL);
-    if (qh->hull_dim <= 2)
-      qh_printfacet2geom(qh, fp, facet, color);
-    else if (qh->hull_dim == 3) {
-      if (facet->simplicial)
-        qh_printfacet3geom_simplicial(qh, fp, facet, color);
-      else
-        qh_printfacet3geom_nonsimplicial(qh, fp, facet, color);
-    }else {
-      if (facet->simplicial)
-        qh_printfacet4geom_simplicial(qh, fp, facet, color);
-      else
-        qh_printfacet4geom_nonsimplicial(qh, fp, facet, color);
-    }
-    break;
-  case qh_PRINTids:
-    qh_fprintf(qh, fp, 9015, "%d\n", facet->id);
-    break;
-  case qh_PRINTincidences:
-  case qh_PRINToff:
-  case qh_PRINTtriangles:
-    if (qh->hull_dim == 3 && format != qh_PRINTtriangles)
-      qh_printfacet3vertex(qh, fp, facet, format);
-    else if (facet->simplicial || qh->hull_dim == 2 || format == qh_PRINToff)
-      qh_printfacetNvertex_simplicial(qh, fp, facet, format);
-    else
-      qh_printfacetNvertex_nonsimplicial(qh, fp, facet, qh->printoutvar++, format);
-    break;
-  case qh_PRINTinner:
-    qh_outerinner(qh, facet, NULL, &innerplane);
-    offset= facet->offset - innerplane;
-    goto LABELprintnorm;
-    break; /* prevent warning */
-  case qh_PRINTmerges:
-    qh_fprintf(qh, fp, 9016, "%d\n", facet->nummerge);
-    break;
-  case qh_PRINTnormals:
-    offset= facet->offset;
-    goto LABELprintnorm;
-    break; /* prevent warning */
-  case qh_PRINTouter:
-    qh_outerinner(qh, facet, &outerplane, NULL);
-    offset= facet->offset - outerplane;
-  LABELprintnorm:
-    if (!facet->normal) {
-      qh_fprintf(qh, fp, 9017, "no normal for facet f%d\n", facet->id);
-      break;
-    }
-    if (qh->CDDoutput) {
-      qh_fprintf(qh, fp, 9018, qh_REAL_1, -offset);
-      for (k=0; k < qh->hull_dim; k++)
-        qh_fprintf(qh, fp, 9019, qh_REAL_1, -facet->normal[k]);
-    }else {
-      for (k=0; k < qh->hull_dim; k++)
-        qh_fprintf(qh, fp, 9020, qh_REAL_1, facet->normal[k]);
-      qh_fprintf(qh, fp, 9021, qh_REAL_1, offset);
-    }
-    qh_fprintf(qh, fp, 9022, "\n");
-    break;
-  case qh_PRINTmathematica:  /* either 2 or 3-d by qh_printbegin */
-  case qh_PRINTmaple:
-    if (qh->hull_dim == 2)
-      qh_printfacet2math(qh, fp, facet, format, qh->printoutvar++);
-    else
-      qh_printfacet3math(qh, fp, facet, format, qh->printoutvar++);
-    break;
-  case qh_PRINTneighbors:
-    qh_fprintf(qh, fp, 9023, "%d", qh_setsize(qh, facet->neighbors));
-    FOREACHneighbor_(facet)
-      qh_fprintf(qh, fp, 9024, " %d",
-               neighbor->visitid ? neighbor->visitid - 1: 0 - neighbor->id);
-    qh_fprintf(qh, fp, 9025, "\n");
-    break;
-  case qh_PRINTpointintersect:
-    if (!qh->feasible_point) {
-      qh_fprintf(qh, qh->ferr, 6067, "qhull input error (qh_printafacet): option 'Fp' needs qh->feasible_point\n");
-      qh_errexit(qh, qh_ERRinput, NULL, NULL);
-    }
-    if (facet->offset > 0)
-      goto LABELprintinfinite;
-    point= coordp= (coordT*)qh_memalloc(qh, qh->normal_size);
-    normp= facet->normal;
-    feasiblep= qh->feasible_point;
-    if (facet->offset < -qh->MINdenom) {
-      for (k=qh->hull_dim; k--; )
-        *(coordp++)= (*(normp++) / - facet->offset) + *(feasiblep++);
-    }else {
-      for (k=qh->hull_dim; k--; ) {
-        *(coordp++)= qh_divzero(*(normp++), facet->offset, qh->MINdenom_1,
-                                 &zerodiv) + *(feasiblep++);
-        if (zerodiv) {
-          qh_memfree(qh, point, qh->normal_size);
-          goto LABELprintinfinite;
-        }
-      }
-    }
-    qh_printpoint(qh, fp, NULL, point);
-    qh_memfree(qh, point, qh->normal_size);
-    break;
-  LABELprintinfinite:
-    for (k=qh->hull_dim; k--; )
-      qh_fprintf(qh, fp, 9026, qh_REAL_1, qh_INFINITE);
-    qh_fprintf(qh, fp, 9027, "\n");
-    break;
-  case qh_PRINTpointnearest:
-    FOREACHpoint_(facet->coplanarset) {
-      int id, id2;
-      vertex= qh_nearvertex(qh, facet, point, &dist);
-      id= qh_pointid(qh, vertex->point);
-      id2= qh_pointid(qh, point);
-      qh_fprintf(qh, fp, 9028, "%d %d %d " qh_REAL_1 "\n", id, id2, facet->id, dist);
-    }
-    break;
-  case qh_PRINTpoints:  /* VORONOI only by qh_printbegin */
-    if (qh->CDDoutput)
-      qh_fprintf(qh, fp, 9029, "1 ");
-    qh_printcenter(qh, fp, format, NULL, facet);
-    break;
-  case qh_PRINTvertices:
-    qh_fprintf(qh, fp, 9030, "%d", qh_setsize(qh, facet->vertices));
-    FOREACHvertex_(facet->vertices)
-      qh_fprintf(qh, fp, 9031, " %d", qh_pointid(qh, vertex->point));
-    qh_fprintf(qh, fp, 9032, "\n");
-    break;
-  default:
-    break;
-  }
-} /* printafacet */
-
-/*---------------------------------
-
-  qh_printbegin(qh, )
-    prints header for all output formats
-
-  returns:
-    checks for valid format
-
-  notes:
-    uses qh.visit_id for 3/4off
-    changes qh.interior_point if printing centrums
-    qh_countfacets clears facet->visitid for non-good facets
-
-  see
-    qh_printend() and qh_printafacet()
-
-  design:
-    count facets and related statistics
-    print header for format
-*/
-void qh_printbegin(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall) {
-  int numfacets, numsimplicial, numridges, totneighbors, numcoplanars, numtricoplanars;
-  int i, num;
-  facetT *facet, **facetp;
-  vertexT *vertex, **vertexp;
-  setT *vertices;
-  pointT *point, **pointp, *pointtemp;
-
-  qh->printoutnum= 0;
-  qh_countfacets(qh, facetlist, facets, printall, &numfacets, &numsimplicial,
-      &totneighbors, &numridges, &numcoplanars, &numtricoplanars);
-  switch (format) {
-  case qh_PRINTnone:
-    break;
-  case qh_PRINTarea:
-    qh_fprintf(qh, fp, 9033, "%d\n", numfacets);
-    break;
-  case qh_PRINTcoplanars:
-    qh_fprintf(qh, fp, 9034, "%d\n", numfacets);
-    break;
-  case qh_PRINTcentrums:
-    if (qh->CENTERtype == qh_ASnone)
-      qh_clearcenters(qh, qh_AScentrum);
-    qh_fprintf(qh, fp, 9035, "%d\n%d\n", qh->hull_dim, numfacets);
-    break;
-  case qh_PRINTfacets:
-  case qh_PRINTfacets_xridge:
-    if (facetlist)
-      qh_printvertexlist(qh, fp, "Vertices and facets:\n", facetlist, facets, printall);
-    break;
-  case qh_PRINTgeom:
-    if (qh->hull_dim > 4)  /* qh_initqhull_globals also checks */
-      goto LABELnoformat;
-    if (qh->VORONOI && qh->hull_dim > 3)  /* PRINTdim == DROPdim == hull_dim-1 */
-      goto LABELnoformat;
-    if (qh->hull_dim == 2 && (qh->PRINTridges || qh->DOintersections))
-      qh_fprintf(qh, qh->ferr, 7049, "qhull warning: output for ridges and intersections not implemented in 2-d\n");
-    if (qh->hull_dim == 4 && (qh->PRINTinner || qh->PRINTouter ||
-                             (qh->PRINTdim == 4 && qh->PRINTcentrums)))
-      qh_fprintf(qh, qh->ferr, 7050, "qhull warning: output for outer/inner planes and centrums not implemented in 4-d\n");
-    if (qh->PRINTdim == 4 && (qh->PRINTspheres))
-      qh_fprintf(qh, qh->ferr, 7051, "qhull warning: output for vertices not implemented in 4-d\n");
-    if (qh->PRINTdim == 4 && qh->DOintersections && qh->PRINTnoplanes)
-      qh_fprintf(qh, qh->ferr, 7052, "qhull warning: 'Gnh' generates no output in 4-d\n");
-    if (qh->PRINTdim == 2) {
-      qh_fprintf(qh, fp, 9036, "{appearance {linewidth 3} LIST # %s | %s\n",
-              qh->rbox_command, qh->qhull_command);
-    }else if (qh->PRINTdim == 3) {
-      qh_fprintf(qh, fp, 9037, "{appearance {+edge -evert linewidth 2} LIST # %s | %s\n",
-              qh->rbox_command, qh->qhull_command);
-    }else if (qh->PRINTdim == 4) {
-      qh->visit_id++;
-      num= 0;
-      FORALLfacet_(facetlist)    /* get number of ridges to be printed */
-        qh_printend4geom(qh, NULL, facet, &num, printall);
-      FOREACHfacet_(facets)
-        qh_printend4geom(qh, NULL, facet, &num, printall);
-      qh->ridgeoutnum= num;
-      qh->printoutvar= 0;  /* counts number of ridges in output */
-      qh_fprintf(qh, fp, 9038, "LIST # %s | %s\n", qh->rbox_command, qh->qhull_command);
-    }
-
-    if (qh->PRINTdots) {
-      qh->printoutnum++;
-      num= qh->num_points + qh_setsize(qh, qh->other_points);
-      if (qh->DELAUNAY && qh->ATinfinity)
-        num--;
-      if (qh->PRINTdim == 4)
-        qh_fprintf(qh, fp, 9039, "4VECT %d %d 1\n", num, num);
-      else
-        qh_fprintf(qh, fp, 9040, "VECT %d %d 1\n", num, num);
-
-      for (i=num; i--; ) {
-        if (i % 20 == 0)
-          qh_fprintf(qh, fp, 9041, "\n");
-        qh_fprintf(qh, fp, 9042, "1 ");
-      }
-      qh_fprintf(qh, fp, 9043, "# 1 point per line\n1 ");
-      for (i=num-1; i--; ) { /* num at least 3 for D2 */
-        if (i % 20 == 0)
-          qh_fprintf(qh, fp, 9044, "\n");
-        qh_fprintf(qh, fp, 9045, "0 ");
-      }
-      qh_fprintf(qh, fp, 9046, "# 1 color for all\n");
-      FORALLpoints {
-        if (!qh->DELAUNAY || !qh->ATinfinity || qh_pointid(qh, point) != qh->num_points-1) {
-          if (qh->PRINTdim == 4)
-            qh_printpoint(qh, fp, NULL, point);
-            else
-              qh_printpoint3(qh, fp, point);
-        }
-      }
-      FOREACHpoint_(qh->other_points) {
-        if (qh->PRINTdim == 4)
-          qh_printpoint(qh, fp, NULL, point);
-        else
-          qh_printpoint3(qh, fp, point);
-      }
-      qh_fprintf(qh, fp, 9047, "0 1 1 1  # color of points\n");
-    }
-
-    if (qh->PRINTdim == 4  && !qh->PRINTnoplanes)
-      /* 4dview loads up multiple 4OFF objects slowly */
-      qh_fprintf(qh, fp, 9048, "4OFF %d %d 1\n", 3*qh->ridgeoutnum, qh->ridgeoutnum);
-    qh->PRINTcradius= 2 * qh->DISTround;  /* include test DISTround */
-    if (qh->PREmerge) {
-      maximize_(qh->PRINTcradius, qh->premerge_centrum + qh->DISTround);
-    }else if (qh->POSTmerge)
-      maximize_(qh->PRINTcradius, qh->postmerge_centrum + qh->DISTround);
-    qh->PRINTradius= qh->PRINTcradius;
-    if (qh->PRINTspheres + qh->PRINTcoplanar)
-      maximize_(qh->PRINTradius, qh->MAXabs_coord * qh_MINradius);
-    if (qh->premerge_cos < REALmax/2) {
-      maximize_(qh->PRINTradius, (1- qh->premerge_cos) * qh->MAXabs_coord);
-    }else if (!qh->PREmerge && qh->POSTmerge && qh->postmerge_cos < REALmax/2) {
-      maximize_(qh->PRINTradius, (1- qh->postmerge_cos) * qh->MAXabs_coord);
-    }
-    maximize_(qh->PRINTradius, qh->MINvisible);
-    if (qh->JOGGLEmax < REALmax/2)
-      qh->PRINTradius += qh->JOGGLEmax * sqrt((realT)qh->hull_dim);
-    if (qh->PRINTdim != 4 &&
-        (qh->PRINTcoplanar || qh->PRINTspheres || qh->PRINTcentrums)) {
-      vertices= qh_facetvertices(qh, facetlist, facets, printall);
-      if (qh->PRINTspheres && qh->PRINTdim <= 3)
-        qh_printspheres(qh, fp, vertices, qh->PRINTradius);
-      if (qh->PRINTcoplanar || qh->PRINTcentrums) {
-        qh->firstcentrum= True;
-        if (qh->PRINTcoplanar&& !qh->PRINTspheres) {
-          FOREACHvertex_(vertices)
-            qh_printpointvect2(qh, fp, vertex->point, NULL, qh->interior_point, qh->PRINTradius);
-        }
-        FORALLfacet_(facetlist) {
-          if (!printall && qh_skipfacet(qh, facet))
-            continue;
-          if (!facet->normal)
-            continue;
-          if (qh->PRINTcentrums && qh->PRINTdim <= 3)
-            qh_printcentrum(qh, fp, facet, qh->PRINTcradius);
-          if (!qh->PRINTcoplanar)
-            continue;
-          FOREACHpoint_(facet->coplanarset)
-            qh_printpointvect2(qh, fp, point, facet->normal, NULL, qh->PRINTradius);
-          FOREACHpoint_(facet->outsideset)
-            qh_printpointvect2(qh, fp, point, facet->normal, NULL, qh->PRINTradius);
-        }
-        FOREACHfacet_(facets) {
-          if (!printall && qh_skipfacet(qh, facet))
-            continue;
-          if (!facet->normal)
-            continue;
-          if (qh->PRINTcentrums && qh->PRINTdim <= 3)
-            qh_printcentrum(qh, fp, facet, qh->PRINTcradius);
-          if (!qh->PRINTcoplanar)
-            continue;
-          FOREACHpoint_(facet->coplanarset)
-            qh_printpointvect2(qh, fp, point, facet->normal, NULL, qh->PRINTradius);
-          FOREACHpoint_(facet->outsideset)
-            qh_printpointvect2(qh, fp, point, facet->normal, NULL, qh->PRINTradius);
-        }
-      }
-      qh_settempfree(qh, &vertices);
-    }
-    qh->visit_id++; /* for printing hyperplane intersections */
-    break;
-  case qh_PRINTids:
-    qh_fprintf(qh, fp, 9049, "%d\n", numfacets);
-    break;
-  case qh_PRINTincidences:
-    if (qh->VORONOI && qh->PRINTprecision)
-      qh_fprintf(qh, qh->ferr, 7053, "qhull warning: writing Delaunay.  Use 'p' or 'o' for Voronoi centers\n");
-    qh->printoutvar= qh->vertex_id;  /* centrum id for non-simplicial facets */
-    if (qh->hull_dim <= 3)
-      qh_fprintf(qh, fp, 9050, "%d\n", numfacets);
-    else
-      qh_fprintf(qh, fp, 9051, "%d\n", numsimplicial+numridges);
-    break;
-  case qh_PRINTinner:
-  case qh_PRINTnormals:
-  case qh_PRINTouter:
-    if (qh->CDDoutput)
-      qh_fprintf(qh, fp, 9052, "%s | %s\nbegin\n    %d %d real\n", qh->rbox_command,
-            qh->qhull_command, numfacets, qh->hull_dim+1);
-    else
-      qh_fprintf(qh, fp, 9053, "%d\n%d\n", qh->hull_dim+1, numfacets);
-    break;
-  case qh_PRINTmathematica:
-  case qh_PRINTmaple:
-    if (qh->hull_dim > 3)  /* qh_initbuffers also checks */
-      goto LABELnoformat;
-    if (qh->VORONOI)
-      qh_fprintf(qh, qh->ferr, 7054, "qhull warning: output is the Delaunay triangulation\n");
-    if (format == qh_PRINTmaple) {
-      if (qh->hull_dim == 2)
-        qh_fprintf(qh, fp, 9054, "PLOT(CURVES(\n");
-      else
-        qh_fprintf(qh, fp, 9055, "PLOT3D(POLYGONS(\n");
-    }else
-      qh_fprintf(qh, fp, 9056, "{\n");
-    qh->printoutvar= 0;   /* counts number of facets for notfirst */
-    break;
-  case qh_PRINTmerges:
-    qh_fprintf(qh, fp, 9057, "%d\n", numfacets);
-    break;
-  case qh_PRINTpointintersect:
-    qh_fprintf(qh, fp, 9058, "%d\n%d\n", qh->hull_dim, numfacets);
-    break;
-  case qh_PRINTneighbors:
-    qh_fprintf(qh, fp, 9059, "%d\n", numfacets);
-    break;
-  case qh_PRINToff:
-  case qh_PRINTtriangles:
-    if (qh->VORONOI)
-      goto LABELnoformat;
-    num = qh->hull_dim;
-    if (format == qh_PRINToff || qh->hull_dim == 2)
-      qh_fprintf(qh, fp, 9060, "%d\n%d %d %d\n", num,
-        qh->num_points+qh_setsize(qh, qh->other_points), numfacets, totneighbors/2);
-    else { /* qh_PRINTtriangles */
-      qh->printoutvar= qh->num_points+qh_setsize(qh, qh->other_points); /* first centrum */
-      if (qh->DELAUNAY)
-        num--;  /* drop last dimension */
-      qh_fprintf(qh, fp, 9061, "%d\n%d %d %d\n", num, qh->printoutvar
-        + numfacets - numsimplicial, numsimplicial + numridges, totneighbors/2);
-    }
-    FORALLpoints
-      qh_printpointid(qh, qh->fout, NULL, num, point, qh_IDunknown);
-    FOREACHpoint_(qh->other_points)
-      qh_printpointid(qh, qh->fout, NULL, num, point, qh_IDunknown);
-    if (format == qh_PRINTtriangles && qh->hull_dim > 2) {
-      FORALLfacets {
-        if (!facet->simplicial && facet->visitid)
-          qh_printcenter(qh, qh->fout, format, NULL, facet);
-      }
-    }
-    break;
-  case qh_PRINTpointnearest:
-    qh_fprintf(qh, fp, 9062, "%d\n", numcoplanars);
-    break;
-  case qh_PRINTpoints:
-    if (!qh->VORONOI)
-      goto LABELnoformat;
-    if (qh->CDDoutput)
-      qh_fprintf(qh, fp, 9063, "%s | %s\nbegin\n%d %d real\n", qh->rbox_command,
-           qh->qhull_command, numfacets, qh->hull_dim);
-    else
-      qh_fprintf(qh, fp, 9064, "%d\n%d\n", qh->hull_dim-1, numfacets);
-    break;
-  case qh_PRINTvertices:
-    qh_fprintf(qh, fp, 9065, "%d\n", numfacets);
-    break;
-  case qh_PRINTsummary:
-  default:
-  LABELnoformat:
-    qh_fprintf(qh, qh->ferr, 6068, "qhull internal error (qh_printbegin): can not use this format for dimension %d\n",
-         qh->hull_dim);
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }
-} /* printbegin */
-
-/*---------------------------------
-
-  qh_printcenter(qh, fp, string, facet )
-    print facet->center as centrum or Voronoi center
-    string may be NULL.  Don't include '%' codes.
-    nop if qh->CENTERtype neither CENTERvoronoi nor CENTERcentrum
-    if upper envelope of Delaunay triangulation and point at-infinity
-      prints qh_INFINITE instead;
-
-  notes:
-    defines facet->center if needed
-    if format=PRINTgeom, adds a 0 if would otherwise be 2-d
-    Same as QhullFacet::printCenter
-*/
-void qh_printcenter(qhT *qh, FILE *fp, qh_PRINT format, const char *string, facetT *facet) {
-  int k, num;
-
-  if (qh->CENTERtype != qh_ASvoronoi && qh->CENTERtype != qh_AScentrum)
-    return;
-  if (string)
-    qh_fprintf(qh, fp, 9066, string);
-  if (qh->CENTERtype == qh_ASvoronoi) {
-    num= qh->hull_dim-1;
-    if (!facet->normal || !facet->upperdelaunay || !qh->ATinfinity) {
-      if (!facet->center)
-        facet->center= qh_facetcenter(qh, facet->vertices);
-      for (k=0; k < num; k++)
-        qh_fprintf(qh, fp, 9067, qh_REAL_1, facet->center[k]);
-    }else {
-      for (k=0; k < num; k++)
-        qh_fprintf(qh, fp, 9068, qh_REAL_1, qh_INFINITE);
-    }
-  }else /* qh->CENTERtype == qh_AScentrum */ {
-    num= qh->hull_dim;
-    if (format == qh_PRINTtriangles && qh->DELAUNAY)
-      num--;
-    if (!facet->center)
-      facet->center= qh_getcentrum(qh, facet);
-    for (k=0; k < num; k++)
-      qh_fprintf(qh, fp, 9069, qh_REAL_1, facet->center[k]);
-  }
-  if (format == qh_PRINTgeom && num == 2)
-    qh_fprintf(qh, fp, 9070, " 0\n");
-  else
-    qh_fprintf(qh, fp, 9071, "\n");
-} /* printcenter */
-
-/*---------------------------------
-
-  qh_printcentrum(qh, fp, facet, radius )
-    print centrum for a facet in OOGL format
-    radius defines size of centrum
-    2-d or 3-d only
-
-  returns:
-    defines facet->center if needed
-*/
-void qh_printcentrum(qhT *qh, FILE *fp, facetT *facet, realT radius) {
-  pointT *centrum, *projpt;
-  boolT tempcentrum= False;
-  realT xaxis[4], yaxis[4], normal[4], dist;
-  realT green[3]={0, 1, 0};
-  vertexT *apex;
-  int k;
-
-  if (qh->CENTERtype == qh_AScentrum) {
-    if (!facet->center)
-      facet->center= qh_getcentrum(qh, facet);
-    centrum= facet->center;
-  }else {
-    centrum= qh_getcentrum(qh, facet);
-    tempcentrum= True;
-  }
-  qh_fprintf(qh, fp, 9072, "{appearance {-normal -edge normscale 0} ");
-  if (qh->firstcentrum) {
-    qh->firstcentrum= False;
-    qh_fprintf(qh, fp, 9073, "{INST geom { define centrum CQUAD  # f%d\n\
--0.3 -0.3 0.0001     0 0 1 1\n\
- 0.3 -0.3 0.0001     0 0 1 1\n\
- 0.3  0.3 0.0001     0 0 1 1\n\
--0.3  0.3 0.0001     0 0 1 1 } transform { \n", facet->id);
-  }else
-    qh_fprintf(qh, fp, 9074, "{INST geom { : centrum } transform { # f%d\n", facet->id);
-  apex= SETfirstt_(facet->vertices, vertexT);
-  qh_distplane(qh, apex->point, facet, &dist);
-  projpt= qh_projectpoint(qh, apex->point, facet, dist);
-  for (k=qh->hull_dim; k--; ) {
-    xaxis[k]= projpt[k] - centrum[k];
-    normal[k]= facet->normal[k];
-  }
-  if (qh->hull_dim == 2) {
-    xaxis[2]= 0;
-    normal[2]= 0;
-  }else if (qh->hull_dim == 4) {
-    qh_projectdim3(qh, xaxis, xaxis);
-    qh_projectdim3(qh, normal, normal);
-    qh_normalize2(qh, normal, qh->PRINTdim, True, NULL, NULL);
-  }
-  qh_crossproduct(3, xaxis, normal, yaxis);
-  qh_fprintf(qh, fp, 9075, "%8.4g %8.4g %8.4g 0\n", xaxis[0], xaxis[1], xaxis[2]);
-  qh_fprintf(qh, fp, 9076, "%8.4g %8.4g %8.4g 0\n", yaxis[0], yaxis[1], yaxis[2]);
-  qh_fprintf(qh, fp, 9077, "%8.4g %8.4g %8.4g 0\n", normal[0], normal[1], normal[2]);
-  qh_printpoint3(qh, fp, centrum);
-  qh_fprintf(qh, fp, 9078, "1 }}}\n");
-  qh_memfree(qh, projpt, qh->normal_size);
-  qh_printpointvect(qh, fp, centrum, facet->normal, NULL, radius, green);
-  if (tempcentrum)
-    qh_memfree(qh, centrum, qh->normal_size);
-} /* printcentrum */
-
-/*---------------------------------
-
-  qh_printend(qh, fp, format )
-    prints trailer for all output formats
-
-  see:
-    qh_printbegin() and qh_printafacet()
-
-*/
-void qh_printend(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall) {
-  int num;
-  facetT *facet, **facetp;
-
-  if (!qh->printoutnum)
-    qh_fprintf(qh, qh->ferr, 7055, "qhull warning: no facets printed\n");
-  switch (format) {
-  case qh_PRINTgeom:
-    if (qh->hull_dim == 4 && qh->DROPdim < 0  && !qh->PRINTnoplanes) {
-      qh->visit_id++;
-      num= 0;
-      FORALLfacet_(facetlist)
-        qh_printend4geom(qh, fp, facet,&num, printall);
-      FOREACHfacet_(facets)
-        qh_printend4geom(qh, fp, facet, &num, printall);
-      if (num != qh->ridgeoutnum || qh->printoutvar != qh->ridgeoutnum) {
-        qh_fprintf(qh, qh->ferr, 6069, "qhull internal error (qh_printend): number of ridges %d != number printed %d and at end %d\n", qh->ridgeoutnum, qh->printoutvar, num);
-        qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-      }
-    }else
-      qh_fprintf(qh, fp, 9079, "}\n");
-    break;
-  case qh_PRINTinner:
-  case qh_PRINTnormals:
-  case qh_PRINTouter:
-    if (qh->CDDoutput)
-      qh_fprintf(qh, fp, 9080, "end\n");
-    break;
-  case qh_PRINTmaple:
-    qh_fprintf(qh, fp, 9081, "));\n");
-    break;
-  case qh_PRINTmathematica:
-    qh_fprintf(qh, fp, 9082, "}\n");
-    break;
-  case qh_PRINTpoints:
-    if (qh->CDDoutput)
-      qh_fprintf(qh, fp, 9083, "end\n");
-    break;
-  default:
-    break;
-  }
-} /* printend */
-
-/*---------------------------------
-
-  qh_printend4geom(qh, fp, facet, numridges, printall )
-    helper function for qh_printbegin/printend
-
-  returns:
-    number of printed ridges
-
-  notes:
-    just counts printed ridges if fp=NULL
-    uses facet->visitid
-    must agree with qh_printfacet4geom...
-
-  design:
-    computes color for facet from its normal
-    prints each ridge of facet
-*/
-void qh_printend4geom(qhT *qh, FILE *fp, facetT *facet, int *nump, boolT printall) {
-  realT color[3];
-  int i, num= *nump;
-  facetT *neighbor, **neighborp;
-  ridgeT *ridge, **ridgep;
-
-  if (!printall && qh_skipfacet(qh, facet))
-    return;
-  if (qh->PRINTnoplanes || (facet->visible && qh->NEWfacets))
-    return;
-  if (!facet->normal)
-    return;
-  if (fp) {
-    for (i=0; i < 3; i++) {
-      color[i]= (facet->normal[i]+1.0)/2.0;
-      maximize_(color[i], -1.0);
-      minimize_(color[i], +1.0);
-    }
-  }
-  facet->visitid= qh->visit_id;
-  if (facet->simplicial) {
-    FOREACHneighbor_(facet) {
-      if (neighbor->visitid != qh->visit_id) {
-        if (fp)
-          qh_fprintf(qh, fp, 9084, "3 %d %d %d %8.4g %8.4g %8.4g 1 # f%d f%d\n",
-                 3*num, 3*num+1, 3*num+2, color[0], color[1], color[2],
-                 facet->id, neighbor->id);
-        num++;
-      }
-    }
-  }else {
-    FOREACHridge_(facet->ridges) {
-      neighbor= otherfacet_(ridge, facet);
-      if (neighbor->visitid != qh->visit_id) {
-        if (fp)
-          qh_fprintf(qh, fp, 9085, "3 %d %d %d %8.4g %8.4g %8.4g 1 #r%d f%d f%d\n",
-                 3*num, 3*num+1, 3*num+2, color[0], color[1], color[2],
-                 ridge->id, facet->id, neighbor->id);
-        num++;
-      }
-    }
-  }
-  *nump= num;
-} /* printend4geom */
-
-/*---------------------------------
-
-  qh_printextremes(qh, fp, facetlist, facets, printall )
-    print extreme points for convex hulls or halfspace intersections
-
-  notes:
-    #points, followed by ids, one per line
-
-    sorted by id
-    same order as qh_printpoints_out if no coplanar/interior points
-*/
-void qh_printextremes(qhT *qh, FILE *fp, facetT *facetlist, setT *facets, boolT printall) {
-  setT *vertices, *points;
-  pointT *point;
-  vertexT *vertex, **vertexp;
-  int id;
-  int numpoints=0, point_i, point_n;
-  int allpoints= qh->num_points + qh_setsize(qh, qh->other_points);
-
-  points= qh_settemp(qh, allpoints);
-  qh_setzero(qh, points, 0, allpoints);
-  vertices= qh_facetvertices(qh, facetlist, facets, printall);
-  FOREACHvertex_(vertices) {
-    id= qh_pointid(qh, vertex->point);
-    if (id >= 0) {
-      SETelem_(points, id)= vertex->point;
-      numpoints++;
-    }
-  }
-  qh_settempfree(qh, &vertices);
-  qh_fprintf(qh, fp, 9086, "%d\n", numpoints);
-  FOREACHpoint_i_(qh, points) {
-    if (point)
-      qh_fprintf(qh, fp, 9087, "%d\n", point_i);
-  }
-  qh_settempfree(qh, &points);
-} /* printextremes */
-
-/*---------------------------------
-
-  qh_printextremes_2d(qh, fp, facetlist, facets, printall )
-    prints point ids for facets in qh_ORIENTclock order
-
-  notes:
-    #points, followed by ids, one per line
-    if facetlist/facets are disjoint than the output includes skips
-    errors if facets form a loop
-    does not print coplanar points
-*/
-void qh_printextremes_2d(qhT *qh, FILE *fp, facetT *facetlist, setT *facets, boolT printall) {
-  int numfacets, numridges, totneighbors, numcoplanars, numsimplicial, numtricoplanars;
-  setT *vertices;
-  facetT *facet, *startfacet, *nextfacet;
-  vertexT *vertexA, *vertexB;
-
-  qh_countfacets(qh, facetlist, facets, printall, &numfacets, &numsimplicial,
-      &totneighbors, &numridges, &numcoplanars, &numtricoplanars); /* marks qh->visit_id */
-  vertices= qh_facetvertices(qh, facetlist, facets, printall);
-  qh_fprintf(qh, fp, 9088, "%d\n", qh_setsize(qh, vertices));
-  qh_settempfree(qh, &vertices);
-  if (!numfacets)
-    return;
-  facet= startfacet= facetlist ? facetlist : SETfirstt_(facets, facetT);
-  qh->vertex_visit++;
-  qh->visit_id++;
-  do {
-    if (facet->toporient ^ qh_ORIENTclock) {
-      vertexA= SETfirstt_(facet->vertices, vertexT);
-      vertexB= SETsecondt_(facet->vertices, vertexT);
-      nextfacet= SETfirstt_(facet->neighbors, facetT);
-    }else {
-      vertexA= SETsecondt_(facet->vertices, vertexT);
-      vertexB= SETfirstt_(facet->vertices, vertexT);
-      nextfacet= SETsecondt_(facet->neighbors, facetT);
-    }
-    if (facet->visitid == qh->visit_id) {
-      qh_fprintf(qh, qh->ferr, 6218, "Qhull internal error (qh_printextremes_2d): loop in facet list.  facet %d nextfacet %d\n",
-                 facet->id, nextfacet->id);
-      qh_errexit2(qh, qh_ERRqhull, facet, nextfacet);
-    }
-    if (facet->visitid) {
-      if (vertexA->visitid != qh->vertex_visit) {
-        vertexA->visitid= qh->vertex_visit;
-        qh_fprintf(qh, fp, 9089, "%d\n", qh_pointid(qh, vertexA->point));
-      }
-      if (vertexB->visitid != qh->vertex_visit) {
-        vertexB->visitid= qh->vertex_visit;
-        qh_fprintf(qh, fp, 9090, "%d\n", qh_pointid(qh, vertexB->point));
-      }
-    }
-    facet->visitid= qh->visit_id;
-    facet= nextfacet;
-  }while (facet && facet != startfacet);
-} /* printextremes_2d */
-
-/*---------------------------------
-
-  qh_printextremes_d(qh, fp, facetlist, facets, printall )
-    print extreme points of input sites for Delaunay triangulations
-
-  notes:
-    #points, followed by ids, one per line
-
-    unordered
-*/
-void qh_printextremes_d(qhT *qh, FILE *fp, facetT *facetlist, setT *facets, boolT printall) {
-  setT *vertices;
-  vertexT *vertex, **vertexp;
-  boolT upperseen, lowerseen;
-  facetT *neighbor, **neighborp;
-  int numpoints=0;
-
-  vertices= qh_facetvertices(qh, facetlist, facets, printall);
-  qh_vertexneighbors(qh);
-  FOREACHvertex_(vertices) {
-    upperseen= lowerseen= False;
-    FOREACHneighbor_(vertex) {
-      if (neighbor->upperdelaunay)
-        upperseen= True;
-      else
-        lowerseen= True;
-    }
-    if (upperseen && lowerseen) {
-      vertex->seen= True;
-      numpoints++;
-    }else
-      vertex->seen= False;
-  }
-  qh_fprintf(qh, fp, 9091, "%d\n", numpoints);
-  FOREACHvertex_(vertices) {
-    if (vertex->seen)
-      qh_fprintf(qh, fp, 9092, "%d\n", qh_pointid(qh, vertex->point));
-  }
-  qh_settempfree(qh, &vertices);
-} /* printextremes_d */
-
-/*---------------------------------
-
-  qh_printfacet(qh, fp, facet )
-    prints all fields of a facet to fp
-
-  notes:
-    ridges printed in neighbor order
-*/
-void qh_printfacet(qhT *qh, FILE *fp, facetT *facet) {
-
-  qh_printfacetheader(qh, fp, facet);
-  if (facet->ridges)
-    qh_printfacetridges(qh, fp, facet);
-} /* printfacet */
-
-
-/*---------------------------------
-
-  qh_printfacet2geom(qh, fp, facet, color )
-    print facet as part of a 2-d VECT for Geomview
-
-    notes:
-      assume precise calculations in io_r.c with roundoff covered by qh_GEOMepsilon
-      mindist is calculated within io_r.c.  maxoutside is calculated elsewhere
-      so a DISTround error may have occurred.
-*/
-void qh_printfacet2geom(qhT *qh, FILE *fp, facetT *facet, realT color[3]) {
-  pointT *point0, *point1;
-  realT mindist, innerplane, outerplane;
-  int k;
-
-  qh_facet2point(qh, facet, &point0, &point1, &mindist);
-  qh_geomplanes(qh, facet, &outerplane, &innerplane);
-  if (qh->PRINTouter || (!qh->PRINTnoplanes && !qh->PRINTinner))
-    qh_printfacet2geom_points(qh, fp, point0, point1, facet, outerplane, color);
-  if (qh->PRINTinner || (!qh->PRINTnoplanes && !qh->PRINTouter &&
-                outerplane - innerplane > 2 * qh->MAXabs_coord * qh_GEOMepsilon)) {
-    for (k=3; k--; )
-      color[k]= 1.0 - color[k];
-    qh_printfacet2geom_points(qh, fp, point0, point1, facet, innerplane, color);
-  }
-  qh_memfree(qh, point1, qh->normal_size);
-  qh_memfree(qh, point0, qh->normal_size);
-} /* printfacet2geom */
-
-/*---------------------------------
-
-  qh_printfacet2geom_points(qh, fp, point1, point2, facet, offset, color )
-    prints a 2-d facet as a VECT with 2 points at some offset.
-    The points are on the facet's plane.
-*/
-void qh_printfacet2geom_points(qhT *qh, FILE *fp, pointT *point1, pointT *point2,
-                               facetT *facet, realT offset, realT color[3]) {
-  pointT *p1= point1, *p2= point2;
-
-  qh_fprintf(qh, fp, 9093, "VECT 1 2 1 2 1 # f%d\n", facet->id);
-  if (offset != 0.0) {
-    p1= qh_projectpoint(qh, p1, facet, -offset);
-    p2= qh_projectpoint(qh, p2, facet, -offset);
-  }
-  qh_fprintf(qh, fp, 9094, "%8.4g %8.4g %8.4g\n%8.4g %8.4g %8.4g\n",
-           p1[0], p1[1], 0.0, p2[0], p2[1], 0.0);
-  if (offset != 0.0) {
-    qh_memfree(qh, p1, qh->normal_size);
-    qh_memfree(qh, p2, qh->normal_size);
-  }
-  qh_fprintf(qh, fp, 9095, "%8.4g %8.4g %8.4g 1.0\n", color[0], color[1], color[2]);
-} /* printfacet2geom_points */
-
-
-/*---------------------------------
-
-  qh_printfacet2math(qh, fp, facet, format, notfirst )
-    print 2-d Maple or Mathematica output for a facet
-    may be non-simplicial
-
-  notes:
-    use %16.8f since Mathematica 2.2 does not handle exponential format
-    see qh_printfacet3math
-*/
-void qh_printfacet2math(qhT *qh, FILE *fp, facetT *facet, qh_PRINT format, int notfirst) {
-  pointT *point0, *point1;
-  realT mindist;
-  const char *pointfmt;
-
-  qh_facet2point(qh, facet, &point0, &point1, &mindist);
-  if (notfirst)
-    qh_fprintf(qh, fp, 9096, ",");
-  if (format == qh_PRINTmaple)
-    pointfmt= "[[%16.8f, %16.8f], [%16.8f, %16.8f]]\n";
-  else
-    pointfmt= "Line[{{%16.8f, %16.8f}, {%16.8f, %16.8f}}]\n";
-  qh_fprintf(qh, fp, 9097, pointfmt, point0[0], point0[1], point1[0], point1[1]);
-  qh_memfree(qh, point1, qh->normal_size);
-  qh_memfree(qh, point0, qh->normal_size);
-} /* printfacet2math */
-
-
-/*---------------------------------
-
-  qh_printfacet3geom_nonsimplicial(qh, fp, facet, color )
-    print Geomview OFF for a 3-d nonsimplicial facet.
-    if DOintersections, prints ridges to unvisited neighbors(qh->visit_id)
-
-  notes
-    uses facet->visitid for intersections and ridges
-*/
-void qh_printfacet3geom_nonsimplicial(qhT *qh, FILE *fp, facetT *facet, realT color[3]) {
-  ridgeT *ridge, **ridgep;
-  setT *projectedpoints, *vertices;
-  vertexT *vertex, **vertexp, *vertexA, *vertexB;
-  pointT *projpt, *point, **pointp;
-  facetT *neighbor;
-  realT dist, outerplane, innerplane;
-  int cntvertices, k;
-  realT black[3]={0, 0, 0}, green[3]={0, 1, 0};
-
-  qh_geomplanes(qh, facet, &outerplane, &innerplane);
-  vertices= qh_facet3vertex(qh, facet); /* oriented */
-  cntvertices= qh_setsize(qh, vertices);
-  projectedpoints= qh_settemp(qh, cntvertices);
-  FOREACHvertex_(vertices) {
-    zinc_(Zdistio);
-    qh_distplane(qh, vertex->point, facet, &dist);
-    projpt= qh_projectpoint(qh, vertex->point, facet, dist);
-    qh_setappend(qh, &projectedpoints, projpt);
-  }
-  if (qh->PRINTouter || (!qh->PRINTnoplanes && !qh->PRINTinner))
-    qh_printfacet3geom_points(qh, fp, projectedpoints, facet, outerplane, color);
-  if (qh->PRINTinner || (!qh->PRINTnoplanes && !qh->PRINTouter &&
-                outerplane - innerplane > 2 * qh->MAXabs_coord * qh_GEOMepsilon)) {
-    for (k=3; k--; )
-      color[k]= 1.0 - color[k];
-    qh_printfacet3geom_points(qh, fp, projectedpoints, facet, innerplane, color);
-  }
-  FOREACHpoint_(projectedpoints)
-    qh_memfree(qh, point, qh->normal_size);
-  qh_settempfree(qh, &projectedpoints);
-  qh_settempfree(qh, &vertices);
-  if ((qh->DOintersections || qh->PRINTridges)
-  && (!facet->visible || !qh->NEWfacets)) {
-    facet->visitid= qh->visit_id;
-    FOREACHridge_(facet->ridges) {
-      neighbor= otherfacet_(ridge, facet);
-      if (neighbor->visitid != qh->visit_id) {
-        if (qh->DOintersections)
-          qh_printhyperplaneintersection(qh, fp, facet, neighbor, ridge->vertices, black);
-        if (qh->PRINTridges) {
-          vertexA= SETfirstt_(ridge->vertices, vertexT);
-          vertexB= SETsecondt_(ridge->vertices, vertexT);
-          qh_printline3geom(qh, fp, vertexA->point, vertexB->point, green);
-        }
-      }
-    }
-  }
-} /* printfacet3geom_nonsimplicial */
-
-/*---------------------------------
-
-  qh_printfacet3geom_points(qh, fp, points, facet, offset )
-    prints a 3-d facet as OFF Geomview object.
-    offset is relative to the facet's hyperplane
-    Facet is determined as a list of points
-*/
-void qh_printfacet3geom_points(qhT *qh, FILE *fp, setT *points, facetT *facet, realT offset, realT color[3]) {
-  int k, n= qh_setsize(qh, points), i;
-  pointT *point, **pointp;
-  setT *printpoints;
-
-  qh_fprintf(qh, fp, 9098, "{ OFF %d 1 1 # f%d\n", n, facet->id);
-  if (offset != 0.0) {
-    printpoints= qh_settemp(qh, n);
-    FOREACHpoint_(points)
-      qh_setappend(qh, &printpoints, qh_projectpoint(qh, point, facet, -offset));
-  }else
-    printpoints= points;
-  FOREACHpoint_(printpoints) {
-    for (k=0; k < qh->hull_dim; k++) {
-      if (k == qh->DROPdim)
-        qh_fprintf(qh, fp, 9099, "0 ");
-      else
-        qh_fprintf(qh, fp, 9100, "%8.4g ", point[k]);
-    }
-    if (printpoints != points)
-      qh_memfree(qh, point, qh->normal_size);
-    qh_fprintf(qh, fp, 9101, "\n");
-  }
-  if (printpoints != points)
-    qh_settempfree(qh, &printpoints);
-  qh_fprintf(qh, fp, 9102, "%d ", n);
-  for (i=0; i < n; i++)
-    qh_fprintf(qh, fp, 9103, "%d ", i);
-  qh_fprintf(qh, fp, 9104, "%8.4g %8.4g %8.4g 1.0 }\n", color[0], color[1], color[2]);
-} /* printfacet3geom_points */
-
-
-/*---------------------------------
-
-  qh_printfacet3geom_simplicial(qh, )
-    print Geomview OFF for a 3-d simplicial facet.
-
-  notes:
-    may flip color
-    uses facet->visitid for intersections and ridges
-
-    assume precise calculations in io_r.c with roundoff covered by qh_GEOMepsilon
-    innerplane may be off by qh->DISTround.  Maxoutside is calculated elsewhere
-    so a DISTround error may have occurred.
-*/
-void qh_printfacet3geom_simplicial(qhT *qh, FILE *fp, facetT *facet, realT color[3]) {
-  setT *points, *vertices;
-  vertexT *vertex, **vertexp, *vertexA, *vertexB;
-  facetT *neighbor, **neighborp;
-  realT outerplane, innerplane;
-  realT black[3]={0, 0, 0}, green[3]={0, 1, 0};
-  int k;
-
-  qh_geomplanes(qh, facet, &outerplane, &innerplane);
-  vertices= qh_facet3vertex(qh, facet);
-  points= qh_settemp(qh, qh->TEMPsize);
-  FOREACHvertex_(vertices)
-    qh_setappend(qh, &points, vertex->point);
-  if (qh->PRINTouter || (!qh->PRINTnoplanes && !qh->PRINTinner))
-    qh_printfacet3geom_points(qh, fp, points, facet, outerplane, color);
-  if (qh->PRINTinner || (!qh->PRINTnoplanes && !qh->PRINTouter &&
-              outerplane - innerplane > 2 * qh->MAXabs_coord * qh_GEOMepsilon)) {
-    for (k=3; k--; )
-      color[k]= 1.0 - color[k];
-    qh_printfacet3geom_points(qh, fp, points, facet, innerplane, color);
-  }
-  qh_settempfree(qh, &points);
-  qh_settempfree(qh, &vertices);
-  if ((qh->DOintersections || qh->PRINTridges)
-  && (!facet->visible || !qh->NEWfacets)) {
-    facet->visitid= qh->visit_id;
-    FOREACHneighbor_(facet) {
-      if (neighbor->visitid != qh->visit_id) {
-        vertices= qh_setnew_delnthsorted(qh, facet->vertices, qh->hull_dim,
-                          SETindex_(facet->neighbors, neighbor), 0);
-        if (qh->DOintersections)
-           qh_printhyperplaneintersection(qh, fp, facet, neighbor, vertices, black);
-        if (qh->PRINTridges) {
-          vertexA= SETfirstt_(vertices, vertexT);
-          vertexB= SETsecondt_(vertices, vertexT);
-          qh_printline3geom(qh, fp, vertexA->point, vertexB->point, green);
-        }
-        qh_setfree(qh, &vertices);
-      }
-    }
-  }
-} /* printfacet3geom_simplicial */
-
-/*---------------------------------
-
-  qh_printfacet3math(qh, fp, facet, notfirst )
-    print 3-d Maple or Mathematica output for a facet
-
-  notes:
-    may be non-simplicial
-    use %16.8f since Mathematica 2.2 does not handle exponential format
-    see qh_printfacet2math
-*/
-void qh_printfacet3math(qhT *qh, FILE *fp, facetT *facet, qh_PRINT format, int notfirst) {
-  vertexT *vertex, **vertexp;
-  setT *points, *vertices;
-  pointT *point, **pointp;
-  boolT firstpoint= True;
-  realT dist;
-  const char *pointfmt, *endfmt;
-
-  if (notfirst)
-    qh_fprintf(qh, fp, 9105, ",\n");
-  vertices= qh_facet3vertex(qh, facet);
-  points= qh_settemp(qh, qh_setsize(qh, vertices));
-  FOREACHvertex_(vertices) {
-    zinc_(Zdistio);
-    qh_distplane(qh, vertex->point, facet, &dist);
-    point= qh_projectpoint(qh, vertex->point, facet, dist);
-    qh_setappend(qh, &points, point);
-  }
-  if (format == qh_PRINTmaple) {
-    qh_fprintf(qh, fp, 9106, "[");
-    pointfmt= "[%16.8f, %16.8f, %16.8f]";
-    endfmt= "]";
-  }else {
-    qh_fprintf(qh, fp, 9107, "Polygon[{");
-    pointfmt= "{%16.8f, %16.8f, %16.8f}";
-    endfmt= "}]";
-  }
-  FOREACHpoint_(points) {
-    if (firstpoint)
-      firstpoint= False;
-    else
-      qh_fprintf(qh, fp, 9108, ",\n");
-    qh_fprintf(qh, fp, 9109, pointfmt, point[0], point[1], point[2]);
-  }
-  FOREACHpoint_(points)
-    qh_memfree(qh, point, qh->normal_size);
-  qh_settempfree(qh, &points);
-  qh_settempfree(qh, &vertices);
-  qh_fprintf(qh, fp, 9110, "%s", endfmt);
-} /* printfacet3math */
-
-
-/*---------------------------------
-
-  qh_printfacet3vertex(qh, fp, facet, format )
-    print vertices in a 3-d facet as point ids
-
-  notes:
-    prints number of vertices first if format == qh_PRINToff
-    the facet may be non-simplicial
-*/
-void qh_printfacet3vertex(qhT *qh, FILE *fp, facetT *facet, qh_PRINT format) {
-  vertexT *vertex, **vertexp;
-  setT *vertices;
-
-  vertices= qh_facet3vertex(qh, facet);
-  if (format == qh_PRINToff)
-    qh_fprintf(qh, fp, 9111, "%d ", qh_setsize(qh, vertices));
-  FOREACHvertex_(vertices)
-    qh_fprintf(qh, fp, 9112, "%d ", qh_pointid(qh, vertex->point));
-  qh_fprintf(qh, fp, 9113, "\n");
-  qh_settempfree(qh, &vertices);
-} /* printfacet3vertex */
-
-
-/*---------------------------------
-
-  qh_printfacet4geom_nonsimplicial(qh, )
-    print Geomview 4OFF file for a 4d nonsimplicial facet
-    prints all ridges to unvisited neighbors (qh.visit_id)
-    if qh.DROPdim
-      prints in OFF format
-
-  notes:
-    must agree with printend4geom()
-*/
-void qh_printfacet4geom_nonsimplicial(qhT *qh, FILE *fp, facetT *facet, realT color[3]) {
-  facetT *neighbor;
-  ridgeT *ridge, **ridgep;
-  vertexT *vertex, **vertexp;
-  pointT *point;
-  int k;
-  realT dist;
-
-  facet->visitid= qh->visit_id;
-  if (qh->PRINTnoplanes || (facet->visible && qh->NEWfacets))
-    return;
-  FOREACHridge_(facet->ridges) {
-    neighbor= otherfacet_(ridge, facet);
-    if (neighbor->visitid == qh->visit_id)
-      continue;
-    if (qh->PRINTtransparent && !neighbor->good)
-      continue;
-    if (qh->DOintersections)
-      qh_printhyperplaneintersection(qh, fp, facet, neighbor, ridge->vertices, color);
-    else {
-      if (qh->DROPdim >= 0)
-        qh_fprintf(qh, fp, 9114, "OFF 3 1 1 # f%d\n", facet->id);
-      else {
-        qh->printoutvar++;
-        qh_fprintf(qh, fp, 9115, "# r%d between f%d f%d\n", ridge->id, facet->id, neighbor->id);
-      }
-      FOREACHvertex_(ridge->vertices) {
-        zinc_(Zdistio);
-        qh_distplane(qh, vertex->point,facet, &dist);
-        point=qh_projectpoint(qh, vertex->point,facet, dist);
-        for (k=0; k < qh->hull_dim; k++) {
-          if (k != qh->DROPdim)
-            qh_fprintf(qh, fp, 9116, "%8.4g ", point[k]);
-        }
-        qh_fprintf(qh, fp, 9117, "\n");
-        qh_memfree(qh, point, qh->normal_size);
-      }
-      if (qh->DROPdim >= 0)
-        qh_fprintf(qh, fp, 9118, "3 0 1 2 %8.4g %8.4g %8.4g\n", color[0], color[1], color[2]);
-    }
-  }
-} /* printfacet4geom_nonsimplicial */
-
-
-/*---------------------------------
-
-  qh_printfacet4geom_simplicial(qh, fp, facet, color )
-    print Geomview 4OFF file for a 4d simplicial facet
-    prints triangles for unvisited neighbors (qh.visit_id)
-
-  notes:
-    must agree with printend4geom()
-*/
-void qh_printfacet4geom_simplicial(qhT *qh, FILE *fp, facetT *facet, realT color[3]) {
-  setT *vertices;
-  facetT *neighbor, **neighborp;
-  vertexT *vertex, **vertexp;
-  int k;
-
-  facet->visitid= qh->visit_id;
-  if (qh->PRINTnoplanes || (facet->visible && qh->NEWfacets))
-    return;
-  FOREACHneighbor_(facet) {
-    if (neighbor->visitid == qh->visit_id)
-      continue;
-    if (qh->PRINTtransparent && !neighbor->good)
-      continue;
-    vertices= qh_setnew_delnthsorted(qh, facet->vertices, qh->hull_dim,
-                          SETindex_(facet->neighbors, neighbor), 0);
-    if (qh->DOintersections)
-      qh_printhyperplaneintersection(qh, fp, facet, neighbor, vertices, color);
-    else {
-      if (qh->DROPdim >= 0)
-        qh_fprintf(qh, fp, 9119, "OFF 3 1 1 # ridge between f%d f%d\n",
-                facet->id, neighbor->id);
-      else {
-        qh->printoutvar++;
-        qh_fprintf(qh, fp, 9120, "# ridge between f%d f%d\n", facet->id, neighbor->id);
-      }
-      FOREACHvertex_(vertices) {
-        for (k=0; k < qh->hull_dim; k++) {
-          if (k != qh->DROPdim)
-            qh_fprintf(qh, fp, 9121, "%8.4g ", vertex->point[k]);
-        }
-        qh_fprintf(qh, fp, 9122, "\n");
-      }
-      if (qh->DROPdim >= 0)
-        qh_fprintf(qh, fp, 9123, "3 0 1 2 %8.4g %8.4g %8.4g\n", color[0], color[1], color[2]);
-    }
-    qh_setfree(qh, &vertices);
-  }
-} /* printfacet4geom_simplicial */
-
-
-/*---------------------------------
-
-  qh_printfacetNvertex_nonsimplicial(qh, fp, facet, id, format )
-    print vertices for an N-d non-simplicial facet
-    triangulates each ridge to the id
-*/
-void qh_printfacetNvertex_nonsimplicial(qhT *qh, FILE *fp, facetT *facet, int id, qh_PRINT format) {
-  vertexT *vertex, **vertexp;
-  ridgeT *ridge, **ridgep;
-
-  if (facet->visible && qh->NEWfacets)
-    return;
-  FOREACHridge_(facet->ridges) {
-    if (format == qh_PRINTtriangles)
-      qh_fprintf(qh, fp, 9124, "%d ", qh->hull_dim);
-    qh_fprintf(qh, fp, 9125, "%d ", id);
-    if ((ridge->top == facet) ^ qh_ORIENTclock) {
-      FOREACHvertex_(ridge->vertices)
-        qh_fprintf(qh, fp, 9126, "%d ", qh_pointid(qh, vertex->point));
-    }else {
-      FOREACHvertexreverse12_(ridge->vertices)
-        qh_fprintf(qh, fp, 9127, "%d ", qh_pointid(qh, vertex->point));
-    }
-    qh_fprintf(qh, fp, 9128, "\n");
-  }
-} /* printfacetNvertex_nonsimplicial */
-
-
-/*---------------------------------
-
-  qh_printfacetNvertex_simplicial(qh, fp, facet, format )
-    print vertices for an N-d simplicial facet
-    prints vertices for non-simplicial facets
-      2-d facets (orientation preserved by qh_mergefacet2d)
-      PRINToff ('o') for 4-d and higher
-*/
-void qh_printfacetNvertex_simplicial(qhT *qh, FILE *fp, facetT *facet, qh_PRINT format) {
-  vertexT *vertex, **vertexp;
-
-  if (format == qh_PRINToff || format == qh_PRINTtriangles)
-    qh_fprintf(qh, fp, 9129, "%d ", qh_setsize(qh, facet->vertices));
-  if ((facet->toporient ^ qh_ORIENTclock)
-  || (qh->hull_dim > 2 && !facet->simplicial)) {
-    FOREACHvertex_(facet->vertices)
-      qh_fprintf(qh, fp, 9130, "%d ", qh_pointid(qh, vertex->point));
-  }else {
-    FOREACHvertexreverse12_(facet->vertices)
-      qh_fprintf(qh, fp, 9131, "%d ", qh_pointid(qh, vertex->point));
-  }
-  qh_fprintf(qh, fp, 9132, "\n");
-} /* printfacetNvertex_simplicial */
-
-
-/*---------------------------------
-
-  qh_printfacetheader(qh, fp, facet )
-    prints header fields of a facet to fp
-
-  notes:
-    for 'f' output and debugging
-    Same as QhullFacet::printHeader()
-*/
-void qh_printfacetheader(qhT *qh, FILE *fp, facetT *facet) {
-  pointT *point, **pointp, *furthest;
-  facetT *neighbor, **neighborp;
-  realT dist;
-
-  if (facet == qh_MERGEridge) {
-    qh_fprintf(qh, fp, 9133, " MERGEridge\n");
-    return;
-  }else if (facet == qh_DUPLICATEridge) {
-    qh_fprintf(qh, fp, 9134, " DUPLICATEridge\n");
-    return;
-  }else if (!facet) {
-    qh_fprintf(qh, fp, 9135, " NULLfacet\n");
-    return;
-  }
-  qh->old_randomdist= qh->RANDOMdist;
-  qh->RANDOMdist= False;
-  qh_fprintf(qh, fp, 9136, "- f%d\n", facet->id);
-  qh_fprintf(qh, fp, 9137, "    - flags:");
-  if (facet->toporient)
-    qh_fprintf(qh, fp, 9138, " top");
-  else
-    qh_fprintf(qh, fp, 9139, " bottom");
-  if (facet->simplicial)
-    qh_fprintf(qh, fp, 9140, " simplicial");
-  if (facet->tricoplanar)
-    qh_fprintf(qh, fp, 9141, " tricoplanar");
-  if (facet->upperdelaunay)
-    qh_fprintf(qh, fp, 9142, " upperDelaunay");
-  if (facet->visible)
-    qh_fprintf(qh, fp, 9143, " visible");
-  if (facet->newfacet)
-    qh_fprintf(qh, fp, 9144, " new");
-  if (facet->tested)
-    qh_fprintf(qh, fp, 9145, " tested");
-  if (!facet->good)
-    qh_fprintf(qh, fp, 9146, " notG");
-  if (facet->seen)
-    qh_fprintf(qh, fp, 9147, " seen");
-  if (facet->coplanar)
-    qh_fprintf(qh, fp, 9148, " coplanar");
-  if (facet->mergehorizon)
-    qh_fprintf(qh, fp, 9149, " mergehorizon");
-  if (facet->keepcentrum)
-    qh_fprintf(qh, fp, 9150, " keepcentrum");
-  if (facet->dupridge)
-    qh_fprintf(qh, fp, 9151, " dupridge");
-  if (facet->mergeridge && !facet->mergeridge2)
-    qh_fprintf(qh, fp, 9152, " mergeridge1");
-  if (facet->mergeridge2)
-    qh_fprintf(qh, fp, 9153, " mergeridge2");
-  if (facet->newmerge)
-    qh_fprintf(qh, fp, 9154, " newmerge");
-  if (facet->flipped)
-    qh_fprintf(qh, fp, 9155, " flipped");
-  if (facet->notfurthest)
-    qh_fprintf(qh, fp, 9156, " notfurthest");
-  if (facet->degenerate)
-    qh_fprintf(qh, fp, 9157, " degenerate");
-  if (facet->redundant)
-    qh_fprintf(qh, fp, 9158, " redundant");
-  qh_fprintf(qh, fp, 9159, "\n");
-  if (facet->isarea)
-    qh_fprintf(qh, fp, 9160, "    - area: %2.2g\n", facet->f.area);
-  else if (qh->NEWfacets && facet->visible && facet->f.replace)
-    qh_fprintf(qh, fp, 9161, "    - replacement: f%d\n", facet->f.replace->id);
-  else if (facet->newfacet) {
-    if (facet->f.samecycle && facet->f.samecycle != facet)
-      qh_fprintf(qh, fp, 9162, "    - shares same visible/horizon as f%d\n", facet->f.samecycle->id);
-  }else if (facet->tricoplanar /* !isarea */) {
-    if (facet->f.triowner)
-      qh_fprintf(qh, fp, 9163, "    - owner of normal & centrum is facet f%d\n", facet->f.triowner->id);
-  }else if (facet->f.newcycle)
-    qh_fprintf(qh, fp, 9164, "    - was horizon to f%d\n", facet->f.newcycle->id);
-  if (facet->nummerge)
-    qh_fprintf(qh, fp, 9165, "    - merges: %d\n", facet->nummerge);
-  qh_printpointid(qh, fp, "    - normal: ", qh->hull_dim, facet->normal, qh_IDunknown);
-  qh_fprintf(qh, fp, 9166, "    - offset: %10.7g\n", facet->offset);
-  if (qh->CENTERtype == qh_ASvoronoi || facet->center)
-    qh_printcenter(qh, fp, qh_PRINTfacets, "    - center: ", facet);
-#if qh_MAXoutside
-  if (facet->maxoutside > qh->DISTround)
-    qh_fprintf(qh, fp, 9167, "    - maxoutside: %10.7g\n", facet->maxoutside);
-#endif
-  if (!SETempty_(facet->outsideset)) {
-    furthest= (pointT*)qh_setlast(facet->outsideset);
-    if (qh_setsize(qh, facet->outsideset) < 6) {
-      qh_fprintf(qh, fp, 9168, "    - outside set(furthest p%d):\n", qh_pointid(qh, furthest));
-      FOREACHpoint_(facet->outsideset)
-        qh_printpoint(qh, fp, "     ", point);
-    }else if (qh_setsize(qh, facet->outsideset) < 21) {
-      qh_printpoints(qh, fp, "    - outside set:", facet->outsideset);
-    }else {
-      qh_fprintf(qh, fp, 9169, "    - outside set:  %d points.", qh_setsize(qh, facet->outsideset));
-      qh_printpoint(qh, fp, "  Furthest", furthest);
-    }
-#if !qh_COMPUTEfurthest
-    qh_fprintf(qh, fp, 9170, "    - furthest distance= %2.2g\n", facet->furthestdist);
-#endif
-  }
-  if (!SETempty_(facet->coplanarset)) {
-    furthest= (pointT*)qh_setlast(facet->coplanarset);
-    if (qh_setsize(qh, facet->coplanarset) < 6) {
-      qh_fprintf(qh, fp, 9171, "    - coplanar set(furthest p%d):\n", qh_pointid(qh, furthest));
-      FOREACHpoint_(facet->coplanarset)
-        qh_printpoint(qh, fp, "     ", point);
-    }else if (qh_setsize(qh, facet->coplanarset) < 21) {
-      qh_printpoints(qh, fp, "    - coplanar set:", facet->coplanarset);
-    }else {
-      qh_fprintf(qh, fp, 9172, "    - coplanar set:  %d points.", qh_setsize(qh, facet->coplanarset));
-      qh_printpoint(qh, fp, "  Furthest", furthest);
-    }
-    zinc_(Zdistio);
-    qh_distplane(qh, furthest, facet, &dist);
-    qh_fprintf(qh, fp, 9173, "      furthest distance= %2.2g\n", dist);
-  }
-  qh_printvertices(qh, fp, "    - vertices:", facet->vertices);
-  qh_fprintf(qh, fp, 9174, "    - neighboring facets:");
-  FOREACHneighbor_(facet) {
-    if (neighbor == qh_MERGEridge)
-      qh_fprintf(qh, fp, 9175, " MERGE");
-    else if (neighbor == qh_DUPLICATEridge)
-      qh_fprintf(qh, fp, 9176, " DUP");
-    else
-      qh_fprintf(qh, fp, 9177, " f%d", neighbor->id);
-  }
-  qh_fprintf(qh, fp, 9178, "\n");
-  qh->RANDOMdist= qh->old_randomdist;
-} /* printfacetheader */
-
-
-/*---------------------------------
-
-  qh_printfacetridges(qh, fp, facet )
-    prints ridges of a facet to fp
-
-  notes:
-    ridges printed in neighbor order
-    assumes the ridges exist
-    for 'f' output
-    same as QhullFacet::printRidges
-*/
-void qh_printfacetridges(qhT *qh, FILE *fp, facetT *facet) {
-  facetT *neighbor, **neighborp;
-  ridgeT *ridge, **ridgep;
-  int numridges= 0;
-
-
-  if (facet->visible && qh->NEWfacets) {
-    qh_fprintf(qh, fp, 9179, "    - ridges(ids may be garbage):");
-    FOREACHridge_(facet->ridges)
-      qh_fprintf(qh, fp, 9180, " r%d", ridge->id);
-    qh_fprintf(qh, fp, 9181, "\n");
-  }else {
-    qh_fprintf(qh, fp, 9182, "    - ridges:\n");
-    FOREACHridge_(facet->ridges)
-      ridge->seen= False;
-    if (qh->hull_dim == 3) {
-      ridge= SETfirstt_(facet->ridges, ridgeT);
-      while (ridge && !ridge->seen) {
-        ridge->seen= True;
-        qh_printridge(qh, fp, ridge);
-        numridges++;
-        ridge= qh_nextridge3d(ridge, facet, NULL);
-        }
-    }else {
-      FOREACHneighbor_(facet) {
-        FOREACHridge_(facet->ridges) {
-          if (otherfacet_(ridge,facet) == neighbor) {
-            ridge->seen= True;
-            qh_printridge(qh, fp, ridge);
-            numridges++;
-          }
-        }
-      }
-    }
-    if (numridges != qh_setsize(qh, facet->ridges)) {
-      qh_fprintf(qh, fp, 9183, "     - all ridges:");
-      FOREACHridge_(facet->ridges)
-        qh_fprintf(qh, fp, 9184, " r%d", ridge->id);
-        qh_fprintf(qh, fp, 9185, "\n");
-    }
-    FOREACHridge_(facet->ridges) {
-      if (!ridge->seen)
-        qh_printridge(qh, fp, ridge);
-    }
-  }
-} /* printfacetridges */
-
-/*---------------------------------
-
-  qh_printfacets(qh, fp, format, facetlist, facets, printall )
-    prints facetlist and/or facet set in output format
-
-  notes:
-    also used for specialized formats ('FO' and summary)
-    turns off 'Rn' option since want actual numbers
-*/
-void qh_printfacets(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall) {
-  int numfacets, numsimplicial, numridges, totneighbors, numcoplanars, numtricoplanars;
-  facetT *facet, **facetp;
-  setT *vertices;
-  coordT *center;
-  realT outerplane, innerplane;
-
-  qh->old_randomdist= qh->RANDOMdist;
-  qh->RANDOMdist= False;
-  if (qh->CDDoutput && (format == qh_PRINTcentrums || format == qh_PRINTpointintersect || format == qh_PRINToff))
-    qh_fprintf(qh, qh->ferr, 7056, "qhull warning: CDD format is not available for centrums, halfspace\nintersections, and OFF file format.\n");
-  if (format == qh_PRINTnone)
-    ; /* print nothing */
-  else if (format == qh_PRINTaverage) {
-    vertices= qh_facetvertices(qh, facetlist, facets, printall);
-    center= qh_getcenter(qh, vertices);
-    qh_fprintf(qh, fp, 9186, "%d 1\n", qh->hull_dim);
-    qh_printpointid(qh, fp, NULL, qh->hull_dim, center, qh_IDunknown);
-    qh_memfree(qh, center, qh->normal_size);
-    qh_settempfree(qh, &vertices);
-  }else if (format == qh_PRINTextremes) {
-    if (qh->DELAUNAY)
-      qh_printextremes_d(qh, fp, facetlist, facets, printall);
-    else if (qh->hull_dim == 2)
-      qh_printextremes_2d(qh, fp, facetlist, facets, printall);
-    else
-      qh_printextremes(qh, fp, facetlist, facets, printall);
-  }else if (format == qh_PRINToptions)
-    qh_fprintf(qh, fp, 9187, "Options selected for Qhull %s:\n%s\n", qh_version, qh->qhull_options);
-  else if (format == qh_PRINTpoints && !qh->VORONOI)
-    qh_printpoints_out(qh, fp, facetlist, facets, printall);
-  else if (format == qh_PRINTqhull)
-    qh_fprintf(qh, fp, 9188, "%s | %s\n", qh->rbox_command, qh->qhull_command);
-  else if (format == qh_PRINTsize) {
-    qh_fprintf(qh, fp, 9189, "0\n2 ");
-    qh_fprintf(qh, fp, 9190, qh_REAL_1, qh->totarea);
-    qh_fprintf(qh, fp, 9191, qh_REAL_1, qh->totvol);
-    qh_fprintf(qh, fp, 9192, "\n");
-  }else if (format == qh_PRINTsummary) {
-    qh_countfacets(qh, facetlist, facets, printall, &numfacets, &numsimplicial,
-      &totneighbors, &numridges, &numcoplanars, &numtricoplanars);
-    vertices= qh_facetvertices(qh, facetlist, facets, printall);
-    qh_fprintf(qh, fp, 9193, "10 %d %d %d %d %d %d %d %d %d %d\n2 ", qh->hull_dim,
-                qh->num_points + qh_setsize(qh, qh->other_points),
-                qh->num_vertices, qh->num_facets - qh->num_visible,
-                qh_setsize(qh, vertices), numfacets, numcoplanars,
-                numfacets - numsimplicial, zzval_(Zdelvertextot),
-                numtricoplanars);
-    qh_settempfree(qh, &vertices);
-    qh_outerinner(qh, NULL, &outerplane, &innerplane);
-    qh_fprintf(qh, fp, 9194, qh_REAL_2n, outerplane, innerplane);
-  }else if (format == qh_PRINTvneighbors)
-    qh_printvneighbors(qh, fp, facetlist, facets, printall);
-  else if (qh->VORONOI && format == qh_PRINToff)
-    qh_printvoronoi(qh, fp, format, facetlist, facets, printall);
-  else if (qh->VORONOI && format == qh_PRINTgeom) {
-    qh_printbegin(qh, fp, format, facetlist, facets, printall);
-    qh_printvoronoi(qh, fp, format, facetlist, facets, printall);
-    qh_printend(qh, fp, format, facetlist, facets, printall);
-  }else if (qh->VORONOI
-  && (format == qh_PRINTvertices || format == qh_PRINTinner || format == qh_PRINTouter))
-    qh_printvdiagram(qh, fp, format, facetlist, facets, printall);
-  else {
-    qh_printbegin(qh, fp, format, facetlist, facets, printall);
-    FORALLfacet_(facetlist)
-      qh_printafacet(qh, fp, format, facet, printall);
-    FOREACHfacet_(facets)
-      qh_printafacet(qh, fp, format, facet, printall);
-    qh_printend(qh, fp, format, facetlist, facets, printall);
-  }
-  qh->RANDOMdist= qh->old_randomdist;
-} /* printfacets */
-
-
-/*---------------------------------
-
-  qh_printhyperplaneintersection(qh, fp, facet1, facet2, vertices, color )
-    print Geomview OFF or 4OFF for the intersection of two hyperplanes in 3-d or 4-d
-*/
-void qh_printhyperplaneintersection(qhT *qh, FILE *fp, facetT *facet1, facetT *facet2,
-                   setT *vertices, realT color[3]) {
-  realT costheta, denominator, dist1, dist2, s, t, mindenom, p[4];
-  vertexT *vertex, **vertexp;
-  int i, k;
-  boolT nearzero1, nearzero2;
-
-  costheta= qh_getangle(qh, facet1->normal, facet2->normal);
-  denominator= 1 - costheta * costheta;
-  i= qh_setsize(qh, vertices);
-  if (qh->hull_dim == 3)
-    qh_fprintf(qh, fp, 9195, "VECT 1 %d 1 %d 1 ", i, i);
-  else if (qh->hull_dim == 4 && qh->DROPdim >= 0)
-    qh_fprintf(qh, fp, 9196, "OFF 3 1 1 ");
-  else
-    qh->printoutvar++;
-  qh_fprintf(qh, fp, 9197, "# intersect f%d f%d\n", facet1->id, facet2->id);
-  mindenom= 1 / (10.0 * qh->MAXabs_coord);
-  FOREACHvertex_(vertices) {
-    zadd_(Zdistio, 2);
-    qh_distplane(qh, vertex->point, facet1, &dist1);
-    qh_distplane(qh, vertex->point, facet2, &dist2);
-    s= qh_divzero(-dist1 + costheta * dist2, denominator,mindenom,&nearzero1);
-    t= qh_divzero(-dist2 + costheta * dist1, denominator,mindenom,&nearzero2);
-    if (nearzero1 || nearzero2)
-      s= t= 0.0;
-    for (k=qh->hull_dim; k--; )
-      p[k]= vertex->point[k] + facet1->normal[k] * s + facet2->normal[k] * t;
-    if (qh->PRINTdim <= 3) {
-      qh_projectdim3(qh, p, p);
-      qh_fprintf(qh, fp, 9198, "%8.4g %8.4g %8.4g # ", p[0], p[1], p[2]);
-    }else
-      qh_fprintf(qh, fp, 9199, "%8.4g %8.4g %8.4g %8.4g # ", p[0], p[1], p[2], p[3]);
-    if (nearzero1+nearzero2)
-      qh_fprintf(qh, fp, 9200, "p%d(coplanar facets)\n", qh_pointid(qh, vertex->point));
-    else
-      qh_fprintf(qh, fp, 9201, "projected p%d\n", qh_pointid(qh, vertex->point));
-  }
-  if (qh->hull_dim == 3)
-    qh_fprintf(qh, fp, 9202, "%8.4g %8.4g %8.4g 1.0\n", color[0], color[1], color[2]);
-  else if (qh->hull_dim == 4 && qh->DROPdim >= 0)
-    qh_fprintf(qh, fp, 9203, "3 0 1 2 %8.4g %8.4g %8.4g 1.0\n", color[0], color[1], color[2]);
-} /* printhyperplaneintersection */
-
-/*---------------------------------
-
-  qh_printline3geom(qh, fp, pointA, pointB, color )
-    prints a line as a VECT
-    prints 0's for qh.DROPdim
-
-  notes:
-    if pointA == pointB,
-      it's a 1 point VECT
-*/
-void qh_printline3geom(qhT *qh, FILE *fp, pointT *pointA, pointT *pointB, realT color[3]) {
-  int k;
-  realT pA[4], pB[4];
-
-  qh_projectdim3(qh, pointA, pA);
-  qh_projectdim3(qh, pointB, pB);
-  if ((fabs(pA[0] - pB[0]) > 1e-3) ||
-      (fabs(pA[1] - pB[1]) > 1e-3) ||
-      (fabs(pA[2] - pB[2]) > 1e-3)) {
-    qh_fprintf(qh, fp, 9204, "VECT 1 2 1 2 1\n");
-    for (k=0; k < 3; k++)
-       qh_fprintf(qh, fp, 9205, "%8.4g ", pB[k]);
-    qh_fprintf(qh, fp, 9206, " # p%d\n", qh_pointid(qh, pointB));
-  }else
-    qh_fprintf(qh, fp, 9207, "VECT 1 1 1 1 1\n");
-  for (k=0; k < 3; k++)
-    qh_fprintf(qh, fp, 9208, "%8.4g ", pA[k]);
-  qh_fprintf(qh, fp, 9209, " # p%d\n", qh_pointid(qh, pointA));
-  qh_fprintf(qh, fp, 9210, "%8.4g %8.4g %8.4g 1\n", color[0], color[1], color[2]);
-}
-
-/*---------------------------------
-
-  qh_printneighborhood(qh, fp, format, facetA, facetB, printall )
-    print neighborhood of one or two facets
-
-  notes:
-    calls qh_findgood_all()
-    bumps qh.visit_id
-*/
-void qh_printneighborhood(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetA, facetT *facetB, boolT printall) {
-  facetT *neighbor, **neighborp, *facet;
-  setT *facets;
-
-  if (format == qh_PRINTnone)
-    return;
-  qh_findgood_all(qh, qh->facet_list);
-  if (facetA == facetB)
-    facetB= NULL;
-  facets= qh_settemp(qh, 2*(qh_setsize(qh, facetA->neighbors)+1));
-  qh->visit_id++;
-  for (facet= facetA; facet; facet= ((facet == facetA) ? facetB : NULL)) {
-    if (facet->visitid != qh->visit_id) {
-      facet->visitid= qh->visit_id;
-      qh_setappend(qh, &facets, facet);
-    }
-    FOREACHneighbor_(facet) {
-      if (neighbor->visitid == qh->visit_id)
-        continue;
-      neighbor->visitid= qh->visit_id;
-      if (printall || !qh_skipfacet(qh, neighbor))
-        qh_setappend(qh, &facets, neighbor);
-    }
-  }
-  qh_printfacets(qh, fp, format, NULL, facets, printall);
-  qh_settempfree(qh, &facets);
-} /* printneighborhood */
-
-/*---------------------------------
-
-  qh_printpoint(qh, fp, string, point )
-  qh_printpointid(qh, fp, string, dim, point, id )
-    prints the coordinates of a point
-
-  returns:
-    if string is defined
-      prints 'string p%d'.  Skips p%d if id=qh_IDunknown(-1) or qh_IDnone(-3)
-
-  notes:
-    nop if point is NULL
-    Same as QhullPoint's printPoint
-*/
-void qh_printpoint(qhT *qh, FILE *fp, const char *string, pointT *point) {
-  int id= qh_pointid(qh, point);
-
-  qh_printpointid(qh, fp, string, qh->hull_dim, point, id);
-} /* printpoint */
-
-void qh_printpointid(qhT *qh, FILE *fp, const char *string, int dim, pointT *point, int id) {
-  int k;
-  realT r; /*bug fix*/
-
-  if (!point)
-    return;
-  if (string) {
-    qh_fprintf(qh, fp, 9211, "%s", string);
-    if (id != qh_IDunknown && id != qh_IDnone)
-      qh_fprintf(qh, fp, 9212, " p%d: ", id);
-  }
-  for (k=dim; k--; ) {
-    r= *point++;
-    if (string)
-      qh_fprintf(qh, fp, 9213, " %8.4g", r);
-    else
-      qh_fprintf(qh, fp, 9214, qh_REAL_1, r);
-  }
-  qh_fprintf(qh, fp, 9215, "\n");
-} /* printpointid */
-
-/*---------------------------------
-
-  qh_printpoint3(qh, fp, point )
-    prints 2-d, 3-d, or 4-d point as Geomview 3-d coordinates
-*/
-void qh_printpoint3(qhT *qh, FILE *fp, pointT *point) {
-  int k;
-  realT p[4];
-
-  qh_projectdim3(qh, point, p);
-  for (k=0; k < 3; k++)
-    qh_fprintf(qh, fp, 9216, "%8.4g ", p[k]);
-  qh_fprintf(qh, fp, 9217, " # p%d\n", qh_pointid(qh, point));
-} /* printpoint3 */
-
-/*----------------------------------------
--printpoints- print pointids for a set of points starting at index
-   see geom_r.c
-*/
-
-/*---------------------------------
-
-  qh_printpoints_out(qh, fp, facetlist, facets, printall )
-    prints vertices, coplanar/inside points, for facets by their point coordinates
-    allows qh.CDDoutput
-
-  notes:
-    same format as qhull input
-    if no coplanar/interior points,
-      same order as qh_printextremes
-*/
-void qh_printpoints_out(qhT *qh, FILE *fp, facetT *facetlist, setT *facets, boolT printall) {
-  int allpoints= qh->num_points + qh_setsize(qh, qh->other_points);
-  int numpoints=0, point_i, point_n;
-  setT *vertices, *points;
-  facetT *facet, **facetp;
-  pointT *point, **pointp;
-  vertexT *vertex, **vertexp;
-  int id;
-
-  points= qh_settemp(qh, allpoints);
-  qh_setzero(qh, points, 0, allpoints);
-  vertices= qh_facetvertices(qh, facetlist, facets, printall);
-  FOREACHvertex_(vertices) {
-    id= qh_pointid(qh, vertex->point);
-    if (id >= 0)
-      SETelem_(points, id)= vertex->point;
-  }
-  if (qh->KEEPinside || qh->KEEPcoplanar || qh->KEEPnearinside) {
-    FORALLfacet_(facetlist) {
-      if (!printall && qh_skipfacet(qh, facet))
-        continue;
-      FOREACHpoint_(facet->coplanarset) {
-        id= qh_pointid(qh, point);
-        if (id >= 0)
-          SETelem_(points, id)= point;
-      }
-    }
-    FOREACHfacet_(facets) {
-      if (!printall && qh_skipfacet(qh, facet))
-        continue;
-      FOREACHpoint_(facet->coplanarset) {
-        id= qh_pointid(qh, point);
-        if (id >= 0)
-          SETelem_(points, id)= point;
-      }
-    }
-  }
-  qh_settempfree(qh, &vertices);
-  FOREACHpoint_i_(qh, points) {
-    if (point)
-      numpoints++;
-  }
-  if (qh->CDDoutput)
-    qh_fprintf(qh, fp, 9218, "%s | %s\nbegin\n%d %d real\n", qh->rbox_command,
-             qh->qhull_command, numpoints, qh->hull_dim + 1);
-  else
-    qh_fprintf(qh, fp, 9219, "%d\n%d\n", qh->hull_dim, numpoints);
-  FOREACHpoint_i_(qh, points) {
-    if (point) {
-      if (qh->CDDoutput)
-        qh_fprintf(qh, fp, 9220, "1 ");
-      qh_printpoint(qh, fp, NULL, point);
-    }
-  }
-  if (qh->CDDoutput)
-    qh_fprintf(qh, fp, 9221, "end\n");
-  qh_settempfree(qh, &points);
-} /* printpoints_out */
-
-
-/*---------------------------------
-
-  qh_printpointvect(qh, fp, point, normal, center, radius, color )
-    prints a 2-d, 3-d, or 4-d point as 3-d VECT's relative to normal or to center point
-*/
-void qh_printpointvect(qhT *qh, FILE *fp, pointT *point, coordT *normal, pointT *center, realT radius, realT color[3]) {
-  realT diff[4], pointA[4];
-  int k;
-
-  for (k=qh->hull_dim; k--; ) {
-    if (center)
-      diff[k]= point[k]-center[k];
-    else if (normal)
-      diff[k]= normal[k];
-    else
-      diff[k]= 0;
-  }
-  if (center)
-    qh_normalize2(qh, diff, qh->hull_dim, True, NULL, NULL);
-  for (k=qh->hull_dim; k--; )
-    pointA[k]= point[k]+diff[k] * radius;
-  qh_printline3geom(qh, fp, point, pointA, color);
-} /* printpointvect */
-
-/*---------------------------------
-
-  qh_printpointvect2(qh, fp, point, normal, center, radius )
-    prints a 2-d, 3-d, or 4-d point as 2 3-d VECT's for an imprecise point
-*/
-void qh_printpointvect2(qhT *qh, FILE *fp, pointT *point, coordT *normal, pointT *center, realT radius) {
-  realT red[3]={1, 0, 0}, yellow[3]={1, 1, 0};
-
-  qh_printpointvect(qh, fp, point, normal, center, radius, red);
-  qh_printpointvect(qh, fp, point, normal, center, -radius, yellow);
-} /* printpointvect2 */
-
-/*---------------------------------
-
-  qh_printridge(qh, fp, ridge )
-    prints the information in a ridge
-
-  notes:
-    for qh_printfacetridges()
-    same as operator<< [QhullRidge.cpp]
-*/
-void qh_printridge(qhT *qh, FILE *fp, ridgeT *ridge) {
-
-  qh_fprintf(qh, fp, 9222, "     - r%d", ridge->id);
-  if (ridge->tested)
-    qh_fprintf(qh, fp, 9223, " tested");
-  if (ridge->nonconvex)
-    qh_fprintf(qh, fp, 9224, " nonconvex");
-  qh_fprintf(qh, fp, 9225, "\n");
-  qh_printvertices(qh, fp, "           vertices:", ridge->vertices);
-  if (ridge->top && ridge->bottom)
-    qh_fprintf(qh, fp, 9226, "           between f%d and f%d\n",
-            ridge->top->id, ridge->bottom->id);
-} /* printridge */
-
-/*---------------------------------
-
-  qh_printspheres(qh, fp, vertices, radius )
-    prints 3-d vertices as OFF spheres
-
-  notes:
-    inflated octahedron from Stuart Levy earth/mksphere2
-*/
-void qh_printspheres(qhT *qh, FILE *fp, setT *vertices, realT radius) {
-  vertexT *vertex, **vertexp;
-
-  qh->printoutnum++;
-  qh_fprintf(qh, fp, 9227, "{appearance {-edge -normal normscale 0} {\n\
-INST geom {define vsphere OFF\n\
-18 32 48\n\
-\n\
-0 0 1\n\
-1 0 0\n\
-0 1 0\n\
--1 0 0\n\
-0 -1 0\n\
-0 0 -1\n\
-0.707107 0 0.707107\n\
-0 -0.707107 0.707107\n\
-0.707107 -0.707107 0\n\
--0.707107 0 0.707107\n\
--0.707107 -0.707107 0\n\
-0 0.707107 0.707107\n\
--0.707107 0.707107 0\n\
-0.707107 0.707107 0\n\
-0.707107 0 -0.707107\n\
-0 0.707107 -0.707107\n\
--0.707107 0 -0.707107\n\
-0 -0.707107 -0.707107\n\
-\n\
-3 0 6 11\n\
-3 0 7 6 \n\
-3 0 9 7 \n\
-3 0 11 9\n\
-3 1 6 8 \n\
-3 1 8 14\n\
-3 1 13 6\n\
-3 1 14 13\n\
-3 2 11 13\n\
-3 2 12 11\n\
-3 2 13 15\n\
-3 2 15 12\n\
-3 3 9 12\n\
-3 3 10 9\n\
-3 3 12 16\n\
-3 3 16 10\n\
-3 4 7 10\n\
-3 4 8 7\n\
-3 4 10 17\n\
-3 4 17 8\n\
-3 5 14 17\n\
-3 5 15 14\n\
-3 5 16 15\n\
-3 5 17 16\n\
-3 6 13 11\n\
-3 7 8 6\n\
-3 9 10 7\n\
-3 11 12 9\n\
-3 14 8 17\n\
-3 15 13 14\n\
-3 16 12 15\n\
-3 17 10 16\n} transforms { TLIST\n");
-  FOREACHvertex_(vertices) {
-    qh_fprintf(qh, fp, 9228, "%8.4g 0 0 0 # v%d\n 0 %8.4g 0 0\n0 0 %8.4g 0\n",
-      radius, vertex->id, radius, radius);
-    qh_printpoint3(qh, fp, vertex->point);
-    qh_fprintf(qh, fp, 9229, "1\n");
-  }
-  qh_fprintf(qh, fp, 9230, "}}}\n");
-} /* printspheres */
-
-
-/*----------------------------------------------
--printsummary-
-                see libqhull_r.c
-*/
-
-/*---------------------------------
-
-  qh_printvdiagram(qh, fp, format, facetlist, facets, printall )
-    print voronoi diagram
-      # of pairs of input sites
-      #indices site1 site2 vertex1 ...
-
-    sites indexed by input point id
-      point 0 is the first input point
-    vertices indexed by 'o' and 'p' order
-      vertex 0 is the 'vertex-at-infinity'
-      vertex 1 is the first Voronoi vertex
-
-  see:
-    qh_printvoronoi()
-    qh_eachvoronoi_all()
-
-  notes:
-    if all facets are upperdelaunay,
-      prints upper hull (furthest-site Voronoi diagram)
-*/
-void qh_printvdiagram(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall) {
-  setT *vertices;
-  int totcount, numcenters;
-  boolT isLower;
-  qh_RIDGE innerouter= qh_RIDGEall;
-  printvridgeT printvridge= NULL;
-
-  if (format == qh_PRINTvertices) {
-    innerouter= qh_RIDGEall;
-    printvridge= qh_printvridge;
-  }else if (format == qh_PRINTinner) {
-    innerouter= qh_RIDGEinner;
-    printvridge= qh_printvnorm;
-  }else if (format == qh_PRINTouter) {
-    innerouter= qh_RIDGEouter;
-    printvridge= qh_printvnorm;
-  }else {
-    qh_fprintf(qh, qh->ferr, 6219, "Qhull internal error (qh_printvdiagram): unknown print format %d.\n", format);
-    qh_errexit(qh, qh_ERRinput, NULL, NULL);
-  }
-  vertices= qh_markvoronoi(qh, facetlist, facets, printall, &isLower, &numcenters);
-  totcount= qh_printvdiagram2(qh, NULL, NULL, vertices, innerouter, False);
-  qh_fprintf(qh, fp, 9231, "%d\n", totcount);
-  totcount= qh_printvdiagram2(qh, fp, printvridge, vertices, innerouter, True /* inorder*/);
-  qh_settempfree(qh, &vertices);
-#if 0  /* for testing qh_eachvoronoi_all */
-  qh_fprintf(qh, fp, 9232, "\n");
-  totcount= qh_eachvoronoi_all(qh, fp, printvridge, qh->UPPERdelaunay, innerouter, True /* inorder*/);
-  qh_fprintf(qh, fp, 9233, "%d\n", totcount);
-#endif
-} /* printvdiagram */
-
-/*---------------------------------
-
-  qh_printvdiagram2(qh, fp, printvridge, vertices, innerouter, inorder )
-    visit all pairs of input sites (vertices) for selected Voronoi vertices
-    vertices may include NULLs
-
-  innerouter:
-    qh_RIDGEall   print inner ridges(bounded) and outer ridges(unbounded)
-    qh_RIDGEinner print only inner ridges
-    qh_RIDGEouter print only outer ridges
-
-  inorder:
-    print 3-d Voronoi vertices in order
-
-  assumes:
-    qh_markvoronoi marked facet->visitid for Voronoi vertices
-    all facet->seen= False
-    all facet->seen2= True
-
-  returns:
-    total number of Voronoi ridges
-    if printvridge,
-      calls printvridge( fp, vertex, vertexA, centers) for each ridge
-      [see qh_eachvoronoi()]
-
-  see:
-    qh_eachvoronoi_all()
-*/
-int qh_printvdiagram2(qhT *qh, FILE *fp, printvridgeT printvridge, setT *vertices, qh_RIDGE innerouter, boolT inorder) {
-  int totcount= 0;
-  int vertex_i, vertex_n;
-  vertexT *vertex;
-
-  FORALLvertices
-    vertex->seen= False;
-  FOREACHvertex_i_(qh, vertices) {
-    if (vertex) {
-      if (qh->GOODvertex > 0 && qh_pointid(qh, vertex->point)+1 != qh->GOODvertex)
-        continue;
-      totcount += qh_eachvoronoi(qh, fp, printvridge, vertex, !qh_ALL, innerouter, inorder);
-    }
-  }
-  return totcount;
-} /* printvdiagram2 */
-
-/*---------------------------------
-
-  qh_printvertex(qh, fp, vertex )
-    prints the information in a vertex
-    Duplicated as operator<< [QhullVertex.cpp]
-*/
-void qh_printvertex(qhT *qh, FILE *fp, vertexT *vertex) {
-  pointT *point;
-  int k, count= 0;
-  facetT *neighbor, **neighborp;
-  realT r; /*bug fix*/
-
-  if (!vertex) {
-    qh_fprintf(qh, fp, 9234, "  NULLvertex\n");
-    return;
-  }
-  qh_fprintf(qh, fp, 9235, "- p%d(v%d):", qh_pointid(qh, vertex->point), vertex->id);
-  point= vertex->point;
-  if (point) {
-    for (k=qh->hull_dim; k--; ) {
-      r= *point++;
-      qh_fprintf(qh, fp, 9236, " %5.2g", r);
-    }
-  }
-  if (vertex->deleted)
-    qh_fprintf(qh, fp, 9237, " deleted");
-  if (vertex->delridge)
-    qh_fprintf(qh, fp, 9238, " ridgedeleted");
-  qh_fprintf(qh, fp, 9239, "\n");
-  if (vertex->neighbors) {
-    qh_fprintf(qh, fp, 9240, "  neighbors:");
-    FOREACHneighbor_(vertex) {
-      if (++count % 100 == 0)
-        qh_fprintf(qh, fp, 9241, "\n     ");
-      qh_fprintf(qh, fp, 9242, " f%d", neighbor->id);
-    }
-    qh_fprintf(qh, fp, 9243, "\n");
-  }
-} /* printvertex */
-
-
-/*---------------------------------
-
-  qh_printvertexlist(qh, fp, string, facetlist, facets, printall )
-    prints vertices used by a facetlist or facet set
-    tests qh_skipfacet() if !printall
-*/
-void qh_printvertexlist(qhT *qh, FILE *fp, const char* string, facetT *facetlist,
-                         setT *facets, boolT printall) {
-  vertexT *vertex, **vertexp;
-  setT *vertices;
-
-  vertices= qh_facetvertices(qh, facetlist, facets, printall);
-  qh_fprintf(qh, fp, 9244, "%s", string);
-  FOREACHvertex_(vertices)
-    qh_printvertex(qh, fp, vertex);
-  qh_settempfree(qh, &vertices);
-} /* printvertexlist */
-
-
-/*---------------------------------
-
-  qh_printvertices(qh, fp, string, vertices )
-    prints vertices in a set
-    duplicated as printVertexSet [QhullVertex.cpp]
-*/
-void qh_printvertices(qhT *qh, FILE *fp, const char* string, setT *vertices) {
-  vertexT *vertex, **vertexp;
-
-  qh_fprintf(qh, fp, 9245, "%s", string);
-  FOREACHvertex_(vertices)
-    qh_fprintf(qh, fp, 9246, " p%d(v%d)", qh_pointid(qh, vertex->point), vertex->id);
-  qh_fprintf(qh, fp, 9247, "\n");
-} /* printvertices */
-
-/*---------------------------------
-
-  qh_printvneighbors(qh, fp, facetlist, facets, printall )
-    print vertex neighbors of vertices in facetlist and facets ('FN')
-
-  notes:
-    qh_countfacets clears facet->visitid for non-printed facets
-
-  design:
-    collect facet count and related statistics
-    if necessary, build neighbor sets for each vertex
-    collect vertices in facetlist and facets
-    build a point array for point->vertex and point->coplanar facet
-    for each point
-      list vertex neighbors or coplanar facet
-*/
-void qh_printvneighbors(qhT *qh, FILE *fp, facetT* facetlist, setT *facets, boolT printall) {
-  int numfacets, numsimplicial, numridges, totneighbors, numneighbors, numcoplanars, numtricoplanars;
-  setT *vertices, *vertex_points, *coplanar_points;
-  int numpoints= qh->num_points + qh_setsize(qh, qh->other_points);
-  vertexT *vertex, **vertexp;
-  int vertex_i, vertex_n;
-  facetT *facet, **facetp, *neighbor, **neighborp;
-  pointT *point, **pointp;
-
-  qh_countfacets(qh, facetlist, facets, printall, &numfacets, &numsimplicial,
-      &totneighbors, &numridges, &numcoplanars, &numtricoplanars);  /* sets facet->visitid */
-  qh_fprintf(qh, fp, 9248, "%d\n", numpoints);
-  qh_vertexneighbors(qh);
-  vertices= qh_facetvertices(qh, facetlist, facets, printall);
-  vertex_points= qh_settemp(qh, numpoints);
-  coplanar_points= qh_settemp(qh, numpoints);
-  qh_setzero(qh, vertex_points, 0, numpoints);
-  qh_setzero(qh, coplanar_points, 0, numpoints);
-  FOREACHvertex_(vertices)
-    qh_point_add(qh, vertex_points, vertex->point, vertex);
-  FORALLfacet_(facetlist) {
-    FOREACHpoint_(facet->coplanarset)
-      qh_point_add(qh, coplanar_points, point, facet);
-  }
-  FOREACHfacet_(facets) {
-    FOREACHpoint_(facet->coplanarset)
-      qh_point_add(qh, coplanar_points, point, facet);
-  }
-  FOREACHvertex_i_(qh, vertex_points) {
-    if (vertex) {
-      numneighbors= qh_setsize(qh, vertex->neighbors);
-      qh_fprintf(qh, fp, 9249, "%d", numneighbors);
-      if (qh->hull_dim == 3)
-        qh_order_vertexneighbors(qh, vertex);
-      else if (qh->hull_dim >= 4)
-        qsort(SETaddr_(vertex->neighbors, facetT), (size_t)numneighbors,
-             sizeof(facetT *), qh_compare_facetvisit);
-      FOREACHneighbor_(vertex)
-        qh_fprintf(qh, fp, 9250, " %d",
-                 neighbor->visitid ? neighbor->visitid - 1 : 0 - neighbor->id);
-      qh_fprintf(qh, fp, 9251, "\n");
-    }else if ((facet= SETelemt_(coplanar_points, vertex_i, facetT)))
-      qh_fprintf(qh, fp, 9252, "1 %d\n",
-                  facet->visitid ? facet->visitid - 1 : 0 - facet->id);
-    else
-      qh_fprintf(qh, fp, 9253, "0\n");
-  }
-  qh_settempfree(qh, &coplanar_points);
-  qh_settempfree(qh, &vertex_points);
-  qh_settempfree(qh, &vertices);
-} /* printvneighbors */
-
-/*---------------------------------
-
-  qh_printvoronoi(qh, fp, format, facetlist, facets, printall )
-    print voronoi diagram in 'o' or 'G' format
-    for 'o' format
-      prints voronoi centers for each facet and for infinity
-      for each vertex, lists ids of printed facets or infinity
-      assumes facetlist and facets are disjoint
-    for 'G' format
-      prints an OFF object
-      adds a 0 coordinate to center
-      prints infinity but does not list in vertices
-
-  see:
-    qh_printvdiagram()
-
-  notes:
-    if 'o',
-      prints a line for each point except "at-infinity"
-    if all facets are upperdelaunay,
-      reverses lower and upper hull
-*/
-void qh_printvoronoi(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall) {
-  int k, numcenters, numvertices= 0, numneighbors, numinf, vid=1, vertex_i, vertex_n;
-  facetT *facet, **facetp, *neighbor, **neighborp;
-  setT *vertices;
-  vertexT *vertex;
-  boolT isLower;
-  unsigned int numfacets= (unsigned int) qh->num_facets;
-
-  vertices= qh_markvoronoi(qh, facetlist, facets, printall, &isLower, &numcenters);
-  FOREACHvertex_i_(qh, vertices) {
-    if (vertex) {
-      numvertices++;
-      numneighbors = numinf = 0;
-      FOREACHneighbor_(vertex) {
-        if (neighbor->visitid == 0)
-          numinf= 1;
-        else if (neighbor->visitid < numfacets)
-          numneighbors++;
-      }
-      if (numinf && !numneighbors) {
-        SETelem_(vertices, vertex_i)= NULL;
-        numvertices--;
-      }
-    }
-  }
-  if (format == qh_PRINTgeom)
-    qh_fprintf(qh, fp, 9254, "{appearance {+edge -face} OFF %d %d 1 # Voronoi centers and cells\n",
-                numcenters, numvertices);
-  else
-    qh_fprintf(qh, fp, 9255, "%d\n%d %d 1\n", qh->hull_dim-1, numcenters, qh_setsize(qh, vertices));
-  if (format == qh_PRINTgeom) {
-    for (k=qh->hull_dim-1; k--; )
-      qh_fprintf(qh, fp, 9256, qh_REAL_1, 0.0);
-    qh_fprintf(qh, fp, 9257, " 0 # infinity not used\n");
-  }else {
-    for (k=qh->hull_dim-1; k--; )
-      qh_fprintf(qh, fp, 9258, qh_REAL_1, qh_INFINITE);
-    qh_fprintf(qh, fp, 9259, "\n");
-  }
-  FORALLfacet_(facetlist) {
-    if (facet->visitid && facet->visitid < numfacets) {
-      if (format == qh_PRINTgeom)
-        qh_fprintf(qh, fp, 9260, "# %d f%d\n", vid++, facet->id);
-      qh_printcenter(qh, fp, format, NULL, facet);
-    }
-  }
-  FOREACHfacet_(facets) {
-    if (facet->visitid && facet->visitid < numfacets) {
-      if (format == qh_PRINTgeom)
-        qh_fprintf(qh, fp, 9261, "# %d f%d\n", vid++, facet->id);
-      qh_printcenter(qh, fp, format, NULL, facet);
-    }
-  }
-  FOREACHvertex_i_(qh, vertices) {
-    numneighbors= 0;
-    numinf=0;
-    if (vertex) {
-      if (qh->hull_dim == 3)
-        qh_order_vertexneighbors(qh, vertex);
-      else if (qh->hull_dim >= 4)
-        qsort(SETaddr_(vertex->neighbors, facetT),
-             (size_t)qh_setsize(qh, vertex->neighbors),
-             sizeof(facetT *), qh_compare_facetvisit);
-      FOREACHneighbor_(vertex) {
-        if (neighbor->visitid == 0)
-          numinf= 1;
-        else if (neighbor->visitid < numfacets)
-          numneighbors++;
-      }
-    }
-    if (format == qh_PRINTgeom) {
-      if (vertex) {
-        qh_fprintf(qh, fp, 9262, "%d", numneighbors);
-        FOREACHneighbor_(vertex) {
-          if (neighbor->visitid && neighbor->visitid < numfacets)
-            qh_fprintf(qh, fp, 9263, " %d", neighbor->visitid);
-        }
-        qh_fprintf(qh, fp, 9264, " # p%d(v%d)\n", vertex_i, vertex->id);
-      }else
-        qh_fprintf(qh, fp, 9265, " # p%d is coplanar or isolated\n", vertex_i);
-    }else {
-      if (numinf)
-        numneighbors++;
-      qh_fprintf(qh, fp, 9266, "%d", numneighbors);
-      if (vertex) {
-        FOREACHneighbor_(vertex) {
-          if (neighbor->visitid == 0) {
-            if (numinf) {
-              numinf= 0;
-              qh_fprintf(qh, fp, 9267, " %d", neighbor->visitid);
-            }
-          }else if (neighbor->visitid < numfacets)
-            qh_fprintf(qh, fp, 9268, " %d", neighbor->visitid);
-        }
-      }
-      qh_fprintf(qh, fp, 9269, "\n");
-    }
-  }
-  if (format == qh_PRINTgeom)
-    qh_fprintf(qh, fp, 9270, "}\n");
-  qh_settempfree(qh, &vertices);
-} /* printvoronoi */
-
-/*---------------------------------
-
-  qh_printvnorm(qh, fp, vertex, vertexA, centers, unbounded )
-    print one separating plane of the Voronoi diagram for a pair of input sites
-    unbounded==True if centers includes vertex-at-infinity
-
-  assumes:
-    qh_ASvoronoi and qh_vertexneighbors() already set
-
-  note:
-    parameter unbounded is UNUSED by this callback
-
-  see:
-    qh_printvdiagram()
-    qh_eachvoronoi()
-*/
-void qh_printvnorm(qhT *qh, FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded) {
-  pointT *normal;
-  realT offset;
-  int k;
-  QHULL_UNUSED(unbounded);
-
-  normal= qh_detvnorm(qh, vertex, vertexA, centers, &offset);
-  qh_fprintf(qh, fp, 9271, "%d %d %d ",
-      2+qh->hull_dim, qh_pointid(qh, vertex->point), qh_pointid(qh, vertexA->point));
-  for (k=0; k< qh->hull_dim-1; k++)
-    qh_fprintf(qh, fp, 9272, qh_REAL_1, normal[k]);
-  qh_fprintf(qh, fp, 9273, qh_REAL_1, offset);
-  qh_fprintf(qh, fp, 9274, "\n");
-} /* printvnorm */
-
-/*---------------------------------
-
-  qh_printvridge(qh, fp, vertex, vertexA, centers, unbounded )
-    print one ridge of the Voronoi diagram for a pair of input sites
-    unbounded==True if centers includes vertex-at-infinity
-
-  see:
-    qh_printvdiagram()
-
-  notes:
-    the user may use a different function
-    parameter unbounded is UNUSED
-*/
-void qh_printvridge(qhT *qh, FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded) {
-  facetT *facet, **facetp;
-  QHULL_UNUSED(unbounded);
-
-  qh_fprintf(qh, fp, 9275, "%d %d %d", qh_setsize(qh, centers)+2,
-       qh_pointid(qh, vertex->point), qh_pointid(qh, vertexA->point));
-  FOREACHfacet_(centers)
-    qh_fprintf(qh, fp, 9276, " %d", facet->visitid);
-  qh_fprintf(qh, fp, 9277, "\n");
-} /* printvridge */
-
-/*---------------------------------
-
-  qh_projectdim3(qh, source, destination )
-    project 2-d 3-d or 4-d point to a 3-d point
-    uses qh.DROPdim and qh.hull_dim
-    source and destination may be the same
-
-  notes:
-    allocate 4 elements to destination just in case
-*/
-void qh_projectdim3(qhT *qh, pointT *source, pointT *destination) {
-  int i,k;
-
-  for (k=0, i=0; k < qh->hull_dim; k++) {
-    if (qh->hull_dim == 4) {
-      if (k != qh->DROPdim)
-        destination[i++]= source[k];
-    }else if (k == qh->DROPdim)
-      destination[i++]= 0;
-    else
-      destination[i++]= source[k];
-  }
-  while (i < 3)
-    destination[i++]= 0.0;
-} /* projectdim3 */
-
-/*---------------------------------
-
-  qh_readfeasible(qh, dim, curline )
-    read feasible point from current line and qh.fin
-
-  returns:
-    number of lines read from qh.fin
-    sets qh.feasible_point with malloc'd coordinates
-
-  notes:
-    checks for qh.HALFspace
-    assumes dim > 1
-
-  see:
-    qh_setfeasible
-*/
-int qh_readfeasible(qhT *qh, int dim, const char *curline) {
-  boolT isfirst= True;
-  int linecount= 0, tokcount= 0;
-  const char *s;
-  char *t, firstline[qh_MAXfirst+1];
-  coordT *coords, value;
-
-  if (!qh->HALFspace) {
-    qh_fprintf(qh, qh->ferr, 6070, "qhull input error: feasible point(dim 1 coords) is only valid for halfspace intersection\n");
-    qh_errexit(qh, qh_ERRinput, NULL, NULL);
-  }
-  if (qh->feasible_string)
-    qh_fprintf(qh, qh->ferr, 7057, "qhull input warning: feasible point(dim 1 coords) overrides 'Hn,n,n' feasible point for halfspace intersection\n");
-  if (!(qh->feasible_point= (coordT*)qh_malloc(dim* sizeof(coordT)))) {
-    qh_fprintf(qh, qh->ferr, 6071, "qhull error: insufficient memory for feasible point\n");
-    qh_errexit(qh, qh_ERRmem, NULL, NULL);
-  }
-  coords= qh->feasible_point;
-  while ((s= (isfirst ?  curline : fgets(firstline, qh_MAXfirst, qh->fin)))) {
-    if (isfirst)
-      isfirst= False;
-    else
-      linecount++;
-    while (*s) {
-      while (isspace(*s))
-        s++;
-      value= qh_strtod(s, &t);
-      if (s == t)
-        break;
-      s= t;
-      *(coords++)= value;
-      if (++tokcount == dim) {
-        while (isspace(*s))
-          s++;
-        qh_strtod(s, &t);
-        if (s != t) {
-          qh_fprintf(qh, qh->ferr, 6072, "qhull input error: coordinates for feasible point do not finish out the line: %s\n",
-               s);
-          qh_errexit(qh, qh_ERRinput, NULL, NULL);
-        }
-        return linecount;
-      }
-    }
-  }
-  qh_fprintf(qh, qh->ferr, 6073, "qhull input error: only %d coordinates.  Could not read %d-d feasible point.\n",
-           tokcount, dim);
-  qh_errexit(qh, qh_ERRinput, NULL, NULL);
-  return 0;
-} /* readfeasible */
-
-/*---------------------------------
-
-  qh_readpoints(qh, numpoints, dimension, ismalloc )
-    read points from qh.fin into qh.first_point, qh.num_points
-    qh.fin is lines of coordinates, one per vertex, first line number of points
-    if 'rbox D4',
-      gives message
-    if qh.ATinfinity,
-      adds point-at-infinity for Delaunay triangulations
-
-  returns:
-    number of points, array of point coordinates, dimension, ismalloc True
-    if qh.DELAUNAY & !qh.PROJECTinput, projects points to paraboloid
-        and clears qh.PROJECTdelaunay
-    if qh.HALFspace, reads optional feasible point, reads halfspaces,
-        converts to dual.
-
-  for feasible point in "cdd format" in 3-d:
-    3 1
-    coordinates
-    comments
-    begin
-    n 4 real/integer
-    ...
-    end
-
-  notes:
-    dimension will change in qh_initqhull_globals if qh.PROJECTinput
-    uses malloc() since qh_mem not initialized
-    FIXUP QH11012: qh_readpoints needs rewriting, too long
-*/
-coordT *qh_readpoints(qhT *qh, int *numpoints, int *dimension, boolT *ismalloc) {
-  coordT *points, *coords, *infinity= NULL;
-  realT paraboloid, maxboloid= -REALmax, value;
-  realT *coordp= NULL, *offsetp= NULL, *normalp= NULL;
-  char *s= 0, *t, firstline[qh_MAXfirst+1];
-  int diminput=0, numinput=0, dimfeasible= 0, newnum, k, tempi;
-  int firsttext=0, firstshort=0, firstlong=0, firstpoint=0;
-  int tokcount= 0, linecount=0, maxcount, coordcount=0;
-  boolT islong, isfirst= True, wasbegin= False;
-  boolT isdelaunay= qh->DELAUNAY && !qh->PROJECTinput;
-
-  if (qh->CDDinput) {
-    while ((s= fgets(firstline, qh_MAXfirst, qh->fin))) {
-      linecount++;
-      if (qh->HALFspace && linecount == 1 && isdigit(*s)) {
-        dimfeasible= qh_strtol(s, &s);
-        while (isspace(*s))
-          s++;
-        if (qh_strtol(s, &s) == 1)
-          linecount += qh_readfeasible(qh, dimfeasible, s);
-        else
-          dimfeasible= 0;
-      }else if (!memcmp(firstline, "begin", (size_t)5) || !memcmp(firstline, "BEGIN", (size_t)5))
-        break;
-      else if (!*qh->rbox_command)
-        strncat(qh->rbox_command, s, sizeof(qh->rbox_command)-1);
-    }
-    if (!s) {
-      qh_fprintf(qh, qh->ferr, 6074, "qhull input error: missing \"begin\" for cdd-formated input\n");
-      qh_errexit(qh, qh_ERRinput, NULL, NULL);
-    }
-  }
-  while (!numinput && (s= fgets(firstline, qh_MAXfirst, qh->fin))) {
-    linecount++;
-    if (!memcmp(s, "begin", (size_t)5) || !memcmp(s, "BEGIN", (size_t)5))
-      wasbegin= True;
-    while (*s) {
-      while (isspace(*s))
-        s++;
-      if (!*s)
-        break;
-      if (!isdigit(*s)) {
-        if (!*qh->rbox_command) {
-          strncat(qh->rbox_command, s, sizeof(qh->rbox_command)-1);
-          firsttext= linecount;
-        }
-        break;
-      }
-      if (!diminput)
-        diminput= qh_strtol(s, &s);
-      else {
-        numinput= qh_strtol(s, &s);
-        if (numinput == 1 && diminput >= 2 && qh->HALFspace && !qh->CDDinput) {
-          linecount += qh_readfeasible(qh, diminput, s); /* checks if ok */
-          dimfeasible= diminput;
-          diminput= numinput= 0;
-        }else
-          break;
-      }
-    }
-  }
-  if (!s) {
-    qh_fprintf(qh, qh->ferr, 6075, "qhull input error: short input file.  Did not find dimension and number of points\n");
-    qh_errexit(qh, qh_ERRinput, NULL, NULL);
-  }
-  if (diminput > numinput) {
-    tempi= diminput;    /* exchange dim and n, e.g., for cdd input format */
-    diminput= numinput;
-    numinput= tempi;
-  }
-  if (diminput < 2) {
-    qh_fprintf(qh, qh->ferr, 6220,"qhull input error: dimension %d(first number) should be at least 2\n",
-            diminput);
-    qh_errexit(qh, qh_ERRinput, NULL, NULL);
-  }
-  if (isdelaunay) {
-    qh->PROJECTdelaunay= False;
-    if (qh->CDDinput)
-      *dimension= diminput;
-    else
-      *dimension= diminput+1;
-    *numpoints= numinput;
-    if (qh->ATinfinity)
-      (*numpoints)++;
-  }else if (qh->HALFspace) {
-    *dimension= diminput - 1;
-    *numpoints= numinput;
-    if (diminput < 3) {
-      qh_fprintf(qh, qh->ferr, 6221,"qhull input error: dimension %d(first number, includes offset) should be at least 3 for halfspaces\n",
-            diminput);
-      qh_errexit(qh, qh_ERRinput, NULL, NULL);
-    }
-    if (dimfeasible) {
-      if (dimfeasible != *dimension) {
-        qh_fprintf(qh, qh->ferr, 6222,"qhull input error: dimension %d of feasible point is not one less than dimension %d for halfspaces\n",
-          dimfeasible, diminput);
-        qh_errexit(qh, qh_ERRinput, NULL, NULL);
-      }
-    }else
-      qh_setfeasible(qh, *dimension);
-  }else {
-    if (qh->CDDinput)
-      *dimension= diminput-1;
-    else
-      *dimension= diminput;
-    *numpoints= numinput;
-  }
-  qh->normal_size= *dimension * sizeof(coordT); /* for tracing with qh_printpoint */
-  if (qh->HALFspace) {
-    qh->half_space= coordp= (coordT*)qh_malloc(qh->normal_size + sizeof(coordT));
-    if (qh->CDDinput) {
-      offsetp= qh->half_space;
-      normalp= offsetp + 1;
-    }else {
-      normalp= qh->half_space;
-      offsetp= normalp + *dimension;
-    }
-  }
-  qh->maxline= diminput * (qh_REALdigits + 5);
-  maximize_(qh->maxline, 500);
-  qh->line= (char*)qh_malloc((qh->maxline+1) * sizeof(char));
-  *ismalloc= True;  /* use malloc since memory not setup */
-  coords= points= qh->temp_malloc=  /* numinput and diminput >=2 by QH6220 */
-        (coordT*)qh_malloc((*numpoints)*(*dimension)*sizeof(coordT));
-  if (!coords || !qh->line || (qh->HALFspace && !qh->half_space)) {
-    qh_fprintf(qh, qh->ferr, 6076, "qhull error: insufficient memory to read %d points\n",
-            numinput);
-    qh_errexit(qh, qh_ERRmem, NULL, NULL);
-  }
-  if (isdelaunay && qh->ATinfinity) {
-    infinity= points + numinput * (*dimension);
-    for (k= (*dimension) - 1; k--; )
-      infinity[k]= 0.0;
-  }
-  maxcount= numinput * diminput;
-  paraboloid= 0.0;
-  while ((s= (isfirst ?  s : fgets(qh->line, qh->maxline, qh->fin)))) {
-    if (!isfirst) {
-      linecount++;
-      if (*s == 'e' || *s == 'E') {
-        if (!memcmp(s, "end", (size_t)3) || !memcmp(s, "END", (size_t)3)) {
-          if (qh->CDDinput )
-            break;
-          else if (wasbegin)
-            qh_fprintf(qh, qh->ferr, 7058, "qhull input warning: the input appears to be in cdd format.  If so, use 'Fd'\n");
-        }
-      }
-    }
-    islong= False;
-    while (*s) {
-      while (isspace(*s))
-        s++;
-      value= qh_strtod(s, &t);
-      if (s == t) {
-        if (!*qh->rbox_command)
-         strncat(qh->rbox_command, s, sizeof(qh->rbox_command)-1);
-        if (*s && !firsttext)
-          firsttext= linecount;
-        if (!islong && !firstshort && coordcount)
-          firstshort= linecount;
-        break;
-      }
-      if (!firstpoint)
-        firstpoint= linecount;
-      s= t;
-      if (++tokcount > maxcount)
-        continue;
-      if (qh->HALFspace) {
-        if (qh->CDDinput)
-          *(coordp++)= -value; /* both coefficients and offset */
-        else
-          *(coordp++)= value;
-      }else {
-        *(coords++)= value;
-        if (qh->CDDinput && !coordcount) {
-          if (value != 1.0) {
-            qh_fprintf(qh, qh->ferr, 6077, "qhull input error: for cdd format, point at line %d does not start with '1'\n",
-                   linecount);
-            qh_errexit(qh, qh_ERRinput, NULL, NULL);
-          }
-          coords--;
-        }else if (isdelaunay) {
-          paraboloid += value * value;
-          if (qh->ATinfinity) {
-            if (qh->CDDinput)
-              infinity[coordcount-1] += value;
-            else
-              infinity[coordcount] += value;
-          }
-        }
-      }
-      if (++coordcount == diminput) {
-        coordcount= 0;
-        if (isdelaunay) {
-          *(coords++)= paraboloid;
-          maximize_(maxboloid, paraboloid);
-          paraboloid= 0.0;
-        }else if (qh->HALFspace) {
-          if (!qh_sethalfspace(qh, *dimension, coords, &coords, normalp, offsetp, qh->feasible_point)) {
-            qh_fprintf(qh, qh->ferr, 8048, "The halfspace was on line %d\n", linecount);
-            if (wasbegin)
-              qh_fprintf(qh, qh->ferr, 8049, "The input appears to be in cdd format.  If so, you should use option 'Fd'\n");
-            qh_errexit(qh, qh_ERRinput, NULL, NULL);
-          }
-          coordp= qh->half_space;
-        }
-        while (isspace(*s))
-          s++;
-        if (*s) {
-          islong= True;
-          if (!firstlong)
-            firstlong= linecount;
-        }
-      }
-    }
-    if (!islong && !firstshort && coordcount)
-      firstshort= linecount;
-    if (!isfirst && s - qh->line >= qh->maxline) {
-      qh_fprintf(qh, qh->ferr, 6078, "qhull input error: line %d contained more than %d characters\n",
-              linecount, (int) (s - qh->line));   /* WARN64 */
-      qh_errexit(qh, qh_ERRinput, NULL, NULL);
-    }
-    isfirst= False;
-  }
-  if (tokcount != maxcount) {
-    newnum= fmin_(numinput, tokcount/diminput);
-    qh_fprintf(qh, qh->ferr, 7073,"\
-qhull warning: instead of %d %d-dimensional points, input contains\n\
-%d points and %d extra coordinates.  Line %d is the first\npoint",
-       numinput, diminput, tokcount/diminput, tokcount % diminput, firstpoint);
-    if (firsttext)
-      qh_fprintf(qh, qh->ferr, 8051, ", line %d is the first comment", firsttext);
-    if (firstshort)
-      qh_fprintf(qh, qh->ferr, 8052, ", line %d is the first short\nline", firstshort);
-    if (firstlong)
-      qh_fprintf(qh, qh->ferr, 8053, ", line %d is the first long line", firstlong);
-    qh_fprintf(qh, qh->ferr, 8054, ".  Continue with %d points.\n", newnum);
-    numinput= newnum;
-    if (isdelaunay && qh->ATinfinity) {
-      for (k= tokcount % diminput; k--; )
-        infinity[k] -= *(--coords);
-      *numpoints= newnum+1;
-    }else {
-      coords -= tokcount % diminput;
-      *numpoints= newnum;
-    }
-  }
-  if (isdelaunay && qh->ATinfinity) {
-    for (k= (*dimension) -1; k--; )
-      infinity[k] /= numinput;
-    if (coords == infinity)
-      coords += (*dimension) -1;
-    else {
-      for (k=0; k < (*dimension) -1; k++)
-        *(coords++)= infinity[k];
-    }
-    *(coords++)= maxboloid * 1.1;
-  }
-  if (qh->rbox_command[0]) {
-    qh->rbox_command[strlen(qh->rbox_command)-1]= '\0';
-    if (!strcmp(qh->rbox_command, "./rbox D4"))
-      qh_fprintf(qh, qh->ferr, 8055, "\n\
-This is the qhull test case.  If any errors or core dumps occur,\n\
-recompile qhull with 'make new'.  If errors still occur, there is\n\
-an incompatibility.  You should try a different compiler.  You can also\n\
-change the choices in user.h.  If you discover the source of the problem,\n\
-please send mail to qhull_bug@qhull.org.\n\
-\n\
-Type 'qhull' for a short list of options.\n");
-  }
-  qh_free(qh->line);
-  qh->line= NULL;
-  if (qh->half_space) {
-    qh_free(qh->half_space);
-    qh->half_space= NULL;
-  }
-  qh->temp_malloc= NULL;
-  trace1((qh, qh->ferr, 1008,"qh_readpoints: read in %d %d-dimensional points\n",
-          numinput, diminput));
-  return(points);
-} /* readpoints */
-
-
-/*---------------------------------
-
-  qh_setfeasible(qh, dim )
-    set qh.feasible_point from qh.feasible_string in "n,n,n" or "n n n" format
-
-  notes:
-    "n,n,n" already checked by qh_initflags()
-    see qh_readfeasible()
-    called only once from qh_new_qhull, otherwise leaks memory
-*/
-void qh_setfeasible(qhT *qh, int dim) {
-  int tokcount= 0;
-  char *s;
-  coordT *coords, value;
-
-  if (!(s= qh->feasible_string)) {
-    qh_fprintf(qh, qh->ferr, 6223, "\
-qhull input error: halfspace intersection needs a feasible point.\n\
-Either prepend the input with 1 point or use 'Hn,n,n'.  See manual.\n");
-    qh_errexit(qh, qh_ERRinput, NULL, NULL);
-  }
-  if (!(qh->feasible_point= (pointT*)qh_malloc(dim * sizeof(coordT)))) {
-    qh_fprintf(qh, qh->ferr, 6079, "qhull error: insufficient memory for 'Hn,n,n'\n");
-    qh_errexit(qh, qh_ERRmem, NULL, NULL);
-  }
-  coords= qh->feasible_point;
-  while (*s) {
-    value= qh_strtod(s, &s);
-    if (++tokcount > dim) {
-      qh_fprintf(qh, qh->ferr, 7059, "qhull input warning: more coordinates for 'H%s' than dimension %d\n",
-          qh->feasible_string, dim);
-      break;
-    }
-    *(coords++)= value;
-    if (*s)
-      s++;
-  }
-  while (++tokcount <= dim)
-    *(coords++)= 0.0;
-} /* setfeasible */
-
-/*---------------------------------
-
-  qh_skipfacet(qh, facet )
-    returns 'True' if this facet is not to be printed
-
-  notes:
-    based on the user provided slice thresholds and 'good' specifications
-*/
-boolT qh_skipfacet(qhT *qh, facetT *facet) {
-  facetT *neighbor, **neighborp;
-
-  if (qh->PRINTneighbors) {
-    if (facet->good)
-      return !qh->PRINTgood;
-    FOREACHneighbor_(facet) {
-      if (neighbor->good)
-        return False;
-    }
-    return True;
-  }else if (qh->PRINTgood)
-    return !facet->good;
-  else if (!facet->normal)
-    return True;
-  return(!qh_inthresholds(qh, facet->normal, NULL));
-} /* skipfacet */
-
-/*---------------------------------
-
-  qh_skipfilename(qh, string )
-    returns pointer to character after filename
-
-  notes:
-    skips leading spaces
-    ends with spacing or eol
-    if starts with ' or " ends with the same, skipping \' or \"
-    For qhull, qh_argv_to_command() only uses double quotes
-*/
-char *qh_skipfilename(qhT *qh, char *filename) {
-  char *s= filename;  /* non-const due to return */
-  char c;
-
-  while (*s && isspace(*s))
-    s++;
-  c= *s++;
-  if (c == '\0') {
-    qh_fprintf(qh, qh->ferr, 6204, "qhull input error: filename expected, none found.\n");
-    qh_errexit(qh, qh_ERRinput, NULL, NULL);
-  }
-  if (c == '\'' || c == '"') {
-    while (*s !=c || s[-1] == '\\') {
-      if (!*s) {
-        qh_fprintf(qh, qh->ferr, 6203, "qhull input error: missing quote after filename -- %s\n", filename);
-        qh_errexit(qh, qh_ERRinput, NULL, NULL);
-      }
-      s++;
-    }
-    s++;
-  }
-  else while (*s && !isspace(*s))
-      s++;
-  return s;
-} /* skipfilename */
-
diff --git a/C/libqhull_r.c b/C/libqhull_r.c
deleted file mode 100644
--- a/C/libqhull_r.c
+++ /dev/null
@@ -1,1403 +0,0 @@
-/*
  ---------------------------------
-
-   libqhull_r.c
-   Quickhull algorithm for convex hulls
-
-   qhull() and top-level routines
-
-   see qh-qhull_r.htm, libqhull.h, unix_r.c
-
-   see qhull_ra.h for internal functions
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull_r/libqhull_r.c#2 $$Change: 2047 $
-   $DateTime: 2016/01/04 22:03:18 $$Author: bbarber $
-*/
-
-#include "qhull_ra.h"
-
-/*============= functions in alphabetic order after qhull() =======*/
-
-/*---------------------------------
-
-  qh_qhull(qh)
-    compute DIM3 convex hull of qh.num_points starting at qh.first_point
-    qh->contains all global options and variables
-
-  returns:
-    returns polyhedron
-      qh.facet_list, qh.num_facets, qh.vertex_list, qh.num_vertices,
-
-    returns global variables
-      qh.hulltime, qh.max_outside, qh.interior_point, qh.max_vertex, qh.min_vertex
-
-    returns precision constants
-      qh.ANGLEround, centrum_radius, cos_max, DISTround, MAXabs_coord, ONEmerge
-
-  notes:
-    unless needed for output
-      qh.max_vertex and qh.min_vertex are max/min due to merges
-
-  see:
-    to add individual points to either qh.num_points
-      use qh_addpoint()
-
-    if qh.GETarea
-      qh_produceoutput() returns qh.totarea and qh.totvol via qh_getarea()
-
-  design:
-    record starting time
-    initialize hull and partition points
-    build convex hull
-    unless early termination
-      update facet->maxoutside for vertices, coplanar, and near-inside points
-    error if temporary sets exist
-    record end time
-*/
-
-void qh_qhull(qhT *qh) {
-  int numoutside;
-
-  qh->hulltime= qh_CPUclock;
-  if (qh->RERUN || qh->JOGGLEmax < REALmax/2)
-    qh_build_withrestart(qh);
-  else {
-    qh_initbuild(qh);
-    qh_buildhull(qh);
-  }
-  if (!qh->STOPpoint && !qh->STOPcone) {
-    if (qh->ZEROall_ok && !qh->TESTvneighbors && qh->MERGEexact)
-      qh_checkzero(qh, qh_ALL);
-    if (qh->ZEROall_ok && !qh->TESTvneighbors && !qh->WAScoplanar) {
-      trace2((qh, qh->ferr, 2055, "qh_qhull: all facets are clearly convex and no coplanar points.  Post-merging and check of maxout not needed.\n"));
-      qh->DOcheckmax= False;
-    }else {
-      if (qh->MERGEexact || (qh->hull_dim > qh_DIMreduceBuild && qh->PREmerge))
-        qh_postmerge(qh, "First post-merge", qh->premerge_centrum, qh->premerge_cos,
-             (qh->POSTmerge ? False : qh->TESTvneighbors));
-      else if (!qh->POSTmerge && qh->TESTvneighbors)
-        qh_postmerge(qh, "For testing vertex neighbors", qh->premerge_centrum,
-             qh->premerge_cos, True);
-      if (qh->POSTmerge)
-        qh_postmerge(qh, "For post-merging", qh->postmerge_centrum,
-             qh->postmerge_cos, qh->TESTvneighbors);
-      if (qh->visible_list == qh->facet_list) { /* i.e., merging done */
-        qh->findbestnew= True;
-        qh_partitionvisible(qh /*qh.visible_list*/, !qh_ALL, &numoutside);
-        qh->findbestnew= False;
-        qh_deletevisible(qh /*qh.visible_list*/);
-        qh_resetlists(qh, False, qh_RESETvisible /*qh.visible_list newvertex_list newfacet_list */);
-      }
-    }
-    if (qh->DOcheckmax){
-      if (qh->REPORTfreq) {
-        qh_buildtracing(qh, NULL, NULL);
-        qh_fprintf(qh, qh->ferr, 8115, "\nTesting all coplanar points.\n");
-      }
-      qh_check_maxout(qh);
-    }
-    if (qh->KEEPnearinside && !qh->maxoutdone)
-      qh_nearcoplanar(qh);
-  }
-  if (qh_setsize(qh, qh->qhmem.tempstack) != 0) {
-    qh_fprintf(qh, qh->ferr, 6164, "qhull internal error (qh_qhull): temporary sets not empty(%d)\n",
-             qh_setsize(qh, qh->qhmem.tempstack));
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }
-  qh->hulltime= qh_CPUclock - qh->hulltime;
-  qh->QHULLfinished= True;
-  trace1((qh, qh->ferr, 1036, "Qhull: algorithm completed\n"));
-} /* qhull */
-
-/*---------------------------------
-
-  qh_addpoint(qh, furthest, facet, checkdist )
-    add point (usually furthest point) above facet to hull
-    if checkdist,
-      check that point is above facet.
-      if point is not outside of the hull, uses qh_partitioncoplanar()
-      assumes that facet is defined by qh_findbestfacet()
-    else if facet specified,
-      assumes that point is above facet (major damage if below)
-    for Delaunay triangulations,
-      Use qh_setdelaunay() to lift point to paraboloid and scale by 'Qbb' if needed
-      Do not use options 'Qbk', 'QBk', or 'QbB' since they scale the coordinates.
-
-  returns:
-    returns False if user requested an early termination
-     qh.visible_list, newfacet_list, delvertex_list, NEWfacets may be defined
-    updates qh.facet_list, qh.num_facets, qh.vertex_list, qh.num_vertices
-    clear qh.maxoutdone (will need to call qh_check_maxout() for facet->maxoutside)
-    if unknown point, adds a pointer to qh.other_points
-      do not deallocate the point's coordinates
-
-  notes:
-    assumes point is near its best facet and not at a local minimum of a lens
-      distributions.  Use qh_findbestfacet to avoid this case.
-    uses qh.visible_list, qh.newfacet_list, qh.delvertex_list, qh.NEWfacets
-
-  see also:
-    qh_triangulate() -- triangulate non-simplicial facets
-
-  design:
-    add point to other_points if needed
-    if checkdist
-      if point not above facet
-        partition coplanar point
-        exit
-    exit if pre STOPpoint requested
-    find horizon and visible facets for point
-    make new facets for point to horizon
-    make hyperplanes for point
-    compute balance statistics
-    match neighboring new facets
-    update vertex neighbors and delete interior vertices
-    exit if STOPcone requested
-    merge non-convex new facets
-    if merge found, many merges, or 'Qf'
-       use qh_findbestnew() instead of qh_findbest()
-    partition outside points from visible facets
-    delete visible facets
-    check polyhedron if requested
-    exit if post STOPpoint requested
-    reset working lists of facets and vertices
-*/
-boolT qh_addpoint(qhT *qh, pointT *furthest, facetT *facet, boolT checkdist) {
-  int goodvisible, goodhorizon;
-  vertexT *vertex;
-  facetT *newfacet;
-  realT dist, newbalance, pbalance;
-  boolT isoutside= False;
-  int numpart, numpoints, numnew, firstnew;
-
-  qh->maxoutdone= False;
-  if (qh_pointid(qh, furthest) == qh_IDunknown)
-    qh_setappend(qh, &qh->other_points, furthest);
-  if (!facet) {
-    qh_fprintf(qh, qh->ferr, 6213, "qhull internal error (qh_addpoint): NULL facet.  Need to call qh_findbestfacet first\n");
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }
-  if (checkdist) {
-    facet= qh_findbest(qh, furthest, facet, !qh_ALL, !qh_ISnewfacets, !qh_NOupper,
-                        &dist, &isoutside, &numpart);
-    zzadd_(Zpartition, numpart);
-    if (!isoutside) {
-      zinc_(Znotmax);  /* last point of outsideset is no longer furthest. */
-      facet->notfurthest= True;
-      qh_partitioncoplanar(qh, furthest, facet, &dist);
-      return True;
-    }
-  }
-  qh_buildtracing(qh, furthest, facet);
-  if (qh->STOPpoint < 0 && qh->furthest_id == -qh->STOPpoint-1) {
-    facet->notfurthest= True;
-    return False;
-  }
-  qh_findhorizon(qh, furthest, facet, &goodvisible, &goodhorizon);
-  if (qh->ONLYgood && !(goodvisible+goodhorizon) && !qh->GOODclosest) {
-    zinc_(Znotgood);
-    facet->notfurthest= True;
-    /* last point of outsideset is no longer furthest.  This is ok
-       since all points of the outside are likely to be bad */
-    qh_resetlists(qh, False, qh_RESETvisible /*qh.visible_list newvertex_list newfacet_list */);
-    return True;
-  }
-  zzinc_(Zprocessed);
-  firstnew= qh->facet_id;
-  vertex= qh_makenewfacets(qh, furthest /*visible_list, attaches if !ONLYgood */);
-  qh_makenewplanes(qh /* newfacet_list */);
-  numnew= qh->facet_id - firstnew;
-  newbalance= numnew - (realT) (qh->num_facets-qh->num_visible)
-                         * qh->hull_dim/qh->num_vertices;
-  wadd_(Wnewbalance, newbalance);
-  wadd_(Wnewbalance2, newbalance * newbalance);
-  if (qh->ONLYgood
-  && !qh_findgood(qh, qh->newfacet_list, goodhorizon) && !qh->GOODclosest) {
-    FORALLnew_facets
-      qh_delfacet(qh, newfacet);
-    qh_delvertex(qh, vertex);
-    qh_resetlists(qh, True, qh_RESETvisible /*qh.visible_list newvertex_list newfacet_list */);
-    zinc_(Znotgoodnew);
-    facet->notfurthest= True;
-    return True;
-  }
-  if (qh->ONLYgood)
-    qh_attachnewfacets(qh /*visible_list*/);
-  qh_matchnewfacets(qh);
-  qh_updatevertices(qh);
-  if (qh->STOPcone && qh->furthest_id == qh->STOPcone-1) {
-    facet->notfurthest= True;
-    return False;  /* visible_list etc. still defined */
-  }
-  qh->findbestnew= False;
-  if (qh->PREmerge || qh->MERGEexact) {
-    qh_premerge(qh, vertex, qh->premerge_centrum, qh->premerge_cos);
-    if (qh_USEfindbestnew)
-      qh->findbestnew= True;
-    else {
-      FORALLnew_facets {
-        if (!newfacet->simplicial) {
-          qh->findbestnew= True;  /* use qh_findbestnew instead of qh_findbest*/
-          break;
-        }
-      }
-    }
-  }else if (qh->BESToutside)
-    qh->findbestnew= True;
-  qh_partitionvisible(qh /*qh.visible_list*/, !qh_ALL, &numpoints);
-  qh->findbestnew= False;
-  qh->findbest_notsharp= False;
-  zinc_(Zpbalance);
-  pbalance= numpoints - (realT) qh->hull_dim /* assumes all points extreme */
-                * (qh->num_points - qh->num_vertices)/qh->num_vertices;
-  wadd_(Wpbalance, pbalance);
-  wadd_(Wpbalance2, pbalance * pbalance);
-  qh_deletevisible(qh /*qh.visible_list*/);
-  zmax_(Zmaxvertex, qh->num_vertices);
-  qh->NEWfacets= False;
-  if (qh->IStracing >= 4) {
-    if (qh->num_facets < 2000)
-      qh_printlists(qh);
-    qh_printfacetlist(qh, qh->newfacet_list, NULL, True);
-    qh_checkpolygon(qh, qh->facet_list);
-  }else if (qh->CHECKfrequently) {
-    if (qh->num_facets < 50)
-      qh_checkpolygon(qh, qh->facet_list);
-    else
-      qh_checkpolygon(qh, qh->newfacet_list);
-  }
-  if (qh->STOPpoint > 0 && qh->furthest_id == qh->STOPpoint-1)
-    return False;
-  qh_resetlists(qh, True, qh_RESETvisible /*qh.visible_list newvertex_list newfacet_list */);
-  /* qh_triangulate(qh); to test qh.TRInormals */
-  trace2((qh, qh->ferr, 2056, "qh_addpoint: added p%d new facets %d new balance %2.2g point balance %2.2g\n",
-    qh_pointid(qh, furthest), numnew, newbalance, pbalance));
-  return True;
-} /* addpoint */
-
-/*---------------------------------
-
-  qh_build_withrestart(qh)
-    allow restarts due to qh.JOGGLEmax while calling qh_buildhull()
-       qh_errexit always undoes qh_build_withrestart()
-    qh.FIRSTpoint/qh.NUMpoints is point array
-       it may be moved by qh_joggleinput(qh)
-*/
-void qh_build_withrestart(qhT *qh) {
-  int restart;
-
-  qh->ALLOWrestart= True;
-  while (True) {
-    restart= setjmp(qh->restartexit); /* simple statement for CRAY J916 */
-    if (restart) {       /* only from qh_precision() */
-      zzinc_(Zretry);
-      wmax_(Wretrymax, qh->JOGGLEmax);
-      /* QH7078 warns about using 'TCn' with 'QJn' */
-      qh->STOPcone= qh_IDunknown; /* if break from joggle, prevents normal output */
-    }
-    if (!qh->RERUN && qh->JOGGLEmax < REALmax/2) {
-      if (qh->build_cnt > qh_JOGGLEmaxretry) {
-        qh_fprintf(qh, qh->ferr, 6229, "qhull precision error: %d attempts to construct a convex hull\n\
-        with joggled input.  Increase joggle above 'QJ%2.2g'\n\
-        or modify qh_JOGGLE... parameters in user.h\n",
-           qh->build_cnt, qh->JOGGLEmax);
-        qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-      }
-      if (qh->build_cnt && !restart)
-        break;
-    }else if (qh->build_cnt && qh->build_cnt >= qh->RERUN)
-      break;
-    qh->STOPcone= 0;
-    qh_freebuild(qh, True);  /* first call is a nop */
-    qh->build_cnt++;
-    if (!qh->qhull_optionsiz)
-      qh->qhull_optionsiz= (int)strlen(qh->qhull_options);   /* WARN64 */
-    else {
-      qh->qhull_options [qh->qhull_optionsiz]= '\0';
-      qh->qhull_optionlen= qh_OPTIONline;  /* starts a new line */
-    }
-    qh_option(qh, "_run", &qh->build_cnt, NULL);
-    if (qh->build_cnt == qh->RERUN) {
-      qh->IStracing= qh->TRACElastrun;  /* duplicated from qh_initqhull_globals */
-      if (qh->TRACEpoint != qh_IDunknown || qh->TRACEdist < REALmax/2 || qh->TRACEmerge) {
-        qh->TRACElevel= (qh->IStracing? qh->IStracing : 3);
-        qh->IStracing= 0;
-      }
-      qh->qhmem.IStracing= qh->IStracing;
-    }
-    if (qh->JOGGLEmax < REALmax/2)
-      qh_joggleinput(qh);
-    qh_initbuild(qh);
-    qh_buildhull(qh);
-    if (qh->JOGGLEmax < REALmax/2 && !qh->MERGING)
-      qh_checkconvex(qh, qh->facet_list, qh_ALGORITHMfault);
-  }
-  qh->ALLOWrestart= False;
-} /* qh_build_withrestart */
-
-/*---------------------------------
-
-  qh_buildhull(qh)
-    construct a convex hull by adding outside points one at a time
-
-  returns:
-
-  notes:
-    may be called multiple times
-    checks facet and vertex lists for incorrect flags
-    to recover from STOPcone, call qh_deletevisible and qh_resetlists
-
-  design:
-    check visible facet and newfacet flags
-    check newlist vertex flags and qh.STOPcone/STOPpoint
-    for each facet with a furthest outside point
-      add point to facet
-      exit if qh.STOPcone or qh.STOPpoint requested
-    if qh.NARROWhull for initial simplex
-      partition remaining outside points to coplanar sets
-*/
-void qh_buildhull(qhT *qh) {
-  facetT *facet;
-  pointT *furthest;
-  vertexT *vertex;
-  int id;
-
-  trace1((qh, qh->ferr, 1037, "qh_buildhull: start build hull\n"));
-  FORALLfacets {
-    if (facet->visible || facet->newfacet) {
-      qh_fprintf(qh, qh->ferr, 6165, "qhull internal error (qh_buildhull): visible or new facet f%d in facet list\n",
-                   facet->id);
-      qh_errexit(qh, qh_ERRqhull, facet, NULL);
-    }
-  }
-  FORALLvertices {
-    if (vertex->newlist) {
-      qh_fprintf(qh, qh->ferr, 6166, "qhull internal error (qh_buildhull): new vertex f%d in vertex list\n",
-                   vertex->id);
-      qh_errprint(qh, "ERRONEOUS", NULL, NULL, NULL, vertex);
-      qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-    }
-    id= qh_pointid(qh, vertex->point);
-    if ((qh->STOPpoint>0 && id == qh->STOPpoint-1) ||
-        (qh->STOPpoint<0 && id == -qh->STOPpoint-1) ||
-        (qh->STOPcone>0 && id == qh->STOPcone-1)) {
-      trace1((qh, qh->ferr, 1038,"qh_buildhull: stop point or cone P%d in initial hull\n", id));
-      return;
-    }
-  }
-  qh->facet_next= qh->facet_list;      /* advance facet when processed */
-  while ((furthest= qh_nextfurthest(qh, &facet))) {
-    qh->num_outside--;  /* if ONLYmax, furthest may not be outside */
-    if (!qh_addpoint(qh, furthest, facet, qh->ONLYmax))
-      break;
-  }
-  if (qh->NARROWhull) /* move points from outsideset to coplanarset */
-    qh_outcoplanar(qh /* facet_list */ );
-  if (qh->num_outside && !furthest) {
-    qh_fprintf(qh, qh->ferr, 6167, "qhull internal error (qh_buildhull): %d outside points were never processed.\n", qh->num_outside);
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }
-  trace1((qh, qh->ferr, 1039, "qh_buildhull: completed the hull construction\n"));
-} /* buildhull */
-
-
-/*---------------------------------
-
-  qh_buildtracing(qh, furthest, facet )
-    trace an iteration of qh_buildhull() for furthest point and facet
-    if !furthest, prints progress message
-
-  returns:
-    tracks progress with qh.lastreport
-    updates qh.furthest_id (-3 if furthest is NULL)
-    also resets visit_id, vertext_visit on wrap around
-
-  see:
-    qh_tracemerging()
-
-  design:
-    if !furthest
-      print progress message
-      exit
-    if 'TFn' iteration
-      print progress message
-    else if tracing
-      trace furthest point and facet
-    reset qh.visit_id and qh.vertex_visit if overflow may occur
-    set qh.furthest_id for tracing
-*/
-void qh_buildtracing(qhT *qh, pointT *furthest, facetT *facet) {
-  realT dist= 0;
-  float cpu;
-  int total, furthestid;
-  time_t timedata;
-  struct tm *tp;
-  vertexT *vertex;
-
-  qh->old_randomdist= qh->RANDOMdist;
-  qh->RANDOMdist= False;
-  if (!furthest) {
-    time(&timedata);
-    tp= localtime(&timedata);
-    cpu= (float)qh_CPUclock - (float)qh->hulltime;
-    cpu /= (float)qh_SECticks;
-    total= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
-    qh_fprintf(qh, qh->ferr, 8118, "\n\
-At %02d:%02d:%02d & %2.5g CPU secs, qhull has created %d facets and merged %d.\n\
- The current hull contains %d facets and %d vertices.  Last point was p%d\n",
-      tp->tm_hour, tp->tm_min, tp->tm_sec, cpu, qh->facet_id -1,
-      total, qh->num_facets, qh->num_vertices, qh->furthest_id);
-    return;
-  }
-  furthestid= qh_pointid(qh, furthest);
-  if (qh->TRACEpoint == furthestid) {
-    qh->IStracing= qh->TRACElevel;
-    qh->qhmem.IStracing= qh->TRACElevel;
-  }else if (qh->TRACEpoint != qh_IDunknown && qh->TRACEdist < REALmax/2) {
-    qh->IStracing= 0;
-    qh->qhmem.IStracing= 0;
-  }
-  if (qh->REPORTfreq && (qh->facet_id-1 > qh->lastreport+qh->REPORTfreq)) {
-    qh->lastreport= qh->facet_id-1;
-    time(&timedata);
-    tp= localtime(&timedata);
-    cpu= (float)qh_CPUclock - (float)qh->hulltime;
-    cpu /= (float)qh_SECticks;
-    total= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
-    zinc_(Zdistio);
-    qh_distplane(qh, furthest, facet, &dist);
-    qh_fprintf(qh, qh->ferr, 8119, "\n\
-At %02d:%02d:%02d & %2.5g CPU secs, qhull has created %d facets and merged %d.\n\
- The current hull contains %d facets and %d vertices.  There are %d\n\
- outside points.  Next is point p%d(v%d), %2.2g above f%d.\n",
-      tp->tm_hour, tp->tm_min, tp->tm_sec, cpu, qh->facet_id -1,
-      total, qh->num_facets, qh->num_vertices, qh->num_outside+1,
-      furthestid, qh->vertex_id, dist, getid_(facet));
-  }else if (qh->IStracing >=1) {
-    cpu= (float)qh_CPUclock - (float)qh->hulltime;
-    cpu /= (float)qh_SECticks;
-    qh_distplane(qh, furthest, facet, &dist);
-    qh_fprintf(qh, qh->ferr, 8120, "qh_addpoint: add p%d(v%d) to hull of %d facets(%2.2g above f%d) and %d outside at %4.4g CPU secs.  Previous was p%d.\n",
-      furthestid, qh->vertex_id, qh->num_facets, dist,
-      getid_(facet), qh->num_outside+1, cpu, qh->furthest_id);
-  }
-  zmax_(Zvisit2max, (int)qh->visit_id/2);
-  if (qh->visit_id > (unsigned) INT_MAX) { /* 31 bits */
-    zinc_(Zvisit);
-    qh->visit_id= 0;
-    FORALLfacets
-      facet->visitid= 0;
-  }
-  zmax_(Zvvisit2max, (int)qh->vertex_visit/2);
-  if (qh->vertex_visit > (unsigned) INT_MAX) { /* 31 bits */ 
-    zinc_(Zvvisit);
-    qh->vertex_visit= 0;
-    FORALLvertices
-      vertex->visitid= 0;
-  }
-  qh->furthest_id= furthestid;
-  qh->RANDOMdist= qh->old_randomdist;
-} /* buildtracing */
-
-/*---------------------------------
-
-  qh_errexit2(qh, exitcode, facet, otherfacet )
-    return exitcode to system after an error
-    report two facets
-
-  returns:
-    assumes exitcode non-zero
-
-  see:
-    normally use qh_errexit() in user.c(reports a facet and a ridge)
-*/
-void qh_errexit2(qhT *qh, int exitcode, facetT *facet, facetT *otherfacet) {
-
-  qh_errprint(qh, "ERRONEOUS", facet, otherfacet, NULL, NULL);
-  qh_errexit(qh, exitcode, NULL, NULL);
-} /* errexit2 */
-
-
-/*---------------------------------
-
-  qh_findhorizon(qh, point, facet, goodvisible, goodhorizon )
-    given a visible facet, find the point's horizon and visible facets
-    for all facets, !facet-visible
-
-  returns:
-    returns qh.visible_list/num_visible with all visible facets
-      marks visible facets with ->visible
-    updates count of good visible and good horizon facets
-    updates qh.max_outside, qh.max_vertex, facet->maxoutside
-
-  see:
-    similar to qh_delpoint()
-
-  design:
-    move facet to qh.visible_list at end of qh.facet_list
-    for all visible facets
-     for each unvisited neighbor of a visible facet
-       compute distance of point to neighbor
-       if point above neighbor
-         move neighbor to end of qh.visible_list
-       else if point is coplanar with neighbor
-         update qh.max_outside, qh.max_vertex, neighbor->maxoutside
-         mark neighbor coplanar (will create a samecycle later)
-         update horizon statistics
-*/
-void qh_findhorizon(qhT *qh, pointT *point, facetT *facet, int *goodvisible, int *goodhorizon) {
-  facetT *neighbor, **neighborp, *visible;
-  int numhorizon= 0, coplanar= 0;
-  realT dist;
-
-  trace1((qh, qh->ferr, 1040,"qh_findhorizon: find horizon for point p%d facet f%d\n",qh_pointid(qh, point),facet->id));
-  *goodvisible= *goodhorizon= 0;
-  zinc_(Ztotvisible);
-  qh_removefacet(qh, facet);  /* visible_list at end of qh->facet_list */
-  qh_appendfacet(qh, facet);
-  qh->num_visible= 1;
-  if (facet->good)
-    (*goodvisible)++;
-  qh->visible_list= facet;
-  facet->visible= True;
-  facet->f.replace= NULL;
-  if (qh->IStracing >=4)
-    qh_errprint(qh, "visible", facet, NULL, NULL, NULL);
-  qh->visit_id++;
-  FORALLvisible_facets {
-    if (visible->tricoplanar && !qh->TRInormals) {
-      qh_fprintf(qh, qh->ferr, 6230, "Qhull internal error (qh_findhorizon): does not work for tricoplanar facets.  Use option 'Q11'\n");
-      qh_errexit(qh, qh_ERRqhull, visible, NULL);
-    }
-    visible->visitid= qh->visit_id;
-    FOREACHneighbor_(visible) {
-      if (neighbor->visitid == qh->visit_id)
-        continue;
-      neighbor->visitid= qh->visit_id;
-      zzinc_(Znumvisibility);
-      qh_distplane(qh, point, neighbor, &dist);
-      if (dist > qh->MINvisible) {
-        zinc_(Ztotvisible);
-        qh_removefacet(qh, neighbor);  /* append to end of qh->visible_list */
-        qh_appendfacet(qh, neighbor);
-        neighbor->visible= True;
-        neighbor->f.replace= NULL;
-        qh->num_visible++;
-        if (neighbor->good)
-          (*goodvisible)++;
-        if (qh->IStracing >=4)
-          qh_errprint(qh, "visible", neighbor, NULL, NULL, NULL);
-      }else {
-        if (dist > - qh->MAXcoplanar) {
-          neighbor->coplanar= True;
-          zzinc_(Zcoplanarhorizon);
-          qh_precision(qh, "coplanar horizon");
-          coplanar++;
-          if (qh->MERGING) {
-            if (dist > 0) {
-              maximize_(qh->max_outside, dist);
-              maximize_(qh->max_vertex, dist);
-#if qh_MAXoutside
-              maximize_(neighbor->maxoutside, dist);
-#endif
-            }else
-              minimize_(qh->min_vertex, dist);  /* due to merge later */
-          }
-          trace2((qh, qh->ferr, 2057, "qh_findhorizon: point p%d is coplanar to horizon f%d, dist=%2.7g < qh->MINvisible(%2.7g)\n",
-              qh_pointid(qh, point), neighbor->id, dist, qh->MINvisible));
-        }else
-          neighbor->coplanar= False;
-        zinc_(Ztothorizon);
-        numhorizon++;
-        if (neighbor->good)
-          (*goodhorizon)++;
-        if (qh->IStracing >=4)
-          qh_errprint(qh, "horizon", neighbor, NULL, NULL, NULL);
-      }
-    }
-  }
-  if (!numhorizon) {
-    qh_precision(qh, "empty horizon");
-    qh_fprintf(qh, qh->ferr, 6168, "qhull precision error (qh_findhorizon): empty horizon\n\
-QhullPoint p%d was above all facets.\n", qh_pointid(qh, point));
-    qh_printfacetlist(qh, qh->facet_list, NULL, True);
-    qh_errexit(qh, qh_ERRprec, NULL, NULL);
-  }
-  trace1((qh, qh->ferr, 1041, "qh_findhorizon: %d horizon facets(good %d), %d visible(good %d), %d coplanar\n",
-       numhorizon, *goodhorizon, qh->num_visible, *goodvisible, coplanar));
-  if (qh->IStracing >= 4 && qh->num_facets < 50)
-    qh_printlists(qh);
-} /* findhorizon */
-
-/*---------------------------------
-
-  qh_nextfurthest(qh, visible )
-    returns next furthest point and visible facet for qh_addpoint()
-    starts search at qh.facet_next
-
-  returns:
-    removes furthest point from outside set
-    NULL if none available
-    advances qh.facet_next over facets with empty outside sets
-
-  design:
-    for each facet from qh.facet_next
-      if empty outside set
-        advance qh.facet_next
-      else if qh.NARROWhull
-        determine furthest outside point
-        if furthest point is not outside
-          advance qh.facet_next(point will be coplanar)
-    remove furthest point from outside set
-*/
-pointT *qh_nextfurthest(qhT *qh, facetT **visible) {
-  facetT *facet;
-  int size, idx;
-  realT randr, dist;
-  pointT *furthest;
-
-  while ((facet= qh->facet_next) != qh->facet_tail) {
-    if (!facet->outsideset) {
-      qh->facet_next= facet->next;
-      continue;
-    }
-    SETreturnsize_(facet->outsideset, size);
-    if (!size) {
-      qh_setfree(qh, &facet->outsideset);
-      qh->facet_next= facet->next;
-      continue;
-    }
-    if (qh->NARROWhull) {
-      if (facet->notfurthest)
-        qh_furthestout(qh, facet);
-      furthest= (pointT*)qh_setlast(facet->outsideset);
-#if qh_COMPUTEfurthest
-      qh_distplane(qh, furthest, facet, &dist);
-      zinc_(Zcomputefurthest);
-#else
-      dist= facet->furthestdist;
-#endif
-      if (dist < qh->MINoutside) { /* remainder of outside set is coplanar for qh_outcoplanar */
-        qh->facet_next= facet->next;
-        continue;
-      }
-    }
-    if (!qh->RANDOMoutside && !qh->VIRTUALmemory) {
-      if (qh->PICKfurthest) {
-        qh_furthestnext(qh /* qh->facet_list */);
-        facet= qh->facet_next;
-      }
-      *visible= facet;
-      return((pointT*)qh_setdellast(facet->outsideset));
-    }
-    if (qh->RANDOMoutside) {
-      int outcoplanar = 0;
-      if (qh->NARROWhull) {
-        FORALLfacets {
-          if (facet == qh->facet_next)
-            break;
-          if (facet->outsideset)
-            outcoplanar += qh_setsize(qh, facet->outsideset);
-        }
-      }
-      randr= qh_RANDOMint;
-      randr= randr/(qh_RANDOMmax+1);
-      idx= (int)floor((qh->num_outside - outcoplanar) * randr);
-      FORALLfacet_(qh->facet_next) {
-        if (facet->outsideset) {
-          SETreturnsize_(facet->outsideset, size);
-          if (!size)
-            qh_setfree(qh, &facet->outsideset);
-          else if (size > idx) {
-            *visible= facet;
-            return((pointT*)qh_setdelnth(qh, facet->outsideset, idx));
-          }else
-            idx -= size;
-        }
-      }
-      qh_fprintf(qh, qh->ferr, 6169, "qhull internal error (qh_nextfurthest): num_outside %d is too low\nby at least %d, or a random real %g >= 1.0\n",
-              qh->num_outside, idx+1, randr);
-      qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-    }else { /* VIRTUALmemory */
-      facet= qh->facet_tail->previous;
-      if (!(furthest= (pointT*)qh_setdellast(facet->outsideset))) {
-        if (facet->outsideset)
-          qh_setfree(qh, &facet->outsideset);
-        qh_removefacet(qh, facet);
-        qh_prependfacet(qh, facet, &qh->facet_list);
-        continue;
-      }
-      *visible= facet;
-      return furthest;
-    }
-  }
-  return NULL;
-} /* nextfurthest */
-
-/*---------------------------------
-
-  qh_partitionall(qh, vertices, points, numpoints )
-    partitions all points in points/numpoints to the outsidesets of facets
-    vertices= vertices in qh.facet_list(!partitioned)
-
-  returns:
-    builds facet->outsideset
-    does not partition qh.GOODpoint
-    if qh.ONLYgood && !qh.MERGING,
-      does not partition qh.GOODvertex
-
-  notes:
-    faster if qh.facet_list sorted by anticipated size of outside set
-
-  design:
-    initialize pointset with all points
-    remove vertices from pointset
-    remove qh.GOODpointp from pointset (unless it's qh.STOPcone or qh.STOPpoint)
-    for all facets
-      for all remaining points in pointset
-        compute distance from point to facet
-        if point is outside facet
-          remove point from pointset (by not reappending)
-          update bestpoint
-          append point or old bestpoint to facet's outside set
-      append bestpoint to facet's outside set (furthest)
-    for all points remaining in pointset
-      partition point into facets' outside sets and coplanar sets
-*/
-void qh_partitionall(qhT *qh, setT *vertices, pointT *points, int numpoints){
-  setT *pointset;
-  vertexT *vertex, **vertexp;
-  pointT *point, **pointp, *bestpoint;
-  int size, point_i, point_n, point_end, remaining, i, id;
-  facetT *facet;
-  realT bestdist= -REALmax, dist, distoutside;
-
-  trace1((qh, qh->ferr, 1042, "qh_partitionall: partition all points into outside sets\n"));
-  pointset= qh_settemp(qh, numpoints);
-  qh->num_outside= 0;
-  pointp= SETaddr_(pointset, pointT);
-  for (i=numpoints, point= points; i--; point += qh->hull_dim)
-    *(pointp++)= point;
-  qh_settruncate(qh, pointset, numpoints);
-  FOREACHvertex_(vertices) {
-    if ((id= qh_pointid(qh, vertex->point)) >= 0)
-      SETelem_(pointset, id)= NULL;
-  }
-  id= qh_pointid(qh, qh->GOODpointp);
-  if (id >=0 && qh->STOPcone-1 != id && -qh->STOPpoint-1 != id)
-    SETelem_(pointset, id)= NULL;
-  if (qh->GOODvertexp && qh->ONLYgood && !qh->MERGING) { /* matches qhull()*/
-    if ((id= qh_pointid(qh, qh->GOODvertexp)) >= 0)
-      SETelem_(pointset, id)= NULL;
-  }
-  if (!qh->BESToutside) {  /* matches conditional for qh_partitionpoint below */
-    distoutside= qh_DISToutside; /* multiple of qh.MINoutside & qh.max_outside, see user.h */
-    zval_(Ztotpartition)= qh->num_points - qh->hull_dim - 1; /*misses GOOD... */
-    remaining= qh->num_facets;
-    point_end= numpoints;
-    FORALLfacets {
-      size= point_end/(remaining--) + 100;
-      facet->outsideset= qh_setnew(qh, size);
-      bestpoint= NULL;
-      point_end= 0;
-      FOREACHpoint_i_(qh, pointset) {
-        if (point) {
-          zzinc_(Zpartitionall);
-          qh_distplane(qh, point, facet, &dist);
-          if (dist < distoutside)
-            SETelem_(pointset, point_end++)= point;
-          else {
-            qh->num_outside++;
-            if (!bestpoint) {
-              bestpoint= point;
-              bestdist= dist;
-            }else if (dist > bestdist) {
-              qh_setappend(qh, &facet->outsideset, bestpoint);
-              bestpoint= point;
-              bestdist= dist;
-            }else
-              qh_setappend(qh, &facet->outsideset, point);
-          }
-        }
-      }
-      if (bestpoint) {
-        qh_setappend(qh, &facet->outsideset, bestpoint);
-#if !qh_COMPUTEfurthest
-        facet->furthestdist= bestdist;
-#endif
-      }else
-        qh_setfree(qh, &facet->outsideset);
-      qh_settruncate(qh, pointset, point_end);
-    }
-  }
-  /* if !qh->BESToutside, pointset contains points not assigned to outsideset */
-  if (qh->BESToutside || qh->MERGING || qh->KEEPcoplanar || qh->KEEPinside) {
-    qh->findbestnew= True;
-    FOREACHpoint_i_(qh, pointset) {
-      if (point)
-        qh_partitionpoint(qh, point, qh->facet_list);
-    }
-    qh->findbestnew= False;
-  }
-  zzadd_(Zpartitionall, zzval_(Zpartition));
-  zzval_(Zpartition)= 0;
-  qh_settempfree(qh, &pointset);
-  if (qh->IStracing >= 4)
-    qh_printfacetlist(qh, qh->facet_list, NULL, True);
-} /* partitionall */
-
-
-/*---------------------------------
-
-  qh_partitioncoplanar(qh, point, facet, dist )
-    partition coplanar point to a facet
-    dist is distance from point to facet
-    if dist NULL,
-      searches for bestfacet and does nothing if inside
-    if qh.findbestnew set,
-      searches new facets instead of using qh_findbest()
-
-  returns:
-    qh.max_ouside updated
-    if qh.KEEPcoplanar or qh.KEEPinside
-      point assigned to best coplanarset
-
-  notes:
-    facet->maxoutside is updated at end by qh_check_maxout
-
-  design:
-    if dist undefined
-      find best facet for point
-      if point sufficiently below facet (depends on qh.NEARinside and qh.KEEPinside)
-        exit
-    if keeping coplanar/nearinside/inside points
-      if point is above furthest coplanar point
-        append point to coplanar set (it is the new furthest)
-        update qh.max_outside
-      else
-        append point one before end of coplanar set
-    else if point is clearly outside of qh.max_outside and bestfacet->coplanarset
-    and bestfacet is more than perpendicular to facet
-      repartition the point using qh_findbest() -- it may be put on an outsideset
-    else
-      update qh.max_outside
-*/
-void qh_partitioncoplanar(qhT *qh, pointT *point, facetT *facet, realT *dist) {
-  facetT *bestfacet;
-  pointT *oldfurthest;
-  realT bestdist, dist2= 0, angle;
-  int numpart= 0, oldfindbest;
-  boolT isoutside;
-
-  qh->WAScoplanar= True;
-  if (!dist) {
-    if (qh->findbestnew)
-      bestfacet= qh_findbestnew(qh, point, facet, &bestdist, qh_ALL, &isoutside, &numpart);
-    else
-      bestfacet= qh_findbest(qh, point, facet, qh_ALL, !qh_ISnewfacets, qh->DELAUNAY,
-                          &bestdist, &isoutside, &numpart);
-    zinc_(Ztotpartcoplanar);
-    zzadd_(Zpartcoplanar, numpart);
-    if (!qh->DELAUNAY && !qh->KEEPinside) { /*  for 'd', bestdist skips upperDelaunay facets */
-      if (qh->KEEPnearinside) {
-        if (bestdist < -qh->NEARinside) {
-          zinc_(Zcoplanarinside);
-          trace4((qh, qh->ferr, 4062, "qh_partitioncoplanar: point p%d is more than near-inside facet f%d dist %2.2g findbestnew %d\n",
-                  qh_pointid(qh, point), bestfacet->id, bestdist, qh->findbestnew));
-          return;
-        }
-      }else if (bestdist < -qh->MAXcoplanar) {
-          trace4((qh, qh->ferr, 4063, "qh_partitioncoplanar: point p%d is inside facet f%d dist %2.2g findbestnew %d\n",
-                  qh_pointid(qh, point), bestfacet->id, bestdist, qh->findbestnew));
-        zinc_(Zcoplanarinside);
-        return;
-      }
-    }
-  }else {
-    bestfacet= facet;
-    bestdist= *dist;
-  }
-  if (bestdist > qh->max_outside) {
-    if (!dist && facet != bestfacet) {
-      zinc_(Zpartangle);
-      angle= qh_getangle(qh, facet->normal, bestfacet->normal);
-      if (angle < 0) {
-        /* typically due to deleted vertex and coplanar facets, e.g.,
-             RBOX 1000 s Z1 G1e-13 t1001185205 | QHULL Tv */
-        zinc_(Zpartflip);
-        trace2((qh, qh->ferr, 2058, "qh_partitioncoplanar: repartition point p%d from f%d.  It is above flipped facet f%d dist %2.2g\n",
-                qh_pointid(qh, point), facet->id, bestfacet->id, bestdist));
-        oldfindbest= qh->findbestnew;
-        qh->findbestnew= False;
-        qh_partitionpoint(qh, point, bestfacet);
-        qh->findbestnew= oldfindbest;
-        return;
-      }
-    }
-    qh->max_outside= bestdist;
-    if (bestdist > qh->TRACEdist) {
-      qh_fprintf(qh, qh->ferr, 8122, "qh_partitioncoplanar: ====== p%d from f%d increases max_outside to %2.2g of f%d last p%d\n",
-                     qh_pointid(qh, point), facet->id, bestdist, bestfacet->id, qh->furthest_id);
-      qh_errprint(qh, "DISTANT", facet, bestfacet, NULL, NULL);
-    }
-  }
-  if (qh->KEEPcoplanar + qh->KEEPinside + qh->KEEPnearinside) {
-    oldfurthest= (pointT*)qh_setlast(bestfacet->coplanarset);
-    if (oldfurthest) {
-      zinc_(Zcomputefurthest);
-      qh_distplane(qh, oldfurthest, bestfacet, &dist2);
-    }
-    if (!oldfurthest || dist2 < bestdist)
-      qh_setappend(qh, &bestfacet->coplanarset, point);
-    else
-      qh_setappend2ndlast(qh, &bestfacet->coplanarset, point);
-  }
-  trace4((qh, qh->ferr, 4064, "qh_partitioncoplanar: point p%d is coplanar with facet f%d(or inside) dist %2.2g\n",
-          qh_pointid(qh, point), bestfacet->id, bestdist));
-} /* partitioncoplanar */
-
-/*---------------------------------
-
-  qh_partitionpoint(qh, point, facet )
-    assigns point to an outside set, coplanar set, or inside set (i.e., dropt)
-    if qh.findbestnew
-      uses qh_findbestnew() to search all new facets
-    else
-      uses qh_findbest()
-
-  notes:
-    after qh_distplane(), this and qh_findbest() are most expensive in 3-d
-
-  design:
-    find best facet for point
-      (either exhaustive search of new facets or directed search from facet)
-    if qh.NARROWhull
-      retain coplanar and nearinside points as outside points
-    if point is outside bestfacet
-      if point above furthest point for bestfacet
-        append point to outside set (it becomes the new furthest)
-        if outside set was empty
-          move bestfacet to end of qh.facet_list (i.e., after qh.facet_next)
-        update bestfacet->furthestdist
-      else
-        append point one before end of outside set
-    else if point is coplanar to bestfacet
-      if keeping coplanar points or need to update qh.max_outside
-        partition coplanar point into bestfacet
-    else if near-inside point
-      partition as coplanar point into bestfacet
-    else is an inside point
-      if keeping inside points
-        partition as coplanar point into bestfacet
-*/
-void qh_partitionpoint(qhT *qh, pointT *point, facetT *facet) {
-  realT bestdist;
-  boolT isoutside;
-  facetT *bestfacet;
-  int numpart;
-#if qh_COMPUTEfurthest
-  realT dist;
-#endif
-
-  if (qh->findbestnew)
-    bestfacet= qh_findbestnew(qh, point, facet, &bestdist, qh->BESToutside, &isoutside, &numpart);
-  else
-    bestfacet= qh_findbest(qh, point, facet, qh->BESToutside, qh_ISnewfacets, !qh_NOupper,
-                          &bestdist, &isoutside, &numpart);
-  zinc_(Ztotpartition);
-  zzadd_(Zpartition, numpart);
-  if (qh->NARROWhull) {
-    if (qh->DELAUNAY && !isoutside && bestdist >= -qh->MAXcoplanar)
-      qh_precision(qh, "nearly incident point(narrow hull)");
-    if (qh->KEEPnearinside) {
-      if (bestdist >= -qh->NEARinside)
-        isoutside= True;
-    }else if (bestdist >= -qh->MAXcoplanar)
-      isoutside= True;
-  }
-
-  if (isoutside) {
-    if (!bestfacet->outsideset
-    || !qh_setlast(bestfacet->outsideset)) {
-      qh_setappend(qh, &(bestfacet->outsideset), point);
-      if (!bestfacet->newfacet) {
-        qh_removefacet(qh, bestfacet);  /* make sure it's after qh->facet_next */
-        qh_appendfacet(qh, bestfacet);
-      }
-#if !qh_COMPUTEfurthest
-      bestfacet->furthestdist= bestdist;
-#endif
-    }else {
-#if qh_COMPUTEfurthest
-      zinc_(Zcomputefurthest);
-      qh_distplane(qh, oldfurthest, bestfacet, &dist);
-      if (dist < bestdist)
-        qh_setappend(qh, &(bestfacet->outsideset), point);
-      else
-        qh_setappend2ndlast(qh, &(bestfacet->outsideset), point);
-#else
-      if (bestfacet->furthestdist < bestdist) {
-        qh_setappend(qh, &(bestfacet->outsideset), point);
-        bestfacet->furthestdist= bestdist;
-      }else
-        qh_setappend2ndlast(qh, &(bestfacet->outsideset), point);
-#endif
-    }
-    qh->num_outside++;
-    trace4((qh, qh->ferr, 4065, "qh_partitionpoint: point p%d is outside facet f%d new? %d (or narrowhull)\n",
-          qh_pointid(qh, point), bestfacet->id, bestfacet->newfacet));
-  }else if (qh->DELAUNAY || bestdist >= -qh->MAXcoplanar) { /* for 'd', bestdist skips upperDelaunay facets */
-    zzinc_(Zcoplanarpart);
-    if (qh->DELAUNAY)
-      qh_precision(qh, "nearly incident point");
-    if ((qh->KEEPcoplanar + qh->KEEPnearinside) || bestdist > qh->max_outside)
-      qh_partitioncoplanar(qh, point, bestfacet, &bestdist);
-    else {
-      trace4((qh, qh->ferr, 4066, "qh_partitionpoint: point p%d is coplanar to facet f%d (dropped)\n",
-          qh_pointid(qh, point), bestfacet->id));
-    }
-  }else if (qh->KEEPnearinside && bestdist > -qh->NEARinside) {
-    zinc_(Zpartnear);
-    qh_partitioncoplanar(qh, point, bestfacet, &bestdist);
-  }else {
-    zinc_(Zpartinside);
-    trace4((qh, qh->ferr, 4067, "qh_partitionpoint: point p%d is inside all facets, closest to f%d dist %2.2g\n",
-          qh_pointid(qh, point), bestfacet->id, bestdist));
-    if (qh->KEEPinside)
-      qh_partitioncoplanar(qh, point, bestfacet, &bestdist);
-  }
-} /* partitionpoint */
-
-/*---------------------------------
-
-  qh_partitionvisible(qh, allpoints, numoutside )
-    partitions points in visible facets to qh.newfacet_list
-    qh.visible_list= visible facets
-    for visible facets
-      1st neighbor (if any) points to a horizon facet or a new facet
-    if allpoints(!used),
-      repartitions coplanar points
-
-  returns:
-    updates outside sets and coplanar sets of qh.newfacet_list
-    updates qh.num_outside (count of outside points)
-
-  notes:
-    qh.findbest_notsharp should be clear (extra work if set)
-
-  design:
-    for all visible facets with outside set or coplanar set
-      select a newfacet for visible facet
-      if outside set
-        partition outside set into new facets
-      if coplanar set and keeping coplanar/near-inside/inside points
-        if allpoints
-          partition coplanar set into new facets, may be assigned outside
-        else
-          partition coplanar set into coplanar sets of new facets
-    for each deleted vertex
-      if allpoints
-        partition vertex into new facets, may be assigned outside
-      else
-        partition vertex into coplanar sets of new facets
-*/
-void qh_partitionvisible(qhT *qh /*qh.visible_list*/, boolT allpoints, int *numoutside) {
-  facetT *visible, *newfacet;
-  pointT *point, **pointp;
-  int coplanar=0, size;
-  unsigned count;
-  vertexT *vertex, **vertexp;
-
-  if (qh->ONLYmax)
-    maximize_(qh->MINoutside, qh->max_vertex);
-  *numoutside= 0;
-  FORALLvisible_facets {
-    if (!visible->outsideset && !visible->coplanarset)
-      continue;
-    newfacet= visible->f.replace;
-    count= 0;
-    while (newfacet && newfacet->visible) {
-      newfacet= newfacet->f.replace;
-      if (count++ > qh->facet_id)
-        qh_infiniteloop(qh, visible);
-    }
-    if (!newfacet)
-      newfacet= qh->newfacet_list;
-    if (newfacet == qh->facet_tail) {
-      qh_fprintf(qh, qh->ferr, 6170, "qhull precision error (qh_partitionvisible): all new facets deleted as\n        degenerate facets. Can not continue.\n");
-      qh_errexit(qh, qh_ERRprec, NULL, NULL);
-    }
-    if (visible->outsideset) {
-      size= qh_setsize(qh, visible->outsideset);
-      *numoutside += size;
-      qh->num_outside -= size;
-      FOREACHpoint_(visible->outsideset)
-        qh_partitionpoint(qh, point, newfacet);
-    }
-    if (visible->coplanarset && (qh->KEEPcoplanar + qh->KEEPinside + qh->KEEPnearinside)) {
-      size= qh_setsize(qh, visible->coplanarset);
-      coplanar += size;
-      FOREACHpoint_(visible->coplanarset) {
-        if (allpoints) /* not used */
-          qh_partitionpoint(qh, point, newfacet);
-        else
-          qh_partitioncoplanar(qh, point, newfacet, NULL);
-      }
-    }
-  }
-  FOREACHvertex_(qh->del_vertices) {
-    if (vertex->point) {
-      if (allpoints) /* not used */
-        qh_partitionpoint(qh, vertex->point, qh->newfacet_list);
-      else
-        qh_partitioncoplanar(qh, vertex->point, qh->newfacet_list, NULL);
-    }
-  }
-  trace1((qh, qh->ferr, 1043,"qh_partitionvisible: partitioned %d points from outsidesets and %d points from coplanarsets\n", *numoutside, coplanar));
-} /* partitionvisible */
-
-
-
-/*---------------------------------
-
-  qh_precision(qh, reason )
-    restart on precision errors if not merging and if 'QJn'
-*/
-void qh_precision(qhT *qh, const char *reason) {
-
-  if (qh->ALLOWrestart && !qh->PREmerge && !qh->MERGEexact) {
-    if (qh->JOGGLEmax < REALmax/2) {
-      trace0((qh, qh->ferr, 26, "qh_precision: qhull restart because of %s\n", reason));
-      /* May be called repeatedly if qh->ALLOWrestart */
-      longjmp(qh->restartexit, qh_ERRprec);
-    }
-  }
-} /* qh_precision */
-
-/*---------------------------------
-
-  qh_printsummary(qh, fp )
-    prints summary to fp
-
-  notes:
-    not in io_r.c so that user_eg.c can prevent io_r.c from loading
-    qh_printsummary and qh_countfacets must match counts
-
-  design:
-    determine number of points, vertices, and coplanar points
-    print summary
-*/
-void qh_printsummary(qhT *qh, FILE *fp) {
-  realT ratio, outerplane, innerplane;
-  float cpu;
-  int size, id, nummerged, numvertices, numcoplanars= 0, nonsimplicial=0;
-  int goodused;
-  facetT *facet;
-  const char *s;
-  int numdel= zzval_(Zdelvertextot);
-  int numtricoplanars= 0;
-
-  size= qh->num_points + qh_setsize(qh, qh->other_points);
-  numvertices= qh->num_vertices - qh_setsize(qh, qh->del_vertices);
-  id= qh_pointid(qh, qh->GOODpointp);
-  FORALLfacets {
-    if (facet->coplanarset)
-      numcoplanars += qh_setsize(qh, facet->coplanarset);
-    if (facet->good) {
-      if (facet->simplicial) {
-        if (facet->keepcentrum && facet->tricoplanar)
-          numtricoplanars++;
-      }else if (qh_setsize(qh, facet->vertices) != qh->hull_dim)
-        nonsimplicial++;
-    }
-  }
-  if (id >=0 && qh->STOPcone-1 != id && -qh->STOPpoint-1 != id)
-    size--;
-  if (qh->STOPcone || qh->STOPpoint)
-      qh_fprintf(qh, fp, 9288, "\nAt a premature exit due to 'TVn', 'TCn', 'TRn', or precision error with 'QJn'.");
-  if (qh->UPPERdelaunay)
-    goodused= qh->GOODvertex + qh->GOODpoint + qh->SPLITthresholds;
-  else if (qh->DELAUNAY)
-    goodused= qh->GOODvertex + qh->GOODpoint + qh->GOODthreshold;
-  else
-    goodused= qh->num_good;
-  nummerged= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
-  if (qh->VORONOI) {
-    if (qh->UPPERdelaunay)
-      qh_fprintf(qh, fp, 9289, "\n\
-Furthest-site Voronoi vertices by the convex hull of %d points in %d-d:\n\n", size, qh->hull_dim);
-    else
-      qh_fprintf(qh, fp, 9290, "\n\
-Voronoi diagram by the convex hull of %d points in %d-d:\n\n", size, qh->hull_dim);
-    qh_fprintf(qh, fp, 9291, "  Number of Voronoi regions%s: %d\n",
-              qh->ATinfinity ? " and at-infinity" : "", numvertices);
-    if (numdel)
-      qh_fprintf(qh, fp, 9292, "  Total number of deleted points due to merging: %d\n", numdel);
-    if (numcoplanars - numdel > 0)
-      qh_fprintf(qh, fp, 9293, "  Number of nearly incident points: %d\n", numcoplanars - numdel);
-    else if (size - numvertices - numdel > 0)
-      qh_fprintf(qh, fp, 9294, "  Total number of nearly incident points: %d\n", size - numvertices - numdel);
-    qh_fprintf(qh, fp, 9295, "  Number of%s Voronoi vertices: %d\n",
-              goodused ? " 'good'" : "", qh->num_good);
-    if (nonsimplicial)
-      qh_fprintf(qh, fp, 9296, "  Number of%s non-simplicial Voronoi vertices: %d\n",
-              goodused ? " 'good'" : "", nonsimplicial);
-  }else if (qh->DELAUNAY) {
-    if (qh->UPPERdelaunay)
-      qh_fprintf(qh, fp, 9297, "\n\
-Furthest-site Delaunay triangulation by the convex hull of %d points in %d-d:\n\n", size, qh->hull_dim);
-    else
-      qh_fprintf(qh, fp, 9298, "\n\
-Delaunay triangulation by the convex hull of %d points in %d-d:\n\n", size, qh->hull_dim);
-    qh_fprintf(qh, fp, 9299, "  Number of input sites%s: %d\n",
-              qh->ATinfinity ? " and at-infinity" : "", numvertices);
-    if (numdel)
-      qh_fprintf(qh, fp, 9300, "  Total number of deleted points due to merging: %d\n", numdel);
-    if (numcoplanars - numdel > 0)
-      qh_fprintf(qh, fp, 9301, "  Number of nearly incident points: %d\n", numcoplanars - numdel);
-    else if (size - numvertices - numdel > 0)
-      qh_fprintf(qh, fp, 9302, "  Total number of nearly incident points: %d\n", size - numvertices - numdel);
-    qh_fprintf(qh, fp, 9303, "  Number of%s Delaunay regions: %d\n",
-              goodused ? " 'good'" : "", qh->num_good);
-    if (nonsimplicial)
-      qh_fprintf(qh, fp, 9304, "  Number of%s non-simplicial Delaunay regions: %d\n",
-              goodused ? " 'good'" : "", nonsimplicial);
-  }else if (qh->HALFspace) {
-    qh_fprintf(qh, fp, 9305, "\n\
-Halfspace intersection by the convex hull of %d points in %d-d:\n\n", size, qh->hull_dim);
-    qh_fprintf(qh, fp, 9306, "  Number of halfspaces: %d\n", size);
-    qh_fprintf(qh, fp, 9307, "  Number of non-redundant halfspaces: %d\n", numvertices);
-    if (numcoplanars) {
-      if (qh->KEEPinside && qh->KEEPcoplanar)
-        s= "similar and redundant";
-      else if (qh->KEEPinside)
-        s= "redundant";
-      else
-        s= "similar";
-      qh_fprintf(qh, fp, 9308, "  Number of %s halfspaces: %d\n", s, numcoplanars);
-    }
-    qh_fprintf(qh, fp, 9309, "  Number of intersection points: %d\n", qh->num_facets - qh->num_visible);
-    if (goodused)
-      qh_fprintf(qh, fp, 9310, "  Number of 'good' intersection points: %d\n", qh->num_good);
-    if (nonsimplicial)
-      qh_fprintf(qh, fp, 9311, "  Number of%s non-simplicial intersection points: %d\n",
-              goodused ? " 'good'" : "", nonsimplicial);
-  }else {
-    qh_fprintf(qh, fp, 9312, "\n\
-Convex hull of %d points in %d-d:\n\n", size, qh->hull_dim);
-    qh_fprintf(qh, fp, 9313, "  Number of vertices: %d\n", numvertices);
-    if (numcoplanars) {
-      if (qh->KEEPinside && qh->KEEPcoplanar)
-        s= "coplanar and interior";
-      else if (qh->KEEPinside)
-        s= "interior";
-      else
-        s= "coplanar";
-      qh_fprintf(qh, fp, 9314, "  Number of %s points: %d\n", s, numcoplanars);
-    }
-    qh_fprintf(qh, fp, 9315, "  Number of facets: %d\n", qh->num_facets - qh->num_visible);
-    if (goodused)
-      qh_fprintf(qh, fp, 9316, "  Number of 'good' facets: %d\n", qh->num_good);
-    if (nonsimplicial)
-      qh_fprintf(qh, fp, 9317, "  Number of%s non-simplicial facets: %d\n",
-              goodused ? " 'good'" : "", nonsimplicial);
-  }
-  if (numtricoplanars)
-      qh_fprintf(qh, fp, 9318, "  Number of triangulated facets: %d\n", numtricoplanars);
-  qh_fprintf(qh, fp, 9319, "\nStatistics for: %s | %s",
-                      qh->rbox_command, qh->qhull_command);
-  if (qh->ROTATErandom != INT_MIN)
-    qh_fprintf(qh, fp, 9320, " QR%d\n\n", qh->ROTATErandom);
-  else
-    qh_fprintf(qh, fp, 9321, "\n\n");
-  qh_fprintf(qh, fp, 9322, "  Number of points processed: %d\n", zzval_(Zprocessed));
-  qh_fprintf(qh, fp, 9323, "  Number of hyperplanes created: %d\n", zzval_(Zsetplane));
-  if (qh->DELAUNAY)
-    qh_fprintf(qh, fp, 9324, "  Number of facets in hull: %d\n", qh->num_facets - qh->num_visible);
-  qh_fprintf(qh, fp, 9325, "  Number of distance tests for qhull: %d\n", zzval_(Zpartition)+
-      zzval_(Zpartitionall)+zzval_(Znumvisibility)+zzval_(Zpartcoplanar));
-#if 0  /* NOTE: must print before printstatistics() */
-  {realT stddev, ave;
-  qh_fprintf(qh, fp, 9326, "  average new facet balance: %2.2g\n",
-          wval_(Wnewbalance)/zval_(Zprocessed));
-  stddev= qh_stddev(zval_(Zprocessed), wval_(Wnewbalance),
-                                 wval_(Wnewbalance2), &ave);
-  qh_fprintf(qh, fp, 9327, "  new facet standard deviation: %2.2g\n", stddev);
-  qh_fprintf(qh, fp, 9328, "  average partition balance: %2.2g\n",
-          wval_(Wpbalance)/zval_(Zpbalance));
-  stddev= qh_stddev(zval_(Zpbalance), wval_(Wpbalance),
-                                 wval_(Wpbalance2), &ave);
-  qh_fprintf(qh, fp, 9329, "  partition standard deviation: %2.2g\n", stddev);
-  }
-#endif
-  if (nummerged) {
-    qh_fprintf(qh, fp, 9330,"  Number of distance tests for merging: %d\n",zzval_(Zbestdist)+
-          zzval_(Zcentrumtests)+zzval_(Zdistconvex)+zzval_(Zdistcheck)+
-          zzval_(Zdistzero));
-    qh_fprintf(qh, fp, 9331,"  Number of distance tests for checking: %d\n",zzval_(Zcheckpart));
-    qh_fprintf(qh, fp, 9332,"  Number of merged facets: %d\n", nummerged);
-  }
-  if (!qh->RANDOMoutside && qh->QHULLfinished) {
-    cpu= (float)qh->hulltime;
-    cpu /= (float)qh_SECticks;
-    wval_(Wcpu)= cpu;
-    qh_fprintf(qh, fp, 9333, "  CPU seconds to compute hull (after input): %2.4g\n", cpu);
-  }
-  if (qh->RERUN) {
-    if (!qh->PREmerge && !qh->MERGEexact)
-      qh_fprintf(qh, fp, 9334, "  Percentage of runs with precision errors: %4.1f\n",
-           zzval_(Zretry)*100.0/qh->build_cnt);  /* careful of order */
-  }else if (qh->JOGGLEmax < REALmax/2) {
-    if (zzval_(Zretry))
-      qh_fprintf(qh, fp, 9335, "  After %d retries, input joggled by: %2.2g\n",
-         zzval_(Zretry), qh->JOGGLEmax);
-    else
-      qh_fprintf(qh, fp, 9336, "  Input joggled by: %2.2g\n", qh->JOGGLEmax);
-  }
-  if (qh->totarea != 0.0)
-    qh_fprintf(qh, fp, 9337, "  %s facet area:   %2.8g\n",
-            zzval_(Ztotmerge) ? "Approximate" : "Total", qh->totarea);
-  if (qh->totvol != 0.0)
-    qh_fprintf(qh, fp, 9338, "  %s volume:       %2.8g\n",
-            zzval_(Ztotmerge) ? "Approximate" : "Total", qh->totvol);
-  if (qh->MERGING) {
-    qh_outerinner(qh, NULL, &outerplane, &innerplane);
-    if (outerplane > 2 * qh->DISTround) {
-      qh_fprintf(qh, fp, 9339, "  Maximum distance of %spoint above facet: %2.2g",
-            (qh->QHULLfinished ? "" : "merged "), outerplane);
-      ratio= outerplane/(qh->ONEmerge + qh->DISTround);
-      /* don't report ratio if MINoutside is large */
-      if (ratio > 0.05 && 2* qh->ONEmerge > qh->MINoutside && qh->JOGGLEmax > REALmax/2)
-        qh_fprintf(qh, fp, 9340, " (%.1fx)\n", ratio);
-      else
-        qh_fprintf(qh, fp, 9341, "\n");
-    }
-    if (innerplane < -2 * qh->DISTround) {
-      qh_fprintf(qh, fp, 9342, "  Maximum distance of %svertex below facet: %2.2g",
-            (qh->QHULLfinished ? "" : "merged "), innerplane);
-      ratio= -innerplane/(qh->ONEmerge+qh->DISTround);
-      if (ratio > 0.05 && qh->JOGGLEmax > REALmax/2)
-        qh_fprintf(qh, fp, 9343, " (%.1fx)\n", ratio);
-      else
-        qh_fprintf(qh, fp, 9344, "\n");
-    }
-  }
-  qh_fprintf(qh, fp, 9345, "\n");
-} /* printsummary */
-
-
diff --git a/C/mem_r.c b/C/mem_r.c
deleted file mode 100644
--- a/C/mem_r.c
+++ /dev/null
@@ -1,562 +0,0 @@
-/*
  ---------------------------------
-
-  mem_r.c
-    memory management routines for qhull
-
-  See libqhull/mem_r.c for a standalone program.
-
-  To initialize memory:
-
-    qh_meminit(qh, stderr);
-    qh_meminitbuffers(qh, qh->IStracing, qh_MEMalign, 7, qh_MEMbufsize,qh_MEMinitbuf);
-    qh_memsize(qh, (int)sizeof(facetT));
-    qh_memsize(qh, (int)sizeof(facetT));
-    ...
-    qh_memsetup(qh);
-
-  To free up all memory buffers:
-    qh_memfreeshort(qh, &curlong, &totlong);
-
-  if qh_NOmem,
-    malloc/free is used instead of mem.c
-
-  notes:
-    uses Quickfit algorithm (freelists for commonly allocated sizes)
-    assumes small sizes for freelists (it discards the tail of memory buffers)
-
-  see:
-    qh-mem_r.htm and mem_r.h
-    global_r.c (qh_initbuffers) for an example of using mem_r.c
-
-  Copyright (c) 1993-2015 The Geometry Center.
-  $Id: //main/2015/qhull/src/libqhull_r/mem_r.c#5 $$Change: 2065 $
-  $DateTime: 2016/01/18 13:51:04 $$Author: bbarber $
-*/
-
-#include "libqhull_r.h"  /* includes user_r.h and mem_r.h */
-
-#include 
-#include 
-#include 
-
-#ifndef qh_NOmem
-
-/*============= internal functions ==============*/
-
-static int qh_intcompare(const void *i, const void *j);
-
-/*========== functions in alphabetical order ======== */
-
-/*---------------------------------
-
-  qh_intcompare( i, j )
-    used by qsort and bsearch to compare two integers
-*/
-static int qh_intcompare(const void *i, const void *j) {
-  return(*((const int *)i) - *((const int *)j));
-} /* intcompare */
-
-
-/*----------------------------------
-
-  qh_memalloc( qh, insize )
-    returns object of insize bytes
-    qhmem is the global memory structure
-
-  returns:
-    pointer to allocated memory
-    errors if insufficient memory
-
-  notes:
-    use explicit type conversion to avoid type warnings on some compilers
-    actual object may be larger than insize
-    use qh_memalloc_() for inline code for quick allocations
-    logs allocations if 'T5'
-    caller is responsible for freeing the memory.
-    short memory is freed on shutdown by qh_memfreeshort unless qh_NOmem
-
-  design:
-    if size < qh->qhmem.LASTsize
-      if qh->qhmem.freelists[size] non-empty
-        return first object on freelist
-      else
-        round up request to size of qh->qhmem.freelists[size]
-        allocate new allocation buffer if necessary
-        allocate object from allocation buffer
-    else
-      allocate object with qh_malloc() in user.c
-*/
-void *qh_memalloc(qhT *qh, int insize) {
-  void **freelistp, *newbuffer;
-  int idx, size, n;
-  int outsize, bufsize;
-  void *object;
-
-  if (insize<0) {
-      qh_fprintf(qh, qh->qhmem.ferr, 6235, "qhull error (qh_memalloc): negative request size (%d).  Did int overflow due to high-D?\n", insize); /* WARN64 */
-      qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
-  }
-  if (insize>=0 && insize <= qh->qhmem.LASTsize) {
-    idx= qh->qhmem.indextable[insize];
-    outsize= qh->qhmem.sizetable[idx];
-    qh->qhmem.totshort += outsize;
-    freelistp= qh->qhmem.freelists+idx;
-    if ((object= *freelistp)) {
-      qh->qhmem.cntquick++;
-      qh->qhmem.totfree -= outsize;
-      *freelistp= *((void **)*freelistp);  /* replace freelist with next object */
-#ifdef qh_TRACEshort
-      n= qh->qhmem.cntshort+qh->qhmem.cntquick+qh->qhmem.freeshort;
-      if (qh->qhmem.IStracing >= 5)
-          qh_fprintf(qh, qh->qhmem.ferr, 8141, "qh_mem %p n %8d alloc quick: %d bytes (tot %d cnt %d)\n", object, n, outsize, qh->qhmem.totshort, qh->qhmem.cntshort+qh->qhmem.cntquick-qh->qhmem.freeshort);
-#endif
-      return(object);
-    }else {
-      qh->qhmem.cntshort++;
-      if (outsize > qh->qhmem.freesize) {
-        qh->qhmem.totdropped += qh->qhmem.freesize;
-        if (!qh->qhmem.curbuffer)
-          bufsize= qh->qhmem.BUFinit;
-        else
-          bufsize= qh->qhmem.BUFsize;
-        if (!(newbuffer= qh_malloc((size_t)bufsize))) {
-          qh_fprintf(qh, qh->qhmem.ferr, 6080, "qhull error (qh_memalloc): insufficient memory to allocate short memory buffer (%d bytes)\n", bufsize);
-          qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
-        }
-        *((void **)newbuffer)= qh->qhmem.curbuffer;  /* prepend newbuffer to curbuffer
-                                                    list.  newbuffer!=0 by QH6080 */
-        qh->qhmem.curbuffer= newbuffer;
-        size= (sizeof(void **) + qh->qhmem.ALIGNmask) & ~qh->qhmem.ALIGNmask;
-        qh->qhmem.freemem= (void *)((char *)newbuffer+size);
-        qh->qhmem.freesize= bufsize - size;
-        qh->qhmem.totbuffer += bufsize - size; /* easier to check */
-        /* Periodically test totbuffer.  It matches at beginning and exit of every call */
-        n = qh->qhmem.totshort + qh->qhmem.totfree + qh->qhmem.totdropped + qh->qhmem.freesize - outsize;
-        if (qh->qhmem.totbuffer != n) {
-            qh_fprintf(qh, qh->qhmem.ferr, 6212, "qh_memalloc internal error: short totbuffer %d != totshort+totfree... %d\n", qh->qhmem.totbuffer, n);
-            qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
-        }
-      }
-      object= qh->qhmem.freemem;
-      qh->qhmem.freemem= (void *)((char *)qh->qhmem.freemem + outsize);
-      qh->qhmem.freesize -= outsize;
-      qh->qhmem.totunused += outsize - insize;
-#ifdef qh_TRACEshort
-      n= qh->qhmem.cntshort+qh->qhmem.cntquick+qh->qhmem.freeshort;
-      if (qh->qhmem.IStracing >= 5)
-          qh_fprintf(qh, qh->qhmem.ferr, 8140, "qh_mem %p n %8d alloc short: %d bytes (tot %d cnt %d)\n", object, n, outsize, qh->qhmem.totshort, qh->qhmem.cntshort+qh->qhmem.cntquick-qh->qhmem.freeshort);
-#endif
-      return object;
-    }
-  }else {                     /* long allocation */
-    if (!qh->qhmem.indextable) {
-      qh_fprintf(qh, qh->qhmem.ferr, 6081, "qhull internal error (qh_memalloc): qhmem has not been initialized.\n");
-      qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
-    }
-    outsize= insize;
-    qh->qhmem.cntlong++;
-    qh->qhmem.totlong += outsize;
-    if (qh->qhmem.maxlong < qh->qhmem.totlong)
-      qh->qhmem.maxlong= qh->qhmem.totlong;
-    if (!(object= qh_malloc((size_t)outsize))) {
-      qh_fprintf(qh, qh->qhmem.ferr, 6082, "qhull error (qh_memalloc): insufficient memory to allocate %d bytes\n", outsize);
-      qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
-    }
-    if (qh->qhmem.IStracing >= 5)
-      qh_fprintf(qh, qh->qhmem.ferr, 8057, "qh_mem %p n %8d alloc long: %d bytes (tot %d cnt %d)\n", object, qh->qhmem.cntlong+qh->qhmem.freelong, outsize, qh->qhmem.totlong, qh->qhmem.cntlong-qh->qhmem.freelong);
-  }
-  return(object);
-} /* memalloc */
-
-
-/*----------------------------------
-
-  qh_memcheck(qh)
-*/
-void qh_memcheck(qhT *qh) {
-  int i, count, totfree= 0;
-  void *object;
-
-  if (!qh) {
-    qh_fprintf_stderr(6243, "qh_memcheck(qh) error: qh is 0.  It does not point to a qhT");
-    qh_exit(qhmem_ERRqhull);  /* can not use qh_errexit() */
-  }
-  if (qh->qhmem.ferr == 0 || qh->qhmem.IStracing < 0 || qh->qhmem.IStracing > 10 || (((qh->qhmem.ALIGNmask+1) & qh->qhmem.ALIGNmask) != 0)) {
-    qh_fprintf_stderr(6244, "qh_memcheck error: either qh->qhmem is overwritten or qh->qhmem is not initialized.  Call qh_mem_new() or qh_new_qhull() before calling qh_mem routines.  ferr 0x%x IsTracing %d ALIGNmask 0x%x", qh->qhmem.ferr, qh->qhmem.IStracing, qh->qhmem.ALIGNmask);
-    qh_exit(qhmem_ERRqhull);  /* can not use qh_errexit() */
-    return;
-  }
-  if (qh->qhmem.IStracing != 0)
-    qh_fprintf(qh, qh->qhmem.ferr, 8143, "qh_memcheck: check size of freelists on qh->qhmem\nqh_memcheck: A segmentation fault indicates an overwrite of qh->qhmem\n");
-  for (i=0; i < qh->qhmem.TABLEsize; i++) {
-    count=0;
-    for (object= qh->qhmem.freelists[i]; object; object= *((void **)object))
-      count++;
-    totfree += qh->qhmem.sizetable[i] * count;
-  }
-  if (totfree != qh->qhmem.totfree) {
-    qh_fprintf(qh, qh->qhmem.ferr, 6211, "Qhull internal error (qh_memcheck): totfree %d not equal to freelist total %d\n", qh->qhmem.totfree, totfree);
-    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
-  }
-  if (qh->qhmem.IStracing != 0)
-    qh_fprintf(qh, qh->qhmem.ferr, 8144, "qh_memcheck: total size of freelists totfree is the same as qh->qhmem.totfree\n", totfree);
-} /* memcheck */
-
-/*----------------------------------
-
-  qh_memfree(qh, object, insize )
-    free up an object of size bytes
-    size is insize from qh_memalloc
-
-  notes:
-    object may be NULL
-    type checking warns if using (void **)object
-    use qh_memfree_() for quick free's of small objects
-
-  design:
-    if size <= qh->qhmem.LASTsize
-      append object to corresponding freelist
-    else
-      call qh_free(object)
-*/
-void qh_memfree(qhT *qh, void *object, int insize) {
-  void **freelistp;
-  int idx, outsize;
-
-  if (!object)
-    return;
-  if (insize <= qh->qhmem.LASTsize) {
-    qh->qhmem.freeshort++;
-    idx= qh->qhmem.indextable[insize];
-    outsize= qh->qhmem.sizetable[idx];
-    qh->qhmem.totfree += outsize;
-    qh->qhmem.totshort -= outsize;
-    freelistp= qh->qhmem.freelists + idx;
-    *((void **)object)= *freelistp;
-    *freelistp= object;
-#ifdef qh_TRACEshort
-    idx= qh->qhmem.cntshort+qh->qhmem.cntquick+qh->qhmem.freeshort;
-    if (qh->qhmem.IStracing >= 5)
-        qh_fprintf(qh, qh->qhmem.ferr, 8142, "qh_mem %p n %8d free short: %d bytes (tot %d cnt %d)\n", object, idx, outsize, qh->qhmem.totshort, qh->qhmem.cntshort+qh->qhmem.cntquick-qh->qhmem.freeshort);
-#endif
-  }else {
-    qh->qhmem.freelong++;
-    qh->qhmem.totlong -= insize;
-    if (qh->qhmem.IStracing >= 5)
-      qh_fprintf(qh, qh->qhmem.ferr, 8058, "qh_mem %p n %8d free long: %d bytes (tot %d cnt %d)\n", object, qh->qhmem.cntlong+qh->qhmem.freelong, insize, qh->qhmem.totlong, qh->qhmem.cntlong-qh->qhmem.freelong);
-    qh_free(object);
-  }
-} /* memfree */
-
-
-/*---------------------------------
-
-  qh_memfreeshort(qh, curlong, totlong )
-    frees up all short and qhmem memory allocations
-
-  returns:
-    number and size of current long allocations
-
-  notes:
-    if qh_NOmem (qh_malloc() for all allocations),
-       short objects (e.g., facetT) are not recovered.
-       use qh_freeqhull(qh, qh_ALL) instead.
-
-  see:
-    qh_freeqhull(qh, allMem)
-    qh_memtotal(qh, curlong, totlong, curshort, totshort, maxlong, totbuffer);
-*/
-void qh_memfreeshort(qhT *qh, int *curlong, int *totlong) {
-  void *buffer, *nextbuffer;
-  FILE *ferr;
-
-  *curlong= qh->qhmem.cntlong - qh->qhmem.freelong;
-  *totlong= qh->qhmem.totlong;
-  for (buffer= qh->qhmem.curbuffer; buffer; buffer= nextbuffer) {
-    nextbuffer= *((void **) buffer);
-    qh_free(buffer);
-  }
-  qh->qhmem.curbuffer= NULL;
-  if (qh->qhmem.LASTsize) {
-    qh_free(qh->qhmem.indextable);
-    qh_free(qh->qhmem.freelists);
-    qh_free(qh->qhmem.sizetable);
-  }
-  ferr= qh->qhmem.ferr;
-  memset((char *)&qh->qhmem, 0, sizeof(qh->qhmem));  /* every field is 0, FALSE, NULL */
-  qh->qhmem.ferr= ferr;
-} /* memfreeshort */
-
-
-/*----------------------------------
-
-  qh_meminit(qh, ferr )
-    initialize qhmem and test sizeof( void*)
-    Does not throw errors.  qh_exit on failure
-*/
-void qh_meminit(qhT *qh, FILE *ferr) {
-
-  memset((char *)&qh->qhmem, 0, sizeof(qh->qhmem));  /* every field is 0, FALSE, NULL */
-  if (ferr)
-      qh->qhmem.ferr= ferr;
-  else
-      qh->qhmem.ferr= stderr;
-  if (sizeof(void*) < sizeof(int)) {
-    qh_fprintf(qh, qh->qhmem.ferr, 6083, "qhull internal error (qh_meminit): sizeof(void*) %d < sizeof(int) %d.  qset.c will not work\n", (int)sizeof(void*), (int)sizeof(int));
-    qh_exit(qhmem_ERRqhull);  /* can not use qh_errexit() */
-  }
-  if (sizeof(void*) > sizeof(ptr_intT)) {
-      qh_fprintf(qh, qh->qhmem.ferr, 6084, "qhull internal error (qh_meminit): sizeof(void*) %d > sizeof(ptr_intT) %d. Change ptr_intT in mem.h to 'long long'\n", (int)sizeof(void*), (int)sizeof(ptr_intT));
-      qh_exit(qhmem_ERRqhull);  /* can not use qh_errexit() */
-  }
-  qh_memcheck(qh);
-} /* meminit */
-
-/*---------------------------------
-
-  qh_meminitbuffers(qh, tracelevel, alignment, numsizes, bufsize, bufinit )
-    initialize qhmem
-    if tracelevel >= 5, trace memory allocations
-    alignment= desired address alignment for memory allocations
-    numsizes= number of freelists
-    bufsize=  size of additional memory buffers for short allocations
-    bufinit=  size of initial memory buffer for short allocations
-*/
-void qh_meminitbuffers(qhT *qh, int tracelevel, int alignment, int numsizes, int bufsize, int bufinit) {
-
-  qh->qhmem.IStracing= tracelevel;
-  qh->qhmem.NUMsizes= numsizes;
-  qh->qhmem.BUFsize= bufsize;
-  qh->qhmem.BUFinit= bufinit;
-  qh->qhmem.ALIGNmask= alignment-1;
-  if (qh->qhmem.ALIGNmask & ~qh->qhmem.ALIGNmask) {
-    qh_fprintf(qh, qh->qhmem.ferr, 6085, "qhull internal error (qh_meminit): memory alignment %d is not a power of 2\n", alignment);
-    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
-  }
-  qh->qhmem.sizetable= (int *) calloc((size_t)numsizes, sizeof(int));
-  qh->qhmem.freelists= (void **) calloc((size_t)numsizes, sizeof(void *));
-  if (!qh->qhmem.sizetable || !qh->qhmem.freelists) {
-    qh_fprintf(qh, qh->qhmem.ferr, 6086, "qhull error (qh_meminit): insufficient memory\n");
-    qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
-  }
-  if (qh->qhmem.IStracing >= 1)
-    qh_fprintf(qh, qh->qhmem.ferr, 8059, "qh_meminitbuffers: memory initialized with alignment %d\n", alignment);
-} /* meminitbuffers */
-
-/*---------------------------------
-
-  qh_memsetup(qh)
-    set up memory after running memsize()
-*/
-void qh_memsetup(qhT *qh) {
-  int k,i;
-
-  qsort(qh->qhmem.sizetable, (size_t)qh->qhmem.TABLEsize, sizeof(int), qh_intcompare);
-  qh->qhmem.LASTsize= qh->qhmem.sizetable[qh->qhmem.TABLEsize-1];
-  if(qh->qhmem.LASTsize >= qh->qhmem.BUFsize || qh->qhmem.LASTsize >= qh->qhmem.BUFinit) {
-    qh_fprintf(qh, qh->qhmem.ferr, 6087, "qhull error (qh_memsetup): largest mem size %d is >= buffer size %d or initial buffer size %d\n",
-            qh->qhmem.LASTsize, qh->qhmem.BUFsize, qh->qhmem.BUFinit);
-    qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
-  }
-  if (!(qh->qhmem.indextable= (int *)qh_malloc((qh->qhmem.LASTsize+1) * sizeof(int)))) {
-    qh_fprintf(qh, qh->qhmem.ferr, 6088, "qhull error (qh_memsetup): insufficient memory\n");
-    qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
-  }
-  for (k=qh->qhmem.LASTsize+1; k--; )
-    qh->qhmem.indextable[k]= k;
-  i= 0;
-  for (k=0; k <= qh->qhmem.LASTsize; k++) {
-    if (qh->qhmem.indextable[k] <= qh->qhmem.sizetable[i])
-      qh->qhmem.indextable[k]= i;
-    else
-      qh->qhmem.indextable[k]= ++i;
-  }
-} /* memsetup */
-
-/*---------------------------------
-
-  qh_memsize(qh, size )
-    define a free list for this size
-*/
-void qh_memsize(qhT *qh, int size) {
-  int k;
-
-  if(qh->qhmem.LASTsize) {
-    qh_fprintf(qh, qh->qhmem.ferr, 6089, "qhull error (qh_memsize): called after qhmem_setup\n");
-    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
-  }
-  size= (size + qh->qhmem.ALIGNmask) & ~qh->qhmem.ALIGNmask;
-  for (k=qh->qhmem.TABLEsize; k--; ) {
-    if (qh->qhmem.sizetable[k] == size)
-      return;
-  }
-  if (qh->qhmem.TABLEsize < qh->qhmem.NUMsizes)
-    qh->qhmem.sizetable[qh->qhmem.TABLEsize++]= size;
-  else
-    qh_fprintf(qh, qh->qhmem.ferr, 7060, "qhull warning (memsize): free list table has room for only %d sizes\n", qh->qhmem.NUMsizes);
-} /* memsize */
-
-
-/*---------------------------------
-
-  qh_memstatistics(qh, fp )
-    print out memory statistics
-
-    Verifies that qh->qhmem.totfree == sum of freelists
-*/
-void qh_memstatistics(qhT *qh, FILE *fp) {
-  int i;
-  int count;
-  void *object;
-
-  qh_memcheck(qh);
-  qh_fprintf(qh, fp, 9278, "\nmemory statistics:\n\
-%7d quick allocations\n\
-%7d short allocations\n\
-%7d long allocations\n\
-%7d short frees\n\
-%7d long frees\n\
-%7d bytes of short memory in use\n\
-%7d bytes of short memory in freelists\n\
-%7d bytes of dropped short memory\n\
-%7d bytes of unused short memory (estimated)\n\
-%7d bytes of long memory allocated (max, except for input)\n\
-%7d bytes of long memory in use (in %d pieces)\n\
-%7d bytes of short memory buffers (minus links)\n\
-%7d bytes per short memory buffer (initially %d bytes)\n",
-           qh->qhmem.cntquick, qh->qhmem.cntshort, qh->qhmem.cntlong,
-           qh->qhmem.freeshort, qh->qhmem.freelong,
-           qh->qhmem.totshort, qh->qhmem.totfree,
-           qh->qhmem.totdropped + qh->qhmem.freesize, qh->qhmem.totunused,
-           qh->qhmem.maxlong, qh->qhmem.totlong, qh->qhmem.cntlong - qh->qhmem.freelong,
-           qh->qhmem.totbuffer, qh->qhmem.BUFsize, qh->qhmem.BUFinit);
-  if (qh->qhmem.cntlarger) {
-    qh_fprintf(qh, fp, 9279, "%7d calls to qh_setlarger\n%7.2g     average copy size\n",
-           qh->qhmem.cntlarger, ((float)qh->qhmem.totlarger)/(float)qh->qhmem.cntlarger);
-    qh_fprintf(qh, fp, 9280, "  freelists(bytes->count):");
-  }
-  for (i=0; i < qh->qhmem.TABLEsize; i++) {
-    count=0;
-    for (object= qh->qhmem.freelists[i]; object; object= *((void **)object))
-      count++;
-    qh_fprintf(qh, fp, 9281, " %d->%d", qh->qhmem.sizetable[i], count);
-  }
-  qh_fprintf(qh, fp, 9282, "\n\n");
-} /* memstatistics */
-
-
-/*---------------------------------
-
-  qh_NOmem
-    turn off quick-fit memory allocation
-
-  notes:
-    uses qh_malloc() and qh_free() instead
-*/
-#else /* qh_NOmem */
-
-void *qh_memalloc(qhT *qh, int insize) {
-  void *object;
-
-  if (!(object= qh_malloc((size_t)insize))) {
-    qh_fprintf(qh, qh->qhmem.ferr, 6090, "qhull error (qh_memalloc): insufficient memory\n");
-    qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
-  }
-  qh->qhmem.cntlong++;
-  qh->qhmem.totlong += insize;
-  if (qh->qhmem.maxlong < qh->qhmem.totlong)
-      qh->qhmem.maxlong= qh->qhmem.totlong;
-  if (qh->qhmem.IStracing >= 5)
-    qh_fprintf(qh, qh->qhmem.ferr, 8060, "qh_mem %p n %8d alloc long: %d bytes (tot %d cnt %d)\n", object, qh->qhmem.cntlong+qh->qhmem.freelong, insize, qh->qhmem.totlong, qh->qhmem.cntlong-qh->qhmem.freelong);
-  return object;
-}
-
-void qh_memfree(qhT *qh, void *object, int insize) {
-
-  if (!object)
-    return;
-  qh_free(object);
-  qh->qhmem.freelong++;
-  qh->qhmem.totlong -= insize;
-  if (qh->qhmem.IStracing >= 5)
-    qh_fprintf(qh, qh->qhmem.ferr, 8061, "qh_mem %p n %8d free long: %d bytes (tot %d cnt %d)\n", object, qh->qhmem.cntlong+qh->qhmem.freelong, insize, qh->qhmem.totlong, qh->qhmem.cntlong-qh->qhmem.freelong);
-}
-
-void qh_memfreeshort(qhT *qh, int *curlong, int *totlong) {
-  *totlong= qh->qhmem.totlong;
-  *curlong= qh->qhmem.cntlong - qh->qhmem.freelong;
-  memset((char *)&qh->qhmem, 0, sizeof(qh->qhmem));  /* every field is 0, FALSE, NULL */
-}
-
-void qh_meminit(qhT *qh, FILE *ferr) {
-
-  memset((char *)&qh->qhmem, 0, sizeof(qh->qhmem));  /* every field is 0, FALSE, NULL */
-  if (ferr)
-      qh->qhmem.ferr= ferr;
-  else
-      qh->qhmem.ferr= stderr;
-  if (sizeof(void*) < sizeof(int)) {
-    qh_fprintf(qh, qh->qhmem.ferr, 6091, "qhull internal error (qh_meminit): sizeof(void*) %d < sizeof(int) %d.  qset.c will not work\n", (int)sizeof(void*), (int)sizeof(int));
-    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
-  }
-}
-
-void qh_meminitbuffers(qhT *qh, int tracelevel, int alignment, int numsizes, int bufsize, int bufinit) {
-
-  qh->qhmem.IStracing= tracelevel;
-}
-
-void qh_memsetup(qhT *qh) {
-
-}
-
-void qh_memsize(qhT *qh, int size) {
-
-}
-
-void qh_memstatistics(qhT *qh, FILE *fp) {
-
-  qh_fprintf(qh, fp, 9409, "\nmemory statistics:\n\
-%7d long allocations\n\
-%7d long frees\n\
-%7d bytes of long memory allocated (max, except for input)\n\
-%7d bytes of long memory in use (in %d pieces)\n",
-           qh->qhmem.cntlong,
-           qh->qhmem.freelong,
-           qh->qhmem.maxlong, qh->qhmem.totlong, qh->qhmem.cntlong - qh->qhmem.freelong);
-}
-
-#endif /* qh_NOmem */
-
-/*---------------------------------
-
-  qh_memtotal(qh, totlong, curlong, totshort, curshort, maxlong, totbuffer )
-    Return the total, allocated long and short memory
-
-  returns:
-    Returns the total current bytes of long and short allocations
-    Returns the current count of long and short allocations
-    Returns the maximum long memory and total short buffer (minus one link per buffer)
-    Does not error (for deprecated UsingLibQhull.cpp (libqhullpcpp))
-*/
-void qh_memtotal(qhT *qh, int *totlong, int *curlong, int *totshort, int *curshort, int *maxlong, int *totbuffer) {
-    *totlong= qh->qhmem.totlong;
-    *curlong= qh->qhmem.cntlong - qh->qhmem.freelong;
-    *totshort= qh->qhmem.totshort;
-    *curshort= qh->qhmem.cntshort + qh->qhmem.cntquick - qh->qhmem.freeshort;
-    *maxlong= qh->qhmem.maxlong;
-    *totbuffer= qh->qhmem.totbuffer;
-} /* memtotlong */
diff --git a/C/merge_r.c b/C/merge_r.c
deleted file mode 100644
--- a/C/merge_r.c
+++ /dev/null
@@ -1,3627 +0,0 @@
-/*
  ---------------------------------
-
-   merge_r.c
-   merges non-convex facets
-
-   see qh-merge_r.htm and merge_r.h
-
-   other modules call qh_premerge() and qh_postmerge()
-
-   the user may call qh_postmerge() to perform additional merges.
-
-   To remove deleted facets and vertices (qhull() in libqhull_r.c):
-     qh_partitionvisible(qh, !qh_ALL, &numoutside);  // visible_list, newfacet_list
-     qh_deletevisible();         // qh.visible_list
-     qh_resetlists(qh, False, qh_RESETvisible);       // qh.visible_list newvertex_list newfacet_list
-
-   assumes qh.CENTERtype= centrum
-
-   merges occur in qh_mergefacet and in qh_mergecycle
-   vertex->neighbors not set until the first merge occurs
-
-   Copyright (c) 1993-2015 C.B. Barber.
-   $Id: //main/2015/qhull/src/libqhull_r/merge_r.c#5 $$Change: 2064 $
-   $DateTime: 2016/01/18 12:36:08 $$Author: bbarber $
-*/
-
-#include "qhull_ra.h"
-
-#ifndef qh_NOmerge
-
-/*===== functions(alphabetical after premerge and postmerge) ======*/
-
-/*---------------------------------
-
-  qh_premerge(qh, apex, maxcentrum )
-    pre-merge nonconvex facets in qh.newfacet_list for apex
-    maxcentrum defines coplanar and concave (qh_test_appendmerge)
-
-  returns:
-    deleted facets added to qh.visible_list with facet->visible set
-
-  notes:
-    uses globals, qh.MERGEexact, qh.PREmerge
-
-  design:
-    mark duplicate ridges in qh.newfacet_list
-    merge facet cycles in qh.newfacet_list
-    merge duplicate ridges and concave facets in qh.newfacet_list
-    check merged facet cycles for degenerate and redundant facets
-    merge degenerate and redundant facets
-    collect coplanar and concave facets
-    merge concave, coplanar, degenerate, and redundant facets
-*/
-void qh_premerge(qhT *qh, vertexT *apex, realT maxcentrum, realT maxangle) {
-  boolT othermerge= False;
-  facetT *newfacet;
-
-  if (qh->ZEROcentrum && qh_checkzero(qh, !qh_ALL))
-    return;
-  trace2((qh, qh->ferr, 2008, "qh_premerge: premerge centrum %2.2g angle %2.2g for apex v%d facetlist f%d\n",
-            maxcentrum, maxangle, apex->id, getid_(qh->newfacet_list)));
-  if (qh->IStracing >= 4 && qh->num_facets < 50)
-    qh_printlists(qh);
-  qh->centrum_radius= maxcentrum;
-  qh->cos_max= maxangle;
-  qh->degen_mergeset= qh_settemp(qh, qh->TEMPsize);
-  qh->facet_mergeset= qh_settemp(qh, qh->TEMPsize);
-  if (qh->hull_dim >=3) {
-    qh_mark_dupridges(qh, qh->newfacet_list); /* facet_mergeset */
-    qh_mergecycle_all(qh, qh->newfacet_list, &othermerge);
-    qh_forcedmerges(qh, &othermerge /* qh->facet_mergeset */);
-    FORALLnew_facets {  /* test samecycle merges */
-      if (!newfacet->simplicial && !newfacet->mergeridge)
-        qh_degen_redundant_neighbors(qh, newfacet, NULL);
-    }
-    if (qh_merge_degenredundant(qh))
-      othermerge= True;
-  }else /* qh->hull_dim == 2 */
-    qh_mergecycle_all(qh, qh->newfacet_list, &othermerge);
-  qh_flippedmerges(qh, qh->newfacet_list, &othermerge);
-  if (!qh->MERGEexact || zzval_(Ztotmerge)) {
-    zinc_(Zpremergetot);
-    qh->POSTmerging= False;
-    qh_getmergeset_initial(qh, qh->newfacet_list);
-    qh_all_merges(qh, othermerge, False);
-  }
-  qh_settempfree(qh, &qh->facet_mergeset);
-  qh_settempfree(qh, &qh->degen_mergeset);
-} /* premerge */
-
-/*---------------------------------
-
-  qh_postmerge(qh, reason, maxcentrum, maxangle, vneighbors )
-    post-merge nonconvex facets as defined by maxcentrum and maxangle
-    'reason' is for reporting progress
-    if vneighbors,
-      calls qh_test_vneighbors at end of qh_all_merge
-    if firstmerge,
-      calls qh_reducevertices before qh_getmergeset
-
-  returns:
-    if first call (qh.visible_list != qh.facet_list),
-      builds qh.facet_newlist, qh.newvertex_list
-    deleted facets added to qh.visible_list with facet->visible
-    qh.visible_list == qh.facet_list
-
-  notes:
-
-
-  design:
-    if first call
-      set qh.visible_list and qh.newfacet_list to qh.facet_list
-      add all facets to qh.newfacet_list
-      mark non-simplicial facets, facet->newmerge
-      set qh.newvertext_list to qh.vertex_list
-      add all vertices to qh.newvertex_list
-      if a pre-merge occured
-        set vertex->delridge {will retest the ridge}
-        if qh.MERGEexact
-          call qh_reducevertices()
-      if no pre-merging
-        merge flipped facets
-    determine non-convex facets
-    merge all non-convex facets
-*/
-void qh_postmerge(qhT *qh, const char *reason, realT maxcentrum, realT maxangle,
-                      boolT vneighbors) {
-  facetT *newfacet;
-  boolT othermerges= False;
-  vertexT *vertex;
-
-  if (qh->REPORTfreq || qh->IStracing) {
-    qh_buildtracing(qh, NULL, NULL);
-    qh_printsummary(qh, qh->ferr);
-    if (qh->PRINTstatistics)
-      qh_printallstatistics(qh, qh->ferr, "reason");
-    qh_fprintf(qh, qh->ferr, 8062, "\n%s with 'C%.2g' and 'A%.2g'\n",
-        reason, maxcentrum, maxangle);
-  }
-  trace2((qh, qh->ferr, 2009, "qh_postmerge: postmerge.  test vneighbors? %d\n",
-            vneighbors));
-  qh->centrum_radius= maxcentrum;
-  qh->cos_max= maxangle;
-  qh->POSTmerging= True;
-  qh->degen_mergeset= qh_settemp(qh, qh->TEMPsize);
-  qh->facet_mergeset= qh_settemp(qh, qh->TEMPsize);
-  if (qh->visible_list != qh->facet_list) {  /* first call */
-    qh->NEWfacets= True;
-    qh->visible_list= qh->newfacet_list= qh->facet_list;
-    FORALLnew_facets {
-      newfacet->newfacet= True;
-       if (!newfacet->simplicial)
-        newfacet->newmerge= True;
-     zinc_(Zpostfacets);
-    }
-    qh->newvertex_list= qh->vertex_list;
-    FORALLvertices
-      vertex->newlist= True;
-    if (qh->VERTEXneighbors) { /* a merge has occurred */
-      FORALLvertices
-        vertex->delridge= True; /* test for redundant, needed? */
-      if (qh->MERGEexact) {
-        if (qh->hull_dim <= qh_DIMreduceBuild)
-          qh_reducevertices(qh); /* was skipped during pre-merging */
-      }
-    }
-    if (!qh->PREmerge && !qh->MERGEexact)
-      qh_flippedmerges(qh, qh->newfacet_list, &othermerges);
-  }
-  qh_getmergeset_initial(qh, qh->newfacet_list);
-  qh_all_merges(qh, False, vneighbors);
-  qh_settempfree(qh, &qh->facet_mergeset);
-  qh_settempfree(qh, &qh->degen_mergeset);
-} /* post_merge */
-
-/*---------------------------------
-
-  qh_all_merges(qh, othermerge, vneighbors )
-    merge all non-convex facets
-
-    set othermerge if already merged facets (for qh_reducevertices)
-    if vneighbors
-      tests vertex neighbors for convexity at end
-    qh.facet_mergeset lists the non-convex ridges in qh_newfacet_list
-    qh.degen_mergeset is defined
-    if qh.MERGEexact && !qh.POSTmerging,
-      does not merge coplanar facets
-
-  returns:
-    deleted facets added to qh.visible_list with facet->visible
-    deleted vertices added qh.delvertex_list with vertex->delvertex
-
-  notes:
-    unless !qh.MERGEindependent,
-      merges facets in independent sets
-    uses qh.newfacet_list as argument since merges call qh_removefacet()
-
-  design:
-    while merges occur
-      for each merge in qh.facet_mergeset
-        unless one of the facets was already merged in this pass
-          merge the facets
-        test merged facets for additional merges
-        add merges to qh.facet_mergeset
-      if vertices record neighboring facets
-        rename redundant vertices
-          update qh.facet_mergeset
-    if vneighbors ??
-      tests vertex neighbors for convexity at end
-*/
-void qh_all_merges(qhT *qh, boolT othermerge, boolT vneighbors) {
-  facetT *facet1, *facet2;
-  mergeT *merge;
-  boolT wasmerge= True, isreduce;
-  void **freelistp;  /* used if !qh_NOmem by qh_memfree_() */
-  vertexT *vertex;
-  mergeType mergetype;
-  int numcoplanar=0, numconcave=0, numdegenredun= 0, numnewmerges= 0;
-
-  trace2((qh, qh->ferr, 2010, "qh_all_merges: starting to merge facets beginning from f%d\n",
-            getid_(qh->newfacet_list)));
-  while (True) {
-    wasmerge= False;
-    while (qh_setsize(qh, qh->facet_mergeset)) {
-      while ((merge= (mergeT*)qh_setdellast(qh->facet_mergeset))) {
-        facet1= merge->facet1;
-        facet2= merge->facet2;
-        mergetype= merge->type;
-        qh_memfree_(qh, merge, (int)sizeof(mergeT), freelistp);
-        if (facet1->visible || facet2->visible) /*deleted facet*/
-          continue;
-        if ((facet1->newfacet && !facet1->tested)
-                || (facet2->newfacet && !facet2->tested)) {
-          if (qh->MERGEindependent && mergetype <= MRGanglecoplanar)
-            continue;      /* perform independent sets of merges */
-        }
-        qh_merge_nonconvex(qh, facet1, facet2, mergetype);
-        numdegenredun += qh_merge_degenredundant(qh);
-        numnewmerges++;
-        wasmerge= True;
-        if (mergetype == MRGconcave)
-          numconcave++;
-        else /* MRGcoplanar or MRGanglecoplanar */
-          numcoplanar++;
-      } /* while setdellast */
-      if (qh->POSTmerging && qh->hull_dim <= qh_DIMreduceBuild
-      && numnewmerges > qh_MAXnewmerges) {
-        numnewmerges= 0;
-        qh_reducevertices(qh);  /* otherwise large post merges too slow */
-      }
-      qh_getmergeset(qh, qh->newfacet_list); /* facet_mergeset */
-    } /* while mergeset */
-    if (qh->VERTEXneighbors) {
-      isreduce= False;
-      if (qh->hull_dim >=4 && qh->POSTmerging) {
-        FORALLvertices
-          vertex->delridge= True;
-        isreduce= True;
-      }
-      if ((wasmerge || othermerge) && (!qh->MERGEexact || qh->POSTmerging)
-          && qh->hull_dim <= qh_DIMreduceBuild) {
-        othermerge= False;
-        isreduce= True;
-      }
-      if (isreduce) {
-        if (qh_reducevertices(qh)) {
-          qh_getmergeset(qh, qh->newfacet_list); /* facet_mergeset */
-          continue;
-        }
-      }
-    }
-    if (vneighbors && qh_test_vneighbors(qh /* qh->newfacet_list */))
-      continue;
-    break;
-  } /* while (True) */
-  if (qh->CHECKfrequently && !qh->MERGEexact) {
-    qh->old_randomdist= qh->RANDOMdist;
-    qh->RANDOMdist= False;
-    qh_checkconvex(qh, qh->newfacet_list, qh_ALGORITHMfault);
-    /* qh_checkconnect(qh); [this is slow and it changes the facet order] */
-    qh->RANDOMdist= qh->old_randomdist;
-  }
-  trace1((qh, qh->ferr, 1009, "qh_all_merges: merged %d coplanar facets %d concave facets and %d degen or redundant facets.\n",
-    numcoplanar, numconcave, numdegenredun));
-  if (qh->IStracing >= 4 && qh->num_facets < 50)
-    qh_printlists(qh);
-} /* all_merges */
-
-
-/*---------------------------------
-
-  qh_appendmergeset(qh, facet, neighbor, mergetype, angle )
-    appends an entry to qh.facet_mergeset or qh.degen_mergeset
-
-    angle ignored if NULL or !qh.ANGLEmerge
-
-  returns:
-    merge appended to facet_mergeset or degen_mergeset
-      sets ->degenerate or ->redundant if degen_mergeset
-
-  see:
-    qh_test_appendmerge()
-
-  design:
-    allocate merge entry
-    if regular merge
-      append to qh.facet_mergeset
-    else if degenerate merge and qh.facet_mergeset is all degenerate
-      append to qh.degen_mergeset
-    else if degenerate merge
-      prepend to qh.degen_mergeset
-    else if redundant merge
-      append to qh.degen_mergeset
-*/
-void qh_appendmergeset(qhT *qh, facetT *facet, facetT *neighbor, mergeType mergetype, realT *angle) {
-  mergeT *merge, *lastmerge;
-  void **freelistp; /* used if !qh_NOmem by qh_memalloc_() */
-
-  if (facet->redundant)
-    return;
-  if (facet->degenerate && mergetype == MRGdegen)
-    return;
-  qh_memalloc_(qh, (int)sizeof(mergeT), freelistp, merge, mergeT);
-  merge->facet1= facet;
-  merge->facet2= neighbor;
-  merge->type= mergetype;
-  if (angle && qh->ANGLEmerge)
-    merge->angle= *angle;
-  if (mergetype < MRGdegen)
-    qh_setappend(qh, &(qh->facet_mergeset), merge);
-  else if (mergetype == MRGdegen) {
-    facet->degenerate= True;
-    if (!(lastmerge= (mergeT*)qh_setlast(qh->degen_mergeset))
-    || lastmerge->type == MRGdegen)
-      qh_setappend(qh, &(qh->degen_mergeset), merge);
-    else
-      qh_setaddnth(qh, &(qh->degen_mergeset), 0, merge);
-  }else if (mergetype == MRGredundant) {
-    facet->redundant= True;
-    qh_setappend(qh, &(qh->degen_mergeset), merge);
-  }else /* mergetype == MRGmirror */ {
-    if (facet->redundant || neighbor->redundant) {
-      qh_fprintf(qh, qh->ferr, 6092, "qhull error (qh_appendmergeset): facet f%d or f%d is already a mirrored facet\n",
-           facet->id, neighbor->id);
-      qh_errexit2(qh, qh_ERRqhull, facet, neighbor);
-    }
-    if (!qh_setequal(facet->vertices, neighbor->vertices)) {
-      qh_fprintf(qh, qh->ferr, 6093, "qhull error (qh_appendmergeset): mirrored facets f%d and f%d do not have the same vertices\n",
-           facet->id, neighbor->id);
-      qh_errexit2(qh, qh_ERRqhull, facet, neighbor);
-    }
-    facet->redundant= True;
-    neighbor->redundant= True;
-    qh_setappend(qh, &(qh->degen_mergeset), merge);
-  }
-} /* appendmergeset */
-
-
-/*---------------------------------
-
-  qh_basevertices(qh, samecycle )
-    return temporary set of base vertices for samecycle
-    samecycle is first facet in the cycle
-    assumes apex is SETfirst_( samecycle->vertices )
-
-  returns:
-    vertices(settemp)
-    all ->seen are cleared
-
-  notes:
-    uses qh_vertex_visit;
-
-  design:
-    for each facet in samecycle
-      for each unseen vertex in facet->vertices
-        append to result
-*/
-setT *qh_basevertices(qhT *qh, facetT *samecycle) {
-  facetT *same;
-  vertexT *apex, *vertex, **vertexp;
-  setT *vertices= qh_settemp(qh, qh->TEMPsize);
-
-  apex= SETfirstt_(samecycle->vertices, vertexT);
-  apex->visitid= ++qh->vertex_visit;
-  FORALLsame_cycle_(samecycle) {
-    if (same->mergeridge)
-      continue;
-    FOREACHvertex_(same->vertices) {
-      if (vertex->visitid != qh->vertex_visit) {
-        qh_setappend(qh, &vertices, vertex);
-        vertex->visitid= qh->vertex_visit;
-        vertex->seen= False;
-      }
-    }
-  }
-  trace4((qh, qh->ferr, 4019, "qh_basevertices: found %d vertices\n",
-         qh_setsize(qh, vertices)));
-  return vertices;
-} /* basevertices */
-
-/*---------------------------------
-
-  qh_checkconnect(qh)
-    check that new facets are connected
-    new facets are on qh.newfacet_list
-
-  notes:
-    this is slow and it changes the order of the facets
-    uses qh.visit_id
-
-  design:
-    move first new facet to end of qh.facet_list
-    for all newly appended facets
-      append unvisited neighbors to end of qh.facet_list
-    for all new facets
-      report error if unvisited
-*/
-void qh_checkconnect(qhT *qh /* qh->newfacet_list */) {
-  facetT *facet, *newfacet, *errfacet= NULL, *neighbor, **neighborp;
-
-  facet= qh->newfacet_list;
-  qh_removefacet(qh, facet);
-  qh_appendfacet(qh, facet);
-  facet->visitid= ++qh->visit_id;
-  FORALLfacet_(facet) {
-    FOREACHneighbor_(facet) {
-      if (neighbor->visitid != qh->visit_id) {
-        qh_removefacet(qh, neighbor);
-        qh_appendfacet(qh, neighbor);
-        neighbor->visitid= qh->visit_id;
-      }
-    }
-  }
-  FORALLnew_facets {
-    if (newfacet->visitid == qh->visit_id)
-      break;
-    qh_fprintf(qh, qh->ferr, 6094, "qhull error: f%d is not attached to the new facets\n",
-         newfacet->id);
-    errfacet= newfacet;
-  }
-  if (errfacet)
-    qh_errexit(qh, qh_ERRqhull, errfacet, NULL);
-} /* checkconnect */
-
-/*---------------------------------
-
-  qh_checkzero(qh, testall )
-    check that facets are clearly convex for qh.DISTround with qh.MERGEexact
-
-    if testall,
-      test all facets for qh.MERGEexact post-merging
-    else
-      test qh.newfacet_list
-
-    if qh.MERGEexact,
-      allows coplanar ridges
-      skips convexity test while qh.ZEROall_ok
-
-  returns:
-    True if all facets !flipped, !dupridge, normal
-         if all horizon facets are simplicial
-         if all vertices are clearly below neighbor
-         if all opposite vertices of horizon are below
-    clears qh.ZEROall_ok if any problems or coplanar facets
-
-  notes:
-    uses qh.vertex_visit
-    horizon facets may define multiple new facets
-
-  design:
-    for all facets in qh.newfacet_list or qh.facet_list
-      check for flagged faults (flipped, etc.)
-    for all facets in qh.newfacet_list or qh.facet_list
-      for each neighbor of facet
-        skip horizon facets for qh.newfacet_list
-        test the opposite vertex
-      if qh.newfacet_list
-        test the other vertices in the facet's horizon facet
-*/
-boolT qh_checkzero(qhT *qh, boolT testall) {
-  facetT *facet, *neighbor, **neighborp;
-  facetT *horizon, *facetlist;
-  int neighbor_i;
-  vertexT *vertex, **vertexp;
-  realT dist;
-
-  if (testall)
-    facetlist= qh->facet_list;
-  else {
-    facetlist= qh->newfacet_list;
-    FORALLfacet_(facetlist) {
-      horizon= SETfirstt_(facet->neighbors, facetT);
-      if (!horizon->simplicial)
-        goto LABELproblem;
-      if (facet->flipped || facet->dupridge || !facet->normal)
-        goto LABELproblem;
-    }
-    if (qh->MERGEexact && qh->ZEROall_ok) {
-      trace2((qh, qh->ferr, 2011, "qh_checkzero: skip convexity check until first pre-merge\n"));
-      return True;
-    }
-  }
-  FORALLfacet_(facetlist) {
-    qh->vertex_visit++;
-    neighbor_i= 0;
-    horizon= NULL;
-    FOREACHneighbor_(facet) {
-      if (!neighbor_i && !testall) {
-        horizon= neighbor;
-        neighbor_i++;
-        continue; /* horizon facet tested in qh_findhorizon */
-      }
-      vertex= SETelemt_(facet->vertices, neighbor_i++, vertexT);
-      vertex->visitid= qh->vertex_visit;
-      zzinc_(Zdistzero);
-      qh_distplane(qh, vertex->point, neighbor, &dist);
-      if (dist >= -qh->DISTround) {
-        qh->ZEROall_ok= False;
-        if (!qh->MERGEexact || testall || dist > qh->DISTround)
-          goto LABELnonconvex;
-      }
-    }
-    if (!testall && horizon) {
-      FOREACHvertex_(horizon->vertices) {
-        if (vertex->visitid != qh->vertex_visit) {
-          zzinc_(Zdistzero);
-          qh_distplane(qh, vertex->point, facet, &dist);
-          if (dist >= -qh->DISTround) {
-            qh->ZEROall_ok= False;
-            if (!qh->MERGEexact || dist > qh->DISTround)
-              goto LABELnonconvex;
-          }
-          break;
-        }
-      }
-    }
-  }
-  trace2((qh, qh->ferr, 2012, "qh_checkzero: testall %d, facets are %s\n", testall,
-        (qh->MERGEexact && !testall) ?
-           "not concave, flipped, or duplicate ridged" : "clearly convex"));
-  return True;
-
- LABELproblem:
-  qh->ZEROall_ok= False;
-  trace2((qh, qh->ferr, 2013, "qh_checkzero: facet f%d needs pre-merging\n",
-       facet->id));
-  return False;
-
- LABELnonconvex:
-  trace2((qh, qh->ferr, 2014, "qh_checkzero: facet f%d and f%d are not clearly convex.  v%d dist %.2g\n",
-         facet->id, neighbor->id, vertex->id, dist));
-  return False;
-} /* checkzero */
-
-/*---------------------------------
-
-  qh_compareangle(angle1, angle2 )
-    used by qsort() to order merges by angle
-*/
-int qh_compareangle(const void *p1, const void *p2) {
-  const mergeT *a= *((mergeT *const*)p1), *b= *((mergeT *const*)p2);
-
-  return((a->angle > b->angle) ? 1 : -1);
-} /* compareangle */
-
-/*---------------------------------
-
-  qh_comparemerge(merge1, merge2 )
-    used by qsort() to order merges
-*/
-int qh_comparemerge(const void *p1, const void *p2) {
-  const mergeT *a= *((mergeT *const*)p1), *b= *((mergeT *const*)p2);
-
-  return(a->type - b->type);
-} /* comparemerge */
-
-/*---------------------------------
-
-  qh_comparevisit(vertex1, vertex2 )
-    used by qsort() to order vertices by their visitid
-*/
-int qh_comparevisit(const void *p1, const void *p2) {
-  const vertexT *a= *((vertexT *const*)p1), *b= *((vertexT *const*)p2);
-
-  return(a->visitid - b->visitid);
-} /* comparevisit */
-
-/*---------------------------------
-
-  qh_copynonconvex(qh, atridge )
-    set non-convex flag on other ridges (if any) between same neighbors
-
-  notes:
-    may be faster if use smaller ridge set
-
-  design:
-    for each ridge of atridge's top facet
-      if ridge shares the same neighbor
-        set nonconvex flag
-*/
-void qh_copynonconvex(qhT *qh, ridgeT *atridge) {
-  facetT *facet, *otherfacet;
-  ridgeT *ridge, **ridgep;
-
-  facet= atridge->top;
-  otherfacet= atridge->bottom;
-  FOREACHridge_(facet->ridges) {
-    if (otherfacet == otherfacet_(ridge, facet) && ridge != atridge) {
-      ridge->nonconvex= True;
-      trace4((qh, qh->ferr, 4020, "qh_copynonconvex: moved nonconvex flag from r%d to r%d\n",
-              atridge->id, ridge->id));
-      break;
-    }
-  }
-} /* copynonconvex */
-
-/*---------------------------------
-
-  qh_degen_redundant_facet(qh, facet )
-    check facet for degen. or redundancy
-
-  notes:
-    bumps vertex_visit
-    called if a facet was redundant but no longer is (qh_merge_degenredundant)
-    qh_appendmergeset() only appends first reference to facet (i.e., redundant)
-
-  see:
-    qh_degen_redundant_neighbors()
-
-  design:
-    test for redundant neighbor
-    test for degenerate facet
-*/
-void qh_degen_redundant_facet(qhT *qh, facetT *facet) {
-  vertexT *vertex, **vertexp;
-  facetT *neighbor, **neighborp;
-
-  trace4((qh, qh->ferr, 4021, "qh_degen_redundant_facet: test facet f%d for degen/redundant\n",
-          facet->id));
-  FOREACHneighbor_(facet) {
-    qh->vertex_visit++;
-    FOREACHvertex_(neighbor->vertices)
-      vertex->visitid= qh->vertex_visit;
-    FOREACHvertex_(facet->vertices) {
-      if (vertex->visitid != qh->vertex_visit)
-        break;
-    }
-    if (!vertex) {
-      qh_appendmergeset(qh, facet, neighbor, MRGredundant, NULL);
-      trace2((qh, qh->ferr, 2015, "qh_degen_redundant_facet: f%d is contained in f%d.  merge\n", facet->id, neighbor->id));
-      return;
-    }
-  }
-  if (qh_setsize(qh, facet->neighbors) < qh->hull_dim) {
-    qh_appendmergeset(qh, facet, facet, MRGdegen, NULL);
-    trace2((qh, qh->ferr, 2016, "qh_degen_redundant_neighbors: f%d is degenerate.\n", facet->id));
-  }
-} /* degen_redundant_facet */
-
-
-/*---------------------------------
-
-  qh_degen_redundant_neighbors(qh, facet, delfacet,  )
-    append degenerate and redundant neighbors to facet_mergeset
-    if delfacet,
-      only checks neighbors of both delfacet and facet
-    also checks current facet for degeneracy
-
-  notes:
-    bumps vertex_visit
-    called for each qh_mergefacet() and qh_mergecycle()
-    merge and statistics occur in merge_nonconvex
-    qh_appendmergeset() only appends first reference to facet (i.e., redundant)
-      it appends redundant facets after degenerate ones
-
-    a degenerate facet has fewer than hull_dim neighbors
-    a redundant facet's vertices is a subset of its neighbor's vertices
-    tests for redundant merges first (appendmergeset is nop for others)
-    in a merge, only needs to test neighbors of merged facet
-
-  see:
-    qh_merge_degenredundant() and qh_degen_redundant_facet()
-
-  design:
-    test for degenerate facet
-    test for redundant neighbor
-    test for degenerate neighbor
-*/
-void qh_degen_redundant_neighbors(qhT *qh, facetT *facet, facetT *delfacet) {
-  vertexT *vertex, **vertexp;
-  facetT *neighbor, **neighborp;
-  int size;
-
-  trace4((qh, qh->ferr, 4022, "qh_degen_redundant_neighbors: test neighbors of f%d with delfacet f%d\n",
-          facet->id, getid_(delfacet)));
-  if ((size= qh_setsize(qh, facet->neighbors)) < qh->hull_dim) {
-    qh_appendmergeset(qh, facet, facet, MRGdegen, NULL);
-    trace2((qh, qh->ferr, 2017, "qh_degen_redundant_neighbors: f%d is degenerate with %d neighbors.\n", facet->id, size));
-  }
-  if (!delfacet)
-    delfacet= facet;
-  qh->vertex_visit++;
-  FOREACHvertex_(facet->vertices)
-    vertex->visitid= qh->vertex_visit;
-  FOREACHneighbor_(delfacet) {
-    /* uses early out instead of checking vertex count */
-    if (neighbor == facet)
-      continue;
-    FOREACHvertex_(neighbor->vertices) {
-      if (vertex->visitid != qh->vertex_visit)
-        break;
-    }
-    if (!vertex) {
-      qh_appendmergeset(qh, neighbor, facet, MRGredundant, NULL);
-      trace2((qh, qh->ferr, 2018, "qh_degen_redundant_neighbors: f%d is contained in f%d.  merge\n", neighbor->id, facet->id));
-    }
-  }
-  FOREACHneighbor_(delfacet) {   /* redundant merges occur first */
-    if (neighbor == facet)
-      continue;
-    if ((size= qh_setsize(qh, neighbor->neighbors)) < qh->hull_dim) {
-      qh_appendmergeset(qh, neighbor, neighbor, MRGdegen, NULL);
-      trace2((qh, qh->ferr, 2019, "qh_degen_redundant_neighbors: f%d is degenerate with %d neighbors.  Neighbor of f%d.\n", neighbor->id, size, facet->id));
-    }
-  }
-} /* degen_redundant_neighbors */
-
-
-/*---------------------------------
-
-  qh_find_newvertex(qh, oldvertex, vertices, ridges )
-    locate new vertex for renaming old vertex
-    vertices is a set of possible new vertices
-      vertices sorted by number of deleted ridges
-
-  returns:
-    newvertex or NULL
-      each ridge includes both vertex and oldvertex
-    vertices sorted by number of deleted ridges
-
-  notes:
-    modifies vertex->visitid
-    new vertex is in one of the ridges
-    renaming will not cause a duplicate ridge
-    renaming will minimize the number of deleted ridges
-    newvertex may not be adjacent in the dual (though unlikely)
-
-  design:
-    for each vertex in vertices
-      set vertex->visitid to number of references in ridges
-    remove unvisited vertices
-    set qh.vertex_visit above all possible values
-    sort vertices by number of references in ridges
-    add each ridge to qh.hash_table
-    for each vertex in vertices
-      look for a vertex that would not cause a duplicate ridge after a rename
-*/
-vertexT *qh_find_newvertex(qhT *qh, vertexT *oldvertex, setT *vertices, setT *ridges) {
-  vertexT *vertex, **vertexp;
-  setT *newridges;
-  ridgeT *ridge, **ridgep;
-  int size, hashsize;
-  int hash;
-
-#ifndef qh_NOtrace
-  if (qh->IStracing >= 4) {
-    qh_fprintf(qh, qh->ferr, 8063, "qh_find_newvertex: find new vertex for v%d from ",
-             oldvertex->id);
-    FOREACHvertex_(vertices)
-      qh_fprintf(qh, qh->ferr, 8064, "v%d ", vertex->id);
-    FOREACHridge_(ridges)
-      qh_fprintf(qh, qh->ferr, 8065, "r%d ", ridge->id);
-    qh_fprintf(qh, qh->ferr, 8066, "\n");
-  }
-#endif
-  FOREACHvertex_(vertices)
-    vertex->visitid= 0;
-  FOREACHridge_(ridges) {
-    FOREACHvertex_(ridge->vertices)
-      vertex->visitid++;
-  }
-  FOREACHvertex_(vertices) {
-    if (!vertex->visitid) {
-      qh_setdelnth(qh, vertices, SETindex_(vertices,vertex));
-      vertexp--; /* repeat since deleted this vertex */
-    }
-  }
-  qh->vertex_visit += (unsigned int)qh_setsize(qh, ridges);
-  if (!qh_setsize(qh, vertices)) {
-    trace4((qh, qh->ferr, 4023, "qh_find_newvertex: vertices not in ridges for v%d\n",
-            oldvertex->id));
-    return NULL;
-  }
-  qsort(SETaddr_(vertices, vertexT), (size_t)qh_setsize(qh, vertices),
-                sizeof(vertexT *), qh_comparevisit);
-  /* can now use qh->vertex_visit */
-  if (qh->PRINTstatistics) {
-    size= qh_setsize(qh, vertices);
-    zinc_(Zintersect);
-    zadd_(Zintersecttot, size);
-    zmax_(Zintersectmax, size);
-  }
-  hashsize= qh_newhashtable(qh, qh_setsize(qh, ridges));
-  FOREACHridge_(ridges)
-    qh_hashridge(qh, qh->hash_table, hashsize, ridge, oldvertex);
-  FOREACHvertex_(vertices) {
-    newridges= qh_vertexridges(qh, vertex);
-    FOREACHridge_(newridges) {
-      if (qh_hashridge_find(qh, qh->hash_table, hashsize, ridge, vertex, oldvertex, &hash)) {
-        zinc_(Zdupridge);
-        break;
-      }
-    }
-    qh_settempfree(qh, &newridges);
-    if (!ridge)
-      break;  /* found a rename */
-  }
-  if (vertex) {
-    /* counted in qh_renamevertex */
-    trace2((qh, qh->ferr, 2020, "qh_find_newvertex: found v%d for old v%d from %d vertices and %d ridges.\n",
-      vertex->id, oldvertex->id, qh_setsize(qh, vertices), qh_setsize(qh, ridges)));
-  }else {
-    zinc_(Zfindfail);
-    trace0((qh, qh->ferr, 14, "qh_find_newvertex: no vertex for renaming v%d(all duplicated ridges) during p%d\n",
-      oldvertex->id, qh->furthest_id));
-  }
-  qh_setfree(qh, &qh->hash_table);
-  return vertex;
-} /* find_newvertex */
-
-/*---------------------------------
-
-  qh_findbest_test(qh, testcentrum, facet, neighbor, bestfacet, dist, mindist, maxdist )
-    test neighbor of facet for qh_findbestneighbor()
-    if testcentrum,
-      tests centrum (assumes it is defined)
-    else
-      tests vertices
-
-  returns:
-    if a better facet (i.e., vertices/centrum of facet closer to neighbor)
-      updates bestfacet, dist, mindist, and maxdist
-*/
-void qh_findbest_test(qhT *qh, boolT testcentrum, facetT *facet, facetT *neighbor,
-      facetT **bestfacet, realT *distp, realT *mindistp, realT *maxdistp) {
-  realT dist, mindist, maxdist;
-
-  if (testcentrum) {
-    zzinc_(Zbestdist);
-    qh_distplane(qh, facet->center, neighbor, &dist);
-    dist *= qh->hull_dim; /* estimate furthest vertex */
-    if (dist < 0) {
-      maxdist= 0;
-      mindist= dist;
-      dist= -dist;
-    }else {
-      mindist= 0;
-      maxdist= dist;
-    }
-  }else
-    dist= qh_getdistance(qh, facet, neighbor, &mindist, &maxdist);
-  if (dist < *distp) {
-    *bestfacet= neighbor;
-    *mindistp= mindist;
-    *maxdistp= maxdist;
-    *distp= dist;
-  }
-} /* findbest_test */
-
-/*---------------------------------
-
-  qh_findbestneighbor(qh, facet, dist, mindist, maxdist )
-    finds best neighbor (least dist) of a facet for merging
-
-  returns:
-    returns min and max distances and their max absolute value
-
-  notes:
-    error if qh_ASvoronoi
-    avoids merging old into new
-    assumes ridge->nonconvex only set on one ridge between a pair of facets
-    could use an early out predicate but not worth it
-
-  design:
-    if a large facet
-      will test centrum
-    else
-      will test vertices
-    if a large facet
-      test nonconvex neighbors for best merge
-    else
-      test all neighbors for the best merge
-    if testing centrum
-      get distance information
-*/
-facetT *qh_findbestneighbor(qhT *qh, facetT *facet, realT *distp, realT *mindistp, realT *maxdistp) {
-  facetT *neighbor, **neighborp, *bestfacet= NULL;
-  ridgeT *ridge, **ridgep;
-  boolT nonconvex= True, testcentrum= False;
-  int size= qh_setsize(qh, facet->vertices);
-
-  if(qh->CENTERtype==qh_ASvoronoi){
-    qh_fprintf(qh, qh->ferr, 6272, "qhull error: cannot call qh_findbestneighor for f%d while qh.CENTERtype is qh_ASvoronoi\n", facet->id);
-    qh_errexit(qh, qh_ERRqhull, facet, NULL);
-  }
-  *distp= REALmax;
-  if (size > qh_BESTcentrum2 * qh->hull_dim + qh_BESTcentrum) {
-    testcentrum= True;
-    zinc_(Zbestcentrum);
-    if (!facet->center)
-       facet->center= qh_getcentrum(qh, facet);
-  }
-  if (size > qh->hull_dim + qh_BESTnonconvex) {
-    FOREACHridge_(facet->ridges) {
-      if (ridge->nonconvex) {
-        neighbor= otherfacet_(ridge, facet);
-        qh_findbest_test(qh, testcentrum, facet, neighbor,
-                          &bestfacet, distp, mindistp, maxdistp);
-      }
-    }
-  }
-  if (!bestfacet) {
-    nonconvex= False;
-    FOREACHneighbor_(facet)
-      qh_findbest_test(qh, testcentrum, facet, neighbor,
-                        &bestfacet, distp, mindistp, maxdistp);
-  }
-  if (!bestfacet) {
-    qh_fprintf(qh, qh->ferr, 6095, "qhull internal error (qh_findbestneighbor): no neighbors for f%d\n", facet->id);
-    qh_errexit(qh, qh_ERRqhull, facet, NULL);
-  }
-  if (testcentrum)
-    qh_getdistance(qh, facet, bestfacet, mindistp, maxdistp);
-  trace3((qh, qh->ferr, 3002, "qh_findbestneighbor: f%d is best neighbor for f%d testcentrum? %d nonconvex? %d dist %2.2g min %2.2g max %2.2g\n",
-     bestfacet->id, facet->id, testcentrum, nonconvex, *distp, *mindistp, *maxdistp));
-  return(bestfacet);
-} /* findbestneighbor */
-
-
-/*---------------------------------
-
-  qh_flippedmerges(qh, facetlist, wasmerge )
-    merge flipped facets into best neighbor
-    assumes qh.facet_mergeset at top of temporary stack
-
-  returns:
-    no flipped facets on facetlist
-    sets wasmerge if merge occurred
-    degen/redundant merges passed through
-
-  notes:
-    othermerges not needed since qh.facet_mergeset is empty before & after
-      keep it in case of change
-
-  design:
-    append flipped facets to qh.facetmergeset
-    for each flipped merge
-      find best neighbor
-      merge facet into neighbor
-      merge degenerate and redundant facets
-    remove flipped merges from qh.facet_mergeset
-*/
-void qh_flippedmerges(qhT *qh, facetT *facetlist, boolT *wasmerge) {
-  facetT *facet, *neighbor, *facet1;
-  realT dist, mindist, maxdist;
-  mergeT *merge, **mergep;
-  setT *othermerges;
-  int nummerge=0;
-
-  trace4((qh, qh->ferr, 4024, "qh_flippedmerges: begin\n"));
-  FORALLfacet_(facetlist) {
-    if (facet->flipped && !facet->visible)
-      qh_appendmergeset(qh, facet, facet, MRGflip, NULL);
-  }
-  othermerges= qh_settemppop(qh); /* was facet_mergeset */
-  qh->facet_mergeset= qh_settemp(qh, qh->TEMPsize);
-  qh_settemppush(qh, othermerges);
-  FOREACHmerge_(othermerges) {
-    facet1= merge->facet1;
-    if (merge->type != MRGflip || facet1->visible)
-      continue;
-    if (qh->TRACEmerge-1 == zzval_(Ztotmerge))
-      qh->qhmem.IStracing= qh->IStracing= qh->TRACElevel;
-    neighbor= qh_findbestneighbor(qh, facet1, &dist, &mindist, &maxdist);
-    trace0((qh, qh->ferr, 15, "qh_flippedmerges: merge flipped f%d into f%d dist %2.2g during p%d\n",
-      facet1->id, neighbor->id, dist, qh->furthest_id));
-    qh_mergefacet(qh, facet1, neighbor, &mindist, &maxdist, !qh_MERGEapex);
-    nummerge++;
-    if (qh->PRINTstatistics) {
-      zinc_(Zflipped);
-      wadd_(Wflippedtot, dist);
-      wmax_(Wflippedmax, dist);
-    }
-    qh_merge_degenredundant(qh);
-  }
-  FOREACHmerge_(othermerges) {
-    if (merge->facet1->visible || merge->facet2->visible)
-      qh_memfree(qh, merge, (int)sizeof(mergeT));
-    else
-      qh_setappend(qh, &qh->facet_mergeset, merge);
-  }
-  qh_settempfree(qh, &othermerges);
-  if (nummerge)
-    *wasmerge= True;
-  trace1((qh, qh->ferr, 1010, "qh_flippedmerges: merged %d flipped facets into a good neighbor\n", nummerge));
-} /* flippedmerges */
-
-
-/*---------------------------------
-
-  qh_forcedmerges(qh, wasmerge )
-    merge duplicated ridges
-
-  returns:
-    removes all duplicate ridges on facet_mergeset
-    wasmerge set if merge
-    qh.facet_mergeset may include non-forced merges(none for now)
-    qh.degen_mergeset includes degen/redun merges
-
-  notes:
-    duplicate ridges occur when the horizon is pinched,
-        i.e. a subridge occurs in more than two horizon ridges.
-     could rename vertices that pinch the horizon
-    assumes qh_merge_degenredundant() has not be called
-    othermerges isn't needed since facet_mergeset is empty afterwards
-      keep it in case of change
-
-  design:
-    for each duplicate ridge
-      find current facets by chasing f.replace links
-      check for wide merge due to duplicate ridge
-      determine best direction for facet
-      merge one facet into the other
-      remove duplicate ridges from qh.facet_mergeset
-*/
-void qh_forcedmerges(qhT *qh, boolT *wasmerge) {
-  facetT *facet1, *facet2;
-  mergeT *merge, **mergep;
-  realT dist1, dist2, mindist1, mindist2, maxdist1, maxdist2;
-  setT *othermerges;
-  int nummerge=0, numflip=0;
-
-  if (qh->TRACEmerge-1 == zzval_(Ztotmerge))
-    qh->qhmem.IStracing= qh->IStracing= qh->TRACElevel;
-  trace4((qh, qh->ferr, 4025, "qh_forcedmerges: begin\n"));
-  othermerges= qh_settemppop(qh); /* was facet_mergeset */
-  qh->facet_mergeset= qh_settemp(qh, qh->TEMPsize);
-  qh_settemppush(qh, othermerges);
-  FOREACHmerge_(othermerges) {
-    if (merge->type != MRGridge)
-        continue;
-    if (qh->TRACEmerge-1 == zzval_(Ztotmerge))
-        qh->qhmem.IStracing= qh->IStracing= qh->TRACElevel;
-    facet1= merge->facet1;
-    facet2= merge->facet2;
-    while (facet1->visible)      /* must exist, no qh_merge_degenredunant */
-      facet1= facet1->f.replace; /* previously merged facet */
-    while (facet2->visible)
-      facet2= facet2->f.replace; /* previously merged facet */
-    if (facet1 == facet2)
-      continue;
-    if (!qh_setin(facet2->neighbors, facet1)) {
-      qh_fprintf(qh, qh->ferr, 6096, "qhull internal error (qh_forcedmerges): f%d and f%d had a duplicate ridge but as f%d and f%d they are no longer neighbors\n",
-               merge->facet1->id, merge->facet2->id, facet1->id, facet2->id);
-      qh_errexit2(qh, qh_ERRqhull, facet1, facet2);
-    }
-    dist1= qh_getdistance(qh, facet1, facet2, &mindist1, &maxdist1);
-    dist2= qh_getdistance(qh, facet2, facet1, &mindist2, &maxdist2);
-    qh_check_dupridge(qh, facet1, dist1, facet2, dist2);
-    if (dist1 < dist2)
-      qh_mergefacet(qh, facet1, facet2, &mindist1, &maxdist1, !qh_MERGEapex);
-    else {
-      qh_mergefacet(qh, facet2, facet1, &mindist2, &maxdist2, !qh_MERGEapex);
-      dist1= dist2;
-      facet1= facet2;
-    }
-    if (facet1->flipped) {
-      zinc_(Zmergeflipdup);
-      numflip++;
-    }else
-      nummerge++;
-    if (qh->PRINTstatistics) {
-      zinc_(Zduplicate);
-      wadd_(Wduplicatetot, dist1);
-      wmax_(Wduplicatemax, dist1);
-    }
-  }
-  FOREACHmerge_(othermerges) {
-    if (merge->type == MRGridge)
-      qh_memfree(qh, merge, (int)sizeof(mergeT));
-    else
-      qh_setappend(qh, &qh->facet_mergeset, merge);
-  }
-  qh_settempfree(qh, &othermerges);
-  if (nummerge)
-    *wasmerge= True;
-  trace1((qh, qh->ferr, 1011, "qh_forcedmerges: merged %d facets and %d flipped facets across duplicated ridges\n",
-                nummerge, numflip));
-} /* forcedmerges */
-
-
-/*---------------------------------
-
-  qh_getmergeset(qh, facetlist )
-    determines nonconvex facets on facetlist
-    tests !tested ridges and nonconvex ridges of !tested facets
-
-  returns:
-    returns sorted qh.facet_mergeset of facet-neighbor pairs to be merged
-    all ridges tested
-
-  notes:
-    assumes no nonconvex ridges with both facets tested
-    uses facet->tested/ridge->tested to prevent duplicate tests
-    can not limit tests to modified ridges since the centrum changed
-    uses qh.visit_id
-
-  see:
-    qh_getmergeset_initial()
-
-  design:
-    for each facet on facetlist
-      for each ridge of facet
-        if untested ridge
-          test ridge for convexity
-          if non-convex
-            append ridge to qh.facet_mergeset
-    sort qh.facet_mergeset by angle
-*/
-void qh_getmergeset(qhT *qh, facetT *facetlist) {
-  facetT *facet, *neighbor, **neighborp;
-  ridgeT *ridge, **ridgep;
-  int nummerges;
-
-  nummerges= qh_setsize(qh, qh->facet_mergeset);
-  trace4((qh, qh->ferr, 4026, "qh_getmergeset: started.\n"));
-  qh->visit_id++;
-  FORALLfacet_(facetlist) {
-    if (facet->tested)
-      continue;
-    facet->visitid= qh->visit_id;
-    facet->tested= True;  /* must be non-simplicial due to merge */
-    FOREACHneighbor_(facet)
-      neighbor->seen= False;
-    FOREACHridge_(facet->ridges) {
-      if (ridge->tested && !ridge->nonconvex)
-        continue;
-      /* if tested & nonconvex, need to append merge */
-      neighbor= otherfacet_(ridge, facet);
-      if (neighbor->seen) {
-        ridge->tested= True;
-        ridge->nonconvex= False;
-      }else if (neighbor->visitid != qh->visit_id) {
-        ridge->tested= True;
-        ridge->nonconvex= False;
-        neighbor->seen= True;      /* only one ridge is marked nonconvex */
-        if (qh_test_appendmerge(qh, facet, neighbor))
-          ridge->nonconvex= True;
-      }
-    }
-  }
-  nummerges= qh_setsize(qh, qh->facet_mergeset);
-  if (qh->ANGLEmerge)
-    qsort(SETaddr_(qh->facet_mergeset, mergeT), (size_t)nummerges, sizeof(mergeT *), qh_compareangle);
-  else
-    qsort(SETaddr_(qh->facet_mergeset, mergeT), (size_t)nummerges, sizeof(mergeT *), qh_comparemerge);
-  if (qh->POSTmerging) {
-    zadd_(Zmergesettot2, nummerges);
-  }else {
-    zadd_(Zmergesettot, nummerges);
-    zmax_(Zmergesetmax, nummerges);
-  }
-  trace2((qh, qh->ferr, 2021, "qh_getmergeset: %d merges found\n", nummerges));
-} /* getmergeset */
-
-
-/*---------------------------------
-
-  qh_getmergeset_initial(qh, facetlist )
-    determine initial qh.facet_mergeset for facets
-    tests all facet/neighbor pairs on facetlist
-
-  returns:
-    sorted qh.facet_mergeset with nonconvex ridges
-    sets facet->tested, ridge->tested, and ridge->nonconvex
-
-  notes:
-    uses visit_id, assumes ridge->nonconvex is False
-
-  see:
-    qh_getmergeset()
-
-  design:
-    for each facet on facetlist
-      for each untested neighbor of facet
-        test facet and neighbor for convexity
-        if non-convex
-          append merge to qh.facet_mergeset
-          mark one of the ridges as nonconvex
-    sort qh.facet_mergeset by angle
-*/
-void qh_getmergeset_initial(qhT *qh, facetT *facetlist) {
-  facetT *facet, *neighbor, **neighborp;
-  ridgeT *ridge, **ridgep;
-  int nummerges;
-
-  qh->visit_id++;
-  FORALLfacet_(facetlist) {
-    facet->visitid= qh->visit_id;
-    facet->tested= True;
-    FOREACHneighbor_(facet) {
-      if (neighbor->visitid != qh->visit_id) {
-        if (qh_test_appendmerge(qh, facet, neighbor)) {
-          FOREACHridge_(neighbor->ridges) {
-            if (facet == otherfacet_(ridge, neighbor)) {
-              ridge->nonconvex= True;
-              break;    /* only one ridge is marked nonconvex */
-            }
-          }
-        }
-      }
-    }
-    FOREACHridge_(facet->ridges)
-      ridge->tested= True;
-  }
-  nummerges= qh_setsize(qh, qh->facet_mergeset);
-  if (qh->ANGLEmerge)
-    qsort(SETaddr_(qh->facet_mergeset, mergeT), (size_t)nummerges, sizeof(mergeT *), qh_compareangle);
-  else
-    qsort(SETaddr_(qh->facet_mergeset, mergeT), (size_t)nummerges, sizeof(mergeT *), qh_comparemerge);
-  if (qh->POSTmerging) {
-    zadd_(Zmergeinittot2, nummerges);
-  }else {
-    zadd_(Zmergeinittot, nummerges);
-    zmax_(Zmergeinitmax, nummerges);
-  }
-  trace2((qh, qh->ferr, 2022, "qh_getmergeset_initial: %d merges found\n", nummerges));
-} /* getmergeset_initial */
-
-
-/*---------------------------------
-
-  qh_hashridge(qh, hashtable, hashsize, ridge, oldvertex )
-    add ridge to hashtable without oldvertex
-
-  notes:
-    assumes hashtable is large enough
-
-  design:
-    determine hash value for ridge without oldvertex
-    find next empty slot for ridge
-*/
-void qh_hashridge(qhT *qh, setT *hashtable, int hashsize, ridgeT *ridge, vertexT *oldvertex) {
-  int hash;
-  ridgeT *ridgeA;
-
-  hash= qh_gethash(qh, hashsize, ridge->vertices, qh->hull_dim-1, 0, oldvertex);
-  while (True) {
-    if (!(ridgeA= SETelemt_(hashtable, hash, ridgeT))) {
-      SETelem_(hashtable, hash)= ridge;
-      break;
-    }else if (ridgeA == ridge)
-      break;
-    if (++hash == hashsize)
-      hash= 0;
-  }
-} /* hashridge */
-
-
-/*---------------------------------
-
-  qh_hashridge_find(qh, hashtable, hashsize, ridge, vertex, oldvertex, hashslot )
-    returns matching ridge without oldvertex in hashtable
-      for ridge without vertex
-    if oldvertex is NULL
-      matches with any one skip
-
-  returns:
-    matching ridge or NULL
-    if no match,
-      if ridge already in   table
-        hashslot= -1
-      else
-        hashslot= next NULL index
-
-  notes:
-    assumes hashtable is large enough
-    can't match ridge to itself
-
-  design:
-    get hash value for ridge without vertex
-    for each hashslot
-      return match if ridge matches ridgeA without oldvertex
-*/
-ridgeT *qh_hashridge_find(qhT *qh, setT *hashtable, int hashsize, ridgeT *ridge,
-              vertexT *vertex, vertexT *oldvertex, int *hashslot) {
-  int hash;
-  ridgeT *ridgeA;
-
-  *hashslot= 0;
-  zinc_(Zhashridge);
-  hash= qh_gethash(qh, hashsize, ridge->vertices, qh->hull_dim-1, 0, vertex);
-  while ((ridgeA= SETelemt_(hashtable, hash, ridgeT))) {
-    if (ridgeA == ridge)
-      *hashslot= -1;
-    else {
-      zinc_(Zhashridgetest);
-      if (qh_setequal_except(ridge->vertices, vertex, ridgeA->vertices, oldvertex))
-        return ridgeA;
-    }
-    if (++hash == hashsize)
-      hash= 0;
-  }
-  if (!*hashslot)
-    *hashslot= hash;
-  return NULL;
-} /* hashridge_find */
-
-
-/*---------------------------------
-
-  qh_makeridges(qh, facet )
-    creates explicit ridges between simplicial facets
-
-  returns:
-    facet with ridges and without qh_MERGEridge
-    ->simplicial is False
-
-  notes:
-    allows qh_MERGEridge flag
-    uses existing ridges
-    duplicate neighbors ok if ridges already exist (qh_mergecycle_ridges)
-
-  see:
-    qh_mergecycle_ridges()
-
-  design:
-    look for qh_MERGEridge neighbors
-    mark neighbors that already have ridges
-    for each unprocessed neighbor of facet
-      create a ridge for neighbor and facet
-    if any qh_MERGEridge neighbors
-      delete qh_MERGEridge flags (already handled by qh_mark_dupridges)
-*/
-void qh_makeridges(qhT *qh, facetT *facet) {
-  facetT *neighbor, **neighborp;
-  ridgeT *ridge, **ridgep;
-  int neighbor_i, neighbor_n;
-  boolT toporient, mergeridge= False;
-
-  if (!facet->simplicial)
-    return;
-  trace4((qh, qh->ferr, 4027, "qh_makeridges: make ridges for f%d\n", facet->id));
-  facet->simplicial= False;
-  FOREACHneighbor_(facet) {
-    if (neighbor == qh_MERGEridge)
-      mergeridge= True;
-    else
-      neighbor->seen= False;
-  }
-  FOREACHridge_(facet->ridges)
-    otherfacet_(ridge, facet)->seen= True;
-  FOREACHneighbor_i_(qh, facet) {
-    if (neighbor == qh_MERGEridge)
-      continue;  /* fixed by qh_mark_dupridges */
-    else if (!neighbor->seen) {  /* no current ridges */
-      ridge= qh_newridge(qh);
-      ridge->vertices= qh_setnew_delnthsorted(qh, facet->vertices, qh->hull_dim,
-                                                          neighbor_i, 0);
-      toporient= facet->toporient ^ (neighbor_i & 0x1);
-      if (toporient) {
-        ridge->top= facet;
-        ridge->bottom= neighbor;
-      }else {
-        ridge->top= neighbor;
-        ridge->bottom= facet;
-      }
-#if 0 /* this also works */
-      flip= (facet->toporient ^ neighbor->toporient)^(skip1 & 0x1) ^ (skip2 & 0x1);
-      if (facet->toporient ^ (skip1 & 0x1) ^ flip) {
-        ridge->top= neighbor;
-        ridge->bottom= facet;
-      }else {
-        ridge->top= facet;
-        ridge->bottom= neighbor;
-      }
-#endif
-      qh_setappend(qh, &(facet->ridges), ridge);
-      qh_setappend(qh, &(neighbor->ridges), ridge);
-    }
-  }
-  if (mergeridge) {
-    while (qh_setdel(facet->neighbors, qh_MERGEridge))
-      ; /* delete each one */
-  }
-} /* makeridges */
-
-
-/*---------------------------------
-
-  qh_mark_dupridges(qh, facetlist )
-    add duplicated ridges to qh.facet_mergeset
-    facet->dupridge is true
-
-  returns:
-    duplicate ridges on qh.facet_mergeset
-    ->mergeridge/->mergeridge2 set
-    duplicate ridges marked by qh_MERGEridge and both sides facet->dupridge
-    no MERGEridges in neighbor sets
-
-  notes:
-    duplicate ridges occur when the horizon is pinched,
-        i.e. a subridge occurs in more than two horizon ridges.
-    could rename vertices that pinch the horizon (thus removing subridge)
-    uses qh.visit_id
-
-  design:
-    for all facets on facetlist
-      if facet contains a duplicate ridge
-        for each neighbor of facet
-          if neighbor marked qh_MERGEridge (one side of the merge)
-            set facet->mergeridge
-          else
-            if neighbor contains a duplicate ridge
-            and the back link is qh_MERGEridge
-              append duplicate ridge to qh.facet_mergeset
-   for each duplicate ridge
-     make ridge sets in preparation for merging
-     remove qh_MERGEridge from neighbor set
-   for each duplicate ridge
-     restore the missing neighbor from the neighbor set that was qh_MERGEridge
-     add the missing ridge for this neighbor
-*/
-void qh_mark_dupridges(qhT *qh, facetT *facetlist) {
-  facetT *facet, *neighbor, **neighborp;
-  int nummerge=0;
-  mergeT *merge, **mergep;
-
-
-  trace4((qh, qh->ferr, 4028, "qh_mark_dupridges: identify duplicate ridges\n"));
-  FORALLfacet_(facetlist) {
-    if (facet->dupridge) {
-      FOREACHneighbor_(facet) {
-        if (neighbor == qh_MERGEridge) {
-          facet->mergeridge= True;
-          continue;
-        }
-        if (neighbor->dupridge
-        && !qh_setin(neighbor->neighbors, facet)) { /* qh_MERGEridge */
-          qh_appendmergeset(qh, facet, neighbor, MRGridge, NULL);
-          facet->mergeridge2= True;
-          facet->mergeridge= True;
-          nummerge++;
-        }
-      }
-    }
-  }
-  if (!nummerge)
-    return;
-  FORALLfacet_(facetlist) {            /* gets rid of qh_MERGEridge */
-    if (facet->mergeridge && !facet->mergeridge2)
-      qh_makeridges(qh, facet);
-  }
-  FOREACHmerge_(qh->facet_mergeset) {   /* restore the missing neighbors */
-    if (merge->type == MRGridge) {
-      qh_setappend(qh, &merge->facet2->neighbors, merge->facet1);
-      qh_makeridges(qh, merge->facet1);   /* and the missing ridges */
-    }
-  }
-  trace1((qh, qh->ferr, 1012, "qh_mark_dupridges: found %d duplicated ridges\n",
-                nummerge));
-} /* mark_dupridges */
-
-/*---------------------------------
-
-  qh_maydropneighbor(qh, facet )
-    drop neighbor relationship if no ridge between facet and neighbor
-
-  returns:
-    neighbor sets updated
-    appends degenerate facets to qh.facet_mergeset
-
-  notes:
-    won't cause redundant facets since vertex inclusion is the same
-    may drop vertex and neighbor if no ridge
-    uses qh.visit_id
-
-  design:
-    visit all neighbors with ridges
-    for each unvisited neighbor of facet
-      delete neighbor and facet from the neighbor sets
-      if neighbor becomes degenerate
-        append neighbor to qh.degen_mergeset
-    if facet is degenerate
-      append facet to qh.degen_mergeset
-*/
-void qh_maydropneighbor(qhT *qh, facetT *facet) {
-  ridgeT *ridge, **ridgep;
-  realT angledegen= qh_ANGLEdegen;
-  facetT *neighbor, **neighborp;
-
-  qh->visit_id++;
-  trace4((qh, qh->ferr, 4029, "qh_maydropneighbor: test f%d for no ridges to a neighbor\n",
-          facet->id));
-  FOREACHridge_(facet->ridges) {
-    ridge->top->visitid= qh->visit_id;
-    ridge->bottom->visitid= qh->visit_id;
-  }
-  FOREACHneighbor_(facet) {
-    if (neighbor->visitid != qh->visit_id) {
-      trace0((qh, qh->ferr, 17, "qh_maydropneighbor: facets f%d and f%d are no longer neighbors during p%d\n",
-            facet->id, neighbor->id, qh->furthest_id));
-      zinc_(Zdropneighbor);
-      qh_setdel(facet->neighbors, neighbor);
-      neighborp--;  /* repeat, deleted a neighbor */
-      qh_setdel(neighbor->neighbors, facet);
-      if (qh_setsize(qh, neighbor->neighbors) < qh->hull_dim) {
-        zinc_(Zdropdegen);
-        qh_appendmergeset(qh, neighbor, neighbor, MRGdegen, &angledegen);
-        trace2((qh, qh->ferr, 2023, "qh_maydropneighbors: f%d is degenerate.\n", neighbor->id));
-      }
-    }
-  }
-  if (qh_setsize(qh, facet->neighbors) < qh->hull_dim) {
-    zinc_(Zdropdegen);
-    qh_appendmergeset(qh, facet, facet, MRGdegen, &angledegen);
-    trace2((qh, qh->ferr, 2024, "qh_maydropneighbors: f%d is degenerate.\n", facet->id));
-  }
-} /* maydropneighbor */
-
-
-/*---------------------------------
-
-  qh_merge_degenredundant(qh)
-    merge all degenerate and redundant facets
-    qh.degen_mergeset contains merges from qh_degen_redundant_neighbors()
-
-  returns:
-    number of merges performed
-    resets facet->degenerate/redundant
-    if deleted (visible) facet has no neighbors
-      sets ->f.replace to NULL
-
-  notes:
-    redundant merges happen before degenerate ones
-    merging and renaming vertices can result in degen/redundant facets
-
-  design:
-    for each merge on qh.degen_mergeset
-      if redundant merge
-        if non-redundant facet merged into redundant facet
-          recheck facet for redundancy
-        else
-          merge redundant facet into other facet
-*/
-int qh_merge_degenredundant(qhT *qh) {
-  int size;
-  mergeT *merge;
-  facetT *bestneighbor, *facet1, *facet2;
-  realT dist, mindist, maxdist;
-  vertexT *vertex, **vertexp;
-  int nummerges= 0;
-  mergeType mergetype;
-
-  while ((merge= (mergeT*)qh_setdellast(qh->degen_mergeset))) {
-    facet1= merge->facet1;
-    facet2= merge->facet2;
-    mergetype= merge->type;
-    qh_memfree(qh, merge, (int)sizeof(mergeT));
-    if (facet1->visible)
-      continue;
-    facet1->degenerate= False;
-    facet1->redundant= False;
-    if (qh->TRACEmerge-1 == zzval_(Ztotmerge))
-      qh->qhmem.IStracing= qh->IStracing= qh->TRACElevel;
-    if (mergetype == MRGredundant) {
-      zinc_(Zneighbor);
-      while (facet2->visible) {
-        if (!facet2->f.replace) {
-          qh_fprintf(qh, qh->ferr, 6097, "qhull internal error (qh_merge_degenredunant): f%d redundant but f%d has no replacement\n",
-               facet1->id, facet2->id);
-          qh_errexit2(qh, qh_ERRqhull, facet1, facet2);
-        }
-        facet2= facet2->f.replace;
-      }
-      if (facet1 == facet2) {
-        qh_degen_redundant_facet(qh, facet1); /* in case of others */
-        continue;
-      }
-      trace2((qh, qh->ferr, 2025, "qh_merge_degenredundant: facet f%d is contained in f%d, will merge\n",
-            facet1->id, facet2->id));
-      qh_mergefacet(qh, facet1, facet2, NULL, NULL, !qh_MERGEapex);
-      /* merge distance is already accounted for */
-      nummerges++;
-    }else {  /* mergetype == MRGdegen, other merges may have fixed */
-      if (!(size= qh_setsize(qh, facet1->neighbors))) {
-        zinc_(Zdelfacetdup);
-        trace2((qh, qh->ferr, 2026, "qh_merge_degenredundant: facet f%d has no neighbors.  Deleted\n", facet1->id));
-        qh_willdelete(qh, facet1, NULL);
-        FOREACHvertex_(facet1->vertices) {
-          qh_setdel(vertex->neighbors, facet1);
-          if (!SETfirst_(vertex->neighbors)) {
-            zinc_(Zdegenvertex);
-            trace2((qh, qh->ferr, 2027, "qh_merge_degenredundant: deleted v%d because f%d has no neighbors\n",
-                 vertex->id, facet1->id));
-            vertex->deleted= True;
-            qh_setappend(qh, &qh->del_vertices, vertex);
-          }
-        }
-        nummerges++;
-      }else if (size < qh->hull_dim) {
-        bestneighbor= qh_findbestneighbor(qh, facet1, &dist, &mindist, &maxdist);
-        trace2((qh, qh->ferr, 2028, "qh_merge_degenredundant: facet f%d has %d neighbors, merge into f%d dist %2.2g\n",
-              facet1->id, size, bestneighbor->id, dist));
-        qh_mergefacet(qh, facet1, bestneighbor, &mindist, &maxdist, !qh_MERGEapex);
-        nummerges++;
-        if (qh->PRINTstatistics) {
-          zinc_(Zdegen);
-          wadd_(Wdegentot, dist);
-          wmax_(Wdegenmax, dist);
-        }
-      } /* else, another merge fixed the degeneracy and redundancy tested */
-    }
-  }
-  return nummerges;
-} /* merge_degenredundant */
-
-/*---------------------------------
-
-  qh_merge_nonconvex(qh, facet1, facet2, mergetype )
-    remove non-convex ridge between facet1 into facet2
-    mergetype gives why the facet's are non-convex
-
-  returns:
-    merges one of the facets into the best neighbor
-
-  design:
-    if one of the facets is a new facet
-      prefer merging new facet into old facet
-    find best neighbors for both facets
-    merge the nearest facet into its best neighbor
-    update the statistics
-*/
-void qh_merge_nonconvex(qhT *qh, facetT *facet1, facetT *facet2, mergeType mergetype) {
-  facetT *bestfacet, *bestneighbor, *neighbor;
-  realT dist, dist2, mindist, mindist2, maxdist, maxdist2;
-
-  if (qh->TRACEmerge-1 == zzval_(Ztotmerge))
-    qh->qhmem.IStracing= qh->IStracing= qh->TRACElevel;
-  trace3((qh, qh->ferr, 3003, "qh_merge_nonconvex: merge #%d for f%d and f%d type %d\n",
-      zzval_(Ztotmerge) + 1, facet1->id, facet2->id, mergetype));
-  /* concave or coplanar */
-  if (!facet1->newfacet) {
-    bestfacet= facet2;   /* avoid merging old facet if new is ok */
-    facet2= facet1;
-    facet1= bestfacet;
-  }else
-    bestfacet= facet1;
-  bestneighbor= qh_findbestneighbor(qh, bestfacet, &dist, &mindist, &maxdist);
-  neighbor= qh_findbestneighbor(qh, facet2, &dist2, &mindist2, &maxdist2);
-  if (dist < dist2) {
-    qh_mergefacet(qh, bestfacet, bestneighbor, &mindist, &maxdist, !qh_MERGEapex);
-  }else if (qh->AVOIDold && !facet2->newfacet
-  && ((mindist >= -qh->MAXcoplanar && maxdist <= qh->max_outside)
-       || dist * 1.5 < dist2)) {
-    zinc_(Zavoidold);
-    wadd_(Wavoidoldtot, dist);
-    wmax_(Wavoidoldmax, dist);
-    trace2((qh, qh->ferr, 2029, "qh_merge_nonconvex: avoid merging old facet f%d dist %2.2g.  Use f%d dist %2.2g instead\n",
-           facet2->id, dist2, facet1->id, dist2));
-    qh_mergefacet(qh, bestfacet, bestneighbor, &mindist, &maxdist, !qh_MERGEapex);
-  }else {
-    qh_mergefacet(qh, facet2, neighbor, &mindist2, &maxdist2, !qh_MERGEapex);
-    dist= dist2;
-  }
-  if (qh->PRINTstatistics) {
-    if (mergetype == MRGanglecoplanar) {
-      zinc_(Zacoplanar);
-      wadd_(Wacoplanartot, dist);
-      wmax_(Wacoplanarmax, dist);
-    }else if (mergetype == MRGconcave) {
-      zinc_(Zconcave);
-      wadd_(Wconcavetot, dist);
-      wmax_(Wconcavemax, dist);
-    }else { /* MRGcoplanar */
-      zinc_(Zcoplanar);
-      wadd_(Wcoplanartot, dist);
-      wmax_(Wcoplanarmax, dist);
-    }
-  }
-} /* merge_nonconvex */
-
-/*---------------------------------
-
-  qh_mergecycle(qh, samecycle, newfacet )
-    merge a cycle of facets starting at samecycle into a newfacet
-    newfacet is a horizon facet with ->normal
-    samecycle facets are simplicial from an apex
-
-  returns:
-    initializes vertex neighbors on first merge
-    samecycle deleted (placed on qh.visible_list)
-    newfacet at end of qh.facet_list
-    deleted vertices on qh.del_vertices
-
-  see:
-    qh_mergefacet()
-    called by qh_mergecycle_all() for multiple, same cycle facets
-
-  design:
-    make vertex neighbors if necessary
-    make ridges for newfacet
-    merge neighbor sets of samecycle into newfacet
-    merge ridges of samecycle into newfacet
-    merge vertex neighbors of samecycle into newfacet
-    make apex of samecycle the apex of newfacet
-    if newfacet wasn't a new facet
-      add its vertices to qh.newvertex_list
-    delete samecycle facets a make newfacet a newfacet
-*/
-void qh_mergecycle(qhT *qh, facetT *samecycle, facetT *newfacet) {
-  int traceonce= False, tracerestore= 0;
-  vertexT *apex;
-#ifndef qh_NOtrace
-  facetT *same;
-#endif
-
-  if (newfacet->tricoplanar) {
-    if (!qh->TRInormals) {
-      qh_fprintf(qh, qh->ferr, 6224, "Qhull internal error (qh_mergecycle): does not work for tricoplanar facets.  Use option 'Q11'\n");
-      qh_errexit(qh, qh_ERRqhull, newfacet, NULL);
-    }
-    newfacet->tricoplanar= False;
-    newfacet->keepcentrum= False;
-  }
-  if (!qh->VERTEXneighbors)
-    qh_vertexneighbors(qh);
-  zzinc_(Ztotmerge);
-  if (qh->REPORTfreq2 && qh->POSTmerging) {
-    if (zzval_(Ztotmerge) > qh->mergereport + qh->REPORTfreq2)
-      qh_tracemerging(qh);
-  }
-#ifndef qh_NOtrace
-  if (qh->TRACEmerge == zzval_(Ztotmerge))
-    qh->qhmem.IStracing= qh->IStracing= qh->TRACElevel;
-  trace2((qh, qh->ferr, 2030, "qh_mergecycle: merge #%d for facets from cycle f%d into coplanar horizon f%d\n",
-        zzval_(Ztotmerge), samecycle->id, newfacet->id));
-  if (newfacet == qh->tracefacet) {
-    tracerestore= qh->IStracing;
-    qh->IStracing= 4;
-    qh_fprintf(qh, qh->ferr, 8068, "qh_mergecycle: ========= trace merge %d of samecycle %d into trace f%d, furthest is p%d\n",
-               zzval_(Ztotmerge), samecycle->id, newfacet->id,  qh->furthest_id);
-    traceonce= True;
-  }
-  if (qh->IStracing >=4) {
-    qh_fprintf(qh, qh->ferr, 8069, "  same cycle:");
-    FORALLsame_cycle_(samecycle)
-      qh_fprintf(qh, qh->ferr, 8070, " f%d", same->id);
-    qh_fprintf(qh, qh->ferr, 8071, "\n");
-  }
-  if (qh->IStracing >=4)
-    qh_errprint(qh, "MERGING CYCLE", samecycle, newfacet, NULL, NULL);
-#endif /* !qh_NOtrace */
-  apex= SETfirstt_(samecycle->vertices, vertexT);
-  qh_makeridges(qh, newfacet);
-  qh_mergecycle_neighbors(qh, samecycle, newfacet);
-  qh_mergecycle_ridges(qh, samecycle, newfacet);
-  qh_mergecycle_vneighbors(qh, samecycle, newfacet);
-  if (SETfirstt_(newfacet->vertices, vertexT) != apex)
-    qh_setaddnth(qh, &newfacet->vertices, 0, apex);  /* apex has last id */
-  if (!newfacet->newfacet)
-    qh_newvertices(qh, newfacet->vertices);
-  qh_mergecycle_facets(qh, samecycle, newfacet);
-  qh_tracemerge(qh, samecycle, newfacet);
-  /* check for degen_redundant_neighbors after qh_forcedmerges() */
-  if (traceonce) {
-    qh_fprintf(qh, qh->ferr, 8072, "qh_mergecycle: end of trace facet\n");
-    qh->IStracing= tracerestore;
-  }
-} /* mergecycle */
-
-/*---------------------------------
-
-  qh_mergecycle_all(qh, facetlist, wasmerge )
-    merge all samecycles of coplanar facets into horizon
-    don't merge facets with ->mergeridge (these already have ->normal)
-    all facets are simplicial from apex
-    all facet->cycledone == False
-
-  returns:
-    all newfacets merged into coplanar horizon facets
-    deleted vertices on  qh.del_vertices
-    sets wasmerge if any merge
-
-  see:
-    calls qh_mergecycle for multiple, same cycle facets
-
-  design:
-    for each facet on facetlist
-      skip facets with duplicate ridges and normals
-      check that facet is in a samecycle (->mergehorizon)
-      if facet only member of samecycle
-        sets vertex->delridge for all vertices except apex
-        merge facet into horizon
-      else
-        mark all facets in samecycle
-        remove facets with duplicate ridges from samecycle
-        merge samecycle into horizon (deletes facets from facetlist)
-*/
-void qh_mergecycle_all(qhT *qh, facetT *facetlist, boolT *wasmerge) {
-  facetT *facet, *same, *prev, *horizon;
-  facetT *samecycle= NULL, *nextfacet, *nextsame;
-  vertexT *apex, *vertex, **vertexp;
-  int cycles=0, total=0, facets, nummerge;
-
-  trace2((qh, qh->ferr, 2031, "qh_mergecycle_all: begin\n"));
-  for (facet= facetlist; facet && (nextfacet= facet->next); facet= nextfacet) {
-    if (facet->normal)
-      continue;
-    if (!facet->mergehorizon) {
-      qh_fprintf(qh, qh->ferr, 6225, "Qhull internal error (qh_mergecycle_all): f%d without normal\n", facet->id);
-      qh_errexit(qh, qh_ERRqhull, facet, NULL);
-    }
-    horizon= SETfirstt_(facet->neighbors, facetT);
-    if (facet->f.samecycle == facet) {
-      zinc_(Zonehorizon);
-      /* merge distance done in qh_findhorizon */
-      apex= SETfirstt_(facet->vertices, vertexT);
-      FOREACHvertex_(facet->vertices) {
-        if (vertex != apex)
-          vertex->delridge= True;
-      }
-      horizon->f.newcycle= NULL;
-      qh_mergefacet(qh, facet, horizon, NULL, NULL, qh_MERGEapex);
-    }else {
-      samecycle= facet;
-      facets= 0;
-      prev= facet;
-      for (same= facet->f.samecycle; same;  /* FORALLsame_cycle_(facet) */
-           same= (same == facet ? NULL :nextsame)) { /* ends at facet */
-        nextsame= same->f.samecycle;
-        if (same->cycledone || same->visible)
-          qh_infiniteloop(qh, same);
-        same->cycledone= True;
-        if (same->normal) {
-          prev->f.samecycle= same->f.samecycle; /* unlink ->mergeridge */
-          same->f.samecycle= NULL;
-        }else {
-          prev= same;
-          facets++;
-        }
-      }
-      while (nextfacet && nextfacet->cycledone)  /* will delete samecycle */
-        nextfacet= nextfacet->next;
-      horizon->f.newcycle= NULL;
-      qh_mergecycle(qh, samecycle, horizon);
-      nummerge= horizon->nummerge + facets;
-      if (nummerge > qh_MAXnummerge)
-        horizon->nummerge= qh_MAXnummerge;
-      else
-        horizon->nummerge= (short unsigned int)nummerge;
-      zzinc_(Zcyclehorizon);
-      total += facets;
-      zzadd_(Zcyclefacettot, facets);
-      zmax_(Zcyclefacetmax, facets);
-    }
-    cycles++;
-  }
-  if (cycles)
-    *wasmerge= True;
-  trace1((qh, qh->ferr, 1013, "qh_mergecycle_all: merged %d same cycles or facets into coplanar horizons\n", cycles));
-} /* mergecycle_all */
-
-/*---------------------------------
-
-  qh_mergecycle_facets(qh, samecycle, newfacet )
-    finish merge of samecycle into newfacet
-
-  returns:
-    samecycle prepended to visible_list for later deletion and partitioning
-      each facet->f.replace == newfacet
-
-    newfacet moved to end of qh.facet_list
-      makes newfacet a newfacet (get's facet1->id if it was old)
-      sets newfacet->newmerge
-      clears newfacet->center (unless merging into a large facet)
-      clears newfacet->tested and ridge->tested for facet1
-
-    adds neighboring facets to facet_mergeset if redundant or degenerate
-
-  design:
-    make newfacet a new facet and set its flags
-    move samecycle facets to qh.visible_list for later deletion
-    unless newfacet is large
-      remove its centrum
-*/
-void qh_mergecycle_facets(qhT *qh, facetT *samecycle, facetT *newfacet) {
-  facetT *same, *next;
-
-  trace4((qh, qh->ferr, 4030, "qh_mergecycle_facets: make newfacet new and samecycle deleted\n"));
-  qh_removefacet(qh, newfacet);  /* append as a newfacet to end of qh->facet_list */
-  qh_appendfacet(qh, newfacet);
-  newfacet->newfacet= True;
-  newfacet->simplicial= False;
-  newfacet->newmerge= True;
-
-  for (same= samecycle->f.samecycle; same; same= (same == samecycle ?  NULL : next)) {
-    next= same->f.samecycle;  /* reused by willdelete */
-    qh_willdelete(qh, same, newfacet);
-  }
-  if (newfacet->center
-      && qh_setsize(qh, newfacet->vertices) <= qh->hull_dim + qh_MAXnewcentrum) {
-    qh_memfree(qh, newfacet->center, qh->normal_size);
-    newfacet->center= NULL;
-  }
-  trace3((qh, qh->ferr, 3004, "qh_mergecycle_facets: merged facets from cycle f%d into f%d\n",
-             samecycle->id, newfacet->id));
-} /* mergecycle_facets */
-
-/*---------------------------------
-
-  qh_mergecycle_neighbors(qh, samecycle, newfacet )
-    add neighbors for samecycle facets to newfacet
-
-  returns:
-    newfacet with updated neighbors and vice-versa
-    newfacet has ridges
-    all neighbors of newfacet marked with qh.visit_id
-    samecycle facets marked with qh.visit_id-1
-    ridges updated for simplicial neighbors of samecycle with a ridge
-
-  notes:
-    assumes newfacet not in samecycle
-    usually, samecycle facets are new, simplicial facets without internal ridges
-      not so if horizon facet is coplanar to two different samecycles
-
-  see:
-    qh_mergeneighbors()
-
-  design:
-    check samecycle
-    delete neighbors from newfacet that are also in samecycle
-    for each neighbor of a facet in samecycle
-      if neighbor is simplicial
-        if first visit
-          move the neighbor relation to newfacet
-          update facet links for its ridges
-        else
-          make ridges for neighbor
-          remove samecycle reference
-      else
-        update neighbor sets
-*/
-void qh_mergecycle_neighbors(qhT *qh, facetT *samecycle, facetT *newfacet) {
-  facetT *same, *neighbor, **neighborp;
-  int delneighbors= 0, newneighbors= 0;
-  unsigned int samevisitid;
-  ridgeT *ridge, **ridgep;
-
-  samevisitid= ++qh->visit_id;
-  FORALLsame_cycle_(samecycle) {
-    if (same->visitid == samevisitid || same->visible)
-      qh_infiniteloop(qh, samecycle);
-    same->visitid= samevisitid;
-  }
-  newfacet->visitid= ++qh->visit_id;
-  trace4((qh, qh->ferr, 4031, "qh_mergecycle_neighbors: delete shared neighbors from newfacet\n"));
-  FOREACHneighbor_(newfacet) {
-    if (neighbor->visitid == samevisitid) {
-      SETref_(neighbor)= NULL;  /* samecycle neighbors deleted */
-      delneighbors++;
-    }else
-      neighbor->visitid= qh->visit_id;
-  }
-  qh_setcompact(qh, newfacet->neighbors);
-
-  trace4((qh, qh->ferr, 4032, "qh_mergecycle_neighbors: update neighbors\n"));
-  FORALLsame_cycle_(samecycle) {
-    FOREACHneighbor_(same) {
-      if (neighbor->visitid == samevisitid)
-        continue;
-      if (neighbor->simplicial) {
-        if (neighbor->visitid != qh->visit_id) {
-          qh_setappend(qh, &newfacet->neighbors, neighbor);
-          qh_setreplace(qh, neighbor->neighbors, same, newfacet);
-          newneighbors++;
-          neighbor->visitid= qh->visit_id;
-          FOREACHridge_(neighbor->ridges) { /* update ridge in case of qh_makeridges */
-            if (ridge->top == same) {
-              ridge->top= newfacet;
-              break;
-            }else if (ridge->bottom == same) {
-              ridge->bottom= newfacet;
-              break;
-            }
-          }
-        }else {
-          qh_makeridges(qh, neighbor);
-          qh_setdel(neighbor->neighbors, same);
-          /* same can't be horizon facet for neighbor */
-        }
-      }else { /* non-simplicial neighbor */
-        qh_setdel(neighbor->neighbors, same);
-        if (neighbor->visitid != qh->visit_id) {
-          qh_setappend(qh, &neighbor->neighbors, newfacet);
-          qh_setappend(qh, &newfacet->neighbors, neighbor);
-          neighbor->visitid= qh->visit_id;
-          newneighbors++;
-        }
-      }
-    }
-  }
-  trace2((qh, qh->ferr, 2032, "qh_mergecycle_neighbors: deleted %d neighbors and added %d\n",
-             delneighbors, newneighbors));
-} /* mergecycle_neighbors */
-
-/*---------------------------------
-
-  qh_mergecycle_ridges(qh, samecycle, newfacet )
-    add ridges/neighbors for facets in samecycle to newfacet
-    all new/old neighbors of newfacet marked with qh.visit_id
-    facets in samecycle marked with qh.visit_id-1
-    newfacet marked with qh.visit_id
-
-  returns:
-    newfacet has merged ridges
-
-  notes:
-    ridge already updated for simplicial neighbors of samecycle with a ridge
-
-  see:
-    qh_mergeridges()
-    qh_makeridges()
-
-  design:
-    remove ridges between newfacet and samecycle
-    for each facet in samecycle
-      for each ridge in facet
-        update facet pointers in ridge
-        skip ridges processed in qh_mergecycle_neighors
-        free ridges between newfacet and samecycle
-        free ridges between facets of samecycle (on 2nd visit)
-        append remaining ridges to newfacet
-      if simpilicial facet
-        for each neighbor of facet
-          if simplicial facet
-          and not samecycle facet or newfacet
-            make ridge between neighbor and newfacet
-*/
-void qh_mergecycle_ridges(qhT *qh, facetT *samecycle, facetT *newfacet) {
-  facetT *same, *neighbor= NULL;
-  int numold=0, numnew=0;
-  int neighbor_i, neighbor_n;
-  unsigned int samevisitid;
-  ridgeT *ridge, **ridgep;
-  boolT toporient;
-  void **freelistp; /* used if !qh_NOmem by qh_memfree_() */
-
-  trace4((qh, qh->ferr, 4033, "qh_mergecycle_ridges: delete shared ridges from newfacet\n"));
-  samevisitid= qh->visit_id -1;
-  FOREACHridge_(newfacet->ridges) {
-    neighbor= otherfacet_(ridge, newfacet);
-    if (neighbor->visitid == samevisitid)
-      SETref_(ridge)= NULL; /* ridge free'd below */
-  }
-  qh_setcompact(qh, newfacet->ridges);
-
-  trace4((qh, qh->ferr, 4034, "qh_mergecycle_ridges: add ridges to newfacet\n"));
-  FORALLsame_cycle_(samecycle) {
-    FOREACHridge_(same->ridges) {
-      if (ridge->top == same) {
-        ridge->top= newfacet;
-        neighbor= ridge->bottom;
-      }else if (ridge->bottom == same) {
-        ridge->bottom= newfacet;
-        neighbor= ridge->top;
-      }else if (ridge->top == newfacet || ridge->bottom == newfacet) {
-        qh_setappend(qh, &newfacet->ridges, ridge);
-        numold++;  /* already set by qh_mergecycle_neighbors */
-        continue;
-      }else {
-        qh_fprintf(qh, qh->ferr, 6098, "qhull internal error (qh_mergecycle_ridges): bad ridge r%d\n", ridge->id);
-        qh_errexit(qh, qh_ERRqhull, NULL, ridge);
-      }
-      if (neighbor == newfacet) {
-        qh_setfree(qh, &(ridge->vertices));
-        qh_memfree_(qh, ridge, (int)sizeof(ridgeT), freelistp);
-        numold++;
-      }else if (neighbor->visitid == samevisitid) {
-        qh_setdel(neighbor->ridges, ridge);
-        qh_setfree(qh, &(ridge->vertices));
-        qh_memfree_(qh, ridge, (int)sizeof(ridgeT), freelistp);
-        numold++;
-      }else {
-        qh_setappend(qh, &newfacet->ridges, ridge);
-        numold++;
-      }
-    }
-    if (same->ridges)
-      qh_settruncate(qh, same->ridges, 0);
-    if (!same->simplicial)
-      continue;
-    FOREACHneighbor_i_(qh, same) {       /* note: !newfact->simplicial */
-      if (neighbor->visitid != samevisitid && neighbor->simplicial) {
-        ridge= qh_newridge(qh);
-        ridge->vertices= qh_setnew_delnthsorted(qh, same->vertices, qh->hull_dim,
-                                                          neighbor_i, 0);
-        toporient= same->toporient ^ (neighbor_i & 0x1);
-        if (toporient) {
-          ridge->top= newfacet;
-          ridge->bottom= neighbor;
-        }else {
-          ridge->top= neighbor;
-          ridge->bottom= newfacet;
-        }
-        qh_setappend(qh, &(newfacet->ridges), ridge);
-        qh_setappend(qh, &(neighbor->ridges), ridge);
-        numnew++;
-      }
-    }
-  }
-
-  trace2((qh, qh->ferr, 2033, "qh_mergecycle_ridges: found %d old ridges and %d new ones\n",
-             numold, numnew));
-} /* mergecycle_ridges */
-
-/*---------------------------------
-
-  qh_mergecycle_vneighbors(qh, samecycle, newfacet )
-    create vertex neighbors for newfacet from vertices of facets in samecycle
-    samecycle marked with visitid == qh.visit_id - 1
-
-  returns:
-    newfacet vertices with updated neighbors
-    marks newfacet with qh.visit_id-1
-    deletes vertices that are merged away
-    sets delridge on all vertices (faster here than in mergecycle_ridges)
-
-  see:
-    qh_mergevertex_neighbors()
-
-  design:
-    for each vertex of samecycle facet
-      set vertex->delridge
-      delete samecycle facets from vertex neighbors
-      append newfacet to vertex neighbors
-      if vertex only in newfacet
-        delete it from newfacet
-        add it to qh.del_vertices for later deletion
-*/
-void qh_mergecycle_vneighbors(qhT *qh, facetT *samecycle, facetT *newfacet) {
-  facetT *neighbor, **neighborp;
-  unsigned int mergeid;
-  vertexT *vertex, **vertexp, *apex;
-  setT *vertices;
-
-  trace4((qh, qh->ferr, 4035, "qh_mergecycle_vneighbors: update vertex neighbors for newfacet\n"));
-  mergeid= qh->visit_id - 1;
-  newfacet->visitid= mergeid;
-  vertices= qh_basevertices(qh, samecycle); /* temp */
-  apex= SETfirstt_(samecycle->vertices, vertexT);
-  qh_setappend(qh, &vertices, apex);
-  FOREACHvertex_(vertices) {
-    vertex->delridge= True;
-    FOREACHneighbor_(vertex) {
-      if (neighbor->visitid == mergeid)
-        SETref_(neighbor)= NULL;
-    }
-    qh_setcompact(qh, vertex->neighbors);
-    qh_setappend(qh, &vertex->neighbors, newfacet);
-    if (!SETsecond_(vertex->neighbors)) {
-      zinc_(Zcyclevertex);
-      trace2((qh, qh->ferr, 2034, "qh_mergecycle_vneighbors: deleted v%d when merging cycle f%d into f%d\n",
-        vertex->id, samecycle->id, newfacet->id));
-      qh_setdelsorted(newfacet->vertices, vertex);
-      vertex->deleted= True;
-      qh_setappend(qh, &qh->del_vertices, vertex);
-    }
-  }
-  qh_settempfree(qh, &vertices);
-  trace3((qh, qh->ferr, 3005, "qh_mergecycle_vneighbors: merged vertices from cycle f%d into f%d\n",
-             samecycle->id, newfacet->id));
-} /* mergecycle_vneighbors */
-
-/*---------------------------------
-
-  qh_mergefacet(qh, facet1, facet2, mindist, maxdist, mergeapex )
-    merges facet1 into facet2
-    mergeapex==qh_MERGEapex if merging new facet into coplanar horizon
-
-  returns:
-    qh.max_outside and qh.min_vertex updated
-    initializes vertex neighbors on first merge
-
-  returns:
-    facet2 contains facet1's vertices, neighbors, and ridges
-      facet2 moved to end of qh.facet_list
-      makes facet2 a newfacet
-      sets facet2->newmerge set
-      clears facet2->center (unless merging into a large facet)
-      clears facet2->tested and ridge->tested for facet1
-
-    facet1 prepended to visible_list for later deletion and partitioning
-      facet1->f.replace == facet2
-
-    adds neighboring facets to facet_mergeset if redundant or degenerate
-
-  notes:
-    mindist/maxdist may be NULL (only if both NULL)
-    traces merge if fmax_(maxdist,-mindist) > TRACEdist
-
-  see:
-    qh_mergecycle()
-
-  design:
-    trace merge and check for degenerate simplex
-    make ridges for both facets
-    update qh.max_outside, qh.max_vertex, qh.min_vertex
-    update facet2->maxoutside and keepcentrum
-    update facet2->nummerge
-    update tested flags for facet2
-    if facet1 is simplicial
-      merge facet1 into facet2
-    else
-      merge facet1's neighbors into facet2
-      merge facet1's ridges into facet2
-      merge facet1's vertices into facet2
-      merge facet1's vertex neighbors into facet2
-      add facet2's vertices to qh.new_vertexlist
-      unless qh_MERGEapex
-        test facet2 for degenerate or redundant neighbors
-      move facet1 to qh.visible_list for later deletion
-      move facet2 to end of qh.newfacet_list
-*/
-void qh_mergefacet(qhT *qh, facetT *facet1, facetT *facet2, realT *mindist, realT *maxdist, boolT mergeapex) {
-  boolT traceonce= False;
-  vertexT *vertex, **vertexp;
-  int tracerestore=0, nummerge;
-
-  if (facet1->tricoplanar || facet2->tricoplanar) {
-    if (!qh->TRInormals) {
-      qh_fprintf(qh, qh->ferr, 6226, "Qhull internal error (qh_mergefacet): does not work for tricoplanar facets.  Use option 'Q11'\n");
-      qh_errexit2(qh, qh_ERRqhull, facet1, facet2);
-    }
-    if (facet2->tricoplanar) {
-      facet2->tricoplanar= False;
-      facet2->keepcentrum= False;
-    }
-  }
-  zzinc_(Ztotmerge);
-  if (qh->REPORTfreq2 && qh->POSTmerging) {
-    if (zzval_(Ztotmerge) > qh->mergereport + qh->REPORTfreq2)
-      qh_tracemerging(qh);
-  }
-#ifndef qh_NOtrace
-  if (qh->build_cnt >= qh->RERUN) {
-    if (mindist && (-*mindist > qh->TRACEdist || *maxdist > qh->TRACEdist)) {
-      tracerestore= 0;
-      qh->IStracing= qh->TRACElevel;
-      traceonce= True;
-      qh_fprintf(qh, qh->ferr, 8075, "qh_mergefacet: ========= trace wide merge #%d(%2.2g) for f%d into f%d, last point was p%d\n", zzval_(Ztotmerge),
-             fmax_(-*mindist, *maxdist), facet1->id, facet2->id, qh->furthest_id);
-    }else if (facet1 == qh->tracefacet || facet2 == qh->tracefacet) {
-      tracerestore= qh->IStracing;
-      qh->IStracing= 4;
-      traceonce= True;
-      qh_fprintf(qh, qh->ferr, 8076, "qh_mergefacet: ========= trace merge #%d involving f%d, furthest is p%d\n",
-                 zzval_(Ztotmerge), qh->tracefacet_id,  qh->furthest_id);
-    }
-  }
-  if (qh->IStracing >= 2) {
-    realT mergemin= -2;
-    realT mergemax= -2;
-
-    if (mindist) {
-      mergemin= *mindist;
-      mergemax= *maxdist;
-    }
-    qh_fprintf(qh, qh->ferr, 8077, "qh_mergefacet: #%d merge f%d into f%d, mindist= %2.2g, maxdist= %2.2g\n",
-    zzval_(Ztotmerge), facet1->id, facet2->id, mergemin, mergemax);
-  }
-#endif /* !qh_NOtrace */
-  if (facet1 == facet2 || facet1->visible || facet2->visible) {
-    qh_fprintf(qh, qh->ferr, 6099, "qhull internal error (qh_mergefacet): either f%d and f%d are the same or one is a visible facet\n",
-             facet1->id, facet2->id);
-    qh_errexit2(qh, qh_ERRqhull, facet1, facet2);
-  }
-  if (qh->num_facets - qh->num_visible <= qh->hull_dim + 1) {
-    qh_fprintf(qh, qh->ferr, 6227, "\n\
-qhull precision error: Only %d facets remain.  Can not merge another\n\
-pair.  The input is too degenerate or the convexity constraints are\n\
-too strong.\n", qh->hull_dim+1);
-    if (qh->hull_dim >= 5 && !qh->MERGEexact)
-      qh_fprintf(qh, qh->ferr, 8079, "Option 'Qx' may avoid this problem.\n");
-    qh_errexit(qh, qh_ERRprec, NULL, NULL);
-  }
-  if (!qh->VERTEXneighbors)
-    qh_vertexneighbors(qh);
-  qh_makeridges(qh, facet1);
-  qh_makeridges(qh, facet2);
-  if (qh->IStracing >=4)
-    qh_errprint(qh, "MERGING", facet1, facet2, NULL, NULL);
-  if (mindist) {
-    maximize_(qh->max_outside, *maxdist);
-    maximize_(qh->max_vertex, *maxdist);
-#if qh_MAXoutside
-    maximize_(facet2->maxoutside, *maxdist);
-#endif
-    minimize_(qh->min_vertex, *mindist);
-    if (!facet2->keepcentrum
-    && (*maxdist > qh->WIDEfacet || *mindist < -qh->WIDEfacet)) {
-      facet2->keepcentrum= True;
-      zinc_(Zwidefacet);
-    }
-  }
-  nummerge= facet1->nummerge + facet2->nummerge + 1;
-  if (nummerge >= qh_MAXnummerge)
-    facet2->nummerge= qh_MAXnummerge;
-  else
-    facet2->nummerge= (short unsigned int)nummerge;
-  facet2->newmerge= True;
-  facet2->dupridge= False;
-  qh_updatetested(qh, facet1, facet2);
-  if (qh->hull_dim > 2 && qh_setsize(qh, facet1->vertices) == qh->hull_dim)
-    qh_mergesimplex(qh, facet1, facet2, mergeapex);
-  else {
-    qh->vertex_visit++;
-    FOREACHvertex_(facet2->vertices)
-      vertex->visitid= qh->vertex_visit;
-    if (qh->hull_dim == 2)
-      qh_mergefacet2d(qh, facet1, facet2);
-    else {
-      qh_mergeneighbors(qh, facet1, facet2);
-      qh_mergevertices(qh, facet1->vertices, &facet2->vertices);
-    }
-    qh_mergeridges(qh, facet1, facet2);
-    qh_mergevertex_neighbors(qh, facet1, facet2);
-    if (!facet2->newfacet)
-      qh_newvertices(qh, facet2->vertices);
-  }
-  if (!mergeapex)
-    qh_degen_redundant_neighbors(qh, facet2, facet1);
-  if (facet2->coplanar || !facet2->newfacet) {
-    zinc_(Zmergeintohorizon);
-  }else if (!facet1->newfacet && facet2->newfacet) {
-    zinc_(Zmergehorizon);
-  }else {
-    zinc_(Zmergenew);
-  }
-  qh_willdelete(qh, facet1, facet2);
-  qh_removefacet(qh, facet2);  /* append as a newfacet to end of qh->facet_list */
-  qh_appendfacet(qh, facet2);
-  facet2->newfacet= True;
-  facet2->tested= False;
-  qh_tracemerge(qh, facet1, facet2);
-  if (traceonce) {
-    qh_fprintf(qh, qh->ferr, 8080, "qh_mergefacet: end of wide tracing\n");
-    qh->IStracing= tracerestore;
-  }
-} /* mergefacet */
-
-
-/*---------------------------------
-
-  qh_mergefacet2d(qh, facet1, facet2 )
-    in 2d, merges neighbors and vertices of facet1 into facet2
-
-  returns:
-    build ridges for neighbors if necessary
-    facet2 looks like a simplicial facet except for centrum, ridges
-      neighbors are opposite the corresponding vertex
-      maintains orientation of facet2
-
-  notes:
-    qh_mergefacet() retains non-simplicial structures
-      they are not needed in 2d, but later routines may use them
-    preserves qh.vertex_visit for qh_mergevertex_neighbors()
-
-  design:
-    get vertices and neighbors
-    determine new vertices and neighbors
-    set new vertices and neighbors and adjust orientation
-    make ridges for new neighbor if needed
-*/
-void qh_mergefacet2d(qhT *qh, facetT *facet1, facetT *facet2) {
-  vertexT *vertex1A, *vertex1B, *vertex2A, *vertex2B, *vertexA, *vertexB;
-  facetT *neighbor1A, *neighbor1B, *neighbor2A, *neighbor2B, *neighborA, *neighborB;
-
-  vertex1A= SETfirstt_(facet1->vertices, vertexT);
-  vertex1B= SETsecondt_(facet1->vertices, vertexT);
-  vertex2A= SETfirstt_(facet2->vertices, vertexT);
-  vertex2B= SETsecondt_(facet2->vertices, vertexT);
-  neighbor1A= SETfirstt_(facet1->neighbors, facetT);
-  neighbor1B= SETsecondt_(facet1->neighbors, facetT);
-  neighbor2A= SETfirstt_(facet2->neighbors, facetT);
-  neighbor2B= SETsecondt_(facet2->neighbors, facetT);
-  if (vertex1A == vertex2A) {
-    vertexA= vertex1B;
-    vertexB= vertex2B;
-    neighborA= neighbor2A;
-    neighborB= neighbor1A;
-  }else if (vertex1A == vertex2B) {
-    vertexA= vertex1B;
-    vertexB= vertex2A;
-    neighborA= neighbor2B;
-    neighborB= neighbor1A;
-  }else if (vertex1B == vertex2A) {
-    vertexA= vertex1A;
-    vertexB= vertex2B;
-    neighborA= neighbor2A;
-    neighborB= neighbor1B;
-  }else { /* 1B == 2B */
-    vertexA= vertex1A;
-    vertexB= vertex2A;
-    neighborA= neighbor2B;
-    neighborB= neighbor1B;
-  }
-  /* vertexB always from facet2, neighborB always from facet1 */
-  if (vertexA->id > vertexB->id) {
-    SETfirst_(facet2->vertices)= vertexA;
-    SETsecond_(facet2->vertices)= vertexB;
-    if (vertexB == vertex2A)
-      facet2->toporient= !facet2->toporient;
-    SETfirst_(facet2->neighbors)= neighborA;
-    SETsecond_(facet2->neighbors)= neighborB;
-  }else {
-    SETfirst_(facet2->vertices)= vertexB;
-    SETsecond_(facet2->vertices)= vertexA;
-    if (vertexB == vertex2B)
-      facet2->toporient= !facet2->toporient;
-    SETfirst_(facet2->neighbors)= neighborB;
-    SETsecond_(facet2->neighbors)= neighborA;
-  }
-  qh_makeridges(qh, neighborB);
-  qh_setreplace(qh, neighborB->neighbors, facet1, facet2);
-  trace4((qh, qh->ferr, 4036, "qh_mergefacet2d: merged v%d and neighbor f%d of f%d into f%d\n",
-       vertexA->id, neighborB->id, facet1->id, facet2->id));
-} /* mergefacet2d */
-
-
-/*---------------------------------
-
-  qh_mergeneighbors(qh, facet1, facet2 )
-    merges the neighbors of facet1 into facet2
-
-  see:
-    qh_mergecycle_neighbors()
-
-  design:
-    for each neighbor of facet1
-      if neighbor is also a neighbor of facet2
-        if neighbor is simpilicial
-          make ridges for later deletion as a degenerate facet
-        update its neighbor set
-      else
-        move the neighbor relation to facet2
-    remove the neighbor relation for facet1 and facet2
-*/
-void qh_mergeneighbors(qhT *qh, facetT *facet1, facetT *facet2) {
-  facetT *neighbor, **neighborp;
-
-  trace4((qh, qh->ferr, 4037, "qh_mergeneighbors: merge neighbors of f%d and f%d\n",
-          facet1->id, facet2->id));
-  qh->visit_id++;
-  FOREACHneighbor_(facet2) {
-    neighbor->visitid= qh->visit_id;
-  }
-  FOREACHneighbor_(facet1) {
-    if (neighbor->visitid == qh->visit_id) {
-      if (neighbor->simplicial)    /* is degen, needs ridges */
-        qh_makeridges(qh, neighbor);
-      if (SETfirstt_(neighbor->neighbors, facetT) != facet1) /*keep newfacet->horizon*/
-        qh_setdel(neighbor->neighbors, facet1);
-      else {
-        qh_setdel(neighbor->neighbors, facet2);
-        qh_setreplace(qh, neighbor->neighbors, facet1, facet2);
-      }
-    }else if (neighbor != facet2) {
-      qh_setappend(qh, &(facet2->neighbors), neighbor);
-      qh_setreplace(qh, neighbor->neighbors, facet1, facet2);
-    }
-  }
-  qh_setdel(facet1->neighbors, facet2);  /* here for makeridges */
-  qh_setdel(facet2->neighbors, facet1);
-} /* mergeneighbors */
-
-
-/*---------------------------------
-
-  qh_mergeridges(qh, facet1, facet2 )
-    merges the ridge set of facet1 into facet2
-
-  returns:
-    may delete all ridges for a vertex
-    sets vertex->delridge on deleted ridges
-
-  see:
-    qh_mergecycle_ridges()
-
-  design:
-    delete ridges between facet1 and facet2
-      mark (delridge) vertices on these ridges for later testing
-    for each remaining ridge
-      rename facet1 to facet2
-*/
-void qh_mergeridges(qhT *qh, facetT *facet1, facetT *facet2) {
-  ridgeT *ridge, **ridgep;
-  vertexT *vertex, **vertexp;
-
-  trace4((qh, qh->ferr, 4038, "qh_mergeridges: merge ridges of f%d and f%d\n",
-          facet1->id, facet2->id));
-  FOREACHridge_(facet2->ridges) {
-    if ((ridge->top == facet1) || (ridge->bottom == facet1)) {
-      FOREACHvertex_(ridge->vertices)
-        vertex->delridge= True;
-      qh_delridge(qh, ridge);  /* expensive in high-d, could rebuild */
-      ridgep--; /*repeat*/
-    }
-  }
-  FOREACHridge_(facet1->ridges) {
-    if (ridge->top == facet1)
-      ridge->top= facet2;
-    else
-      ridge->bottom= facet2;
-    qh_setappend(qh, &(facet2->ridges), ridge);
-  }
-} /* mergeridges */
-
-
-/*---------------------------------
-
-  qh_mergesimplex(qh, facet1, facet2, mergeapex )
-    merge simplicial facet1 into facet2
-    mergeapex==qh_MERGEapex if merging samecycle into horizon facet
-      vertex id is latest (most recently created)
-    facet1 may be contained in facet2
-    ridges exist for both facets
-
-  returns:
-    facet2 with updated vertices, ridges, neighbors
-    updated neighbors for facet1's vertices
-    facet1 not deleted
-    sets vertex->delridge on deleted ridges
-
-  notes:
-    special case code since this is the most common merge
-    called from qh_mergefacet()
-
-  design:
-    if qh_MERGEapex
-      add vertices of facet2 to qh.new_vertexlist if necessary
-      add apex to facet2
-    else
-      for each ridge between facet1 and facet2
-        set vertex->delridge
-      determine the apex for facet1 (i.e., vertex to be merged)
-      unless apex already in facet2
-        insert apex into vertices for facet2
-      add vertices of facet2 to qh.new_vertexlist if necessary
-      add apex to qh.new_vertexlist if necessary
-      for each vertex of facet1
-        if apex
-          rename facet1 to facet2 in its vertex neighbors
-        else
-          delete facet1 from vertex neighors
-          if only in facet2
-            add vertex to qh.del_vertices for later deletion
-      for each ridge of facet1
-        delete ridges between facet1 and facet2
-        append other ridges to facet2 after renaming facet to facet2
-*/
-void qh_mergesimplex(qhT *qh, facetT *facet1, facetT *facet2, boolT mergeapex) {
-  vertexT *vertex, **vertexp, *apex;
-  ridgeT *ridge, **ridgep;
-  boolT issubset= False;
-  int vertex_i= -1, vertex_n;
-  facetT *neighbor, **neighborp, *otherfacet;
-
-  if (mergeapex) {
-    if (!facet2->newfacet)
-      qh_newvertices(qh, facet2->vertices);  /* apex is new */
-    apex= SETfirstt_(facet1->vertices, vertexT);
-    if (SETfirstt_(facet2->vertices, vertexT) != apex)
-      qh_setaddnth(qh, &facet2->vertices, 0, apex);  /* apex has last id */
-    else
-      issubset= True;
-  }else {
-    zinc_(Zmergesimplex);
-    FOREACHvertex_(facet1->vertices)
-      vertex->seen= False;
-    FOREACHridge_(facet1->ridges) {
-      if (otherfacet_(ridge, facet1) == facet2) {
-        FOREACHvertex_(ridge->vertices) {
-          vertex->seen= True;
-          vertex->delridge= True;
-        }
-        break;
-      }
-    }
-    FOREACHvertex_(facet1->vertices) {
-      if (!vertex->seen)
-        break;  /* must occur */
-    }
-    apex= vertex;
-    trace4((qh, qh->ferr, 4039, "qh_mergesimplex: merge apex v%d of f%d into facet f%d\n",
-          apex->id, facet1->id, facet2->id));
-    FOREACHvertex_i_(qh, facet2->vertices) {
-      if (vertex->id < apex->id) {
-        break;
-      }else if (vertex->id == apex->id) {
-        issubset= True;
-        break;
-      }
-    }
-    if (!issubset)
-      qh_setaddnth(qh, &facet2->vertices, vertex_i, apex);
-    if (!facet2->newfacet)
-      qh_newvertices(qh, facet2->vertices);
-    else if (!apex->newlist) {
-      qh_removevertex(qh, apex);
-      qh_appendvertex(qh, apex);
-    }
-  }
-  trace4((qh, qh->ferr, 4040, "qh_mergesimplex: update vertex neighbors of f%d\n",
-          facet1->id));
-  FOREACHvertex_(facet1->vertices) {
-    if (vertex == apex && !issubset)
-      qh_setreplace(qh, vertex->neighbors, facet1, facet2);
-    else {
-      qh_setdel(vertex->neighbors, facet1);
-      if (!SETsecond_(vertex->neighbors))
-        qh_mergevertex_del(qh, vertex, facet1, facet2);
-    }
-  }
-  trace4((qh, qh->ferr, 4041, "qh_mergesimplex: merge ridges and neighbors of f%d into f%d\n",
-          facet1->id, facet2->id));
-  qh->visit_id++;
-  FOREACHneighbor_(facet2)
-    neighbor->visitid= qh->visit_id;
-  FOREACHridge_(facet1->ridges) {
-    otherfacet= otherfacet_(ridge, facet1);
-    if (otherfacet == facet2) {
-      qh_setdel(facet2->ridges, ridge);
-      qh_setfree(qh, &(ridge->vertices));
-      qh_memfree(qh, ridge, (int)sizeof(ridgeT));
-      qh_setdel(facet2->neighbors, facet1);
-    }else {
-      qh_setappend(qh, &facet2->ridges, ridge);
-      if (otherfacet->visitid != qh->visit_id) {
-        qh_setappend(qh, &facet2->neighbors, otherfacet);
-        qh_setreplace(qh, otherfacet->neighbors, facet1, facet2);
-        otherfacet->visitid= qh->visit_id;
-      }else {
-        if (otherfacet->simplicial)    /* is degen, needs ridges */
-          qh_makeridges(qh, otherfacet);
-        if (SETfirstt_(otherfacet->neighbors, facetT) != facet1)
-          qh_setdel(otherfacet->neighbors, facet1);
-        else {   /*keep newfacet->neighbors->horizon*/
-          qh_setdel(otherfacet->neighbors, facet2);
-          qh_setreplace(qh, otherfacet->neighbors, facet1, facet2);
-        }
-      }
-      if (ridge->top == facet1) /* wait until after qh_makeridges */
-        ridge->top= facet2;
-      else
-        ridge->bottom= facet2;
-    }
-  }
-  SETfirst_(facet1->ridges)= NULL; /* it will be deleted */
-  trace3((qh, qh->ferr, 3006, "qh_mergesimplex: merged simplex f%d apex v%d into facet f%d\n",
-          facet1->id, getid_(apex), facet2->id));
-} /* mergesimplex */
-
-/*---------------------------------
-
-  qh_mergevertex_del(qh, vertex, facet1, facet2 )
-    delete a vertex because of merging facet1 into facet2
-
-  returns:
-    deletes vertex from facet2
-    adds vertex to qh.del_vertices for later deletion
-*/
-void qh_mergevertex_del(qhT *qh, vertexT *vertex, facetT *facet1, facetT *facet2) {
-
-  zinc_(Zmergevertex);
-  trace2((qh, qh->ferr, 2035, "qh_mergevertex_del: deleted v%d when merging f%d into f%d\n",
-          vertex->id, facet1->id, facet2->id));
-  qh_setdelsorted(facet2->vertices, vertex);
-  vertex->deleted= True;
-  qh_setappend(qh, &qh->del_vertices, vertex);
-} /* mergevertex_del */
-
-/*---------------------------------
-
-  qh_mergevertex_neighbors(qh, facet1, facet2 )
-    merge the vertex neighbors of facet1 to facet2
-
-  returns:
-    if vertex is current qh.vertex_visit
-      deletes facet1 from vertex->neighbors
-    else
-      renames facet1 to facet2 in vertex->neighbors
-    deletes vertices if only one neighbor
-
-  notes:
-    assumes vertex neighbor sets are good
-*/
-void qh_mergevertex_neighbors(qhT *qh, facetT *facet1, facetT *facet2) {
-  vertexT *vertex, **vertexp;
-
-  trace4((qh, qh->ferr, 4042, "qh_mergevertex_neighbors: merge vertex neighbors of f%d and f%d\n",
-          facet1->id, facet2->id));
-  if (qh->tracevertex) {
-    qh_fprintf(qh, qh->ferr, 8081, "qh_mergevertex_neighbors: of f%d and f%d at furthest p%d f0= %p\n",
-             facet1->id, facet2->id, qh->furthest_id, qh->tracevertex->neighbors->e[0].p);
-    qh_errprint(qh, "TRACE", NULL, NULL, NULL, qh->tracevertex);
-  }
-  FOREACHvertex_(facet1->vertices) {
-    if (vertex->visitid != qh->vertex_visit)
-      qh_setreplace(qh, vertex->neighbors, facet1, facet2);
-    else {
-      qh_setdel(vertex->neighbors, facet1);
-      if (!SETsecond_(vertex->neighbors))
-        qh_mergevertex_del(qh, vertex, facet1, facet2);
-    }
-  }
-  if (qh->tracevertex)
-    qh_errprint(qh, "TRACE", NULL, NULL, NULL, qh->tracevertex);
-} /* mergevertex_neighbors */
-
-
-/*---------------------------------
-
-  qh_mergevertices(qh, vertices1, vertices2 )
-    merges the vertex set of facet1 into facet2
-
-  returns:
-    replaces vertices2 with merged set
-    preserves vertex_visit for qh_mergevertex_neighbors
-    updates qh.newvertex_list
-
-  design:
-    create a merged set of both vertices (in inverse id order)
-*/
-void qh_mergevertices(qhT *qh, setT *vertices1, setT **vertices2) {
-  int newsize= qh_setsize(qh, vertices1)+qh_setsize(qh, *vertices2) - qh->hull_dim + 1;
-  setT *mergedvertices;
-  vertexT *vertex, **vertexp, **vertex2= SETaddr_(*vertices2, vertexT);
-
-  mergedvertices= qh_settemp(qh, newsize);
-  FOREACHvertex_(vertices1) {
-    if (!*vertex2 || vertex->id > (*vertex2)->id)
-      qh_setappend(qh, &mergedvertices, vertex);
-    else {
-      while (*vertex2 && (*vertex2)->id > vertex->id)
-        qh_setappend(qh, &mergedvertices, *vertex2++);
-      if (!*vertex2 || (*vertex2)->id < vertex->id)
-        qh_setappend(qh, &mergedvertices, vertex);
-      else
-        qh_setappend(qh, &mergedvertices, *vertex2++);
-    }
-  }
-  while (*vertex2)
-    qh_setappend(qh, &mergedvertices, *vertex2++);
-  if (newsize < qh_setsize(qh, mergedvertices)) {
-    qh_fprintf(qh, qh->ferr, 6100, "qhull internal error (qh_mergevertices): facets did not share a ridge\n");
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }
-  qh_setfree(qh, vertices2);
-  *vertices2= mergedvertices;
-  qh_settemppop(qh);
-} /* mergevertices */
-
-
-/*---------------------------------
-
-  qh_neighbor_intersections(qh, vertex )
-    return intersection of all vertices in vertex->neighbors except for vertex
-
-  returns:
-    returns temporary set of vertices
-    does not include vertex
-    NULL if a neighbor is simplicial
-    NULL if empty set
-
-  notes:
-    used for renaming vertices
-
-  design:
-    initialize the intersection set with vertices of the first two neighbors
-    delete vertex from the intersection
-    for each remaining neighbor
-      intersect its vertex set with the intersection set
-      return NULL if empty
-    return the intersection set
-*/
-setT *qh_neighbor_intersections(qhT *qh, vertexT *vertex) {
-  facetT *neighbor, **neighborp, *neighborA, *neighborB;
-  setT *intersect;
-  int neighbor_i, neighbor_n;
-
-  FOREACHneighbor_(vertex) {
-    if (neighbor->simplicial)
-      return NULL;
-  }
-  neighborA= SETfirstt_(vertex->neighbors, facetT);
-  neighborB= SETsecondt_(vertex->neighbors, facetT);
-  zinc_(Zintersectnum);
-  if (!neighborA)
-    return NULL;
-  if (!neighborB)
-    intersect= qh_setcopy(qh, neighborA->vertices, 0);
-  else
-    intersect= qh_vertexintersect_new(qh, neighborA->vertices, neighborB->vertices);
-  qh_settemppush(qh, intersect);
-  qh_setdelsorted(intersect, vertex);
-  FOREACHneighbor_i_(qh, vertex) {
-    if (neighbor_i >= 2) {
-      zinc_(Zintersectnum);
-      qh_vertexintersect(qh, &intersect, neighbor->vertices);
-      if (!SETfirst_(intersect)) {
-        zinc_(Zintersectfail);
-        qh_settempfree(qh, &intersect);
-        return NULL;
-      }
-    }
-  }
-  trace3((qh, qh->ferr, 3007, "qh_neighbor_intersections: %d vertices in neighbor intersection of v%d\n",
-          qh_setsize(qh, intersect), vertex->id));
-  return intersect;
-} /* neighbor_intersections */
-
-/*---------------------------------
-
-  qh_newvertices(qh, vertices )
-    add vertices to end of qh.vertex_list (marks as new vertices)
-
-  returns:
-    vertices on qh.newvertex_list
-    vertex->newlist set
-*/
-void qh_newvertices(qhT *qh, setT *vertices) {
-  vertexT *vertex, **vertexp;
-
-  FOREACHvertex_(vertices) {
-    if (!vertex->newlist) {
-      qh_removevertex(qh, vertex);
-      qh_appendvertex(qh, vertex);
-    }
-  }
-} /* newvertices */
-
-/*---------------------------------
-
-  qh_reducevertices(qh)
-    reduce extra vertices, shared vertices, and redundant vertices
-    facet->newmerge is set if merged since last call
-    if !qh.MERGEvertices, only removes extra vertices
-
-  returns:
-    True if also merged degen_redundant facets
-    vertices are renamed if possible
-    clears facet->newmerge and vertex->delridge
-
-  notes:
-    ignored if 2-d
-
-  design:
-    merge any degenerate or redundant facets
-    for each newly merged facet
-      remove extra vertices
-    if qh.MERGEvertices
-      for each newly merged facet
-        for each vertex
-          if vertex was on a deleted ridge
-            rename vertex if it is shared
-      remove delridge flag from new vertices
-*/
-boolT qh_reducevertices(qhT *qh) {
-  int numshare=0, numrename= 0;
-  boolT degenredun= False;
-  facetT *newfacet;
-  vertexT *vertex, **vertexp;
-
-  if (qh->hull_dim == 2)
-    return False;
-  if (qh_merge_degenredundant(qh))
-    degenredun= True;
- LABELrestart:
-  FORALLnew_facets {
-    if (newfacet->newmerge) {
-      if (!qh->MERGEvertices)
-        newfacet->newmerge= False;
-      qh_remove_extravertices(qh, newfacet);
-    }
-  }
-  if (!qh->MERGEvertices)
-    return False;
-  FORALLnew_facets {
-    if (newfacet->newmerge) {
-      newfacet->newmerge= False;
-      FOREACHvertex_(newfacet->vertices) {
-        if (vertex->delridge) {
-          if (qh_rename_sharedvertex(qh, vertex, newfacet)) {
-            numshare++;
-            vertexp--; /* repeat since deleted vertex */
-          }
-        }
-      }
-    }
-  }
-  FORALLvertex_(qh->newvertex_list) {
-    if (vertex->delridge && !vertex->deleted) {
-      vertex->delridge= False;
-      if (qh->hull_dim >= 4 && qh_redundant_vertex(qh, vertex)) {
-        numrename++;
-        if (qh_merge_degenredundant(qh)) {
-          degenredun= True;
-          goto LABELrestart;
-        }
-      }
-    }
-  }
-  trace1((qh, qh->ferr, 1014, "qh_reducevertices: renamed %d shared vertices and %d redundant vertices. Degen? %d\n",
-          numshare, numrename, degenredun));
-  return degenredun;
-} /* reducevertices */
-
-/*---------------------------------
-
-  qh_redundant_vertex(qh, vertex )
-    detect and rename a redundant vertex
-    vertices have full vertex->neighbors
-
-  returns:
-    returns true if find a redundant vertex
-      deletes vertex(vertex->deleted)
-
-  notes:
-    only needed if vertex->delridge and hull_dim >= 4
-    may add degenerate facets to qh.facet_mergeset
-    doesn't change vertex->neighbors or create redundant facets
-
-  design:
-    intersect vertices of all facet neighbors of vertex
-    determine ridges for these vertices
-    if find a new vertex for vertex amoung these ridges and vertices
-      rename vertex to the new vertex
-*/
-vertexT *qh_redundant_vertex(qhT *qh, vertexT *vertex) {
-  vertexT *newvertex= NULL;
-  setT *vertices, *ridges;
-
-  trace3((qh, qh->ferr, 3008, "qh_redundant_vertex: check if v%d can be renamed\n", vertex->id));
-  if ((vertices= qh_neighbor_intersections(qh, vertex))) {
-    ridges= qh_vertexridges(qh, vertex);
-    if ((newvertex= qh_find_newvertex(qh, vertex, vertices, ridges)))
-      qh_renamevertex(qh, vertex, newvertex, ridges, NULL, NULL);
-    qh_settempfree(qh, &ridges);
-    qh_settempfree(qh, &vertices);
-  }
-  return newvertex;
-} /* redundant_vertex */
-
-/*---------------------------------
-
-  qh_remove_extravertices(qh, facet )
-    remove extra vertices from non-simplicial facets
-
-  returns:
-    returns True if it finds them
-
-  design:
-    for each vertex in facet
-      if vertex not in a ridge (i.e., no longer used)
-        delete vertex from facet
-        delete facet from vertice's neighbors
-        unless vertex in another facet
-          add vertex to qh.del_vertices for later deletion
-*/
-boolT qh_remove_extravertices(qhT *qh, facetT *facet) {
-  ridgeT *ridge, **ridgep;
-  vertexT *vertex, **vertexp;
-  boolT foundrem= False;
-
-  trace4((qh, qh->ferr, 4043, "qh_remove_extravertices: test f%d for extra vertices\n",
-          facet->id));
-  FOREACHvertex_(facet->vertices)
-    vertex->seen= False;
-  FOREACHridge_(facet->ridges) {
-    FOREACHvertex_(ridge->vertices)
-      vertex->seen= True;
-  }
-  FOREACHvertex_(facet->vertices) {
-    if (!vertex->seen) {
-      foundrem= True;
-      zinc_(Zremvertex);
-      qh_setdelsorted(facet->vertices, vertex);
-      qh_setdel(vertex->neighbors, facet);
-      if (!qh_setsize(qh, vertex->neighbors)) {
-        vertex->deleted= True;
-        qh_setappend(qh, &qh->del_vertices, vertex);
-        zinc_(Zremvertexdel);
-        trace2((qh, qh->ferr, 2036, "qh_remove_extravertices: v%d deleted because it's lost all ridges\n", vertex->id));
-      }else
-        trace3((qh, qh->ferr, 3009, "qh_remove_extravertices: v%d removed from f%d because it's lost all ridges\n", vertex->id, facet->id));
-      vertexp--; /*repeat*/
-    }
-  }
-  return foundrem;
-} /* remove_extravertices */
-
-/*---------------------------------
-
-  qh_rename_sharedvertex(qh, vertex, facet )
-    detect and rename if shared vertex in facet
-    vertices have full ->neighbors
-
-  returns:
-    newvertex or NULL
-    the vertex may still exist in other facets (i.e., a neighbor was pinched)
-    does not change facet->neighbors
-    updates vertex->neighbors
-
-  notes:
-    a shared vertex for a facet is only in ridges to one neighbor
-    this may undo a pinched facet
-
-    it does not catch pinches involving multiple facets.  These appear
-      to be difficult to detect, since an exhaustive search is too expensive.
-
-  design:
-    if vertex only has two neighbors
-      determine the ridges that contain the vertex
-      determine the vertices shared by both neighbors
-      if can find a new vertex in this set
-        rename the vertex to the new vertex
-*/
-vertexT *qh_rename_sharedvertex(qhT *qh, vertexT *vertex, facetT *facet) {
-  facetT *neighbor, **neighborp, *neighborA= NULL;
-  setT *vertices, *ridges;
-  vertexT *newvertex;
-
-  if (qh_setsize(qh, vertex->neighbors) == 2) {
-    neighborA= SETfirstt_(vertex->neighbors, facetT);
-    if (neighborA == facet)
-      neighborA= SETsecondt_(vertex->neighbors, facetT);
-  }else if (qh->hull_dim == 3)
-    return NULL;
-  else {
-    qh->visit_id++;
-    FOREACHneighbor_(facet)
-      neighbor->visitid= qh->visit_id;
-    FOREACHneighbor_(vertex) {
-      if (neighbor->visitid == qh->visit_id) {
-        if (neighborA)
-          return NULL;
-        neighborA= neighbor;
-      }
-    }
-    if (!neighborA) {
-      qh_fprintf(qh, qh->ferr, 6101, "qhull internal error (qh_rename_sharedvertex): v%d's neighbors not in f%d\n",
-        vertex->id, facet->id);
-      qh_errprint(qh, "ERRONEOUS", facet, NULL, NULL, vertex);
-      qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-    }
-  }
-  /* the vertex is shared by facet and neighborA */
-  ridges= qh_settemp(qh, qh->TEMPsize);
-  neighborA->visitid= ++qh->visit_id;
-  qh_vertexridges_facet(qh, vertex, facet, &ridges);
-  trace2((qh, qh->ferr, 2037, "qh_rename_sharedvertex: p%d(v%d) is shared by f%d(%d ridges) and f%d\n",
-    qh_pointid(qh, vertex->point), vertex->id, facet->id, qh_setsize(qh, ridges), neighborA->id));
-  zinc_(Zintersectnum);
-  vertices= qh_vertexintersect_new(qh, facet->vertices, neighborA->vertices);
-  qh_setdel(vertices, vertex);
-  qh_settemppush(qh, vertices);
-  if ((newvertex= qh_find_newvertex(qh, vertex, vertices, ridges)))
-    qh_renamevertex(qh, vertex, newvertex, ridges, facet, neighborA);
-  qh_settempfree(qh, &vertices);
-  qh_settempfree(qh, &ridges);
-  return newvertex;
-} /* rename_sharedvertex */
-
-/*---------------------------------
-
-  qh_renameridgevertex(qh, ridge, oldvertex, newvertex )
-    renames oldvertex as newvertex in ridge
-
-  returns:
-
-  design:
-    delete oldvertex from ridge
-    if newvertex already in ridge
-      copy ridge->noconvex to another ridge if possible
-      delete the ridge
-    else
-      insert newvertex into the ridge
-      adjust the ridge's orientation
-*/
-void qh_renameridgevertex(qhT *qh, ridgeT *ridge, vertexT *oldvertex, vertexT *newvertex) {
-  int nth= 0, oldnth;
-  facetT *temp;
-  vertexT *vertex, **vertexp;
-
-  oldnth= qh_setindex(ridge->vertices, oldvertex);
-  qh_setdelnthsorted(qh, ridge->vertices, oldnth);
-  FOREACHvertex_(ridge->vertices) {
-    if (vertex == newvertex) {
-      zinc_(Zdelridge);
-      if (ridge->nonconvex) /* only one ridge has nonconvex set */
-        qh_copynonconvex(qh, ridge);
-      trace2((qh, qh->ferr, 2038, "qh_renameridgevertex: ridge r%d deleted.  It contained both v%d and v%d\n",
-        ridge->id, oldvertex->id, newvertex->id));
-      qh_delridge(qh, ridge);
-      return;
-    }
-    if (vertex->id < newvertex->id)
-      break;
-    nth++;
-  }
-  qh_setaddnth(qh, &ridge->vertices, nth, newvertex);
-  if (abs(oldnth - nth)%2) {
-    trace3((qh, qh->ferr, 3010, "qh_renameridgevertex: swapped the top and bottom of ridge r%d\n",
-            ridge->id));
-    temp= ridge->top;
-    ridge->top= ridge->bottom;
-    ridge->bottom= temp;
-  }
-} /* renameridgevertex */
-
-
-/*---------------------------------
-
-  qh_renamevertex(qh, oldvertex, newvertex, ridges, oldfacet, neighborA )
-    renames oldvertex as newvertex in ridges
-    gives oldfacet/neighborA if oldvertex is shared between two facets
-
-  returns:
-    oldvertex may still exist afterwards
-
-
-  notes:
-    can not change neighbors of newvertex (since it's a subset)
-
-  design:
-    for each ridge in ridges
-      rename oldvertex to newvertex and delete degenerate ridges
-    if oldfacet not defined
-      for each neighbor of oldvertex
-        delete oldvertex from neighbor's vertices
-        remove extra vertices from neighbor
-      add oldvertex to qh.del_vertices
-    else if oldvertex only between oldfacet and neighborA
-      delete oldvertex from oldfacet and neighborA
-      add oldvertex to qh.del_vertices
-    else oldvertex is in oldfacet and neighborA and other facets (i.e., pinched)
-      delete oldvertex from oldfacet
-      delete oldfacet from oldvertice's neighbors
-      remove extra vertices (e.g., oldvertex) from neighborA
-*/
-void qh_renamevertex(qhT *qh, vertexT *oldvertex, vertexT *newvertex, setT *ridges, facetT *oldfacet, facetT *neighborA) {
-  facetT *neighbor, **neighborp;
-  ridgeT *ridge, **ridgep;
-  boolT istrace= False;
-
-  if (qh->IStracing >= 2 || oldvertex->id == qh->tracevertex_id ||
-        newvertex->id == qh->tracevertex_id)
-    istrace= True;
-  FOREACHridge_(ridges)
-    qh_renameridgevertex(qh, ridge, oldvertex, newvertex);
-  if (!oldfacet) {
-    zinc_(Zrenameall);
-    if (istrace)
-      qh_fprintf(qh, qh->ferr, 8082, "qh_renamevertex: renamed v%d to v%d in several facets\n",
-               oldvertex->id, newvertex->id);
-    FOREACHneighbor_(oldvertex) {
-      qh_maydropneighbor(qh, neighbor);
-      qh_setdelsorted(neighbor->vertices, oldvertex);
-      if (qh_remove_extravertices(qh, neighbor))
-        neighborp--; /* neighbor may be deleted */
-    }
-    if (!oldvertex->deleted) {
-      oldvertex->deleted= True;
-      qh_setappend(qh, &qh->del_vertices, oldvertex);
-    }
-  }else if (qh_setsize(qh, oldvertex->neighbors) == 2) {
-    zinc_(Zrenameshare);
-    if (istrace)
-      qh_fprintf(qh, qh->ferr, 8083, "qh_renamevertex: renamed v%d to v%d in oldfacet f%d\n",
-               oldvertex->id, newvertex->id, oldfacet->id);
-    FOREACHneighbor_(oldvertex)
-      qh_setdelsorted(neighbor->vertices, oldvertex);
-    oldvertex->deleted= True;
-    qh_setappend(qh, &qh->del_vertices, oldvertex);
-  }else {
-    zinc_(Zrenamepinch);
-    if (istrace || qh->IStracing)
-      qh_fprintf(qh, qh->ferr, 8084, "qh_renamevertex: renamed pinched v%d to v%d between f%d and f%d\n",
-               oldvertex->id, newvertex->id, oldfacet->id, neighborA->id);
-    qh_setdelsorted(oldfacet->vertices, oldvertex);
-    qh_setdel(oldvertex->neighbors, oldfacet);
-    qh_remove_extravertices(qh, neighborA);
-  }
-} /* renamevertex */
-
-
-/*---------------------------------
-
-  qh_test_appendmerge(qh, facet, neighbor )
-    tests facet/neighbor for convexity
-    appends to mergeset if non-convex
-    if pre-merging,
-      nop if qh.SKIPconvex, or qh.MERGEexact and coplanar
-
-  returns:
-    true if appends facet/neighbor to mergeset
-    sets facet->center as needed
-    does not change facet->seen
-
-  design:
-    if qh.cos_max is defined
-      if the angle between facet normals is too shallow
-        append an angle-coplanar merge to qh.mergeset
-        return True
-    make facet's centrum if needed
-    if facet's centrum is above the neighbor
-      set isconcave
-    else
-      if facet's centrum is not below the neighbor
-        set iscoplanar
-      make neighbor's centrum if needed
-      if neighbor's centrum is above the facet
-        set isconcave
-      else if neighbor's centrum is not below the facet
-        set iscoplanar
-   if isconcave or iscoplanar
-     get angle if needed
-     append concave or coplanar merge to qh.mergeset
-*/
-boolT qh_test_appendmerge(qhT *qh, facetT *facet, facetT *neighbor) {
-  realT dist, dist2= -REALmax, angle= -REALmax;
-  boolT isconcave= False, iscoplanar= False, okangle= False;
-
-  if (qh->SKIPconvex && !qh->POSTmerging)
-    return False;
-  if ((!qh->MERGEexact || qh->POSTmerging) && qh->cos_max < REALmax/2) {
-    angle= qh_getangle(qh, facet->normal, neighbor->normal);
-    zinc_(Zangletests);
-    if (angle > qh->cos_max) {
-      zinc_(Zcoplanarangle);
-      qh_appendmergeset(qh, facet, neighbor, MRGanglecoplanar, &angle);
-      trace2((qh, qh->ferr, 2039, "qh_test_appendmerge: coplanar angle %4.4g between f%d and f%d\n",
-         angle, facet->id, neighbor->id));
-      return True;
-    }else
-      okangle= True;
-  }
-  if (!facet->center)
-    facet->center= qh_getcentrum(qh, facet);
-  zzinc_(Zcentrumtests);
-  qh_distplane(qh, facet->center, neighbor, &dist);
-  if (dist > qh->centrum_radius)
-    isconcave= True;
-  else {
-    if (dist > -qh->centrum_radius)
-      iscoplanar= True;
-    if (!neighbor->center)
-      neighbor->center= qh_getcentrum(qh, neighbor);
-    zzinc_(Zcentrumtests);
-    qh_distplane(qh, neighbor->center, facet, &dist2);
-    if (dist2 > qh->centrum_radius)
-      isconcave= True;
-    else if (!iscoplanar && dist2 > -qh->centrum_radius)
-      iscoplanar= True;
-  }
-  if (!isconcave && (!iscoplanar || (qh->MERGEexact && !qh->POSTmerging)))
-    return False;
-  if (!okangle && qh->ANGLEmerge) {
-    angle= qh_getangle(qh, facet->normal, neighbor->normal);
-    zinc_(Zangletests);
-  }
-  if (isconcave) {
-    zinc_(Zconcaveridge);
-    if (qh->ANGLEmerge)
-      angle += qh_ANGLEconcave + 0.5;
-    qh_appendmergeset(qh, facet, neighbor, MRGconcave, &angle);
-    trace0((qh, qh->ferr, 18, "qh_test_appendmerge: concave f%d to f%d dist %4.4g and reverse dist %4.4g angle %4.4g during p%d\n",
-           facet->id, neighbor->id, dist, dist2, angle, qh->furthest_id));
-  }else /* iscoplanar */ {
-    zinc_(Zcoplanarcentrum);
-    qh_appendmergeset(qh, facet, neighbor, MRGcoplanar, &angle);
-    trace2((qh, qh->ferr, 2040, "qh_test_appendmerge: coplanar f%d to f%d dist %4.4g, reverse dist %4.4g angle %4.4g\n",
-              facet->id, neighbor->id, dist, dist2, angle));
-  }
-  return True;
-} /* test_appendmerge */
-
-/*---------------------------------
-
-  qh_test_vneighbors(qh)
-    test vertex neighbors for convexity
-    tests all facets on qh.newfacet_list
-
-  returns:
-    true if non-convex vneighbors appended to qh.facet_mergeset
-    initializes vertex neighbors if needed
-
-  notes:
-    assumes all facet neighbors have been tested
-    this can be expensive
-    this does not guarantee that a centrum is below all facets
-      but it is unlikely
-    uses qh.visit_id
-
-  design:
-    build vertex neighbors if necessary
-    for all new facets
-      for all vertices
-        for each unvisited facet neighbor of the vertex
-          test new facet and neighbor for convexity
-*/
-boolT qh_test_vneighbors(qhT *qh /* qh->newfacet_list */) {
-  facetT *newfacet, *neighbor, **neighborp;
-  vertexT *vertex, **vertexp;
-  int nummerges= 0;
-
-  trace1((qh, qh->ferr, 1015, "qh_test_vneighbors: testing vertex neighbors for convexity\n"));
-  if (!qh->VERTEXneighbors)
-    qh_vertexneighbors(qh);
-  FORALLnew_facets
-    newfacet->seen= False;
-  FORALLnew_facets {
-    newfacet->seen= True;
-    newfacet->visitid= qh->visit_id++;
-    FOREACHneighbor_(newfacet)
-      newfacet->visitid= qh->visit_id;
-    FOREACHvertex_(newfacet->vertices) {
-      FOREACHneighbor_(vertex) {
-        if (neighbor->seen || neighbor->visitid == qh->visit_id)
-          continue;
-        if (qh_test_appendmerge(qh, newfacet, neighbor))
-          nummerges++;
-      }
-    }
-  }
-  zadd_(Ztestvneighbor, nummerges);
-  trace1((qh, qh->ferr, 1016, "qh_test_vneighbors: found %d non-convex, vertex neighbors\n",
-           nummerges));
-  return (nummerges > 0);
-} /* test_vneighbors */
-
-/*---------------------------------
-
-  qh_tracemerge(qh, facet1, facet2 )
-    print trace message after merge
-*/
-void qh_tracemerge(qhT *qh, facetT *facet1, facetT *facet2) {
-  boolT waserror= False;
-
-#ifndef qh_NOtrace
-  if (qh->IStracing >= 4)
-    qh_errprint(qh, "MERGED", facet2, NULL, NULL, NULL);
-  if (facet2 == qh->tracefacet || (qh->tracevertex && qh->tracevertex->newlist)) {
-    qh_fprintf(qh, qh->ferr, 8085, "qh_tracemerge: trace facet and vertex after merge of f%d and f%d, furthest p%d\n", facet1->id, facet2->id, qh->furthest_id);
-    if (facet2 != qh->tracefacet)
-      qh_errprint(qh, "TRACE", qh->tracefacet,
-        (qh->tracevertex && qh->tracevertex->neighbors) ?
-           SETfirstt_(qh->tracevertex->neighbors, facetT) : NULL,
-        NULL, qh->tracevertex);
-  }
-  if (qh->tracevertex) {
-    if (qh->tracevertex->deleted)
-      qh_fprintf(qh, qh->ferr, 8086, "qh_tracemerge: trace vertex deleted at furthest p%d\n",
-            qh->furthest_id);
-    else
-      qh_checkvertex(qh, qh->tracevertex);
-  }
-  if (qh->tracefacet) {
-    qh_checkfacet(qh, qh->tracefacet, True, &waserror);
-    if (waserror)
-      qh_errexit(qh, qh_ERRqhull, qh->tracefacet, NULL);
-  }
-#endif /* !qh_NOtrace */
-  if (qh->CHECKfrequently || qh->IStracing >= 4) { /* can't check polygon here */
-    qh_checkfacet(qh, facet2, True, &waserror);
-    if (waserror)
-      qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }
-} /* tracemerge */
-
-/*---------------------------------
-
-  qh_tracemerging(qh)
-    print trace message during POSTmerging
-
-  returns:
-    updates qh.mergereport
-
-  notes:
-    called from qh_mergecycle() and qh_mergefacet()
-
-  see:
-    qh_buildtracing()
-*/
-void qh_tracemerging(qhT *qh) {
-  realT cpu;
-  int total;
-  time_t timedata;
-  struct tm *tp;
-
-  qh->mergereport= zzval_(Ztotmerge);
-  time(&timedata);
-  tp= localtime(&timedata);
-  cpu= qh_CPUclock;
-  cpu /= qh_SECticks;
-  total= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
-  qh_fprintf(qh, qh->ferr, 8087, "\n\
-At %d:%d:%d & %2.5g CPU secs, qhull has merged %d facets.  The hull\n\
-  contains %d facets and %d vertices.\n",
-      tp->tm_hour, tp->tm_min, tp->tm_sec, cpu,
-      total, qh->num_facets - qh->num_visible,
-      qh->num_vertices-qh_setsize(qh, qh->del_vertices));
-} /* tracemerging */
-
-/*---------------------------------
-
-  qh_updatetested(qh, facet1, facet2 )
-    clear facet2->tested and facet1->ridge->tested for merge
-
-  returns:
-    deletes facet2->center unless it's already large
-      if so, clears facet2->ridge->tested
-
-  design:
-    clear facet2->tested
-    clear ridge->tested for facet1's ridges
-    if facet2 has a centrum
-      if facet2 is large
-        set facet2->keepcentrum
-      else if facet2 has 3 vertices due to many merges, or not large and post merging
-        clear facet2->keepcentrum
-      unless facet2->keepcentrum
-        clear facet2->center to recompute centrum later
-        clear ridge->tested for facet2's ridges
-*/
-void qh_updatetested(qhT *qh, facetT *facet1, facetT *facet2) {
-  ridgeT *ridge, **ridgep;
-  int size;
-
-  facet2->tested= False;
-  FOREACHridge_(facet1->ridges)
-    ridge->tested= False;
-  if (!facet2->center)
-    return;
-  size= qh_setsize(qh, facet2->vertices);
-  if (!facet2->keepcentrum) {
-    if (size > qh->hull_dim + qh_MAXnewcentrum) {
-      facet2->keepcentrum= True;
-      zinc_(Zwidevertices);
-    }
-  }else if (size <= qh->hull_dim + qh_MAXnewcentrum) {
-    /* center and keepcentrum was set */
-    if (size == qh->hull_dim || qh->POSTmerging)
-      facet2->keepcentrum= False; /* if many merges need to recompute centrum */
-  }
-  if (!facet2->keepcentrum) {
-    qh_memfree(qh, facet2->center, qh->normal_size);
-    facet2->center= NULL;
-    FOREACHridge_(facet2->ridges)
-      ridge->tested= False;
-  }
-} /* updatetested */
-
-/*---------------------------------
-
-  qh_vertexridges(qh, vertex )
-    return temporary set of ridges adjacent to a vertex
-    vertex->neighbors defined
-
-  ntoes:
-    uses qh.visit_id
-    does not include implicit ridges for simplicial facets
-
-  design:
-    for each neighbor of vertex
-      add ridges that include the vertex to ridges
-*/
-setT *qh_vertexridges(qhT *qh, vertexT *vertex) {
-  facetT *neighbor, **neighborp;
-  setT *ridges= qh_settemp(qh, qh->TEMPsize);
-  int size;
-
-  qh->visit_id++;
-  FOREACHneighbor_(vertex)
-    neighbor->visitid= qh->visit_id;
-  FOREACHneighbor_(vertex) {
-    if (*neighborp)   /* no new ridges in last neighbor */
-      qh_vertexridges_facet(qh, vertex, neighbor, &ridges);
-  }
-  if (qh->PRINTstatistics || qh->IStracing) {
-    size= qh_setsize(qh, ridges);
-    zinc_(Zvertexridge);
-    zadd_(Zvertexridgetot, size);
-    zmax_(Zvertexridgemax, size);
-    trace3((qh, qh->ferr, 3011, "qh_vertexridges: found %d ridges for v%d\n",
-             size, vertex->id));
-  }
-  return ridges;
-} /* vertexridges */
-
-/*---------------------------------
-
-  qh_vertexridges_facet(qh, vertex, facet, ridges )
-    add adjacent ridges for vertex in facet
-    neighbor->visitid==qh.visit_id if it hasn't been visited
-
-  returns:
-    ridges updated
-    sets facet->visitid to qh.visit_id-1
-
-  design:
-    for each ridge of facet
-      if ridge of visited neighbor (i.e., unprocessed)
-        if vertex in ridge
-          append ridge to vertex
-    mark facet processed
-*/
-void qh_vertexridges_facet(qhT *qh, vertexT *vertex, facetT *facet, setT **ridges) {
-  ridgeT *ridge, **ridgep;
-  facetT *neighbor;
-
-  FOREACHridge_(facet->ridges) {
-    neighbor= otherfacet_(ridge, facet);
-    if (neighbor->visitid == qh->visit_id
-    && qh_setin(ridge->vertices, vertex))
-      qh_setappend(qh, ridges, ridge);
-  }
-  facet->visitid= qh->visit_id-1;
-} /* vertexridges_facet */
-
-/*---------------------------------
-
-  qh_willdelete(qh, facet, replace )
-    moves facet to visible list
-    sets facet->f.replace to replace (may be NULL)
-
-  returns:
-    bumps qh.num_visible
-*/
-void qh_willdelete(qhT *qh, facetT *facet, facetT *replace) {
-
-  qh_removefacet(qh, facet);
-  qh_prependfacet(qh, facet, &qh->visible_list);
-  qh->num_visible++;
-  facet->visible= True;
-  facet->f.replace= replace;
-} /* willdelete */
-
-#else /* qh_NOmerge */
-void qh_premerge(qhT *qh, vertexT *apex, realT maxcentrum, realT maxangle) {
-}
-void qh_postmerge(qhT *qh, const char *reason, realT maxcentrum, realT maxangle,
-                      boolT vneighbors) {
-}
-boolT qh_checkzero(qhT *qh, boolT testall) {
-   }
-#endif /* qh_NOmerge */
-
diff --git a/C/poly2_r.c b/C/poly2_r.c
deleted file mode 100644
--- a/C/poly2_r.c
+++ /dev/null
@@ -1,3222 +0,0 @@
-/*
  ---------------------------------
-
-   poly2_r.c
-   implements polygons and simplicies
-
-   see qh-poly_r.htm, poly_r.h and libqhull_r.h
-
-   frequently used code is in poly_r.c
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull_r/poly2_r.c#10 $$Change: 2069 $
-   $DateTime: 2016/01/18 22:05:03 $$Author: bbarber $
-*/
-
-#include "qhull_ra.h"
-
-/*======== functions in alphabetical order ==========*/
-
-/*---------------------------------
-
-  qh_addhash( newelem, hashtable, hashsize, hash )
-    add newelem to linear hash table at hash if not already there
-*/
-void qh_addhash(void *newelem, setT *hashtable, int hashsize, int hash) {
-  int scan;
-  void *elem;
-
-  for (scan= (int)hash; (elem= SETelem_(hashtable, scan));
-       scan= (++scan >= hashsize ? 0 : scan)) {
-    if (elem == newelem)
-      break;
-  }
-  /* loop terminates because qh_HASHfactor >= 1.1 by qh_initbuffers */
-  if (!elem)
-    SETelem_(hashtable, scan)= newelem;
-} /* addhash */
-
-/*---------------------------------
-
-  qh_check_bestdist(qh)
-    check that all points are within max_outside of the nearest facet
-    if qh.ONLYgood,
-      ignores !good facets
-
-  see:
-    qh_check_maxout(), qh_outerinner()
-
-  notes:
-    only called from qh_check_points()
-      seldom used since qh.MERGING is almost always set
-    if notverified>0 at end of routine
-      some points were well inside the hull.  If the hull contains
-      a lens-shaped component, these points were not verified.  Use
-      options 'Qi Tv' to verify all points.  (Exhaustive check also verifies)
-
-  design:
-    determine facet for each point (if any)
-    for each point
-      start with the assigned facet or with the first facet
-      find the best facet for the point and check all coplanar facets
-      error if point is outside of facet
-*/
-void qh_check_bestdist(qhT *qh) {
-  boolT waserror= False, unassigned;
-  facetT *facet, *bestfacet, *errfacet1= NULL, *errfacet2= NULL;
-  facetT *facetlist;
-  realT dist, maxoutside, maxdist= -REALmax;
-  pointT *point;
-  int numpart= 0, facet_i, facet_n, notgood= 0, notverified= 0;
-  setT *facets;
-
-  trace1((qh, qh->ferr, 1020, "qh_check_bestdist: check points below nearest facet.  Facet_list f%d\n",
-      qh->facet_list->id));
-  maxoutside= qh_maxouter(qh);
-  maxoutside += qh->DISTround;
-  /* one more qh.DISTround for check computation */
-  trace1((qh, qh->ferr, 1021, "qh_check_bestdist: check that all points are within %2.2g of best facet\n", maxoutside));
-  facets= qh_pointfacet(qh /*qh.facet_list*/);
-  if (!qh_QUICKhelp && qh->PRINTprecision)
-    qh_fprintf(qh, qh->ferr, 8091, "\n\
-qhull output completed.  Verifying that %d points are\n\
-below %2.2g of the nearest %sfacet.\n",
-             qh_setsize(qh, facets), maxoutside, (qh->ONLYgood ?  "good " : ""));
-  FOREACHfacet_i_(qh, facets) {  /* for each point with facet assignment */
-    if (facet)
-      unassigned= False;
-    else {
-      unassigned= True;
-      facet= qh->facet_list;
-    }
-    point= qh_point(qh, facet_i);
-    if (point == qh->GOODpointp)
-      continue;
-    qh_distplane(qh, point, facet, &dist);
-    numpart++;
-    bestfacet= qh_findbesthorizon(qh, !qh_IScheckmax, point, facet, qh_NOupper, &dist, &numpart);
-    /* occurs after statistics reported */
-    maximize_(maxdist, dist);
-    if (dist > maxoutside) {
-      if (qh->ONLYgood && !bestfacet->good
-          && !((bestfacet= qh_findgooddist(qh, point, bestfacet, &dist, &facetlist))
-               && dist > maxoutside))
-        notgood++;
-      else {
-        waserror= True;
-        qh_fprintf(qh, qh->ferr, 6109, "qhull precision error: point p%d is outside facet f%d, distance= %6.8g maxoutside= %6.8g\n",
-                facet_i, bestfacet->id, dist, maxoutside);
-        if (errfacet1 != bestfacet) {
-          errfacet2= errfacet1;
-          errfacet1= bestfacet;
-        }
-      }
-    }else if (unassigned && dist < -qh->MAXcoplanar)
-      notverified++;
-  }
-  qh_settempfree(qh, &facets);
-  if (notverified && !qh->DELAUNAY && !qh_QUICKhelp && qh->PRINTprecision)
-    qh_fprintf(qh, qh->ferr, 8092, "\n%d points were well inside the hull.  If the hull contains\n\
-a lens-shaped component, these points were not verified.  Use\n\
-options 'Qci Tv' to verify all points.\n", notverified);
-  if (maxdist > qh->outside_err) {
-    qh_fprintf(qh, qh->ferr, 6110, "qhull precision error (qh_check_bestdist): a coplanar point is %6.2g from convex hull.  The maximum value(qh.outside_err) is %6.2g\n",
-              maxdist, qh->outside_err);
-    qh_errexit2(qh, qh_ERRprec, errfacet1, errfacet2);
-  }else if (waserror && qh->outside_err > REALmax/2)
-    qh_errexit2(qh, qh_ERRprec, errfacet1, errfacet2);
-  /* else if waserror, the error was logged to qh.ferr but does not effect the output */
-  trace0((qh, qh->ferr, 20, "qh_check_bestdist: max distance outside %2.2g\n", maxdist));
-} /* check_bestdist */
-
-/*---------------------------------
-
-  qh_check_dupridge(qh, facet1, dist1, facet2, dist2)
-    Check duplicate ridge between facet1 and facet2 for wide merge
-    dist1 is the maximum distance of facet1's vertices to facet2
-    dist2 is the maximum distance of facet2's vertices to facet1
-
-  Returns
-    Level 1 log of the duplicate ridge with the minimum distance between vertices
-    Throws error if the merge will increase the maximum facet width by qh_WIDEduplicate (100x)
-
-  called from:
-    qh_forcedmerges()
-*/
-#ifndef qh_NOmerge
-void qh_check_dupridge(qhT *qh, facetT *facet1, realT dist1, facetT *facet2, realT dist2) {
-  vertexT *vertex, **vertexp, *vertexA, **vertexAp;
-  realT dist, innerplane, mergedist, outerplane, prevdist, ratio;
-  realT minvertex= REALmax;
-
-  mergedist= fmin_(dist1, dist2);
-  qh_outerinner(qh, NULL, &outerplane, &innerplane);  /* ratio from qh_printsummary */
-  prevdist= fmax_(outerplane, innerplane);
-  maximize_(prevdist, qh->ONEmerge + qh->DISTround);
-  maximize_(prevdist, qh->MINoutside + qh->DISTround);
-  ratio= mergedist/prevdist;
-  FOREACHvertex_(facet1->vertices) {     /* The duplicate ridge is between facet1 and facet2, so either facet can be tested */
-    FOREACHvertexA_(facet1->vertices) {
-      if (vertex > vertexA){   /* Test each pair once */
-        dist= qh_pointdist(vertex->point, vertexA->point, qh->hull_dim);
-        minimize_(minvertex, dist);
-      }
-    }
-  }
-  trace0((qh, qh->ferr, 16, "qh_check_dupridge: duplicate ridge between f%d and f%d due to nearly-coincident vertices (%2.2g), dist %2.2g, reverse dist %2.2g, ratio %2.2g while processing p%d\n",
-        facet1->id, facet2->id, minvertex, dist1, dist2, ratio, qh->furthest_id));
-  if (ratio > qh_WIDEduplicate) {
-    qh_fprintf(qh, qh->ferr, 6271, "qhull precision error (qh_check_dupridge): wide merge (%.0f times wider) due to duplicate ridge with nearly coincident points (%2.2g) between f%d and f%d, merge dist %2.2g, while processing p%d\n- Ignore error with option 'Q12'\n- To be fixed in a later version of Qhull\n",
-          ratio, minvertex, facet1->id, facet2->id, mergedist, qh->furthest_id);
-    if (qh->DELAUNAY)
-      qh_fprintf(qh, qh->ferr, 8145, "- A bounding box for the input sites may alleviate this error.\n");
-    if(minvertex > qh_WIDEduplicate*prevdist)
-      qh_fprintf(qh, qh->ferr, 8146, "- Vertex distance %2.2g is greater than %d times maximum distance %2.2g\n  Please report to bradb@shore.net with steps to reproduce and all output\n",
-          minvertex, qh_WIDEduplicate, prevdist);
-    if (!qh->NOwide)
-      qh_errexit2(qh, qh_ERRqhull, facet1, facet2);
-  }
-} /* check_dupridge */
-#endif
-
-/*---------------------------------
-
-  qh_check_maxout(qh)
-    updates qh.max_outside by checking all points against bestfacet
-    if qh.ONLYgood, ignores !good facets
-
-  returns:
-    updates facet->maxoutside via qh_findbesthorizon()
-    sets qh.maxoutdone
-    if printing qh.min_vertex (qh_outerinner),
-      it is updated to the current vertices
-    removes inside/coplanar points from coplanarset as needed
-
-  notes:
-    defines coplanar as min_vertex instead of MAXcoplanar
-    may not need to check near-inside points because of qh.MAXcoplanar
-      and qh.KEEPnearinside (before it was -DISTround)
-
-  see also:
-    qh_check_bestdist()
-
-  design:
-    if qh.min_vertex is needed
-      for all neighbors of all vertices
-        test distance from vertex to neighbor
-    determine facet for each point (if any)
-    for each point with an assigned facet
-      find the best facet for the point and check all coplanar facets
-        (updates outer planes)
-    remove near-inside points from coplanar sets
-*/
-#ifndef qh_NOmerge
-void qh_check_maxout(qhT *qh) {
-  facetT *facet, *bestfacet, *neighbor, **neighborp, *facetlist;
-  realT dist, maxoutside, minvertex, old_maxoutside;
-  pointT *point;
-  int numpart= 0, facet_i, facet_n, notgood= 0;
-  setT *facets, *vertices;
-  vertexT *vertex;
-
-  trace1((qh, qh->ferr, 1022, "qh_check_maxout: check and update maxoutside for each facet.\n"));
-  maxoutside= minvertex= 0;
-  if (qh->VERTEXneighbors
-  && (qh->PRINTsummary || qh->KEEPinside || qh->KEEPcoplanar
-        || qh->TRACElevel || qh->PRINTstatistics
-        || qh->PRINTout[0] == qh_PRINTsummary || qh->PRINTout[0] == qh_PRINTnone)) {
-    trace1((qh, qh->ferr, 1023, "qh_check_maxout: determine actual maxoutside and minvertex\n"));
-    vertices= qh_pointvertex(qh /*qh.facet_list*/);
-    FORALLvertices {
-      FOREACHneighbor_(vertex) {
-        zinc_(Zdistvertex);  /* distance also computed by main loop below */
-        qh_distplane(qh, vertex->point, neighbor, &dist);
-        minimize_(minvertex, dist);
-        if (-dist > qh->TRACEdist || dist > qh->TRACEdist
-        || neighbor == qh->tracefacet || vertex == qh->tracevertex)
-          qh_fprintf(qh, qh->ferr, 8093, "qh_check_maxout: p%d(v%d) is %.2g from f%d\n",
-                    qh_pointid(qh, vertex->point), vertex->id, dist, neighbor->id);
-      }
-    }
-    if (qh->MERGING) {
-      wmin_(Wminvertex, qh->min_vertex);
-    }
-    qh->min_vertex= minvertex;
-    qh_settempfree(qh, &vertices);
-  }
-  facets= qh_pointfacet(qh /*qh.facet_list*/);
-  do {
-    old_maxoutside= fmax_(qh->max_outside, maxoutside);
-    FOREACHfacet_i_(qh, facets) {     /* for each point with facet assignment */
-      if (facet) {
-        point= qh_point(qh, facet_i);
-        if (point == qh->GOODpointp)
-          continue;
-        zzinc_(Ztotcheck);
-        qh_distplane(qh, point, facet, &dist);
-        numpart++;
-        bestfacet= qh_findbesthorizon(qh, qh_IScheckmax, point, facet, !qh_NOupper, &dist, &numpart);
-        if (bestfacet && dist > maxoutside) {
-          if (qh->ONLYgood && !bestfacet->good
-          && !((bestfacet= qh_findgooddist(qh, point, bestfacet, &dist, &facetlist))
-               && dist > maxoutside))
-            notgood++;
-          else
-            maxoutside= dist;
-        }
-        if (dist > qh->TRACEdist || (bestfacet && bestfacet == qh->tracefacet))
-          qh_fprintf(qh, qh->ferr, 8094, "qh_check_maxout: p%d is %.2g above f%d\n",
-          qh_pointid(qh, point), dist, (bestfacet ? bestfacet->id : UINT_MAX));
-      }
-    }
-  }while
-    (maxoutside > 2*old_maxoutside);
-    /* if qh.maxoutside increases substantially, qh_SEARCHdist is not valid
-          e.g., RBOX 5000 s Z1 G1e-13 t1001200614 | qhull */
-  zzadd_(Zcheckpart, numpart);
-  qh_settempfree(qh, &facets);
-  wval_(Wmaxout)= maxoutside - qh->max_outside;
-  wmax_(Wmaxoutside, qh->max_outside);
-  qh->max_outside= maxoutside;
-  qh_nearcoplanar(qh /*qh.facet_list*/);
-  qh->maxoutdone= True;
-  trace1((qh, qh->ferr, 1024, "qh_check_maxout: maxoutside %2.2g, min_vertex %2.2g, outside of not good %d\n",
-       maxoutside, qh->min_vertex, notgood));
-} /* check_maxout */
-#else /* qh_NOmerge */
-void qh_check_maxout(qhT *qh) {
-}
-#endif
-
-/*---------------------------------
-
-  qh_check_output(qh)
-    performs the checks at the end of qhull algorithm
-    Maybe called after voronoi output.  Will recompute otherwise centrums are Voronoi centers instead
-*/
-void qh_check_output(qhT *qh) {
-  int i;
-
-  if (qh->STOPcone)
-    return;
-  if (qh->VERIFYoutput | qh->IStracing | qh->CHECKfrequently) {
-    qh_checkpolygon(qh, qh->facet_list);
-    qh_checkflipped_all(qh, qh->facet_list);
-    qh_checkconvex(qh, qh->facet_list, qh_ALGORITHMfault);
-  }else if (!qh->MERGING && qh_newstats(qh, qh->qhstat.precision, &i)) {
-    qh_checkflipped_all(qh, qh->facet_list);
-    qh_checkconvex(qh, qh->facet_list, qh_ALGORITHMfault);
-  }
-} /* check_output */
-
-
-
-/*---------------------------------
-
-  qh_check_point(qh, point, facet, maxoutside, maxdist, errfacet1, errfacet2 )
-    check that point is less than maxoutside from facet
-*/
-void qh_check_point(qhT *qh, pointT *point, facetT *facet, realT *maxoutside, realT *maxdist, facetT **errfacet1, facetT **errfacet2) {
-  realT dist;
-
-  /* occurs after statistics reported */
-  qh_distplane(qh, point, facet, &dist);
-  if (dist > *maxoutside) {
-    if (*errfacet1 != facet) {
-      *errfacet2= *errfacet1;
-      *errfacet1= facet;
-    }
-    qh_fprintf(qh, qh->ferr, 6111, "qhull precision error: point p%d is outside facet f%d, distance= %6.8g maxoutside= %6.8g\n",
-              qh_pointid(qh, point), facet->id, dist, *maxoutside);
-  }
-  maximize_(*maxdist, dist);
-} /* qh_check_point */
-
-
-/*---------------------------------
-
-  qh_check_points(qh)
-    checks that all points are inside all facets
-
-  notes:
-    if many points and qh_check_maxout not called (i.e., !qh.MERGING),
-       calls qh_findbesthorizon (seldom done).
-    ignores flipped facets
-    maxoutside includes 2 qh.DISTrounds
-      one qh.DISTround for the computed distances in qh_check_points
-    qh_printafacet and qh_printsummary needs only one qh.DISTround
-    the computation for qh.VERIFYdirect does not account for qh.other_points
-
-  design:
-    if many points
-      use qh_check_bestdist()
-    else
-      for all facets
-        for all points
-          check that point is inside facet
-*/
-void qh_check_points(qhT *qh) {
-  facetT *facet, *errfacet1= NULL, *errfacet2= NULL;
-  realT total, maxoutside, maxdist= -REALmax;
-  pointT *point, **pointp, *pointtemp;
-  boolT testouter;
-
-  maxoutside= qh_maxouter(qh);
-  maxoutside += qh->DISTround;
-  /* one more qh.DISTround for check computation */
-  trace1((qh, qh->ferr, 1025, "qh_check_points: check all points below %2.2g of all facet planes\n",
-          maxoutside));
-  if (qh->num_good)   /* miss counts other_points and !good facets */
-     total= (float)qh->num_good * (float)qh->num_points;
-  else
-     total= (float)qh->num_facets * (float)qh->num_points;
-  if (total >= qh_VERIFYdirect && !qh->maxoutdone) {
-    if (!qh_QUICKhelp && qh->SKIPcheckmax && qh->MERGING)
-      qh_fprintf(qh, qh->ferr, 7075, "qhull input warning: merging without checking outer planes('Q5' or 'Po').\n\
-Verify may report that a point is outside of a facet.\n");
-    qh_check_bestdist(qh);
-  }else {
-    if (qh_MAXoutside && qh->maxoutdone)
-      testouter= True;
-    else
-      testouter= False;
-    if (!qh_QUICKhelp) {
-      if (qh->MERGEexact)
-        qh_fprintf(qh, qh->ferr, 7076, "qhull input warning: exact merge ('Qx').  Verify may report that a point\n\
-is outside of a facet.  See qh-optq.htm#Qx\n");
-      else if (qh->SKIPcheckmax || qh->NOnearinside)
-        qh_fprintf(qh, qh->ferr, 7077, "qhull input warning: no outer plane check ('Q5') or no processing of\n\
-near-inside points ('Q8').  Verify may report that a point is outside\n\
-of a facet.\n");
-    }
-    if (qh->PRINTprecision) {
-      if (testouter)
-        qh_fprintf(qh, qh->ferr, 8098, "\n\
-Output completed.  Verifying that all points are below outer planes of\n\
-all %sfacets.  Will make %2.0f distance computations.\n",
-              (qh->ONLYgood ?  "good " : ""), total);
-      else
-        qh_fprintf(qh, qh->ferr, 8099, "\n\
-Output completed.  Verifying that all points are below %2.2g of\n\
-all %sfacets.  Will make %2.0f distance computations.\n",
-              maxoutside, (qh->ONLYgood ?  "good " : ""), total);
-    }
-    FORALLfacets {
-      if (!facet->good && qh->ONLYgood)
-        continue;
-      if (facet->flipped)
-        continue;
-      if (!facet->normal) {
-        qh_fprintf(qh, qh->ferr, 7061, "qhull warning (qh_check_points): missing normal for facet f%d\n", facet->id);
-        continue;
-      }
-      if (testouter) {
-#if qh_MAXoutside
-        maxoutside= facet->maxoutside + 2* qh->DISTround;
-        /* one DISTround to actual point and another to computed point */
-#endif
-      }
-      FORALLpoints {
-        if (point != qh->GOODpointp)
-          qh_check_point(qh, point, facet, &maxoutside, &maxdist, &errfacet1, &errfacet2);
-      }
-      FOREACHpoint_(qh->other_points) {
-        if (point != qh->GOODpointp)
-          qh_check_point(qh, point, facet, &maxoutside, &maxdist, &errfacet1, &errfacet2);
-      }
-    }
-    if (maxdist > qh->outside_err) {
-      qh_fprintf(qh, qh->ferr, 6112, "qhull precision error (qh_check_points): a coplanar point is %6.2g from convex hull.  The maximum value(qh.outside_err) is %6.2g\n",
-                maxdist, qh->outside_err );
-      qh_errexit2(qh, qh_ERRprec, errfacet1, errfacet2 );
-    }else if (errfacet1 && qh->outside_err > REALmax/2)
-        qh_errexit2(qh, qh_ERRprec, errfacet1, errfacet2 );
-    /* else if errfacet1, the error was logged to qh.ferr but does not effect the output */
-    trace0((qh, qh->ferr, 21, "qh_check_points: max distance outside %2.2g\n", maxdist));
-  }
-} /* check_points */
-
-
-/*---------------------------------
-
-  qh_checkconvex(qh, facetlist, fault )
-    check that each ridge in facetlist is convex
-    fault = qh_DATAfault if reporting errors
-          = qh_ALGORITHMfault otherwise
-
-  returns:
-    counts Zconcaveridges and Zcoplanarridges
-    errors if concaveridge or if merging an coplanar ridge
-
-  note:
-    if not merging,
-      tests vertices for neighboring simplicial facets
-    else if ZEROcentrum,
-      tests vertices for neighboring simplicial   facets
-    else
-      tests centrums of neighboring facets
-
-  design:
-    for all facets
-      report flipped facets
-      if ZEROcentrum and simplicial neighbors
-        test vertices for neighboring simplicial facets
-      else
-        test centrum against all neighbors
-*/
-void qh_checkconvex(qhT *qh, facetT *facetlist, int fault) {
-  facetT *facet, *neighbor, **neighborp, *errfacet1=NULL, *errfacet2=NULL;
-  vertexT *vertex;
-  realT dist;
-  pointT *centrum;
-  boolT waserror= False, centrum_warning= False, tempcentrum= False, allsimplicial;
-  int neighbor_i;
-
-  trace1((qh, qh->ferr, 1026, "qh_checkconvex: check all ridges are convex\n"));
-  if (!qh->RERUN) {
-    zzval_(Zconcaveridges)= 0;
-    zzval_(Zcoplanarridges)= 0;
-  }
-  FORALLfacet_(facetlist) {
-    if (facet->flipped) {
-      qh_precision(qh, "flipped facet");
-      qh_fprintf(qh, qh->ferr, 6113, "qhull precision error: f%d is flipped(interior point is outside)\n",
-               facet->id);
-      errfacet1= facet;
-      waserror= True;
-      continue;
-    }
-    if (qh->MERGING && (!qh->ZEROcentrum || !facet->simplicial || facet->tricoplanar))
-      allsimplicial= False;
-    else {
-      allsimplicial= True;
-      neighbor_i= 0;
-      FOREACHneighbor_(facet) {
-        vertex= SETelemt_(facet->vertices, neighbor_i++, vertexT);
-        if (!neighbor->simplicial || neighbor->tricoplanar) {
-          allsimplicial= False;
-          continue;
-        }
-        qh_distplane(qh, vertex->point, neighbor, &dist);
-        if (dist > -qh->DISTround) {
-          if (fault == qh_DATAfault) {
-            qh_precision(qh, "coplanar or concave ridge");
-            qh_fprintf(qh, qh->ferr, 6114, "qhull precision error: initial simplex is not convex. Distance=%.2g\n", dist);
-            qh_errexit(qh, qh_ERRsingular, NULL, NULL);
-          }
-          if (dist > qh->DISTround) {
-            zzinc_(Zconcaveridges);
-            qh_precision(qh, "concave ridge");
-            qh_fprintf(qh, qh->ferr, 6115, "qhull precision error: f%d is concave to f%d, since p%d(v%d) is %6.4g above\n",
-              facet->id, neighbor->id, qh_pointid(qh, vertex->point), vertex->id, dist);
-            errfacet1= facet;
-            errfacet2= neighbor;
-            waserror= True;
-          }else if (qh->ZEROcentrum) {
-            if (dist > 0) {     /* qh_checkzero checks that dist < - qh->DISTround */
-              zzinc_(Zcoplanarridges);
-              qh_precision(qh, "coplanar ridge");
-              qh_fprintf(qh, qh->ferr, 6116, "qhull precision error: f%d is clearly not convex to f%d, since p%d(v%d) is %6.4g above\n",
-                facet->id, neighbor->id, qh_pointid(qh, vertex->point), vertex->id, dist);
-              errfacet1= facet;
-              errfacet2= neighbor;
-              waserror= True;
-            }
-          }else {
-            zzinc_(Zcoplanarridges);
-            qh_precision(qh, "coplanar ridge");
-            trace0((qh, qh->ferr, 22, "qhull precision error: f%d may be coplanar to f%d, since p%d(v%d) is within %6.4g during p%d\n",
-              facet->id, neighbor->id, qh_pointid(qh, vertex->point), vertex->id, dist, qh->furthest_id));
-          }
-        }
-      }
-    }
-    if (!allsimplicial) {
-      if (qh->CENTERtype == qh_AScentrum) {
-        if (!facet->center)
-          facet->center= qh_getcentrum(qh, facet);
-        centrum= facet->center;
-      }else {
-        if (!centrum_warning && (!facet->simplicial || facet->tricoplanar)) {
-           centrum_warning= True;
-           qh_fprintf(qh, qh->ferr, 7062, "qhull warning: recomputing centrums for convexity test.  This may lead to false, precision errors.\n");
-        }
-        centrum= qh_getcentrum(qh, facet);
-        tempcentrum= True;
-      }
-      FOREACHneighbor_(facet) {
-        if (qh->ZEROcentrum && facet->simplicial && neighbor->simplicial)
-          continue;
-        if (facet->tricoplanar || neighbor->tricoplanar)
-          continue;
-        zzinc_(Zdistconvex);
-        qh_distplane(qh, centrum, neighbor, &dist);
-        if (dist > qh->DISTround) {
-          zzinc_(Zconcaveridges);
-          qh_precision(qh, "concave ridge");
-          qh_fprintf(qh, qh->ferr, 6117, "qhull precision error: f%d is concave to f%d.  Centrum of f%d is %6.4g above f%d\n",
-            facet->id, neighbor->id, facet->id, dist, neighbor->id);
-          errfacet1= facet;
-          errfacet2= neighbor;
-          waserror= True;
-        }else if (dist >= 0.0) {   /* if arithmetic always rounds the same,
-                                     can test against centrum radius instead */
-          zzinc_(Zcoplanarridges);
-          qh_precision(qh, "coplanar ridge");
-          qh_fprintf(qh, qh->ferr, 6118, "qhull precision error: f%d is coplanar or concave to f%d.  Centrum of f%d is %6.4g above f%d\n",
-            facet->id, neighbor->id, facet->id, dist, neighbor->id);
-          errfacet1= facet;
-          errfacet2= neighbor;
-          waserror= True;
-        }
-      }
-      if (tempcentrum)
-        qh_memfree(qh, centrum, qh->normal_size);
-    }
-  }
-  if (waserror && !qh->FORCEoutput)
-    qh_errexit2(qh, qh_ERRprec, errfacet1, errfacet2);
-} /* checkconvex */
-
-
-/*---------------------------------
-
-  qh_checkfacet(qh, facet, newmerge, waserror )
-    checks for consistency errors in facet
-    newmerge set if from merge_r.c
-
-  returns:
-    sets waserror if any error occurs
-
-  checks:
-    vertex ids are inverse sorted
-    unless newmerge, at least hull_dim neighbors and vertices (exactly if simplicial)
-    if non-simplicial, at least as many ridges as neighbors
-    neighbors are not duplicated
-    ridges are not duplicated
-    in 3-d, ridges=verticies
-    (qh.hull_dim-1) ridge vertices
-    neighbors are reciprocated
-    ridge neighbors are facet neighbors and a ridge for every neighbor
-    simplicial neighbors match facetintersect
-    vertex intersection matches vertices of common ridges
-    vertex neighbors and facet vertices agree
-    all ridges have distinct vertex sets
-
-  notes:
-    uses neighbor->seen
-
-  design:
-    check sets
-    check vertices
-    check sizes of neighbors and vertices
-    check for qh_MERGEridge and qh_DUPLICATEridge flags
-    check neighbor set
-    check ridge set
-    check ridges, neighbors, and vertices
-*/
-void qh_checkfacet(qhT *qh, facetT *facet, boolT newmerge, boolT *waserrorp) {
-  facetT *neighbor, **neighborp, *errother=NULL;
-  ridgeT *ridge, **ridgep, *errridge= NULL, *ridge2;
-  vertexT *vertex, **vertexp;
-  unsigned previousid= INT_MAX;
-  int numneighbors, numvertices, numridges=0, numRvertices=0;
-  boolT waserror= False;
-  int skipA, skipB, ridge_i, ridge_n, i;
-  setT *intersection;
-
-  if (facet->visible) {
-    qh_fprintf(qh, qh->ferr, 6119, "qhull internal error (qh_checkfacet): facet f%d is on the visible_list\n",
-      facet->id);
-    qh_errexit(qh, qh_ERRqhull, facet, NULL);
-  }
-  if (!facet->normal) {
-    qh_fprintf(qh, qh->ferr, 6120, "qhull internal error (qh_checkfacet): facet f%d does not have  a normal\n",
-      facet->id);
-    waserror= True;
-  }
-  qh_setcheck(qh, facet->vertices, "vertices for f", facet->id);
-  qh_setcheck(qh, facet->ridges, "ridges for f", facet->id);
-  qh_setcheck(qh, facet->outsideset, "outsideset for f", facet->id);
-  qh_setcheck(qh, facet->coplanarset, "coplanarset for f", facet->id);
-  qh_setcheck(qh, facet->neighbors, "neighbors for f", facet->id);
-  FOREACHvertex_(facet->vertices) {
-    if (vertex->deleted) {
-      qh_fprintf(qh, qh->ferr, 6121, "qhull internal error (qh_checkfacet): deleted vertex v%d in f%d\n", vertex->id, facet->id);
-      qh_errprint(qh, "ERRONEOUS", NULL, NULL, NULL, vertex);
-      waserror= True;
-    }
-    if (vertex->id >= previousid) {
-      qh_fprintf(qh, qh->ferr, 6122, "qhull internal error (qh_checkfacet): vertices of f%d are not in descending id order at v%d\n", facet->id, vertex->id);
-      waserror= True;
-      break;
-    }
-    previousid= vertex->id;
-  }
-  numneighbors= qh_setsize(qh, facet->neighbors);
-  numvertices= qh_setsize(qh, facet->vertices);
-  numridges= qh_setsize(qh, facet->ridges);
-  if (facet->simplicial) {
-    if (numvertices+numneighbors != 2*qh->hull_dim
-    && !facet->degenerate && !facet->redundant) {
-      qh_fprintf(qh, qh->ferr, 6123, "qhull internal error (qh_checkfacet): for simplicial facet f%d, #vertices %d + #neighbors %d != 2*qh->hull_dim\n",
-                facet->id, numvertices, numneighbors);
-      qh_setprint(qh, qh->ferr, "", facet->neighbors);
-      waserror= True;
-    }
-  }else { /* non-simplicial */
-    if (!newmerge
-    &&(numvertices < qh->hull_dim || numneighbors < qh->hull_dim)
-    && !facet->degenerate && !facet->redundant) {
-      qh_fprintf(qh, qh->ferr, 6124, "qhull internal error (qh_checkfacet): for facet f%d, #vertices %d or #neighbors %d < qh->hull_dim\n",
-         facet->id, numvertices, numneighbors);
-       waserror= True;
-    }
-    /* in 3-d, can get a vertex twice in an edge list, e.g., RBOX 1000 s W1e-13 t995849315 D2 | QHULL d Tc Tv TP624 TW1e-13 T4 */
-    if (numridges < numneighbors
-    ||(qh->hull_dim == 3 && numvertices > numridges && !qh->NEWfacets)
-    ||(qh->hull_dim == 2 && numridges + numvertices + numneighbors != 6)) {
-      if (!facet->degenerate && !facet->redundant) {
-        qh_fprintf(qh, qh->ferr, 6125, "qhull internal error (qh_checkfacet): for facet f%d, #ridges %d < #neighbors %d or(3-d) > #vertices %d or(2-d) not all 2\n",
-            facet->id, numridges, numneighbors, numvertices);
-        waserror= True;
-      }
-    }
-  }
-  FOREACHneighbor_(facet) {
-    if (neighbor == qh_MERGEridge || neighbor == qh_DUPLICATEridge) {
-      qh_fprintf(qh, qh->ferr, 6126, "qhull internal error (qh_checkfacet): facet f%d still has a MERGE or DUP neighbor\n", facet->id);
-      qh_errexit(qh, qh_ERRqhull, facet, NULL);
-    }
-    neighbor->seen= True;
-  }
-  FOREACHneighbor_(facet) {
-    if (!qh_setin(neighbor->neighbors, facet)) {
-      qh_fprintf(qh, qh->ferr, 6127, "qhull internal error (qh_checkfacet): facet f%d has neighbor f%d, but f%d does not have neighbor f%d\n",
-              facet->id, neighbor->id, neighbor->id, facet->id);
-      errother= neighbor;
-      waserror= True;
-    }
-    if (!neighbor->seen) {
-      qh_fprintf(qh, qh->ferr, 6128, "qhull internal error (qh_checkfacet): facet f%d has a duplicate neighbor f%d\n",
-              facet->id, neighbor->id);
-      errother= neighbor;
-      waserror= True;
-    }
-    neighbor->seen= False;
-  }
-  FOREACHridge_(facet->ridges) {
-    qh_setcheck(qh, ridge->vertices, "vertices for r", ridge->id);
-    ridge->seen= False;
-  }
-  FOREACHridge_(facet->ridges) {
-    if (ridge->seen) {
-      qh_fprintf(qh, qh->ferr, 6129, "qhull internal error (qh_checkfacet): facet f%d has a duplicate ridge r%d\n",
-              facet->id, ridge->id);
-      errridge= ridge;
-      waserror= True;
-    }
-    ridge->seen= True;
-    numRvertices= qh_setsize(qh, ridge->vertices);
-    if (numRvertices != qh->hull_dim - 1) {
-      qh_fprintf(qh, qh->ferr, 6130, "qhull internal error (qh_checkfacet): ridge between f%d and f%d has %d vertices\n",
-                ridge->top->id, ridge->bottom->id, numRvertices);
-      errridge= ridge;
-      waserror= True;
-    }
-    neighbor= otherfacet_(ridge, facet);
-    neighbor->seen= True;
-    if (!qh_setin(facet->neighbors, neighbor)) {
-      qh_fprintf(qh, qh->ferr, 6131, "qhull internal error (qh_checkfacet): for facet f%d, neighbor f%d of ridge r%d not in facet\n",
-           facet->id, neighbor->id, ridge->id);
-      errridge= ridge;
-      waserror= True;
-    }
-  }
-  if (!facet->simplicial) {
-    FOREACHneighbor_(facet) {
-      if (!neighbor->seen) {
-        qh_fprintf(qh, qh->ferr, 6132, "qhull internal error (qh_checkfacet): facet f%d does not have a ridge for neighbor f%d\n",
-              facet->id, neighbor->id);
-        errother= neighbor;
-        waserror= True;
-      }
-      intersection= qh_vertexintersect_new(qh, facet->vertices, neighbor->vertices);
-      qh_settemppush(qh, intersection);
-      FOREACHvertex_(facet->vertices) {
-        vertex->seen= False;
-        vertex->seen2= False;
-      }
-      FOREACHvertex_(intersection)
-        vertex->seen= True;
-      FOREACHridge_(facet->ridges) {
-        if (neighbor != otherfacet_(ridge, facet))
-            continue;
-        FOREACHvertex_(ridge->vertices) {
-          if (!vertex->seen) {
-            qh_fprintf(qh, qh->ferr, 6133, "qhull internal error (qh_checkfacet): vertex v%d in r%d not in f%d intersect f%d\n",
-                  vertex->id, ridge->id, facet->id, neighbor->id);
-            qh_errexit(qh, qh_ERRqhull, facet, ridge);
-          }
-          vertex->seen2= True;
-        }
-      }
-      if (!newmerge) {
-        FOREACHvertex_(intersection) {
-          if (!vertex->seen2) {
-            if (qh->IStracing >=3 || !qh->MERGING) {
-              qh_fprintf(qh, qh->ferr, 6134, "qhull precision error (qh_checkfacet): vertex v%d in f%d intersect f%d but\n\
- not in a ridge.  This is ok under merging.  Last point was p%d\n",
-                     vertex->id, facet->id, neighbor->id, qh->furthest_id);
-              if (!qh->FORCEoutput && !qh->MERGING) {
-                qh_errprint(qh, "ERRONEOUS", facet, neighbor, NULL, vertex);
-                if (!qh->MERGING)
-                  qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-              }
-            }
-          }
-        }
-      }
-      qh_settempfree(qh, &intersection);
-    }
-  }else { /* simplicial */
-    FOREACHneighbor_(facet) {
-      if (neighbor->simplicial) {
-        skipA= SETindex_(facet->neighbors, neighbor);
-        skipB= qh_setindex(neighbor->neighbors, facet);
-        if (skipA<0 || skipB<0 || !qh_setequal_skip(facet->vertices, skipA, neighbor->vertices, skipB)) {
-          qh_fprintf(qh, qh->ferr, 6135, "qhull internal error (qh_checkfacet): facet f%d skip %d and neighbor f%d skip %d do not match \n",
-                   facet->id, skipA, neighbor->id, skipB);
-          errother= neighbor;
-          waserror= True;
-        }
-      }
-    }
-  }
-  if (qh->hull_dim < 5 && (qh->IStracing > 2 || qh->CHECKfrequently)) {
-    FOREACHridge_i_(qh, facet->ridges) {           /* expensive */
-      for (i=ridge_i+1; i < ridge_n; i++) {
-        ridge2= SETelemt_(facet->ridges, i, ridgeT);
-        if (qh_setequal(ridge->vertices, ridge2->vertices)) {
-          qh_fprintf(qh, qh->ferr, 6227, "Qhull internal error (qh_checkfacet): ridges r%d and r%d have the same vertices\n",
-                  ridge->id, ridge2->id);
-          errridge= ridge;
-          waserror= True;
-        }
-      }
-    }
-  }
-  if (waserror) {
-    qh_errprint(qh, "ERRONEOUS", facet, errother, errridge, NULL);
-    *waserrorp= True;
-  }
-} /* checkfacet */
-
-
-/*---------------------------------
-
-  qh_checkflipped_all(qh, facetlist )
-    checks orientation of facets in list against interior point
-*/
-void qh_checkflipped_all(qhT *qh, facetT *facetlist) {
-  facetT *facet;
-  boolT waserror= False;
-  realT dist;
-
-  if (facetlist == qh->facet_list)
-    zzval_(Zflippedfacets)= 0;
-  FORALLfacet_(facetlist) {
-    if (facet->normal && !qh_checkflipped(qh, facet, &dist, !qh_ALL)) {
-      qh_fprintf(qh, qh->ferr, 6136, "qhull precision error: facet f%d is flipped, distance= %6.12g\n",
-              facet->id, dist);
-      if (!qh->FORCEoutput) {
-        qh_errprint(qh, "ERRONEOUS", facet, NULL, NULL, NULL);
-        waserror= True;
-      }
-    }
-  }
-  if (waserror) {
-    qh_fprintf(qh, qh->ferr, 8101, "\n\
-A flipped facet occurs when its distance to the interior point is\n\
-greater than %2.2g, the maximum roundoff error.\n", -qh->DISTround);
-    qh_errexit(qh, qh_ERRprec, NULL, NULL);
-  }
-} /* checkflipped_all */
-
-/*---------------------------------
-
-  qh_checkpolygon(qh, facetlist )
-    checks the correctness of the structure
-
-  notes:
-    call with either qh.facet_list or qh.newfacet_list
-    checks num_facets and num_vertices if qh.facet_list
-
-  design:
-    for each facet
-      checks facet and outside set
-    initializes vertexlist
-    for each facet
-      checks vertex set
-    if checking all facets(qh.facetlist)
-      check facet count
-      if qh.VERTEXneighbors
-        check vertex neighbors and count
-      check vertex count
-*/
-void qh_checkpolygon(qhT *qh, facetT *facetlist) {
-  facetT *facet;
-  vertexT *vertex, **vertexp, *vertexlist;
-  int numfacets= 0, numvertices= 0, numridges= 0;
-  int totvneighbors= 0, totvertices= 0;
-  boolT waserror= False, nextseen= False, visibleseen= False;
-
-  trace1((qh, qh->ferr, 1027, "qh_checkpolygon: check all facets from f%d\n", facetlist->id));
-  if (facetlist != qh->facet_list || qh->ONLYgood)
-    nextseen= True;
-  FORALLfacet_(facetlist) {
-    if (facet == qh->visible_list)
-      visibleseen= True;
-    if (!facet->visible) {
-      if (!nextseen) {
-        if (facet == qh->facet_next)
-          nextseen= True;
-        else if (qh_setsize(qh, facet->outsideset)) {
-          if (!qh->NARROWhull
-#if !qh_COMPUTEfurthest
-               || facet->furthestdist >= qh->MINoutside
-#endif
-                        ) {
-            qh_fprintf(qh, qh->ferr, 6137, "qhull internal error (qh_checkpolygon): f%d has outside points before qh->facet_next\n",
-                     facet->id);
-            qh_errexit(qh, qh_ERRqhull, facet, NULL);
-          }
-        }
-      }
-      numfacets++;
-      qh_checkfacet(qh, facet, False, &waserror);
-    }
-  }
-  if (qh->visible_list && !visibleseen && facetlist == qh->facet_list) {
-    qh_fprintf(qh, qh->ferr, 6138, "qhull internal error (qh_checkpolygon): visible list f%d no longer on facet list\n", qh->visible_list->id);
-    qh_printlists(qh);
-    qh_errexit(qh, qh_ERRqhull, qh->visible_list, NULL);
-  }
-  if (facetlist == qh->facet_list)
-    vertexlist= qh->vertex_list;
-  else if (facetlist == qh->newfacet_list)
-    vertexlist= qh->newvertex_list;
-  else
-    vertexlist= NULL;
-  FORALLvertex_(vertexlist) {
-    vertex->seen= False;
-    vertex->visitid= 0;
-  }
-  FORALLfacet_(facetlist) {
-    if (facet->visible)
-      continue;
-    if (facet->simplicial)
-      numridges += qh->hull_dim;
-    else
-      numridges += qh_setsize(qh, facet->ridges);
-    FOREACHvertex_(facet->vertices) {
-      vertex->visitid++;
-      if (!vertex->seen) {
-        vertex->seen= True;
-        numvertices++;
-        if (qh_pointid(qh, vertex->point) == qh_IDunknown) {
-          qh_fprintf(qh, qh->ferr, 6139, "qhull internal error (qh_checkpolygon): unknown point %p for vertex v%d first_point %p\n",
-                   vertex->point, vertex->id, qh->first_point);
-          waserror= True;
-        }
-      }
-    }
-  }
-  qh->vertex_visit += (unsigned int)numfacets;
-  if (facetlist == qh->facet_list) {
-    if (numfacets != qh->num_facets - qh->num_visible) {
-      qh_fprintf(qh, qh->ferr, 6140, "qhull internal error (qh_checkpolygon): actual number of facets is %d, cumulative facet count is %d - %d visible facets\n",
-              numfacets, qh->num_facets, qh->num_visible);
-      waserror= True;
-    }
-    qh->vertex_visit++;
-    if (qh->VERTEXneighbors) {
-      FORALLvertices {
-        qh_setcheck(qh, vertex->neighbors, "neighbors for v", vertex->id);
-        if (vertex->deleted)
-          continue;
-        totvneighbors += qh_setsize(qh, vertex->neighbors);
-      }
-      FORALLfacet_(facetlist)
-        totvertices += qh_setsize(qh, facet->vertices);
-      if (totvneighbors != totvertices) {
-        qh_fprintf(qh, qh->ferr, 6141, "qhull internal error (qh_checkpolygon): vertex neighbors inconsistent.  Totvneighbors %d, totvertices %d\n",
-                totvneighbors, totvertices);
-        waserror= True;
-      }
-    }
-    if (numvertices != qh->num_vertices - qh_setsize(qh, qh->del_vertices)) {
-      qh_fprintf(qh, qh->ferr, 6142, "qhull internal error (qh_checkpolygon): actual number of vertices is %d, cumulative vertex count is %d\n",
-              numvertices, qh->num_vertices - qh_setsize(qh, qh->del_vertices));
-      waserror= True;
-    }
-    if (qh->hull_dim == 2 && numvertices != numfacets) {
-      qh_fprintf(qh, qh->ferr, 6143, "qhull internal error (qh_checkpolygon): #vertices %d != #facets %d\n",
-        numvertices, numfacets);
-      waserror= True;
-    }
-    if (qh->hull_dim == 3 && numvertices + numfacets - numridges/2 != 2) {
-      qh_fprintf(qh, qh->ferr, 7063, "qhull warning: #vertices %d + #facets %d - #edges %d != 2\n\
-        A vertex appears twice in a edge list.  May occur during merging.",
-        numvertices, numfacets, numridges/2);
-      /* occurs if lots of merging and a vertex ends up twice in an edge list.  e.g., RBOX 1000 s W1e-13 t995849315 D2 | QHULL d Tc Tv */
-    }
-  }
-  if (waserror)
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-} /* checkpolygon */
-
-
-/*---------------------------------
-
-  qh_checkvertex(qh, vertex )
-    check vertex for consistency
-    checks vertex->neighbors
-
-  notes:
-    neighbors checked efficiently in checkpolygon
-*/
-void qh_checkvertex(qhT *qh, vertexT *vertex) {
-  boolT waserror= False;
-  facetT *neighbor, **neighborp, *errfacet=NULL;
-
-  if (qh_pointid(qh, vertex->point) == qh_IDunknown) {
-    qh_fprintf(qh, qh->ferr, 6144, "qhull internal error (qh_checkvertex): unknown point id %p\n", vertex->point);
-    waserror= True;
-  }
-  if (vertex->id >= qh->vertex_id) {
-    qh_fprintf(qh, qh->ferr, 6145, "qhull internal error (qh_checkvertex): unknown vertex id %d\n", vertex->id);
-    waserror= True;
-  }
-  if (!waserror && !vertex->deleted) {
-    if (qh_setsize(qh, vertex->neighbors)) {
-      FOREACHneighbor_(vertex) {
-        if (!qh_setin(neighbor->vertices, vertex)) {
-          qh_fprintf(qh, qh->ferr, 6146, "qhull internal error (qh_checkvertex): neighbor f%d does not contain v%d\n", neighbor->id, vertex->id);
-          errfacet= neighbor;
-          waserror= True;
-        }
-      }
-    }
-  }
-  if (waserror) {
-    qh_errprint(qh, "ERRONEOUS", NULL, NULL, NULL, vertex);
-    qh_errexit(qh, qh_ERRqhull, errfacet, NULL);
-  }
-} /* checkvertex */
-
-/*---------------------------------
-
-  qh_clearcenters(qh, type )
-    clear old data from facet->center
-
-  notes:
-    sets new centertype
-    nop if CENTERtype is the same
-*/
-void qh_clearcenters(qhT *qh, qh_CENTER type) {
-  facetT *facet;
-
-  if (qh->CENTERtype != type) {
-    FORALLfacets {
-      if (facet->tricoplanar && !facet->keepcentrum)
-          facet->center= NULL;  /* center is owned by the ->keepcentrum facet */
-      else if (qh->CENTERtype == qh_ASvoronoi){
-        if (facet->center) {
-          qh_memfree(qh, facet->center, qh->center_size);
-          facet->center= NULL;
-        }
-      }else /* qh->CENTERtype == qh_AScentrum */ {
-        if (facet->center) {
-          qh_memfree(qh, facet->center, qh->normal_size);
-          facet->center= NULL;
-        }
-      }
-    }
-    qh->CENTERtype= type;
-  }
-  trace2((qh, qh->ferr, 2043, "qh_clearcenters: switched to center type %d\n", type));
-} /* clearcenters */
-
-/*---------------------------------
-
-  qh_createsimplex(qh, vertices )
-    creates a simplex from a set of vertices
-
-  returns:
-    initializes qh.facet_list to the simplex
-    initializes qh.newfacet_list, .facet_tail
-    initializes qh.vertex_list, .newvertex_list, .vertex_tail
-
-  design:
-    initializes lists
-    for each vertex
-      create a new facet
-    for each new facet
-      create its neighbor set
-*/
-void qh_createsimplex(qhT *qh, setT *vertices) {
-  facetT *facet= NULL, *newfacet;
-  boolT toporient= True;
-  int vertex_i, vertex_n, nth;
-  setT *newfacets= qh_settemp(qh, qh->hull_dim+1);
-  vertexT *vertex;
-
-  qh->facet_list= qh->newfacet_list= qh->facet_tail= qh_newfacet(qh);
-  qh->num_facets= qh->num_vertices= qh->num_visible= 0;
-  qh->vertex_list= qh->newvertex_list= qh->vertex_tail= qh_newvertex(qh, NULL);
-  FOREACHvertex_i_(qh, vertices) {
-    newfacet= qh_newfacet(qh);
-    newfacet->vertices= qh_setnew_delnthsorted(qh, vertices, vertex_n,
-                                                vertex_i, 0);
-    newfacet->toporient= (unsigned char)toporient;
-    qh_appendfacet(qh, newfacet);
-    newfacet->newfacet= True;
-    qh_appendvertex(qh, vertex);
-    qh_setappend(qh, &newfacets, newfacet);
-    toporient ^= True;
-  }
-  FORALLnew_facets {
-    nth= 0;
-    FORALLfacet_(qh->newfacet_list) {
-      if (facet != newfacet)
-        SETelem_(newfacet->neighbors, nth++)= facet;
-    }
-    qh_settruncate(qh, newfacet->neighbors, qh->hull_dim);
-  }
-  qh_settempfree(qh, &newfacets);
-  trace1((qh, qh->ferr, 1028, "qh_createsimplex: created simplex\n"));
-} /* createsimplex */
-
-/*---------------------------------
-
-  qh_delridge(qh, ridge )
-    deletes ridge from data structures it belongs to
-    frees up its memory
-
-  notes:
-    in merge_r.c, caller sets vertex->delridge for each vertex
-    ridges also freed in qh_freeqhull
-*/
-void qh_delridge(qhT *qh, ridgeT *ridge) {
-  void **freelistp; /* used if !qh_NOmem by qh_memfree_() */
-
-  qh_setdel(ridge->top->ridges, ridge);
-  qh_setdel(ridge->bottom->ridges, ridge);
-  qh_setfree(qh, &(ridge->vertices));
-  qh_memfree_(qh, ridge, (int)sizeof(ridgeT), freelistp);
-} /* delridge */
-
-
-/*---------------------------------
-
-  qh_delvertex(qh, vertex )
-    deletes a vertex and frees its memory
-
-  notes:
-    assumes vertex->adjacencies have been updated if needed
-    unlinks from vertex_list
-*/
-void qh_delvertex(qhT *qh, vertexT *vertex) {
-
-  if (vertex == qh->tracevertex)
-    qh->tracevertex= NULL;
-  qh_removevertex(qh, vertex);
-  qh_setfree(qh, &vertex->neighbors);
-  qh_memfree(qh, vertex, (int)sizeof(vertexT));
-} /* delvertex */
-
-
-/*---------------------------------
-
-  qh_facet3vertex(qh, )
-    return temporary set of 3-d vertices in qh_ORIENTclock order
-
-  design:
-    if simplicial facet
-      build set from facet->vertices with facet->toporient
-    else
-      for each ridge in order
-        build set from ridge's vertices
-*/
-setT *qh_facet3vertex(qhT *qh, facetT *facet) {
-  ridgeT *ridge, *firstridge;
-  vertexT *vertex;
-  int cntvertices, cntprojected=0;
-  setT *vertices;
-
-  cntvertices= qh_setsize(qh, facet->vertices);
-  vertices= qh_settemp(qh, cntvertices);
-  if (facet->simplicial) {
-    if (cntvertices != 3) {
-      qh_fprintf(qh, qh->ferr, 6147, "qhull internal error (qh_facet3vertex): only %d vertices for simplicial facet f%d\n",
-                  cntvertices, facet->id);
-      qh_errexit(qh, qh_ERRqhull, facet, NULL);
-    }
-    qh_setappend(qh, &vertices, SETfirst_(facet->vertices));
-    if (facet->toporient ^ qh_ORIENTclock)
-      qh_setappend(qh, &vertices, SETsecond_(facet->vertices));
-    else
-      qh_setaddnth(qh, &vertices, 0, SETsecond_(facet->vertices));
-    qh_setappend(qh, &vertices, SETelem_(facet->vertices, 2));
-  }else {
-    ridge= firstridge= SETfirstt_(facet->ridges, ridgeT);   /* no infinite */
-    while ((ridge= qh_nextridge3d(ridge, facet, &vertex))) {
-      qh_setappend(qh, &vertices, vertex);
-      if (++cntprojected > cntvertices || ridge == firstridge)
-        break;
-    }
-    if (!ridge || cntprojected != cntvertices) {
-      qh_fprintf(qh, qh->ferr, 6148, "qhull internal error (qh_facet3vertex): ridges for facet %d don't match up.  got at least %d\n",
-                  facet->id, cntprojected);
-      qh_errexit(qh, qh_ERRqhull, facet, ridge);
-    }
-  }
-  return vertices;
-} /* facet3vertex */
-
-/*---------------------------------
-
-  qh_findbestfacet(qh, point, bestoutside, bestdist, isoutside )
-    find facet that is furthest below a point
-
-    for Delaunay triangulations,
-      Use qh_setdelaunay() to lift point to paraboloid and scale by 'Qbb' if needed
-      Do not use options 'Qbk', 'QBk', or 'QbB' since they scale the coordinates.
-
-  returns:
-    if bestoutside is set (e.g., qh_ALL)
-      returns best facet that is not upperdelaunay
-      if Delaunay and inside, point is outside circumsphere of bestfacet
-    else
-      returns first facet below point
-      if point is inside, returns nearest, !upperdelaunay facet
-    distance to facet
-    isoutside set if outside of facet
-
-  notes:
-    For tricoplanar facets, this finds one of the tricoplanar facets closest
-    to the point.  For Delaunay triangulations, the point may be inside a
-    different tricoplanar facet. See locate a facet with qh_findbestfacet()
-
-    If inside, qh_findbestfacet performs an exhaustive search
-       this may be too conservative.  Sometimes it is clearly required.
-
-    qh_findbestfacet is not used by qhull.
-    uses qh.visit_id and qh.coplanarset
-
-  see:
-    qh_findbest
-*/
-facetT *qh_findbestfacet(qhT *qh, pointT *point, boolT bestoutside,
-           realT *bestdist, boolT *isoutside) {
-  facetT *bestfacet= NULL;
-  int numpart, totpart= 0;
-
-  bestfacet= qh_findbest(qh, point, qh->facet_list,
-                            bestoutside, !qh_ISnewfacets, bestoutside /* qh_NOupper */,
-                            bestdist, isoutside, &totpart);
-  if (*bestdist < -qh->DISTround) {
-    bestfacet= qh_findfacet_all(qh, point, bestdist, isoutside, &numpart);
-    totpart += numpart;
-    if ((isoutside && *isoutside && bestoutside)
-    || (isoutside && !*isoutside && bestfacet->upperdelaunay)) {
-      bestfacet= qh_findbest(qh, point, bestfacet,
-                            bestoutside, False, bestoutside,
-                            bestdist, isoutside, &totpart);
-      totpart += numpart;
-    }
-  }
-  trace3((qh, qh->ferr, 3014, "qh_findbestfacet: f%d dist %2.2g isoutside %d totpart %d\n",
-          bestfacet->id, *bestdist, (isoutside ? *isoutside : UINT_MAX), totpart));
-  return bestfacet;
-} /* findbestfacet */
-
-/*---------------------------------
-
-  qh_findbestlower(qh, facet, point, bestdist, numpart )
-    returns best non-upper, non-flipped neighbor of facet for point
-    if needed, searches vertex neighbors
-
-  returns:
-    returns bestdist and updates numpart
-
-  notes:
-    if Delaunay and inside, point is outside of circumsphere of bestfacet
-    called by qh_findbest() for points above an upperdelaunay facet
-
-*/
-facetT *qh_findbestlower(qhT *qh, facetT *upperfacet, pointT *point, realT *bestdistp, int *numpart) {
-  facetT *neighbor, **neighborp, *bestfacet= NULL;
-  realT bestdist= -REALmax/2 /* avoid underflow */;
-  realT dist;
-  vertexT *vertex;
-  boolT isoutside= False;  /* not used */
-
-  zinc_(Zbestlower);
-  FOREACHneighbor_(upperfacet) {
-    if (neighbor->upperdelaunay || neighbor->flipped)
-      continue;
-    (*numpart)++;
-    qh_distplane(qh, point, neighbor, &dist);
-    if (dist > bestdist) {
-      bestfacet= neighbor;
-      bestdist= dist;
-    }
-  }
-  if (!bestfacet) {
-    zinc_(Zbestlowerv);
-    /* rarely called, numpart does not count nearvertex computations */
-    vertex= qh_nearvertex(qh, upperfacet, point, &dist);
-    qh_vertexneighbors(qh);
-    FOREACHneighbor_(vertex) {
-      if (neighbor->upperdelaunay || neighbor->flipped)
-        continue;
-      (*numpart)++;
-      qh_distplane(qh, point, neighbor, &dist);
-      if (dist > bestdist) {
-        bestfacet= neighbor;
-        bestdist= dist;
-      }
-    }
-  }
-  if (!bestfacet) {
-    zinc_(Zbestlowerall);  /* invoked once per point in outsideset */
-    zmax_(Zbestloweralln, qh->num_facets);
-    /* [dec'15] Previously reported as QH6228 */
-    trace3((qh, qh->ferr, 3025, "qh_findbestlower: all neighbors of facet %d are flipped or upper Delaunay.  Search all facets\n",
-       upperfacet->id));
-    /* rarely called */
-    bestfacet= qh_findfacet_all(qh, point, &bestdist, &isoutside, numpart);
-  }
-  *bestdistp= bestdist;
-  trace3((qh, qh->ferr, 3015, "qh_findbestlower: f%d dist %2.2g for f%d p%d\n",
-          bestfacet->id, bestdist, upperfacet->id, qh_pointid(qh, point)));
-  return bestfacet;
-} /* findbestlower */
-
-/*---------------------------------
-
-  qh_findfacet_all(qh, point, bestdist, isoutside, numpart )
-    exhaustive search for facet below a point
-
-    for Delaunay triangulations,
-      Use qh_setdelaunay() to lift point to paraboloid and scale by 'Qbb' if needed
-      Do not use options 'Qbk', 'QBk', or 'QbB' since they scale the coordinates.
-
-  returns:
-    returns first facet below point
-    if point is inside,
-      returns nearest facet
-    distance to facet
-    isoutside if point is outside of the hull
-    number of distance tests
-
-  notes:
-    primarily for library users, rarely used by Qhull
-*/
-facetT *qh_findfacet_all(qhT *qh, pointT *point, realT *bestdist, boolT *isoutside,
-                          int *numpart) {
-  facetT *bestfacet= NULL, *facet;
-  realT dist;
-  int totpart= 0;
-
-  *bestdist= -REALmax;
-  *isoutside= False;
-  FORALLfacets {
-    if (facet->flipped || !facet->normal)
-      continue;
-    totpart++;
-    qh_distplane(qh, point, facet, &dist);
-    if (dist > *bestdist) {
-      *bestdist= dist;
-      bestfacet= facet;
-      if (dist > qh->MINoutside) {
-        *isoutside= True;
-        break;
-      }
-    }
-  }
-  *numpart= totpart;
-  trace3((qh, qh->ferr, 3016, "qh_findfacet_all: f%d dist %2.2g isoutside %d totpart %d\n",
-          getid_(bestfacet), *bestdist, *isoutside, totpart));
-  return bestfacet;
-} /* findfacet_all */
-
-/*---------------------------------
-
-  qh_findgood(qh, facetlist, goodhorizon )
-    identify good facets for qh.PRINTgood
-    if qh.GOODvertex>0
-      facet includes point as vertex
-      if !match, returns goodhorizon
-      inactive if qh.MERGING
-    if qh.GOODpoint
-      facet is visible or coplanar (>0) or not visible (<0)
-    if qh.GOODthreshold
-      facet->normal matches threshold
-    if !goodhorizon and !match,
-      selects facet with closest angle
-      sets GOODclosest
-
-  returns:
-    number of new, good facets found
-    determines facet->good
-    may update qh.GOODclosest
-
-  notes:
-    qh_findgood_all further reduces the good region
-
-  design:
-    count good facets
-    mark good facets for qh.GOODpoint
-    mark good facets for qh.GOODthreshold
-    if necessary
-      update qh.GOODclosest
-*/
-int qh_findgood(qhT *qh, facetT *facetlist, int goodhorizon) {
-  facetT *facet, *bestfacet= NULL;
-  realT angle, bestangle= REALmax, dist;
-  int  numgood=0;
-
-  FORALLfacet_(facetlist) {
-    if (facet->good)
-      numgood++;
-  }
-  if (qh->GOODvertex>0 && !qh->MERGING) {
-    FORALLfacet_(facetlist) {
-      if (!qh_isvertex(qh->GOODvertexp, facet->vertices)) {
-        facet->good= False;
-        numgood--;
-      }
-    }
-  }
-  if (qh->GOODpoint && numgood) {
-    FORALLfacet_(facetlist) {
-      if (facet->good && facet->normal) {
-        zinc_(Zdistgood);
-        qh_distplane(qh, qh->GOODpointp, facet, &dist);
-        if ((qh->GOODpoint > 0) ^ (dist > 0.0)) {
-          facet->good= False;
-          numgood--;
-        }
-      }
-    }
-  }
-  if (qh->GOODthreshold && (numgood || goodhorizon || qh->GOODclosest)) {
-    FORALLfacet_(facetlist) {
-      if (facet->good && facet->normal) {
-        if (!qh_inthresholds(qh, facet->normal, &angle)) {
-          facet->good= False;
-          numgood--;
-          if (angle < bestangle) {
-            bestangle= angle;
-            bestfacet= facet;
-          }
-        }
-      }
-    }
-    if (!numgood && (!goodhorizon || qh->GOODclosest)) {
-      if (qh->GOODclosest) {
-        if (qh->GOODclosest->visible)
-          qh->GOODclosest= NULL;
-        else {
-          qh_inthresholds(qh, qh->GOODclosest->normal, &angle);
-          if (angle < bestangle)
-            bestfacet= qh->GOODclosest;
-        }
-      }
-      if (bestfacet && bestfacet != qh->GOODclosest) {
-        if (qh->GOODclosest)
-          qh->GOODclosest->good= False;
-        qh->GOODclosest= bestfacet;
-        bestfacet->good= True;
-        numgood++;
-        trace2((qh, qh->ferr, 2044, "qh_findgood: f%d is closest(%2.2g) to thresholds\n",
-           bestfacet->id, bestangle));
-        return numgood;
-      }
-    }else if (qh->GOODclosest) { /* numgood > 0 */
-      qh->GOODclosest->good= False;
-      qh->GOODclosest= NULL;
-    }
-  }
-  zadd_(Zgoodfacet, numgood);
-  trace2((qh, qh->ferr, 2045, "qh_findgood: found %d good facets with %d good horizon\n",
-               numgood, goodhorizon));
-  if (!numgood && qh->GOODvertex>0 && !qh->MERGING)
-    return goodhorizon;
-  return numgood;
-} /* findgood */
-
-/*---------------------------------
-
-  qh_findgood_all(qh, facetlist )
-    apply other constraints for good facets (used by qh.PRINTgood)
-    if qh.GOODvertex
-      facet includes (>0) or doesn't include (<0) point as vertex
-      if last good facet and ONLYgood, prints warning and continues
-    if qh.SPLITthresholds
-      facet->normal matches threshold, or if none, the closest one
-    calls qh_findgood
-    nop if good not used
-
-  returns:
-    clears facet->good if not good
-    sets qh.num_good
-
-  notes:
-    this is like qh_findgood but more restrictive
-
-  design:
-    uses qh_findgood to mark good facets
-    marks facets for qh.GOODvertex
-    marks facets for qh.SPLITthreholds
-*/
-void qh_findgood_all(qhT *qh, facetT *facetlist) {
-  facetT *facet, *bestfacet=NULL;
-  realT angle, bestangle= REALmax;
-  int  numgood=0, startgood;
-
-  if (!qh->GOODvertex && !qh->GOODthreshold && !qh->GOODpoint
-  && !qh->SPLITthresholds)
-    return;
-  if (!qh->ONLYgood)
-    qh_findgood(qh, qh->facet_list, 0);
-  FORALLfacet_(facetlist) {
-    if (facet->good)
-      numgood++;
-  }
-  if (qh->GOODvertex <0 || (qh->GOODvertex > 0 && qh->MERGING)) {
-    FORALLfacet_(facetlist) {
-      if (facet->good && ((qh->GOODvertex > 0) ^ !!qh_isvertex(qh->GOODvertexp, facet->vertices))) {
-        if (!--numgood) {
-          if (qh->ONLYgood) {
-            qh_fprintf(qh, qh->ferr, 7064, "qhull warning: good vertex p%d does not match last good facet f%d.  Ignored.\n",
-               qh_pointid(qh, qh->GOODvertexp), facet->id);
-            return;
-          }else if (qh->GOODvertex > 0)
-            qh_fprintf(qh, qh->ferr, 7065, "qhull warning: point p%d is not a vertex('QV%d').\n",
-                qh->GOODvertex-1, qh->GOODvertex-1);
-          else
-            qh_fprintf(qh, qh->ferr, 7066, "qhull warning: point p%d is a vertex for every facet('QV-%d').\n",
-                -qh->GOODvertex - 1, -qh->GOODvertex - 1);
-        }
-        facet->good= False;
-      }
-    }
-  }
-  startgood= numgood;
-  if (qh->SPLITthresholds) {
-    FORALLfacet_(facetlist) {
-      if (facet->good) {
-        if (!qh_inthresholds(qh, facet->normal, &angle)) {
-          facet->good= False;
-          numgood--;
-          if (angle < bestangle) {
-            bestangle= angle;
-            bestfacet= facet;
-          }
-        }
-      }
-    }
-    if (!numgood && bestfacet) {
-      bestfacet->good= True;
-      numgood++;
-      trace0((qh, qh->ferr, 23, "qh_findgood_all: f%d is closest(%2.2g) to thresholds\n",
-           bestfacet->id, bestangle));
-      return;
-    }
-  }
-  qh->num_good= numgood;
-  trace0((qh, qh->ferr, 24, "qh_findgood_all: %d good facets remain out of %d facets\n",
-        numgood, startgood));
-} /* findgood_all */
-
-/*---------------------------------
-
-  qh_furthestnext()
-    set qh.facet_next to facet with furthest of all furthest points
-    searches all facets on qh.facet_list
-
-  notes:
-    this may help avoid precision problems
-*/
-void qh_furthestnext(qhT *qh /* qh->facet_list */) {
-  facetT *facet, *bestfacet= NULL;
-  realT dist, bestdist= -REALmax;
-
-  FORALLfacets {
-    if (facet->outsideset) {
-#if qh_COMPUTEfurthest
-      pointT *furthest;
-      furthest= (pointT*)qh_setlast(facet->outsideset);
-      zinc_(Zcomputefurthest);
-      qh_distplane(qh, furthest, facet, &dist);
-#else
-      dist= facet->furthestdist;
-#endif
-      if (dist > bestdist) {
-        bestfacet= facet;
-        bestdist= dist;
-      }
-    }
-  }
-  if (bestfacet) {
-    qh_removefacet(qh, bestfacet);
-    qh_prependfacet(qh, bestfacet, &qh->facet_next);
-    trace1((qh, qh->ferr, 1029, "qh_furthestnext: made f%d next facet(dist %.2g)\n",
-            bestfacet->id, bestdist));
-  }
-} /* furthestnext */
-
-/*---------------------------------
-
-  qh_furthestout(qh, facet )
-    make furthest outside point the last point of outsideset
-
-  returns:
-    updates facet->outsideset
-    clears facet->notfurthest
-    sets facet->furthestdist
-
-  design:
-    determine best point of outsideset
-    make it the last point of outsideset
-*/
-void qh_furthestout(qhT *qh, facetT *facet) {
-  pointT *point, **pointp, *bestpoint= NULL;
-  realT dist, bestdist= -REALmax;
-
-  FOREACHpoint_(facet->outsideset) {
-    qh_distplane(qh, point, facet, &dist);
-    zinc_(Zcomputefurthest);
-    if (dist > bestdist) {
-      bestpoint= point;
-      bestdist= dist;
-    }
-  }
-  if (bestpoint) {
-    qh_setdel(facet->outsideset, point);
-    qh_setappend(qh, &facet->outsideset, point);
-#if !qh_COMPUTEfurthest
-    facet->furthestdist= bestdist;
-#endif
-  }
-  facet->notfurthest= False;
-  trace3((qh, qh->ferr, 3017, "qh_furthestout: p%d is furthest outside point of f%d\n",
-          qh_pointid(qh, point), facet->id));
-} /* furthestout */
-
-
-/*---------------------------------
-
-  qh_infiniteloop(qh, facet )
-    report infinite loop error due to facet
-*/
-void qh_infiniteloop(qhT *qh, facetT *facet) {
-
-  qh_fprintf(qh, qh->ferr, 6149, "qhull internal error (qh_infiniteloop): potential infinite loop detected\n");
-  qh_errexit(qh, qh_ERRqhull, facet, NULL);
-} /* qh_infiniteloop */
-
-/*---------------------------------
-
-  qh_initbuild()
-    initialize hull and outside sets with point array
-    qh.FIRSTpoint/qh.NUMpoints is point array
-    if qh.GOODpoint
-      adds qh.GOODpoint to initial hull
-
-  returns:
-    qh_facetlist with initial hull
-    points partioned into outside sets, coplanar sets, or inside
-    initializes qh.GOODpointp, qh.GOODvertexp,
-
-  design:
-    initialize global variables used during qh_buildhull
-    determine precision constants and points with max/min coordinate values
-      if qh.SCALElast, scale last coordinate(for 'd')
-    build initial simplex
-    partition input points into facets of initial simplex
-    set up lists
-    if qh.ONLYgood
-      check consistency
-      add qh.GOODvertex if defined
-*/
-void qh_initbuild(qhT *qh) {
-  setT *maxpoints, *vertices;
-  facetT *facet;
-  int i, numpart;
-  realT dist;
-  boolT isoutside;
-
-  qh->furthest_id= qh_IDunknown;
-  qh->lastreport= 0;
-  qh->facet_id= qh->vertex_id= qh->ridge_id= 0;
-  qh->visit_id= qh->vertex_visit= 0;
-  qh->maxoutdone= False;
-
-  if (qh->GOODpoint > 0)
-    qh->GOODpointp= qh_point(qh, qh->GOODpoint-1);
-  else if (qh->GOODpoint < 0)
-    qh->GOODpointp= qh_point(qh, -qh->GOODpoint-1);
-  if (qh->GOODvertex > 0)
-    qh->GOODvertexp= qh_point(qh, qh->GOODvertex-1);
-  else if (qh->GOODvertex < 0)
-    qh->GOODvertexp= qh_point(qh, -qh->GOODvertex-1);
-  if ((qh->GOODpoint
-       && (qh->GOODpointp < qh->first_point  /* also catches !GOODpointp */
-           || qh->GOODpointp > qh_point(qh, qh->num_points-1)))
-    || (qh->GOODvertex
-        && (qh->GOODvertexp < qh->first_point  /* also catches !GOODvertexp */
-            || qh->GOODvertexp > qh_point(qh, qh->num_points-1)))) {
-    qh_fprintf(qh, qh->ferr, 6150, "qhull input error: either QGn or QVn point is > p%d\n",
-             qh->num_points-1);
-    qh_errexit(qh, qh_ERRinput, NULL, NULL);
-  }
-  maxpoints= qh_maxmin(qh, qh->first_point, qh->num_points, qh->hull_dim);
-  if (qh->SCALElast)
-    qh_scalelast(qh, qh->first_point, qh->num_points, qh->hull_dim,
-               qh->MINlastcoord, qh->MAXlastcoord, qh->MAXwidth);
-  qh_detroundoff(qh);
-  if (qh->DELAUNAY && qh->upper_threshold[qh->hull_dim-1] > REALmax/2
-                  && qh->lower_threshold[qh->hull_dim-1] < -REALmax/2) {
-    for (i=qh_PRINTEND; i--; ) {
-      if (qh->PRINTout[i] == qh_PRINTgeom && qh->DROPdim < 0
-          && !qh->GOODthreshold && !qh->SPLITthresholds)
-        break;  /* in this case, don't set upper_threshold */
-    }
-    if (i < 0) {
-      if (qh->UPPERdelaunay) { /* matches qh.upperdelaunay in qh_setfacetplane */
-        qh->lower_threshold[qh->hull_dim-1]= qh->ANGLEround * qh_ZEROdelaunay;
-        qh->GOODthreshold= True;
-      }else {
-        qh->upper_threshold[qh->hull_dim-1]= -qh->ANGLEround * qh_ZEROdelaunay;
-        if (!qh->GOODthreshold)
-          qh->SPLITthresholds= True; /* build upper-convex hull even if Qg */
-          /* qh_initqhull_globals errors if Qg without Pdk/etc. */
-      }
-    }
-  }
-  vertices= qh_initialvertices(qh, qh->hull_dim, maxpoints, qh->first_point, qh->num_points);
-  qh_initialhull(qh, vertices);  /* initial qh->facet_list */
-  qh_partitionall(qh, vertices, qh->first_point, qh->num_points);
-  if (qh->PRINToptions1st || qh->TRACElevel || qh->IStracing) {
-    if (qh->TRACElevel || qh->IStracing)
-      qh_fprintf(qh, qh->ferr, 8103, "\nTrace level %d for %s | %s\n",
-         qh->IStracing ? qh->IStracing : qh->TRACElevel, qh->rbox_command, qh->qhull_command);
-    qh_fprintf(qh, qh->ferr, 8104, "Options selected for Qhull %s:\n%s\n", qh_version, qh->qhull_options);
-  }
-  qh_resetlists(qh, False, qh_RESETvisible /*qh.visible_list newvertex_list newfacet_list */);
-  qh->facet_next= qh->facet_list;
-  qh_furthestnext(qh /* qh->facet_list */);
-  if (qh->PREmerge) {
-    qh->cos_max= qh->premerge_cos;
-    qh->centrum_radius= qh->premerge_centrum;
-  }
-  if (qh->ONLYgood) {
-    if (qh->GOODvertex > 0 && qh->MERGING) {
-      qh_fprintf(qh, qh->ferr, 6151, "qhull input error: 'Qg QVn' (only good vertex) does not work with merging.\nUse 'QJ' to joggle the input or 'Q0' to turn off merging.\n");
-      qh_errexit(qh, qh_ERRinput, NULL, NULL);
-    }
-    if (!(qh->GOODthreshold || qh->GOODpoint
-         || (!qh->MERGEexact && !qh->PREmerge && qh->GOODvertexp))) {
-      qh_fprintf(qh, qh->ferr, 6152, "qhull input error: 'Qg' (ONLYgood) needs a good threshold('Pd0D0'), a\n\
-good point(QGn or QG-n), or a good vertex with 'QJ' or 'Q0' (QVn).\n");
-      qh_errexit(qh, qh_ERRinput, NULL, NULL);
-    }
-    if (qh->GOODvertex > 0  && !qh->MERGING  /* matches qh_partitionall */
-        && !qh_isvertex(qh->GOODvertexp, vertices)) {
-      facet= qh_findbestnew(qh, qh->GOODvertexp, qh->facet_list,
-                          &dist, !qh_ALL, &isoutside, &numpart);
-      zadd_(Zdistgood, numpart);
-      if (!isoutside) {
-        qh_fprintf(qh, qh->ferr, 6153, "qhull input error: point for QV%d is inside initial simplex.  It can not be made a vertex.\n",
-               qh_pointid(qh, qh->GOODvertexp));
-        qh_errexit(qh, qh_ERRinput, NULL, NULL);
-      }
-      if (!qh_addpoint(qh, qh->GOODvertexp, facet, False)) {
-        qh_settempfree(qh, &vertices);
-        qh_settempfree(qh, &maxpoints);
-        return;
-      }
-    }
-    qh_findgood(qh, qh->facet_list, 0);
-  }
-  qh_settempfree(qh, &vertices);
-  qh_settempfree(qh, &maxpoints);
-  trace1((qh, qh->ferr, 1030, "qh_initbuild: initial hull created and points partitioned\n"));
-} /* initbuild */
-
-/*---------------------------------
-
-  qh_initialhull(qh, vertices )
-    constructs the initial hull as a DIM3 simplex of vertices
-
-  design:
-    creates a simplex (initializes lists)
-    determines orientation of simplex
-    sets hyperplanes for facets
-    doubles checks orientation (in case of axis-parallel facets with Gaussian elimination)
-    checks for flipped facets and qh.NARROWhull
-    checks the result
-*/
-void qh_initialhull(qhT *qh, setT *vertices) {
-  facetT *facet, *firstfacet, *neighbor, **neighborp;
-  realT dist, angle, minangle= REALmax;
-#ifndef qh_NOtrace
-  int k;
-#endif
-
-  qh_createsimplex(qh, vertices);  /* qh->facet_list */
-  qh_resetlists(qh, False, qh_RESETvisible);
-  qh->facet_next= qh->facet_list;      /* advance facet when processed */
-  qh->interior_point= qh_getcenter(qh, vertices);
-  firstfacet= qh->facet_list;
-  qh_setfacetplane(qh, firstfacet);
-  zinc_(Znumvisibility); /* needs to be in printsummary */
-  qh_distplane(qh, qh->interior_point, firstfacet, &dist);
-  if (dist > 0) {
-    FORALLfacets
-      facet->toporient ^= (unsigned char)True;
-  }
-  FORALLfacets
-    qh_setfacetplane(qh, facet);
-  FORALLfacets {
-    if (!qh_checkflipped(qh, facet, NULL, qh_ALL)) {/* due to axis-parallel facet */
-      trace1((qh, qh->ferr, 1031, "qh_initialhull: initial orientation incorrect.  Correct all facets\n"));
-      facet->flipped= False;
-      FORALLfacets {
-        facet->toporient ^= (unsigned char)True;
-        qh_orientoutside(qh, facet);
-      }
-      break;
-    }
-  }
-  FORALLfacets {
-    if (!qh_checkflipped(qh, facet, NULL, !qh_ALL)) {  /* can happen with 'R0.1' */
-      if (qh->DELAUNAY && ! qh->ATinfinity) {
-        if (qh->UPPERdelaunay)
-          qh_fprintf(qh, qh->ferr, 6240, "Qhull precision error: Initial simplex is cocircular or cospherical.  Option 'Qs' searches all points.  Can not compute the upper Delaunay triangulation or upper Voronoi diagram of cocircular/cospherical points.\n");
-        else
-          qh_fprintf(qh, qh->ferr, 6239, "Qhull precision error: Initial simplex is cocircular or cospherical.  Use option 'Qz' for the Delaunay triangulation or Voronoi diagram of cocircular/cospherical points.  Option 'Qz' adds a point \"at infinity\".  Use option 'Qs' to search all points for the initial simplex.\n");
-        qh_errexit(qh, qh_ERRinput, NULL, NULL);
-      }
-      qh_precision(qh, "initial simplex is flat");
-      qh_fprintf(qh, qh->ferr, 6154, "Qhull precision error: Initial simplex is flat (facet %d is coplanar with the interior point)\n",
-                   facet->id);
-      qh_errexit(qh, qh_ERRsingular, NULL, NULL);  /* calls qh_printhelp_singular */
-    }
-    FOREACHneighbor_(facet) {
-      angle= qh_getangle(qh, facet->normal, neighbor->normal);
-      minimize_( minangle, angle);
-    }
-  }
-  if (minangle < qh_MAXnarrow && !qh->NOnarrow) {
-    realT diff= 1.0 + minangle;
-
-    qh->NARROWhull= True;
-    qh_option(qh, "_narrow-hull", NULL, &diff);
-    if (minangle < qh_WARNnarrow && !qh->RERUN && qh->PRINTprecision)
-      qh_printhelp_narrowhull(qh, qh->ferr, minangle);
-  }
-  zzval_(Zprocessed)= qh->hull_dim+1;
-  qh_checkpolygon(qh, qh->facet_list);
-  qh_checkconvex(qh, qh->facet_list,   qh_DATAfault);
-#ifndef qh_NOtrace
-  if (qh->IStracing >= 1) {
-    qh_fprintf(qh, qh->ferr, 8105, "qh_initialhull: simplex constructed, interior point:");
-    for (k=0; k < qh->hull_dim; k++)
-      qh_fprintf(qh, qh->ferr, 8106, " %6.4g", qh->interior_point[k]);
-    qh_fprintf(qh, qh->ferr, 8107, "\n");
-  }
-#endif
-} /* initialhull */
-
-/*---------------------------------
-
-  qh_initialvertices(qh, dim, maxpoints, points, numpoints )
-    determines a non-singular set of initial vertices
-    maxpoints may include duplicate points
-
-  returns:
-    temporary set of dim+1 vertices in descending order by vertex id
-    if qh.RANDOMoutside && !qh.ALLpoints
-      picks random points
-    if dim >= qh_INITIALmax,
-      uses min/max x and max points with non-zero determinants
-
-  notes:
-    unless qh.ALLpoints,
-      uses maxpoints as long as determinate is non-zero
-*/
-setT *qh_initialvertices(qhT *qh, int dim, setT *maxpoints, pointT *points, int numpoints) {
-  pointT *point, **pointp;
-  setT *vertices, *simplex, *tested;
-  realT randr;
-  int idx, point_i, point_n, k;
-  boolT nearzero= False;
-
-  vertices= qh_settemp(qh, dim + 1);
-  simplex= qh_settemp(qh, dim+1);
-  if (qh->ALLpoints)
-    qh_maxsimplex(qh, dim, NULL, points, numpoints, &simplex);
-  else if (qh->RANDOMoutside) {
-    while (qh_setsize(qh, simplex) != dim+1) {
-      randr= qh_RANDOMint;
-      randr= randr/(qh_RANDOMmax+1);
-      idx= (int)floor(qh->num_points * randr);
-      while (qh_setin(simplex, qh_point(qh, idx))) {
-            idx++; /* in case qh_RANDOMint always returns the same value */
-        idx= idx < qh->num_points ? idx : 0;
-      }
-      qh_setappend(qh, &simplex, qh_point(qh, idx));
-    }
-  }else if (qh->hull_dim >= qh_INITIALmax) {
-    tested= qh_settemp(qh, dim+1);
-    qh_setappend(qh, &simplex, SETfirst_(maxpoints));   /* max and min X coord */
-    qh_setappend(qh, &simplex, SETsecond_(maxpoints));
-    qh_maxsimplex(qh, fmin_(qh_INITIALsearch, dim), maxpoints, points, numpoints, &simplex);
-    k= qh_setsize(qh, simplex);
-    FOREACHpoint_i_(qh, maxpoints) {
-      if (point_i & 0x1) {     /* first pick up max. coord. points */
-        if (!qh_setin(simplex, point) && !qh_setin(tested, point)){
-          qh_detsimplex(qh, point, simplex, k, &nearzero);
-          if (nearzero)
-            qh_setappend(qh, &tested, point);
-          else {
-            qh_setappend(qh, &simplex, point);
-            if (++k == dim)  /* use search for last point */
-              break;
-          }
-        }
-      }
-    }
-    while (k != dim && (point= (pointT*)qh_setdellast(maxpoints))) {
-      if (!qh_setin(simplex, point) && !qh_setin(tested, point)){
-        qh_detsimplex(qh, point, simplex, k, &nearzero);
-        if (nearzero)
-          qh_setappend(qh, &tested, point);
-        else {
-          qh_setappend(qh, &simplex, point);
-          k++;
-        }
-      }
-    }
-    idx= 0;
-    while (k != dim && (point= qh_point(qh, idx++))) {
-      if (!qh_setin(simplex, point) && !qh_setin(tested, point)){
-        qh_detsimplex(qh, point, simplex, k, &nearzero);
-        if (!nearzero){
-          qh_setappend(qh, &simplex, point);
-          k++;
-        }
-      }
-    }
-    qh_settempfree(qh, &tested);
-    qh_maxsimplex(qh, dim, maxpoints, points, numpoints, &simplex);
-  }else
-    qh_maxsimplex(qh, dim, maxpoints, points, numpoints, &simplex);
-  FOREACHpoint_(simplex)
-    qh_setaddnth(qh, &vertices, 0, qh_newvertex(qh, point)); /* descending order */
-  qh_settempfree(qh, &simplex);
-  return vertices;
-} /* initialvertices */
-
-
-/*---------------------------------
-
-  qh_isvertex( point, vertices )
-    returns vertex if point is in vertex set, else returns NULL
-
-  notes:
-    for qh.GOODvertex
-*/
-vertexT *qh_isvertex(pointT *point, setT *vertices) {
-  vertexT *vertex, **vertexp;
-
-  FOREACHvertex_(vertices) {
-    if (vertex->point == point)
-      return vertex;
-  }
-  return NULL;
-} /* isvertex */
-
-/*---------------------------------
-
-  qh_makenewfacets(qh, point )
-    make new facets from point and qh.visible_list
-
-  returns:
-    qh.newfacet_list= list of new facets with hyperplanes and ->newfacet
-    qh.newvertex_list= list of vertices in new facets with ->newlist set
-
-    if (qh.ONLYgood)
-      newfacets reference horizon facets, but not vice versa
-      ridges reference non-simplicial horizon ridges, but not vice versa
-      does not change existing facets
-    else
-      sets qh.NEWfacets
-      new facets attached to horizon facets and ridges
-      for visible facets,
-        visible->r.replace is corresponding new facet
-
-  see also:
-    qh_makenewplanes() -- make hyperplanes for facets
-    qh_attachnewfacets() -- attachnewfacets if not done here(qh->ONLYgood)
-    qh_matchnewfacets() -- match up neighbors
-    qh_updatevertices() -- update vertex neighbors and delvertices
-    qh_deletevisible() -- delete visible facets
-    qh_checkpolygon() --check the result
-    qh_triangulate() -- triangulate a non-simplicial facet
-
-  design:
-    for each visible facet
-      make new facets to its horizon facets
-      update its f.replace
-      clear its neighbor set
-*/
-vertexT *qh_makenewfacets(qhT *qh, pointT *point /*visible_list*/) {
-  facetT *visible, *newfacet= NULL, *newfacet2= NULL, *neighbor, **neighborp;
-  vertexT *apex;
-  int numnew=0;
-
-  qh->newfacet_list= qh->facet_tail;
-  qh->newvertex_list= qh->vertex_tail;
-  apex= qh_newvertex(qh, point);
-  qh_appendvertex(qh, apex);
-  qh->visit_id++;
-  if (!qh->ONLYgood)
-    qh->NEWfacets= True;
-  FORALLvisible_facets {
-    FOREACHneighbor_(visible)
-      neighbor->seen= False;
-    if (visible->ridges) {
-      visible->visitid= qh->visit_id;
-      newfacet2= qh_makenew_nonsimplicial(qh, visible, apex, &numnew);
-    }
-    if (visible->simplicial)
-      newfacet= qh_makenew_simplicial(qh, visible, apex, &numnew);
-    if (!qh->ONLYgood) {
-      if (newfacet2)  /* newfacet is null if all ridges defined */
-        newfacet= newfacet2;
-      if (newfacet)
-        visible->f.replace= newfacet;
-      else
-        zinc_(Zinsidevisible);
-      SETfirst_(visible->neighbors)= NULL;
-    }
-  }
-  trace1((qh, qh->ferr, 1032, "qh_makenewfacets: created %d new facets from point p%d to horizon\n",
-          numnew, qh_pointid(qh, point)));
-  if (qh->IStracing >= 4)
-    qh_printfacetlist(qh, qh->newfacet_list, NULL, qh_ALL);
-  return apex;
-} /* makenewfacets */
-
-/*---------------------------------
-
-  qh_matchduplicates(qh, atfacet, atskip, hashsize, hashcount )
-    match duplicate ridges in qh.hash_table for atfacet/atskip
-    duplicates marked with ->dupridge and qh_DUPLICATEridge
-
-  returns:
-    picks match with worst merge (min distance apart)
-    updates hashcount
-
-  see also:
-    qh_matchneighbor
-
-  notes:
-
-  design:
-    compute hash value for atfacet and atskip
-    repeat twice -- once to make best matches, once to match the rest
-      for each possible facet in qh.hash_table
-        if it is a matching facet and pass 2
-          make match
-          unless tricoplanar, mark match for merging (qh_MERGEridge)
-          [e.g., tricoplanar RBOX s 1000 t993602376 | QHULL C-1e-3 d Qbb FA Qt]
-        if it is a matching facet and pass 1
-          test if this is a better match
-      if pass 1,
-        make best match (it will not be merged)
-*/
-#ifndef qh_NOmerge
-void qh_matchduplicates(qhT *qh, facetT *atfacet, int atskip, int hashsize, int *hashcount) {
-  boolT same, ismatch;
-  int hash, scan;
-  facetT *facet, *newfacet, *maxmatch= NULL, *maxmatch2= NULL, *nextfacet;
-  int skip, newskip, nextskip= 0, maxskip= 0, maxskip2= 0, makematch;
-  realT maxdist= -REALmax, mindist, dist2, low, high;
-
-  hash= qh_gethash(qh, hashsize, atfacet->vertices, qh->hull_dim, 1,
-                     SETelem_(atfacet->vertices, atskip));
-  trace2((qh, qh->ferr, 2046, "qh_matchduplicates: find duplicate matches for f%d skip %d hash %d hashcount %d\n",
-          atfacet->id, atskip, hash, *hashcount));
-  for (makematch= 0; makematch < 2; makematch++) {
-    qh->visit_id++;
-    for (newfacet= atfacet, newskip= atskip; newfacet; newfacet= nextfacet, newskip= nextskip) {
-      zinc_(Zhashlookup);
-      nextfacet= NULL;
-      newfacet->visitid= qh->visit_id;
-      for (scan= hash; (facet= SETelemt_(qh->hash_table, scan, facetT));
-           scan= (++scan >= hashsize ? 0 : scan)) {
-        if (!facet->dupridge || facet->visitid == qh->visit_id)
-          continue;
-        zinc_(Zhashtests);
-        if (qh_matchvertices(qh, 1, newfacet->vertices, newskip, facet->vertices, &skip, &same)) {
-          ismatch= (same == (boolT)(newfacet->toporient ^ facet->toporient));
-          if (SETelemt_(facet->neighbors, skip, facetT) != qh_DUPLICATEridge) {
-            if (!makematch) {
-              qh_fprintf(qh, qh->ferr, 6155, "qhull internal error (qh_matchduplicates): missing dupridge at f%d skip %d for new f%d skip %d hash %d\n",
-                     facet->id, skip, newfacet->id, newskip, hash);
-              qh_errexit2(qh, qh_ERRqhull, facet, newfacet);
-            }
-          }else if (ismatch && makematch) {
-            if (SETelemt_(newfacet->neighbors, newskip, facetT) == qh_DUPLICATEridge) {
-              SETelem_(facet->neighbors, skip)= newfacet;
-              if (newfacet->tricoplanar)
-                SETelem_(newfacet->neighbors, newskip)= facet;
-              else
-                SETelem_(newfacet->neighbors, newskip)= qh_MERGEridge;
-              *hashcount -= 2; /* removed two unmatched facets */
-              trace4((qh, qh->ferr, 4059, "qh_matchduplicates: duplicate f%d skip %d matched with new f%d skip %d merge\n",
-                    facet->id, skip, newfacet->id, newskip));
-            }
-          }else if (ismatch) {
-            mindist= qh_getdistance(qh, facet, newfacet, &low, &high);
-            dist2= qh_getdistance(qh, newfacet, facet, &low, &high);
-            minimize_(mindist, dist2);
-            if (mindist > maxdist) {
-              maxdist= mindist;
-              maxmatch= facet;
-              maxskip= skip;
-              maxmatch2= newfacet;
-              maxskip2= newskip;
-            }
-            trace3((qh, qh->ferr, 3018, "qh_matchduplicates: duplicate f%d skip %d new f%d skip %d at dist %2.2g, max is now f%d f%d\n",
-                    facet->id, skip, newfacet->id, newskip, mindist,
-                    maxmatch->id, maxmatch2->id));
-          }else { /* !ismatch */
-            nextfacet= facet;
-            nextskip= skip;
-          }
-        }
-        if (makematch && !facet
-        && SETelemt_(facet->neighbors, skip, facetT) == qh_DUPLICATEridge) {
-          qh_fprintf(qh, qh->ferr, 6156, "qhull internal error (qh_matchduplicates): no MERGEridge match for duplicate f%d skip %d at hash %d\n",
-                     newfacet->id, newskip, hash);
-          qh_errexit(qh, qh_ERRqhull, newfacet, NULL);
-        }
-      }
-    } /* end of for each new facet at hash */
-    if (!makematch) {
-      if (!maxmatch) {
-        qh_fprintf(qh, qh->ferr, 6157, "qhull internal error (qh_matchduplicates): no maximum match at duplicate f%d skip %d at hash %d\n",
-                     atfacet->id, atskip, hash);
-        qh_errexit(qh, qh_ERRqhull, atfacet, NULL);
-      }
-      SETelem_(maxmatch->neighbors, maxskip)= maxmatch2; /* maxmatch!=0 by QH6157 */
-      SETelem_(maxmatch2->neighbors, maxskip2)= maxmatch;
-      *hashcount -= 2; /* removed two unmatched facets */
-      zzinc_(Zmultiridge);
-      trace0((qh, qh->ferr, 25, "qh_matchduplicates: duplicate f%d skip %d matched with new f%d skip %d keep\n",
-              maxmatch->id, maxskip, maxmatch2->id, maxskip2));
-      qh_precision(qh, "ridge with multiple neighbors");
-      if (qh->IStracing >= 4)
-        qh_errprint(qh, "DUPLICATED/MATCH", maxmatch, maxmatch2, NULL, NULL);
-    }
-  }
-} /* matchduplicates */
-
-/*---------------------------------
-
-  qh_nearcoplanar()
-    for all facets, remove near-inside points from facet->coplanarset
-    coplanar points defined by innerplane from qh_outerinner()
-
-  returns:
-    if qh->KEEPcoplanar && !qh->KEEPinside
-      facet->coplanarset only contains coplanar points
-    if qh.JOGGLEmax
-      drops inner plane by another qh.JOGGLEmax diagonal since a
-        vertex could shift out while a coplanar point shifts in
-
-  notes:
-    used for qh.PREmerge and qh.JOGGLEmax
-    must agree with computation of qh.NEARcoplanar in qh_detroundoff(qh)
-  design:
-    if not keeping coplanar or inside points
-      free all coplanar sets
-    else if not keeping both coplanar and inside points
-      remove !coplanar or !inside points from coplanar sets
-*/
-void qh_nearcoplanar(qhT *qh /* qh.facet_list */) {
-  facetT *facet;
-  pointT *point, **pointp;
-  int numpart;
-  realT dist, innerplane;
-
-  if (!qh->KEEPcoplanar && !qh->KEEPinside) {
-    FORALLfacets {
-      if (facet->coplanarset)
-        qh_setfree(qh, &facet->coplanarset);
-    }
-  }else if (!qh->KEEPcoplanar || !qh->KEEPinside) {
-    qh_outerinner(qh, NULL, NULL, &innerplane);
-    if (qh->JOGGLEmax < REALmax/2)
-      innerplane -= qh->JOGGLEmax * sqrt((realT)qh->hull_dim);
-    numpart= 0;
-    FORALLfacets {
-      if (facet->coplanarset) {
-        FOREACHpoint_(facet->coplanarset) {
-          numpart++;
-          qh_distplane(qh, point, facet, &dist);
-          if (dist < innerplane) {
-            if (!qh->KEEPinside)
-              SETref_(point)= NULL;
-          }else if (!qh->KEEPcoplanar)
-            SETref_(point)= NULL;
-        }
-        qh_setcompact(qh, facet->coplanarset);
-      }
-    }
-    zzadd_(Zcheckpart, numpart);
-  }
-} /* nearcoplanar */
-
-/*---------------------------------
-
-  qh_nearvertex(qh, facet, point, bestdist )
-    return nearest vertex in facet to point
-
-  returns:
-    vertex and its distance
-
-  notes:
-    if qh.DELAUNAY
-      distance is measured in the input set
-    searches neighboring tricoplanar facets (requires vertexneighbors)
-      Slow implementation.  Recomputes vertex set for each point.
-    The vertex set could be stored in the qh.keepcentrum facet.
-*/
-vertexT *qh_nearvertex(qhT *qh, facetT *facet, pointT *point, realT *bestdistp) {
-  realT bestdist= REALmax, dist;
-  vertexT *bestvertex= NULL, *vertex, **vertexp, *apex;
-  coordT *center;
-  facetT *neighbor, **neighborp;
-  setT *vertices;
-  int dim= qh->hull_dim;
-
-  if (qh->DELAUNAY)
-    dim--;
-  if (facet->tricoplanar) {
-    if (!qh->VERTEXneighbors || !facet->center) {
-      qh_fprintf(qh, qh->ferr, 6158, "qhull internal error (qh_nearvertex): qh.VERTEXneighbors and facet->center required for tricoplanar facets\n");
-      qh_errexit(qh, qh_ERRqhull, facet, NULL);
-    }
-    vertices= qh_settemp(qh, qh->TEMPsize);
-    apex= SETfirstt_(facet->vertices, vertexT);
-    center= facet->center;
-    FOREACHneighbor_(apex) {
-      if (neighbor->center == center) {
-        FOREACHvertex_(neighbor->vertices)
-          qh_setappend(qh, &vertices, vertex);
-      }
-    }
-  }else
-    vertices= facet->vertices;
-  FOREACHvertex_(vertices) {
-    dist= qh_pointdist(vertex->point, point, -dim);
-    if (dist < bestdist) {
-      bestdist= dist;
-      bestvertex= vertex;
-    }
-  }
-  if (facet->tricoplanar)
-    qh_settempfree(qh, &vertices);
-  *bestdistp= sqrt(bestdist);
-  if (!bestvertex) {
-      qh_fprintf(qh, qh->ferr, 6261, "qhull internal error (qh_nearvertex): did not find bestvertex for f%d p%d\n", facet->id, qh_pointid(qh, point));
-      qh_errexit(qh, qh_ERRqhull, facet, NULL);
-  }
-  trace3((qh, qh->ferr, 3019, "qh_nearvertex: v%d dist %2.2g for f%d p%d\n",
-        bestvertex->id, *bestdistp, facet->id, qh_pointid(qh, point))); /* bestvertex!=0 by QH2161 */
-  return bestvertex;
-} /* nearvertex */
-
-/*---------------------------------
-
-  qh_newhashtable(qh, newsize )
-    returns size of qh.hash_table of at least newsize slots
-
-  notes:
-    assumes qh.hash_table is NULL
-    qh_HASHfactor determines the number of extra slots
-    size is not divisible by 2, 3, or 5
-*/
-int qh_newhashtable(qhT *qh, int newsize) {
-  int size;
-
-  size= ((newsize+1)*qh_HASHfactor) | 0x1;  /* odd number */
-  while (True) {
-    if (newsize<0 || size<0) {
-        qh_fprintf(qh, qh->qhmem.ferr, 6236, "qhull error (qh_newhashtable): negative request (%d) or size (%d).  Did int overflow due to high-D?\n", newsize, size); /* WARN64 */
-        qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
-    }
-    if ((size%3) && (size%5))
-      break;
-    size += 2;
-    /* loop terminates because there is an infinite number of primes */
-  }
-  qh->hash_table= qh_setnew(qh, size);
-  qh_setzero(qh, qh->hash_table, 0, size);
-  return size;
-} /* newhashtable */
-
-/*---------------------------------
-
-  qh_newvertex(qh, point )
-    returns a new vertex for point
-*/
-vertexT *qh_newvertex(qhT *qh, pointT *point) {
-  vertexT *vertex;
-
-  zinc_(Ztotvertices);
-  vertex= (vertexT *)qh_memalloc(qh, (int)sizeof(vertexT));
-  memset((char *) vertex, (size_t)0, sizeof(vertexT));
-  if (qh->vertex_id == UINT_MAX) {
-    qh_memfree(qh, vertex, (int)sizeof(vertexT));
-    qh_fprintf(qh, qh->ferr, 6159, "qhull error: more than 2^32 vertices.  vertexT.id field overflows.  Vertices would not be sorted correctly.\n");
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }
-  if (qh->vertex_id == qh->tracevertex_id)
-    qh->tracevertex= vertex;
-  vertex->id= qh->vertex_id++;
-  vertex->point= point;
-  trace4((qh, qh->ferr, 4060, "qh_newvertex: vertex p%d(v%d) created\n", qh_pointid(qh, vertex->point),
-          vertex->id));
-  return(vertex);
-} /* newvertex */
-
-/*---------------------------------
-
-  qh_nextridge3d( atridge, facet, vertex )
-    return next ridge and vertex for a 3d facet
-    returns NULL on error
-    [for QhullFacet::nextRidge3d] Does not call qh_errexit nor access qhT.
-
-  notes:
-    in qh_ORIENTclock order
-    this is a O(n^2) implementation to trace all ridges
-    be sure to stop on any 2nd visit
-    same as QhullRidge::nextRidge3d
-    does not use qhT or qh_errexit [QhullFacet.cpp]
-
-  design:
-    for each ridge
-      exit if it is the ridge after atridge
-*/
-ridgeT *qh_nextridge3d(ridgeT *atridge, facetT *facet, vertexT **vertexp) {
-  vertexT *atvertex, *vertex, *othervertex;
-  ridgeT *ridge, **ridgep;
-
-  if ((atridge->top == facet) ^ qh_ORIENTclock)
-    atvertex= SETsecondt_(atridge->vertices, vertexT);
-  else
-    atvertex= SETfirstt_(atridge->vertices, vertexT);
-  FOREACHridge_(facet->ridges) {
-    if (ridge == atridge)
-      continue;
-    if ((ridge->top == facet) ^ qh_ORIENTclock) {
-      othervertex= SETsecondt_(ridge->vertices, vertexT);
-      vertex= SETfirstt_(ridge->vertices, vertexT);
-    }else {
-      vertex= SETsecondt_(ridge->vertices, vertexT);
-      othervertex= SETfirstt_(ridge->vertices, vertexT);
-    }
-    if (vertex == atvertex) {
-      if (vertexp)
-        *vertexp= othervertex;
-      return ridge;
-    }
-  }
-  return NULL;
-} /* nextridge3d */
-#else /* qh_NOmerge */
-void qh_matchduplicates(qhT *qh, facetT *atfacet, int atskip, int hashsize, int *hashcount) {
-}
-ridgeT *qh_nextridge3d(ridgeT *atridge, facetT *facet, vertexT **vertexp) {
-
-  return NULL;
-}
-#endif /* qh_NOmerge */
-
-/*---------------------------------
-
-  qh_outcoplanar()
-    move points from all facets' outsidesets to their coplanarsets
-
-  notes:
-    for post-processing under qh.NARROWhull
-
-  design:
-    for each facet
-      for each outside point for facet
-        partition point into coplanar set
-*/
-void qh_outcoplanar(qhT *qh /* facet_list */) {
-  pointT *point, **pointp;
-  facetT *facet;
-  realT dist;
-
-  trace1((qh, qh->ferr, 1033, "qh_outcoplanar: move outsideset to coplanarset for qh->NARROWhull\n"));
-  FORALLfacets {
-    FOREACHpoint_(facet->outsideset) {
-      qh->num_outside--;
-      if (qh->KEEPcoplanar || qh->KEEPnearinside) {
-        qh_distplane(qh, point, facet, &dist);
-        zinc_(Zpartition);
-        qh_partitioncoplanar(qh, point, facet, &dist);
-      }
-    }
-    qh_setfree(qh, &facet->outsideset);
-  }
-} /* outcoplanar */
-
-/*---------------------------------
-
-  qh_point(qh, id )
-    return point for a point id, or NULL if unknown
-
-  alternative code:
-    return((pointT *)((unsigned   long)qh.first_point
-           + (unsigned long)((id)*qh.normal_size)));
-*/
-pointT *qh_point(qhT *qh, int id) {
-
-  if (id < 0)
-    return NULL;
-  if (id < qh->num_points)
-    return qh->first_point + id * qh->hull_dim;
-  id -= qh->num_points;
-  if (id < qh_setsize(qh, qh->other_points))
-    return SETelemt_(qh->other_points, id, pointT);
-  return NULL;
-} /* point */
-
-/*---------------------------------
-
-  qh_point_add(qh, set, point, elem )
-    stores elem at set[point.id]
-
-  returns:
-    access function for qh_pointfacet and qh_pointvertex
-
-  notes:
-    checks point.id
-*/
-void qh_point_add(qhT *qh, setT *set, pointT *point, void *elem) {
-  int id, size;
-
-  SETreturnsize_(set, size);
-  if ((id= qh_pointid(qh, point)) < 0)
-    qh_fprintf(qh, qh->ferr, 7067, "qhull internal warning (point_add): unknown point %p id %d\n",
-      point, id);
-  else if (id >= size) {
-    qh_fprintf(qh, qh->ferr, 6160, "qhull internal errror(point_add): point p%d is out of bounds(%d)\n",
-             id, size);
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }else
-    SETelem_(set, id)= elem;
-} /* point_add */
-
-
-/*---------------------------------
-
-  qh_pointfacet()
-    return temporary set of facet for each point
-    the set is indexed by point id
-
-  notes:
-    vertices assigned to one of the facets
-    coplanarset assigned to the facet
-    outside set assigned to the facet
-    NULL if no facet for point (inside)
-      includes qh.GOODpointp
-
-  access:
-    FOREACHfacet_i_(qh, facets) { ... }
-    SETelem_(facets, i)
-
-  design:
-    for each facet
-      add each vertex
-      add each coplanar point
-      add each outside point
-*/
-setT *qh_pointfacet(qhT *qh /*qh.facet_list*/) {
-  int numpoints= qh->num_points + qh_setsize(qh, qh->other_points);
-  setT *facets;
-  facetT *facet;
-  vertexT *vertex, **vertexp;
-  pointT *point, **pointp;
-
-  facets= qh_settemp(qh, numpoints);
-  qh_setzero(qh, facets, 0, numpoints);
-  qh->vertex_visit++;
-  FORALLfacets {
-    FOREACHvertex_(facet->vertices) {
-      if (vertex->visitid != qh->vertex_visit) {
-        vertex->visitid= qh->vertex_visit;
-        qh_point_add(qh, facets, vertex->point, facet);
-      }
-    }
-    FOREACHpoint_(facet->coplanarset)
-      qh_point_add(qh, facets, point, facet);
-    FOREACHpoint_(facet->outsideset)
-      qh_point_add(qh, facets, point, facet);
-  }
-  return facets;
-} /* pointfacet */
-
-/*---------------------------------
-
-  qh_pointvertex(qh, )
-    return temporary set of vertices indexed by point id
-    entry is NULL if no vertex for a point
-      this will include qh.GOODpointp
-
-  access:
-    FOREACHvertex_i_(qh, vertices) { ... }
-    SETelem_(vertices, i)
-*/
-setT *qh_pointvertex(qhT *qh /*qh.facet_list*/) {
-  int numpoints= qh->num_points + qh_setsize(qh, qh->other_points);
-  setT *vertices;
-  vertexT *vertex;
-
-  vertices= qh_settemp(qh, numpoints);
-  qh_setzero(qh, vertices, 0, numpoints);
-  FORALLvertices
-    qh_point_add(qh, vertices, vertex->point, vertex);
-  return vertices;
-} /* pointvertex */
-
-
-/*---------------------------------
-
-  qh_prependfacet(qh, facet, facetlist )
-    prepend facet to the start of a facetlist
-
-  returns:
-    increments qh.numfacets
-    updates facetlist, qh.facet_list, facet_next
-
-  notes:
-    be careful of prepending since it can lose a pointer.
-      e.g., can lose _next by deleting and then prepending before _next
-*/
-void qh_prependfacet(qhT *qh, facetT *facet, facetT **facetlist) {
-  facetT *prevfacet, *list;
-
-
-  trace4((qh, qh->ferr, 4061, "qh_prependfacet: prepend f%d before f%d\n",
-          facet->id, getid_(*facetlist)));
-  if (!*facetlist)
-    (*facetlist)= qh->facet_tail;
-  list= *facetlist;
-  prevfacet= list->previous;
-  facet->previous= prevfacet;
-  if (prevfacet)
-    prevfacet->next= facet;
-  list->previous= facet;
-  facet->next= *facetlist;
-  if (qh->facet_list == list)  /* this may change *facetlist */
-    qh->facet_list= facet;
-  if (qh->facet_next == list)
-    qh->facet_next= facet;
-  *facetlist= facet;
-  qh->num_facets++;
-} /* prependfacet */
-
-
-/*---------------------------------
-
-  qh_printhashtable(qh, fp )
-    print hash table to fp
-
-  notes:
-    not in I/O to avoid bringing io_r.c in
-
-  design:
-    for each hash entry
-      if defined
-        if unmatched or will merge (NULL, qh_MERGEridge, qh_DUPLICATEridge)
-          print entry and neighbors
-*/
-void qh_printhashtable(qhT *qh, FILE *fp) {
-  facetT *facet, *neighbor;
-  int id, facet_i, facet_n, neighbor_i= 0, neighbor_n= 0;
-  vertexT *vertex, **vertexp;
-
-  FOREACHfacet_i_(qh, qh->hash_table) {
-    if (facet) {
-      FOREACHneighbor_i_(qh, facet) {
-        if (!neighbor || neighbor == qh_MERGEridge || neighbor == qh_DUPLICATEridge)
-          break;
-      }
-      if (neighbor_i == neighbor_n)
-        continue;
-      qh_fprintf(qh, fp, 9283, "hash %d f%d ", facet_i, facet->id);
-      FOREACHvertex_(facet->vertices)
-        qh_fprintf(qh, fp, 9284, "v%d ", vertex->id);
-      qh_fprintf(qh, fp, 9285, "\n neighbors:");
-      FOREACHneighbor_i_(qh, facet) {
-        if (neighbor == qh_MERGEridge)
-          id= -3;
-        else if (neighbor == qh_DUPLICATEridge)
-          id= -2;
-        else
-          id= getid_(neighbor);
-        qh_fprintf(qh, fp, 9286, " %d", id);
-      }
-      qh_fprintf(qh, fp, 9287, "\n");
-    }
-  }
-} /* printhashtable */
-
-
-/*---------------------------------
-
-  qh_printlists(qh, fp )
-    print out facet and vertex list for debugging (without 'f/v' tags)
-*/
-void qh_printlists(qhT *qh) {
-  facetT *facet;
-  vertexT *vertex;
-  int count= 0;
-
-  qh_fprintf(qh, qh->ferr, 8108, "qh_printlists: facets:");
-  FORALLfacets {
-    if (++count % 100 == 0)
-      qh_fprintf(qh, qh->ferr, 8109, "\n     ");
-    qh_fprintf(qh, qh->ferr, 8110, " %d", facet->id);
-  }
-  qh_fprintf(qh, qh->ferr, 8111, "\n  new facets %d visible facets %d next facet for qh_addpoint %d\n  vertices(new %d):",
-     getid_(qh->newfacet_list), getid_(qh->visible_list), getid_(qh->facet_next),
-     getid_(qh->newvertex_list));
-  count = 0;
-  FORALLvertices {
-    if (++count % 100 == 0)
-      qh_fprintf(qh, qh->ferr, 8112, "\n     ");
-    qh_fprintf(qh, qh->ferr, 8113, " %d", vertex->id);
-  }
-  qh_fprintf(qh, qh->ferr, 8114, "\n");
-} /* printlists */
-
-/*---------------------------------
-
-  qh_resetlists(qh, stats, qh_RESETvisible )
-    reset newvertex_list, newfacet_list, visible_list
-    if stats,
-      maintains statistics
-
-  returns:
-    visible_list is empty if qh_deletevisible was called
-*/
-void qh_resetlists(qhT *qh, boolT stats, boolT resetVisible /*qh.newvertex_list newfacet_list visible_list*/) {
-  vertexT *vertex;
-  facetT *newfacet, *visible;
-  int totnew=0, totver=0;
-
-  if (stats) {
-    FORALLvertex_(qh->newvertex_list)
-      totver++;
-    FORALLnew_facets
-      totnew++;
-    zadd_(Zvisvertextot, totver);
-    zmax_(Zvisvertexmax, totver);
-    zadd_(Znewfacettot, totnew);
-    zmax_(Znewfacetmax, totnew);
-  }
-  FORALLvertex_(qh->newvertex_list)
-    vertex->newlist= False;
-  qh->newvertex_list= NULL;
-  FORALLnew_facets
-    newfacet->newfacet= False;
-  qh->newfacet_list= NULL;
-  if (resetVisible) {
-    FORALLvisible_facets {
-      visible->f.replace= NULL;
-      visible->visible= False;
-    }
-    qh->num_visible= 0;
-  }
-  qh->visible_list= NULL; /* may still have visible facets via qh_triangulate */
-  qh->NEWfacets= False;
-} /* resetlists */
-
-/*---------------------------------
-
-  qh_setvoronoi_all(qh)
-    compute Voronoi centers for all facets
-    includes upperDelaunay facets if qh.UPPERdelaunay ('Qu')
-
-  returns:
-    facet->center is the Voronoi center
-
-  notes:
-    this is unused/untested code
-      please email bradb@shore.net if this works ok for you
-
-  use:
-    FORALLvertices {...} to locate the vertex for a point.
-    FOREACHneighbor_(vertex) {...} to visit the Voronoi centers for a Voronoi cell.
-*/
-void qh_setvoronoi_all(qhT *qh) {
-  facetT *facet;
-
-  qh_clearcenters(qh, qh_ASvoronoi);
-  qh_vertexneighbors(qh);
-
-  FORALLfacets {
-    if (!facet->normal || !facet->upperdelaunay || qh->UPPERdelaunay) {
-      if (!facet->center)
-        facet->center= qh_facetcenter(qh, facet->vertices);
-    }
-  }
-} /* setvoronoi_all */
-
-#ifndef qh_NOmerge
-
-/*---------------------------------
-
-  qh_triangulate()
-    triangulate non-simplicial facets on qh.facet_list,
-    if qh->VORONOI, sets Voronoi centers of non-simplicial facets
-    nop if hasTriangulation
-
-  returns:
-    all facets simplicial
-    each tricoplanar facet has ->f.triowner == owner of ->center,normal,etc.
-
-  notes:
-    call after qh_check_output since may switch to Voronoi centers
-    Output may overwrite ->f.triowner with ->f.area
-*/
-void qh_triangulate(qhT *qh /*qh.facet_list*/) {
-  facetT *facet, *nextfacet, *owner;
-  int onlygood= qh->ONLYgood;
-  facetT *neighbor, *visible= NULL, *facet1, *facet2, *new_facet_list= NULL;
-  facetT *orig_neighbor= NULL, *otherfacet;
-  vertexT *new_vertex_list= NULL;
-  mergeT *merge;
-  mergeType mergetype;
-  int neighbor_i, neighbor_n;
-
-  if (qh->hasTriangulation)
-      return;
-  trace1((qh, qh->ferr, 1034, "qh_triangulate: triangulate non-simplicial facets\n"));
-  if (qh->hull_dim == 2)
-    return;
-  if (qh->VORONOI) {  /* otherwise lose Voronoi centers [could rebuild vertex set from tricoplanar] */
-    qh_clearcenters(qh, qh_ASvoronoi);
-    qh_vertexneighbors(qh);
-  }
-  qh->ONLYgood= False; /* for makenew_nonsimplicial */
-  qh->visit_id++;
-  qh->NEWfacets= True;
-  qh->degen_mergeset= qh_settemp(qh, qh->TEMPsize);
-  qh->newvertex_list= qh->vertex_tail;
-  for (facet= qh->facet_list; facet && facet->next; facet= nextfacet) { /* non-simplicial facets moved to end */
-    nextfacet= facet->next;
-    if (facet->visible || facet->simplicial)
-      continue;
-    /* triangulate all non-simplicial facets, otherwise merging does not work, e.g., RBOX c P-0.1 P+0.1 P+0.1 D3 | QHULL d Qt Tv */
-    if (!new_facet_list)
-      new_facet_list= facet;  /* will be moved to end */
-    qh_triangulate_facet(qh, facet, &new_vertex_list);
-  }
-  trace2((qh, qh->ferr, 2047, "qh_triangulate: delete null facets from f%d -- apex same as second vertex\n", getid_(new_facet_list)));
-  for (facet= new_facet_list; facet && facet->next; facet= nextfacet) { /* null facets moved to end */
-    nextfacet= facet->next;
-    if (facet->visible)
-      continue;
-    if (facet->ridges) {
-      if (qh_setsize(qh, facet->ridges) > 0) {
-        qh_fprintf(qh, qh->ferr, 6161, "qhull error (qh_triangulate): ridges still defined for f%d\n", facet->id);
-        qh_errexit(qh, qh_ERRqhull, facet, NULL);
-      }
-      qh_setfree(qh, &facet->ridges);
-    }
-    if (SETfirst_(facet->vertices) == SETsecond_(facet->vertices)) {
-      zinc_(Ztrinull);
-      qh_triangulate_null(qh, facet);
-    }
-  }
-  trace2((qh, qh->ferr, 2048, "qh_triangulate: delete %d or more mirror facets -- same vertices and neighbors\n", qh_setsize(qh, qh->degen_mergeset)));
-  qh->visible_list= qh->facet_tail;
-  while ((merge= (mergeT*)qh_setdellast(qh->degen_mergeset))) {
-    facet1= merge->facet1;
-    facet2= merge->facet2;
-    mergetype= merge->type;
-    qh_memfree(qh, merge, (int)sizeof(mergeT));
-    if (mergetype == MRGmirror) {
-      zinc_(Ztrimirror);
-      qh_triangulate_mirror(qh, facet1, facet2);
-    }
-  }
-  qh_settempfree(qh, &qh->degen_mergeset);
-  trace2((qh, qh->ferr, 2049, "qh_triangulate: update neighbor lists for vertices from v%d\n", getid_(new_vertex_list)));
-  qh->newvertex_list= new_vertex_list;  /* all vertices of new facets */
-  qh->visible_list= NULL;
-  qh_updatevertices(qh /*qh.newvertex_list, empty newfacet_list and visible_list*/);
-  qh_resetlists(qh, False, !qh_RESETvisible /*qh.newvertex_list, empty newfacet_list and visible_list*/);
-
-  trace2((qh, qh->ferr, 2050, "qh_triangulate: identify degenerate tricoplanar facets from f%d\n", getid_(new_facet_list)));
-  trace2((qh, qh->ferr, 2051, "qh_triangulate: and replace facet->f.triowner with tricoplanar facets that own center, normal, etc.\n"));
-  FORALLfacet_(new_facet_list) {
-    if (facet->tricoplanar && !facet->visible) {
-      FOREACHneighbor_i_(qh, facet) {
-        if (neighbor_i == 0) {  /* first iteration */
-          if (neighbor->tricoplanar)
-            orig_neighbor= neighbor->f.triowner;
-          else
-            orig_neighbor= neighbor;
-        }else {
-          if (neighbor->tricoplanar)
-            otherfacet= neighbor->f.triowner;
-          else
-            otherfacet= neighbor;
-          if (orig_neighbor == otherfacet) {
-            zinc_(Ztridegen);
-            facet->degenerate= True;
-            break;
-          }
-        }
-      }
-    }
-  }
-
-  trace2((qh, qh->ferr, 2052, "qh_triangulate: delete visible facets -- non-simplicial, null, and mirrored facets\n"));
-  owner= NULL;
-  visible= NULL;
-  for (facet= new_facet_list; facet && facet->next; facet= nextfacet) { /* may delete facet */
-    nextfacet= facet->next;
-    if (facet->visible) {
-      if (facet->tricoplanar) { /* a null or mirrored facet */
-        qh_delfacet(qh, facet);
-        qh->num_visible--;
-      }else {  /* a non-simplicial facet followed by its tricoplanars */
-        if (visible && !owner) {
-          /*  RBOX 200 s D5 t1001471447 | QHULL Qt C-0.01 Qx Qc Tv Qt -- f4483 had 6 vertices/neighbors and 8 ridges */
-          trace2((qh, qh->ferr, 2053, "qh_triangulate: all tricoplanar facets degenerate for non-simplicial facet f%d\n",
-                       visible->id));
-          qh_delfacet(qh, visible);
-          qh->num_visible--;
-        }
-        visible= facet;
-        owner= NULL;
-      }
-    }else if (facet->tricoplanar) {
-      if (facet->f.triowner != visible || visible==NULL) {
-        qh_fprintf(qh, qh->ferr, 6162, "qhull error (qh_triangulate): tricoplanar facet f%d not owned by its visible, non-simplicial facet f%d\n", facet->id, getid_(visible));
-        qh_errexit2(qh, qh_ERRqhull, facet, visible);
-      }
-      if (owner)
-        facet->f.triowner= owner;
-      else if (!facet->degenerate) {
-        owner= facet;
-        nextfacet= visible->next; /* rescan tricoplanar facets with owner, visible!=0 by QH6162 */
-        facet->keepcentrum= True;  /* one facet owns ->normal, etc. */
-        facet->coplanarset= visible->coplanarset;
-        facet->outsideset= visible->outsideset;
-        visible->coplanarset= NULL;
-        visible->outsideset= NULL;
-        if (!qh->TRInormals) { /* center and normal copied to tricoplanar facets */
-          visible->center= NULL;
-          visible->normal= NULL;
-        }
-        qh_delfacet(qh, visible);
-        qh->num_visible--;
-      }
-    }
-  }
-  if (visible && !owner) {
-    trace2((qh, qh->ferr, 2054, "qh_triangulate: all tricoplanar facets degenerate for last non-simplicial facet f%d\n",
-                 visible->id));
-    qh_delfacet(qh, visible);
-    qh->num_visible--;
-  }
-  qh->NEWfacets= False;
-  qh->ONLYgood= onlygood; /* restore value */
-  if (qh->CHECKfrequently)
-    qh_checkpolygon(qh, qh->facet_list);
-  qh->hasTriangulation= True;
-} /* triangulate */
-
-
-/*---------------------------------
-
-  qh_triangulate_facet(qh, facetA, &firstVertex )
-    triangulate a non-simplicial facet
-      if qh.CENTERtype=qh_ASvoronoi, sets its Voronoi center
-  returns:
-    qh.newfacet_list == simplicial facets
-      facet->tricoplanar set and ->keepcentrum false
-      facet->degenerate set if duplicated apex
-      facet->f.trivisible set to facetA
-      facet->center copied from facetA (created if qh_ASvoronoi)
-        qh_eachvoronoi, qh_detvridge, qh_detvridge3 assume centers copied
-      facet->normal,offset,maxoutside copied from facetA
-
-  notes:
-      only called by qh_triangulate
-      qh_makenew_nonsimplicial uses neighbor->seen for the same
-      if qh.TRInormals, newfacet->normal will need qh_free
-        if qh.TRInormals and qh_AScentrum, newfacet->center will need qh_free
-        keepcentrum is also set on Zwidefacet in qh_mergefacet
-        freed by qh_clearcenters
-
-  see also:
-      qh_addpoint() -- add a point
-      qh_makenewfacets() -- construct a cone of facets for a new vertex
-
-  design:
-      if qh_ASvoronoi,
-         compute Voronoi center (facet->center)
-      select first vertex (highest ID to preserve ID ordering of ->vertices)
-      triangulate from vertex to ridges
-      copy facet->center, normal, offset
-      update vertex neighbors
-*/
-void qh_triangulate_facet(qhT *qh, facetT *facetA, vertexT **first_vertex) {
-  facetT *newfacet;
-  facetT *neighbor, **neighborp;
-  vertexT *apex;
-  int numnew=0;
-
-  trace3((qh, qh->ferr, 3020, "qh_triangulate_facet: triangulate facet f%d\n", facetA->id));
-
-  if (qh->IStracing >= 4)
-    qh_printfacet(qh, qh->ferr, facetA);
-  FOREACHneighbor_(facetA) {
-    neighbor->seen= False;
-    neighbor->coplanar= False;
-  }
-  if (qh->CENTERtype == qh_ASvoronoi && !facetA->center  /* matches upperdelaunay in qh_setfacetplane() */
-        && fabs_(facetA->normal[qh->hull_dim -1]) >= qh->ANGLEround * qh_ZEROdelaunay) {
-    facetA->center= qh_facetcenter(qh, facetA->vertices);
-  }
-  qh_willdelete(qh, facetA, NULL);
-  qh->newfacet_list= qh->facet_tail;
-  facetA->visitid= qh->visit_id;
-  apex= SETfirstt_(facetA->vertices, vertexT);
-  qh_makenew_nonsimplicial(qh, facetA, apex, &numnew);
-  SETfirst_(facetA->neighbors)= NULL;
-  FORALLnew_facets {
-    newfacet->tricoplanar= True;
-    newfacet->f.trivisible= facetA;
-    newfacet->degenerate= False;
-    newfacet->upperdelaunay= facetA->upperdelaunay;
-    newfacet->good= facetA->good;
-    if (qh->TRInormals) { /* 'Q11' triangulate duplicates ->normal and ->center */
-      newfacet->keepcentrum= True;
-      if(facetA->normal){
-        newfacet->normal= qh_memalloc(qh, qh->normal_size);
-        memcpy((char *)newfacet->normal, facetA->normal, qh->normal_size);
-      }
-      if (qh->CENTERtype == qh_AScentrum)
-        newfacet->center= qh_getcentrum(qh, newfacet);
-      else if (qh->CENTERtype == qh_ASvoronoi && facetA->center){
-        newfacet->center= qh_memalloc(qh, qh->center_size);
-        memcpy((char *)newfacet->center, facetA->center, qh->center_size);
-      }
-    }else {
-      newfacet->keepcentrum= False;
-      /* one facet will have keepcentrum=True at end of qh_triangulate */
-      newfacet->normal= facetA->normal;
-      newfacet->center= facetA->center;
-    }
-    newfacet->offset= facetA->offset;
-#if qh_MAXoutside
-    newfacet->maxoutside= facetA->maxoutside;
-#endif
-  }
-  qh_matchnewfacets(qh /*qh.newfacet_list*/);
-  zinc_(Ztricoplanar);
-  zadd_(Ztricoplanartot, numnew);
-  zmax_(Ztricoplanarmax, numnew);
-  qh->visible_list= NULL;
-  if (!(*first_vertex))
-    (*first_vertex)= qh->newvertex_list;
-  qh->newvertex_list= NULL;
-  qh_updatevertices(qh /*qh.newfacet_list, qh.empty visible_list and qh.newvertex_list*/);
-  qh_resetlists(qh, False, !qh_RESETvisible /*qh.newfacet_list, qh.empty visible_list and qh.newvertex_list*/);
-} /* triangulate_facet */
-
-/*---------------------------------
-
-  qh_triangulate_link(qh, oldfacetA, facetA, oldfacetB, facetB)
-    relink facetA to facetB via oldfacets
-  returns:
-    adds mirror facets to qh->degen_mergeset (4-d and up only)
-  design:
-    if they are already neighbors, the opposing neighbors become MRGmirror facets
-*/
-void qh_triangulate_link(qhT *qh, facetT *oldfacetA, facetT *facetA, facetT *oldfacetB, facetT *facetB) {
-  int errmirror= False;
-
-  trace3((qh, qh->ferr, 3021, "qh_triangulate_link: relink old facets f%d and f%d between neighbors f%d and f%d\n",
-         oldfacetA->id, oldfacetB->id, facetA->id, facetB->id));
-  if (qh_setin(facetA->neighbors, facetB)) {
-    if (!qh_setin(facetB->neighbors, facetA))
-      errmirror= True;
-    else
-      qh_appendmergeset(qh, facetA, facetB, MRGmirror, NULL);
-  }else if (qh_setin(facetB->neighbors, facetA))
-    errmirror= True;
-  if (errmirror) {
-    qh_fprintf(qh, qh->ferr, 6163, "qhull error (qh_triangulate_link): mirror facets f%d and f%d do not match for old facets f%d and f%d\n",
-       facetA->id, facetB->id, oldfacetA->id, oldfacetB->id);
-    qh_errexit2(qh, qh_ERRqhull, facetA, facetB);
-  }
-  qh_setreplace(qh, facetB->neighbors, oldfacetB, facetA);
-  qh_setreplace(qh, facetA->neighbors, oldfacetA, facetB);
-} /* triangulate_link */
-
-/*---------------------------------
-
-  qh_triangulate_mirror(qh, facetA, facetB)
-    delete mirrored facets from qh_triangulate_null() and qh_triangulate_mirror
-      a mirrored facet shares the same vertices of a logical ridge
-  design:
-    since a null facet duplicates the first two vertices, the opposing neighbors absorb the null facet
-    if they are already neighbors, the opposing neighbors become MRGmirror facets
-*/
-void qh_triangulate_mirror(qhT *qh, facetT *facetA, facetT *facetB) {
-  facetT *neighbor, *neighborB;
-  int neighbor_i, neighbor_n;
-
-  trace3((qh, qh->ferr, 3022, "qh_triangulate_mirror: delete mirrored facets f%d and f%d\n",
-         facetA->id, facetB->id));
-  FOREACHneighbor_i_(qh, facetA) {
-    neighborB= SETelemt_(facetB->neighbors, neighbor_i, facetT);
-    if (neighbor == neighborB)
-      continue; /* occurs twice */
-    qh_triangulate_link(qh, facetA, neighbor, facetB, neighborB);
-  }
-  qh_willdelete(qh, facetA, NULL);
-  qh_willdelete(qh, facetB, NULL);
-} /* triangulate_mirror */
-
-/*---------------------------------
-
-  qh_triangulate_null(qh, facetA)
-    remove null facetA from qh_triangulate_facet()
-      a null facet has vertex #1 (apex) == vertex #2
-  returns:
-    adds facetA to ->visible for deletion after qh_updatevertices
-    qh->degen_mergeset contains mirror facets (4-d and up only)
-  design:
-    since a null facet duplicates the first two vertices, the opposing neighbors absorb the null facet
-    if they are already neighbors, the opposing neighbors become MRGmirror facets
-*/
-void qh_triangulate_null(qhT *qh, facetT *facetA) {
-  facetT *neighbor, *otherfacet;
-
-  trace3((qh, qh->ferr, 3023, "qh_triangulate_null: delete null facet f%d\n", facetA->id));
-  neighbor= SETfirstt_(facetA->neighbors, facetT);
-  otherfacet= SETsecondt_(facetA->neighbors, facetT);
-  qh_triangulate_link(qh, facetA, neighbor, facetA, otherfacet);
-  qh_willdelete(qh, facetA, NULL);
-} /* triangulate_null */
-
-#else /* qh_NOmerge */
-void qh_triangulate(qhT *qh) {
-}
-#endif /* qh_NOmerge */
-
-   /*---------------------------------
-
-  qh_vertexintersect(qh, vertexsetA, vertexsetB )
-    intersects two vertex sets (inverse id ordered)
-    vertexsetA is a temporary set at the top of qh->qhmem.tempstack
-
-  returns:
-    replaces vertexsetA with the intersection
-
-  notes:
-    could overwrite vertexsetA if currently too slow
-*/
-void qh_vertexintersect(qhT *qh, setT **vertexsetA,setT *vertexsetB) {
-  setT *intersection;
-
-  intersection= qh_vertexintersect_new(qh, *vertexsetA, vertexsetB);
-  qh_settempfree(qh, vertexsetA);
-  *vertexsetA= intersection;
-  qh_settemppush(qh, intersection);
-} /* vertexintersect */
-
-/*---------------------------------
-
-  qh_vertexintersect_new(qh, )
-    intersects two vertex sets (inverse id ordered)
-
-  returns:
-    a new set
-*/
-setT *qh_vertexintersect_new(qhT *qh, setT *vertexsetA,setT *vertexsetB) {
-  setT *intersection= qh_setnew(qh, qh->hull_dim - 1);
-  vertexT **vertexA= SETaddr_(vertexsetA, vertexT);
-  vertexT **vertexB= SETaddr_(vertexsetB, vertexT);
-
-  while (*vertexA && *vertexB) {
-    if (*vertexA  == *vertexB) {
-      qh_setappend(qh, &intersection, *vertexA);
-      vertexA++; vertexB++;
-    }else {
-      if ((*vertexA)->id > (*vertexB)->id)
-        vertexA++;
-      else
-        vertexB++;
-    }
-  }
-  return intersection;
-} /* vertexintersect_new */
-
-/*---------------------------------
-
-  qh_vertexneighbors(qh)
-    for each vertex in qh.facet_list,
-      determine its neighboring facets
-
-  returns:
-    sets qh.VERTEXneighbors
-      nop if qh.VERTEXneighbors already set
-      qh_addpoint() will maintain them
-
-  notes:
-    assumes all vertex->neighbors are NULL
-
-  design:
-    for each facet
-      for each vertex
-        append facet to vertex->neighbors
-*/
-void qh_vertexneighbors(qhT *qh /*qh.facet_list*/) {
-  facetT *facet;
-  vertexT *vertex, **vertexp;
-
-  if (qh->VERTEXneighbors)
-    return;
-  trace1((qh, qh->ferr, 1035, "qh_vertexneighbors: determining neighboring facets for each vertex\n"));
-  qh->vertex_visit++;
-  FORALLfacets {
-    if (facet->visible)
-      continue;
-    FOREACHvertex_(facet->vertices) {
-      if (vertex->visitid != qh->vertex_visit) {
-        vertex->visitid= qh->vertex_visit;
-        vertex->neighbors= qh_setnew(qh, qh->hull_dim);
-      }
-      qh_setappend(qh, &vertex->neighbors, facet);
-    }
-  }
-  qh->VERTEXneighbors= True;
-} /* vertexneighbors */
-
-/*---------------------------------
-
-  qh_vertexsubset( vertexsetA, vertexsetB )
-    returns True if vertexsetA is a subset of vertexsetB
-    assumes vertexsets are sorted
-
-  note:
-    empty set is a subset of any other set
-*/
-boolT qh_vertexsubset(setT *vertexsetA, setT *vertexsetB) {
-  vertexT **vertexA= (vertexT **) SETaddr_(vertexsetA, vertexT);
-  vertexT **vertexB= (vertexT **) SETaddr_(vertexsetB, vertexT);
-
-  while (True) {
-    if (!*vertexA)
-      return True;
-    if (!*vertexB)
-      return False;
-    if ((*vertexA)->id > (*vertexB)->id)
-      return False;
-    if (*vertexA  == *vertexB)
-      vertexA++;
-    vertexB++;
-  }
-  return False; /* avoid warnings */
-} /* vertexsubset */
diff --git a/C/poly_r.c b/C/poly_r.c
deleted file mode 100644
--- a/C/poly_r.c
+++ /dev/null
@@ -1,1205 +0,0 @@
-/*
  ---------------------------------
-
-   poly_r.c
-   implements polygons and simplices
-
-   see qh-poly_r.htm, poly_r.h and libqhull_r.h
-
-   infrequent code is in poly2_r.c
-   (all but top 50 and their callers 12/3/95)
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull_r/poly_r.c#3 $$Change: 2064 $
-   $DateTime: 2016/01/18 12:36:08 $$Author: bbarber $
-*/
-
-#include "qhull_ra.h"
-
-/*======== functions in alphabetical order ==========*/
-
-/*---------------------------------
-
-  qh_appendfacet(qh, facet )
-    appends facet to end of qh.facet_list,
-
-  returns:
-    updates qh.newfacet_list, facet_next, facet_list
-    increments qh.numfacets
-
-  notes:
-    assumes qh.facet_list/facet_tail is defined (createsimplex)
-
-  see:
-    qh_removefacet()
-
-*/
-void qh_appendfacet(qhT *qh, facetT *facet) {
-  facetT *tail= qh->facet_tail;
-
-  if (tail == qh->newfacet_list)
-    qh->newfacet_list= facet;
-  if (tail == qh->facet_next)
-    qh->facet_next= facet;
-  facet->previous= tail->previous;
-  facet->next= tail;
-  if (tail->previous)
-    tail->previous->next= facet;
-  else
-    qh->facet_list= facet;
-  tail->previous= facet;
-  qh->num_facets++;
-  trace4((qh, qh->ferr, 4044, "qh_appendfacet: append f%d to facet_list\n", facet->id));
-} /* appendfacet */
-
-
-/*---------------------------------
-
-  qh_appendvertex(qh, vertex )
-    appends vertex to end of qh.vertex_list,
-
-  returns:
-    sets vertex->newlist
-    updates qh.vertex_list, newvertex_list
-    increments qh.num_vertices
-
-  notes:
-    assumes qh.vertex_list/vertex_tail is defined (createsimplex)
-
-*/
-void qh_appendvertex(qhT *qh, vertexT *vertex) {
-  vertexT *tail= qh->vertex_tail;
-
-  if (tail == qh->newvertex_list)
-    qh->newvertex_list= vertex;
-  vertex->newlist= True;
-  vertex->previous= tail->previous;
-  vertex->next= tail;
-  if (tail->previous)
-    tail->previous->next= vertex;
-  else
-    qh->vertex_list= vertex;
-  tail->previous= vertex;
-  qh->num_vertices++;
-  trace4((qh, qh->ferr, 4045, "qh_appendvertex: append v%d to vertex_list\n", vertex->id));
-} /* appendvertex */
-
-
-/*---------------------------------
-
-  qh_attachnewfacets(qh, )
-    attach horizon facets to new facets in qh.newfacet_list
-    newfacets have neighbor and ridge links to horizon but not vice versa
-    only needed for qh.ONLYgood
-
-  returns:
-    set qh.NEWfacets
-    horizon facets linked to new facets
-      ridges changed from visible facets to new facets
-      simplicial ridges deleted
-    qh.visible_list, no ridges valid
-    facet->f.replace is a newfacet (if any)
-
-  design:
-    delete interior ridges and neighbor sets by
-      for each visible, non-simplicial facet
-        for each ridge
-          if last visit or if neighbor is simplicial
-            if horizon neighbor
-              delete ridge for horizon's ridge set
-            delete ridge
-        erase neighbor set
-    attach horizon facets and new facets by
-      for all new facets
-        if corresponding horizon facet is simplicial
-          locate corresponding visible facet {may be more than one}
-          link visible facet to new facet
-          replace visible facet with new facet in horizon
-        else it's non-simplicial
-          for all visible neighbors of the horizon facet
-            link visible neighbor to new facet
-            delete visible neighbor from horizon facet
-          append new facet to horizon's neighbors
-          the first ridge of the new facet is the horizon ridge
-          link the new facet into the horizon ridge
-*/
-void qh_attachnewfacets(qhT *qh /* qh.visible_list, newfacet_list */) {
-  facetT *newfacet= NULL, *neighbor, **neighborp, *horizon, *visible;
-  ridgeT *ridge, **ridgep;
-
-  qh->NEWfacets= True;
-  trace3((qh, qh->ferr, 3012, "qh_attachnewfacets: delete interior ridges\n"));
-  qh->visit_id++;
-  FORALLvisible_facets {
-    visible->visitid= qh->visit_id;
-    if (visible->ridges) {
-      FOREACHridge_(visible->ridges) {
-        neighbor= otherfacet_(ridge, visible);
-        if (neighbor->visitid == qh->visit_id
-            || (!neighbor->visible && neighbor->simplicial)) {
-          if (!neighbor->visible)  /* delete ridge for simplicial horizon */
-            qh_setdel(neighbor->ridges, ridge);
-          qh_setfree(qh, &(ridge->vertices)); /* delete on 2nd visit */
-          qh_memfree(qh, ridge, (int)sizeof(ridgeT));
-        }
-      }
-      SETfirst_(visible->ridges)= NULL;
-    }
-    SETfirst_(visible->neighbors)= NULL;
-  }
-  trace1((qh, qh->ferr, 1017, "qh_attachnewfacets: attach horizon facets to new facets\n"));
-  FORALLnew_facets {
-    horizon= SETfirstt_(newfacet->neighbors, facetT);
-    if (horizon->simplicial) {
-      visible= NULL;
-      FOREACHneighbor_(horizon) {   /* may have more than one horizon ridge */
-        if (neighbor->visible) {
-          if (visible) {
-            if (qh_setequal_skip(newfacet->vertices, 0, horizon->vertices,
-                                  SETindex_(horizon->neighbors, neighbor))) {
-              visible= neighbor;
-              break;
-            }
-          }else
-            visible= neighbor;
-        }
-      }
-      if (visible) {
-        visible->f.replace= newfacet;
-        qh_setreplace(qh, horizon->neighbors, visible, newfacet);
-      }else {
-        qh_fprintf(qh, qh->ferr, 6102, "qhull internal error (qh_attachnewfacets): couldn't find visible facet for horizon f%d of newfacet f%d\n",
-                 horizon->id, newfacet->id);
-        qh_errexit2(qh, qh_ERRqhull, horizon, newfacet);
-      }
-    }else { /* non-simplicial, with a ridge for newfacet */
-      FOREACHneighbor_(horizon) {    /* may hold for many new facets */
-        if (neighbor->visible) {
-          neighbor->f.replace= newfacet;
-          qh_setdelnth(qh, horizon->neighbors,
-                        SETindex_(horizon->neighbors, neighbor));
-          neighborp--; /* repeat */
-        }
-      }
-      qh_setappend(qh, &horizon->neighbors, newfacet);
-      ridge= SETfirstt_(newfacet->ridges, ridgeT);
-      if (ridge->top == horizon)
-        ridge->bottom= newfacet;
-      else
-        ridge->top= newfacet;
-      }
-  } /* newfacets */
-  if (qh->PRINTstatistics) {
-    FORALLvisible_facets {
-      if (!visible->f.replace)
-        zinc_(Zinsidevisible);
-    }
-  }
-} /* attachnewfacets */
-
-/*---------------------------------
-
-  qh_checkflipped(qh, facet, dist, allerror )
-    checks facet orientation to interior point
-
-    if allerror set,
-      tests against qh.DISTround
-    else
-      tests against 0 since tested against DISTround before
-
-  returns:
-    False if it flipped orientation (sets facet->flipped)
-    distance if non-NULL
-*/
-boolT qh_checkflipped(qhT *qh, facetT *facet, realT *distp, boolT allerror) {
-  realT dist;
-
-  if (facet->flipped && !distp)
-    return False;
-  zzinc_(Zdistcheck);
-  qh_distplane(qh, qh->interior_point, facet, &dist);
-  if (distp)
-    *distp= dist;
-  if ((allerror && dist > -qh->DISTround)|| (!allerror && dist >= 0.0)) {
-    facet->flipped= True;
-    zzinc_(Zflippedfacets);
-    trace0((qh, qh->ferr, 19, "qh_checkflipped: facet f%d is flipped, distance= %6.12g during p%d\n",
-              facet->id, dist, qh->furthest_id));
-    qh_precision(qh, "flipped facet");
-    return False;
-  }
-  return True;
-} /* checkflipped */
-
-/*---------------------------------
-
-  qh_delfacet(qh, facet )
-    removes facet from facet_list and frees up its memory
-
-  notes:
-    assumes vertices and ridges already freed
-*/
-void qh_delfacet(qhT *qh, facetT *facet) {
-  void **freelistp; /* used if !qh_NOmem by qh_memfree_() */
-
-  trace4((qh, qh->ferr, 4046, "qh_delfacet: delete f%d\n", facet->id));
-  if (facet == qh->tracefacet)
-    qh->tracefacet= NULL;
-  if (facet == qh->GOODclosest)
-    qh->GOODclosest= NULL;
-  qh_removefacet(qh, facet);
-  if (!facet->tricoplanar || facet->keepcentrum) {
-    qh_memfree_(qh, facet->normal, qh->normal_size, freelistp);
-    if (qh->CENTERtype == qh_ASvoronoi) {   /* braces for macro calls */
-      qh_memfree_(qh, facet->center, qh->center_size, freelistp);
-    }else /* AScentrum */ {
-      qh_memfree_(qh, facet->center, qh->normal_size, freelistp);
-    }
-  }
-  qh_setfree(qh, &(facet->neighbors));
-  if (facet->ridges)
-    qh_setfree(qh, &(facet->ridges));
-  qh_setfree(qh, &(facet->vertices));
-  if (facet->outsideset)
-    qh_setfree(qh, &(facet->outsideset));
-  if (facet->coplanarset)
-    qh_setfree(qh, &(facet->coplanarset));
-  qh_memfree_(qh, facet, (int)sizeof(facetT), freelistp);
-} /* delfacet */
-
-
-/*---------------------------------
-
-  qh_deletevisible()
-    delete visible facets and vertices
-
-  returns:
-    deletes each facet and removes from facetlist
-    at exit, qh.visible_list empty (== qh.newfacet_list)
-
-  notes:
-    ridges already deleted
-    horizon facets do not reference facets on qh.visible_list
-    new facets in qh.newfacet_list
-    uses   qh.visit_id;
-*/
-void qh_deletevisible(qhT *qh /*qh.visible_list*/) {
-  facetT *visible, *nextfacet;
-  vertexT *vertex, **vertexp;
-  int numvisible= 0, numdel= qh_setsize(qh, qh->del_vertices);
-
-  trace1((qh, qh->ferr, 1018, "qh_deletevisible: delete %d visible facets and %d vertices\n",
-         qh->num_visible, numdel));
-  for (visible= qh->visible_list; visible && visible->visible;
-                visible= nextfacet) { /* deleting current */
-    nextfacet= visible->next;
-    numvisible++;
-    qh_delfacet(qh, visible);
-  }
-  if (numvisible != qh->num_visible) {
-    qh_fprintf(qh, qh->ferr, 6103, "qhull internal error (qh_deletevisible): qh->num_visible %d is not number of visible facets %d\n",
-             qh->num_visible, numvisible);
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }
-  qh->num_visible= 0;
-  zadd_(Zvisfacettot, numvisible);
-  zmax_(Zvisfacetmax, numvisible);
-  zzadd_(Zdelvertextot, numdel);
-  zmax_(Zdelvertexmax, numdel);
-  FOREACHvertex_(qh->del_vertices)
-    qh_delvertex(qh, vertex);
-  qh_settruncate(qh, qh->del_vertices, 0);
-} /* deletevisible */
-
-/*---------------------------------
-
-  qh_facetintersect(qh, facetA, facetB, skipa, skipB, prepend )
-    return vertices for intersection of two simplicial facets
-    may include 1 prepended entry (if more, need to settemppush)
-
-  returns:
-    returns set of qh.hull_dim-1 + prepend vertices
-    returns skipped index for each test and checks for exactly one
-
-  notes:
-    does not need settemp since set in quick memory
-
-  see also:
-    qh_vertexintersect and qh_vertexintersect_new
-    use qh_setnew_delnthsorted to get nth ridge (no skip information)
-
-  design:
-    locate skipped vertex by scanning facet A's neighbors
-    locate skipped vertex by scanning facet B's neighbors
-    intersect the vertex sets
-*/
-setT *qh_facetintersect(qhT *qh, facetT *facetA, facetT *facetB,
-                         int *skipA,int *skipB, int prepend) {
-  setT *intersect;
-  int dim= qh->hull_dim, i, j;
-  facetT **neighborsA, **neighborsB;
-
-  neighborsA= SETaddr_(facetA->neighbors, facetT);
-  neighborsB= SETaddr_(facetB->neighbors, facetT);
-  i= j= 0;
-  if (facetB == *neighborsA++)
-    *skipA= 0;
-  else if (facetB == *neighborsA++)
-    *skipA= 1;
-  else if (facetB == *neighborsA++)
-    *skipA= 2;
-  else {
-    for (i=3; i < dim; i++) {
-      if (facetB == *neighborsA++) {
-        *skipA= i;
-        break;
-      }
-    }
-  }
-  if (facetA == *neighborsB++)
-    *skipB= 0;
-  else if (facetA == *neighborsB++)
-    *skipB= 1;
-  else if (facetA == *neighborsB++)
-    *skipB= 2;
-  else {
-    for (j=3; j < dim; j++) {
-      if (facetA == *neighborsB++) {
-        *skipB= j;
-        break;
-      }
-    }
-  }
-  if (i >= dim || j >= dim) {
-    qh_fprintf(qh, qh->ferr, 6104, "qhull internal error (qh_facetintersect): f%d or f%d not in others neighbors\n",
-            facetA->id, facetB->id);
-    qh_errexit2(qh, qh_ERRqhull, facetA, facetB);
-  }
-  intersect= qh_setnew_delnthsorted(qh, facetA->vertices, qh->hull_dim, *skipA, prepend);
-  trace4((qh, qh->ferr, 4047, "qh_facetintersect: f%d skip %d matches f%d skip %d\n",
-          facetA->id, *skipA, facetB->id, *skipB));
-  return(intersect);
-} /* facetintersect */
-
-/*---------------------------------
-
-  qh_gethash(qh, hashsize, set, size, firstindex, skipelem )
-    return hashvalue for a set with firstindex and skipelem
-
-  notes:
-    returned hash is in [0,hashsize)
-    assumes at least firstindex+1 elements
-    assumes skipelem is NULL, in set, or part of hash
-
-    hashes memory addresses which may change over different runs of the same data
-    using sum for hash does badly in high d
-*/
-int qh_gethash(qhT *qh, int hashsize, setT *set, int size, int firstindex, void *skipelem) {
-  void **elemp= SETelemaddr_(set, firstindex, void);
-  ptr_intT hash = 0, elem;
-  unsigned result;
-  int i;
-#ifdef _MSC_VER                   /* Microsoft Visual C++ -- warn about 64-bit issues */
-#pragma warning( push)            /* WARN64 -- ptr_intT holds a 64-bit pointer */
-#pragma warning( disable : 4311)  /* 'type cast': pointer truncation from 'void*' to 'ptr_intT' */
-#endif
-
-  switch (size-firstindex) {
-  case 1:
-    hash= (ptr_intT)(*elemp) - (ptr_intT) skipelem;
-    break;
-  case 2:
-    hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] - (ptr_intT) skipelem;
-    break;
-  case 3:
-    hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] + (ptr_intT)elemp[2]
-      - (ptr_intT) skipelem;
-    break;
-  case 4:
-    hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] + (ptr_intT)elemp[2]
-      + (ptr_intT)elemp[3] - (ptr_intT) skipelem;
-    break;
-  case 5:
-    hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] + (ptr_intT)elemp[2]
-      + (ptr_intT)elemp[3] + (ptr_intT)elemp[4] - (ptr_intT) skipelem;
-    break;
-  case 6:
-    hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] + (ptr_intT)elemp[2]
-      + (ptr_intT)elemp[3] + (ptr_intT)elemp[4]+ (ptr_intT)elemp[5]
-      - (ptr_intT) skipelem;
-    break;
-  default:
-    hash= 0;
-    i= 3;
-    do {     /* this is about 10% in 10-d */
-      if ((elem= (ptr_intT)*elemp++) != (ptr_intT)skipelem) {
-        hash ^= (elem << i) + (elem >> (32-i));
-        i += 3;
-        if (i >= 32)
-          i -= 32;
-      }
-    }while (*elemp);
-    break;
-  }
-  if (hashsize<0) {
-    qh_fprintf(qh, qh->ferr, 6202, "qhull internal error: negative hashsize %d passed to qh_gethash [poly.c]\n", hashsize);
-    qh_errexit2(qh, qh_ERRqhull, NULL, NULL);
-  }
-  result= (unsigned)hash;
-  result %= (unsigned)hashsize;
-  /* result= 0; for debugging */
-  return result;
-#ifdef _MSC_VER
-#pragma warning( pop)
-#endif
-} /* gethash */
-
-/*---------------------------------
-
-  qh_makenewfacet(qh, vertices, toporient, horizon )
-    creates a toporient? facet from vertices
-
-  returns:
-    returns newfacet
-      adds newfacet to qh.facet_list
-      newfacet->vertices= vertices
-      if horizon
-        newfacet->neighbor= horizon, but not vice versa
-    newvertex_list updated with vertices
-*/
-facetT *qh_makenewfacet(qhT *qh, setT *vertices, boolT toporient,facetT *horizon) {
-  facetT *newfacet;
-  vertexT *vertex, **vertexp;
-
-  FOREACHvertex_(vertices) {
-    if (!vertex->newlist) {
-      qh_removevertex(qh, vertex);
-      qh_appendvertex(qh, vertex);
-    }
-  }
-  newfacet= qh_newfacet(qh);
-  newfacet->vertices= vertices;
-  newfacet->toporient= (unsigned char)toporient;
-  if (horizon)
-    qh_setappend(qh, &(newfacet->neighbors), horizon);
-  qh_appendfacet(qh, newfacet);
-  return(newfacet);
-} /* makenewfacet */
-
-
-/*---------------------------------
-
-  qh_makenewplanes()
-    make new hyperplanes for facets on qh.newfacet_list
-
-  returns:
-    all facets have hyperplanes or are marked for   merging
-    doesn't create hyperplane if horizon is coplanar (will merge)
-    updates qh.min_vertex if qh.JOGGLEmax
-
-  notes:
-    facet->f.samecycle is defined for facet->mergehorizon facets
-*/
-void qh_makenewplanes(qhT *qh /* qh.newfacet_list */) {
-  facetT *newfacet;
-
-  FORALLnew_facets {
-    if (!newfacet->mergehorizon)
-      qh_setfacetplane(qh, newfacet);
-  }
-  if (qh->JOGGLEmax < REALmax/2)
-    minimize_(qh->min_vertex, -wwval_(Wnewvertexmax));
-} /* makenewplanes */
-
-/*---------------------------------
-
-  qh_makenew_nonsimplicial(qh, visible, apex, numnew )
-    make new facets for ridges of a visible facet
-
-  returns:
-    first newfacet, bumps numnew as needed
-    attaches new facets if !qh.ONLYgood
-    marks ridge neighbors for simplicial visible
-    if (qh.ONLYgood)
-      ridges on newfacet, horizon, and visible
-    else
-      ridge and neighbors between newfacet and   horizon
-      visible facet's ridges are deleted
-
-  notes:
-    qh.visit_id if visible has already been processed
-    sets neighbor->seen for building f.samecycle
-      assumes all 'seen' flags initially false
-
-  design:
-    for each ridge of visible facet
-      get neighbor of visible facet
-      if neighbor was already processed
-        delete the ridge (will delete all visible facets later)
-      if neighbor is a horizon facet
-        create a new facet
-        if neighbor coplanar
-          adds newfacet to f.samecycle for later merging
-        else
-          updates neighbor's neighbor set
-          (checks for non-simplicial facet with multiple ridges to visible facet)
-        updates neighbor's ridge set
-        (checks for simplicial neighbor to non-simplicial visible facet)
-        (deletes ridge if neighbor is simplicial)
-
-*/
-#ifndef qh_NOmerge
-facetT *qh_makenew_nonsimplicial(qhT *qh, facetT *visible, vertexT *apex, int *numnew) {
-  void **freelistp; /* used if !qh_NOmem by qh_memfree_() */
-  ridgeT *ridge, **ridgep;
-  facetT *neighbor, *newfacet= NULL, *samecycle;
-  setT *vertices;
-  boolT toporient;
-  int ridgeid;
-
-  FOREACHridge_(visible->ridges) {
-    ridgeid= ridge->id;
-    neighbor= otherfacet_(ridge, visible);
-    if (neighbor->visible) {
-      if (!qh->ONLYgood) {
-        if (neighbor->visitid == qh->visit_id) {
-          qh_setfree(qh, &(ridge->vertices));  /* delete on 2nd visit */
-          qh_memfree_(qh, ridge, (int)sizeof(ridgeT), freelistp);
-        }
-      }
-    }else {  /* neighbor is an horizon facet */
-      toporient= (ridge->top == visible);
-      vertices= qh_setnew(qh, qh->hull_dim); /* makes sure this is quick */
-      qh_setappend(qh, &vertices, apex);
-      qh_setappend_set(qh, &vertices, ridge->vertices);
-      newfacet= qh_makenewfacet(qh, vertices, toporient, neighbor);
-      (*numnew)++;
-      if (neighbor->coplanar) {
-        newfacet->mergehorizon= True;
-        if (!neighbor->seen) {
-          newfacet->f.samecycle= newfacet;
-          neighbor->f.newcycle= newfacet;
-        }else {
-          samecycle= neighbor->f.newcycle;
-          newfacet->f.samecycle= samecycle->f.samecycle;
-          samecycle->f.samecycle= newfacet;
-        }
-      }
-      if (qh->ONLYgood) {
-        if (!neighbor->simplicial)
-          qh_setappend(qh, &(newfacet->ridges), ridge);
-      }else {  /* qh_attachnewfacets */
-        if (neighbor->seen) {
-          if (neighbor->simplicial) {
-            qh_fprintf(qh, qh->ferr, 6105, "qhull internal error (qh_makenew_nonsimplicial): simplicial f%d sharing two ridges with f%d\n",
-                   neighbor->id, visible->id);
-            qh_errexit2(qh, qh_ERRqhull, neighbor, visible);
-          }
-          qh_setappend(qh, &(neighbor->neighbors), newfacet);
-        }else
-          qh_setreplace(qh, neighbor->neighbors, visible, newfacet);
-        if (neighbor->simplicial) {
-          qh_setdel(neighbor->ridges, ridge);
-          qh_setfree(qh, &(ridge->vertices));
-          qh_memfree(qh, ridge, (int)sizeof(ridgeT));
-        }else {
-          qh_setappend(qh, &(newfacet->ridges), ridge);
-          if (toporient)
-            ridge->top= newfacet;
-          else
-            ridge->bottom= newfacet;
-        }
-      trace4((qh, qh->ferr, 4048, "qh_makenew_nonsimplicial: created facet f%d from v%d and r%d of horizon f%d\n",
-            newfacet->id, apex->id, ridgeid, neighbor->id));
-      }
-    }
-    neighbor->seen= True;
-  } /* for each ridge */
-  if (!qh->ONLYgood)
-    SETfirst_(visible->ridges)= NULL;
-  return newfacet;
-} /* makenew_nonsimplicial */
-#else /* qh_NOmerge */
-facetT *qh_makenew_nonsimplicial(qhT *qh, facetT *visible, vertexT *apex, int *numnew) {
-  return NULL;
-}
-#endif /* qh_NOmerge */
-
-/*---------------------------------
-
-  qh_makenew_simplicial(qh, visible, apex, numnew )
-    make new facets for simplicial visible facet and apex
-
-  returns:
-    attaches new facets if (!qh.ONLYgood)
-      neighbors between newfacet and horizon
-
-  notes:
-    nop if neighbor->seen or neighbor->visible(see qh_makenew_nonsimplicial)
-
-  design:
-    locate neighboring horizon facet for visible facet
-    determine vertices and orientation
-    create new facet
-    if coplanar,
-      add new facet to f.samecycle
-    update horizon facet's neighbor list
-*/
-facetT *qh_makenew_simplicial(qhT *qh, facetT *visible, vertexT *apex, int *numnew) {
-  facetT *neighbor, **neighborp, *newfacet= NULL;
-  setT *vertices;
-  boolT flip, toporient;
-  int horizonskip= 0, visibleskip= 0;
-
-  FOREACHneighbor_(visible) {
-    if (!neighbor->seen && !neighbor->visible) {
-      vertices= qh_facetintersect(qh, neighbor,visible, &horizonskip, &visibleskip, 1);
-      SETfirst_(vertices)= apex;
-      flip= ((horizonskip & 0x1) ^ (visibleskip & 0x1));
-      if (neighbor->toporient)
-        toporient= horizonskip & 0x1;
-      else
-        toporient= (horizonskip & 0x1) ^ 0x1;
-      newfacet= qh_makenewfacet(qh, vertices, toporient, neighbor);
-      (*numnew)++;
-      if (neighbor->coplanar && (qh->PREmerge || qh->MERGEexact)) {
-#ifndef qh_NOmerge
-        newfacet->f.samecycle= newfacet;
-        newfacet->mergehorizon= True;
-#endif
-      }
-      if (!qh->ONLYgood)
-        SETelem_(neighbor->neighbors, horizonskip)= newfacet;
-      trace4((qh, qh->ferr, 4049, "qh_makenew_simplicial: create facet f%d top %d from v%d and horizon f%d skip %d top %d and visible f%d skip %d, flip? %d\n",
-            newfacet->id, toporient, apex->id, neighbor->id, horizonskip,
-              neighbor->toporient, visible->id, visibleskip, flip));
-    }
-  }
-  return newfacet;
-} /* makenew_simplicial */
-
-/*---------------------------------
-
-  qh_matchneighbor(qh, newfacet, newskip, hashsize, hashcount )
-    either match subridge of newfacet with neighbor or add to hash_table
-
-  returns:
-    duplicate ridges are unmatched and marked by qh_DUPLICATEridge
-
-  notes:
-    ridge is newfacet->vertices w/o newskip vertex
-    do not allocate memory (need to free hash_table cleanly)
-    uses linear hash chains
-
-  see also:
-    qh_matchduplicates
-
-  design:
-    for each possible matching facet in qh.hash_table
-      if vertices match
-        set ismatch, if facets have opposite orientation
-        if ismatch and matching facet doesn't have a match
-          match the facets by updating their neighbor sets
-        else
-          indicate a duplicate ridge
-          set facet hyperplane for later testing
-          add facet to hashtable
-          unless the other facet was already a duplicate ridge
-            mark both facets with a duplicate ridge
-            add other facet (if defined) to hash table
-*/
-void qh_matchneighbor(qhT *qh, facetT *newfacet, int newskip, int hashsize, int *hashcount) {
-  boolT newfound= False;   /* True, if new facet is already in hash chain */
-  boolT same, ismatch;
-  int hash, scan;
-  facetT *facet, *matchfacet;
-  int skip, matchskip;
-
-  hash= qh_gethash(qh, hashsize, newfacet->vertices, qh->hull_dim, 1,
-                     SETelem_(newfacet->vertices, newskip));
-  trace4((qh, qh->ferr, 4050, "qh_matchneighbor: newfacet f%d skip %d hash %d hashcount %d\n",
-          newfacet->id, newskip, hash, *hashcount));
-  zinc_(Zhashlookup);
-  for (scan= hash; (facet= SETelemt_(qh->hash_table, scan, facetT));
-       scan= (++scan >= hashsize ? 0 : scan)) {
-    if (facet == newfacet) {
-      newfound= True;
-      continue;
-    }
-    zinc_(Zhashtests);
-    if (qh_matchvertices(qh, 1, newfacet->vertices, newskip, facet->vertices, &skip, &same)) {
-      if (SETelem_(newfacet->vertices, newskip) ==
-          SETelem_(facet->vertices, skip)) {
-        qh_precision(qh, "two facets with the same vertices");
-        qh_fprintf(qh, qh->ferr, 6106, "qhull precision error: Vertex sets are the same for f%d and f%d.  Can not force output.\n",
-          facet->id, newfacet->id);
-        qh_errexit2(qh, qh_ERRprec, facet, newfacet);
-      }
-      ismatch= (same == (boolT)((newfacet->toporient ^ facet->toporient)));
-      matchfacet= SETelemt_(facet->neighbors, skip, facetT);
-      if (ismatch && !matchfacet) {
-        SETelem_(facet->neighbors, skip)= newfacet;
-        SETelem_(newfacet->neighbors, newskip)= facet;
-        (*hashcount)--;
-        trace4((qh, qh->ferr, 4051, "qh_matchneighbor: f%d skip %d matched with new f%d skip %d\n",
-           facet->id, skip, newfacet->id, newskip));
-        return;
-      }
-      if (!qh->PREmerge && !qh->MERGEexact) {
-        qh_precision(qh, "a ridge with more than two neighbors");
-        qh_fprintf(qh, qh->ferr, 6107, "qhull precision error: facets f%d, f%d and f%d meet at a ridge with more than 2 neighbors.  Can not continue.\n",
-                 facet->id, newfacet->id, getid_(matchfacet));
-        qh_errexit2(qh, qh_ERRprec, facet, newfacet);
-      }
-      SETelem_(newfacet->neighbors, newskip)= qh_DUPLICATEridge;
-      newfacet->dupridge= True;
-      if (!newfacet->normal)
-        qh_setfacetplane(qh, newfacet);
-      qh_addhash(newfacet, qh->hash_table, hashsize, hash);
-      (*hashcount)++;
-      if (!facet->normal)
-        qh_setfacetplane(qh, facet);
-      if (matchfacet != qh_DUPLICATEridge) {
-        SETelem_(facet->neighbors, skip)= qh_DUPLICATEridge;
-        facet->dupridge= True;
-        if (!facet->normal)
-          qh_setfacetplane(qh, facet);
-        if (matchfacet) {
-          matchskip= qh_setindex(matchfacet->neighbors, facet);
-          if (matchskip<0) {
-              qh_fprintf(qh, qh->ferr, 6260, "qhull internal error (qh_matchneighbor): matchfacet f%d is in f%d neighbors but not vice versa.  Can not continue.\n",
-                  matchfacet->id, facet->id);
-              qh_errexit2(qh, qh_ERRqhull, matchfacet, facet);
-          }
-          SETelem_(matchfacet->neighbors, matchskip)= qh_DUPLICATEridge; /* matchskip>=0 by QH6260 */
-          matchfacet->dupridge= True;
-          if (!matchfacet->normal)
-            qh_setfacetplane(qh, matchfacet);
-          qh_addhash(matchfacet, qh->hash_table, hashsize, hash);
-          *hashcount += 2;
-        }
-      }
-      trace4((qh, qh->ferr, 4052, "qh_matchneighbor: new f%d skip %d duplicates ridge for f%d skip %d matching f%d ismatch %d at hash %d\n",
-           newfacet->id, newskip, facet->id, skip,
-           (matchfacet == qh_DUPLICATEridge ? -2 : getid_(matchfacet)),
-           ismatch, hash));
-      return; /* end of duplicate ridge */
-    }
-  }
-  if (!newfound)
-    SETelem_(qh->hash_table, scan)= newfacet;  /* same as qh_addhash */
-  (*hashcount)++;
-  trace4((qh, qh->ferr, 4053, "qh_matchneighbor: no match for f%d skip %d at hash %d\n",
-           newfacet->id, newskip, hash));
-} /* matchneighbor */
-
-
-/*---------------------------------
-
-  qh_matchnewfacets()
-    match newfacets in qh.newfacet_list to their newfacet neighbors
-
-  returns:
-    qh.newfacet_list with full neighbor sets
-      get vertices with nth neighbor by deleting nth vertex
-    if qh.PREmerge/MERGEexact or qh.FORCEoutput
-      sets facet->flippped if flipped normal (also prevents point partitioning)
-    if duplicate ridges and qh.PREmerge/MERGEexact
-      sets facet->dupridge
-      missing neighbor links identifies extra ridges to be merging (qh_MERGEridge)
-
-  notes:
-    newfacets already have neighbor[0] (horizon facet)
-    assumes qh.hash_table is NULL
-    vertex->neighbors has not been updated yet
-    do not allocate memory after qh.hash_table (need to free it cleanly)
-
-  design:
-    delete neighbor sets for all new facets
-    initialize a hash table
-    for all new facets
-      match facet with neighbors
-    if unmatched facets (due to duplicate ridges)
-      for each new facet with a duplicate ridge
-        match it with a facet
-    check for flipped facets
-*/
-void qh_matchnewfacets(qhT *qh /* qh.newfacet_list */) {
-  int numnew=0, hashcount=0, newskip;
-  facetT *newfacet, *neighbor;
-  int dim= qh->hull_dim, hashsize, neighbor_i, neighbor_n;
-  setT *neighbors;
-#ifndef qh_NOtrace
-  int facet_i, facet_n, numfree= 0;
-  facetT *facet;
-#endif
-
-  trace1((qh, qh->ferr, 1019, "qh_matchnewfacets: match neighbors for new facets.\n"));
-  FORALLnew_facets {
-    numnew++;
-    {  /* inline qh_setzero(qh, newfacet->neighbors, 1, qh->hull_dim); */
-      neighbors= newfacet->neighbors;
-      neighbors->e[neighbors->maxsize].i= dim+1; /*may be overwritten*/
-      memset((char *)SETelemaddr_(neighbors, 1, void), 0, dim * SETelemsize);
-    }
-  }
-
-  qh_newhashtable(qh, numnew*(qh->hull_dim-1)); /* twice what is normally needed,
-                                     but every ridge could be DUPLICATEridge */
-  hashsize= qh_setsize(qh, qh->hash_table);
-  FORALLnew_facets {
-    for (newskip=1; newskiphull_dim; newskip++) /* furthest/horizon already matched */
-      /* hashsize>0 because hull_dim>1 and numnew>0 */
-      qh_matchneighbor(qh, newfacet, newskip, hashsize, &hashcount);
-#if 0   /* use the following to trap hashcount errors */
-    {
-      int count= 0, k;
-      facetT *facet, *neighbor;
-
-      count= 0;
-      FORALLfacet_(qh->newfacet_list) {  /* newfacet already in use */
-        for (k=1; k < qh->hull_dim; k++) {
-          neighbor= SETelemt_(facet->neighbors, k, facetT);
-          if (!neighbor || neighbor == qh_DUPLICATEridge)
-            count++;
-        }
-        if (facet == newfacet)
-          break;
-      }
-      if (count != hashcount) {
-        qh_fprintf(qh, qh->ferr, 8088, "qh_matchnewfacets: after adding facet %d, hashcount %d != count %d\n",
-                 newfacet->id, hashcount, count);
-        qh_errexit(qh, qh_ERRqhull, newfacet, NULL);
-      }
-    }
-#endif  /* end of trap code */
-  }
-  if (hashcount) {
-    FORALLnew_facets {
-      if (newfacet->dupridge) {
-        FOREACHneighbor_i_(qh, newfacet) {
-          if (neighbor == qh_DUPLICATEridge) {
-            qh_matchduplicates(qh, newfacet, neighbor_i, hashsize, &hashcount);
-                    /* this may report MERGEfacet */
-          }
-        }
-      }
-    }
-  }
-  if (hashcount) {
-    qh_fprintf(qh, qh->ferr, 6108, "qhull internal error (qh_matchnewfacets): %d neighbors did not match up\n",
-        hashcount);
-    qh_printhashtable(qh, qh->ferr);
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }
-#ifndef qh_NOtrace
-  if (qh->IStracing >= 2) {
-    FOREACHfacet_i_(qh, qh->hash_table) {
-      if (!facet)
-        numfree++;
-    }
-    qh_fprintf(qh, qh->ferr, 8089, "qh_matchnewfacets: %d new facets, %d unused hash entries .  hashsize %d\n",
-             numnew, numfree, qh_setsize(qh, qh->hash_table));
-  }
-#endif /* !qh_NOtrace */
-  qh_setfree(qh, &qh->hash_table);
-  if (qh->PREmerge || qh->MERGEexact) {
-    if (qh->IStracing >= 4)
-      qh_printfacetlist(qh, qh->newfacet_list, NULL, qh_ALL);
-    FORALLnew_facets {
-      if (newfacet->normal)
-        qh_checkflipped(qh, newfacet, NULL, qh_ALL);
-    }
-  }else if (qh->FORCEoutput)
-    qh_checkflipped_all(qh, qh->newfacet_list);  /* prints warnings for flipped */
-} /* matchnewfacets */
-
-
-/*---------------------------------
-
-  qh_matchvertices(qh, firstindex, verticesA, skipA, verticesB, skipB, same )
-    tests whether vertices match with a single skip
-    starts match at firstindex since all new facets have a common vertex
-
-  returns:
-    true if matched vertices
-    skip index for each set
-    sets same iff vertices have the same orientation
-
-  notes:
-    assumes skipA is in A and both sets are the same size
-
-  design:
-    set up pointers
-    scan both sets checking for a match
-    test orientation
-*/
-boolT qh_matchvertices(qhT *qh, int firstindex, setT *verticesA, int skipA,
-       setT *verticesB, int *skipB, boolT *same) {
-  vertexT **elemAp, **elemBp, **skipBp=NULL, **skipAp;
-
-  elemAp= SETelemaddr_(verticesA, firstindex, vertexT);
-  elemBp= SETelemaddr_(verticesB, firstindex, vertexT);
-  skipAp= SETelemaddr_(verticesA, skipA, vertexT);
-  do if (elemAp != skipAp) {
-    while (*elemAp != *elemBp++) {
-      if (skipBp)
-        return False;
-      skipBp= elemBp;  /* one extra like FOREACH */
-    }
-  }while (*(++elemAp));
-  if (!skipBp)
-    skipBp= ++elemBp;
-  *skipB= SETindex_(verticesB, skipB); /* i.e., skipBp - verticesB */
-  *same= !((skipA & 0x1) ^ (*skipB & 0x1)); /* result is 0 or 1 */
-  trace4((qh, qh->ferr, 4054, "qh_matchvertices: matched by skip %d(v%d) and skip %d(v%d) same? %d\n",
-          skipA, (*skipAp)->id, *skipB, (*(skipBp-1))->id, *same));
-  return(True);
-} /* matchvertices */
-
-/*---------------------------------
-
-  qh_newfacet(qh)
-    return a new facet
-
-  returns:
-    all fields initialized or cleared   (NULL)
-    preallocates neighbors set
-*/
-facetT *qh_newfacet(qhT *qh) {
-  facetT *facet;
-  void **freelistp; /* used if !qh_NOmem by qh_memalloc_() */
-
-  qh_memalloc_(qh, (int)sizeof(facetT), freelistp, facet, facetT);
-  memset((char *)facet, (size_t)0, sizeof(facetT));
-  if (qh->facet_id == qh->tracefacet_id)
-    qh->tracefacet= facet;
-  facet->id= qh->facet_id++;
-  facet->neighbors= qh_setnew(qh, qh->hull_dim);
-#if !qh_COMPUTEfurthest
-  facet->furthestdist= 0.0;
-#endif
-#if qh_MAXoutside
-  if (qh->FORCEoutput && qh->APPROXhull)
-    facet->maxoutside= qh->MINoutside;
-  else
-    facet->maxoutside= qh->DISTround;
-#endif
-  facet->simplicial= True;
-  facet->good= True;
-  facet->newfacet= True;
-  trace4((qh, qh->ferr, 4055, "qh_newfacet: created facet f%d\n", facet->id));
-  return(facet);
-} /* newfacet */
-
-
-/*---------------------------------
-
-  qh_newridge()
-    return a new ridge
-*/
-ridgeT *qh_newridge(qhT *qh) {
-  ridgeT *ridge;
-  void **freelistp;   /* used if !qh_NOmem by qh_memalloc_() */
-
-  qh_memalloc_(qh, (int)sizeof(ridgeT), freelistp, ridge, ridgeT);
-  memset((char *)ridge, (size_t)0, sizeof(ridgeT));
-  zinc_(Ztotridges);
-  if (qh->ridge_id == UINT_MAX) {
-    qh_fprintf(qh, qh->ferr, 7074, "\
-qhull warning: more than 2^32 ridges.  Qhull results are OK.  Since the ridge ID wraps around to 0, two ridges may have the same identifier.\n");
-  }
-  ridge->id= qh->ridge_id++;
-  trace4((qh, qh->ferr, 4056, "qh_newridge: created ridge r%d\n", ridge->id));
-  return(ridge);
-} /* newridge */
-
-
-/*---------------------------------
-
-  qh_pointid(qh, point )
-    return id for a point,
-    returns qh_IDnone(-3) if null, qh_IDinterior(-2) if interior, or qh_IDunknown(-1) if not known
-
-  alternative code if point is in qh.first_point...
-    unsigned long id;
-    id= ((unsigned long)point - (unsigned long)qh.first_point)/qh.normal_size;
-
-  notes:
-    Valid points are non-negative
-    WARN64 -- id truncated to 32-bits, at most 2G points
-    NOerrors returned (QhullPoint::id)
-    if point not in point array
-      the code does a comparison of unrelated pointers.
-*/
-int qh_pointid(qhT *qh, pointT *point) {
-  ptr_intT offset, id;
-
-  if (!point || !qh)
-    return qh_IDnone;
-  else if (point == qh->interior_point)
-    return qh_IDinterior;
-  else if (point >= qh->first_point
-  && point < qh->first_point + qh->num_points * qh->hull_dim) {
-    offset= (ptr_intT)(point - qh->first_point);
-    id= offset / qh->hull_dim;
-  }else if ((id= qh_setindex(qh->other_points, point)) != -1)
-    id += qh->num_points;
-  else
-    return qh_IDunknown;
-  return (int)id;
-} /* pointid */
-
-/*---------------------------------
-
-  qh_removefacet(qh, facet )
-    unlinks facet from qh.facet_list,
-
-  returns:
-    updates qh.facet_list .newfacet_list .facet_next visible_list
-    decrements qh.num_facets
-
-  see:
-    qh_appendfacet
-*/
-void qh_removefacet(qhT *qh, facetT *facet) {
-  facetT *next= facet->next, *previous= facet->previous;
-
-  if (facet == qh->newfacet_list)
-    qh->newfacet_list= next;
-  if (facet == qh->facet_next)
-    qh->facet_next= next;
-  if (facet == qh->visible_list)
-    qh->visible_list= next;
-  if (previous) {
-    previous->next= next;
-    next->previous= previous;
-  }else {  /* 1st facet in qh->facet_list */
-    qh->facet_list= next;
-    qh->facet_list->previous= NULL;
-  }
-  qh->num_facets--;
-  trace4((qh, qh->ferr, 4057, "qh_removefacet: remove f%d from facet_list\n", facet->id));
-} /* removefacet */
-
-
-/*---------------------------------
-
-  qh_removevertex(qh, vertex )
-    unlinks vertex from qh.vertex_list,
-
-  returns:
-    updates qh.vertex_list .newvertex_list
-    decrements qh.num_vertices
-*/
-void qh_removevertex(qhT *qh, vertexT *vertex) {
-  vertexT *next= vertex->next, *previous= vertex->previous;
-
-  if (vertex == qh->newvertex_list)
-    qh->newvertex_list= next;
-  if (previous) {
-    previous->next= next;
-    next->previous= previous;
-  }else {  /* 1st vertex in qh->vertex_list */
-    qh->vertex_list= vertex->next;
-    qh->vertex_list->previous= NULL;
-  }
-  qh->num_vertices--;
-  trace4((qh, qh->ferr, 4058, "qh_removevertex: remove v%d from vertex_list\n", vertex->id));
-} /* removevertex */
-
-
-/*---------------------------------
-
-  qh_updatevertices()
-    update vertex neighbors and delete interior vertices
-
-  returns:
-    if qh.VERTEXneighbors, updates neighbors for each vertex
-      if qh.newvertex_list,
-         removes visible neighbors  from vertex neighbors
-      if qh.newfacet_list
-         adds new facets to vertex neighbors
-    if qh.visible_list
-       interior vertices added to qh.del_vertices for later partitioning
-
-  design:
-    if qh.VERTEXneighbors
-      deletes references to visible facets from vertex neighbors
-      appends new facets to the neighbor list for each vertex
-      checks all vertices of visible facets
-        removes visible facets from neighbor lists
-        marks unused vertices for deletion
-*/
-void qh_updatevertices(qhT *qh /*qh.newvertex_list, newfacet_list, visible_list*/) {
-  facetT *newfacet= NULL, *neighbor, **neighborp, *visible;
-  vertexT *vertex, **vertexp;
-
-  trace3((qh, qh->ferr, 3013, "qh_updatevertices: delete interior vertices and update vertex->neighbors\n"));
-  if (qh->VERTEXneighbors) {
-    FORALLvertex_(qh->newvertex_list) {
-      FOREACHneighbor_(vertex) {
-        if (neighbor->visible)
-          SETref_(neighbor)= NULL;
-      }
-      qh_setcompact(qh, vertex->neighbors);
-    }
-    FORALLnew_facets {
-      FOREACHvertex_(newfacet->vertices)
-        qh_setappend(qh, &vertex->neighbors, newfacet);
-    }
-    FORALLvisible_facets {
-      FOREACHvertex_(visible->vertices) {
-        if (!vertex->newlist && !vertex->deleted) {
-          FOREACHneighbor_(vertex) { /* this can happen under merging */
-            if (!neighbor->visible)
-              break;
-          }
-          if (neighbor)
-            qh_setdel(vertex->neighbors, visible);
-          else {
-            vertex->deleted= True;
-            qh_setappend(qh, &qh->del_vertices, vertex);
-            trace2((qh, qh->ferr, 2041, "qh_updatevertices: delete vertex p%d(v%d) in f%d\n",
-                  qh_pointid(qh, vertex->point), vertex->id, visible->id));
-          }
-        }
-      }
-    }
-  }else {  /* !VERTEXneighbors */
-    FORALLvisible_facets {
-      FOREACHvertex_(visible->vertices) {
-        if (!vertex->newlist && !vertex->deleted) {
-          vertex->deleted= True;
-          qh_setappend(qh, &qh->del_vertices, vertex);
-          trace2((qh, qh->ferr, 2042, "qh_updatevertices: delete vertex p%d(v%d) in f%d\n",
-                  qh_pointid(qh, vertex->point), vertex->id, visible->id));
-        }
-      }
-    }
-  }
-} /* updatevertices */
-
-
-
diff --git a/C/qset_r.c b/C/qset_r.c
deleted file mode 100644
--- a/C/qset_r.c
+++ /dev/null
@@ -1,1340 +0,0 @@
-/*
  ---------------------------------
-
-   qset_r.c
-   implements set manipulations needed for quickhull
-
-   see qh-set_r.htm and qset_r.h
-
-   Be careful of strict aliasing (two pointers of different types
-   that reference the same location).  The last slot of a set is
-   either the actual size of the set plus 1, or the NULL terminator
-   of the set (i.e., setelemT).
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull_r/qset_r.c#3 $$Change: 2062 $
-   $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
-*/
-
-#include "libqhull_r.h" /* for qhT and QHULL_CRTDBG */
-#include "qset_r.h"
-#include "mem_r.h"
-#include 
-#include 
-/*** uncomment here and qhull_ra.h
-     if string.h does not define memcpy()
-#include 
-*/
-
-#ifndef qhDEFlibqhull
-typedef struct ridgeT ridgeT;
-typedef struct facetT facetT;
-void    qh_errexit(qhT *qh, int exitcode, facetT *, ridgeT *);
-void    qh_fprintf(qhT *qh, FILE *fp, int msgcode, const char *fmt, ... );
-#  ifdef _MSC_VER  /* Microsoft Visual C++ -- warning level 4 */
-#  pragma warning( disable : 4127)  /* conditional expression is constant */
-#  pragma warning( disable : 4706)  /* assignment within conditional function */
-#  endif
-#endif
-
-/*=============== internal macros ===========================*/
-
-/*============ functions in alphabetical order ===================*/
-
-/*----------------------------------
-
-  qh_setaddnth(qh, setp, nth, newelem)
-    adds newelem as n'th element of sorted or unsorted *setp
-
-  notes:
-    *setp and newelem must be defined
-    *setp may be a temp set
-    nth=0 is first element
-    errors if nth is out of bounds
-
-  design:
-    expand *setp if empty or full
-    move tail of *setp up one
-    insert newelem
-*/
-void qh_setaddnth(qhT *qh, setT **setp, int nth, void *newelem) {
-  int oldsize, i;
-  setelemT *sizep;          /* avoid strict aliasing */
-  setelemT *oldp, *newp;
-
-  if (!*setp || (sizep= SETsizeaddr_(*setp))->i==0) {
-    qh_setlarger(qh, setp);
-    sizep= SETsizeaddr_(*setp);
-  }
-  oldsize= sizep->i - 1;
-  if (nth < 0 || nth > oldsize) {
-    qh_fprintf(qh, qh->qhmem.ferr, 6171, "qhull internal error (qh_setaddnth): nth %d is out-of-bounds for set:\n", nth);
-    qh_setprint(qh, qh->qhmem.ferr, "", *setp);
-    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
-  }
-  sizep->i++;
-  oldp= (setelemT *)SETelemaddr_(*setp, oldsize, void);   /* NULL */
-  newp= oldp+1;
-  for (i=oldsize-nth+1; i--; )  /* move at least NULL  */
-    (newp--)->p= (oldp--)->p;       /* may overwrite *sizep */
-  newp->p= newelem;
-} /* setaddnth */
-
-
-/*----------------------------------
-
-  setaddsorted( setp, newelem )
-    adds an newelem into sorted *setp
-
-  notes:
-    *setp and newelem must be defined
-    *setp may be a temp set
-    nop if newelem already in set
-
-  design:
-    find newelem's position in *setp
-    insert newelem
-*/
-void qh_setaddsorted(qhT *qh, setT **setp, void *newelem) {
-  int newindex=0;
-  void *elem, **elemp;
-
-  FOREACHelem_(*setp) {          /* could use binary search instead */
-    if (elem < newelem)
-      newindex++;
-    else if (elem == newelem)
-      return;
-    else
-      break;
-  }
-  qh_setaddnth(qh, setp, newindex, newelem);
-} /* setaddsorted */
-
-
-/*---------------------------------
-
-  qh_setappend(qh, setp, newelem)
-    append newelem to *setp
-
-  notes:
-    *setp may be a temp set
-    *setp and newelem may be NULL
-
-  design:
-    expand *setp if empty or full
-    append newelem to *setp
-
-*/
-void qh_setappend(qhT *qh, setT **setp, void *newelem) {
-  setelemT *sizep;  /* Avoid strict aliasing.  Writing to *endp may overwrite *sizep */
-  setelemT *endp;
-  int count;
-
-  if (!newelem)
-    return;
-  if (!*setp || (sizep= SETsizeaddr_(*setp))->i==0) {
-    qh_setlarger(qh, setp);
-    sizep= SETsizeaddr_(*setp);
-  }
-  count= (sizep->i)++ - 1;
-  endp= (setelemT *)SETelemaddr_(*setp, count, void);
-  (endp++)->p= newelem;
-  endp->p= NULL;
-} /* setappend */
-
-/*---------------------------------
-
-  qh_setappend_set(qh, setp, setA)
-    appends setA to *setp
-
-  notes:
-    *setp can not be a temp set
-    *setp and setA may be NULL
-
-  design:
-    setup for copy
-    expand *setp if it is too small
-    append all elements of setA to *setp
-*/
-void qh_setappend_set(qhT *qh, setT **setp, setT *setA) {
-  int sizeA, size;
-  setT *oldset;
-  setelemT *sizep;
-
-  if (!setA)
-    return;
-  SETreturnsize_(setA, sizeA);
-  if (!*setp)
-    *setp= qh_setnew(qh, sizeA);
-  sizep= SETsizeaddr_(*setp);
-  if (!(size= sizep->i))
-    size= (*setp)->maxsize;
-  else
-    size--;
-  if (size + sizeA > (*setp)->maxsize) {
-    oldset= *setp;
-    *setp= qh_setcopy(qh, oldset, sizeA);
-    qh_setfree(qh, &oldset);
-    sizep= SETsizeaddr_(*setp);
-  }
-  if (sizeA > 0) {
-    sizep->i= size+sizeA+1;   /* memcpy may overwrite */
-    memcpy((char *)&((*setp)->e[size].p), (char *)&(setA->e[0].p), (size_t)(sizeA+1) * SETelemsize);
-  }
-} /* setappend_set */
-
-
-/*---------------------------------
-
-  qh_setappend2ndlast(qh, setp, newelem )
-    makes newelem the next to the last element in *setp
-
-  notes:
-    *setp must have at least one element
-    newelem must be defined
-    *setp may be a temp set
-
-  design:
-    expand *setp if empty or full
-    move last element of *setp up one
-    insert newelem
-*/
-void qh_setappend2ndlast(qhT *qh, setT **setp, void *newelem) {
-    setelemT *sizep;  /* Avoid strict aliasing.  Writing to *endp may overwrite *sizep */
-    setelemT *endp, *lastp;
-    int count;
-
-    if (!*setp || (sizep= SETsizeaddr_(*setp))->i==0) {
-        qh_setlarger(qh, setp);
-        sizep= SETsizeaddr_(*setp);
-    }
-    count= (sizep->i)++ - 1;
-    endp= (setelemT *)SETelemaddr_(*setp, count, void); /* NULL */
-    lastp= endp-1;
-    *(endp++)= *lastp;
-    endp->p= NULL;    /* may overwrite *sizep */
-    lastp->p= newelem;
-} /* setappend2ndlast */
-
-/*---------------------------------
-
-  qh_setcheck(qh, set, typename, id )
-    check set for validity
-    report errors with typename and id
-
-  design:
-    checks that maxsize, actual size, and NULL terminator agree
-*/
-void qh_setcheck(qhT *qh, setT *set, const char *tname, unsigned id) {
-  int maxsize, size;
-  int waserr= 0;
-
-  if (!set)
-    return;
-  SETreturnsize_(set, size);
-  maxsize= set->maxsize;
-  if (size > maxsize || !maxsize) {
-    qh_fprintf(qh, qh->qhmem.ferr, 6172, "qhull internal error (qh_setcheck): actual size %d of %s%d is greater than max size %d\n",
-             size, tname, id, maxsize);
-    waserr= 1;
-  }else if (set->e[size].p) {
-    qh_fprintf(qh, qh->qhmem.ferr, 6173, "qhull internal error (qh_setcheck): %s%d(size %d max %d) is not null terminated.\n",
-             tname, id, size-1, maxsize);
-    waserr= 1;
-  }
-  if (waserr) {
-    qh_setprint(qh, qh->qhmem.ferr, "ERRONEOUS", set);
-    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
-  }
-} /* setcheck */
-
-
-/*---------------------------------
-
-  qh_setcompact(qh, set )
-    remove internal NULLs from an unsorted set
-
-  returns:
-    updated set
-
-  notes:
-    set may be NULL
-    it would be faster to swap tail of set into holes, like qh_setdel
-
-  design:
-    setup pointers into set
-    skip NULLs while copying elements to start of set
-    update the actual size
-*/
-void qh_setcompact(qhT *qh, setT *set) {
-  int size;
-  void **destp, **elemp, **endp, **firstp;
-
-  if (!set)
-    return;
-  SETreturnsize_(set, size);
-  destp= elemp= firstp= SETaddr_(set, void);
-  endp= destp + size;
-  while (1) {
-    if (!(*destp++ = *elemp++)) {
-      destp--;
-      if (elemp > endp)
-        break;
-    }
-  }
-  qh_settruncate(qh, set, (int)(destp-firstp));   /* WARN64 */
-} /* setcompact */
-
-
-/*---------------------------------
-
-  qh_setcopy(qh, set, extra )
-    make a copy of a sorted or unsorted set with extra slots
-
-  returns:
-    new set
-
-  design:
-    create a newset with extra slots
-    copy the elements to the newset
-
-*/
-setT *qh_setcopy(qhT *qh, setT *set, int extra) {
-  setT *newset;
-  int size;
-
-  if (extra < 0)
-    extra= 0;
-  SETreturnsize_(set, size);
-  newset= qh_setnew(qh, size+extra);
-  SETsizeaddr_(newset)->i= size+1;    /* memcpy may overwrite */
-  memcpy((char *)&(newset->e[0].p), (char *)&(set->e[0].p), (size_t)(size+1) * SETelemsize);
-  return(newset);
-} /* setcopy */
-
-
-/*---------------------------------
-
-  qh_setdel(set, oldelem )
-    delete oldelem from an unsorted set
-
-  returns:
-    returns oldelem if found
-    returns NULL otherwise
-
-  notes:
-    set may be NULL
-    oldelem must not be NULL;
-    only deletes one copy of oldelem in set
-
-  design:
-    locate oldelem
-    update actual size if it was full
-    move the last element to the oldelem's location
-*/
-void *qh_setdel(setT *set, void *oldelem) {
-  setelemT *sizep;
-  setelemT *elemp;
-  setelemT *lastp;
-
-  if (!set)
-    return NULL;
-  elemp= (setelemT *)SETaddr_(set, void);
-  while (elemp->p != oldelem && elemp->p)
-    elemp++;
-  if (elemp->p) {
-    sizep= SETsizeaddr_(set);
-    if (!(sizep->i)--)         /*  if was a full set */
-      sizep->i= set->maxsize;  /*     *sizep= (maxsize-1)+ 1 */
-    lastp= (setelemT *)SETelemaddr_(set, sizep->i-1, void);
-    elemp->p= lastp->p;      /* may overwrite itself */
-    lastp->p= NULL;
-    return oldelem;
-  }
-  return NULL;
-} /* setdel */
-
-
-/*---------------------------------
-
-  qh_setdellast(set)
-    return last element of set or NULL
-
-  notes:
-    deletes element from set
-    set may be NULL
-
-  design:
-    return NULL if empty
-    if full set
-      delete last element and set actual size
-    else
-      delete last element and update actual size
-*/
-void *qh_setdellast(setT *set) {
-  int setsize;  /* actually, actual_size + 1 */
-  int maxsize;
-  setelemT *sizep;
-  void *returnvalue;
-
-  if (!set || !(set->e[0].p))
-    return NULL;
-  sizep= SETsizeaddr_(set);
-  if ((setsize= sizep->i)) {
-    returnvalue= set->e[setsize - 2].p;
-    set->e[setsize - 2].p= NULL;
-    sizep->i--;
-  }else {
-    maxsize= set->maxsize;
-    returnvalue= set->e[maxsize - 1].p;
-    set->e[maxsize - 1].p= NULL;
-    sizep->i= maxsize;
-  }
-  return returnvalue;
-} /* setdellast */
-
-
-/*---------------------------------
-
-  qh_setdelnth(qh, set, nth )
-    deletes nth element from unsorted set
-    0 is first element
-
-  returns:
-    returns the element (needs type conversion)
-
-  notes:
-    errors if nth invalid
-
-  design:
-    setup points and check nth
-    delete nth element and overwrite with last element
-*/
-void *qh_setdelnth(qhT *qh, setT *set, int nth) {
-  void *elem;
-  setelemT *sizep;
-  setelemT *elemp, *lastp;
-
-  sizep= SETsizeaddr_(set);
-  if ((sizep->i--)==0)         /*  if was a full set */
-    sizep->i= set->maxsize;  /*     *sizep= (maxsize-1)+ 1 */
-  if (nth < 0 || nth >= sizep->i) {
-    qh_fprintf(qh, qh->qhmem.ferr, 6174, "qhull internal error (qh_setdelnth): nth %d is out-of-bounds for set:\n", nth);
-    qh_setprint(qh, qh->qhmem.ferr, "", set);
-    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
-  }
-  elemp= (setelemT *)SETelemaddr_(set, nth, void); /* nth valid by QH6174 */
-  lastp= (setelemT *)SETelemaddr_(set, sizep->i-1, void);
-  elem= elemp->p;
-  elemp->p= lastp->p;      /* may overwrite itself */
-  lastp->p= NULL;
-  return elem;
-} /* setdelnth */
-
-/*---------------------------------
-
-  qh_setdelnthsorted(qh, set, nth )
-    deletes nth element from sorted set
-
-  returns:
-    returns the element (use type conversion)
-
-  notes:
-    errors if nth invalid
-
-  see also:
-    setnew_delnthsorted
-
-  design:
-    setup points and check nth
-    copy remaining elements down one
-    update actual size
-*/
-void *qh_setdelnthsorted(qhT *qh, setT *set, int nth) {
-  void *elem;
-  setelemT *sizep;
-  setelemT *newp, *oldp;
-
-  sizep= SETsizeaddr_(set);
-  if (nth < 0 || (sizep->i && nth >= sizep->i-1) || nth >= set->maxsize) {
-    qh_fprintf(qh, qh->qhmem.ferr, 6175, "qhull internal error (qh_setdelnthsorted): nth %d is out-of-bounds for set:\n", nth);
-    qh_setprint(qh, qh->qhmem.ferr, "", set);
-    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
-  }
-  newp= (setelemT *)SETelemaddr_(set, nth, void);
-  elem= newp->p;
-  oldp= newp+1;
-  while (((newp++)->p= (oldp++)->p))
-    ; /* copy remaining elements and NULL */
-  if ((sizep->i--)==0)         /*  if was a full set */
-    sizep->i= set->maxsize;  /*     *sizep= (max size-1)+ 1 */
-  return elem;
-} /* setdelnthsorted */
-
-
-/*---------------------------------
-
-  qh_setdelsorted(set, oldelem )
-    deletes oldelem from sorted set
-
-  returns:
-    returns oldelem if it was deleted
-
-  notes:
-    set may be NULL
-
-  design:
-    locate oldelem in set
-    copy remaining elements down one
-    update actual size
-*/
-void *qh_setdelsorted(setT *set, void *oldelem) {
-  setelemT *sizep;
-  setelemT *newp, *oldp;
-
-  if (!set)
-    return NULL;
-  newp= (setelemT *)SETaddr_(set, void);
-  while(newp->p != oldelem && newp->p)
-    newp++;
-  if (newp->p) {
-    oldp= newp+1;
-    while (((newp++)->p= (oldp++)->p))
-      ; /* copy remaining elements */
-    sizep= SETsizeaddr_(set);
-    if ((sizep->i--)==0)    /*  if was a full set */
-      sizep->i= set->maxsize;  /*     *sizep= (max size-1)+ 1 */
-    return oldelem;
-  }
-  return NULL;
-} /* setdelsorted */
-
-
-/*---------------------------------
-
-  qh_setduplicate(qh, set, elemsize )
-    duplicate a set of elemsize elements
-
-  notes:
-    use setcopy if retaining old elements
-
-  design:
-    create a new set
-    for each elem of the old set
-      create a newelem
-      append newelem to newset
-*/
-setT *qh_setduplicate(qhT *qh, setT *set, int elemsize) {
-  void          *elem, **elemp, *newElem;
-  setT          *newSet;
-  int           size;
-
-  if (!(size= qh_setsize(qh, set)))
-    return NULL;
-  newSet= qh_setnew(qh, size);
-  FOREACHelem_(set) {
-    newElem= qh_memalloc(qh, elemsize);
-    memcpy(newElem, elem, (size_t)elemsize);
-    qh_setappend(qh, &newSet, newElem);
-  }
-  return newSet;
-} /* setduplicate */
-
-
-/*---------------------------------
-
-  qh_setendpointer( set )
-    Returns pointer to NULL terminator of a set's elements
-    set can not be NULL
-
-*/
-void **qh_setendpointer(setT *set) {
-
-  setelemT *sizep= SETsizeaddr_(set);
-  int n= sizep->i;
-  return (n ? &set->e[n-1].p : &sizep->p);
-} /* qh_setendpointer */
-
-/*---------------------------------
-
-  qh_setequal( setA, setB )
-    returns 1 if two sorted sets are equal, otherwise returns 0
-
-  notes:
-    either set may be NULL
-
-  design:
-    check size of each set
-    setup pointers
-    compare elements of each set
-*/
-int qh_setequal(setT *setA, setT *setB) {
-  void **elemAp, **elemBp;
-  int sizeA= 0, sizeB= 0;
-
-  if (setA) {
-    SETreturnsize_(setA, sizeA);
-  }
-  if (setB) {
-    SETreturnsize_(setB, sizeB);
-  }
-  if (sizeA != sizeB)
-    return 0;
-  if (!sizeA)
-    return 1;
-  elemAp= SETaddr_(setA, void);
-  elemBp= SETaddr_(setB, void);
-  if (!memcmp((char *)elemAp, (char *)elemBp, sizeA*SETelemsize))
-    return 1;
-  return 0;
-} /* setequal */
-
-
-/*---------------------------------
-
-  qh_setequal_except( setA, skipelemA, setB, skipelemB )
-    returns 1 if sorted setA and setB are equal except for skipelemA & B
-
-  returns:
-    false if either skipelemA or skipelemB are missing
-
-  notes:
-    neither set may be NULL
-
-    if skipelemB is NULL,
-      can skip any one element of setB
-
-  design:
-    setup pointers
-    search for skipelemA, skipelemB, and mismatches
-    check results
-*/
-int qh_setequal_except(setT *setA, void *skipelemA, setT *setB, void *skipelemB) {
-  void **elemA, **elemB;
-  int skip=0;
-
-  elemA= SETaddr_(setA, void);
-  elemB= SETaddr_(setB, void);
-  while (1) {
-    if (*elemA == skipelemA) {
-      skip++;
-      elemA++;
-    }
-    if (skipelemB) {
-      if (*elemB == skipelemB) {
-        skip++;
-        elemB++;
-      }
-    }else if (*elemA != *elemB) {
-      skip++;
-      if (!(skipelemB= *elemB++))
-        return 0;
-    }
-    if (!*elemA)
-      break;
-    if (*elemA++ != *elemB++)
-      return 0;
-  }
-  if (skip != 2 || *elemB)
-    return 0;
-  return 1;
-} /* setequal_except */
-
-
-/*---------------------------------
-
-  qh_setequal_skip( setA, skipA, setB, skipB )
-    returns 1 if sorted setA and setB are equal except for elements skipA & B
-
-  returns:
-    false if different size
-
-  notes:
-    neither set may be NULL
-
-  design:
-    setup pointers
-    search for mismatches while skipping skipA and skipB
-*/
-int qh_setequal_skip(setT *setA, int skipA, setT *setB, int skipB) {
-  void **elemA, **elemB, **skipAp, **skipBp;
-
-  elemA= SETaddr_(setA, void);
-  elemB= SETaddr_(setB, void);
-  skipAp= SETelemaddr_(setA, skipA, void);
-  skipBp= SETelemaddr_(setB, skipB, void);
-  while (1) {
-    if (elemA == skipAp)
-      elemA++;
-    if (elemB == skipBp)
-      elemB++;
-    if (!*elemA)
-      break;
-    if (*elemA++ != *elemB++)
-      return 0;
-  }
-  if (*elemB)
-    return 0;
-  return 1;
-} /* setequal_skip */
-
-
-/*---------------------------------
-
-  qh_setfree(qh, setp )
-    frees the space occupied by a sorted or unsorted set
-
-  returns:
-    sets setp to NULL
-
-  notes:
-    set may be NULL
-
-  design:
-    free array
-    free set
-*/
-void qh_setfree(qhT *qh, setT **setp) {
-  int size;
-  void **freelistp;  /* used if !qh_NOmem by qh_memfree_() */
-
-  if (*setp) {
-    size= sizeof(setT) + ((*setp)->maxsize)*SETelemsize;
-    if (size <= qh->qhmem.LASTsize) {
-      qh_memfree_(qh, *setp, size, freelistp);
-    }else
-      qh_memfree(qh, *setp, size);
-    *setp= NULL;
-  }
-} /* setfree */
-
-
-/*---------------------------------
-
-  qh_setfree2(qh, setp, elemsize )
-    frees the space occupied by a set and its elements
-
-  notes:
-    set may be NULL
-
-  design:
-    free each element
-    free set
-*/
-void qh_setfree2(qhT *qh, setT **setp, int elemsize) {
-  void          *elem, **elemp;
-
-  FOREACHelem_(*setp)
-    qh_memfree(qh, elem, elemsize);
-  qh_setfree(qh, setp);
-} /* setfree2 */
-
-
-
-/*---------------------------------
-
-  qh_setfreelong(qh, setp )
-    frees a set only if it's in long memory
-
-  returns:
-    sets setp to NULL if it is freed
-
-  notes:
-    set may be NULL
-
-  design:
-    if set is large
-      free it
-*/
-void qh_setfreelong(qhT *qh, setT **setp) {
-  int size;
-
-  if (*setp) {
-    size= sizeof(setT) + ((*setp)->maxsize)*SETelemsize;
-    if (size > qh->qhmem.LASTsize) {
-      qh_memfree(qh, *setp, size);
-      *setp= NULL;
-    }
-  }
-} /* setfreelong */
-
-
-/*---------------------------------
-
-  qh_setin(set, setelem )
-    returns 1 if setelem is in a set, 0 otherwise
-
-  notes:
-    set may be NULL or unsorted
-
-  design:
-    scans set for setelem
-*/
-int qh_setin(setT *set, void *setelem) {
-  void *elem, **elemp;
-
-  FOREACHelem_(set) {
-    if (elem == setelem)
-      return 1;
-  }
-  return 0;
-} /* setin */
-
-
-/*---------------------------------
-
-  qh_setindex(set, atelem )
-    returns the index of atelem in set.
-    returns -1, if not in set or maxsize wrong
-
-  notes:
-    set may be NULL and may contain nulls.
-    NOerrors returned (qh_pointid, QhullPoint::id)
-
-  design:
-    checks maxsize
-    scans set for atelem
-*/
-int qh_setindex(setT *set, void *atelem) {
-  void **elem;
-  int size, i;
-
-  if (!set)
-    return -1;
-  SETreturnsize_(set, size);
-  if (size > set->maxsize)
-    return -1;
-  elem= SETaddr_(set, void);
-  for (i=0; i < size; i++) {
-    if (*elem++ == atelem)
-      return i;
-  }
-  return -1;
-} /* setindex */
-
-
-/*---------------------------------
-
-  qh_setlarger(qh, oldsetp )
-    returns a larger set that contains all elements of *oldsetp
-
-  notes:
-    the set is at least twice as large
-    if temp set, updates qh->qhmem.tempstack
-
-  design:
-    creates a new set
-    copies the old set to the new set
-    updates pointers in tempstack
-    deletes the old set
-*/
-void qh_setlarger(qhT *qh, setT **oldsetp) {
-  int size= 1;
-  setT *newset, *set, **setp, *oldset;
-  setelemT *sizep;
-  setelemT *newp, *oldp;
-
-  if (*oldsetp) {
-    oldset= *oldsetp;
-    SETreturnsize_(oldset, size);
-    qh->qhmem.cntlarger++;
-    qh->qhmem.totlarger += size+1;
-    newset= qh_setnew(qh, 2 * size);
-    oldp= (setelemT *)SETaddr_(oldset, void);
-    newp= (setelemT *)SETaddr_(newset, void);
-    memcpy((char *)newp, (char *)oldp, (size_t)(size+1) * SETelemsize);
-    sizep= SETsizeaddr_(newset);
-    sizep->i= size+1;
-    FOREACHset_((setT *)qh->qhmem.tempstack) {
-      if (set == oldset)
-        *(setp-1)= newset;
-    }
-    qh_setfree(qh, oldsetp);
-  }else
-    newset= qh_setnew(qh, 3);
-  *oldsetp= newset;
-} /* setlarger */
-
-
-/*---------------------------------
-
-  qh_setlast( set )
-    return last element of set or NULL (use type conversion)
-
-  notes:
-    set may be NULL
-
-  design:
-    return last element
-*/
-void *qh_setlast(setT *set) {
-  int size;
-
-  if (set) {
-    size= SETsizeaddr_(set)->i;
-    if (!size)
-      return SETelem_(set, set->maxsize - 1);
-    else if (size > 1)
-      return SETelem_(set, size - 2);
-  }
-  return NULL;
-} /* setlast */
-
-
-/*---------------------------------
-
-  qh_setnew(qh, setsize )
-    creates and allocates space for a set
-
-  notes:
-    setsize means the number of elements (!including the NULL terminator)
-    use qh_settemp/qh_setfreetemp if set is temporary
-
-  design:
-    allocate memory for set
-    roundup memory if small set
-    initialize as empty set
-*/
-setT *qh_setnew(qhT *qh, int setsize) {
-  setT *set;
-  int sizereceived; /* used if !qh_NOmem */
-  int size;
-  void **freelistp; /* used if !qh_NOmem by qh_memalloc_() */
-
-  if (!setsize)
-    setsize++;
-  size= sizeof(setT) + setsize * SETelemsize;
-  if (size>0 && size <= qh->qhmem.LASTsize) {
-    qh_memalloc_(qh, size, freelistp, set, setT);
-#ifndef qh_NOmem
-    sizereceived= qh->qhmem.sizetable[ qh->qhmem.indextable[size]];
-    if (sizereceived > size)
-      setsize += (sizereceived - size)/SETelemsize;
-#endif
-  }else
-    set= (setT*)qh_memalloc(qh, size);
-  set->maxsize= setsize;
-  set->e[setsize].i= 1;
-  set->e[0].p= NULL;
-  return(set);
-} /* setnew */
-
-
-/*---------------------------------
-
-  qh_setnew_delnthsorted(qh, set, size, nth, prepend )
-    creates a sorted set not containing nth element
-    if prepend, the first prepend elements are undefined
-
-  notes:
-    set must be defined
-    checks nth
-    see also: setdelnthsorted
-
-  design:
-    create new set
-    setup pointers and allocate room for prepend'ed entries
-    append head of old set to new set
-    append tail of old set to new set
-*/
-setT *qh_setnew_delnthsorted(qhT *qh, setT *set, int size, int nth, int prepend) {
-  setT *newset;
-  void **oldp, **newp;
-  int tailsize= size - nth -1, newsize;
-
-  if (tailsize < 0) {
-    qh_fprintf(qh, qh->qhmem.ferr, 6176, "qhull internal error (qh_setnew_delnthsorted): nth %d is out-of-bounds for set:\n", nth);
-    qh_setprint(qh, qh->qhmem.ferr, "", set);
-    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
-  }
-  newsize= size-1 + prepend;
-  newset= qh_setnew(qh, newsize);
-  newset->e[newset->maxsize].i= newsize+1;  /* may be overwritten */
-  oldp= SETaddr_(set, void);
-  newp= SETaddr_(newset, void) + prepend;
-  switch (nth) {
-  case 0:
-    break;
-  case 1:
-    *(newp++)= *oldp++;
-    break;
-  case 2:
-    *(newp++)= *oldp++;
-    *(newp++)= *oldp++;
-    break;
-  case 3:
-    *(newp++)= *oldp++;
-    *(newp++)= *oldp++;
-    *(newp++)= *oldp++;
-    break;
-  case 4:
-    *(newp++)= *oldp++;
-    *(newp++)= *oldp++;
-    *(newp++)= *oldp++;
-    *(newp++)= *oldp++;
-    break;
-  default:
-    memcpy((char *)newp, (char *)oldp, (size_t)nth * SETelemsize);
-    newp += nth;
-    oldp += nth;
-    break;
-  }
-  oldp++;
-  switch (tailsize) {
-  case 0:
-    break;
-  case 1:
-    *(newp++)= *oldp++;
-    break;
-  case 2:
-    *(newp++)= *oldp++;
-    *(newp++)= *oldp++;
-    break;
-  case 3:
-    *(newp++)= *oldp++;
-    *(newp++)= *oldp++;
-    *(newp++)= *oldp++;
-    break;
-  case 4:
-    *(newp++)= *oldp++;
-    *(newp++)= *oldp++;
-    *(newp++)= *oldp++;
-    *(newp++)= *oldp++;
-    break;
-  default:
-    memcpy((char *)newp, (char *)oldp, (size_t)tailsize * SETelemsize);
-    newp += tailsize;
-  }
-  *newp= NULL;
-  return(newset);
-} /* setnew_delnthsorted */
-
-
-/*---------------------------------
-
-  qh_setprint(qh, fp, string, set )
-    print set elements to fp with identifying string
-
-  notes:
-    never errors
-*/
-void qh_setprint(qhT *qh, FILE *fp, const char* string, setT *set) {
-  int size, k;
-
-  if (!set)
-    qh_fprintf(qh, fp, 9346, "%s set is null\n", string);
-  else {
-    SETreturnsize_(set, size);
-    qh_fprintf(qh, fp, 9347, "%s set=%p maxsize=%d size=%d elems=",
-             string, set, set->maxsize, size);
-    if (size > set->maxsize)
-      size= set->maxsize+1;
-    for (k=0; k < size; k++)
-      qh_fprintf(qh, fp, 9348, " %p", set->e[k].p);
-    qh_fprintf(qh, fp, 9349, "\n");
-  }
-} /* setprint */
-
-/*---------------------------------
-
-  qh_setreplace(qh, set, oldelem, newelem )
-    replaces oldelem in set with newelem
-
-  notes:
-    errors if oldelem not in the set
-    newelem may be NULL, but it turns the set into an indexed set (no FOREACH)
-
-  design:
-    find oldelem
-    replace with newelem
-*/
-void qh_setreplace(qhT *qh, setT *set, void *oldelem, void *newelem) {
-  void **elemp;
-
-  elemp= SETaddr_(set, void);
-  while (*elemp != oldelem && *elemp)
-    elemp++;
-  if (*elemp)
-    *elemp= newelem;
-  else {
-    qh_fprintf(qh, qh->qhmem.ferr, 6177, "qhull internal error (qh_setreplace): elem %p not found in set\n",
-       oldelem);
-    qh_setprint(qh, qh->qhmem.ferr, "", set);
-    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
-  }
-} /* setreplace */
-
-
-/*---------------------------------
-
-  qh_setsize(qh, set )
-    returns the size of a set
-
-  notes:
-    errors if set's maxsize is incorrect
-    same as SETreturnsize_(set)
-    same code for qh_setsize [qset_r.c] and QhullSetBase::count
-
-  design:
-    determine actual size of set from maxsize
-*/
-int qh_setsize(qhT *qh, setT *set) {
-  int size;
-  setelemT *sizep;
-
-  if (!set)
-    return(0);
-  sizep= SETsizeaddr_(set);
-  if ((size= sizep->i)) {
-    size--;
-    if (size > set->maxsize) {
-      qh_fprintf(qh, qh->qhmem.ferr, 6178, "qhull internal error (qh_setsize): current set size %d is greater than maximum size %d\n",
-               size, set->maxsize);
-      qh_setprint(qh, qh->qhmem.ferr, "set: ", set);
-      qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
-    }
-  }else
-    size= set->maxsize;
-  return size;
-} /* setsize */
-
-/*---------------------------------
-
-  qh_settemp(qh, setsize )
-    return a stacked, temporary set of upto setsize elements
-
-  notes:
-    use settempfree or settempfree_all to release from qh->qhmem.tempstack
-    see also qh_setnew
-
-  design:
-    allocate set
-    append to qh->qhmem.tempstack
-
-*/
-setT *qh_settemp(qhT *qh, int setsize) {
-  setT *newset;
-
-  newset= qh_setnew(qh, setsize);
-  qh_setappend(qh, &qh->qhmem.tempstack, newset);
-  if (qh->qhmem.IStracing >= 5)
-    qh_fprintf(qh, qh->qhmem.ferr, 8123, "qh_settemp: temp set %p of %d elements, depth %d\n",
-       newset, newset->maxsize, qh_setsize(qh, qh->qhmem.tempstack));
-  return newset;
-} /* settemp */
-
-/*---------------------------------
-
-  qh_settempfree(qh, set )
-    free temporary set at top of qh->qhmem.tempstack
-
-  notes:
-    nop if set is NULL
-    errors if set not from previous   qh_settemp
-
-  to locate errors:
-    use 'T2' to find source and then find mis-matching qh_settemp
-
-  design:
-    check top of qh->qhmem.tempstack
-    free it
-*/
-void qh_settempfree(qhT *qh, setT **set) {
-  setT *stackedset;
-
-  if (!*set)
-    return;
-  stackedset= qh_settemppop(qh);
-  if (stackedset != *set) {
-    qh_settemppush(qh, stackedset);
-    qh_fprintf(qh, qh->qhmem.ferr, 6179, "qhull internal error (qh_settempfree): set %p(size %d) was not last temporary allocated(depth %d, set %p, size %d)\n",
-             *set, qh_setsize(qh, *set), qh_setsize(qh, qh->qhmem.tempstack)+1,
-             stackedset, qh_setsize(qh, stackedset));
-    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
-  }
-  qh_setfree(qh, set);
-} /* settempfree */
-
-/*---------------------------------
-
-  qh_settempfree_all(qh)
-    free all temporary sets in qh->qhmem.tempstack
-
-  design:
-    for each set in tempstack
-      free set
-    free qh->qhmem.tempstack
-*/
-void qh_settempfree_all(qhT *qh) {
-  setT *set, **setp;
-
-  FOREACHset_(qh->qhmem.tempstack)
-    qh_setfree(qh, &set);
-  qh_setfree(qh, &qh->qhmem.tempstack);
-} /* settempfree_all */
-
-/*---------------------------------
-
-  qh_settemppop(qh)
-    pop and return temporary set from qh->qhmem.tempstack
-
-  notes:
-    the returned set is permanent
-
-  design:
-    pop and check top of qh->qhmem.tempstack
-*/
-setT *qh_settemppop(qhT *qh) {
-  setT *stackedset;
-
-  stackedset= (setT*)qh_setdellast(qh->qhmem.tempstack);
-  if (!stackedset) {
-    qh_fprintf(qh, qh->qhmem.ferr, 6180, "qhull internal error (qh_settemppop): pop from empty temporary stack\n");
-    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
-  }
-  if (qh->qhmem.IStracing >= 5)
-    qh_fprintf(qh, qh->qhmem.ferr, 8124, "qh_settemppop: depth %d temp set %p of %d elements\n",
-       qh_setsize(qh, qh->qhmem.tempstack)+1, stackedset, qh_setsize(qh, stackedset));
-  return stackedset;
-} /* settemppop */
-
-/*---------------------------------
-
-  qh_settemppush(qh, set )
-    push temporary set unto qh->qhmem.tempstack (makes it temporary)
-
-  notes:
-    duplicates settemp() for tracing
-
-  design:
-    append set to tempstack
-*/
-void qh_settemppush(qhT *qh, setT *set) {
-  if (!set) {
-    qh_fprintf(qh, qh->qhmem.ferr, 6267, "qhull error (qh_settemppush): can not push a NULL temp\n");
-    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
-  }
-  qh_setappend(qh, &qh->qhmem.tempstack, set);
-  if (qh->qhmem.IStracing >= 5)
-    qh_fprintf(qh, qh->qhmem.ferr, 8125, "qh_settemppush: depth %d temp set %p of %d elements\n",
-      qh_setsize(qh, qh->qhmem.tempstack), set, qh_setsize(qh, set));
-} /* settemppush */
-
-
-/*---------------------------------
-
-  qh_settruncate(qh, set, size )
-    truncate set to size elements
-
-  notes:
-    set must be defined
-
-  see:
-    SETtruncate_
-
-  design:
-    check size
-    update actual size of set
-*/
-void qh_settruncate(qhT *qh, setT *set, int size) {
-
-  if (size < 0 || size > set->maxsize) {
-    qh_fprintf(qh, qh->qhmem.ferr, 6181, "qhull internal error (qh_settruncate): size %d out of bounds for set:\n", size);
-    qh_setprint(qh, qh->qhmem.ferr, "", set);
-    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
-  }
-  set->e[set->maxsize].i= size+1;   /* maybe overwritten */
-  set->e[size].p= NULL;
-} /* settruncate */
-
-/*---------------------------------
-
-  qh_setunique(qh, set, elem )
-    add elem to unsorted set unless it is already in set
-
-  notes:
-    returns 1 if it is appended
-
-  design:
-    if elem not in set
-      append elem to set
-*/
-int qh_setunique(qhT *qh, setT **set, void *elem) {
-
-  if (!qh_setin(*set, elem)) {
-    qh_setappend(qh, set, elem);
-    return 1;
-  }
-  return 0;
-} /* setunique */
-
-/*---------------------------------
-
-  qh_setzero(qh, set, index, size )
-    zero elements from index on
-    set actual size of set to size
-
-  notes:
-    set must be defined
-    the set becomes an indexed set (can not use FOREACH...)
-
-  see also:
-    qh_settruncate
-
-  design:
-    check index and size
-    update actual size
-    zero elements starting at e[index]
-*/
-void qh_setzero(qhT *qh, setT *set, int idx, int size) {
-  int count;
-
-  if (idx < 0 || idx >= size || size > set->maxsize) {
-    qh_fprintf(qh, qh->qhmem.ferr, 6182, "qhull internal error (qh_setzero): index %d or size %d out of bounds for set:\n", idx, size);
-    qh_setprint(qh, qh->qhmem.ferr, "", set);
-    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
-  }
-  set->e[set->maxsize].i=  size+1;  /* may be overwritten */
-  count= size - idx + 1;   /* +1 for NULL terminator */
-  memset((char *)SETelemaddr_(set, idx, void), 0, (size_t)count * SETelemsize);
-} /* setzero */
-
-
diff --git a/C/random_r.c b/C/random_r.c
deleted file mode 100644
--- a/C/random_r.c
+++ /dev/null
@@ -1,247 +0,0 @@
-/*
  ---------------------------------
-
-   random_r.c and utilities
-     Park & Miller's minimimal standard random number generator
-     argc/argv conversion
-
-     Used by rbox.  Do not use 'qh' 
-*/
-
-#include "libqhull_r.h"
-#include "random_r.h"
-
-#include 
-#include 
-#include 
-
-#ifdef _MSC_VER  /* Microsoft Visual C++ -- warning level 4 */
-#pragma warning( disable : 4706)  /* assignment within conditional function */
-#pragma warning( disable : 4996)  /* function was declared deprecated(strcpy, localtime, etc.) */
-#endif
-
-/*---------------------------------
-
- qh_argv_to_command(argc, argv, command, max_size )
-
-    build command from argc/argv
-    max_size is at least
-
- returns:
-    a space-delimited string of options (just as typed)
-    returns false if max_size is too short
-
- notes:
-    silently removes
-    makes option string easy to input and output
-    matches qh_argv_to_command_size()
-
-    argc may be 0
-*/
-int qh_argv_to_command(int argc, char *argv[], char* command, int max_size) {
-  int i, remaining;
-  char *s;
-  *command= '\0';  /* max_size > 0 */
-
-  if (argc) {
-    if ((s= strrchr( argv[0], '\\')) /* get filename w/o .exe extension */
-    || (s= strrchr( argv[0], '/')))
-        s++;
-    else
-        s= argv[0];
-    if ((int)strlen(s) < max_size)   /* WARN64 */
-        strcpy(command, s);
-    else
-        goto error_argv;
-    if ((s= strstr(command, ".EXE"))
-    ||  (s= strstr(command, ".exe")))
-        *s= '\0';
-  }
-  for (i=1; i < argc; i++) {
-    s= argv[i];
-    remaining= max_size - (int)strlen(command) - (int)strlen(s) - 2;   /* WARN64 */
-    if (!*s || strchr(s, ' ')) {
-      char *t= command + strlen(command);
-      remaining -= 2;
-      if (remaining < 0) {
-        goto error_argv;
-      }
-      *t++= ' ';
-      *t++= '"';
-      while (*s) {
-        if (*s == '"') {
-          if (--remaining < 0)
-            goto error_argv;
-          *t++= '\\';
-        }
-        *t++= *s++;
-      }
-      *t++= '"';
-      *t= '\0';
-    }else if (remaining < 0) {
-      goto error_argv;
-    }else
-      strcat(command, " ");
-      strcat(command, s);
-  }
-  return 1;
-
-error_argv:
-  return 0;
-} /* argv_to_command */
-
-/*---------------------------------
-
-qh_argv_to_command_size(argc, argv )
-
-    return size to allocate for qh_argv_to_command()
-
-notes:
-    argc may be 0
-    actual size is usually shorter
-*/
-int qh_argv_to_command_size(int argc, char *argv[]) {
-    unsigned int count= 1; /* null-terminator if argc==0 */
-    int i;
-    char *s;
-
-    for (i=0; i0 && strchr(argv[i], ' ')) {
-        count += 2;  /* quote delimiters */
-        for (s=argv[i]; *s; s++) {
-          if (*s == '"') {
-            count++;
-          }
-        }
-      }
-    }
-    return count;
-} /* argv_to_command_size */
-
-/*---------------------------------
-
-  qh_rand()
-  qh_srand(qh, seed )
-    generate pseudo-random number between 1 and 2^31 -2
-
-  notes:
-    For qhull and rbox, called from qh_RANDOMint(),etc. [user.h]
-
-    From Park & Miller's minimal standard random number generator
-      Communications of the ACM, 31:1192-1201, 1988.
-    Does not use 0 or 2^31 -1
-      this is silently enforced by qh_srand()
-    Can make 'Rn' much faster by moving qh_rand to qh_distplane
-*/
-
-/* Global variables and constants */
-
-#define qh_rand_a 16807
-#define qh_rand_m 2147483647
-#define qh_rand_q 127773  /* m div a */
-#define qh_rand_r 2836    /* m mod a */
-
-int qh_rand(qhT *qh) {
-    int lo, hi, test;
-    int seed = qh->last_random;
-
-    hi = seed / qh_rand_q;  /* seed div q */
-    lo = seed % qh_rand_q;  /* seed mod q */
-    test = qh_rand_a * lo - qh_rand_r * hi;
-    if (test > 0)
-        seed= test;
-    else
-        seed= test + qh_rand_m;
-    qh->last_random= seed;
-    /* seed = seed < qh_RANDOMmax/2 ? 0 : qh_RANDOMmax;  for testing */
-    /* seed = qh_RANDOMmax;  for testing */
-    return seed;
-} /* rand */
-
-void qh_srand(qhT *qh, int seed) {
-    if (seed < 1)
-        qh->last_random= 1;
-    else if (seed >= qh_rand_m)
-        qh->last_random= qh_rand_m - 1;
-    else
-        qh->last_random= seed;
-} /* qh_srand */
-
-/*---------------------------------
-
-qh_randomfactor(qh, scale, offset )
-  return a random factor r * scale + offset
-
-notes:
-  qh.RANDOMa/b are defined in global_r.c
-  qh_RANDOMint requires 'qh'
-*/
-realT qh_randomfactor(qhT *qh, realT scale, realT offset) {
-    realT randr;
-
-    randr= qh_RANDOMint;
-    return randr * scale + offset;
-} /* randomfactor */
-
-/*---------------------------------
-
-qh_randommatrix(qh, buffer, dim, rows )
-  generate a random dim X dim matrix in range [-1,1]
-  assumes buffer is [dim+1, dim]
-
-  returns:
-    sets buffer to random numbers
-    sets rows to rows of buffer
-    sets row[dim] as scratch row
-
-  notes:
-    qh_RANDOMint requires 'qh'
-*/
-void qh_randommatrix(qhT *qh, realT *buffer, int dim, realT **rows) {
-    int i, k;
-    realT **rowi, *coord, realr;
-
-    coord= buffer;
-    rowi= rows;
-    for (i=0; i < dim; i++) {
-        *(rowi++)= coord;
-        for (k=0; k < dim; k++) {
-            realr= qh_RANDOMint;
-            *(coord++)= 2.0 * realr/(qh_RANDOMmax+1) - 1.0;
-        }
-    }
-    *rowi= coord;
-} /* randommatrix */
-
-/*---------------------------------
-
-  qh_strtol( s, endp) qh_strtod( s, endp)
-    internal versions of strtol() and strtod()
-    does not skip trailing spaces
-  notes:
-    some implementations of strtol()/strtod() skip trailing spaces
-*/
-double qh_strtod(const char *s, char **endp) {
-  double result;
-
-  result= strtod(s, endp);
-  if (s < (*endp) && (*endp)[-1] == ' ')
-    (*endp)--;
-  return result;
-} /* strtod */
-
-int qh_strtol(const char *s, char **endp) {
-  int result;
-
-  result= (int) strtol(s, endp, 10);     /* WARN64 */
-  if (s< (*endp) && (*endp)[-1] == ' ')
-    (*endp)--;
-  return result;
-} /* strtol */
diff --git a/C/stat_r.c b/C/stat_r.c
deleted file mode 100644
--- a/C/stat_r.c
+++ /dev/null
@@ -1,682 +0,0 @@
-/*
  ---------------------------------
-
-   stat_r.c
-   contains all statistics that are collected for qhull
-
-   see qh-stat_r.htm and stat_r.h
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull_r/stat_r.c#5 $$Change: 2062 $
-   $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
-*/
-
-#include "qhull_ra.h"
-
-/*========== functions in alphabetic order ================*/
-
-/*---------------------------------
-
-  qh_allstatA()
-    define statistics in groups of 20
-
-  notes:
-    (otherwise, 'gcc -O2' uses too much memory)
-    uses qhstat.next
-*/
-void qh_allstatA(qhT *qh) {
-
-   /* zdef_(type,name,doc,average) */
-  zzdef_(zdoc, Zdoc2, "precision statistics", -1);
-  zdef_(zinc, Znewvertex, NULL, -1);
-  zdef_(wadd, Wnewvertex, "ave. distance of a new vertex to a facet(!0s)", Znewvertex);
-  zzdef_(wmax, Wnewvertexmax, "max. distance of a new vertex to a facet", -1);
-  zdef_(wmax, Wvertexmax, "max. distance of an output vertex to a facet", -1);
-  zdef_(wmin, Wvertexmin, "min. distance of an output vertex to a facet", -1);
-  zdef_(wmin, Wmindenom, "min. denominator in hyperplane computation", -1);
-
-  qh->qhstat.precision= qh->qhstat.next;  /* call qh_precision for each of these */
-  zzdef_(zdoc, Zdoc3, "precision problems (corrected unless 'Q0' or an error)", -1);
-  zzdef_(zinc, Zcoplanarridges, "coplanar half ridges in output", -1);
-  zzdef_(zinc, Zconcaveridges, "concave half ridges in output", -1);
-  zzdef_(zinc, Zflippedfacets, "flipped facets", -1);
-  zzdef_(zinc, Zcoplanarhorizon, "coplanar horizon facets for new vertices", -1);
-  zzdef_(zinc, Zcoplanarpart, "coplanar points during partitioning", -1);
-  zzdef_(zinc, Zminnorm, "degenerate hyperplanes recomputed with gaussian elimination", -1);
-  zzdef_(zinc, Znearlysingular, "nearly singular or axis-parallel hyperplanes", -1);
-  zzdef_(zinc, Zback0, "zero divisors during back substitute", -1);
-  zzdef_(zinc, Zgauss0, "zero divisors during gaussian elimination", -1);
-  zzdef_(zinc, Zmultiridge, "ridges with multiple neighbors", -1);
-}
-void qh_allstatB(qhT *qh) {
-  zzdef_(zdoc, Zdoc1, "summary information", -1);
-  zdef_(zinc, Zvertices, "number of vertices in output", -1);
-  zdef_(zinc, Znumfacets, "number of facets in output", -1);
-  zdef_(zinc, Znonsimplicial, "number of non-simplicial facets in output", -1);
-  zdef_(zinc, Znowsimplicial, "number of simplicial facets that were merged", -1);
-  zdef_(zinc, Znumridges, "number of ridges in output", -1);
-  zdef_(zadd, Znumridges, "average number of ridges per facet", Znumfacets);
-  zdef_(zmax, Zmaxridges, "maximum number of ridges", -1);
-  zdef_(zadd, Znumneighbors, "average number of neighbors per facet", Znumfacets);
-  zdef_(zmax, Zmaxneighbors, "maximum number of neighbors", -1);
-  zdef_(zadd, Znumvertices, "average number of vertices per facet", Znumfacets);
-  zdef_(zmax, Zmaxvertices, "maximum number of vertices", -1);
-  zdef_(zadd, Znumvneighbors, "average number of neighbors per vertex", Zvertices);
-  zdef_(zmax, Zmaxvneighbors, "maximum number of neighbors", -1);
-  zdef_(wadd, Wcpu, "cpu seconds for qhull after input", -1);
-  zdef_(zinc, Ztotvertices, "vertices created altogether", -1);
-  zzdef_(zinc, Zsetplane, "facets created altogether", -1);
-  zdef_(zinc, Ztotridges, "ridges created altogether", -1);
-  zdef_(zinc, Zpostfacets, "facets before post merge", -1);
-  zdef_(zadd, Znummergetot, "average merges per facet(at most 511)", Znumfacets);
-  zdef_(zmax, Znummergemax, "  maximum merges for a facet(at most 511)", -1);
-  zdef_(zinc, Zangle, NULL, -1);
-  zdef_(wadd, Wangle, "average angle(cosine) of facet normals for all ridges", Zangle);
-  zdef_(wmax, Wanglemax, "  maximum angle(cosine) of facet normals across a ridge", -1);
-  zdef_(wmin, Wanglemin, "  minimum angle(cosine) of facet normals across a ridge", -1);
-  zdef_(wadd, Wareatot, "total area of facets", -1);
-  zdef_(wmax, Wareamax, "  maximum facet area", -1);
-  zdef_(wmin, Wareamin, "  minimum facet area", -1);
-}
-void qh_allstatC(qhT *qh) {
-  zdef_(zdoc, Zdoc9, "build hull statistics", -1);
-  zzdef_(zinc, Zprocessed, "points processed", -1);
-  zzdef_(zinc, Zretry, "retries due to precision problems", -1);
-  zdef_(wmax, Wretrymax, "  max. random joggle", -1);
-  zdef_(zmax, Zmaxvertex, "max. vertices at any one time", -1);
-  zdef_(zinc, Ztotvisible, "ave. visible facets per iteration", Zprocessed);
-  zdef_(zinc, Zinsidevisible, "  ave. visible facets without an horizon neighbor", Zprocessed);
-  zdef_(zadd, Zvisfacettot,  "  ave. facets deleted per iteration", Zprocessed);
-  zdef_(zmax, Zvisfacetmax,  "    maximum", -1);
-  zdef_(zadd, Zvisvertextot, "ave. visible vertices per iteration", Zprocessed);
-  zdef_(zmax, Zvisvertexmax, "    maximum", -1);
-  zdef_(zinc, Ztothorizon, "ave. horizon facets per iteration", Zprocessed);
-  zdef_(zadd, Znewfacettot,  "ave. new or merged facets per iteration", Zprocessed);
-  zdef_(zmax, Znewfacetmax,  "    maximum(includes initial simplex)", -1);
-  zdef_(wadd, Wnewbalance, "average new facet balance", Zprocessed);
-  zdef_(wadd, Wnewbalance2, "  standard deviation", -1);
-  zdef_(wadd, Wpbalance, "average partition balance", Zpbalance);
-  zdef_(wadd, Wpbalance2, "  standard deviation", -1);
-  zdef_(zinc, Zpbalance, "  number of trials", -1);
-  zdef_(zinc, Zsearchpoints, "searches of all points for initial simplex", -1);
-  zdef_(zinc, Zdetsimplex, "determinants computed(area & initial hull)", -1);
-  zdef_(zinc, Znoarea, "determinants not computed because vertex too low", -1);
-  zdef_(zinc, Znotmax, "points ignored(!above max_outside)", -1);
-  zdef_(zinc, Znotgood, "points ignored(!above a good facet)", -1);
-  zdef_(zinc, Znotgoodnew, "points ignored(didn't create a good new facet)", -1);
-  zdef_(zinc, Zgoodfacet, "good facets found", -1);
-  zzdef_(zinc, Znumvisibility, "distance tests for facet visibility", -1);
-  zdef_(zinc, Zdistvertex, "distance tests to report minimum vertex", -1);
-  zzdef_(zinc, Ztotcheck, "points checked for facets' outer planes", -1);
-  zzdef_(zinc, Zcheckpart, "  ave. distance tests per check", Ztotcheck);
-}
-void qh_allstatD(qhT *qh) {
-  zdef_(zinc, Zvisit, "resets of visit_id", -1);
-  zdef_(zinc, Zvvisit, "  resets of vertex_visit", -1);
-  zdef_(zmax, Zvisit2max, "  max visit_id/2", -1);
-  zdef_(zmax, Zvvisit2max, "  max vertex_visit/2", -1);
-
-  zdef_(zdoc, Zdoc4, "partitioning statistics(see previous for outer planes)", -1);
-  zzdef_(zadd, Zdelvertextot, "total vertices deleted", -1);
-  zdef_(zmax, Zdelvertexmax, "    maximum vertices deleted per iteration", -1);
-  zdef_(zinc, Zfindbest, "calls to findbest", -1);
-  zdef_(zadd, Zfindbesttot, " ave. facets tested", Zfindbest);
-  zdef_(zmax, Zfindbestmax, " max. facets tested", -1);
-  zdef_(zadd, Zfindcoplanar, " ave. coplanar search", Zfindbest);
-  zdef_(zinc, Zfindnew, "calls to findbestnew", -1);
-  zdef_(zadd, Zfindnewtot, " ave. facets tested", Zfindnew);
-  zdef_(zmax, Zfindnewmax, " max. facets tested", -1);
-  zdef_(zinc, Zfindnewjump, " ave. clearly better", Zfindnew);
-  zdef_(zinc, Zfindnewsharp, " calls due to qh_sharpnewfacets", -1);
-  zdef_(zinc, Zfindhorizon, "calls to findhorizon", -1);
-  zdef_(zadd, Zfindhorizontot, " ave. facets tested", Zfindhorizon);
-  zdef_(zmax, Zfindhorizonmax, " max. facets tested", -1);
-  zdef_(zinc, Zfindjump,       " ave. clearly better", Zfindhorizon);
-  zdef_(zinc, Zparthorizon, " horizon facets better than bestfacet", -1);
-  zdef_(zinc, Zpartangle, "angle tests for repartitioned coplanar points", -1);
-  zdef_(zinc, Zpartflip, "  repartitioned coplanar points for flipped orientation", -1);
-}
-void qh_allstatE(qhT *qh) {
-  zdef_(zinc, Zpartinside, "inside points", -1);
-  zdef_(zinc, Zpartnear, "  inside points kept with a facet", -1);
-  zdef_(zinc, Zcoplanarinside, "  inside points that were coplanar with a facet", -1);
-  zdef_(zinc, Zbestlower, "calls to findbestlower", -1);
-  zdef_(zinc, Zbestlowerv, "  with search of vertex neighbors", -1);
-  zdef_(zinc, Zbestlowerall, "  with rare search of all facets", -1);
-  zdef_(zmax, Zbestloweralln, "  facets per search of all facets", -1);
-  zdef_(wadd, Wmaxout, "difference in max_outside at final check", -1);
-  zzdef_(zinc, Zpartitionall, "distance tests for initial partition", -1);
-  zdef_(zinc, Ztotpartition, "partitions of a point", -1);
-  zzdef_(zinc, Zpartition, "distance tests for partitioning", -1);
-  zzdef_(zinc, Zdistcheck, "distance tests for checking flipped facets", -1);
-  zzdef_(zinc, Zdistconvex, "distance tests for checking convexity", -1);
-  zdef_(zinc, Zdistgood, "distance tests for checking good point", -1);
-  zdef_(zinc, Zdistio, "distance tests for output", -1);
-  zdef_(zinc, Zdiststat, "distance tests for statistics", -1);
-  zdef_(zinc, Zdistplane, "total number of distance tests", -1);
-  zdef_(zinc, Ztotpartcoplanar, "partitions of coplanar points or deleted vertices", -1);
-  zzdef_(zinc, Zpartcoplanar, "   distance tests for these partitions", -1);
-  zdef_(zinc, Zcomputefurthest, "distance tests for computing furthest", -1);
-}
-void qh_allstatE2(qhT *qh) {
-  zdef_(zdoc, Zdoc5, "statistics for matching ridges", -1);
-  zdef_(zinc, Zhashlookup, "total lookups for matching ridges of new facets", -1);
-  zdef_(zinc, Zhashtests, "average number of tests to match a ridge", Zhashlookup);
-  zdef_(zinc, Zhashridge, "total lookups of subridges(duplicates and boundary)", -1);
-  zdef_(zinc, Zhashridgetest, "average number of tests per subridge", Zhashridge);
-  zdef_(zinc, Zdupsame, "duplicated ridges in same merge cycle", -1);
-  zdef_(zinc, Zdupflip, "duplicated ridges with flipped facets", -1);
-
-  zdef_(zdoc, Zdoc6, "statistics for determining merges", -1);
-  zdef_(zinc, Zangletests, "angles computed for ridge convexity", -1);
-  zdef_(zinc, Zbestcentrum, "best merges used centrum instead of vertices",-1);
-  zzdef_(zinc, Zbestdist, "distance tests for best merge", -1);
-  zzdef_(zinc, Zcentrumtests, "distance tests for centrum convexity", -1);
-  zzdef_(zinc, Zdistzero, "distance tests for checking simplicial convexity", -1);
-  zdef_(zinc, Zcoplanarangle, "coplanar angles in getmergeset", -1);
-  zdef_(zinc, Zcoplanarcentrum, "coplanar centrums in getmergeset", -1);
-  zdef_(zinc, Zconcaveridge, "concave ridges in getmergeset", -1);
-}
-void qh_allstatF(qhT *qh) {
-  zdef_(zdoc, Zdoc7, "statistics for merging", -1);
-  zdef_(zinc, Zpremergetot, "merge iterations", -1);
-  zdef_(zadd, Zmergeinittot, "ave. initial non-convex ridges per iteration", Zpremergetot);
-  zdef_(zadd, Zmergeinitmax, "  maximum", -1);
-  zdef_(zadd, Zmergesettot, "  ave. additional non-convex ridges per iteration", Zpremergetot);
-  zdef_(zadd, Zmergesetmax, "  maximum additional in one pass", -1);
-  zdef_(zadd, Zmergeinittot2, "initial non-convex ridges for post merging", -1);
-  zdef_(zadd, Zmergesettot2, "  additional non-convex ridges", -1);
-  zdef_(wmax, Wmaxoutside, "max distance of vertex or coplanar point above facet(w/roundoff)", -1);
-  zdef_(wmin, Wminvertex, "max distance of merged vertex below facet(or roundoff)", -1);
-  zdef_(zinc, Zwidefacet, "centrums frozen due to a wide merge", -1);
-  zdef_(zinc, Zwidevertices, "centrums frozen due to extra vertices", -1);
-  zzdef_(zinc, Ztotmerge, "total number of facets or cycles of facets merged", -1);
-  zdef_(zinc, Zmergesimplex, "merged a simplex", -1);
-  zdef_(zinc, Zonehorizon, "simplices merged into coplanar horizon", -1);
-  zzdef_(zinc, Zcyclehorizon, "cycles of facets merged into coplanar horizon", -1);
-  zzdef_(zadd, Zcyclefacettot, "  ave. facets per cycle", Zcyclehorizon);
-  zdef_(zmax, Zcyclefacetmax, "  max. facets", -1);
-  zdef_(zinc, Zmergeintohorizon, "new facets merged into horizon", -1);
-  zdef_(zinc, Zmergenew, "new facets merged", -1);
-  zdef_(zinc, Zmergehorizon, "horizon facets merged into new facets", -1);
-  zdef_(zinc, Zmergevertex, "vertices deleted by merging", -1);
-  zdef_(zinc, Zcyclevertex, "vertices deleted by merging into coplanar horizon", -1);
-  zdef_(zinc, Zdegenvertex, "vertices deleted by degenerate facet", -1);
-  zdef_(zinc, Zmergeflipdup, "merges due to flipped facets in duplicated ridge", -1);
-  zdef_(zinc, Zneighbor, "merges due to redundant neighbors", -1);
-  zdef_(zadd, Ztestvneighbor, "non-convex vertex neighbors", -1);
-}
-void qh_allstatG(qhT *qh) {
-  zdef_(zinc, Zacoplanar, "merges due to angle coplanar facets", -1);
-  zdef_(wadd, Wacoplanartot, "  average merge distance", Zacoplanar);
-  zdef_(wmax, Wacoplanarmax, "  maximum merge distance", -1);
-  zdef_(zinc, Zcoplanar, "merges due to coplanar facets", -1);
-  zdef_(wadd, Wcoplanartot, "  average merge distance", Zcoplanar);
-  zdef_(wmax, Wcoplanarmax, "  maximum merge distance", -1);
-  zdef_(zinc, Zconcave, "merges due to concave facets", -1);
-  zdef_(wadd, Wconcavetot, "  average merge distance", Zconcave);
-  zdef_(wmax, Wconcavemax, "  maximum merge distance", -1);
-  zdef_(zinc, Zavoidold, "coplanar/concave merges due to avoiding old merge", -1);
-  zdef_(wadd, Wavoidoldtot, "  average merge distance", Zavoidold);
-  zdef_(wmax, Wavoidoldmax, "  maximum merge distance", -1);
-  zdef_(zinc, Zdegen, "merges due to degenerate facets", -1);
-  zdef_(wadd, Wdegentot, "  average merge distance", Zdegen);
-  zdef_(wmax, Wdegenmax, "  maximum merge distance", -1);
-  zdef_(zinc, Zflipped, "merges due to removing flipped facets", -1);
-  zdef_(wadd, Wflippedtot, "  average merge distance", Zflipped);
-  zdef_(wmax, Wflippedmax, "  maximum merge distance", -1);
-  zdef_(zinc, Zduplicate, "merges due to duplicated ridges", -1);
-  zdef_(wadd, Wduplicatetot, "  average merge distance", Zduplicate);
-  zdef_(wmax, Wduplicatemax, "  maximum merge distance", -1);
-}
-void qh_allstatH(qhT *qh) {
-  zdef_(zdoc, Zdoc8, "renamed vertex statistics", -1);
-  zdef_(zinc, Zrenameshare, "renamed vertices shared by two facets", -1);
-  zdef_(zinc, Zrenamepinch, "renamed vertices in a pinched facet", -1);
-  zdef_(zinc, Zrenameall, "renamed vertices shared by multiple facets", -1);
-  zdef_(zinc, Zfindfail, "rename failures due to duplicated ridges", -1);
-  zdef_(zinc, Zdupridge, "  duplicate ridges detected", -1);
-  zdef_(zinc, Zdelridge, "deleted ridges due to renamed vertices", -1);
-  zdef_(zinc, Zdropneighbor, "dropped neighbors due to renamed vertices", -1);
-  zdef_(zinc, Zdropdegen, "degenerate facets due to dropped neighbors", -1);
-  zdef_(zinc, Zdelfacetdup, "  facets deleted because of no neighbors", -1);
-  zdef_(zinc, Zremvertex, "vertices removed from facets due to no ridges", -1);
-  zdef_(zinc, Zremvertexdel, "  deleted", -1);
-  zdef_(zinc, Zintersectnum, "vertex intersections for locating redundant vertices", -1);
-  zdef_(zinc, Zintersectfail, "intersections failed to find a redundant vertex", -1);
-  zdef_(zinc, Zintersect, "intersections found redundant vertices", -1);
-  zdef_(zadd, Zintersecttot, "   ave. number found per vertex", Zintersect);
-  zdef_(zmax, Zintersectmax, "   max. found for a vertex", -1);
-  zdef_(zinc, Zvertexridge, NULL, -1);
-  zdef_(zadd, Zvertexridgetot, "  ave. number of ridges per tested vertex", Zvertexridge);
-  zdef_(zmax, Zvertexridgemax, "  max. number of ridges per tested vertex", -1);
-
-  zdef_(zdoc, Zdoc10, "memory usage statistics(in bytes)", -1);
-  zdef_(zadd, Zmemfacets, "for facets and their normals, neighbor and vertex sets", -1);
-  zdef_(zadd, Zmemvertices, "for vertices and their neighbor sets", -1);
-  zdef_(zadd, Zmempoints, "for input points, outside and coplanar sets, and qhT",-1);
-  zdef_(zadd, Zmemridges, "for ridges and their vertex sets", -1);
-} /* allstat */
-
-void qh_allstatI(qhT *qh) {
-  qh->qhstat.vridges= qh->qhstat.next;
-  zzdef_(zdoc, Zdoc11, "Voronoi ridge statistics", -1);
-  zzdef_(zinc, Zridge, "non-simplicial Voronoi vertices for all ridges", -1);
-  zzdef_(wadd, Wridge, "  ave. distance to ridge", Zridge);
-  zzdef_(wmax, Wridgemax, "  max. distance to ridge", -1);
-  zzdef_(zinc, Zridgemid, "bounded ridges", -1);
-  zzdef_(wadd, Wridgemid, "  ave. distance of midpoint to ridge", Zridgemid);
-  zzdef_(wmax, Wridgemidmax, "  max. distance of midpoint to ridge", -1);
-  zzdef_(zinc, Zridgeok, "bounded ridges with ok normal", -1);
-  zzdef_(wadd, Wridgeok, "  ave. angle to ridge", Zridgeok);
-  zzdef_(wmax, Wridgeokmax, "  max. angle to ridge", -1);
-  zzdef_(zinc, Zridge0, "bounded ridges with near-zero normal", -1);
-  zzdef_(wadd, Wridge0, "  ave. angle to ridge", Zridge0);
-  zzdef_(wmax, Wridge0max, "  max. angle to ridge", -1);
-
-  zdef_(zdoc, Zdoc12, "Triangulation statistics(Qt)", -1);
-  zdef_(zinc, Ztricoplanar, "non-simplicial facets triangulated", -1);
-  zdef_(zadd, Ztricoplanartot, "  ave. new facets created(may be deleted)", Ztricoplanar);
-  zdef_(zmax, Ztricoplanarmax, "  max. new facets created", -1);
-  zdef_(zinc, Ztrinull, "null new facets deleted(duplicated vertex)", -1);
-  zdef_(zinc, Ztrimirror, "mirrored pairs of new facets deleted(same vertices)", -1);
-  zdef_(zinc, Ztridegen, "degenerate new facets in output(same ridge)", -1);
-} /* allstat */
-
-/*---------------------------------
-
-  qh_allstatistics()
-    reset printed flag for all statistics
-*/
-void qh_allstatistics(qhT *qh) {
-  int i;
-
-  for(i=ZEND; i--; )
-    qh->qhstat.printed[i]= False;
-} /* allstatistics */
-
-#if qh_KEEPstatistics
-/*---------------------------------
-
-  qh_collectstatistics()
-    collect statistics for qh.facet_list
-
-*/
-void qh_collectstatistics(qhT *qh) {
-  facetT *facet, *neighbor, **neighborp;
-  vertexT *vertex, **vertexp;
-  realT dotproduct, dist;
-  int sizneighbors, sizridges, sizvertices, i;
-
-  qh->old_randomdist= qh->RANDOMdist;
-  qh->RANDOMdist= False;
-  zval_(Zmempoints)= qh->num_points * qh->normal_size + sizeof(qhT);
-  zval_(Zmemfacets)= 0;
-  zval_(Zmemridges)= 0;
-  zval_(Zmemvertices)= 0;
-  zval_(Zangle)= 0;
-  wval_(Wangle)= 0.0;
-  zval_(Znumridges)= 0;
-  zval_(Znumfacets)= 0;
-  zval_(Znumneighbors)= 0;
-  zval_(Znumvertices)= 0;
-  zval_(Znumvneighbors)= 0;
-  zval_(Znummergetot)= 0;
-  zval_(Znummergemax)= 0;
-  zval_(Zvertices)= qh->num_vertices - qh_setsize(qh, qh->del_vertices);
-  if (qh->MERGING || qh->APPROXhull || qh->JOGGLEmax < REALmax/2)
-    wmax_(Wmaxoutside, qh->max_outside);
-  if (qh->MERGING)
-    wmin_(Wminvertex, qh->min_vertex);
-  FORALLfacets
-    facet->seen= False;
-  if (qh->DELAUNAY) {
-    FORALLfacets {
-      if (facet->upperdelaunay != qh->UPPERdelaunay)
-        facet->seen= True; /* remove from angle statistics */
-    }
-  }
-  FORALLfacets {
-    if (facet->visible && qh->NEWfacets)
-      continue;
-    sizvertices= qh_setsize(qh, facet->vertices);
-    sizneighbors= qh_setsize(qh, facet->neighbors);
-    sizridges= qh_setsize(qh, facet->ridges);
-    zinc_(Znumfacets);
-    zadd_(Znumvertices, sizvertices);
-    zmax_(Zmaxvertices, sizvertices);
-    zadd_(Znumneighbors, sizneighbors);
-    zmax_(Zmaxneighbors, sizneighbors);
-    zadd_(Znummergetot, facet->nummerge);
-    i= facet->nummerge; /* avoid warnings */
-    zmax_(Znummergemax, i);
-    if (!facet->simplicial) {
-      if (sizvertices == qh->hull_dim) {
-        zinc_(Znowsimplicial);
-      }else {
-        zinc_(Znonsimplicial);
-      }
-    }
-    if (sizridges) {
-      zadd_(Znumridges, sizridges);
-      zmax_(Zmaxridges, sizridges);
-    }
-    zadd_(Zmemfacets, sizeof(facetT) + qh->normal_size + 2*sizeof(setT)
-       + SETelemsize * (sizneighbors + sizvertices));
-    if (facet->ridges) {
-      zadd_(Zmemridges,
-         sizeof(setT) + SETelemsize * sizridges + sizridges *
-         (sizeof(ridgeT) + sizeof(setT) + SETelemsize * (qh->hull_dim-1))/2);
-    }
-    if (facet->outsideset)
-      zadd_(Zmempoints, sizeof(setT) + SETelemsize * qh_setsize(qh, facet->outsideset));
-    if (facet->coplanarset)
-      zadd_(Zmempoints, sizeof(setT) + SETelemsize * qh_setsize(qh, facet->coplanarset));
-    if (facet->seen) /* Delaunay upper envelope */
-      continue;
-    facet->seen= True;
-    FOREACHneighbor_(facet) {
-      if (neighbor == qh_DUPLICATEridge || neighbor == qh_MERGEridge
-          || neighbor->seen || !facet->normal || !neighbor->normal)
-        continue;
-      dotproduct= qh_getangle(qh, facet->normal, neighbor->normal);
-      zinc_(Zangle);
-      wadd_(Wangle, dotproduct);
-      wmax_(Wanglemax, dotproduct)
-      wmin_(Wanglemin, dotproduct)
-    }
-    if (facet->normal) {
-      FOREACHvertex_(facet->vertices) {
-        zinc_(Zdiststat);
-        qh_distplane(qh, vertex->point, facet, &dist);
-        wmax_(Wvertexmax, dist);
-        wmin_(Wvertexmin, dist);
-      }
-    }
-  }
-  FORALLvertices {
-    if (vertex->deleted)
-      continue;
-    zadd_(Zmemvertices, sizeof(vertexT));
-    if (vertex->neighbors) {
-      sizneighbors= qh_setsize(qh, vertex->neighbors);
-      zadd_(Znumvneighbors, sizneighbors);
-      zmax_(Zmaxvneighbors, sizneighbors);
-      zadd_(Zmemvertices, sizeof(vertexT) + SETelemsize * sizneighbors);
-    }
-  }
-  qh->RANDOMdist= qh->old_randomdist;
-} /* collectstatistics */
-#endif /* qh_KEEPstatistics */
-
-/*---------------------------------
-
-  qh_initstatistics(qh)
-    initialize statistics
-
-  notes:
-  NOerrors -- qh_initstatistics can not use qh_errexit(), qh_fprintf, or qh.ferr
-  On first call, only qhmem.ferr is defined.  qh_memalloc is not setup.
-  Also invoked by QhullQh().
-*/
-void qh_initstatistics(qhT *qh) {
-  int i;
-  realT realx;
-  int intx;
-
-  qh->qhstat.next= 0;
-  qh_allstatA(qh);
-  qh_allstatB(qh);
-  qh_allstatC(qh);
-  qh_allstatD(qh);
-  qh_allstatE(qh);
-  qh_allstatE2(qh);
-  qh_allstatF(qh);
-  qh_allstatG(qh);
-  qh_allstatH(qh);
-  qh_allstatI(qh);
-  if (qh->qhstat.next > (int)sizeof(qh->qhstat.id)) {
-    qh_fprintf(qh, qh->qhmem.ferr, 6184, "qhull error (qh_initstatistics): increase size of qhstat.id[].\n\
-      qhstat.next %d should be <= sizeof(qh->qhstat.id) %d\n", qh->qhstat.next, (int)sizeof(qh->qhstat.id));
-#if 0 /* for locating error, Znumridges should be duplicated */
-    for(i=0; i < ZEND; i++) {
-      int j;
-      for(j=i+1; j < ZEND; j++) {
-        if (qh->qhstat.id[i] == qh->qhstat.id[j]) {
-          qh_fprintf(qh, qh->qhmem.ferr, 6185, "qhull error (qh_initstatistics): duplicated statistic %d at indices %d and %d\n",
-              qh->qhstat.id[i], i, j);
-        }
-      }
-    }
-#endif
-    qh_exit(qh_ERRqhull);  /* can not use qh_errexit() */
-  }
-  qh->qhstat.init[zinc].i= 0;
-  qh->qhstat.init[zadd].i= 0;
-  qh->qhstat.init[zmin].i= INT_MAX;
-  qh->qhstat.init[zmax].i= INT_MIN;
-  qh->qhstat.init[wadd].r= 0;
-  qh->qhstat.init[wmin].r= REALmax;
-  qh->qhstat.init[wmax].r= -REALmax;
-  for(i=0; i < ZEND; i++) {
-    if (qh->qhstat.type[i] > ZTYPEreal) {
-      realx= qh->qhstat.init[(unsigned char)(qh->qhstat.type[i])].r;
-      qh->qhstat.stats[i].r= realx;
-    }else if (qh->qhstat.type[i] != zdoc) {
-      intx= qh->qhstat.init[(unsigned char)(qh->qhstat.type[i])].i;
-      qh->qhstat.stats[i].i= intx;
-    }
-  }
-} /* initstatistics */
-
-/*---------------------------------
-
-  qh_newstats(qh, )
-    returns True if statistics for zdoc
-
-  returns:
-    next zdoc
-*/
-boolT qh_newstats(qhT *qh, int idx, int *nextindex) {
-  boolT isnew= False;
-  int start, i;
-
-  if (qh->qhstat.type[qh->qhstat.id[idx]] == zdoc)
-    start= idx+1;
-  else
-    start= idx;
-  for(i= start; i < qh->qhstat.next && qh->qhstat.type[qh->qhstat.id[i]] != zdoc; i++) {
-    if (!qh_nostatistic(qh, qh->qhstat.id[i]) && !qh->qhstat.printed[qh->qhstat.id[i]])
-        isnew= True;
-  }
-  *nextindex= i;
-  return isnew;
-} /* newstats */
-
-/*---------------------------------
-
-  qh_nostatistic(qh, index )
-    true if no statistic to print
-*/
-boolT qh_nostatistic(qhT *qh, int i) {
-
-  if ((qh->qhstat.type[i] > ZTYPEreal
-       &&qh->qhstat.stats[i].r == qh->qhstat.init[(unsigned char)(qh->qhstat.type[i])].r)
-      || (qh->qhstat.type[i] < ZTYPEreal
-          &&qh->qhstat.stats[i].i == qh->qhstat.init[(unsigned char)(qh->qhstat.type[i])].i))
-    return True;
-  return False;
-} /* nostatistic */
-
-#if qh_KEEPstatistics
-/*---------------------------------
-
-  qh_printallstatistics(qh, fp, string )
-    print all statistics with header 'string'
-*/
-void qh_printallstatistics(qhT *qh, FILE *fp, const char *string) {
-
-  qh_allstatistics(qh);
-  qh_collectstatistics(qh);
-  qh_printstatistics(qh, fp, string);
-  qh_memstatistics(qh, fp);
-}
-
-
-/*---------------------------------
-
-  qh_printstatistics(qh, fp, string )
-    print statistics to a file with header 'string'
-    skips statistics with qhstat.printed[] (reset with qh_allstatistics)
-
-  see:
-    qh_printallstatistics()
-*/
-void qh_printstatistics(qhT *qh, FILE *fp, const char *string) {
-  int i, k;
-  realT ave;
-
-  if (qh->num_points != qh->num_vertices) {
-    wval_(Wpbalance)= 0;
-    wval_(Wpbalance2)= 0;
-  }else
-    wval_(Wpbalance2)= qh_stddev(zval_(Zpbalance), wval_(Wpbalance),
-                                 wval_(Wpbalance2), &ave);
-  wval_(Wnewbalance2)= qh_stddev(zval_(Zprocessed), wval_(Wnewbalance),
-                                 wval_(Wnewbalance2), &ave);
-  qh_fprintf(qh, fp, 9350, "\n\
-%s\n\
- qhull invoked by: %s | %s\n%s with options:\n%s\n", string, qh->rbox_command,
-     qh->qhull_command, qh_version, qh->qhull_options);
-  qh_fprintf(qh, fp, 9351, "\nprecision constants:\n\
- %6.2g max. abs. coordinate in the (transformed) input('Qbd:n')\n\
- %6.2g max. roundoff error for distance computation('En')\n\
- %6.2g max. roundoff error for angle computations\n\
- %6.2g min. distance for outside points ('Wn')\n\
- %6.2g min. distance for visible facets ('Vn')\n\
- %6.2g max. distance for coplanar facets ('Un')\n\
- %6.2g max. facet width for recomputing centrum and area\n\
-",
-  qh->MAXabs_coord, qh->DISTround, qh->ANGLEround, qh->MINoutside,
-        qh->MINvisible, qh->MAXcoplanar, qh->WIDEfacet);
-  if (qh->KEEPnearinside)
-    qh_fprintf(qh, fp, 9352, "\
- %6.2g max. distance for near-inside points\n", qh->NEARinside);
-  if (qh->premerge_cos < REALmax/2) qh_fprintf(qh, fp, 9353, "\
- %6.2g max. cosine for pre-merge angle\n", qh->premerge_cos);
-  if (qh->PREmerge) qh_fprintf(qh, fp, 9354, "\
- %6.2g radius of pre-merge centrum\n", qh->premerge_centrum);
-  if (qh->postmerge_cos < REALmax/2) qh_fprintf(qh, fp, 9355, "\
- %6.2g max. cosine for post-merge angle\n", qh->postmerge_cos);
-  if (qh->POSTmerge) qh_fprintf(qh, fp, 9356, "\
- %6.2g radius of post-merge centrum\n", qh->postmerge_centrum);
-  qh_fprintf(qh, fp, 9357, "\
- %6.2g max. distance for merging two simplicial facets\n\
- %6.2g max. roundoff error for arithmetic operations\n\
- %6.2g min. denominator for divisions\n\
-  zero diagonal for Gauss: ", qh->ONEmerge, REALepsilon, qh->MINdenom);
-  for(k=0; k < qh->hull_dim; k++)
-    qh_fprintf(qh, fp, 9358, "%6.2e ", qh->NEARzero[k]);
-  qh_fprintf(qh, fp, 9359, "\n\n");
-  for(i=0 ; i < qh->qhstat.next; )
-    qh_printstats(qh, fp, i, &i);
-} /* printstatistics */
-#endif /* qh_KEEPstatistics */
-
-/*---------------------------------
-
-  qh_printstatlevel(qh, fp, id )
-    print level information for a statistic
-
-  notes:
-    nop if id >= ZEND, printed, or same as initial value
-*/
-void qh_printstatlevel(qhT *qh, FILE *fp, int id) {
-#define NULLfield "       "
-
-  if (id >= ZEND || qh->qhstat.printed[id])
-    return;
-  if (qh->qhstat.type[id] == zdoc) {
-    qh_fprintf(qh, fp, 9360, "%s\n", qh->qhstat.doc[id]);
-    return;
-  }
-  if (qh_nostatistic(qh, id) || !qh->qhstat.doc[id])
-    return;
-  qh->qhstat.printed[id]= True;
-  if (qh->qhstat.count[id] != -1
-      && qh->qhstat.stats[(unsigned char)(qh->qhstat.count[id])].i == 0)
-    qh_fprintf(qh, fp, 9361, " *0 cnt*");
-  else if (qh->qhstat.type[id] >= ZTYPEreal && qh->qhstat.count[id] == -1)
-    qh_fprintf(qh, fp, 9362, "%7.2g", qh->qhstat.stats[id].r);
-  else if (qh->qhstat.type[id] >= ZTYPEreal && qh->qhstat.count[id] != -1)
-    qh_fprintf(qh, fp, 9363, "%7.2g", qh->qhstat.stats[id].r/ qh->qhstat.stats[(unsigned char)(qh->qhstat.count[id])].i);
-  else if (qh->qhstat.type[id] < ZTYPEreal && qh->qhstat.count[id] == -1)
-    qh_fprintf(qh, fp, 9364, "%7d", qh->qhstat.stats[id].i);
-  else if (qh->qhstat.type[id] < ZTYPEreal && qh->qhstat.count[id] != -1)
-    qh_fprintf(qh, fp, 9365, "%7.3g", (realT) qh->qhstat.stats[id].i / qh->qhstat.stats[(unsigned char)(qh->qhstat.count[id])].i);
-  qh_fprintf(qh, fp, 9366, " %s\n", qh->qhstat.doc[id]);
-} /* printstatlevel */
-
-
-/*---------------------------------
-
-  qh_printstats(qh, fp, index, nextindex )
-    print statistics for a zdoc group
-
-  returns:
-    next zdoc if non-null
-*/
-void qh_printstats(qhT *qh, FILE *fp, int idx, int *nextindex) {
-  int j, nexti;
-
-  if (qh_newstats(qh, idx, &nexti)) {
-    qh_fprintf(qh, fp, 9367, "\n");
-    for (j=idx; jqhstat.id[j]);
-  }
-  if (nextindex)
-    *nextindex= nexti;
-} /* printstats */
-
-#if qh_KEEPstatistics
-
-/*---------------------------------
-
-  qh_stddev(num, tot, tot2, ave )
-    compute the standard deviation and average from statistics
-
-    tot2 is the sum of the squares
-  notes:
-    computes r.m.s.:
-      (x-ave)^2
-      == x^2 - 2x tot/num +   (tot/num)^2
-      == tot2 - 2 tot tot/num + tot tot/num
-      == tot2 - tot ave
-*/
-realT qh_stddev(int num, realT tot, realT tot2, realT *ave) {
-  realT stddev;
-
-  *ave= tot/num;
-  stddev= sqrt(tot2/num - *ave * *ave);
-  return stddev;
-} /* stddev */
-
-#endif /* qh_KEEPstatistics */
-
-#if !qh_KEEPstatistics
-void    qh_collectstatistics(qhT *qh) {}
-void    qh_printallstatistics(qhT *qh, FILE *fp, char *string) {};
-void    qh_printstatistics(qhT *qh, FILE *fp, char *string) {}
-#endif
-
diff --git a/C/user_r.c b/C/user_r.c
deleted file mode 100644
--- a/C/user_r.c
+++ /dev/null
@@ -1,527 +0,0 @@
-/*
  ---------------------------------
-
-   user.c
-   user redefinable functions
-
-   see user2_r.c for qh_fprintf, qh_malloc, qh_free
-
-   see README.txt  see COPYING.txt for copyright information.
-
-   see libqhull_r.h for data structures, macros, and user-callable functions.
-
-   see user_eg.c, user_eg2.c, and unix.c for examples.
-
-   see user.h for user-definable constants
-
-      use qh_NOmem in mem_r.h to turn off memory management
-      use qh_NOmerge in user.h to turn off facet merging
-      set qh_KEEPstatistics in user.h to 0 to turn off statistics
-
-   This is unsupported software.  You're welcome to make changes,
-   but you're on your own if something goes wrong.  Use 'Tc' to
-   check frequently.  Usually qhull will report an error if
-   a data structure becomes inconsistent.  If so, it also reports
-   the last point added to the hull, e.g., 102.  You can then trace
-   the execution of qhull with "T4P102".
-
-   Please report any errors that you fix to qhull@qhull.org
-
-   Qhull-template is a template for calling qhull from within your application
-
-   if you recompile and load this module, then user.o will not be loaded
-   from qhull.a
-
-   you can add additional quick allocation sizes in qh_user_memsizes
-
-   if the other functions here are redefined to not use qh_print...,
-   then io.o will not be loaded from qhull.a.  See user_eg_r.c for an
-   example.  We recommend keeping io.o for the extra debugging
-   information it supplies.
-*/
-
-#include "qhull_ra.h"
-
-#include 
-
-/*---------------------------------
-
-  Qhull-template
-    Template for calling qhull from inside your program
-
-  returns:
-    exit code(see qh_ERR... in libqhull_r.h)
-    all memory freed
-
-  notes:
-    This can be called any number of times.
-
-*/
-#if 0
-{
-  int dim;                  /* dimension of points */
-  int numpoints;            /* number of points */
-  coordT *points;           /* array of coordinates for each point */
-  boolT ismalloc;           /* True if qhull should free points in qh_freeqhull() or reallocation */
-  char flags[]= "qhull Tv"; /* option flags for qhull, see qh_opt.htm */
-  FILE *outfile= stdout;    /* output from qh_produce_output(qh)
-                               use NULL to skip qh_produce_output(qh) */
-  FILE *errfile= stderr;    /* error messages from qhull code */
-  int exitcode;             /* 0 if no error from qhull */
-  facetT *facet;            /* set by FORALLfacets */
-  int curlong, totlong;     /* memory remaining after qh_memfreeshort */
-
-  qhT qh_qh;                /* Qhull's data structure.  First argument of most calls */
-  qhT *qh= &qh_qh;          /* Alternatively -- qhT *qh= (qhT*)malloc(sizeof(qhT)) */
-
-  QHULL_LIB_CHECK /* Check for compatible library */
-
-  qh_zero(qh, errfile);
-
-  /* initialize dim, numpoints, points[], ismalloc here */
-  exitcode= qh_new_qhull(qh, dim, numpoints, points, ismalloc,
-                      flags, outfile, errfile);
-  if (!exitcode) {                  /* if no error */
-    /* 'qh->facet_list' contains the convex hull */
-    FORALLfacets {
-       /* ... your code ... */
-    }
-  }
-  qh_freeqhull(qh, !qh_ALL);
-  qh_memfreeshort(qh, &curlong, &totlong);
-  if (curlong || totlong)
-    qh_fprintf(qh, errfile, 7068, "qhull internal warning (main): did not free %d bytes of long memory(%d pieces)\n", totlong, curlong);
-}
-#endif
-
-/*---------------------------------
-
-  qh_new_qhull(qh, dim, numpoints, points, ismalloc, qhull_cmd, outfile, errfile )
-    Run qhull and return results in qh.
-    Returns exitcode (0 if no errors).
-    Before first call, either call qh_zero(qh, errfile), or set qh to all zero.
-
-  notes:
-    do not modify points until finished with results.
-      The qhull data structure contains pointers into the points array.
-    do not call qhull functions before qh_new_qhull().
-      The qhull data structure is not initialized until qh_new_qhull().
-    do not call qh_init_A (global_r.c)
-
-    Default errfile is stderr, outfile may be null
-    qhull_cmd must start with "qhull "
-    projects points to a new point array for Delaunay triangulations ('d' and 'v')
-    transforms points into a new point array for halfspace intersection ('H')
-
-  see:
-    Qhull-template at the beginning of this file.
-    An example of using qh_new_qhull is user_eg_r.c
-*/
-int qh_new_qhull(qhT *qh, int dim, int numpoints, coordT *points, boolT ismalloc,
-                char *qhull_cmd, FILE *outfile, FILE *errfile) {
-  /* gcc may issue a "might be clobbered" warning for dim, points, and ismalloc [-Wclobbered].
-     These parameters are not referenced after a longjmp() and hence not clobbered.
-     See http://stackoverflow.com/questions/7721854/what-sense-do-these-clobbered-variable-warnings-make */
-  int exitcode, hulldim;
-  boolT new_ismalloc;
-  coordT *new_points;
-
-  if(!errfile){
-    errfile= stderr;
-  }
-  if (!qh->qhmem.ferr) {
-    qh_meminit(qh, errfile);
-  } else {
-    qh_memcheck(qh);
-  }
-  if (strncmp(qhull_cmd, "qhull ", (size_t)6)) {
-    qh_fprintf(qh, errfile, 6186, "qhull error (qh_new_qhull): start qhull_cmd argument with \"qhull \"\n");
-    return qh_ERRinput;
-  }
-  qh_initqhull_start(qh, NULL, outfile, errfile);
-  trace1((qh, qh->ferr, 1044, "qh_new_qhull: build new Qhull for %d %d-d points with %s\n", numpoints, dim, qhull_cmd));
-  exitcode = setjmp(qh->errexit);
-  if (!exitcode)
-  {
-    qh->NOerrexit = False;
-    qh_initflags(qh, qhull_cmd);
-    if (qh->DELAUNAY)
-      qh->PROJECTdelaunay= True;
-    if (qh->HALFspace) {
-      /* points is an array of halfspaces,
-         the last coordinate of each halfspace is its offset */
-      hulldim= dim-1;
-      qh_setfeasible(qh, hulldim);
-      new_points= qh_sethalfspace_all(qh, dim, numpoints, points, qh->feasible_point);
-      new_ismalloc= True;
-      if (ismalloc)
-        qh_free(points);
-    }else {
-      hulldim= dim;
-      new_points= points;
-      new_ismalloc= ismalloc;
-    }
-    qh_init_B(qh, new_points, numpoints, hulldim, new_ismalloc);
-    qh_qhull(qh);
-    qh_check_output(qh);
-    if (outfile) {
-      qh_produce_output(qh);
-    }else {
-      qh_prepare_output(qh);
-    }
-    if (qh->VERIFYoutput && !qh->STOPpoint && !qh->STOPcone)
-      qh_check_points(qh);
-  }
-  qh->NOerrexit = True;
-  return exitcode;
-} /* new_qhull */
-
-/*---------------------------------
-
-  qh_errexit(qh, exitcode, facet, ridge )
-    report and exit from an error
-    report facet and ridge if non-NULL
-    reports useful information such as last point processed
-    set qh.FORCEoutput to print neighborhood of facet
-
-  see:
-    qh_errexit2() in libqhull_r.c for printing 2 facets
-
-  design:
-    check for error within error processing
-    compute qh.hulltime
-    print facet and ridge (if any)
-    report commandString, options, qh.furthest_id
-    print summary and statistics (including precision statistics)
-    if qh_ERRsingular
-      print help text for singular data set
-    exit program via long jump (if defined) or exit()
-*/
-void qh_errexit(qhT *qh, int exitcode, facetT *facet, ridgeT *ridge) {
-
-  if (qh->ERREXITcalled) {
-    qh_fprintf(qh, qh->ferr, 8126, "\nqhull error while processing previous error.  Exit program\n");
-    qh_exit(qh_ERRqhull);
-  }
-  qh->ERREXITcalled= True;
-  if (!qh->QHULLfinished)
-    qh->hulltime= qh_CPUclock - qh->hulltime;
-  qh_errprint(qh, "ERRONEOUS", facet, NULL, ridge, NULL);
-  qh_fprintf(qh, qh->ferr, 8127, "\nWhile executing: %s | %s\n", qh->rbox_command, qh->qhull_command);
-  qh_fprintf(qh, qh->ferr, 8128, "Options selected for Qhull %s:\n%s\n", qh_version, qh->qhull_options);
-  if (qh->furthest_id >= 0) {
-    qh_fprintf(qh, qh->ferr, 8129, "Last point added to hull was p%d.", qh->furthest_id);
-    if (zzval_(Ztotmerge))
-      qh_fprintf(qh, qh->ferr, 8130, "  Last merge was #%d.", zzval_(Ztotmerge));
-    if (qh->QHULLfinished)
-      qh_fprintf(qh, qh->ferr, 8131, "\nQhull has finished constructing the hull.");
-    else if (qh->POSTmerging)
-      qh_fprintf(qh, qh->ferr, 8132, "\nQhull has started post-merging.");
-    qh_fprintf(qh, qh->ferr, 8133, "\n");
-  }
-  if (qh->FORCEoutput && (qh->QHULLfinished || (!facet && !ridge)))
-    qh_produce_output(qh);
-  else if (exitcode != qh_ERRinput) {
-    if (exitcode != qh_ERRsingular && zzval_(Zsetplane) > qh->hull_dim+1) {
-      qh_fprintf(qh, qh->ferr, 8134, "\nAt error exit:\n");
-      qh_printsummary(qh, qh->ferr);
-      if (qh->PRINTstatistics) {
-        qh_collectstatistics(qh);
-        qh_printstatistics(qh, qh->ferr, "at error exit");
-        qh_memstatistics(qh, qh->ferr);
-      }
-    }
-    if (qh->PRINTprecision)
-      qh_printstats(qh, qh->ferr, qh->qhstat.precision, NULL);
-  }
-  if (!exitcode)
-    exitcode= qh_ERRqhull;
-  else if (exitcode == qh_ERRsingular)
-    qh_printhelp_singular(qh, qh->ferr);
-  else if (exitcode == qh_ERRprec && !qh->PREmerge)
-    qh_printhelp_degenerate(qh, qh->ferr);
-  if (qh->NOerrexit) {
-    qh_fprintf(qh, qh->ferr, 6187, "qhull error while ending program, or qh->NOerrexit not cleared after setjmp(). Exit program with error.\n");
-    qh_exit(qh_ERRqhull);
-  }
-  qh->ERREXITcalled= False;
-  qh->NOerrexit= True;
-  qh->ALLOWrestart= False;  /* longjmp will undo qh_build_withrestart */
-  longjmp(qh->errexit, exitcode);
-} /* errexit */
-
-
-/*---------------------------------
-
-  qh_errprint(qh, fp, string, atfacet, otherfacet, atridge, atvertex )
-    prints out the information of facets and ridges to fp
-    also prints neighbors and geomview output
-
-  notes:
-    except for string, any parameter may be NULL
-*/
-void qh_errprint(qhT *qh, const char *string, facetT *atfacet, facetT *otherfacet, ridgeT *atridge, vertexT *atvertex) {
-  int i;
-
-  if (atfacet) {
-    qh_fprintf(qh, qh->ferr, 8135, "%s FACET:\n", string);
-    qh_printfacet(qh, qh->ferr, atfacet);
-  }
-  if (otherfacet) {
-    qh_fprintf(qh, qh->ferr, 8136, "%s OTHER FACET:\n", string);
-    qh_printfacet(qh, qh->ferr, otherfacet);
-  }
-  if (atridge) {
-    qh_fprintf(qh, qh->ferr, 8137, "%s RIDGE:\n", string);
-    qh_printridge(qh, qh->ferr, atridge);
-    if (atridge->top && atridge->top != atfacet && atridge->top != otherfacet)
-      qh_printfacet(qh, qh->ferr, atridge->top);
-    if (atridge->bottom
-        && atridge->bottom != atfacet && atridge->bottom != otherfacet)
-      qh_printfacet(qh, qh->ferr, atridge->bottom);
-    if (!atfacet)
-      atfacet= atridge->top;
-    if (!otherfacet)
-      otherfacet= otherfacet_(atridge, atfacet);
-  }
-  if (atvertex) {
-    qh_fprintf(qh, qh->ferr, 8138, "%s VERTEX:\n", string);
-    qh_printvertex(qh, qh->ferr, atvertex);
-  }
-  if (qh->fout && qh->FORCEoutput && atfacet && !qh->QHULLfinished && !qh->IStracing) {
-    qh_fprintf(qh, qh->ferr, 8139, "ERRONEOUS and NEIGHBORING FACETS to output\n");
-    for (i=0; i < qh_PRINTEND; i++)  /* use fout for geomview output */
-      qh_printneighborhood(qh, qh->fout, qh->PRINTout[i], atfacet, otherfacet,
-                            !qh_ALL);
-  }
-} /* errprint */
-
-
-/*---------------------------------
-
-  qh_printfacetlist(qh, fp, facetlist, facets, printall )
-    print all fields for a facet list and/or set of facets to fp
-    if !printall,
-      only prints good facets
-
-  notes:
-    also prints all vertices
-*/
-void qh_printfacetlist(qhT *qh, facetT *facetlist, setT *facets, boolT printall) {
-  facetT *facet, **facetp;
-
-  qh_printbegin(qh, qh->ferr, qh_PRINTfacets, facetlist, facets, printall);
-  FORALLfacet_(facetlist)
-    qh_printafacet(qh, qh->ferr, qh_PRINTfacets, facet, printall);
-  FOREACHfacet_(facets)
-    qh_printafacet(qh, qh->ferr, qh_PRINTfacets, facet, printall);
-  qh_printend(qh, qh->ferr, qh_PRINTfacets, facetlist, facets, printall);
-} /* printfacetlist */
-
-
-/*---------------------------------
-
-  qh_printhelp_degenerate(qh, fp )
-    prints descriptive message for precision error
-
-  notes:
-    no message if qh_QUICKhelp
-*/
-void qh_printhelp_degenerate(qhT *qh, FILE *fp) {
-
-  if (qh->MERGEexact || qh->PREmerge || qh->JOGGLEmax < REALmax/2)
-    qh_fprintf(qh, fp, 9368, "\n\
-A Qhull error has occurred.  Qhull should have corrected the above\n\
-precision error.  Please send the input and all of the output to\n\
-qhull_bug@qhull.org\n");
-  else if (!qh_QUICKhelp) {
-    qh_fprintf(qh, fp, 9369, "\n\
-Precision problems were detected during construction of the convex hull.\n\
-This occurs because convex hull algorithms assume that calculations are\n\
-exact, but floating-point arithmetic has roundoff errors.\n\
-\n\
-To correct for precision problems, do not use 'Q0'.  By default, Qhull\n\
-selects 'C-0' or 'Qx' and merges non-convex facets.  With option 'QJ',\n\
-Qhull joggles the input to prevent precision problems.  See \"Imprecision\n\
-in Qhull\" (qh-impre.htm).\n\
-\n\
-If you use 'Q0', the output may include\n\
-coplanar ridges, concave ridges, and flipped facets.  In 4-d and higher,\n\
-Qhull may produce a ridge with four neighbors or two facets with the same \n\
-vertices.  Qhull reports these events when they occur.  It stops when a\n\
-concave ridge, flipped facet, or duplicate facet occurs.\n");
-#if REALfloat
-    qh_fprintf(qh, fp, 9370, "\
-\n\
-Qhull is currently using single precision arithmetic.  The following\n\
-will probably remove the precision problems:\n\
-  - recompile qhull for realT precision(#define REALfloat 0 in user.h).\n");
-#endif
-    if (qh->DELAUNAY && !qh->SCALElast && qh->MAXabs_coord > 1e4)
-      qh_fprintf(qh, fp, 9371, "\
-\n\
-When computing the Delaunay triangulation of coordinates > 1.0,\n\
-  - use 'Qbb' to scale the last coordinate to [0,m] (max previous coordinate)\n");
-    if (qh->DELAUNAY && !qh->ATinfinity)
-      qh_fprintf(qh, fp, 9372, "\
-When computing the Delaunay triangulation:\n\
-  - use 'Qz' to add a point at-infinity.  This reduces precision problems.\n");
-
-    qh_fprintf(qh, fp, 9373, "\
-\n\
-If you need triangular output:\n\
-  - use option 'Qt' to triangulate the output\n\
-  - use option 'QJ' to joggle the input points and remove precision errors\n\
-  - use option 'Ft'.  It triangulates non-simplicial facets with added points.\n\
-\n\
-If you must use 'Q0',\n\
-try one or more of the following options.  They can not guarantee an output.\n\
-  - use 'QbB' to scale the input to a cube.\n\
-  - use 'Po' to produce output and prevent partitioning for flipped facets\n\
-  - use 'V0' to set min. distance to visible facet as 0 instead of roundoff\n\
-  - use 'En' to specify a maximum roundoff error less than %2.2g.\n\
-  - options 'Qf', 'Qbb', and 'QR0' may also help\n",
-               qh->DISTround);
-    qh_fprintf(qh, fp, 9374, "\
-\n\
-To guarantee simplicial output:\n\
-  - use option 'Qt' to triangulate the output\n\
-  - use option 'QJ' to joggle the input points and remove precision errors\n\
-  - use option 'Ft' to triangulate the output by adding points\n\
-  - use exact arithmetic (see \"Imprecision in Qhull\", qh-impre.htm)\n\
-");
-  }
-} /* printhelp_degenerate */
-
-
-/*---------------------------------
-
-  qh_printhelp_narrowhull(qh, minangle )
-    Warn about a narrow hull
-
-  notes:
-    Alternatively, reduce qh_WARNnarrow in user.h
-
-*/
-void qh_printhelp_narrowhull(qhT *qh, FILE *fp, realT minangle) {
-
-    qh_fprintf(qh, fp, 9375, "qhull precision warning: \n\
-The initial hull is narrow (cosine of min. angle is %.16f).\n\
-Is the input lower dimensional (e.g., on a plane in 3-d)?  Qhull may\n\
-produce a wide facet.  Options 'QbB' (scale to unit box) or 'Qbb' (scale\n\
-last coordinate) may remove this warning.  Use 'Pp' to skip this warning.\n\
-See 'Limitations' in qh-impre.htm.\n",
-          -minangle);   /* convert from angle between normals to angle between facets */
-} /* printhelp_narrowhull */
-
-/*---------------------------------
-
-  qh_printhelp_singular(qh, fp )
-    prints descriptive message for singular input
-*/
-void qh_printhelp_singular(qhT *qh, FILE *fp) {
-  facetT *facet;
-  vertexT *vertex, **vertexp;
-  realT min, max, *coord, dist;
-  int i,k;
-
-  qh_fprintf(qh, fp, 9376, "\n\
-The input to qhull appears to be less than %d dimensional, or a\n\
-computation has overflowed.\n\n\
-Qhull could not construct a clearly convex simplex from points:\n",
-           qh->hull_dim);
-  qh_printvertexlist(qh, fp, "", qh->facet_list, NULL, qh_ALL);
-  if (!qh_QUICKhelp)
-    qh_fprintf(qh, fp, 9377, "\n\
-The center point is coplanar with a facet, or a vertex is coplanar\n\
-with a neighboring facet.  The maximum round off error for\n\
-computing distances is %2.2g.  The center point, facets and distances\n\
-to the center point are as follows:\n\n", qh->DISTround);
-  qh_printpointid(qh, fp, "center point", qh->hull_dim, qh->interior_point, qh_IDunknown);
-  qh_fprintf(qh, fp, 9378, "\n");
-  FORALLfacets {
-    qh_fprintf(qh, fp, 9379, "facet");
-    FOREACHvertex_(facet->vertices)
-      qh_fprintf(qh, fp, 9380, " p%d", qh_pointid(qh, vertex->point));
-    zinc_(Zdistio);
-    qh_distplane(qh, qh->interior_point, facet, &dist);
-    qh_fprintf(qh, fp, 9381, " distance= %4.2g\n", dist);
-  }
-  if (!qh_QUICKhelp) {
-    if (qh->HALFspace)
-      qh_fprintf(qh, fp, 9382, "\n\
-These points are the dual of the given halfspaces.  They indicate that\n\
-the intersection is degenerate.\n");
-    qh_fprintf(qh, fp, 9383,"\n\
-These points either have a maximum or minimum x-coordinate, or\n\
-they maximize the determinant for k coordinates.  Trial points\n\
-are first selected from points that maximize a coordinate.\n");
-    if (qh->hull_dim >= qh_INITIALmax)
-      qh_fprintf(qh, fp, 9384, "\n\
-Because of the high dimension, the min x-coordinate and max-coordinate\n\
-points are used if the determinant is non-zero.  Option 'Qs' will\n\
-do a better, though much slower, job.  Instead of 'Qs', you can change\n\
-the points by randomly rotating the input with 'QR0'.\n");
-  }
-  qh_fprintf(qh, fp, 9385, "\nThe min and max coordinates for each dimension are:\n");
-  for (k=0; k < qh->hull_dim; k++) {
-    min= REALmax;
-    max= -REALmin;
-    for (i=qh->num_points, coord= qh->first_point+k; i--; coord += qh->hull_dim) {
-      maximize_(max, *coord);
-      minimize_(min, *coord);
-    }
-    qh_fprintf(qh, fp, 9386, "  %d:  %8.4g  %8.4g  difference= %4.4g\n", k, min, max, max-min);
-  }
-  if (!qh_QUICKhelp) {
-    qh_fprintf(qh, fp, 9387, "\n\
-If the input should be full dimensional, you have several options that\n\
-may determine an initial simplex:\n\
-  - use 'QJ'  to joggle the input and make it full dimensional\n\
-  - use 'QbB' to scale the points to the unit cube\n\
-  - use 'QR0' to randomly rotate the input for different maximum points\n\
-  - use 'Qs'  to search all points for the initial simplex\n\
-  - use 'En'  to specify a maximum roundoff error less than %2.2g.\n\
-  - trace execution with 'T3' to see the determinant for each point.\n",
-                     qh->DISTround);
-#if REALfloat
-    qh_fprintf(qh, fp, 9388, "\
-  - recompile qhull for realT precision(#define REALfloat 0 in libqhull_r.h).\n");
-#endif
-    qh_fprintf(qh, fp, 9389, "\n\
-If the input is lower dimensional:\n\
-  - use 'QJ' to joggle the input and make it full dimensional\n\
-  - use 'Qbk:0Bk:0' to delete coordinate k from the input.  You should\n\
-    pick the coordinate with the least range.  The hull will have the\n\
-    correct topology.\n\
-  - determine the flat containing the points, rotate the points\n\
-    into a coordinate plane, and delete the other coordinates.\n\
-  - add one or more points to make the input full dimensional.\n\
-");
-  }
-} /* printhelp_singular */
-
-/*---------------------------------
-
-  qh_user_memsizes(qh)
-    allocate up to 10 additional, quick allocation sizes
-
-  notes:
-    increase maximum number of allocations in qh_initqhull_mem()
-*/
-void qh_user_memsizes(qhT *qh) {
-
-  QHULL_UNUSED(qh)
-  /* qh_memsize(qh, size); */
-} /* user_memsizes */
-
-
diff --git a/C/usermem_r.c b/C/usermem_r.c
deleted file mode 100644
--- a/C/usermem_r.c
+++ /dev/null
@@ -1,94 +0,0 @@
-/*
  ---------------------------------
-
-   usermem_r.c
-   qh_exit(), qh_free(), and qh_malloc()
-
-   See README.txt.
-
-   If you redefine one of these functions you must redefine all of them.
-   If you recompile and load this file, then usermem.o will not be loaded
-   from qhull.a or qhull.lib
-
-   See libqhull_r.h for data structures, macros, and user-callable functions.
-   See user_r.c for qhull-related, redefinable functions
-   see user_r.h for user-definable constants
-   See userprintf_r.c for qh_fprintf and userprintf_rbox_r.c for qh_fprintf_rbox
-
-   Please report any errors that you fix to qhull@qhull.org
-*/
-
-#include "libqhull_r.h"
-
-#include 
-#include 
-
-/*---------------------------------
-
-  qh_exit( exitcode )
-    exit program
-
-  notes:
-    qh_exit() is called when qh_errexit() and longjmp() are not available.
-
-    This is the only use of exit() in Qhull
-    To replace qh_exit with 'throw', see libqhullcpp/usermem_r-cpp.cpp
-*/
-void qh_exit(int exitcode) {
-    exit(exitcode);
-} /* exit */
-
-/*---------------------------------
-
-  qh_fprintf_stderr( msgcode, format, list of args )
-    fprintf to stderr with msgcode (non-zero)
-
-  notes:
-    qh_fprintf_stderr() is called when qh->ferr is not defined, usually due to an initialization error
-    
-    It is typically followed by qh_errexit().
-
-    Redefine this function to avoid using stderr
-
-    Use qh_fprintf [userprintf_r.c] for normal printing
-*/
-void qh_fprintf_stderr(int msgcode, const char *fmt, ... ) {
-    va_list args;
-
-    va_start(args, fmt);
-    if(msgcode)
-      fprintf(stderr, "QH%.4d ", msgcode);
-    vfprintf(stderr, fmt, args);
-    va_end(args);
-} /* fprintf_stderr */
-
-/*---------------------------------
-
-  qh_free(qhT *qh, mem )
-    free memory
-
-  notes:
-    same as free()
-    No calls to qh_errexit() 
-*/
-void qh_free(void *mem) {
-    free(mem);
-} /* free */
-
-/*---------------------------------
-
-    qh_malloc( mem )
-      allocate memory
-
-    notes:
-      same as malloc()
-*/
-void *qh_malloc(size_t size) {
-    return malloc(size);
-} /* malloc */
-
-
diff --git a/C/userprintf_r.c b/C/userprintf_r.c
deleted file mode 100644
--- a/C/userprintf_r.c
+++ /dev/null
@@ -1,65 +0,0 @@
-/*
  ---------------------------------
-
-   userprintf_r.c
-   qh_fprintf()
-
-   see README.txt  see COPYING.txt for copyright information.
-
-   If you recompile and load this file, then userprintf_r.o will not be loaded
-   from qhull.a or qhull.lib
-
-   See libqhull_r.h for data structures, macros, and user-callable functions.
-   See user_r.c for qhull-related, redefinable functions
-   see user_r.h for user-definable constants
-   See usermem_r.c for qh_exit(), qh_free(), and qh_malloc()
-   see Qhull.cpp and RboxPoints.cpp for examples.
-
-   Please report any errors that you fix to qhull@qhull.org
-*/
-
-#include "libqhull_r.h"
-
-#include 
-#include 
-#include 
-
-/*---------------------------------
-
-   qh_fprintf(qh, fp, msgcode, format, list of args )
-     print arguments to *fp according to format
-     Use qh_fprintf_rbox() for rboxlib_r.c
-
-   notes:
-     same as fprintf()
-     fgets() is not trapped like fprintf()
-     exit qh_fprintf via qh_errexit()
-     may be called for errors in qh_initstatistics and qh_meminit
-*/
-
-void qh_fprintf(qhT *qh, FILE *fp, int msgcode, const char *fmt, ... ) {
-    va_list args;
-
-    if (!fp) {
-        if(!qh){
-            qh_fprintf_stderr(6241, "userprintf_r.c: fp and qh not defined for qh_fprintf '%s'", fmt);
-            qh_exit(qhmem_ERRqhull);  /* can not use qh_errexit() */
-        }
-        /* could use qh->qhmem.ferr, but probably better to be cautious */
-        qh_fprintf_stderr(6232, "Qhull internal error (userprintf_r.c): fp is 0.  Wrong qh_fprintf called.\n");
-        qh_errexit(qh, 6232, NULL, NULL);
-    }
-    va_start(args, fmt);
-    if (qh && qh->ANNOTATEoutput) {
-      fprintf(fp, "[QH%.4d]", msgcode);
-    }else if (msgcode >= MSG_ERROR && msgcode < MSG_STDERR ) {
-      fprintf(fp, "QH%.4d ", msgcode);
-    }
-    vfprintf(fp, fmt, args);
-    va_end(args);
-
-    /* Place debugging traps here. Use with option 'Tn' */
-
-} /* qh_fprintf */
-
diff --git a/C/utils.c b/C/utils.c
deleted file mode 100644
--- a/C/utils.c
+++ /dev/null
@@ -1,91 +0,0 @@
-#include  // to use realloc
-#include  // to use NAN
-#include  // to use printf
-
-double* getpoint(double* points, unsigned dim, unsigned id){
-  double* out = malloc(dim * sizeof(double));
-  for(unsigned i=0; i < dim; i++){
-    out[i] = points[id*dim+i];
-  }
-  return out;
-}
-
-/* dot product of two vectors */
-double dotproduct(double* p1, double* p2, unsigned dim){
-  double out = 0;
-  for(unsigned i=0; i < dim; i++){
-    out += p1[i] * p2[i];
-  }
-  return out;
-}
-
-/* middle of segment [p1,p2] */
-double* middle(double* p1, double* p2, unsigned dim){
-  double* out = malloc(dim * sizeof(double));
-  for(unsigned i=0; i 0 ? 1 : -1);
-}
-void qsortu(unsigned* vector, unsigned length){
-  qsort(vector, length, sizeof(unsigned), cmpfunc);
-}
-
-
-double square(double x){
-  return x*x;
-}
-
-/* append to a vector of unsigned */
-void appendu(unsigned x, unsigned** array, unsigned length, unsigned* flag){
-  *flag = 1;
-  for(unsigned i=0; i (*(unsigned**)b)[0]){
+    return 1;
+  }else if((*(unsigned**)a)[0] == (*(unsigned**)b)[0]){
+    return (*(unsigned**)a)[1] - (*(unsigned**)b)[1];
+  }else{
+    return -1;
+  }
+}
+
+/* test equality of two _sorted_ arrays */
+unsigned equalarraysu(unsigned* array1, unsigned* array2, unsigned length){
+  unsigned i;
+  for(i=0; i < length; i++){
+    if(array1[i] != array2[i]){
+      break;
+    }
+  }
+  return i == length;
+}
+
+/* return ids of a vector of VertexT */
+unsigned* map_vertexid(VertexT* vertices, unsigned nvertices){
+  unsigned* ids = malloc(nvertices * sizeof(unsigned));
+  for(unsigned v=0; v < nvertices; v++){
+    ids[v] = vertices[v].id;
+  }
+  return ids;
+}
+
+/* return ids of a vector of RidgeT */
+unsigned* map_ridgeid(RidgeT* ridges, unsigned nridges){
+  unsigned* ids = malloc(nridges * sizeof(unsigned));
+  for(unsigned r=0; r < nridges; r++){
+    ids[r] = ridges[r].id;
+  }
+  return ids;
+}
+
+// void deepCopyRidge(RidgeT* src, RidgeT* dest) { et dim !
+//     dest = malloc(sizeof(RidgeT));
+//     *dest = *src;
+//     dest->vertices = malloc(src->nvertices * sizeof(VertexT));
+//     for(unsigned v=0; vnvertices; v++){
+//       dest->vertices[v].id = src.vertices[v].id;
+//       memcpy(dest->vertices[v].point, dest->vertices[v].point, dim * sizeof(double));
+//     }
+// }
+
+/* deep copy of a ridge */
+RidgeT copyRidge(RidgeT ridge, unsigned dim){
+  RidgeT out;
+  out.ridgeOf1  = ridge.ridgeOf1;
+  out.ridgeOf2  = ridge.ridgeOf2;
+  out.nvertices = ridge.nvertices;
+  out.nedges    = ridge.nedges;
+  out.vertices  = malloc(out.nvertices * sizeof(VertexT));
+  for(unsigned v=0; v < out.nvertices; v++){
+    out.vertices[v].id    = ridge.vertices[v].id;
+    out.vertices[v].point = malloc(dim * sizeof(double));
+    for(unsigned i=0; i < dim; i++){
+      out.vertices[v].point[i] = ridge.vertices[v].point[i];
+    }
+  }
+  // out.edges = malloc(out.nedges * sizeof(unsigned*));
+  // for(unsigned e=0; e < out.nedges; e++){
+  //   out.edges[e] = malloc(2 * sizeof(unsigned));
+  //   out.edges[e][0] = ridge.edges[e][0];
+  //   out.edges[e][1] = ridge.edges[e][1];
+  // }
+  return out;
+}
+
+/* append to a vector of VertexT */
+void appendv(VertexT x, VertexT** array, unsigned length, unsigned* flag){
+  *flag = 1;
+  for(unsigned i=0; i < length; i++){
+    if(x.id == (*(*array + i)).id){
+      *flag = 0;
+      break;
+    }
+  }
+  if(*flag == 1){
+    *array = realloc(*array, (length+1) * sizeof(VertexT));
+    if(*array == NULL){
+      printf("realloc failure - exiting\n");
+      exit(1);
+    }
+    *(*array + length) = x;
+  }
+}
+
+/* union of two vectors of VertexT */
+void unionv(VertexT** vs1, VertexT* vs2, unsigned l1, unsigned l2, unsigned* l){
+  *l = l1;
+  for(unsigned v=0; v < l2; v++){
+    unsigned pushed;
+    appendv(vs2[v], vs1, *l, &pushed);
+    if(pushed){
+      (*l)++;
+    }
+  }
+  /* sort vertices according to their ids */
+  qsort(*vs1, *l, sizeof(VertexT), cmpvertices);
+}
+
+/* merge ridges with same ridgeOf's */
+RidgeT* mergeRidges(RidgeT* ridges, unsigned nridges, unsigned* newlength){
+  // http://www.c4learn.com/c-programs/to-delete-duplicate-elements-in-array.html
+  *newlength = nridges;
+  unsigned i,j,k;
+  for(i = 0; i < nridges; i++){
+    for(j = i+1; j < nridges; ){
+      if(ridges[i].ridgeOf1 == ridges[j].ridgeOf1 &&
+         ridges[i].ridgeOf2 == ridges[j].ridgeOf2)
+      {
+        unsigned l;
+        unionv(&(ridges[i].vertices), ridges[j].vertices,
+                 ridges[i].nvertices, ridges[j].nvertices, &l);
+        ridges[i].nvertices = l;
+        (*newlength)--;
+        for(k = j; k+1 < nridges; k++){
+          ridges[k] = ridges[k+1];
+        }
+        nridges--;
+      }else{
+        j++;
+      }
+    }
+  }
+  RidgeT* out = malloc(*newlength * sizeof(RidgeT));
+  for(unsigned r=0; r < *newlength; r++){
+    out[r] = ridges[r];
+  }
+  return out;
+}
+
+/* all ridges from the ridges stored in the faces */
+RidgeT* allRidges(FaceT *faces, unsigned nfaces, unsigned dim, unsigned* length){
+  RidgeT* out = malloc(faces[0].nridges * sizeof(RidgeT));
+  for(unsigned i=0; i < faces[0].nridges; i++){
+    out[i] = copyRidge(faces[0].ridges[i], dim);
+    out[i].id = i;
+    out[i].nedges = 0;
+    // RidgeT out[i];
+    // deepCopyRidge(&(faces[0].ridges[i]), &(out[i]));
+  }
+  *length    = faces[0].nridges;
+  unsigned n = faces[0].nridges;
+  for(unsigned f=1; f < nfaces; f++){
+    for(unsigned j=0; j < faces[f].nridges; j++){
+      unsigned count = 0;
+      for(unsigned i=0; i < n; i++){
+        unsigned flag = 0;
+        for(unsigned v=0; v < faces[f].ridges[j].nvertices; v++){
+          if(faces[f].ridges[j].vertices[v].id != out[i].vertices[v].id){
+            flag = 1;
+            break;
+          }
+        }
+        if(flag){
+          count++;
+        }else{
+          break;
+        }
+      }
+      if(count == n){
+        out          = realloc(out, (*length+1) * sizeof(RidgeT));
+        if(out == NULL){
+          printf("realloc failure - exiting\n");
+          exit(1);
+        }
+        out[*length] = copyRidge(faces[f].ridges[j], dim);
+        out[*length].id = *length;
+        out[*length].nedges = 0;
+        // RidgeT out[*length];
+        // deepCopyRidge(&(faces[f].ridges[j]), &(out[*length]));
+        (*length)++;
+      }
+    }
+    n = *length;
+  }
+  return out;
+}
+
+/* assign ids to the ridges stored in the faces */
+void assignRidgesIds(FaceT** faces, unsigned nfaces, RidgeT* allridges,
+                     unsigned nallridges)
+{
+  for(unsigned f=0; f < nfaces; f++){
+    for(unsigned fr=0; fr < (*(*faces + f)).nridges; fr++){
+      for(unsigned r=0; r < nallridges; r++){
+        if((allridges[r].nvertices == (*(*faces + f)).ridges[fr].nvertices) &&
+            equalarraysu(map_vertexid(allridges[r].vertices,
+                                      allridges[r].nvertices),
+                         map_vertexid((*(*faces + f)).ridges[fr].vertices,
+                                      allridges[r].nvertices),
+                         allridges[r].nvertices))
+        {
+          (*(*faces + f)).ridges[fr].id = allridges[r].id;
+          break;
+        }
+      }
+    }
+  }
+}
+
+// double* ridgeCentroid(RidgeT ridge, unsigned dim){
+//   double* out = malloc(dim * sizeof(double));
+//   for(unsigned i=0; i2 */
+unsigned* neighVertices(unsigned id, RidgeT* allridges, unsigned nridges,
+                        unsigned dim, unsigned triangulate, unsigned* lengthout)
+{
+  unsigned* neighs = malloc(0);
+  *lengthout = 0;
+  for(unsigned e=0; e < nridges; e++){
+    for(unsigned v=0; v < allridges[e].nvertices; v++){
+      if(id == allridges[e].vertices[v].id){
+        for(unsigned w=0; w < allridges[e].nvertices; w++){
+          if(w != v && (triangulate || dim == 3 || // dim3 pas besoin de tester la distance: il n'y a que deux vertices connectés
+             squaredDistance(allridges[e].vertices[w].point,
+                             allridges[e].vertices[v].point, dim) <=
+              ridgeMaxDistance(allridges[e], v, dim)))
+          {
+            unsigned pushed;
+            appendu(allridges[e].vertices[w].id, &neighs, *lengthout, &pushed);
+            if(pushed){
+              (*lengthout)++;
+            }
+          }
+        }
+        break;
+      }
+    }
+  }
+  return neighs;
+}
+
+/* neighbor ridges of a vertex */
+unsigned* neighRidges(unsigned id, RidgeT* allridges, unsigned nridges,
+                     unsigned* length)
+{
+  unsigned* neighs = malloc(0);
+  *length = 0;
+  for(unsigned e=0; e < nridges; e++){
+    unsigned flag = 0;
+    for(unsigned v=0; v < allridges[e].nvertices; v++){
+      if(id == allridges[e].vertices[v].id){
+        flag = 1;
+        break;
+      }
+    }
+    if(flag){
+      neighs = realloc(neighs, (*length+1)*sizeof(unsigned));
+      if(neighs == NULL){
+        printf("realloc failure - exiting\n");
+        exit(1);
+      }
+      neighs[*length] = e;
+      (*length)++;
+    }
+  }
+  return neighs;
+}
+
+/* whether distinct x1 and x2 belong to array of distinct values */
+unsigned areElementsOf(unsigned x1, unsigned x2, unsigned* array,
+                       unsigned length)
+{
+  unsigned count = 0;
+  for(unsigned i=0; (i < length) && (count < 2); i++){
+    if(x1 == array[i] || x2 == array[i]){
+      count++;
+    }
+  }
+  return count==2;
+}
+
+/* make face/ridge edges from all edges */
+unsigned** makeEdges(SetOfVerticesT face, unsigned** alledges,
+                     unsigned nalledges, unsigned* lengthout)
+{
+  *lengthout = 0;
+  unsigned* faceverticesids = map_vertexid(face.vertices, face.nvertices);
+  unsigned flags[nalledges];
+  for(unsigned e=0; e < nalledges; e++){
+    if(areElementsOf(alledges[e][0], alledges[e][1], faceverticesids,
+                     face.nvertices))
+    {
+      flags[e] = 1;
+      (*lengthout)++;
+    }else{
+      flags[e] = 0;
+    }
+  }
+  unsigned** out = malloc(*lengthout * sizeof(unsigned*));
+  unsigned count = 0;
+  for(unsigned e=0; e < nalledges; e++){
+    if(flags[e] == 1){
+      out[count] = alledges[e];
+      count++;
+    }
+  }
+  return out;
+}
+
+/* all edges from all vertices */
+unsigned** allEdges(FullVertexT* vertices, unsigned nvertices,
+                    unsigned outlength)
+{
+  unsigned** out = malloc(outlength * sizeof(unsigned*));
+  for(unsigned i=0; i < vertices[0].nneighsvertices; i++){
+    out[i] = malloc(2 * sizeof(unsigned));
+    out[i][0] = vertices[0].id;
+    out[i][1] = vertices[0].neighvertices[i];
+    qsortu(out[i], 2);
+  }
+  unsigned n = vertices[0].nneighsvertices;
+  for(unsigned v=1; v < nvertices; v++){
+    unsigned ids[2];
+    for(unsigned i=0; i < vertices[v].nneighsvertices; i++){
+      ids[0] = vertices[v].id;
+      ids[1] = vertices[v].neighvertices[i];
+      qsortu(ids, 2);
+      unsigned j;
+      for(j=0; j < n; j++){
+        if(ids[0] == out[j][0] && ids[1] == out[j][1]){
+          break;
+        }
+      }
+      if(j == n){
+        out[n] = malloc(2 * sizeof(unsigned));
+        out[n][0] = ids[0]; out[n][1] = ids[1];
+        n++;
+      }
+      if(n == outlength){
+        break;
+      }
+    }
+    if(n == outlength){
+      break;
+    }
+  }
+  return out;
+}
+
+// ATTENTION avec Qt le center dans facet->center est le centre de l'union des triangles,
+//  (ainsi que normal et offset mais ça ok)
+
+// un ridge est simplicial ; pour l'hypercube il y a 2 ridges entre 2 faces,
+// ils forment le carré à l'intersection
+
+/* main function */
+ConvexHullT* convexHull(
+	double*   points,
+	unsigned  dim,
+	unsigned  n,
+  unsigned  triangulate,
+  unsigned  print,
+  char*     summaryFile,
+	unsigned* exitcode
+)
+{
+	char opts[250]; /* option flags for qhull, see qh_opt.htm */
+  sprintf(opts, "qhull s FF %s", triangulate ? "Qt" : "");
+	qhT qh_qh;       /* Qhull's data structure */
+  qhT *qh= &qh_qh;
+  QHULL_LIB_CHECK
+  qh_meminit(qh, stderr);
+	boolT ismalloc  = False; /* True if qhull should free points in qh_freeqhull() or reallocation */
+	FILE *errfile   = NULL;
+  FILE* outfile;
+  if(print){
+    outfile = stdout;
+  }else{
+    outfile = NULL;
+  }
+  qh_zero(qh, errfile);
+	exitcode[0] = qh_new_qhull(qh, dim, n, points, ismalloc, opts, outfile,
+                             errfile);
+  //fclose(tmpstdout);
+  printf("exitcode: %u\n", exitcode[0]);
+
+  ConvexHullT* out = malloc(sizeof(ConvexHullT));
+
+	if (!exitcode[0]) {  /* 0 if no error from qhull */
+
+    /* print summary to file */
+    if(*summaryFile != 0){
+      FILE* sfile = fopen(summaryFile, "w");
+    	qh_printsummary(qh, sfile);
+    	fclose(sfile);
+    }
+
+    //qh_getarea(qh, qh->facet_list); // no triowner if I do that; do qh_facetarea, not facet->f.area
+
+    unsigned   nfaces    = qh->num_facets;
+    FaceT*     faces     = malloc(nfaces * sizeof(FaceT));
+    {
+      facetT *facet; unsigned i_facet = 0;
+      FORALLfacets{
+        facet->id                  = i_facet; /* for neighbors and ridgeOf */
+        faces[i_facet].area        = qh_facetarea(qh, facet);
+        double* center             = qh_getcenter(qh, facet->vertices);
+        faces[i_facet].center      = malloc(dim * sizeof(double));
+        for(unsigned i=0; i < dim; i++){
+          faces[i_facet].center[i] = center[i];
+        }
+        double* normal = facet->normal;
+        faces[i_facet].normal      = malloc(dim * sizeof(double));
+        for(unsigned i=0; i < dim; i++){
+          faces[i_facet].normal[i] = normal[i];
+        }
+        faces[i_facet].offset      = facet->offset;
+        faces[i_facet].nvertices   = (unsigned) qh_setsize(qh, facet->vertices);
+        { /* face vertices */
+          faces[i_facet].vertices =
+            (VertexT*) malloc(faces[i_facet].nvertices * sizeof(VertexT));
+          vertexT *vertex, **vertexp;
+          unsigned i_vertex = 0;
+          FOREACHvertex_(facet->vertices){
+            faces[i_facet].vertices[i_vertex].id =
+              (unsigned) qh_pointid(qh, vertex->point);
+            faces[i_facet].vertices[i_vertex].point =
+              malloc(dim * sizeof(double));
+            faces[i_facet].vertices[i_vertex].point =
+              getpoint(points, dim, faces[i_facet].vertices[i_vertex].id);
+            // plante dans Haskell: (faces[i_facet].vertices)[i_vertex].point = vertex->point;
+            i_vertex++;
+          }
+          qsort(faces[i_facet].vertices, faces[i_facet].nvertices,
+                sizeof(VertexT), cmpvertices);
+        }
+        if(dim == 3){ /* orientation of the normals */
+          pointT* onepoint = ((vertexT*)facet->vertices->e[0].p)->point;
+          double thepoint[dim]; /* onepoint+normal */
+          for(unsigned i=0; i < dim; i++){
+            thepoint[i] = onepoint[i] + faces[i_facet].normal[i];
+          }
+          /* we check that these two points are on the same side of the ridge */
+          double h1 = dotproduct(qh->interior_point,
+                                 faces[i_facet].normal, dim) +
+                      faces[i_facet].offset;
+          double h2 = dotproduct(thepoint, faces[i_facet].normal, dim) +
+                      faces[i_facet].offset;
+          if(h1*h2 > 0){
+            for(unsigned i=0; i < dim; i++){
+              faces[i_facet].normal[i] *= -1;
+            }
+            printf("change sign\n"); // seems to never occur
+          }else{
+            printf("not change sign\n");
+          }
+        }
+        /**/
+        i_facet++;
+      }
+    }
+
+    { /* neighbor faces, faces families, and ridges */
+      facetT *facet;
+      unsigned i_facet = 0;
+      FORALLfacets{
+        {
+          faces[i_facet].neighborsize = qh_setsize(qh, facet->neighbors);
+          faces[i_facet].neighbors =
+            malloc(faces[i_facet].neighborsize * sizeof(unsigned));
+          unsigned i_neighbor = 0;
+          facetT *neighbor, **neighborp;
+          FOREACHneighbor_(facet){
+            faces[i_facet].neighbors[i_neighbor] = (unsigned) neighbor->id;
+            i_neighbor++;
+          }
+          qsortu(faces[i_facet].neighbors, faces[i_facet].neighborsize);
+        }
+        { /* face family, when option Qt */
+          if(facet->tricoplanar){
+            faces[i_facet].family = facet->f.triowner->id;
+          }else{
+            faces[i_facet].family = -1;
+          }
+        }
+        { /* face ridges */
+          qh_makeridges(qh, facet);
+          unsigned nridges = qh_setsize(qh, facet->ridges);
+          RidgeT* ridges = malloc(nridges * sizeof(RidgeT));
+          ridgeT *ridge, **ridgep;
+          unsigned i_ridge = 0;
+          FOREACHridge_(facet->ridges){
+            ridges[i_ridge].nedges = 0;
+            unsigned ridgeSize = qh_setsize(qh, ridge->vertices); // dim-1
+//            printf("ridge size: %u\n", ridgeSize);
+            ridges[i_ridge].nvertices = ridgeSize;
+            unsigned ids[ridgeSize];
+            for(unsigned v=0; v < ridgeSize; v++){
+              ids[v] =
+                qh_pointid(qh, ((vertexT*)ridge->vertices->e[v].p)->point);
+            }
+            qsortu(ids, ridgeSize);
+            ridges[i_ridge].vertices = malloc(ridgeSize * sizeof(VertexT));
+            for(unsigned v=0; v < ridgeSize; v++){
+              ridges[i_ridge].vertices[v].id = ids[v];
+              ridges[i_ridge].vertices[v].point = getpoint(points, dim, ids[v]);
+            }
+            unsigned ridgeofs[2];
+            ridgeofs[0] = ridge->bottom->id;
+            ridgeofs[1] = ridge->top->id;
+            qsortu(ridgeofs, 2);
+            ridges[i_ridge].ridgeOf1 = ridgeofs[0];
+            ridges[i_ridge].ridgeOf2 = ridgeofs[1];
+            /**/
+            i_ridge++;
+          }
+          /* merge triangulated ridges */
+          if(dim > 3 && !triangulate){
+            unsigned l;
+            faces[i_facet].ridges  = mergeRidges(ridges, nridges, &l);
+            faces[i_facet].nridges = l;
+          }else{ /* dim 2 or 3, or triangulate option */
+            faces[i_facet].ridges  = ridges;
+            faces[i_facet].nridges = nridges;
+          }
+        }
+        /**/
+        i_facet++;
+      }
+    }
+
+    /* make unique ridges */
+    unsigned n_allridges;
+    RidgeT* allridges = allRidges(faces, nfaces, dim, &n_allridges);
+//    printf("nallridges: %u\n", n_allridges);
+
+    /* assign ridges ids to the ridges stored in the faces */
+    assignRidgesIds(&faces, nfaces, allridges, n_allridges);
+
+    /* all vertices */
+    unsigned nvertices = qh->num_vertices;
+    FullVertexT* vertices = malloc(nvertices * sizeof(FullVertexT));
+    {
+      qh_vertexneighbors(qh); /* make the neighbor facets of the vertices */
+      vertexT *vertex;
+      unsigned i_vertex=0;
+      FORALLvertices{
+        /* vertex id and coordinates */
+        vertices[i_vertex].id    = (unsigned) qh_pointid(qh, vertex->point);
+        vertices[i_vertex].point = getpoint(points, dim, vertices[i_vertex].id);
+
+        /* neighbor facets of the vertex */
+        vertices[i_vertex].nneighfacets = qh_setsize(qh, vertex->neighbors);
+        vertices[i_vertex].neighfacets =
+          malloc(vertices[i_vertex].nneighfacets * sizeof(unsigned));
+        facetT *neighbor, **neighborp;
+        unsigned i_neighbor = 0;
+        FOREACHneighbor_(vertex){
+          vertices[i_vertex].neighfacets[i_neighbor] = neighbor->id;
+          i_neighbor++;
+        }
+        qsortu(vertices[i_vertex].neighfacets, vertices[i_vertex].nneighfacets);
+
+        /* neighbor vertices of the vertex */
+        if(dim > 2){
+          unsigned nneighsvertices;
+          vertices[i_vertex].neighvertices =
+            neighVertices(vertices[i_vertex].id, allridges, n_allridges,
+                          dim, triangulate, &nneighsvertices);
+          vertices[i_vertex].nneighsvertices = nneighsvertices;
+        }else{ /* dim=2 */
+          vertices[i_vertex].nneighsvertices = 2;
+          vertices[i_vertex].neighvertices   = malloc(2 * sizeof(unsigned));
+          unsigned count = 0;
+          for(unsigned f=0; f < nfaces; f++){
+            for(unsigned i=0; i < 2; i++){
+              if(faces[f].vertices[i].id == vertices[i_vertex].id){
+                vertices[i_vertex].neighvertices[count] =
+                  faces[f].vertices[1-i].id;
+                count++;
+                break;
+              }
+            }
+            if(count == 2){
+              break;
+            }
+          }
+        }
+        qsortu(vertices[i_vertex].neighvertices,
+               vertices[i_vertex].nneighsvertices);
+
+        /* neighbor ridges of the vertex */
+        if(dim > 2){
+          unsigned nneighridges;
+          vertices[i_vertex].neighridges =
+            neighRidges(vertices[i_vertex].id, allridges, n_allridges,
+                       &nneighridges);
+          qsortu(vertices[i_vertex].neighridges, nneighridges);
+          vertices[i_vertex].nneighridges = nneighridges;
+        }else{ /* dim=2 */
+          vertices[i_vertex].nneighridges = 0; /* ridge = vertex singleton */
+        }
+        /**/
+        i_vertex++;
+      }
+      /* sort vertices according to their ids */
+      qsort(vertices, nvertices, sizeof(FullVertexT), cmpfullvertices);
+    }
+
+    /* all edges */
+    unsigned nalledges = 0;
+    for(unsigned v=0; v < nvertices; v++){
+      nalledges += vertices[v].nneighsvertices;
+    }
+    nalledges /= 2;
+    unsigned** alledges = allEdges(vertices, nvertices, nalledges);
+    qsort(alledges, nalledges, sizeof(unsigned*), cmpedges);
+
+    { /* faces edges and ridges ids */
+      facetT *facet; unsigned i_facet=0;
+      FORALLfacets{
+        /* facet ridges ids */
+        faces[i_facet].ridgesids =
+          map_ridgeid(faces[i_facet].ridges, faces[i_facet].nridges);
+        qsortu(faces[i_facet].ridgesids, faces[i_facet].nridges);
+        /* facet edges */
+        SetOfVerticesT facet_vset = {.vertices = faces[i_facet].vertices,
+                                     .nvertices = faces[i_facet].nvertices};
+        unsigned nfaceedges;
+        faces[i_facet].edges =
+          makeEdges(facet_vset, alledges, nalledges, &nfaceedges);
+        //qsort(faces[i_facet].edges, nfaceedges, sizeof(unsigned*), cmpedges); useless, I think
+        faces[i_facet].nedges = nfaceedges;
+        /**/
+        i_facet++;
+      }
+    }
+
+    /* ridges edges */
+    if(dim > 3){
+      for(unsigned r=0; r < n_allridges; r++){
+        unsigned facetid = allridges[r].ridgeOf1;
+        SetOfVerticesT vset = {.vertices = allridges[r].vertices,
+                               .nvertices = allridges[r].nvertices};
+        unsigned nedges;
+        allridges[r].edges =
+          makeEdges(vset, faces[facetid].edges, faces[facetid].nedges, &nedges);
+        allridges[r].nedges = nedges;
+      }
+    }
+
+    /* output */
+    out->dim       = dim;
+    out->vertices  = vertices;
+    out->nvertices = nvertices;
+    out->faces     = faces;
+    out->nfaces    = nfaces;
+    out->ridges    = allridges;
+    out->nridges   = n_allridges;
+    out->edges     = alledges;
+    out->nedges    = nalledges;
+
+  } // end if exitcode
+
+  /* Do cleanup regardless of whether there is an error */
+  int curlong, totlong;
+	qh_freeqhull(qh, !qh_ALL);               /* free long memory */
+	qh_memfreeshort(qh, &curlong, &totlong); /* free short memory and memory allocator */
+
+  printf("RETURN\n");
+  if(*exitcode){
+    free(out);
+    return 0;
+  }else{
+    return out;
+  }
+
+}
diff --git a/Cdir/delaunay.c b/Cdir/delaunay.c
new file mode 100644
--- /dev/null
+++ b/Cdir/delaunay.c
@@ -0,0 +1,577 @@
+#define qh_QHimport
+#include "qhull_ra.h"
+#include "delaunay.h"
+#include "utils.h"
+#include  /* to use NAN */
+
+// void printfacet(qhT* qh, facetT* facet){
+//   vertexT *vertex, **vertexp;
+//   FOREACHvertex_(facet->vertices){
+//     printf("facetid: %d, pointid: %d ", facet->id, qh_pointid(qh, vertex->point));
+//   }
+// }
+
+unsigned facetOK_(facetT* facet, unsigned degenerate){
+  return !facet->upperdelaunay && (degenerate || !facet->degenerate);
+} // && simplicial, && !facet->redundant - pas de simplicial avec Qt
+
+
+
+TesselationT* tesselation(
+	double*   sites,
+	unsigned  dim,
+	unsigned  n,
+  unsigned  atinfinity,
+  unsigned  degenerate,
+  double    vthreshold,
+	unsigned* exitcode
+)
+{
+	char opts[50]; /* option flags for qhull, see qh_opt.htm */
+  sprintf(opts, "qhull d Qt Qbb%s%s",
+          atinfinity ? " Qz" : "", dim>3 ? " Qx" : "");
+	qhT qh_qh; /* Qhull's data structure */
+  qhT *qh= &qh_qh;
+  QHULL_LIB_CHECK
+  qh_meminit(qh, stderr);
+	boolT ismalloc  = False; /* True if qhull should free points in qh_freeqhull() or reallocation */
+	FILE *errfile   = NULL;
+  FILE* outfile   = NULL;
+  qh_zero(qh, errfile);
+	*exitcode = qh_new_qhull(qh, dim, n, sites, ismalloc, opts, outfile, errfile);
+  //fclose(tmpstdout);
+  printf("exitcode: %u\n", *exitcode);
+
+  TesselationT* out = malloc(sizeof(TesselationT)); /* output */
+
+	if (!(*exitcode)) { /* 0 if no error from qhull */
+
+    /* Count the number of facets we keep */
+		unsigned nfacets = 0; /* to store the number of facets */
+    {
+      facetT *facet;  /* set by FORALLfacets */
+  		FORALLfacets {
+  			if(facetOK_(facet, degenerate)){
+          facet->id = nfacets;
+  	      nfacets++;
+        }else{
+  				qh_removefacet(qh, facet);
+  			}
+  		}
+    }
+
+    /* Initialize the tiles */
+    TileT* allfacets = malloc(nfacets * sizeof(TileT));
+
+    { /* tiles families and volumes, and centers of tiles with >0 volume */
+      facetT* facet;
+      unsigned i_facet = 0;
+      FORALLfacets{
+        if(facet->tricoplanar){
+          allfacets[i_facet].family = facet->f.triowner->id;
+          // if(!facet->degenerate){
+          //   if(i_facet == 392){
+          //     printf("area: %f", qh_facetarea(qh, facet));
+          //   }
+          //   allfacets[i_facet].simplex.center =
+          //     qh_facetcenter(qh, facet->vertices);
+          // }else{
+          //   facetT *neighbor, **neighborp;
+          //   FOREACHneighbor_(facet){
+          //     if(facetOK_(neighbor,0) && neighbor->f.triowner->id == facet->f.triowner->id){
+          //       allfacets[i_facet].simplex.center =
+          //         qh_facetcenter(qh, neighbor->vertices);
+          //       break;
+          //     }
+          //   }
+          // }
+        }else{
+          allfacets[i_facet].family = -1;
+        }
+        if(facet->degenerate){ // ?
+          allfacets[i_facet].simplex.volume = 0;
+        }else{
+          allfacets[i_facet].simplex.volume = fmax(0, qh_facetarea(qh, facet));
+        }
+        if(allfacets[i_facet].simplex.volume > vthreshold){
+          allfacets[i_facet].simplex.center = malloc(dim * sizeof(double));
+          double* center = qh_facetcenter(qh, facet->vertices);
+          for(unsigned i=0; i < dim; i++){
+            allfacets[i_facet].simplex.center[i] = center[i];
+          }
+        }
+        i_facet++;
+      }
+    }
+
+  	{ /* facets ids, orientations, centers, sites ids, neighbors */
+      facetT* facet;
+      unsigned i_facet = 0; /* facet counter */
+      FORALLfacets {
+        allfacets[i_facet].id             = facet->id;
+        allfacets[i_facet].orientation    = facet->toporient ? 1 : -1;
+        /* center and circumradius */
+        if(allfacets[i_facet].simplex.volume <= vthreshold){
+          if(facet->tricoplanar){
+            unsigned ok = 0;
+            vertexT* apex = (vertexT*)facet->vertices->e[0].p;
+            facetT *neighbor, **neighborp;
+            FOREACHneighbor_(apex){
+              if(facetOK_(neighbor,degenerate) &&
+                 allfacets[neighbor->id].family == allfacets[i_facet].family &&
+                 allfacets[neighbor->id].simplex.volume > vthreshold)
+              {
+                allfacets[i_facet].simplex.center =
+                  allfacets[neighbor->id].simplex.center;
+                ok = 1;
+                break;
+              }
+            }
+            if(!ok){ /* should not happen */
+              allfacets[i_facet].simplex.center = nanvector(dim);
+            }
+          }else{ /* should not happen */
+            allfacets[i_facet].simplex.center = nanvector(dim);
+          }
+        }
+//        printf("center facet %u: %f %f %f\n", i_facet, allfacets[i_facet].simplex.center[0], allfacets[i_facet].simplex.center[1], allfacets[i_facet].simplex.center[2]);
+        allfacets[i_facet].simplex.radius =
+          sqrt(squaredDistance(((vertexT*)facet->vertices->e[0].p)->point,
+                                allfacets[i_facet].simplex.center, dim));
+        // allfacets[i_facet].simplex.center =
+        //   facet->degenerate ? nanvector(dim)
+        //                       : qh_facetcenter(qh, facet->vertices);
+        // if(!facet->degenerate){
+        //   allfacets[i_facet].simplex.center = //facet->center;
+        //     qh_facetcenter(qh, facet->vertices);
+        //   // faire une première passe : calculer les centres des triowner
+        //   // pour ne pas les calculer pour les facets de la même famille
+        //   printf("center1: %f %f %f\n", facet->center[0], facet->center[1], facet->center[2]);
+        //   printf("center2: %f %f %f\n", allfacets[i_facet].simplex.center[0], allfacets[i_facet].simplex.center[1], allfacets[i_facet].simplex.center[2]);
+        //   pointT* point = ((vertexT*)facet->vertices->e[0].p)->point;
+        //   allfacets[i_facet].simplex.radius =
+        //     sqrt(squaredDistance(point, allfacets[i_facet].simplex.center,
+        //                          dim));
+        // }// }else{
+        // //   allfacets[i_facet].simplex.radius = NAN;
+        // // }
+
+        { /* vertices ids of the facet */
+          allfacets[i_facet].simplex.sitesids =
+            malloc((dim+1) * sizeof(unsigned));
+          vertexT *vertex, **vertexp;
+          unsigned i_vertex = 0;
+          FOREACHvertex_(facet->vertices) {
+            allfacets[i_facet].simplex.sitesids[i_vertex] =
+              qh_pointid(qh, vertex->point);
+            i_vertex++;
+    			}
+          qsortu(allfacets[i_facet].simplex.sitesids, dim+1);
+        }
+
+        { /* neighbors facets of the facet */
+          facetT *neighbor, **neighborp;
+    			unsigned flag[dim+1];
+          allfacets[i_facet].nneighbors = 0;
+          unsigned i_neighbor = 0;
+    			FOREACHneighbor_(facet) {
+            if(flag[i_neighbor] = facetOK_(neighbor, degenerate)){
+              allfacets[i_facet].nneighbors++;
+            }
+            i_neighbor++;
+          }
+          allfacets[i_facet].neighbors =
+            malloc(allfacets[i_facet].nneighbors * sizeof(unsigned));
+          unsigned countok = 0;
+          i_neighbor = 0;
+          FOREACHneighbor_(facet) {
+            if(flag[i_neighbor]){
+              allfacets[i_facet].neighbors[countok] = neighbor->id;
+              countok++;
+            }
+            i_neighbor++;
+          }
+        }
+
+        // /* facet family */
+        // if(facet->tricoplanar){
+        //   allfacets[i_facet].family = facet->f.triowner->id;
+        // }else{
+        //   allfacets[i_facet].family = -1;
+        // }
+
+        /**/
+  			i_facet++;
+  		}
+    }
+
+    //  /* for degenerate facets, take the center of the owner */
+    // if(degenerate){
+    //   facetT *facet;
+    //   unsigned i_facet = 0;
+    //   FORALLfacets{
+    //     if(facet->degenerate){
+    //       allfacets[i_facet].simplex.center =
+    //         allfacets[allfacets[i_facet].family].simplex.center;
+    //       pointT* point = ((vertexT*)facet->vertices->e[0].p)->point;
+    //       allfacets[i_facet].simplex.radius =
+    //         sqrt(squaredDistance(point, allfacets[i_facet].simplex.center,
+    //                              dim));
+    //     }
+    //     i_facet++;
+    //   }
+    // }
+
+		/* neighbor facets and neighbor vertices per vertex */
+    /* --- we will use the following combinations, also used later */
+    /* --- combinations[m] contains all k between 0 and dim but m  */
+    unsigned combinations[dim+1][dim];
+    for(unsigned m=0; m < dim+1; m++){
+      unsigned kk=0;
+      for(unsigned k=0; k < dim+1; k++){
+        if(k != m){
+          combinations[m][kk] = k;
+          kk++;
+        }
+      }
+    }
+    /* --- initialize the sites */
+    SiteT* allsites = malloc(n * sizeof(SiteT));
+    /* --- array to flag neighbors - 0/1 if not neighbour/neighbour */
+    unsigned** verticesFacetsNeighbours = malloc(n * sizeof(unsigned*));
+		  /* unsigned verticesFacetsNeighbours[n][nfacets] => stackoverflow */
+    for(unsigned v=0; v < n; v++){
+      allsites[v].id           = v;
+      allsites[v].nneighsites  = 0;
+      allsites[v].neighsites   = malloc(0); /* will be filled by appending */
+      allsites[v].nneighridges = 0;
+      allsites[v].nneightiles  = 0;
+      verticesFacetsNeighbours[v] = uzeros(nfacets);
+    }
+    /* --- fill verticesFacetsNeighbours, derive number of neighbor facets */
+    /* --- and derive neighbor sites */
+    for(unsigned i_facet=0; i_facet < nfacets; i_facet++){
+      for(unsigned j=0; j < dim+1; j++){
+        unsigned vertexid = allfacets[i_facet].simplex.sitesids[j];
+        if(verticesFacetsNeighbours[vertexid][i_facet] == 0){
+          verticesFacetsNeighbours[vertexid][i_facet] = 1;
+          allsites[vertexid].nneightiles++;
+        }
+        for(unsigned k=0; k < dim; k++){
+          unsigned vertexid2 =
+            allfacets[i_facet].simplex.sitesids[combinations[j][k]];
+          unsigned pushed;
+          appendu(vertexid2, &allsites[vertexid].neighsites,
+                  allsites[vertexid].nneighsites, &pushed);
+          if(pushed){
+            allsites[vertexid].nneighsites++;
+          }
+        }
+      }
+    }
+
+    /************************************************************/
+    /* second pass on facets: ridges and facet volumes          */
+    unsigned n_ridges_dup = nfacets * (dim+1); /* number of ridges with duplicates */
+    SubTileT* allridges_dup = malloc(n_ridges_dup * sizeof(SubTileT));
+    for(unsigned r=0; r < n_ridges_dup; r++){
+      allridges_dup[r].simplex.sitesids = malloc(dim * sizeof(unsigned));
+      allridges_dup[r].flag = 0;
+    }
+//    qh_getarea(qh, qh->facet_list); /* make facets volumes, available in facet->f.area */
+    unsigned n_ridges = 0; /* count distinct ridges */
+
+    { /* loop on facets */
+      facetT *facet;
+      unsigned i_ridge_dup = 0; /* ridge counter */
+      unsigned i_facet = 0; /* facet counter */
+      FORALLfacets {
+
+//        allfacets[i_facet].simplex.volume = facet->f.area;
+        allfacets[i_facet].nridges   = dim+1;
+        allfacets[i_facet].ridgesids = malloc((dim+1) * sizeof(unsigned));
+
+        /* loop on the combinations - it increments i_ridge_dup */
+        for(unsigned m=0; m < dim+1; m++){
+          allridges_dup[i_ridge_dup].ridgeOf1 = facet->id;
+          allridges_dup[i_ridge_dup].ridgeOf2 = -1; /* this means "nothing" */
+          unsigned ids[dim];
+          for(unsigned i=0; i < dim; i++){
+            ids[i] = allfacets[i_facet].simplex.sitesids[combinations[m][i]];
+          }
+          unsigned done = 0; /* flag ridge is already done */
+          for(unsigned r=0; r < i_ridge_dup; r++){
+            if(allridges_dup[r].ridgeOf2 == (int) facet->id &&
+               allridges_dup[r].flag==1)
+            {
+              unsigned ids2[dim];
+              unsigned i;
+              for(i=0; i < dim; i++){
+                ids2[i] = allridges_dup[r].simplex.sitesids[i];
+                if(ids2[i] != ids[i]){
+                  break;
+                }
+              }
+              if(i == dim){
+                allfacets[i_facet].ridgesids[m] = allridges_dup[r].id;
+                done = 1;
+                break;
+              }
+            }
+          }
+          if(done == 0){ /* => then do the ridge */
+            allridges_dup[i_ridge_dup].flag = 1;
+            allridges_dup[i_ridge_dup].id   = n_ridges;
+            allfacets[i_facet].ridgesids[m] = n_ridges;
+            n_ridges++;
+            for(unsigned i=0; i < dim; i++){
+              allridges_dup[i_ridge_dup].simplex.sitesids[i] = ids[i];
+              allsites[ids[i]].nneighridges++;
+            }
+
+            { /* loop on facet neighbors to find ridgeOf2 */
+              facetT *neighbor, **neighborp;
+              FOREACHneighbor_(facet){
+                if(facetOK_(neighbor, degenerate)){
+                  unsigned fnid = neighbor->id;
+                  unsigned ok;
+                  for(unsigned mm=0; mm < dim+1; mm++){
+                    ok = 0;
+                    for(unsigned i=0; i < dim; i++){
+                      if(allfacets[fnid].simplex.sitesids[combinations[mm][i]]
+                          != ids[i])
+                      {
+                        break;
+                      }else{
+                        ok++;
+                      }
+                    }
+                    if(ok==dim){
+                      break;
+                    }
+                  }
+                  if(ok==dim){
+                    allridges_dup[i_ridge_dup].ridgeOf2 = (int) fnid;
+                    break;
+                  }
+                }
+              } /* end FOREACHneighbor_(facet) */
+            }
+
+            pointT* points[dim]; /* the points corresponding to the combination */
+            for(unsigned i=0; i < dim; i++){
+              points[i] = getpoint(sites, dim, ids[i]);
+            }
+            double normal[dim]; /* to store the ridge normal */
+            if(dim == 2){
+              double u1 = points[1][0] - points[0][0];
+              double v1 = points[1][1] - points[0][1];
+              allridges_dup[i_ridge_dup].simplex.volume =
+                sqrt(square(u1)+square(v1));
+              allridges_dup[i_ridge_dup].simplex.center =
+                middle(points[0], points[1], dim);
+              allridges_dup[i_ridge_dup].simplex.radius =
+                sqrt(squaredDistance(allridges_dup[i_ridge_dup].simplex.center,
+                                     points[0], dim));
+              normal[0] = v1; normal[1] = -u1;
+            }else{
+              int parity=1;
+              double squaredNorm = 0;
+              for(unsigned i=0; i < dim; i++){
+                double** rows = malloc((dim-1) * sizeof(double*));
+                for(unsigned j=0; j < dim-1; j++){
+                  rows[j] = (double*) malloc((dim-1) * sizeof(double));
+                  for(unsigned k=0; k < dim-1; k++){
+                    unsigned kk = k 2){ /* ridge center is already done if dim 2 */
+              // if(facet->degenerate){
+              //   allridges_dup[i_ridge_dup].simplex.center = nanvector(dim);
+              //   allridges_dup[i_ridge_dup].simplex.radius = NAN;
+              // }else{
+              allridges_dup[i_ridge_dup].simplex.center =
+                malloc(dim * sizeof(double));
+              double scal = 0;
+              for(unsigned i=0; i < dim; i++){
+                scal += (points[0][i]-allfacets[i_facet].simplex.center[i]) *
+                          normal[i];
+              }
+              for(unsigned i=0; i < dim; i++){
+                allridges_dup[i_ridge_dup].simplex.center[i] =
+                  allfacets[i_facet].simplex.center[i] + scal*normal[i];
+              }
+              allridges_dup[i_ridge_dup].simplex.radius =
+                sqrt(squaredDistance(
+                      allridges_dup[i_ridge_dup].simplex.center,
+                      points[0], dim));
+//              }
+            }
+            /* orient the normal (used for plotting unbounded Voronoi cells) */
+            if(allridges_dup[i_ridge_dup].ridgeOf2 == -1)
+               //&& (!facet->degenerate || dim==2))
+            {
+              pointT* otherpoint = /* the remaining vertex of the facet (the one not in the ridge) */
+                qh->interior_point; // getpoint(sites, dim, allfacets[facet->id].simplex.sitesids[m]);
+              double thepoint[dim]; /* the point center+normal */
+              for(unsigned i=0; i < dim; i++){
+                thepoint[i] = allridges_dup[i_ridge_dup].simplex.center[i] +
+                              allridges_dup[i_ridge_dup].normal[i];
+              }
+              /* we check that these two points are on the same side of the ridge */
+              double h1 = dotproduct(otherpoint,
+                                     allridges_dup[i_ridge_dup].normal, dim) +
+                          allridges_dup[i_ridge_dup].offset;
+              double h2 = dotproduct(thepoint,
+                                     allridges_dup[i_ridge_dup].normal, dim) +
+                          allridges_dup[i_ridge_dup].offset;
+              // printf("deg: %u, h1: %f, h2: %f\n", facet->degenerate, h1, h2);
+              // printf("offset: %f\n", allridges_dup[i_ridge_dup].offset);
+              // printf("normal: %f %f %f\n", allridges_dup[i_ridge_dup].normal[0], allridges_dup[i_ridge_dup].normal[1], allridges_dup[i_ridge_dup].normal[2]);
+              if(h1*h2 >= 0){
+                for(unsigned i=0; i < dim; i++){
+                  allridges_dup[i_ridge_dup].normal[i] *= -1;
+                }
+              }
+            }
+            for(unsigned i=0; i < dim; i++){
+              free(points[i]);
+            }
+          }
+          i_ridge_dup++;
+        } // end loop combinations (m)
+        qsortu(allfacets[i_facet].ridgesids, dim+1);
+        /**/
+        i_facet++;
+      } // end FORALLfacets
+    }
+
+    /* extract unique ridges */
+    SubTileT* allridges = malloc(n_ridges * sizeof(SubTileT));
+    unsigned inc_ridge = 0;
+		for(unsigned l=0; l < n_ridges_dup; l++){
+      if(allridges_dup[l].flag){
+        allridges[inc_ridge] = allridges_dup[l];
+        inc_ridge++;
+      }
+		}
+
+    /* make neighbor ridges per vertex */
+    unsigned* i_ridges_per_vertex = uzeros(n);
+		for(unsigned v=0; v < n; v++){
+      allsites[v].neighridgesids =
+        malloc(allsites[v].nneighridges * sizeof(unsigned));
+    }
+    for(unsigned l=0; l < n_ridges_dup; l++){
+      if(allridges_dup[l].flag){
+        for(unsigned i=0; i < dim; i++){
+          unsigned v = allridges_dup[l].simplex.sitesids[i];
+          allsites[v].neighridgesids[i_ridges_per_vertex[v]] =
+            allridges_dup[l].id;
+          i_ridges_per_vertex[v]++;
+        }
+      }
+    }
+
+    /* order vertices neighbor sites and make neighbor tiles per vertex */
+		for(unsigned v=0; v < n; v++){
+      qsortu(allsites[v].neighsites, allsites[v].nneighsites);
+      allsites[v].neightiles =
+        malloc(allsites[v].nneightiles * sizeof(unsigned));
+			unsigned inc_facet = 0; unsigned inc_vfn = 0;
+			while(inc_vfn < allsites[v].nneightiles){
+				if(verticesFacetsNeighbours[v][inc_facet] == 1){
+          allsites[v].neightiles[inc_vfn] = inc_facet;
+					inc_vfn++;
+				}
+				inc_facet++;
+			}
+		}
+
+    /* make the output */
+	  out->sites      = allsites;
+    out->tiles      = allfacets;
+	  out->ntiles     = nfacets;
+	  out->subtiles   = allridges;
+    out->nsubtiles  = n_ridges;
+
+    free(allridges_dup);
+    free(i_ridges_per_vertex);
+    free(verticesFacetsNeighbours);
+
+	}
+
+	/* Do cleanup regardless of whether there is an error */
+  int curlong, totlong;
+	qh_freeqhull(qh, !qh_ALL);                /* free long memory */
+	qh_memfreeshort(qh, &curlong, &totlong);  /* free short memory and memory allocator */
+
+  printf("RETURN\n");
+  if(*exitcode){
+    free(out);
+    return 0;
+  }else{
+    return out;
+  }
+
+}
+
+
+void testdel2(){
+  double sites[27] = {0,0,0, 0,0,1, 0,1,0, 0,1,1, 1,0,0, 1,0,1, 1,1,0, 1,1,1, 0.5,0.5,0.5};
+  unsigned exitcode;
+  unsigned dim = 3;
+  TesselationT* x = tesselation(sites, dim, 9, 0, 0, 0, &exitcode);
+  printf("TESTDEL2 - nfacets:%u\n", x->ntiles);
+  for(unsigned f=0; f < x->ntiles; f++){
+    printf("facet %u - sites:\n", f);
+    for(unsigned i=0; i < dim+1; i++){
+      printf("%u - ", x->tiles[f].simplex.sitesids[i]);
+    }
+    printf("\n");
+    printf("facet %u - ridges:\n", f);
+    for(unsigned i=0; i < dim+1; i++){
+      printf("%u - ", x->tiles[f].ridgesids[i]);
+    }
+    printf("\n");
+    printf("facet %u - neighbors:\n", f);
+    for(unsigned i=0; i < x->tiles[f].nneighbors; i++){
+      printf("%u - ", x->tiles[f].neighbors[i]);
+    }
+    printf("\n");
+  }
+  printf("nallridges:%u\n", x->nsubtiles);
+  for(unsigned r=0; r < x->nsubtiles; r++){
+    printf("ridge %u - id %u:\n", r, x->subtiles[r].id);
+    for(unsigned i=0; i < dim; i++){
+      printf("%u - ", x->subtiles[r].simplex.sitesids[i]);
+    }
+    printf("ridgeOf: %u %d", x->subtiles[r].ridgeOf1, x->subtiles[r].ridgeOf2);
+    printf("\n");
+  }
+  free(x);
+}
diff --git a/Cdir/geom2_r.c b/Cdir/geom2_r.c
new file mode 100644
--- /dev/null
+++ b/Cdir/geom2_r.c
@@ -0,0 +1,2096 @@
+/*
  ---------------------------------
+
+
+   geom2_r.c
+   infrequently used geometric routines of qhull
+
+   see qh-geom_r.htm and geom_r.h
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull_r/geom2_r.c#6 $$Change: 2065 $
+   $DateTime: 2016/01/18 13:51:04 $$Author: bbarber $
+
+   frequently used code goes into geom_r.c
+*/
+
+#include "qhull_ra.h"
+
+/*================== functions in alphabetic order ============*/
+
+/*---------------------------------
+
+  qh_copypoints(qh, points, numpoints, dimension)
+    return qh_malloc'd copy of points
+  
+  notes:
+    qh_free the returned points to avoid a memory leak
+*/
+coordT *qh_copypoints(qhT *qh, coordT *points, int numpoints, int dimension) {
+  int size;
+  coordT *newpoints;
+
+  size= numpoints * dimension * (int)sizeof(coordT);
+  if (!(newpoints= (coordT*)qh_malloc((size_t)size))) {
+    qh_fprintf(qh, qh->ferr, 6004, "qhull error: insufficient memory to copy %d points\n",
+        numpoints);
+    qh_errexit(qh, qh_ERRmem, NULL, NULL);
+  }
+  memcpy((char *)newpoints, (char *)points, (size_t)size); /* newpoints!=0 by QH6004 */
+  return newpoints;
+} /* copypoints */
+
+/*---------------------------------
+
+  qh_crossproduct( dim, vecA, vecB, vecC )
+    crossproduct of 2 dim vectors
+    C= A x B
+
+  notes:
+    from Glasner, Graphics Gems I, p. 639
+    only defined for dim==3
+*/
+void qh_crossproduct(int dim, realT vecA[3], realT vecB[3], realT vecC[3]){
+
+  if (dim == 3) {
+    vecC[0]=   det2_(vecA[1], vecA[2],
+                     vecB[1], vecB[2]);
+    vecC[1]= - det2_(vecA[0], vecA[2],
+                     vecB[0], vecB[2]);
+    vecC[2]=   det2_(vecA[0], vecA[1],
+                     vecB[0], vecB[1]);
+  }
+} /* vcross */
+
+/*---------------------------------
+
+  qh_determinant(qh, rows, dim, nearzero )
+    compute signed determinant of a square matrix
+    uses qh.NEARzero to test for degenerate matrices
+
+  returns:
+    determinant
+    overwrites rows and the matrix
+    if dim == 2 or 3
+      nearzero iff determinant < qh->NEARzero[dim-1]
+      (!quite correct, not critical)
+    if dim >= 4
+      nearzero iff diagonal[k] < qh->NEARzero[k]
+*/
+realT qh_determinant(qhT *qh, realT **rows, int dim, boolT *nearzero) {
+  realT det=0;
+  int i;
+  boolT sign= False;
+
+  *nearzero= False;
+  if (dim < 2) {
+    qh_fprintf(qh, qh->ferr, 6005, "qhull internal error (qh_determinate): only implemented for dimension >= 2\n");
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }else if (dim == 2) {
+    det= det2_(rows[0][0], rows[0][1],
+                 rows[1][0], rows[1][1]);
+    if (fabs_(det) < 10*qh->NEARzero[1])  /* not really correct, what should this be? */
+      *nearzero= True;
+  }else if (dim == 3) {
+    det= det3_(rows[0][0], rows[0][1], rows[0][2],
+                 rows[1][0], rows[1][1], rows[1][2],
+                 rows[2][0], rows[2][1], rows[2][2]);
+    if (fabs_(det) < 10*qh->NEARzero[2])  /* what should this be?  det 5.5e-12 was flat for qh_maxsimplex of qdelaunay 0,0 27,27 -36,36 -9,63 */
+      *nearzero= True;
+  }else {
+    qh_gausselim(qh, rows, dim, dim, &sign, nearzero);  /* if nearzero, diagonal still ok*/
+    det= 1.0;
+    for (i=dim; i--; )
+      det *= (rows[i])[i];
+    if (sign)
+      det= -det;
+  }
+  return det;
+} /* determinant */
+
+/*---------------------------------
+
+  qh_detjoggle(qh, points, numpoints, dimension )
+    determine default max joggle for point array
+      as qh_distround * qh_JOGGLEdefault
+
+  returns:
+    initial value for JOGGLEmax from points and REALepsilon
+
+  notes:
+    computes DISTround since qh_maxmin not called yet
+    if qh->SCALElast, last dimension will be scaled later to MAXwidth
+
+    loop duplicated from qh_maxmin
+*/
+realT qh_detjoggle(qhT *qh, pointT *points, int numpoints, int dimension) {
+  realT abscoord, distround, joggle, maxcoord, mincoord;
+  pointT *point, *pointtemp;
+  realT maxabs= -REALmax;
+  realT sumabs= 0;
+  realT maxwidth= 0;
+  int k;
+
+  for (k=0; k < dimension; k++) {
+    if (qh->SCALElast && k == dimension-1)
+      abscoord= maxwidth;
+    else if (qh->DELAUNAY && k == dimension-1) /* will qh_setdelaunay() */
+      abscoord= 2 * maxabs * maxabs;  /* may be low by qh->hull_dim/2 */
+    else {
+      maxcoord= -REALmax;
+      mincoord= REALmax;
+      FORALLpoint_(qh, points, numpoints) {
+        maximize_(maxcoord, point[k]);
+        minimize_(mincoord, point[k]);
+      }
+      maximize_(maxwidth, maxcoord-mincoord);
+      abscoord= fmax_(maxcoord, -mincoord);
+    }
+    sumabs += abscoord;
+    maximize_(maxabs, abscoord);
+  } /* for k */
+  distround= qh_distround(qh, qh->hull_dim, maxabs, sumabs);
+  joggle= distround * qh_JOGGLEdefault;
+  maximize_(joggle, REALepsilon * qh_JOGGLEdefault);
+  trace2((qh, qh->ferr, 2001, "qh_detjoggle: joggle=%2.2g maxwidth=%2.2g\n", joggle, maxwidth));
+  return joggle;
+} /* detjoggle */
+
+/*---------------------------------
+
+  qh_detroundoff(qh)
+    determine maximum roundoff errors from
+      REALepsilon, REALmax, REALmin, qh.hull_dim, qh.MAXabs_coord,
+      qh.MAXsumcoord, qh.MAXwidth, qh.MINdenom_1
+
+    accounts for qh.SETroundoff, qh.RANDOMdist, qh->MERGEexact
+      qh.premerge_cos, qh.postmerge_cos, qh.premerge_centrum,
+      qh.postmerge_centrum, qh.MINoutside,
+      qh_RATIOnearinside, qh_COPLANARratio, qh_WIDEcoplanar
+
+  returns:
+    sets qh.DISTround, etc. (see below)
+    appends precision constants to qh.qhull_options
+
+  see:
+    qh_maxmin() for qh.NEARzero
+
+  design:
+    determine qh.DISTround for distance computations
+    determine minimum denominators for qh_divzero
+    determine qh.ANGLEround for angle computations
+    adjust qh.premerge_cos,... for roundoff error
+    determine qh.ONEmerge for maximum error due to a single merge
+    determine qh.NEARinside, qh.MAXcoplanar, qh.MINvisible,
+      qh.MINoutside, qh.WIDEfacet
+    initialize qh.max_vertex and qh.minvertex
+*/
+void qh_detroundoff(qhT *qh) {
+
+  qh_option(qh, "_max-width", NULL, &qh->MAXwidth);
+  if (!qh->SETroundoff) {
+    qh->DISTround= qh_distround(qh, qh->hull_dim, qh->MAXabs_coord, qh->MAXsumcoord);
+    if (qh->RANDOMdist)
+      qh->DISTround += qh->RANDOMfactor * qh->MAXabs_coord;
+    qh_option(qh, "Error-roundoff", NULL, &qh->DISTround);
+  }
+  qh->MINdenom= qh->MINdenom_1 * qh->MAXabs_coord;
+  qh->MINdenom_1_2= sqrt(qh->MINdenom_1 * qh->hull_dim) ;  /* if will be normalized */
+  qh->MINdenom_2= qh->MINdenom_1_2 * qh->MAXabs_coord;
+                                              /* for inner product */
+  qh->ANGLEround= 1.01 * qh->hull_dim * REALepsilon;
+  if (qh->RANDOMdist)
+    qh->ANGLEround += qh->RANDOMfactor;
+  if (qh->premerge_cos < REALmax/2) {
+    qh->premerge_cos -= qh->ANGLEround;
+    if (qh->RANDOMdist)
+      qh_option(qh, "Angle-premerge-with-random", NULL, &qh->premerge_cos);
+  }
+  if (qh->postmerge_cos < REALmax/2) {
+    qh->postmerge_cos -= qh->ANGLEround;
+    if (qh->RANDOMdist)
+      qh_option(qh, "Angle-postmerge-with-random", NULL, &qh->postmerge_cos);
+  }
+  qh->premerge_centrum += 2 * qh->DISTround;    /*2 for centrum and distplane()*/
+  qh->postmerge_centrum += 2 * qh->DISTround;
+  if (qh->RANDOMdist && (qh->MERGEexact || qh->PREmerge))
+    qh_option(qh, "Centrum-premerge-with-random", NULL, &qh->premerge_centrum);
+  if (qh->RANDOMdist && qh->POSTmerge)
+    qh_option(qh, "Centrum-postmerge-with-random", NULL, &qh->postmerge_centrum);
+  { /* compute ONEmerge, max vertex offset for merging simplicial facets */
+    realT maxangle= 1.0, maxrho;
+
+    minimize_(maxangle, qh->premerge_cos);
+    minimize_(maxangle, qh->postmerge_cos);
+    /* max diameter * sin theta + DISTround for vertex to its hyperplane */
+    qh->ONEmerge= sqrt((realT)qh->hull_dim) * qh->MAXwidth *
+      sqrt(1.0 - maxangle * maxangle) + qh->DISTround;
+    maxrho= qh->hull_dim * qh->premerge_centrum + qh->DISTround;
+    maximize_(qh->ONEmerge, maxrho);
+    maxrho= qh->hull_dim * qh->postmerge_centrum + qh->DISTround;
+    maximize_(qh->ONEmerge, maxrho);
+    if (qh->MERGING)
+      qh_option(qh, "_one-merge", NULL, &qh->ONEmerge);
+  }
+  qh->NEARinside= qh->ONEmerge * qh_RATIOnearinside; /* only used if qh->KEEPnearinside */
+  if (qh->JOGGLEmax < REALmax/2 && (qh->KEEPcoplanar || qh->KEEPinside)) {
+    realT maxdist;             /* adjust qh.NEARinside for joggle */
+    qh->KEEPnearinside= True;
+    maxdist= sqrt((realT)qh->hull_dim) * qh->JOGGLEmax + qh->DISTround;
+    maxdist= 2*maxdist;        /* vertex and coplanar point can joggle in opposite directions */
+    maximize_(qh->NEARinside, maxdist);  /* must agree with qh_nearcoplanar() */
+  }
+  if (qh->KEEPnearinside)
+    qh_option(qh, "_near-inside", NULL, &qh->NEARinside);
+  if (qh->JOGGLEmax < qh->DISTround) {
+    qh_fprintf(qh, qh->ferr, 6006, "qhull error: the joggle for 'QJn', %.2g, is below roundoff for distance computations, %.2g\n",
+         qh->JOGGLEmax, qh->DISTround);
+    qh_errexit(qh, qh_ERRinput, NULL, NULL);
+  }
+  if (qh->MINvisible > REALmax/2) {
+    if (!qh->MERGING)
+      qh->MINvisible= qh->DISTround;
+    else if (qh->hull_dim <= 3)
+      qh->MINvisible= qh->premerge_centrum;
+    else
+      qh->MINvisible= qh_COPLANARratio * qh->premerge_centrum;
+    if (qh->APPROXhull && qh->MINvisible > qh->MINoutside)
+      qh->MINvisible= qh->MINoutside;
+    qh_option(qh, "Visible-distance", NULL, &qh->MINvisible);
+  }
+  if (qh->MAXcoplanar > REALmax/2) {
+    qh->MAXcoplanar= qh->MINvisible;
+    qh_option(qh, "U-coplanar-distance", NULL, &qh->MAXcoplanar);
+  }
+  if (!qh->APPROXhull) {             /* user may specify qh->MINoutside */
+    qh->MINoutside= 2 * qh->MINvisible;
+    if (qh->premerge_cos < REALmax/2)
+      maximize_(qh->MINoutside, (1- qh->premerge_cos) * qh->MAXabs_coord);
+    qh_option(qh, "Width-outside", NULL, &qh->MINoutside);
+  }
+  qh->WIDEfacet= qh->MINoutside;
+  maximize_(qh->WIDEfacet, qh_WIDEcoplanar * qh->MAXcoplanar);
+  maximize_(qh->WIDEfacet, qh_WIDEcoplanar * qh->MINvisible);
+  qh_option(qh, "_wide-facet", NULL, &qh->WIDEfacet);
+  if (qh->MINvisible > qh->MINoutside + 3 * REALepsilon
+  && !qh->BESToutside && !qh->FORCEoutput)
+    qh_fprintf(qh, qh->ferr, 7001, "qhull input warning: minimum visibility V%.2g is greater than \nminimum outside W%.2g.  Flipped facets are likely.\n",
+             qh->MINvisible, qh->MINoutside);
+  qh->max_vertex= qh->DISTround;
+  qh->min_vertex= -qh->DISTround;
+  /* numeric constants reported in printsummary */
+} /* detroundoff */
+
+/*---------------------------------
+
+  qh_detsimplex(qh, apex, points, dim, nearzero )
+    compute determinant of a simplex with point apex and base points
+
+  returns:
+     signed determinant and nearzero from qh_determinant
+
+  notes:
+     uses qh.gm_matrix/qh.gm_row (assumes they're big enough)
+
+  design:
+    construct qm_matrix by subtracting apex from points
+    compute determinate
+*/
+realT qh_detsimplex(qhT *qh, pointT *apex, setT *points, int dim, boolT *nearzero) {
+  pointT *coorda, *coordp, *gmcoord, *point, **pointp;
+  coordT **rows;
+  int k,  i=0;
+  realT det;
+
+  zinc_(Zdetsimplex);
+  gmcoord= qh->gm_matrix;
+  rows= qh->gm_row;
+  FOREACHpoint_(points) {
+    if (i == dim)
+      break;
+    rows[i++]= gmcoord;
+    coordp= point;
+    coorda= apex;
+    for (k=dim; k--; )
+      *(gmcoord++)= *coordp++ - *coorda++;
+  }
+  if (i < dim) {
+    qh_fprintf(qh, qh->ferr, 6007, "qhull internal error (qh_detsimplex): #points %d < dimension %d\n",
+               i, dim);
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }
+  det= qh_determinant(qh, rows, dim, nearzero);
+  trace2((qh, qh->ferr, 2002, "qh_detsimplex: det=%2.2g for point p%d, dim %d, nearzero? %d\n",
+          det, qh_pointid(qh, apex), dim, *nearzero));
+  return det;
+} /* detsimplex */
+
+/*---------------------------------
+
+  qh_distnorm( dim, point, normal, offset )
+    return distance from point to hyperplane at normal/offset
+
+  returns:
+    dist
+
+  notes:
+    dist > 0 if point is outside of hyperplane
+
+  see:
+    qh_distplane in geom_r.c
+*/
+realT qh_distnorm(int dim, pointT *point, pointT *normal, realT *offsetp) {
+  coordT *normalp= normal, *coordp= point;
+  realT dist;
+  int k;
+
+  dist= *offsetp;
+  for (k=dim; k--; )
+    dist += *(coordp++) * *(normalp++);
+  return dist;
+} /* distnorm */
+
+/*---------------------------------
+
+  qh_distround(qh, dimension, maxabs, maxsumabs )
+    compute maximum round-off error for a distance computation
+      to a normalized hyperplane
+    maxabs is the maximum absolute value of a coordinate
+    maxsumabs is the maximum possible sum of absolute coordinate values
+
+  returns:
+    max dist round for REALepsilon
+
+  notes:
+    calculate roundoff error according to Golub & van Loan, 1983, Lemma 3.2-1, "Rounding Errors"
+    use sqrt(dim) since one vector is normalized
+      or use maxsumabs since one vector is < 1
+*/
+realT qh_distround(qhT *qh, int dimension, realT maxabs, realT maxsumabs) {
+  realT maxdistsum, maxround;
+
+  maxdistsum= sqrt((realT)dimension) * maxabs;
+  minimize_( maxdistsum, maxsumabs);
+  maxround= REALepsilon * (dimension * maxdistsum * 1.01 + maxabs);
+              /* adds maxabs for offset */
+  trace4((qh, qh->ferr, 4008, "qh_distround: %2.2g maxabs %2.2g maxsumabs %2.2g maxdistsum %2.2g\n",
+                 maxround, maxabs, maxsumabs, maxdistsum));
+  return maxround;
+} /* distround */
+
+/*---------------------------------
+
+  qh_divzero( numer, denom, mindenom1, zerodiv )
+    divide by a number that's nearly zero
+    mindenom1= minimum denominator for dividing into 1.0
+
+  returns:
+    quotient
+    sets zerodiv and returns 0.0 if it would overflow
+
+  design:
+    if numer is nearly zero and abs(numer) < abs(denom)
+      return numer/denom
+    else if numer is nearly zero
+      return 0 and zerodiv
+    else if denom/numer non-zero
+      return numer/denom
+    else
+      return 0 and zerodiv
+*/
+realT qh_divzero(realT numer, realT denom, realT mindenom1, boolT *zerodiv) {
+  realT temp, numerx, denomx;
+
+
+  if (numer < mindenom1 && numer > -mindenom1) {
+    numerx= fabs_(numer);
+    denomx= fabs_(denom);
+    if (numerx < denomx) {
+      *zerodiv= False;
+      return numer/denom;
+    }else {
+      *zerodiv= True;
+      return 0.0;
+    }
+  }
+  temp= denom/numer;
+  if (temp > mindenom1 || temp < -mindenom1) {
+    *zerodiv= False;
+    return numer/denom;
+  }else {
+    *zerodiv= True;
+    return 0.0;
+  }
+} /* divzero */
+
+
+/*---------------------------------
+
+  qh_facetarea(qh, facet )
+    return area for a facet
+
+  notes:
+    if non-simplicial,
+      uses centrum to triangulate facet and sums the projected areas.
+    if (qh->DELAUNAY),
+      computes projected area instead for last coordinate
+    assumes facet->normal exists
+    projecting tricoplanar facets to the hyperplane does not appear to make a difference
+
+  design:
+    if simplicial
+      compute area
+    else
+      for each ridge
+        compute area from centrum to ridge
+    negate area if upper Delaunay facet
+*/
+realT qh_facetarea(qhT *qh, facetT *facet) {
+  vertexT *apex;
+  pointT *centrum;
+  realT area= 0.0;
+  ridgeT *ridge, **ridgep;
+
+  if (facet->simplicial) {
+    apex= SETfirstt_(facet->vertices, vertexT);
+    area= qh_facetarea_simplex(qh, qh->hull_dim, apex->point, facet->vertices,
+                    apex, facet->toporient, facet->normal, &facet->offset);
+  }else {
+    if (qh->CENTERtype == qh_AScentrum)
+      centrum= facet->center;
+    else
+      centrum= qh_getcentrum(qh, facet);
+    FOREACHridge_(facet->ridges)
+      area += qh_facetarea_simplex(qh, qh->hull_dim, centrum, ridge->vertices,
+                 NULL, (boolT)(ridge->top == facet),  facet->normal, &facet->offset);
+    if (qh->CENTERtype != qh_AScentrum)
+      qh_memfree(qh, centrum, qh->normal_size);
+  }
+  if (facet->upperdelaunay && qh->DELAUNAY)
+    area= -area;  /* the normal should be [0,...,1] */
+  trace4((qh, qh->ferr, 4009, "qh_facetarea: f%d area %2.2g\n", facet->id, area));
+  return area;
+} /* facetarea */
+
+/*---------------------------------
+
+  qh_facetarea_simplex(qh, dim, apex, vertices, notvertex, toporient, normal, offset )
+    return area for a simplex defined by
+      an apex, a base of vertices, an orientation, and a unit normal
+    if simplicial or tricoplanar facet,
+      notvertex is defined and it is skipped in vertices
+
+  returns:
+    computes area of simplex projected to plane [normal,offset]
+    returns 0 if vertex too far below plane (qh->WIDEfacet)
+      vertex can't be apex of tricoplanar facet
+
+  notes:
+    if (qh->DELAUNAY),
+      computes projected area instead for last coordinate
+    uses qh->gm_matrix/gm_row and qh->hull_dim
+    helper function for qh_facetarea
+
+  design:
+    if Notvertex
+      translate simplex to apex
+    else
+      project simplex to normal/offset
+      translate simplex to apex
+    if Delaunay
+      set last row/column to 0 with -1 on diagonal
+    else
+      set last row to Normal
+    compute determinate
+    scale and flip sign for area
+*/
+realT qh_facetarea_simplex(qhT *qh, int dim, coordT *apex, setT *vertices,
+        vertexT *notvertex,  boolT toporient, coordT *normal, realT *offset) {
+  pointT *coorda, *coordp, *gmcoord;
+  coordT **rows, *normalp;
+  int k,  i=0;
+  realT area, dist;
+  vertexT *vertex, **vertexp;
+  boolT nearzero;
+
+  gmcoord= qh->gm_matrix;
+  rows= qh->gm_row;
+  FOREACHvertex_(vertices) {
+    if (vertex == notvertex)
+      continue;
+    rows[i++]= gmcoord;
+    coorda= apex;
+    coordp= vertex->point;
+    normalp= normal;
+    if (notvertex) {
+      for (k=dim; k--; )
+        *(gmcoord++)= *coordp++ - *coorda++;
+    }else {
+      dist= *offset;
+      for (k=dim; k--; )
+        dist += *coordp++ * *normalp++;
+      if (dist < -qh->WIDEfacet) {
+        zinc_(Znoarea);
+        return 0.0;
+      }
+      coordp= vertex->point;
+      normalp= normal;
+      for (k=dim; k--; )
+        *(gmcoord++)= (*coordp++ - dist * *normalp++) - *coorda++;
+    }
+  }
+  if (i != dim-1) {
+    qh_fprintf(qh, qh->ferr, 6008, "qhull internal error (qh_facetarea_simplex): #points %d != dim %d -1\n",
+               i, dim);
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }
+  rows[i]= gmcoord;
+  if (qh->DELAUNAY) {
+    for (i=0; i < dim-1; i++)
+      rows[i][dim-1]= 0.0;
+    for (k=dim; k--; )
+      *(gmcoord++)= 0.0;
+    rows[dim-1][dim-1]= -1.0;
+  }else {
+    normalp= normal;
+    for (k=dim; k--; )
+      *(gmcoord++)= *normalp++;
+  }
+  zinc_(Zdetsimplex);
+  area= qh_determinant(qh, rows, dim, &nearzero);
+  if (toporient)
+    area= -area;
+  area *= qh->AREAfactor;
+  trace4((qh, qh->ferr, 4010, "qh_facetarea_simplex: area=%2.2g for point p%d, toporient %d, nearzero? %d\n",
+          area, qh_pointid(qh, apex), toporient, nearzero));
+  return area;
+} /* facetarea_simplex */
+
+/*---------------------------------
+
+  qh_facetcenter(qh, vertices )
+    return Voronoi center (Voronoi vertex) for a facet's vertices
+
+  returns:
+    return temporary point equal to the center
+
+  see:
+    qh_voronoi_center()
+*/
+pointT *qh_facetcenter(qhT *qh, setT *vertices) {
+  setT *points= qh_settemp(qh, qh_setsize(qh, vertices));
+  vertexT *vertex, **vertexp;
+  pointT *center;
+
+  FOREACHvertex_(vertices)
+    qh_setappend(qh, &points, vertex->point);
+  center= qh_voronoi_center(qh, qh->hull_dim-1, points);
+  qh_settempfree(qh, &points);
+  return center;
+} /* facetcenter */
+
+/*---------------------------------
+
+  qh_findgooddist(qh, point, facetA, dist, facetlist )
+    find best good facet visible for point from facetA
+    assumes facetA is visible from point
+
+  returns:
+    best facet, i.e., good facet that is furthest from point
+      distance to best facet
+      NULL if none
+
+    moves good, visible facets (and some other visible facets)
+      to end of qh->facet_list
+
+  notes:
+    uses qh->visit_id
+
+  design:
+    initialize bestfacet if facetA is good
+    move facetA to end of facetlist
+    for each facet on facetlist
+      for each unvisited neighbor of facet
+        move visible neighbors to end of facetlist
+        update best good neighbor
+        if no good neighbors, update best facet
+*/
+facetT *qh_findgooddist(qhT *qh, pointT *point, facetT *facetA, realT *distp,
+               facetT **facetlist) {
+  realT bestdist= -REALmax, dist;
+  facetT *neighbor, **neighborp, *bestfacet=NULL, *facet;
+  boolT goodseen= False;
+
+  if (facetA->good) {
+    zzinc_(Zcheckpart);  /* calls from check_bestdist occur after print stats */
+    qh_distplane(qh, point, facetA, &bestdist);
+    bestfacet= facetA;
+    goodseen= True;
+  }
+  qh_removefacet(qh, facetA);
+  qh_appendfacet(qh, facetA);
+  *facetlist= facetA;
+  facetA->visitid= ++qh->visit_id;
+  FORALLfacet_(*facetlist) {
+    FOREACHneighbor_(facet) {
+      if (neighbor->visitid == qh->visit_id)
+        continue;
+      neighbor->visitid= qh->visit_id;
+      if (goodseen && !neighbor->good)
+        continue;
+      zzinc_(Zcheckpart);
+      qh_distplane(qh, point, neighbor, &dist);
+      if (dist > 0) {
+        qh_removefacet(qh, neighbor);
+        qh_appendfacet(qh, neighbor);
+        if (neighbor->good) {
+          goodseen= True;
+          if (dist > bestdist) {
+            bestdist= dist;
+            bestfacet= neighbor;
+          }
+        }
+      }
+    }
+  }
+  if (bestfacet) {
+    *distp= bestdist;
+    trace2((qh, qh->ferr, 2003, "qh_findgooddist: p%d is %2.2g above good facet f%d\n",
+      qh_pointid(qh, point), bestdist, bestfacet->id));
+    return bestfacet;
+  }
+  trace4((qh, qh->ferr, 4011, "qh_findgooddist: no good facet for p%d above f%d\n",
+      qh_pointid(qh, point), facetA->id));
+  return NULL;
+}  /* findgooddist */
+
+/*---------------------------------
+
+  qh_getarea(qh, facetlist )
+    set area of all facets in facetlist
+    collect statistics
+    nop if hasAreaVolume
+
+  returns:
+    sets qh->totarea/totvol to total area and volume of convex hull
+    for Delaunay triangulation, computes projected area of the lower or upper hull
+      ignores upper hull if qh->ATinfinity
+
+  notes:
+    could compute outer volume by expanding facet area by rays from interior
+    the following attempt at perpendicular projection underestimated badly:
+      qh.totoutvol += (-dist + facet->maxoutside + qh->DISTround)
+                            * area/ qh->hull_dim;
+  design:
+    for each facet on facetlist
+      compute facet->area
+      update qh.totarea and qh.totvol
+*/
+void qh_getarea(qhT *qh, facetT *facetlist) {
+  realT area;
+  realT dist;
+  facetT *facet;
+
+  if (qh->hasAreaVolume)
+    return;
+  if (qh->REPORTfreq)
+    qh_fprintf(qh, qh->ferr, 8020, "computing area of each facet and volume of the convex hull\n");
+  else
+    trace1((qh, qh->ferr, 1001, "qh_getarea: computing volume and area for each facet\n"));
+  qh->totarea= qh->totvol= 0.0;
+  FORALLfacet_(facetlist) {
+    if (!facet->normal)
+      continue;
+    if (facet->upperdelaunay && qh->ATinfinity)
+      continue;
+    if (!facet->isarea) {
+      facet->f.area= qh_facetarea(qh, facet);
+      facet->isarea= True;
+    }
+    area= facet->f.area;
+    if (qh->DELAUNAY) {
+      if (facet->upperdelaunay == qh->UPPERdelaunay)
+        qh->totarea += area;
+    }else {
+      qh->totarea += area;
+      qh_distplane(qh, qh->interior_point, facet, &dist);
+      qh->totvol += -dist * area/ qh->hull_dim;
+    }
+    if (qh->PRINTstatistics) {
+      wadd_(Wareatot, area);
+      wmax_(Wareamax, area);
+      wmin_(Wareamin, area);
+    }
+  }
+  qh->hasAreaVolume= True;
+} /* getarea */
+
+/*---------------------------------
+
+  qh_gram_schmidt(qh, dim, row )
+    implements Gram-Schmidt orthogonalization by rows
+
+  returns:
+    false if zero norm
+    overwrites rows[dim][dim]
+
+  notes:
+    see Golub & van Loan, 1983, Algorithm 6.2-2, "Modified Gram-Schmidt"
+    overflow due to small divisors not handled
+
+  design:
+    for each row
+      compute norm for row
+      if non-zero, normalize row
+      for each remaining rowA
+        compute inner product of row and rowA
+        reduce rowA by row * inner product
+*/
+boolT qh_gram_schmidt(qhT *qh, int dim, realT **row) {
+  realT *rowi, *rowj, norm;
+  int i, j, k;
+
+  for (i=0; i < dim; i++) {
+    rowi= row[i];
+    for (norm= 0.0, k= dim; k--; rowi++)
+      norm += *rowi * *rowi;
+    norm= sqrt(norm);
+    wmin_(Wmindenom, norm);
+    if (norm == 0.0)  /* either 0 or overflow due to sqrt */
+      return False;
+    for (k=dim; k--; )
+      *(--rowi) /= norm;
+    for (j=i+1; j < dim; j++) {
+      rowj= row[j];
+      for (norm= 0.0, k=dim; k--; )
+        norm += *rowi++ * *rowj++;
+      for (k=dim; k--; )
+        *(--rowj) -= *(--rowi) * norm;
+    }
+  }
+  return True;
+} /* gram_schmidt */
+
+
+/*---------------------------------
+
+  qh_inthresholds(qh, normal, angle )
+    return True if normal within qh.lower_/upper_threshold
+
+  returns:
+    estimate of angle by summing of threshold diffs
+      angle may be NULL
+      smaller "angle" is better
+
+  notes:
+    invalid if qh.SPLITthresholds
+
+  see:
+    qh.lower_threshold in qh_initbuild()
+    qh_initthresholds()
+
+  design:
+    for each dimension
+      test threshold
+*/
+boolT qh_inthresholds(qhT *qh, coordT *normal, realT *angle) {
+  boolT within= True;
+  int k;
+  realT threshold;
+
+  if (angle)
+    *angle= 0.0;
+  for (k=0; k < qh->hull_dim; k++) {
+    threshold= qh->lower_threshold[k];
+    if (threshold > -REALmax/2) {
+      if (normal[k] < threshold)
+        within= False;
+      if (angle) {
+        threshold -= normal[k];
+        *angle += fabs_(threshold);
+      }
+    }
+    if (qh->upper_threshold[k] < REALmax/2) {
+      threshold= qh->upper_threshold[k];
+      if (normal[k] > threshold)
+        within= False;
+      if (angle) {
+        threshold -= normal[k];
+        *angle += fabs_(threshold);
+      }
+    }
+  }
+  return within;
+} /* inthresholds */
+
+
+/*---------------------------------
+
+  qh_joggleinput(qh)
+    randomly joggle input to Qhull by qh.JOGGLEmax
+    initial input is qh.first_point/qh.num_points of qh.hull_dim
+      repeated calls use qh.input_points/qh.num_points
+
+  returns:
+    joggles points at qh.first_point/qh.num_points
+    copies data to qh.input_points/qh.input_malloc if first time
+    determines qh.JOGGLEmax if it was zero
+    if qh.DELAUNAY
+      computes the Delaunay projection of the joggled points
+
+  notes:
+    if qh.DELAUNAY, unnecessarily joggles the last coordinate
+    the initial 'QJn' may be set larger than qh_JOGGLEmaxincrease
+
+  design:
+    if qh.DELAUNAY
+      set qh.SCALElast for reduced precision errors
+    if first call
+      initialize qh.input_points to the original input points
+      if qh.JOGGLEmax == 0
+        determine default qh.JOGGLEmax
+    else
+      increase qh.JOGGLEmax according to qh.build_cnt
+    joggle the input by adding a random number in [-qh.JOGGLEmax,qh.JOGGLEmax]
+    if qh.DELAUNAY
+      sets the Delaunay projection
+*/
+void qh_joggleinput(qhT *qh) {
+  int i, seed, size;
+  coordT *coordp, *inputp;
+  realT randr, randa, randb;
+
+  if (!qh->input_points) { /* first call */
+    qh->input_points= qh->first_point;
+    qh->input_malloc= qh->POINTSmalloc;
+    size= qh->num_points * qh->hull_dim * sizeof(coordT);
+    if (!(qh->first_point=(coordT*)qh_malloc((size_t)size))) {
+      qh_fprintf(qh, qh->ferr, 6009, "qhull error: insufficient memory to joggle %d points\n",
+          qh->num_points);
+      qh_errexit(qh, qh_ERRmem, NULL, NULL);
+    }
+    qh->POINTSmalloc= True;
+    if (qh->JOGGLEmax == 0.0) {
+      qh->JOGGLEmax= qh_detjoggle(qh, qh->input_points, qh->num_points, qh->hull_dim);
+      qh_option(qh, "QJoggle", NULL, &qh->JOGGLEmax);
+    }
+  }else {                 /* repeated call */
+    if (!qh->RERUN && qh->build_cnt > qh_JOGGLEretry) {
+      if (((qh->build_cnt-qh_JOGGLEretry-1) % qh_JOGGLEagain) == 0) {
+        realT maxjoggle= qh->MAXwidth * qh_JOGGLEmaxincrease;
+        if (qh->JOGGLEmax < maxjoggle) {
+          qh->JOGGLEmax *= qh_JOGGLEincrease;
+          minimize_(qh->JOGGLEmax, maxjoggle);
+        }
+      }
+    }
+    qh_option(qh, "QJoggle", NULL, &qh->JOGGLEmax);
+  }
+  if (qh->build_cnt > 1 && qh->JOGGLEmax > fmax_(qh->MAXwidth/4, 0.1)) {
+      qh_fprintf(qh, qh->ferr, 6010, "qhull error: the current joggle for 'QJn', %.2g, is too large for the width\nof the input.  If possible, recompile Qhull with higher-precision reals.\n",
+                qh->JOGGLEmax);
+      qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }
+  /* for some reason, using qh->ROTATErandom and qh_RANDOMseed does not repeat the run. Use 'TRn' instead */
+  seed= qh_RANDOMint;
+  qh_option(qh, "_joggle-seed", &seed, NULL);
+  trace0((qh, qh->ferr, 6, "qh_joggleinput: joggle input by %2.2g with seed %d\n",
+    qh->JOGGLEmax, seed));
+  inputp= qh->input_points;
+  coordp= qh->first_point;
+  randa= 2.0 * qh->JOGGLEmax/qh_RANDOMmax;
+  randb= -qh->JOGGLEmax;
+  size= qh->num_points * qh->hull_dim;
+  for (i=size; i--; ) {
+    randr= qh_RANDOMint;
+    *(coordp++)= *(inputp++) + (randr * randa + randb);
+  }
+  if (qh->DELAUNAY) {
+    qh->last_low= qh->last_high= qh->last_newhigh= REALmax;
+    qh_setdelaunay(qh, qh->hull_dim, qh->num_points, qh->first_point);
+  }
+} /* joggleinput */
+
+/*---------------------------------
+
+  qh_maxabsval( normal, dim )
+    return pointer to maximum absolute value of a dim vector
+    returns NULL if dim=0
+*/
+realT *qh_maxabsval(realT *normal, int dim) {
+  realT maxval= -REALmax;
+  realT *maxp= NULL, *colp, absval;
+  int k;
+
+  for (k=dim, colp= normal; k--; colp++) {
+    absval= fabs_(*colp);
+    if (absval > maxval) {
+      maxval= absval;
+      maxp= colp;
+    }
+  }
+  return maxp;
+} /* maxabsval */
+
+
+/*---------------------------------
+
+  qh_maxmin(qh, points, numpoints, dimension )
+    return max/min points for each dimension
+    determine max and min coordinates
+
+  returns:
+    returns a temporary set of max and min points
+      may include duplicate points. Does not include qh.GOODpoint
+    sets qh.NEARzero, qh.MAXabs_coord, qh.MAXsumcoord, qh.MAXwidth
+         qh.MAXlastcoord, qh.MINlastcoord
+    initializes qh.max_outside, qh.min_vertex, qh.WAScoplanar, qh.ZEROall_ok
+
+  notes:
+    loop duplicated in qh_detjoggle()
+
+  design:
+    initialize global precision variables
+    checks definition of REAL...
+    for each dimension
+      for each point
+        collect maximum and minimum point
+      collect maximum of maximums and minimum of minimums
+      determine qh.NEARzero for Gaussian Elimination
+*/
+setT *qh_maxmin(qhT *qh, pointT *points, int numpoints, int dimension) {
+  int k;
+  realT maxcoord, temp;
+  pointT *minimum, *maximum, *point, *pointtemp;
+  setT *set;
+
+  qh->max_outside= 0.0;
+  qh->MAXabs_coord= 0.0;
+  qh->MAXwidth= -REALmax;
+  qh->MAXsumcoord= 0.0;
+  qh->min_vertex= 0.0;
+  qh->WAScoplanar= False;
+  if (qh->ZEROcentrum)
+    qh->ZEROall_ok= True;
+  if (REALmin < REALepsilon && REALmin < REALmax && REALmin > -REALmax
+  && REALmax > 0.0 && -REALmax < 0.0)
+    ; /* all ok */
+  else {
+    qh_fprintf(qh, qh->ferr, 6011, "qhull error: floating point constants in user.h are wrong\n\
+REALepsilon %g REALmin %g REALmax %g -REALmax %g\n",
+             REALepsilon, REALmin, REALmax, -REALmax);
+    qh_errexit(qh, qh_ERRinput, NULL, NULL);
+  }
+  set= qh_settemp(qh, 2*dimension);
+  for (k=0; k < dimension; k++) {
+    if (points == qh->GOODpointp)
+      minimum= maximum= points + dimension;
+    else
+      minimum= maximum= points;
+    FORALLpoint_(qh, points, numpoints) {
+      if (point == qh->GOODpointp)
+        continue;
+      if (maximum[k] < point[k])
+        maximum= point;
+      else if (minimum[k] > point[k])
+        minimum= point;
+    }
+    if (k == dimension-1) {
+      qh->MINlastcoord= minimum[k];
+      qh->MAXlastcoord= maximum[k];
+    }
+    if (qh->SCALElast && k == dimension-1)
+      maxcoord= qh->MAXwidth;
+    else {
+      maxcoord= fmax_(maximum[k], -minimum[k]);
+      if (qh->GOODpointp) {
+        temp= fmax_(qh->GOODpointp[k], -qh->GOODpointp[k]);
+        maximize_(maxcoord, temp);
+      }
+      temp= maximum[k] - minimum[k];
+      maximize_(qh->MAXwidth, temp);
+    }
+    maximize_(qh->MAXabs_coord, maxcoord);
+    qh->MAXsumcoord += maxcoord;
+    qh_setappend(qh, &set, maximum);
+    qh_setappend(qh, &set, minimum);
+    /* calculation of qh NEARzero is based on Golub & van Loan, 1983,
+       Eq. 4.4-13 for "Gaussian elimination with complete pivoting".
+       Golub & van Loan say that n^3 can be ignored and 10 be used in
+       place of rho */
+    qh->NEARzero[k]= 80 * qh->MAXsumcoord * REALepsilon;
+  }
+  if (qh->IStracing >=1)
+    qh_printpoints(qh, qh->ferr, "qh_maxmin: found the max and min points(by dim):", set);
+  return(set);
+} /* maxmin */
+
+/*---------------------------------
+
+  qh_maxouter(qh)
+    return maximum distance from facet to outer plane
+    normally this is qh.max_outside+qh.DISTround
+    does not include qh.JOGGLEmax
+
+  see:
+    qh_outerinner()
+
+  notes:
+    need to add another qh.DISTround if testing actual point with computation
+
+  for joggle:
+    qh_setfacetplane() updated qh.max_outer for Wnewvertexmax (max distance to vertex)
+    need to use Wnewvertexmax since could have a coplanar point for a high
+      facet that is replaced by a low facet
+    need to add qh.JOGGLEmax if testing input points
+*/
+realT qh_maxouter(qhT *qh) {
+  realT dist;
+
+  dist= fmax_(qh->max_outside, qh->DISTround);
+  dist += qh->DISTround;
+  trace4((qh, qh->ferr, 4012, "qh_maxouter: max distance from facet to outer plane is %2.2g max_outside is %2.2g\n", dist, qh->max_outside));
+  return dist;
+} /* maxouter */
+
+/*---------------------------------
+
+  qh_maxsimplex(qh, dim, maxpoints, points, numpoints, simplex )
+    determines maximum simplex for a set of points
+    starts from points already in simplex
+    skips qh.GOODpointp (assumes that it isn't in maxpoints)
+
+  returns:
+    simplex with dim+1 points
+
+  notes:
+    assumes at least pointsneeded points in points
+    maximizes determinate for x,y,z,w, etc.
+    uses maxpoints as long as determinate is clearly non-zero
+
+  design:
+    initialize simplex with at least two points
+      (find points with max or min x coordinate)
+    for each remaining dimension
+      add point that maximizes the determinate
+        (use points from maxpoints first)
+*/
+void qh_maxsimplex(qhT *qh, int dim, setT *maxpoints, pointT *points, int numpoints, setT **simplex) {
+  pointT *point, **pointp, *pointtemp, *maxpoint, *minx=NULL, *maxx=NULL;
+  boolT nearzero, maxnearzero= False;
+  int k, sizinit;
+  realT maxdet= -REALmax, det, mincoord= REALmax, maxcoord= -REALmax;
+
+  sizinit= qh_setsize(qh, *simplex);
+  if (sizinit < 2) {
+    if (qh_setsize(qh, maxpoints) >= 2) {
+      FOREACHpoint_(maxpoints) {
+        if (maxcoord < point[0]) {
+          maxcoord= point[0];
+          maxx= point;
+        }
+        if (mincoord > point[0]) {
+          mincoord= point[0];
+          minx= point;
+        }
+      }
+    }else {
+      FORALLpoint_(qh, points, numpoints) {
+        if (point == qh->GOODpointp)
+          continue;
+        if (maxcoord < point[0]) {
+          maxcoord= point[0];
+          maxx= point;
+        }
+        if (mincoord > point[0]) {
+          mincoord= point[0];
+          minx= point;
+        }
+      }
+    }
+    qh_setunique(qh, simplex, minx);
+    if (qh_setsize(qh, *simplex) < 2)
+      qh_setunique(qh, simplex, maxx);
+    sizinit= qh_setsize(qh, *simplex);
+    if (sizinit < 2) {
+      qh_precision(qh, "input has same x coordinate");
+      if (zzval_(Zsetplane) > qh->hull_dim+1) {
+        qh_fprintf(qh, qh->ferr, 6012, "qhull precision error (qh_maxsimplex for voronoi_center):\n%d points with the same x coordinate.\n",
+                 qh_setsize(qh, maxpoints)+numpoints);
+        qh_errexit(qh, qh_ERRprec, NULL, NULL);
+      }else {
+        qh_fprintf(qh, qh->ferr, 6013, "qhull input error: input is less than %d-dimensional since it has the same x coordinate\n", qh->hull_dim);
+        qh_errexit(qh, qh_ERRinput, NULL, NULL);
+      }
+    }
+  }
+  for (k=sizinit; k < dim+1; k++) {
+    maxpoint= NULL;
+    maxdet= -REALmax;
+    FOREACHpoint_(maxpoints) {
+      if (!qh_setin(*simplex, point)) {
+        det= qh_detsimplex(qh, point, *simplex, k, &nearzero);
+        if ((det= fabs_(det)) > maxdet) {
+          maxdet= det;
+          maxpoint= point;
+          maxnearzero= nearzero;
+        }
+      }
+    }
+    if (!maxpoint || maxnearzero) {
+      zinc_(Zsearchpoints);
+      if (!maxpoint) {
+        trace0((qh, qh->ferr, 7, "qh_maxsimplex: searching all points for %d-th initial vertex.\n", k+1));
+      }else {
+        trace0((qh, qh->ferr, 8, "qh_maxsimplex: searching all points for %d-th initial vertex, better than p%d det %2.2g\n",
+                k+1, qh_pointid(qh, maxpoint), maxdet));
+      }
+      FORALLpoint_(qh, points, numpoints) {
+        if (point == qh->GOODpointp)
+          continue;
+        if (!qh_setin(*simplex, point)) {
+          det= qh_detsimplex(qh, point, *simplex, k, &nearzero);
+          if ((det= fabs_(det)) > maxdet) {
+            maxdet= det;
+            maxpoint= point;
+            maxnearzero= nearzero;
+          }
+        }
+      }
+    } /* !maxpoint */
+    if (!maxpoint) {
+      qh_fprintf(qh, qh->ferr, 6014, "qhull internal error (qh_maxsimplex): not enough points available\n");
+      qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+    }
+    qh_setappend(qh, simplex, maxpoint);
+    trace1((qh, qh->ferr, 1002, "qh_maxsimplex: selected point p%d for %d`th initial vertex, det=%2.2g\n",
+            qh_pointid(qh, maxpoint), k+1, maxdet));
+  } /* k */
+} /* maxsimplex */
+
+/*---------------------------------
+
+  qh_minabsval( normal, dim )
+    return minimum absolute value of a dim vector
+*/
+realT qh_minabsval(realT *normal, int dim) {
+  realT minval= 0;
+  realT maxval= 0;
+  realT *colp;
+  int k;
+
+  for (k=dim, colp=normal; k--; colp++) {
+    maximize_(maxval, *colp);
+    minimize_(minval, *colp);
+  }
+  return fmax_(maxval, -minval);
+} /* minabsval */
+
+
+/*---------------------------------
+
+  qh_mindif(qh, vecA, vecB, dim )
+    return index of min abs. difference of two vectors
+*/
+int qh_mindiff(realT *vecA, realT *vecB, int dim) {
+  realT mindiff= REALmax, diff;
+  realT *vecAp= vecA, *vecBp= vecB;
+  int k, mink= 0;
+
+  for (k=0; k < dim; k++) {
+    diff= *vecAp++ - *vecBp++;
+    diff= fabs_(diff);
+    if (diff < mindiff) {
+      mindiff= diff;
+      mink= k;
+    }
+  }
+  return mink;
+} /* mindiff */
+
+
+
+/*---------------------------------
+
+  qh_orientoutside(qh, facet  )
+    make facet outside oriented via qh.interior_point
+
+  returns:
+    True if facet reversed orientation.
+*/
+boolT qh_orientoutside(qhT *qh, facetT *facet) {
+  int k;
+  realT dist;
+
+  qh_distplane(qh, qh->interior_point, facet, &dist);
+  if (dist > 0) {
+    for (k=qh->hull_dim; k--; )
+      facet->normal[k]= -facet->normal[k];
+    facet->offset= -facet->offset;
+    return True;
+  }
+  return False;
+} /* orientoutside */
+
+/*---------------------------------
+
+  qh_outerinner(qh, facet, outerplane, innerplane  )
+    if facet and qh.maxoutdone (i.e., qh_check_maxout)
+      returns outer and inner plane for facet
+    else
+      returns maximum outer and inner plane
+    accounts for qh.JOGGLEmax
+
+  see:
+    qh_maxouter(qh), qh_check_bestdist(), qh_check_points()
+
+  notes:
+    outerplaner or innerplane may be NULL
+    facet is const
+    Does not error (QhullFacet)
+
+    includes qh.DISTround for actual points
+    adds another qh.DISTround if testing with floating point arithmetic
+*/
+void qh_outerinner(qhT *qh, facetT *facet, realT *outerplane, realT *innerplane) {
+  realT dist, mindist;
+  vertexT *vertex, **vertexp;
+
+  if (outerplane) {
+    if (!qh_MAXoutside || !facet || !qh->maxoutdone) {
+      *outerplane= qh_maxouter(qh);       /* includes qh.DISTround */
+    }else { /* qh_MAXoutside ... */
+#if qh_MAXoutside
+      *outerplane= facet->maxoutside + qh->DISTround;
+#endif
+
+    }
+    if (qh->JOGGLEmax < REALmax/2)
+      *outerplane += qh->JOGGLEmax * sqrt((realT)qh->hull_dim);
+  }
+  if (innerplane) {
+    if (facet) {
+      mindist= REALmax;
+      FOREACHvertex_(facet->vertices) {
+        zinc_(Zdistio);
+        qh_distplane(qh, vertex->point, facet, &dist);
+        minimize_(mindist, dist);
+      }
+      *innerplane= mindist - qh->DISTround;
+    }else
+      *innerplane= qh->min_vertex - qh->DISTround;
+    if (qh->JOGGLEmax < REALmax/2)
+      *innerplane -= qh->JOGGLEmax * sqrt((realT)qh->hull_dim);
+  }
+} /* outerinner */
+
+/*---------------------------------
+
+  qh_pointdist( point1, point2, dim )
+    return distance between two points
+
+  notes:
+    returns distance squared if 'dim' is negative
+*/
+coordT qh_pointdist(pointT *point1, pointT *point2, int dim) {
+  coordT dist, diff;
+  int k;
+
+  dist= 0.0;
+  for (k= (dim > 0 ? dim : -dim); k--; ) {
+    diff= *point1++ - *point2++;
+    dist += diff * diff;
+  }
+  if (dim > 0)
+    return(sqrt(dist));
+  return dist;
+} /* pointdist */
+
+
+/*---------------------------------
+
+  qh_printmatrix(qh, fp, string, rows, numrow, numcol )
+    print matrix to fp given by row vectors
+    print string as header
+    qh may be NULL if fp is defined
+
+  notes:
+    print a vector by qh_printmatrix(qh, fp, "", &vect, 1, len)
+*/
+void qh_printmatrix(qhT *qh, FILE *fp, const char *string, realT **rows, int numrow, int numcol) {
+  realT *rowp;
+  realT r; /*bug fix*/
+  int i,k;
+
+  qh_fprintf(qh, fp, 9001, "%s\n", string);
+  for (i=0; i < numrow; i++) {
+    rowp= rows[i];
+    for (k=0; k < numcol; k++) {
+      r= *rowp++;
+      qh_fprintf(qh, fp, 9002, "%6.3g ", r);
+    }
+    qh_fprintf(qh, fp, 9003, "\n");
+  }
+} /* printmatrix */
+
+
+/*---------------------------------
+
+  qh_printpoints(qh, fp, string, points )
+    print pointids to fp for a set of points
+    if string, prints string and 'p' point ids
+*/
+void qh_printpoints(qhT *qh, FILE *fp, const char *string, setT *points) {
+  pointT *point, **pointp;
+
+  if (string) {
+    qh_fprintf(qh, fp, 9004, "%s", string);
+    FOREACHpoint_(points)
+      qh_fprintf(qh, fp, 9005, " p%d", qh_pointid(qh, point));
+    qh_fprintf(qh, fp, 9006, "\n");
+  }else {
+    FOREACHpoint_(points)
+      qh_fprintf(qh, fp, 9007, " %d", qh_pointid(qh, point));
+    qh_fprintf(qh, fp, 9008, "\n");
+  }
+} /* printpoints */
+
+
+/*---------------------------------
+
+  qh_projectinput(qh)
+    project input points using qh.lower_bound/upper_bound and qh->DELAUNAY
+    if qh.lower_bound[k]=qh.upper_bound[k]= 0,
+      removes dimension k
+    if halfspace intersection
+      removes dimension k from qh.feasible_point
+    input points in qh->first_point, num_points, input_dim
+
+  returns:
+    new point array in qh->first_point of qh->hull_dim coordinates
+    sets qh->POINTSmalloc
+    if qh->DELAUNAY
+      projects points to paraboloid
+      lowbound/highbound is also projected
+    if qh->ATinfinity
+      adds point "at-infinity"
+    if qh->POINTSmalloc
+      frees old point array
+
+  notes:
+    checks that qh.hull_dim agrees with qh.input_dim, PROJECTinput, and DELAUNAY
+
+
+  design:
+    sets project[k] to -1 (delete), 0 (keep), 1 (add for Delaunay)
+    determines newdim and newnum for qh->hull_dim and qh->num_points
+    projects points to newpoints
+    projects qh.lower_bound to itself
+    projects qh.upper_bound to itself
+    if qh->DELAUNAY
+      if qh->ATINFINITY
+        projects points to paraboloid
+        computes "infinity" point as vertex average and 10% above all points
+      else
+        uses qh_setdelaunay to project points to paraboloid
+*/
+void qh_projectinput(qhT *qh) {
+  int k,i;
+  int newdim= qh->input_dim, newnum= qh->num_points;
+  signed char *project;
+  int projectsize= (qh->input_dim+1)*sizeof(*project);
+  pointT *newpoints, *coord, *infinity;
+  realT paraboloid, maxboloid= 0;
+
+  project= (signed char*)qh_memalloc(qh, projectsize);
+  memset((char*)project, 0, (size_t)projectsize);
+  for (k=0; k < qh->input_dim; k++) {   /* skip Delaunay bound */
+    if (qh->lower_bound[k] == 0 && qh->upper_bound[k] == 0) {
+      project[k]= -1;
+      newdim--;
+    }
+  }
+  if (qh->DELAUNAY) {
+    project[k]= 1;
+    newdim++;
+    if (qh->ATinfinity)
+      newnum++;
+  }
+  if (newdim != qh->hull_dim) {
+    qh_memfree(qh, project, projectsize);
+    qh_fprintf(qh, qh->ferr, 6015, "qhull internal error (qh_projectinput): dimension after projection %d != hull_dim %d\n", newdim, qh->hull_dim);
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }
+  if (!(newpoints= qh->temp_malloc= (coordT*)qh_malloc(newnum*newdim*sizeof(coordT)))){
+    qh_memfree(qh, project, projectsize);
+    qh_fprintf(qh, qh->ferr, 6016, "qhull error: insufficient memory to project %d points\n",
+           qh->num_points);
+    qh_errexit(qh, qh_ERRmem, NULL, NULL);
+  }
+  /* qh_projectpoints throws error if mismatched dimensions */
+  qh_projectpoints(qh, project, qh->input_dim+1, qh->first_point,
+                    qh->num_points, qh->input_dim, newpoints, newdim);
+  trace1((qh, qh->ferr, 1003, "qh_projectinput: updating lower and upper_bound\n"));
+  qh_projectpoints(qh, project, qh->input_dim+1, qh->lower_bound,
+                    1, qh->input_dim+1, qh->lower_bound, newdim+1);
+  qh_projectpoints(qh, project, qh->input_dim+1, qh->upper_bound,
+                    1, qh->input_dim+1, qh->upper_bound, newdim+1);
+  if (qh->HALFspace) {
+    if (!qh->feasible_point) {
+      qh_memfree(qh, project, projectsize);
+      qh_fprintf(qh, qh->ferr, 6017, "qhull internal error (qh_projectinput): HALFspace defined without qh.feasible_point\n");
+      qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+    }
+    qh_projectpoints(qh, project, qh->input_dim, qh->feasible_point,
+                      1, qh->input_dim, qh->feasible_point, newdim);
+  }
+  qh_memfree(qh, project, projectsize);
+  if (qh->POINTSmalloc)
+    qh_free(qh->first_point);
+  qh->first_point= newpoints;
+  qh->POINTSmalloc= True;
+  qh->temp_malloc= NULL;
+  if (qh->DELAUNAY && qh->ATinfinity) {
+    coord= qh->first_point;
+    infinity= qh->first_point + qh->hull_dim * qh->num_points;
+    for (k=qh->hull_dim-1; k--; )
+      infinity[k]= 0.0;
+    for (i=qh->num_points; i--; ) {
+      paraboloid= 0.0;
+      for (k=0; k < qh->hull_dim-1; k++) {
+        paraboloid += *coord * *coord;
+        infinity[k] += *coord;
+        coord++;
+      }
+      *(coord++)= paraboloid;
+      maximize_(maxboloid, paraboloid);
+    }
+    /* coord == infinity */
+    for (k=qh->hull_dim-1; k--; )
+      *(coord++) /= qh->num_points;
+    *(coord++)= maxboloid * 1.1;
+    qh->num_points++;
+    trace0((qh, qh->ferr, 9, "qh_projectinput: projected points to paraboloid for Delaunay\n"));
+  }else if (qh->DELAUNAY)  /* !qh->ATinfinity */
+    qh_setdelaunay(qh, qh->hull_dim, qh->num_points, qh->first_point);
+} /* projectinput */
+
+
+/*---------------------------------
+
+  qh_projectpoints(qh, project, n, points, numpoints, dim, newpoints, newdim )
+    project points/numpoints/dim to newpoints/newdim
+    if project[k] == -1
+      delete dimension k
+    if project[k] == 1
+      add dimension k by duplicating previous column
+    n is size of project
+
+  notes:
+    newpoints may be points if only adding dimension at end
+
+  design:
+    check that 'project' and 'newdim' agree
+    for each dimension
+      if project == -1
+        skip dimension
+      else
+        determine start of column in newpoints
+        determine start of column in points
+          if project == +1, duplicate previous column
+        copy dimension (column) from points to newpoints
+*/
+void qh_projectpoints(qhT *qh, signed char *project, int n, realT *points,
+        int numpoints, int dim, realT *newpoints, int newdim) {
+  int testdim= dim, oldk=0, newk=0, i,j=0,k;
+  realT *newp, *oldp;
+
+  for (k=0; k < n; k++)
+    testdim += project[k];
+  if (testdim != newdim) {
+    qh_fprintf(qh, qh->ferr, 6018, "qhull internal error (qh_projectpoints): newdim %d should be %d after projection\n",
+      newdim, testdim);
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }
+  for (j=0; j= dim)
+          continue;
+        oldp= points+oldk;
+      }else
+        oldp= points+oldk++;
+      for (i=numpoints; i--; ) {
+        *newp= *oldp;
+        newp += newdim;
+        oldp += dim;
+      }
+    }
+    if (oldk >= dim)
+      break;
+  }
+  trace1((qh, qh->ferr, 1004, "qh_projectpoints: projected %d points from dim %d to dim %d\n",
+    numpoints, dim, newdim));
+} /* projectpoints */
+
+
+/*---------------------------------
+
+  qh_rotateinput(qh, rows )
+    rotate input using row matrix
+    input points given by qh->first_point, num_points, hull_dim
+    assumes rows[dim] is a scratch buffer
+    if qh->POINTSmalloc, overwrites input points, else mallocs a new array
+
+  returns:
+    rotated input
+    sets qh->POINTSmalloc
+
+  design:
+    see qh_rotatepoints
+*/
+void qh_rotateinput(qhT *qh, realT **rows) {
+
+  if (!qh->POINTSmalloc) {
+    qh->first_point= qh_copypoints(qh, qh->first_point, qh->num_points, qh->hull_dim);
+    qh->POINTSmalloc= True;
+  }
+  qh_rotatepoints(qh, qh->first_point, qh->num_points, qh->hull_dim, rows);
+}  /* rotateinput */
+
+/*---------------------------------
+
+  qh_rotatepoints(qh, points, numpoints, dim, row )
+    rotate numpoints points by a d-dim row matrix
+    assumes rows[dim] is a scratch buffer
+
+  returns:
+    rotated points in place
+
+  design:
+    for each point
+      for each coordinate
+        use row[dim] to compute partial inner product
+      for each coordinate
+        rotate by partial inner product
+*/
+void qh_rotatepoints(qhT *qh, realT *points, int numpoints, int dim, realT **row) {
+  realT *point, *rowi, *coord= NULL, sum, *newval;
+  int i,j,k;
+
+  if (qh->IStracing >= 1)
+    qh_printmatrix(qh, qh->ferr, "qh_rotatepoints: rotate points by", row, dim, dim);
+  for (point= points, j= numpoints; j--; point += dim) {
+    newval= row[dim];
+    for (i=0; i < dim; i++) {
+      rowi= row[i];
+      coord= point;
+      for (sum= 0.0, k= dim; k--; )
+        sum += *rowi++ * *coord++;
+      *(newval++)= sum;
+    }
+    for (k=dim; k--; )
+      *(--coord)= *(--newval);
+  }
+} /* rotatepoints */
+
+
+/*---------------------------------
+
+  qh_scaleinput(qh)
+    scale input points using qh->low_bound/high_bound
+    input points given by qh->first_point, num_points, hull_dim
+    if qh->POINTSmalloc, overwrites input points, else mallocs a new array
+
+  returns:
+    scales coordinates of points to low_bound[k], high_bound[k]
+    sets qh->POINTSmalloc
+
+  design:
+    see qh_scalepoints
+*/
+void qh_scaleinput(qhT *qh) {
+
+  if (!qh->POINTSmalloc) {
+    qh->first_point= qh_copypoints(qh, qh->first_point, qh->num_points, qh->hull_dim);
+    qh->POINTSmalloc= True;
+  }
+  qh_scalepoints(qh, qh->first_point, qh->num_points, qh->hull_dim,
+       qh->lower_bound, qh->upper_bound);
+}  /* scaleinput */
+
+/*---------------------------------
+
+  qh_scalelast(qh, points, numpoints, dim, low, high, newhigh )
+    scale last coordinate to [0,m] for Delaunay triangulations
+    input points given by points, numpoints, dim
+
+  returns:
+    changes scale of last coordinate from [low, high] to [0, newhigh]
+    overwrites last coordinate of each point
+    saves low/high/newhigh in qh.last_low, etc. for qh_setdelaunay()
+
+  notes:
+    when called by qh_setdelaunay, low/high may not match actual data
+
+  design:
+    compute scale and shift factors
+    apply to last coordinate of each point
+*/
+void qh_scalelast(qhT *qh, coordT *points, int numpoints, int dim, coordT low,
+                   coordT high, coordT newhigh) {
+  realT scale, shift;
+  coordT *coord;
+  int i;
+  boolT nearzero= False;
+
+  trace4((qh, qh->ferr, 4013, "qh_scalelast: scale last coordinate from [%2.2g, %2.2g] to [0,%2.2g]\n",
+    low, high, newhigh));
+  qh->last_low= low;
+  qh->last_high= high;
+  qh->last_newhigh= newhigh;
+  scale= qh_divzero(newhigh, high - low,
+                  qh->MINdenom_1, &nearzero);
+  if (nearzero) {
+    if (qh->DELAUNAY)
+      qh_fprintf(qh, qh->ferr, 6019, "qhull input error: can not scale last coordinate.  Input is cocircular\n   or cospherical.   Use option 'Qz' to add a point at infinity.\n");
+    else
+      qh_fprintf(qh, qh->ferr, 6020, "qhull input error: can not scale last coordinate.  New bounds [0, %2.2g] are too wide for\nexisting bounds [%2.2g, %2.2g] (width %2.2g)\n",
+                newhigh, low, high, high-low);
+    qh_errexit(qh, qh_ERRinput, NULL, NULL);
+  }
+  shift= - low * newhigh / (high-low);
+  coord= points + dim - 1;
+  for (i=numpoints; i--; coord += dim)
+    *coord= *coord * scale + shift;
+} /* scalelast */
+
+/*---------------------------------
+
+  qh_scalepoints(qh, points, numpoints, dim, newlows, newhighs )
+    scale points to new lowbound and highbound
+    retains old bound when newlow= -REALmax or newhigh= +REALmax
+
+  returns:
+    scaled points
+    overwrites old points
+
+  design:
+    for each coordinate
+      compute current low and high bound
+      compute scale and shift factors
+      scale all points
+      enforce new low and high bound for all points
+*/
+void qh_scalepoints(qhT *qh, pointT *points, int numpoints, int dim,
+        realT *newlows, realT *newhighs) {
+  int i,k;
+  realT shift, scale, *coord, low, high, newlow, newhigh, mincoord, maxcoord;
+  boolT nearzero= False;
+
+  for (k=0; k < dim; k++) {
+    newhigh= newhighs[k];
+    newlow= newlows[k];
+    if (newhigh > REALmax/2 && newlow < -REALmax/2)
+      continue;
+    low= REALmax;
+    high= -REALmax;
+    for (i=numpoints, coord=points+k; i--; coord += dim) {
+      minimize_(low, *coord);
+      maximize_(high, *coord);
+    }
+    if (newhigh > REALmax/2)
+      newhigh= high;
+    if (newlow < -REALmax/2)
+      newlow= low;
+    if (qh->DELAUNAY && k == dim-1 && newhigh < newlow) {
+      qh_fprintf(qh, qh->ferr, 6021, "qhull input error: 'Qb%d' or 'QB%d' inverts paraboloid since high bound %.2g < low bound %.2g\n",
+               k, k, newhigh, newlow);
+      qh_errexit(qh, qh_ERRinput, NULL, NULL);
+    }
+    scale= qh_divzero(newhigh - newlow, high - low,
+                  qh->MINdenom_1, &nearzero);
+    if (nearzero) {
+      qh_fprintf(qh, qh->ferr, 6022, "qhull input error: %d'th dimension's new bounds [%2.2g, %2.2g] too wide for\nexisting bounds [%2.2g, %2.2g]\n",
+              k, newlow, newhigh, low, high);
+      qh_errexit(qh, qh_ERRinput, NULL, NULL);
+    }
+    shift= (newlow * high - low * newhigh)/(high-low);
+    coord= points+k;
+    for (i=numpoints; i--; coord += dim)
+      *coord= *coord * scale + shift;
+    coord= points+k;
+    if (newlow < newhigh) {
+      mincoord= newlow;
+      maxcoord= newhigh;
+    }else {
+      mincoord= newhigh;
+      maxcoord= newlow;
+    }
+    for (i=numpoints; i--; coord += dim) {
+      minimize_(*coord, maxcoord);  /* because of roundoff error */
+      maximize_(*coord, mincoord);
+    }
+    trace0((qh, qh->ferr, 10, "qh_scalepoints: scaled %d'th coordinate [%2.2g, %2.2g] to [%.2g, %.2g] for %d points by %2.2g and shifted %2.2g\n",
+      k, low, high, newlow, newhigh, numpoints, scale, shift));
+  }
+} /* scalepoints */
+
+
+/*---------------------------------
+
+  qh_setdelaunay(qh, dim, count, points )
+    project count points to dim-d paraboloid for Delaunay triangulation
+
+    dim is one more than the dimension of the input set
+    assumes dim is at least 3 (i.e., at least a 2-d Delaunay triangulation)
+
+    points is a dim*count realT array.  The first dim-1 coordinates
+    are the coordinates of the first input point.  array[dim] is
+    the first coordinate of the second input point.  array[2*dim] is
+    the first coordinate of the third input point.
+
+    if qh.last_low defined (i.e., 'Qbb' called qh_scalelast)
+      calls qh_scalelast to scale the last coordinate the same as the other points
+
+  returns:
+    for each point
+      sets point[dim-1] to sum of squares of coordinates
+    scale points to 'Qbb' if needed
+
+  notes:
+    to project one point, use
+      qh_setdelaunay(qh, qh->hull_dim, 1, point)
+
+    Do not use options 'Qbk', 'QBk', or 'QbB' since they scale
+    the coordinates after the original projection.
+
+*/
+void qh_setdelaunay(qhT *qh, int dim, int count, pointT *points) {
+  int i, k;
+  coordT *coordp, coord;
+  realT paraboloid;
+
+  trace0((qh, qh->ferr, 11, "qh_setdelaunay: project %d points to paraboloid for Delaunay triangulation\n", count));
+  coordp= points;
+  for (i=0; i < count; i++) {
+    coord= *coordp++;
+    paraboloid= coord*coord;
+    for (k=dim-2; k--; ) {
+      coord= *coordp++;
+      paraboloid += coord*coord;
+    }
+    *coordp++ = paraboloid;
+  }
+  if (qh->last_low < REALmax/2)
+    qh_scalelast(qh, points, count, dim, qh->last_low, qh->last_high, qh->last_newhigh);
+} /* setdelaunay */
+
+
+/*---------------------------------
+
+  qh_sethalfspace(qh, dim, coords, nextp, normal, offset, feasible )
+    set point to dual of halfspace relative to feasible point
+    halfspace is normal coefficients and offset.
+
+  returns:
+    false and prints error if feasible point is outside of hull
+    overwrites coordinates for point at dim coords
+    nextp= next point (coords)
+    does not call qh_errexit
+
+  design:
+    compute distance from feasible point to halfspace
+    divide each normal coefficient by -dist
+*/
+boolT qh_sethalfspace(qhT *qh, int dim, coordT *coords, coordT **nextp,
+         coordT *normal, coordT *offset, coordT *feasible) {
+  coordT *normp= normal, *feasiblep= feasible, *coordp= coords;
+  realT dist;
+  realT r; /*bug fix*/
+  int k;
+  boolT zerodiv;
+
+  dist= *offset;
+  for (k=dim; k--; )
+    dist += *(normp++) * *(feasiblep++);
+  if (dist > 0)
+    goto LABELerroroutside;
+  normp= normal;
+  if (dist < -qh->MINdenom) {
+    for (k=dim; k--; )
+      *(coordp++)= *(normp++) / -dist;
+  }else {
+    for (k=dim; k--; ) {
+      *(coordp++)= qh_divzero(*(normp++), -dist, qh->MINdenom_1, &zerodiv);
+      if (zerodiv)
+        goto LABELerroroutside;
+    }
+  }
+  *nextp= coordp;
+  if (qh->IStracing >= 4) {
+    qh_fprintf(qh, qh->ferr, 8021, "qh_sethalfspace: halfspace at offset %6.2g to point: ", *offset);
+    for (k=dim, coordp=coords; k--; ) {
+      r= *coordp++;
+      qh_fprintf(qh, qh->ferr, 8022, " %6.2g", r);
+    }
+    qh_fprintf(qh, qh->ferr, 8023, "\n");
+  }
+  return True;
+LABELerroroutside:
+  feasiblep= feasible;
+  normp= normal;
+  qh_fprintf(qh, qh->ferr, 6023, "qhull input error: feasible point is not clearly inside halfspace\nfeasible point: ");
+  for (k=dim; k--; )
+    qh_fprintf(qh, qh->ferr, 8024, qh_REAL_1, r=*(feasiblep++));
+  qh_fprintf(qh, qh->ferr, 8025, "\n     halfspace: ");
+  for (k=dim; k--; )
+    qh_fprintf(qh, qh->ferr, 8026, qh_REAL_1, r=*(normp++));
+  qh_fprintf(qh, qh->ferr, 8027, "\n     at offset: ");
+  qh_fprintf(qh, qh->ferr, 8028, qh_REAL_1, *offset);
+  qh_fprintf(qh, qh->ferr, 8029, " and distance: ");
+  qh_fprintf(qh, qh->ferr, 8030, qh_REAL_1, dist);
+  qh_fprintf(qh, qh->ferr, 8031, "\n");
+  return False;
+} /* sethalfspace */
+
+/*---------------------------------
+
+  qh_sethalfspace_all(qh, dim, count, halfspaces, feasible )
+    generate dual for halfspace intersection with feasible point
+    array of count halfspaces
+      each halfspace is normal coefficients followed by offset
+      the origin is inside the halfspace if the offset is negative
+    feasible is a point inside all halfspaces (http://www.qhull.org/html/qhalf.htm#notes)
+
+  returns:
+    malloc'd array of count X dim-1 points
+
+  notes:
+    call before qh_init_B or qh_initqhull_globals
+    free memory when done
+    unused/untested code: please email bradb@shore.net if this works ok for you
+    if using option 'Fp', qh->feasible_point must be set (e.g., to 'feasible')
+    qh->feasible_point is a malloc'd array that is freed by qh_freebuffers.
+
+  design:
+    see qh_sethalfspace
+*/
+coordT *qh_sethalfspace_all(qhT *qh, int dim, int count, coordT *halfspaces, pointT *feasible) {
+  int i, newdim;
+  pointT *newpoints;
+  coordT *coordp, *normalp, *offsetp;
+
+  trace0((qh, qh->ferr, 12, "qh_sethalfspace_all: compute dual for halfspace intersection\n"));
+  newdim= dim - 1;
+  if (!(newpoints=(coordT*)qh_malloc(count*newdim*sizeof(coordT)))){
+    qh_fprintf(qh, qh->ferr, 6024, "qhull error: insufficient memory to compute dual of %d halfspaces\n",
+          count);
+    qh_errexit(qh, qh_ERRmem, NULL, NULL);
+  }
+  coordp= newpoints;
+  normalp= halfspaces;
+  for (i=0; i < count; i++) {
+    offsetp= normalp + newdim;
+    if (!qh_sethalfspace(qh, newdim, coordp, &coordp, normalp, offsetp, feasible)) {
+      qh_free(newpoints);  /* feasible is not inside halfspace as reported by qh_sethalfspace */
+      qh_fprintf(qh, qh->ferr, 8032, "The halfspace was at index %d\n", i);
+      qh_errexit(qh, qh_ERRinput, NULL, NULL);
+    }
+    normalp= offsetp + 1;
+  }
+  return newpoints;
+} /* sethalfspace_all */
+
+
+/*---------------------------------
+
+  qh_sharpnewfacets(qh)
+
+  returns:
+    true if could be an acute angle (facets in different quadrants)
+
+  notes:
+    for qh_findbest
+
+  design:
+    for all facets on qh.newfacet_list
+      if two facets are in different quadrants
+        set issharp
+*/
+boolT qh_sharpnewfacets(qhT *qh) {
+  facetT *facet;
+  boolT issharp = False;
+  int *quadrant, k;
+
+  quadrant= (int*)qh_memalloc(qh, qh->hull_dim * sizeof(int));
+  FORALLfacet_(qh->newfacet_list) {
+    if (facet == qh->newfacet_list) {
+      for (k=qh->hull_dim; k--; )
+        quadrant[ k]= (facet->normal[ k] > 0);
+    }else {
+      for (k=qh->hull_dim; k--; ) {
+        if (quadrant[ k] != (facet->normal[ k] > 0)) {
+          issharp= True;
+          break;
+        }
+      }
+    }
+    if (issharp)
+      break;
+  }
+  qh_memfree(qh, quadrant, qh->hull_dim * sizeof(int));
+  trace3((qh, qh->ferr, 3001, "qh_sharpnewfacets: %d\n", issharp));
+  return issharp;
+} /* sharpnewfacets */
+
+/*---------------------------------
+
+  qh_voronoi_center(qh, dim, points )
+    return Voronoi center for a set of points
+    dim is the orginal dimension of the points
+    gh.gm_matrix/qh.gm_row are scratch buffers
+
+  returns:
+    center as a temporary point (qh_memalloc)
+    if non-simplicial,
+      returns center for max simplex of points
+
+  notes:
+    only called by qh_facetcenter
+    from Bowyer & Woodwark, A Programmer's Geometry, 1983, p. 65
+
+  design:
+    if non-simplicial
+      determine max simplex for points
+    translate point0 of simplex to origin
+    compute sum of squares of diagonal
+    compute determinate
+    compute Voronoi center (see Bowyer & Woodwark)
+*/
+pointT *qh_voronoi_center(qhT *qh, int dim, setT *points) {
+  pointT *point, **pointp, *point0;
+  pointT *center= (pointT*)qh_memalloc(qh, qh->center_size);
+  setT *simplex;
+  int i, j, k, size= qh_setsize(qh, points);
+  coordT *gmcoord;
+  realT *diffp, sum2, *sum2row, *sum2p, det, factor;
+  boolT nearzero, infinite;
+
+  if (size == dim+1)
+    simplex= points;
+  else if (size < dim+1) {
+    qh_memfree(qh, center, qh->center_size);
+    qh_fprintf(qh, qh->ferr, 6025, "qhull internal error (qh_voronoi_center):\n  need at least %d points to construct a Voronoi center\n",
+             dim+1);
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+    simplex= points;  /* never executed -- avoids warning */
+  }else {
+    simplex= qh_settemp(qh, dim+1);
+    qh_maxsimplex(qh, dim, points, NULL, 0, &simplex);
+  }
+  point0= SETfirstt_(simplex, pointT);
+  gmcoord= qh->gm_matrix;
+  for (k=0; k < dim; k++) {
+    qh->gm_row[k]= gmcoord;
+    FOREACHpoint_(simplex) {
+      if (point != point0)
+        *(gmcoord++)= point[k] - point0[k];
+    }
+  }
+  sum2row= gmcoord;
+  for (i=0; i < dim; i++) {
+    sum2= 0.0;
+    for (k=0; k < dim; k++) {
+      diffp= qh->gm_row[k] + i;
+      sum2 += *diffp * *diffp;
+    }
+    *(gmcoord++)= sum2;
+  }
+  det= qh_determinant(qh, qh->gm_row, dim, &nearzero);
+  factor= qh_divzero(0.5, det, qh->MINdenom, &infinite);
+  if (infinite) {
+    for (k=dim; k--; )
+      center[k]= qh_INFINITE;
+    if (qh->IStracing)
+      qh_printpoints(qh, qh->ferr, "qh_voronoi_center: at infinity for ", simplex);
+  }else {
+    for (i=0; i < dim; i++) {
+      gmcoord= qh->gm_matrix;
+      sum2p= sum2row;
+      for (k=0; k < dim; k++) {
+        qh->gm_row[k]= gmcoord;
+        if (k == i) {
+          for (j=dim; j--; )
+            *(gmcoord++)= *sum2p++;
+        }else {
+          FOREACHpoint_(simplex) {
+            if (point != point0)
+              *(gmcoord++)= point[k] - point0[k];
+          }
+        }
+      }
+      center[i]= qh_determinant(qh, qh->gm_row, dim, &nearzero)*factor + point0[i];
+    }
+#ifndef qh_NOtrace
+    if (qh->IStracing >= 3) {
+      qh_fprintf(qh, qh->ferr, 8033, "qh_voronoi_center: det %2.2g factor %2.2g ", det, factor);
+      qh_printmatrix(qh, qh->ferr, "center:", ¢er, 1, dim);
+      if (qh->IStracing >= 5) {
+        qh_printpoints(qh, qh->ferr, "points", simplex);
+        FOREACHpoint_(simplex)
+          qh_fprintf(qh, qh->ferr, 8034, "p%d dist %.2g, ", qh_pointid(qh, point),
+                   qh_pointdist(point, center, dim));
+        qh_fprintf(qh, qh->ferr, 8035, "\n");
+      }
+    }
+#endif
+  }
+  if (simplex != points)
+    qh_settempfree(qh, &simplex);
+  return center;
+} /* voronoi_center */
+
diff --git a/Cdir/geom_r.c b/Cdir/geom_r.c
new file mode 100644
--- /dev/null
+++ b/Cdir/geom_r.c
@@ -0,0 +1,1234 @@
+/*
  ---------------------------------
+
+   geom_r.c
+   geometric routines of qhull
+
+   see qh-geom_r.htm and geom_r.h
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull_r/geom_r.c#2 $$Change: 1995 $
+   $DateTime: 2015/10/13 21:59:42 $$Author: bbarber $
+
+   infrequent code goes into geom2_r.c
+*/
+
+#include "qhull_ra.h"
+
+/*---------------------------------
+
+  qh_distplane(qh, point, facet, dist )
+    return distance from point to facet
+
+  returns:
+    dist
+    if qh.RANDOMdist, joggles result
+
+  notes:
+    dist > 0 if point is above facet (i.e., outside)
+    does not error (for qh_sortfacets, qh_outerinner)
+
+  see:
+    qh_distnorm in geom2_r.c
+    qh_distplane [geom_r.c], QhullFacet::distance, and QhullHyperplane::distance are copies
+*/
+void qh_distplane(qhT *qh, pointT *point, facetT *facet, realT *dist) {
+  coordT *normal= facet->normal, *coordp, randr;
+  int k;
+
+  switch (qh->hull_dim){
+  case 2:
+    *dist= facet->offset + point[0] * normal[0] + point[1] * normal[1];
+    break;
+  case 3:
+    *dist= facet->offset + point[0] * normal[0] + point[1] * normal[1] + point[2] * normal[2];
+    break;
+  case 4:
+    *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3];
+    break;
+  case 5:
+    *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4];
+    break;
+  case 6:
+    *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5];
+    break;
+  case 7:
+    *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5]+point[6]*normal[6];
+    break;
+  case 8:
+    *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5]+point[6]*normal[6]+point[7]*normal[7];
+    break;
+  default:
+    *dist= facet->offset;
+    coordp= point;
+    for (k=qh->hull_dim; k--; )
+      *dist += *coordp++ * *normal++;
+    break;
+  }
+  zinc_(Zdistplane);
+  if (!qh->RANDOMdist && qh->IStracing < 4)
+    return;
+  if (qh->RANDOMdist) {
+    randr= qh_RANDOMint;
+    *dist += (2.0 * randr / qh_RANDOMmax - 1.0) *
+      qh->RANDOMfactor * qh->MAXabs_coord;
+  }
+  if (qh->IStracing >= 4) {
+    qh_fprintf(qh, qh->ferr, 8001, "qh_distplane: ");
+    qh_fprintf(qh, qh->ferr, 8002, qh_REAL_1, *dist);
+    qh_fprintf(qh, qh->ferr, 8003, "from p%d to f%d\n", qh_pointid(qh, point), facet->id);
+  }
+  return;
+} /* distplane */
+
+
+/*---------------------------------
+
+  qh_findbest(qh, point, startfacet, bestoutside, qh_ISnewfacets, qh_NOupper, dist, isoutside, numpart )
+    find facet that is furthest below a point
+    for upperDelaunay facets
+      returns facet only if !qh_NOupper and clearly above
+
+  input:
+    starts search at 'startfacet' (can not be flipped)
+    if !bestoutside(qh_ALL), stops at qh.MINoutside
+
+  returns:
+    best facet (reports error if NULL)
+    early out if isoutside defined and bestdist > qh.MINoutside
+    dist is distance to facet
+    isoutside is true if point is outside of facet
+    numpart counts the number of distance tests
+
+  see also:
+    qh_findbestnew()
+
+  notes:
+    If merging (testhorizon), searches horizon facets of coplanar best facets because
+    after qh_distplane, this and qh_partitionpoint are the most expensive in 3-d
+      avoid calls to distplane, function calls, and real number operations.
+    caller traces result
+    Optimized for outside points.   Tried recording a search set for qh_findhorizon.
+    Made code more complicated.
+
+  when called by qh_partitionvisible():
+    indicated by qh_ISnewfacets
+    qh.newfacet_list is list of simplicial, new facets
+    qh_findbestnew set if qh_sharpnewfacets returns True (to use qh_findbestnew)
+    qh.bestfacet_notsharp set if qh_sharpnewfacets returns False
+
+  when called by qh_findfacet(), qh_partitionpoint(), qh_partitioncoplanar(),
+                 qh_check_bestdist(), qh_addpoint()
+    indicated by !qh_ISnewfacets
+    returns best facet in neighborhood of given facet
+      this is best facet overall if dist > -   qh.MAXcoplanar
+        or hull has at least a "spherical" curvature
+
+  design:
+    initialize and test for early exit
+    repeat while there are better facets
+      for each neighbor of facet
+        exit if outside facet found
+        test for better facet
+    if point is inside and partitioning
+      test for new facets with a "sharp" intersection
+      if so, future calls go to qh_findbestnew()
+    test horizon facets
+*/
+facetT *qh_findbest(qhT *qh, pointT *point, facetT *startfacet,
+                     boolT bestoutside, boolT isnewfacets, boolT noupper,
+                     realT *dist, boolT *isoutside, int *numpart) {
+  realT bestdist= -REALmax/2 /* avoid underflow */;
+  facetT *facet, *neighbor, **neighborp;
+  facetT *bestfacet= NULL, *lastfacet= NULL;
+  int oldtrace= qh->IStracing;
+  unsigned int visitid= ++qh->visit_id;
+  int numpartnew=0;
+  boolT testhorizon = True; /* needed if precise, e.g., rbox c D6 | qhull Q0 Tv */
+
+  zinc_(Zfindbest);
+  if (qh->IStracing >= 3 || (qh->TRACElevel && qh->TRACEpoint >= 0 && qh->TRACEpoint == qh_pointid(qh, point))) {
+    if (qh->TRACElevel > qh->IStracing)
+      qh->IStracing= qh->TRACElevel;
+    qh_fprintf(qh, qh->ferr, 8004, "qh_findbest: point p%d starting at f%d isnewfacets? %d, unless %d exit if > %2.2g\n",
+             qh_pointid(qh, point), startfacet->id, isnewfacets, bestoutside, qh->MINoutside);
+    qh_fprintf(qh, qh->ferr, 8005, "  testhorizon? %d noupper? %d", testhorizon, noupper);
+    qh_fprintf(qh, qh->ferr, 8006, "  Last point added was p%d.", qh->furthest_id);
+    qh_fprintf(qh, qh->ferr, 8007, "  Last merge was #%d.  max_outside %2.2g\n", zzval_(Ztotmerge), qh->max_outside);
+  }
+  if (isoutside)
+    *isoutside= True;
+  if (!startfacet->flipped) {  /* test startfacet */
+    *numpart= 1;
+    qh_distplane(qh, point, startfacet, dist);  /* this code is duplicated below */
+    if (!bestoutside && *dist >= qh->MINoutside
+    && (!startfacet->upperdelaunay || !noupper)) {
+      bestfacet= startfacet;
+      goto LABELreturn_best;
+    }
+    bestdist= *dist;
+    if (!startfacet->upperdelaunay) {
+      bestfacet= startfacet;
+    }
+  }else
+    *numpart= 0;
+  startfacet->visitid= visitid;
+  facet= startfacet;
+  while (facet) {
+    trace4((qh, qh->ferr, 4001, "qh_findbest: neighbors of f%d, bestdist %2.2g f%d\n",
+                facet->id, bestdist, getid_(bestfacet)));
+    lastfacet= facet;
+    FOREACHneighbor_(facet) {
+      if (!neighbor->newfacet && isnewfacets)
+        continue;
+      if (neighbor->visitid == visitid)
+        continue;
+      neighbor->visitid= visitid;
+      if (!neighbor->flipped) {  /* code duplicated above */
+        (*numpart)++;
+        qh_distplane(qh, point, neighbor, dist);
+        if (*dist > bestdist) {
+          if (!bestoutside && *dist >= qh->MINoutside
+          && (!neighbor->upperdelaunay || !noupper)) {
+            bestfacet= neighbor;
+            goto LABELreturn_best;
+          }
+          if (!neighbor->upperdelaunay) {
+            bestfacet= neighbor;
+            bestdist= *dist;
+            break; /* switch to neighbor */
+          }else if (!bestfacet) {
+            bestdist= *dist;
+            break; /* switch to neighbor */
+          }
+        } /* end of *dist>bestdist */
+      } /* end of !flipped */
+    } /* end of FOREACHneighbor */
+    facet= neighbor;  /* non-NULL only if *dist>bestdist */
+  } /* end of while facet (directed search) */
+  if (isnewfacets) {
+    if (!bestfacet) {
+      bestdist= -REALmax/2;
+      bestfacet= qh_findbestnew(qh, point, startfacet->next, &bestdist, bestoutside, isoutside, &numpartnew);
+      testhorizon= False; /* qh_findbestnew calls qh_findbesthorizon */
+    }else if (!qh->findbest_notsharp && bestdist < - qh->DISTround) {
+      if (qh_sharpnewfacets(qh)) {
+        /* seldom used, qh_findbestnew will retest all facets */
+        zinc_(Zfindnewsharp);
+        bestfacet= qh_findbestnew(qh, point, bestfacet, &bestdist, bestoutside, isoutside, &numpartnew);
+        testhorizon= False; /* qh_findbestnew calls qh_findbesthorizon */
+        qh->findbestnew= True;
+      }else
+        qh->findbest_notsharp= True;
+    }
+  }
+  if (!bestfacet)
+    bestfacet= qh_findbestlower(qh, lastfacet, point, &bestdist, numpart);
+  if (testhorizon)
+    bestfacet= qh_findbesthorizon(qh, !qh_IScheckmax, point, bestfacet, noupper, &bestdist, &numpartnew);
+  *dist= bestdist;
+  if (isoutside && bestdist < qh->MINoutside)
+    *isoutside= False;
+LABELreturn_best:
+  zadd_(Zfindbesttot, *numpart);
+  zmax_(Zfindbestmax, *numpart);
+  (*numpart) += numpartnew;
+  qh->IStracing= oldtrace;
+  return bestfacet;
+}  /* findbest */
+
+
+/*---------------------------------
+
+  qh_findbesthorizon(qh, qh_IScheckmax, point, startfacet, qh_NOupper, &bestdist, &numpart )
+    search coplanar and better horizon facets from startfacet/bestdist
+    ischeckmax turns off statistics and minsearch update
+    all arguments must be initialized
+  returns(ischeckmax):
+    best facet
+  returns(!ischeckmax):
+    best facet that is not upperdelaunay
+    allows upperdelaunay that is clearly outside
+  returns:
+    bestdist is distance to bestfacet
+    numpart -- updates number of distance tests
+
+  notes:
+    no early out -- use qh_findbest() or qh_findbestnew()
+    Searches coplanar or better horizon facets
+
+  when called by qh_check_maxout() (qh_IScheckmax)
+    startfacet must be closest to the point
+      Otherwise, if point is beyond and below startfacet, startfacet may be a local minimum
+      even though other facets are below the point.
+    updates facet->maxoutside for good, visited facets
+    may return NULL
+
+    searchdist is qh.max_outside + 2 * DISTround
+      + max( MINvisible('Vn'), MAXcoplanar('Un'));
+    This setting is a guess.  It must be at least max_outside + 2*DISTround
+    because a facet may have a geometric neighbor across a vertex
+
+  design:
+    for each horizon facet of coplanar best facets
+      continue if clearly inside
+      unless upperdelaunay or clearly outside
+         update best facet
+*/
+facetT *qh_findbesthorizon(qhT *qh, boolT ischeckmax, pointT* point, facetT *startfacet, boolT noupper, realT *bestdist, int *numpart) {
+  facetT *bestfacet= startfacet;
+  realT dist;
+  facetT *neighbor, **neighborp, *facet;
+  facetT *nextfacet= NULL; /* optimize last facet of coplanarfacetset */
+  int numpartinit= *numpart, coplanarfacetset_size;
+  unsigned int visitid= ++qh->visit_id;
+  boolT newbest= False; /* for tracing */
+  realT minsearch, searchdist;  /* skip facets that are too far from point */
+
+  if (!ischeckmax) {
+    zinc_(Zfindhorizon);
+  }else {
+#if qh_MAXoutside
+    if ((!qh->ONLYgood || startfacet->good) && *bestdist > startfacet->maxoutside)
+      startfacet->maxoutside= *bestdist;
+#endif
+  }
+  searchdist= qh_SEARCHdist; /* multiple of qh.max_outside and precision constants */
+  minsearch= *bestdist - searchdist;
+  if (ischeckmax) {
+    /* Always check coplanar facets.  Needed for RBOX 1000 s Z1 G1e-13 t996564279 | QHULL Tv */
+    minimize_(minsearch, -searchdist);
+  }
+  coplanarfacetset_size= 0;
+  facet= startfacet;
+  while (True) {
+    trace4((qh, qh->ferr, 4002, "qh_findbesthorizon: neighbors of f%d bestdist %2.2g f%d ischeckmax? %d noupper? %d minsearch %2.2g searchdist %2.2g\n",
+                facet->id, *bestdist, getid_(bestfacet), ischeckmax, noupper,
+                minsearch, searchdist));
+    FOREACHneighbor_(facet) {
+      if (neighbor->visitid == visitid)
+        continue;
+      neighbor->visitid= visitid;
+      if (!neighbor->flipped) {
+        qh_distplane(qh, point, neighbor, &dist);
+        (*numpart)++;
+        if (dist > *bestdist) {
+          if (!neighbor->upperdelaunay || ischeckmax || (!noupper && dist >= qh->MINoutside)) {
+            bestfacet= neighbor;
+            *bestdist= dist;
+            newbest= True;
+            if (!ischeckmax) {
+              minsearch= dist - searchdist;
+              if (dist > *bestdist + searchdist) {
+                zinc_(Zfindjump);  /* everything in qh.coplanarfacetset at least searchdist below */
+                coplanarfacetset_size= 0;
+              }
+            }
+          }
+        }else if (dist < minsearch)
+          continue;  /* if ischeckmax, dist can't be positive */
+#if qh_MAXoutside
+        if (ischeckmax && dist > neighbor->maxoutside)
+          neighbor->maxoutside= dist;
+#endif
+      } /* end of !flipped */
+      if (nextfacet) {
+        if (!coplanarfacetset_size++) {
+          SETfirst_(qh->coplanarfacetset)= nextfacet;
+          SETtruncate_(qh->coplanarfacetset, 1);
+        }else
+          qh_setappend(qh, &qh->coplanarfacetset, nextfacet); /* Was needed for RBOX 1000 s W1e-13 P0 t996547055 | QHULL d Qbb Qc Tv
+                                                 and RBOX 1000 s Z1 G1e-13 t996564279 | qhull Tv  */
+      }
+      nextfacet= neighbor;
+    } /* end of EACHneighbor */
+    facet= nextfacet;
+    if (facet)
+      nextfacet= NULL;
+    else if (!coplanarfacetset_size)
+      break;
+    else if (!--coplanarfacetset_size) {
+      facet= SETfirstt_(qh->coplanarfacetset, facetT);
+      SETtruncate_(qh->coplanarfacetset, 0);
+    }else
+      facet= (facetT*)qh_setdellast(qh->coplanarfacetset);
+  } /* while True, for each facet in qh.coplanarfacetset */
+  if (!ischeckmax) {
+    zadd_(Zfindhorizontot, *numpart - numpartinit);
+    zmax_(Zfindhorizonmax, *numpart - numpartinit);
+    if (newbest)
+      zinc_(Zparthorizon);
+  }
+  trace4((qh, qh->ferr, 4003, "qh_findbesthorizon: newbest? %d bestfacet f%d bestdist %2.2g\n", newbest, getid_(bestfacet), *bestdist));
+  return bestfacet;
+}  /* findbesthorizon */
+
+/*---------------------------------
+
+  qh_findbestnew(qh, point, startfacet, dist, isoutside, numpart )
+    find best newfacet for point
+    searches all of qh.newfacet_list starting at startfacet
+    searches horizon facets of coplanar best newfacets
+    searches all facets if startfacet == qh.facet_list
+  returns:
+    best new or horizon facet that is not upperdelaunay
+    early out if isoutside and not 'Qf'
+    dist is distance to facet
+    isoutside is true if point is outside of facet
+    numpart is number of distance tests
+
+  notes:
+    Always used for merged new facets (see qh_USEfindbestnew)
+    Avoids upperdelaunay facet unless (isoutside and outside)
+
+    Uses qh.visit_id, qh.coplanarfacetset.
+    If share visit_id with qh_findbest, coplanarfacetset is incorrect.
+
+    If merging (testhorizon), searches horizon facets of coplanar best facets because
+    a point maybe coplanar to the bestfacet, below its horizon facet,
+    and above a horizon facet of a coplanar newfacet.  For example,
+      rbox 1000 s Z1 G1e-13 | qhull
+      rbox 1000 s W1e-13 P0 t992110337 | QHULL d Qbb Qc
+
+    qh_findbestnew() used if
+       qh_sharpnewfacets -- newfacets contains a sharp angle
+       if many merges, qh_premerge found a merge, or 'Qf' (qh.findbestnew)
+
+  see also:
+    qh_partitionall() and qh_findbest()
+
+  design:
+    for each new facet starting from startfacet
+      test distance from point to facet
+      return facet if clearly outside
+      unless upperdelaunay and a lowerdelaunay exists
+         update best facet
+    test horizon facets
+*/
+facetT *qh_findbestnew(qhT *qh, pointT *point, facetT *startfacet,
+           realT *dist, boolT bestoutside, boolT *isoutside, int *numpart) {
+  realT bestdist= -REALmax/2;
+  facetT *bestfacet= NULL, *facet;
+  int oldtrace= qh->IStracing, i;
+  unsigned int visitid= ++qh->visit_id;
+  realT distoutside= 0.0;
+  boolT isdistoutside; /* True if distoutside is defined */
+  boolT testhorizon = True; /* needed if precise, e.g., rbox c D6 | qhull Q0 Tv */
+
+  if (!startfacet) {
+    if (qh->MERGING)
+      qh_fprintf(qh, qh->ferr, 6001, "qhull precision error (qh_findbestnew): merging has formed and deleted a cone of new facets.  Can not continue.\n");
+    else
+      qh_fprintf(qh, qh->ferr, 6002, "qhull internal error (qh_findbestnew): no new facets for point p%d\n",
+              qh->furthest_id);
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }
+  zinc_(Zfindnew);
+  if (qh->BESToutside || bestoutside)
+    isdistoutside= False;
+  else {
+    isdistoutside= True;
+    distoutside= qh_DISToutside; /* multiple of qh.MINoutside & qh.max_outside, see user.h */
+  }
+  if (isoutside)
+    *isoutside= True;
+  *numpart= 0;
+  if (qh->IStracing >= 3 || (qh->TRACElevel && qh->TRACEpoint >= 0 && qh->TRACEpoint == qh_pointid(qh, point))) {
+    if (qh->TRACElevel > qh->IStracing)
+      qh->IStracing= qh->TRACElevel;
+    qh_fprintf(qh, qh->ferr, 8008, "qh_findbestnew: point p%d facet f%d. Stop? %d if dist > %2.2g\n",
+             qh_pointid(qh, point), startfacet->id, isdistoutside, distoutside);
+    qh_fprintf(qh, qh->ferr, 8009, "  Last point added p%d visitid %d.",  qh->furthest_id, visitid);
+    qh_fprintf(qh, qh->ferr, 8010, "  Last merge was #%d.\n", zzval_(Ztotmerge));
+  }
+  /* visit all new facets starting with startfacet, maybe qh->facet_list */
+  for (i=0, facet=startfacet; i < 2; i++, facet= qh->newfacet_list) {
+    FORALLfacet_(facet) {
+      if (facet == startfacet && i)
+        break;
+      facet->visitid= visitid;
+      if (!facet->flipped) {
+        qh_distplane(qh, point, facet, dist);
+        (*numpart)++;
+        if (*dist > bestdist) {
+          if (!facet->upperdelaunay || *dist >= qh->MINoutside) {
+            bestfacet= facet;
+            if (isdistoutside && *dist >= distoutside)
+              goto LABELreturn_bestnew;
+            bestdist= *dist;
+          }
+        }
+      } /* end of !flipped */
+    } /* FORALLfacet from startfacet or qh->newfacet_list */
+  }
+  if (testhorizon || !bestfacet) /* testhorizon is always True.  Keep the same code as qh_findbest */
+    bestfacet= qh_findbesthorizon(qh, !qh_IScheckmax, point, bestfacet ? bestfacet : startfacet,
+                                        !qh_NOupper, &bestdist, numpart);
+  *dist= bestdist;
+  if (isoutside && *dist < qh->MINoutside)
+    *isoutside= False;
+LABELreturn_bestnew:
+  zadd_(Zfindnewtot, *numpart);
+  zmax_(Zfindnewmax, *numpart);
+  trace4((qh, qh->ferr, 4004, "qh_findbestnew: bestfacet f%d bestdist %2.2g\n", getid_(bestfacet), *dist));
+  qh->IStracing= oldtrace;
+  return bestfacet;
+}  /* findbestnew */
+
+/* ============ hyperplane functions -- keep code together [?] ============ */
+
+/*---------------------------------
+
+  qh_backnormal(qh, rows, numrow, numcol, sign, normal, nearzero )
+    given an upper-triangular rows array and a sign,
+    solve for normal equation x using back substitution over rows U
+
+  returns:
+     normal= x
+
+     if will not be able to divzero() when normalized(qh.MINdenom_2 and qh.MINdenom_1_2),
+       if fails on last row
+         this means that the hyperplane intersects [0,..,1]
+         sets last coordinate of normal to sign
+       otherwise
+         sets tail of normal to [...,sign,0,...], i.e., solves for b= [0...0]
+         sets nearzero
+
+  notes:
+     assumes numrow == numcol-1
+
+     see Golub & van Loan, 1983, Eq. 4.4-9 for "Gaussian elimination with complete pivoting"
+
+     solves Ux=b where Ax=b and PA=LU
+     b= [0,...,0,sign or 0]  (sign is either -1 or +1)
+     last row of A= [0,...,0,1]
+
+     1) Ly=Pb == y=b since P only permutes the 0's of   b
+
+  design:
+    for each row from end
+      perform back substitution
+      if near zero
+        use qh_divzero for division
+        if zero divide and not last row
+          set tail of normal to 0
+*/
+void qh_backnormal(qhT *qh, realT **rows, int numrow, int numcol, boolT sign,
+        coordT *normal, boolT *nearzero) {
+  int i, j;
+  coordT *normalp, *normal_tail, *ai, *ak;
+  realT diagonal;
+  boolT waszero;
+  int zerocol= -1;
+
+  normalp= normal + numcol - 1;
+  *normalp--= (sign ? -1.0 : 1.0);
+  for (i=numrow; i--; ) {
+    *normalp= 0.0;
+    ai= rows[i] + i + 1;
+    ak= normalp+1;
+    for (j=i+1; j < numcol; j++)
+      *normalp -= *ai++ * *ak++;
+    diagonal= (rows[i])[i];
+    if (fabs_(diagonal) > qh->MINdenom_2)
+      *(normalp--) /= diagonal;
+    else {
+      waszero= False;
+      *normalp= qh_divzero(*normalp, diagonal, qh->MINdenom_1_2, &waszero);
+      if (waszero) {
+        zerocol= i;
+        *(normalp--)= (sign ? -1.0 : 1.0);
+        for (normal_tail= normalp+2; normal_tail < normal + numcol; normal_tail++)
+          *normal_tail= 0.0;
+      }else
+        normalp--;
+    }
+  }
+  if (zerocol != -1) {
+    zzinc_(Zback0);
+    *nearzero= True;
+    trace4((qh, qh->ferr, 4005, "qh_backnormal: zero diagonal at column %d.\n", i));
+    qh_precision(qh, "zero diagonal on back substitution");
+  }
+} /* backnormal */
+
+/*---------------------------------
+
+  qh_gausselim(qh, rows, numrow, numcol, sign )
+    Gaussian elimination with partial pivoting
+
+  returns:
+    rows is upper triangular (includes row exchanges)
+    flips sign for each row exchange
+    sets nearzero if pivot[k] < qh.NEARzero[k], else clears it
+
+  notes:
+    if nearzero, the determinant's sign may be incorrect.
+    assumes numrow <= numcol
+
+  design:
+    for each row
+      determine pivot and exchange rows if necessary
+      test for near zero
+      perform gaussian elimination step
+*/
+void qh_gausselim(qhT *qh, realT **rows, int numrow, int numcol, boolT *sign, boolT *nearzero) {
+  realT *ai, *ak, *rowp, *pivotrow;
+  realT n, pivot, pivot_abs= 0.0, temp;
+  int i, j, k, pivoti, flip=0;
+
+  *nearzero= False;
+  for (k=0; k < numrow; k++) {
+    pivot_abs= fabs_((rows[k])[k]);
+    pivoti= k;
+    for (i=k+1; i < numrow; i++) {
+      if ((temp= fabs_((rows[i])[k])) > pivot_abs) {
+        pivot_abs= temp;
+        pivoti= i;
+      }
+    }
+    if (pivoti != k) {
+      rowp= rows[pivoti];
+      rows[pivoti]= rows[k];
+      rows[k]= rowp;
+      *sign ^= 1;
+      flip ^= 1;
+    }
+    if (pivot_abs <= qh->NEARzero[k]) {
+      *nearzero= True;
+      if (pivot_abs == 0.0) {   /* remainder of column == 0 */
+        if (qh->IStracing >= 4) {
+          qh_fprintf(qh, qh->ferr, 8011, "qh_gausselim: 0 pivot at column %d. (%2.2g < %2.2g)\n", k, pivot_abs, qh->DISTround);
+          qh_printmatrix(qh, qh->ferr, "Matrix:", rows, numrow, numcol);
+        }
+        zzinc_(Zgauss0);
+        qh_precision(qh, "zero pivot for Gaussian elimination");
+        goto LABELnextcol;
+      }
+    }
+    pivotrow= rows[k] + k;
+    pivot= *pivotrow++;  /* signed value of pivot, and remainder of row */
+    for (i=k+1; i < numrow; i++) {
+      ai= rows[i] + k;
+      ak= pivotrow;
+      n= (*ai++)/pivot;   /* divzero() not needed since |pivot| >= |*ai| */
+      for (j= numcol - (k+1); j--; )
+        *ai++ -= n * *ak++;
+    }
+  LABELnextcol:
+    ;
+  }
+  wmin_(Wmindenom, pivot_abs);  /* last pivot element */
+  if (qh->IStracing >= 5)
+    qh_printmatrix(qh, qh->ferr, "qh_gausselem: result", rows, numrow, numcol);
+} /* gausselim */
+
+
+/*---------------------------------
+
+  qh_getangle(qh, vect1, vect2 )
+    returns the dot product of two vectors
+    if qh.RANDOMdist, joggles result
+
+  notes:
+    the angle may be > 1.0 or < -1.0 because of roundoff errors
+
+*/
+realT qh_getangle(qhT *qh, pointT *vect1, pointT *vect2) {
+  realT angle= 0, randr;
+  int k;
+
+  for (k=qh->hull_dim; k--; )
+    angle += *vect1++ * *vect2++;
+  if (qh->RANDOMdist) {
+    randr= qh_RANDOMint;
+    angle += (2.0 * randr / qh_RANDOMmax - 1.0) *
+      qh->RANDOMfactor;
+  }
+  trace4((qh, qh->ferr, 4006, "qh_getangle: %2.2g\n", angle));
+  return(angle);
+} /* getangle */
+
+
+/*---------------------------------
+
+  qh_getcenter(qh, vertices )
+    returns arithmetic center of a set of vertices as a new point
+
+  notes:
+    allocates point array for center
+*/
+pointT *qh_getcenter(qhT *qh, setT *vertices) {
+  int k;
+  pointT *center, *coord;
+  vertexT *vertex, **vertexp;
+  int count= qh_setsize(qh, vertices);
+
+  if (count < 2) {
+    qh_fprintf(qh, qh->ferr, 6003, "qhull internal error (qh_getcenter): not defined for %d points\n", count);
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }
+  center= (pointT *)qh_memalloc(qh, qh->normal_size);
+  for (k=0; k < qh->hull_dim; k++) {
+    coord= center+k;
+    *coord= 0.0;
+    FOREACHvertex_(vertices)
+      *coord += vertex->point[k];
+    *coord /= count;  /* count>=2 by QH6003 */
+  }
+  return(center);
+} /* getcenter */
+
+
+/*---------------------------------
+
+  qh_getcentrum(qh, facet )
+    returns the centrum for a facet as a new point
+
+  notes:
+    allocates the centrum
+*/
+pointT *qh_getcentrum(qhT *qh, facetT *facet) {
+  realT dist;
+  pointT *centrum, *point;
+
+  point= qh_getcenter(qh, facet->vertices);
+  zzinc_(Zcentrumtests);
+  qh_distplane(qh, point, facet, &dist);
+  centrum= qh_projectpoint(qh, point, facet, dist);
+  qh_memfree(qh, point, qh->normal_size);
+  trace4((qh, qh->ferr, 4007, "qh_getcentrum: for f%d, %d vertices dist= %2.2g\n",
+          facet->id, qh_setsize(qh, facet->vertices), dist));
+  return centrum;
+} /* getcentrum */
+
+
+/*---------------------------------
+
+  qh_getdistance(qh, facet, neighbor, mindist, maxdist )
+    returns the maxdist and mindist distance of any vertex from neighbor
+
+  returns:
+    the max absolute value
+
+  design:
+    for each vertex of facet that is not in neighbor
+      test the distance from vertex to neighbor
+*/
+realT qh_getdistance(qhT *qh, facetT *facet, facetT *neighbor, realT *mindist, realT *maxdist) {
+  vertexT *vertex, **vertexp;
+  realT dist, maxd, mind;
+
+  FOREACHvertex_(facet->vertices)
+    vertex->seen= False;
+  FOREACHvertex_(neighbor->vertices)
+    vertex->seen= True;
+  mind= 0.0;
+  maxd= 0.0;
+  FOREACHvertex_(facet->vertices) {
+    if (!vertex->seen) {
+      zzinc_(Zbestdist);
+      qh_distplane(qh, vertex->point, neighbor, &dist);
+      if (dist < mind)
+        mind= dist;
+      else if (dist > maxd)
+        maxd= dist;
+    }
+  }
+  *mindist= mind;
+  *maxdist= maxd;
+  mind= -mind;
+  if (maxd > mind)
+    return maxd;
+  else
+    return mind;
+} /* getdistance */
+
+
+/*---------------------------------
+
+  qh_normalize(qh, normal, dim, toporient )
+    normalize a vector and report if too small
+    does not use min norm
+
+  see:
+    qh_normalize2
+*/
+void qh_normalize(qhT *qh, coordT *normal, int dim, boolT toporient) {
+  qh_normalize2(qh, normal, dim, toporient, NULL, NULL);
+} /* normalize */
+
+/*---------------------------------
+
+  qh_normalize2(qh, normal, dim, toporient, minnorm, ismin )
+    normalize a vector and report if too small
+    qh.MINdenom/MINdenom1 are the upper limits for divide overflow
+
+  returns:
+    normalized vector
+    flips sign if !toporient
+    if minnorm non-NULL,
+      sets ismin if normal < minnorm
+
+  notes:
+    if zero norm
+       sets all elements to sqrt(1.0/dim)
+    if divide by zero (divzero())
+       sets largest element to   +/-1
+       bumps Znearlysingular
+
+  design:
+    computes norm
+    test for minnorm
+    if not near zero
+      normalizes normal
+    else if zero norm
+      sets normal to standard value
+    else
+      uses qh_divzero to normalize
+      if nearzero
+        sets norm to direction of maximum value
+*/
+void qh_normalize2(qhT *qh, coordT *normal, int dim, boolT toporient,
+            realT *minnorm, boolT *ismin) {
+  int k;
+  realT *colp, *maxp, norm= 0, temp, *norm1, *norm2, *norm3;
+  boolT zerodiv;
+
+  norm1= normal+1;
+  norm2= normal+2;
+  norm3= normal+3;
+  if (dim == 2)
+    norm= sqrt((*normal)*(*normal) + (*norm1)*(*norm1));
+  else if (dim == 3)
+    norm= sqrt((*normal)*(*normal) + (*norm1)*(*norm1) + (*norm2)*(*norm2));
+  else if (dim == 4) {
+    norm= sqrt((*normal)*(*normal) + (*norm1)*(*norm1) + (*norm2)*(*norm2)
+               + (*norm3)*(*norm3));
+  }else if (dim > 4) {
+    norm= (*normal)*(*normal) + (*norm1)*(*norm1) + (*norm2)*(*norm2)
+               + (*norm3)*(*norm3);
+    for (k=dim-4, colp=normal+4; k--; colp++)
+      norm += (*colp) * (*colp);
+    norm= sqrt(norm);
+  }
+  if (minnorm) {
+    if (norm < *minnorm)
+      *ismin= True;
+    else
+      *ismin= False;
+  }
+  wmin_(Wmindenom, norm);
+  if (norm > qh->MINdenom) {
+    if (!toporient)
+      norm= -norm;
+    *normal /= norm;
+    *norm1 /= norm;
+    if (dim == 2)
+      ; /* all done */
+    else if (dim == 3)
+      *norm2 /= norm;
+    else if (dim == 4) {
+      *norm2 /= norm;
+      *norm3 /= norm;
+    }else if (dim >4) {
+      *norm2 /= norm;
+      *norm3 /= norm;
+      for (k=dim-4, colp=normal+4; k--; )
+        *colp++ /= norm;
+    }
+  }else if (norm == 0.0) {
+    temp= sqrt(1.0/dim);
+    for (k=dim, colp=normal; k--; )
+      *colp++ = temp;
+  }else {
+    if (!toporient)
+      norm= -norm;
+    for (k=dim, colp=normal; k--; colp++) { /* k used below */
+      temp= qh_divzero(*colp, norm, qh->MINdenom_1, &zerodiv);
+      if (!zerodiv)
+        *colp= temp;
+      else {
+        maxp= qh_maxabsval(normal, dim);
+        temp= ((*maxp * norm >= 0.0) ? 1.0 : -1.0);
+        for (k=dim, colp=normal; k--; colp++)
+          *colp= 0.0;
+        *maxp= temp;
+        zzinc_(Znearlysingular);
+        trace0((qh, qh->ferr, 1, "qh_normalize: norm=%2.2g too small during p%d\n",
+               norm, qh->furthest_id));
+        return;
+      }
+    }
+  }
+} /* normalize */
+
+
+/*---------------------------------
+
+  qh_projectpoint(qh, point, facet, dist )
+    project point onto a facet by dist
+
+  returns:
+    returns a new point
+
+  notes:
+    if dist= distplane(point,facet)
+      this projects point to hyperplane
+    assumes qh_memfree_() is valid for normal_size
+*/
+pointT *qh_projectpoint(qhT *qh, pointT *point, facetT *facet, realT dist) {
+  pointT *newpoint, *np, *normal;
+  int normsize= qh->normal_size;
+  int k;
+  void **freelistp; /* used if !qh_NOmem by qh_memalloc_() */
+
+  qh_memalloc_(qh, normsize, freelistp, newpoint, pointT);
+  np= newpoint;
+  normal= facet->normal;
+  for (k=qh->hull_dim; k--; )
+    *(np++)= *point++ - dist * *normal++;
+  return(newpoint);
+} /* projectpoint */
+
+
+/*---------------------------------
+
+  qh_setfacetplane(qh, facet )
+    sets the hyperplane for a facet
+    if qh.RANDOMdist, joggles hyperplane
+
+  notes:
+    uses global buffers qh.gm_matrix and qh.gm_row
+    overwrites facet->normal if already defined
+    updates Wnewvertex if PRINTstatistics
+    sets facet->upperdelaunay if upper envelope of Delaunay triangulation
+
+  design:
+    copy vertex coordinates to qh.gm_matrix/gm_row
+    compute determinate
+    if nearzero
+      recompute determinate with gaussian elimination
+      if nearzero
+        force outside orientation by testing interior point
+*/
+void qh_setfacetplane(qhT *qh, facetT *facet) {
+  pointT *point;
+  vertexT *vertex, **vertexp;
+  int normsize= qh->normal_size;
+  int k,i, oldtrace= 0;
+  realT dist;
+  void **freelistp; /* used if !qh_NOmem by qh_memalloc_() */
+  coordT *coord, *gmcoord;
+  pointT *point0= SETfirstt_(facet->vertices, vertexT)->point;
+  boolT nearzero= False;
+
+  zzinc_(Zsetplane);
+  if (!facet->normal)
+    qh_memalloc_(qh, normsize, freelistp, facet->normal, coordT);
+  if (facet == qh->tracefacet) {
+    oldtrace= qh->IStracing;
+    qh->IStracing= 5;
+    qh_fprintf(qh, qh->ferr, 8012, "qh_setfacetplane: facet f%d created.\n", facet->id);
+    qh_fprintf(qh, qh->ferr, 8013, "  Last point added to hull was p%d.", qh->furthest_id);
+    if (zzval_(Ztotmerge))
+      qh_fprintf(qh, qh->ferr, 8014, "  Last merge was #%d.", zzval_(Ztotmerge));
+    qh_fprintf(qh, qh->ferr, 8015, "\n\nCurrent summary is:\n");
+      qh_printsummary(qh, qh->ferr);
+  }
+  if (qh->hull_dim <= 4) {
+    i= 0;
+    if (qh->RANDOMdist) {
+      gmcoord= qh->gm_matrix;
+      FOREACHvertex_(facet->vertices) {
+        qh->gm_row[i++]= gmcoord;
+        coord= vertex->point;
+        for (k=qh->hull_dim; k--; )
+          *(gmcoord++)= *coord++ * qh_randomfactor(qh, qh->RANDOMa, qh->RANDOMb);
+      }
+    }else {
+      FOREACHvertex_(facet->vertices)
+       qh->gm_row[i++]= vertex->point;
+    }
+    qh_sethyperplane_det(qh, qh->hull_dim, qh->gm_row, point0, facet->toporient,
+                facet->normal, &facet->offset, &nearzero);
+  }
+  if (qh->hull_dim > 4 || nearzero) {
+    i= 0;
+    gmcoord= qh->gm_matrix;
+    FOREACHvertex_(facet->vertices) {
+      if (vertex->point != point0) {
+        qh->gm_row[i++]= gmcoord;
+        coord= vertex->point;
+        point= point0;
+        for (k=qh->hull_dim; k--; )
+          *(gmcoord++)= *coord++ - *point++;
+      }
+    }
+    qh->gm_row[i]= gmcoord;  /* for areasimplex */
+    if (qh->RANDOMdist) {
+      gmcoord= qh->gm_matrix;
+      for (i=qh->hull_dim-1; i--; ) {
+        for (k=qh->hull_dim; k--; )
+          *(gmcoord++) *= qh_randomfactor(qh, qh->RANDOMa, qh->RANDOMb);
+      }
+    }
+    qh_sethyperplane_gauss(qh, qh->hull_dim, qh->gm_row, point0, facet->toporient,
+                facet->normal, &facet->offset, &nearzero);
+    if (nearzero) {
+      if (qh_orientoutside(qh, facet)) {
+        trace0((qh, qh->ferr, 2, "qh_setfacetplane: flipped orientation after testing interior_point during p%d\n", qh->furthest_id));
+      /* this is part of using Gaussian Elimination.  For example in 5-d
+           1 1 1 1 0
+           1 1 1 1 1
+           0 0 0 1 0
+           0 1 0 0 0
+           1 0 0 0 0
+           norm= 0.38 0.38 -0.76 0.38 0
+         has a determinate of 1, but g.e. after subtracting pt. 0 has
+         0's in the diagonal, even with full pivoting.  It does work
+         if you subtract pt. 4 instead. */
+      }
+    }
+  }
+  facet->upperdelaunay= False;
+  if (qh->DELAUNAY) {
+    if (qh->UPPERdelaunay) {     /* matches qh_triangulate_facet and qh.lower_threshold in qh_initbuild */
+      if (facet->normal[qh->hull_dim -1] >= qh->ANGLEround * qh_ZEROdelaunay)
+        facet->upperdelaunay= True;
+    }else {
+      if (facet->normal[qh->hull_dim -1] > -qh->ANGLEround * qh_ZEROdelaunay)
+        facet->upperdelaunay= True;
+    }
+  }
+  if (qh->PRINTstatistics || qh->IStracing || qh->TRACElevel || qh->JOGGLEmax < REALmax) {
+    qh->old_randomdist= qh->RANDOMdist;
+    qh->RANDOMdist= False;
+    FOREACHvertex_(facet->vertices) {
+      if (vertex->point != point0) {
+        boolT istrace= False;
+        zinc_(Zdiststat);
+        qh_distplane(qh, vertex->point, facet, &dist);
+        dist= fabs_(dist);
+        zinc_(Znewvertex);
+        wadd_(Wnewvertex, dist);
+        if (dist > wwval_(Wnewvertexmax)) {
+          wwval_(Wnewvertexmax)= dist;
+          if (dist > qh->max_outside) {
+            qh->max_outside= dist;  /* used by qh_maxouter(qh) */
+            if (dist > qh->TRACEdist)
+              istrace= True;
+          }
+        }else if (-dist > qh->TRACEdist)
+          istrace= True;
+        if (istrace) {
+          qh_fprintf(qh, qh->ferr, 8016, "qh_setfacetplane: ====== vertex p%d(v%d) increases max_outside to %2.2g for new facet f%d last p%d\n",
+                qh_pointid(qh, vertex->point), vertex->id, dist, facet->id, qh->furthest_id);
+          qh_errprint(qh, "DISTANT", facet, NULL, NULL, NULL);
+        }
+      }
+    }
+    qh->RANDOMdist= qh->old_randomdist;
+  }
+  if (qh->IStracing >= 3) {
+    qh_fprintf(qh, qh->ferr, 8017, "qh_setfacetplane: f%d offset %2.2g normal: ",
+             facet->id, facet->offset);
+    for (k=0; k < qh->hull_dim; k++)
+      qh_fprintf(qh, qh->ferr, 8018, "%2.2g ", facet->normal[k]);
+    qh_fprintf(qh, qh->ferr, 8019, "\n");
+  }
+  if (facet == qh->tracefacet)
+    qh->IStracing= oldtrace;
+} /* setfacetplane */
+
+
+/*---------------------------------
+
+  qh_sethyperplane_det(qh, dim, rows, point0, toporient, normal, offset, nearzero )
+    given dim X dim array indexed by rows[], one row per point,
+        toporient(flips all signs),
+        and point0 (any row)
+    set normalized hyperplane equation from oriented simplex
+
+  returns:
+    normal (normalized)
+    offset (places point0 on the hyperplane)
+    sets nearzero if hyperplane not through points
+
+  notes:
+    only defined for dim == 2..4
+    rows[] is not modified
+    solves det(P-V_0, V_n-V_0, ..., V_1-V_0)=0, i.e. every point is on hyperplane
+    see Bower & Woodworth, A programmer's geometry, Butterworths 1983.
+
+  derivation of 3-d minnorm
+    Goal: all vertices V_i within qh.one_merge of hyperplane
+    Plan: exactly translate the facet so that V_0 is the origin
+          exactly rotate the facet so that V_1 is on the x-axis and y_2=0.
+          exactly rotate the effective perturbation to only effect n_0
+             this introduces a factor of sqrt(3)
+    n_0 = ((y_2-y_0)*(z_1-z_0) - (z_2-z_0)*(y_1-y_0)) / norm
+    Let M_d be the max coordinate difference
+    Let M_a be the greater of M_d and the max abs. coordinate
+    Let u be machine roundoff and distround be max error for distance computation
+    The max error for n_0 is sqrt(3) u M_a M_d / norm.  n_1 is approx. 1 and n_2 is approx. 0
+    The max error for distance of V_1 is sqrt(3) u M_a M_d M_d / norm.  Offset=0 at origin
+    Then minnorm = 1.8 u M_a M_d M_d / qh.ONEmerge
+    Note that qh.one_merge is approx. 45.5 u M_a and norm is usually about M_d M_d
+
+  derivation of 4-d minnorm
+    same as above except rotate the facet so that V_1 on x-axis and w_2, y_3, w_3=0
+     [if two vertices fixed on x-axis, can rotate the other two in yzw.]
+    n_0 = det3_(...) = y_2 det2_(z_1, w_1, z_3, w_3) = - y_2 w_1 z_3
+     [all other terms contain at least two factors nearly zero.]
+    The max error for n_0 is sqrt(4) u M_a M_d M_d / norm
+    Then minnorm = 2 u M_a M_d M_d M_d / qh.ONEmerge
+    Note that qh.one_merge is approx. 82 u M_a and norm is usually about M_d M_d M_d
+*/
+void qh_sethyperplane_det(qhT *qh, int dim, coordT **rows, coordT *point0,
+          boolT toporient, coordT *normal, realT *offset, boolT *nearzero) {
+  realT maxround, dist;
+  int i;
+  pointT *point;
+
+
+  if (dim == 2) {
+    normal[0]= dY(1,0);
+    normal[1]= dX(0,1);
+    qh_normalize2(qh, normal, dim, toporient, NULL, NULL);
+    *offset= -(point0[0]*normal[0]+point0[1]*normal[1]);
+    *nearzero= False;  /* since nearzero norm => incident points */
+  }else if (dim == 3) {
+    normal[0]= det2_(dY(2,0), dZ(2,0),
+                     dY(1,0), dZ(1,0));
+    normal[1]= det2_(dX(1,0), dZ(1,0),
+                     dX(2,0), dZ(2,0));
+    normal[2]= det2_(dX(2,0), dY(2,0),
+                     dX(1,0), dY(1,0));
+    qh_normalize2(qh, normal, dim, toporient, NULL, NULL);
+    *offset= -(point0[0]*normal[0] + point0[1]*normal[1]
+               + point0[2]*normal[2]);
+    maxround= qh->DISTround;
+    for (i=dim; i--; ) {
+      point= rows[i];
+      if (point != point0) {
+        dist= *offset + (point[0]*normal[0] + point[1]*normal[1]
+               + point[2]*normal[2]);
+        if (dist > maxround || dist < -maxround) {
+          *nearzero= True;
+          break;
+        }
+      }
+    }
+  }else if (dim == 4) {
+    normal[0]= - det3_(dY(2,0), dZ(2,0), dW(2,0),
+                        dY(1,0), dZ(1,0), dW(1,0),
+                        dY(3,0), dZ(3,0), dW(3,0));
+    normal[1]=   det3_(dX(2,0), dZ(2,0), dW(2,0),
+                        dX(1,0), dZ(1,0), dW(1,0),
+                        dX(3,0), dZ(3,0), dW(3,0));
+    normal[2]= - det3_(dX(2,0), dY(2,0), dW(2,0),
+                        dX(1,0), dY(1,0), dW(1,0),
+                        dX(3,0), dY(3,0), dW(3,0));
+    normal[3]=   det3_(dX(2,0), dY(2,0), dZ(2,0),
+                        dX(1,0), dY(1,0), dZ(1,0),
+                        dX(3,0), dY(3,0), dZ(3,0));
+    qh_normalize2(qh, normal, dim, toporient, NULL, NULL);
+    *offset= -(point0[0]*normal[0] + point0[1]*normal[1]
+               + point0[2]*normal[2] + point0[3]*normal[3]);
+    maxround= qh->DISTround;
+    for (i=dim; i--; ) {
+      point= rows[i];
+      if (point != point0) {
+        dist= *offset + (point[0]*normal[0] + point[1]*normal[1]
+               + point[2]*normal[2] + point[3]*normal[3]);
+        if (dist > maxround || dist < -maxround) {
+          *nearzero= True;
+          break;
+        }
+      }
+    }
+  }
+  if (*nearzero) {
+    zzinc_(Zminnorm);
+    trace0((qh, qh->ferr, 3, "qh_sethyperplane_det: degenerate norm during p%d.\n", qh->furthest_id));
+    zzinc_(Znearlysingular);
+  }
+} /* sethyperplane_det */
+
+
+/*---------------------------------
+
+  qh_sethyperplane_gauss(qh, dim, rows, point0, toporient, normal, offset, nearzero )
+    given(dim-1) X dim array of rows[i]= V_{i+1} - V_0 (point0)
+    set normalized hyperplane equation from oriented simplex
+
+  returns:
+    normal (normalized)
+    offset (places point0 on the hyperplane)
+
+  notes:
+    if nearzero
+      orientation may be incorrect because of incorrect sign flips in gausselim
+    solves [V_n-V_0,...,V_1-V_0, 0 .. 0 1] * N == [0 .. 0 1]
+        or [V_n-V_0,...,V_1-V_0, 0 .. 0 1] * N == [0]
+    i.e., N is normal to the hyperplane, and the unnormalized
+        distance to [0 .. 1] is either 1 or   0
+
+  design:
+    perform gaussian elimination
+    flip sign for negative values
+    perform back substitution
+    normalize result
+    compute offset
+*/
+void qh_sethyperplane_gauss(qhT *qh, int dim, coordT **rows, pointT *point0,
+                boolT toporient, coordT *normal, coordT *offset, boolT *nearzero) {
+  coordT *pointcoord, *normalcoef;
+  int k;
+  boolT sign= toporient, nearzero2= False;
+
+  qh_gausselim(qh, rows, dim-1, dim, &sign, nearzero);
+  for (k=dim-1; k--; ) {
+    if ((rows[k])[k] < 0)
+      sign ^= 1;
+  }
+  if (*nearzero) {
+    zzinc_(Znearlysingular);
+    trace0((qh, qh->ferr, 4, "qh_sethyperplane_gauss: nearly singular or axis parallel hyperplane during p%d.\n", qh->furthest_id));
+    qh_backnormal(qh, rows, dim-1, dim, sign, normal, &nearzero2);
+  }else {
+    qh_backnormal(qh, rows, dim-1, dim, sign, normal, &nearzero2);
+    if (nearzero2) {
+      zzinc_(Znearlysingular);
+      trace0((qh, qh->ferr, 5, "qh_sethyperplane_gauss: singular or axis parallel hyperplane at normalization during p%d.\n", qh->furthest_id));
+    }
+  }
+  if (nearzero2)
+    *nearzero= True;
+  qh_normalize2(qh, normal, dim, True, NULL, NULL);
+  pointcoord= point0;
+  normalcoef= normal;
+  *offset= -(*pointcoord++ * *normalcoef++);
+  for (k=dim-1; k--; )
+    *offset -= *pointcoord++ * *normalcoef++;
+} /* sethyperplane_gauss */
+
+
+
diff --git a/Cdir/global_r.c b/Cdir/global_r.c
new file mode 100644
--- /dev/null
+++ b/Cdir/global_r.c
@@ -0,0 +1,2100 @@
+
+/*
  ---------------------------------
+
+   global_r.c
+   initializes all the globals of the qhull application
+
+   see README
+
+   see libqhull_r.h for qh.globals and function prototypes
+
+   see qhull_ra.h for internal functions
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull_r/global_r.c#16 $$Change: 2066 $
+   $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
+ */
+
+#include "qhull_ra.h"
+
+/*========= qh->definition -- globals defined in libqhull_r.h =======================*/
+
+/*----------------------------------
+
+  qh_version
+    version string by year and date
+    qh_version2 for Unix users and -V
+
+    the revision increases on code changes only
+
+  notes:
+    change date:    Changes.txt, Announce.txt, index.htm, README.txt,
+                    qhull-news.html, Eudora signatures, CMakeLists.txt
+    change version: README.txt, qh-get.htm, File_id.diz, Makefile.txt, CMakeLists.txt
+    check that CmakeLists @version is the same as qh_version2
+    change year:    Copying.txt
+    check download size
+    recompile user_eg_r.c, rbox_r.c, libqhull_r.c, qconvex_r.c, qdelaun_r.c qvoronoi_r.c, qhalf_r.c, testqset_r.c
+*/
+
+const char qh_version[]= "2015.2.r 2016/01/18";
+const char qh_version2[]= "qhull_r 7.2.0 (2015.2.r 2016/01/18)";
+
+/*---------------------------------
+
+  qh_appendprint(qh, printFormat )
+    append printFormat to qh.PRINTout unless already defined
+*/
+void qh_appendprint(qhT *qh, qh_PRINT format) {
+  int i;
+
+  for (i=0; i < qh_PRINTEND; i++) {
+    if (qh->PRINTout[i] == format && format != qh_PRINTqhull)
+      break;
+    if (!qh->PRINTout[i]) {
+      qh->PRINTout[i]= format;
+      break;
+    }
+  }
+} /* appendprint */
+
+/*---------------------------------
+
+  qh_checkflags(qh, commandStr, hiddenFlags )
+    errors if commandStr contains hiddenFlags
+    hiddenFlags starts and ends with a space and is space delimited (checked)
+
+  notes:
+    ignores first word (e.g., "qconvex i")
+    use qh_strtol/strtod since strtol/strtod may or may not skip trailing spaces
+
+  see:
+    qh_initflags() initializes Qhull according to commandStr
+*/
+void qh_checkflags(qhT *qh, char *command, char *hiddenflags) {
+  char *s= command, *t, *chkerr; /* qh_skipfilename is non-const */
+  char key, opt, prevopt;
+  char chkkey[]= "   ";
+  char chkopt[]=  "    ";
+  char chkopt2[]= "     ";
+  boolT waserr= False;
+
+  if (*hiddenflags != ' ' || hiddenflags[strlen(hiddenflags)-1] != ' ') {
+    qh_fprintf(qh, qh->ferr, 6026, "qhull error (qh_checkflags): hiddenflags must start and end with a space: \"%s\"", hiddenflags);
+    qh_errexit(qh, qh_ERRinput, NULL, NULL);
+  }
+  if (strpbrk(hiddenflags, ",\n\r\t")) {
+    qh_fprintf(qh, qh->ferr, 6027, "qhull error (qh_checkflags): hiddenflags contains commas, newlines, or tabs: \"%s\"", hiddenflags);
+    qh_errexit(qh, qh_ERRinput, NULL, NULL);
+  }
+  while (*s && !isspace(*s))  /* skip program name */
+    s++;
+  while (*s) {
+    while (*s && isspace(*s))
+      s++;
+    if (*s == '-')
+      s++;
+    if (!*s)
+      break;
+    key = *s++;
+    chkerr = NULL;
+    if (key == 'T' && (*s == 'I' || *s == 'O')) {  /* TI or TO 'file name' */
+      s= qh_skipfilename(qh, ++s);
+      continue;
+    }
+    chkkey[1]= key;
+    if (strstr(hiddenflags, chkkey)) {
+      chkerr= chkkey;
+    }else if (isupper(key)) {
+      opt= ' ';
+      prevopt= ' ';
+      chkopt[1]= key;
+      chkopt2[1]= key;
+      while (!chkerr && *s && !isspace(*s)) {
+        opt= *s++;
+        if (isalpha(opt)) {
+          chkopt[2]= opt;
+          if (strstr(hiddenflags, chkopt))
+            chkerr= chkopt;
+          if (prevopt != ' ') {
+            chkopt2[2]= prevopt;
+            chkopt2[3]= opt;
+            if (strstr(hiddenflags, chkopt2))
+              chkerr= chkopt2;
+          }
+        }else if (key == 'Q' && isdigit(opt) && prevopt != 'b'
+              && (prevopt == ' ' || islower(prevopt))) {
+            chkopt[2]= opt;
+            if (strstr(hiddenflags, chkopt))
+              chkerr= chkopt;
+        }else {
+          qh_strtod(s-1, &t);
+          if (s < t)
+            s= t;
+        }
+        prevopt= opt;
+      }
+    }
+    if (chkerr) {
+      *chkerr= '\'';
+      chkerr[strlen(chkerr)-1]=  '\'';
+      qh_fprintf(qh, qh->ferr, 6029, "qhull error: option %s is not used with this program.\n             It may be used with qhull.\n", chkerr);
+      waserr= True;
+    }
+  }
+  if (waserr)
+    qh_errexit(qh, qh_ERRinput, NULL, NULL);
+} /* checkflags */
+
+/*---------------------------------
+
+  qh_clear_outputflags(qh)
+    Clear output flags for QhullPoints
+*/
+void qh_clear_outputflags(qhT *qh) {
+  int i,k;
+
+  qh->ANNOTATEoutput= False;
+  qh->DOintersections= False;
+  qh->DROPdim= -1;
+  qh->FORCEoutput= False;
+  qh->GETarea= False;
+  qh->GOODpoint= 0;
+  qh->GOODpointp= NULL;
+  qh->GOODthreshold= False;
+  qh->GOODvertex= 0;
+  qh->GOODvertexp= NULL;
+  qh->IStracing= 0;
+  qh->KEEParea= False;
+  qh->KEEPmerge= False;
+  qh->KEEPminArea= REALmax;
+  qh->PRINTcentrums= False;
+  qh->PRINTcoplanar= False;
+  qh->PRINTdots= False;
+  qh->PRINTgood= False;
+  qh->PRINTinner= False;
+  qh->PRINTneighbors= False;
+  qh->PRINTnoplanes= False;
+  qh->PRINToptions1st= False;
+  qh->PRINTouter= False;
+  qh->PRINTprecision= True;
+  qh->PRINTridges= False;
+  qh->PRINTspheres= False;
+  qh->PRINTstatistics= False;
+  qh->PRINTsummary= False;
+  qh->PRINTtransparent= False;
+  qh->SPLITthresholds= False;
+  qh->TRACElevel= 0;
+  qh->TRInormals= False;
+  qh->USEstdout= False;
+  qh->VERIFYoutput= False;
+  for (k=qh->input_dim+1; k--; ) {  /* duplicated in qh_initqhull_buffers and qh_clear_outputflags */
+    qh->lower_threshold[k]= -REALmax;
+    qh->upper_threshold[k]= REALmax;
+    qh->lower_bound[k]= -REALmax;
+    qh->upper_bound[k]= REALmax;
+  }
+
+  for (i=0; i < qh_PRINTEND; i++) {
+    qh->PRINTout[i]= qh_PRINTnone;
+  }
+
+  if (!qh->qhull_commandsiz2)
+      qh->qhull_commandsiz2= (int)strlen(qh->qhull_command); /* WARN64 */
+  else {
+      qh->qhull_command[qh->qhull_commandsiz2]= '\0';
+  }
+  if (!qh->qhull_optionsiz2)
+    qh->qhull_optionsiz2= (int)strlen(qh->qhull_options);  /* WARN64 */
+  else {
+    qh->qhull_options[qh->qhull_optionsiz2]= '\0';
+    qh->qhull_optionlen= qh_OPTIONline;  /* start a new line */
+  }
+} /* clear_outputflags */
+
+/*---------------------------------
+
+  qh_clock()
+    return user CPU time in 100ths (qh_SECtick)
+    only defined for qh_CLOCKtype == 2
+
+  notes:
+    use first value to determine time 0
+    from Stevens '92 8.15
+*/
+unsigned long qh_clock(qhT *qh) {
+
+#if (qh_CLOCKtype == 2)
+  struct tms time;
+  static long clktck;  /* initialized first call and never updated */
+  double ratio, cpu;
+  unsigned long ticks;
+
+  if (!clktck) {
+    if ((clktck= sysconf(_SC_CLK_TCK)) < 0) {
+      qh_fprintf(qh, qh->ferr, 6030, "qhull internal error (qh_clock): sysconf() failed.  Use qh_CLOCKtype 1 in user.h\n");
+      qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+    }
+  }
+  if (times(&time) == -1) {
+    qh_fprintf(qh, qh->ferr, 6031, "qhull internal error (qh_clock): times() failed.  Use qh_CLOCKtype 1 in user.h\n");
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }
+  ratio= qh_SECticks / (double)clktck;
+  ticks= time.tms_utime * ratio;
+  return ticks;
+#else
+  qh_fprintf(qh, qh->ferr, 6032, "qhull internal error (qh_clock): use qh_CLOCKtype 2 in user.h\n");
+  qh_errexit(qh, qh_ERRqhull, NULL, NULL); /* never returns */
+  return 0;
+#endif
+} /* clock */
+
+/*---------------------------------
+
+  qh_freebuffers()
+    free up global memory buffers
+
+  notes:
+    must match qh_initbuffers()
+*/
+void qh_freebuffers(qhT *qh) {
+
+  trace5((qh, qh->ferr, 5001, "qh_freebuffers: freeing up global memory buffers\n"));
+  /* allocated by qh_initqhull_buffers */
+  qh_memfree(qh, qh->NEARzero, qh->hull_dim * sizeof(realT));
+  qh_memfree(qh, qh->lower_threshold, (qh->input_dim+1) * sizeof(realT));
+  qh_memfree(qh, qh->upper_threshold, (qh->input_dim+1) * sizeof(realT));
+  qh_memfree(qh, qh->lower_bound, (qh->input_dim+1) * sizeof(realT));
+  qh_memfree(qh, qh->upper_bound, (qh->input_dim+1) * sizeof(realT));
+  qh_memfree(qh, qh->gm_matrix, (qh->hull_dim+1) * qh->hull_dim * sizeof(coordT));
+  qh_memfree(qh, qh->gm_row, (qh->hull_dim+1) * sizeof(coordT *));
+  qh->NEARzero= qh->lower_threshold= qh->upper_threshold= NULL;
+  qh->lower_bound= qh->upper_bound= NULL;
+  qh->gm_matrix= NULL;
+  qh->gm_row= NULL;
+  qh_setfree(qh, &qh->other_points);
+  qh_setfree(qh, &qh->del_vertices);
+  qh_setfree(qh, &qh->coplanarfacetset);
+  if (qh->line)                /* allocated by qh_readinput, freed if no error */
+    qh_free(qh->line);
+  if (qh->half_space)
+    qh_free(qh->half_space);
+  if (qh->temp_malloc)
+    qh_free(qh->temp_malloc);
+  if (qh->feasible_point)      /* allocated by qh_readfeasible */
+    qh_free(qh->feasible_point);
+  if (qh->feasible_string)     /* allocated by qh_initflags */
+    qh_free(qh->feasible_string);
+  qh->line= qh->feasible_string= NULL;
+  qh->half_space= qh->feasible_point= qh->temp_malloc= NULL;
+  /* usually allocated by qh_readinput */
+  if (qh->first_point && qh->POINTSmalloc) {
+    qh_free(qh->first_point);
+    qh->first_point= NULL;
+  }
+  if (qh->input_points && qh->input_malloc) { /* set by qh_joggleinput */
+    qh_free(qh->input_points);
+    qh->input_points= NULL;
+  }
+  trace5((qh, qh->ferr, 5002, "qh_freebuffers: finished\n"));
+} /* freebuffers */
+
+
+/*---------------------------------
+
+  qh_freebuild(qh, allmem )
+    free global memory used by qh_initbuild and qh_buildhull
+    if !allmem,
+      does not free short memory (e.g., facetT, freed by qh_memfreeshort)
+
+  design:
+    free centrums
+    free each vertex
+    mark unattached ridges
+    for each facet
+      free ridges
+      free outside set, coplanar set, neighbor set, ridge set, vertex set
+      free facet
+    free hash table
+    free interior point
+    free merge set
+    free temporary sets
+*/
+void qh_freebuild(qhT *qh, boolT allmem) {
+  facetT *facet;
+  vertexT *vertex;
+  ridgeT *ridge, **ridgep;
+  mergeT *merge, **mergep;
+
+  trace1((qh, qh->ferr, 1005, "qh_freebuild: free memory from qh_inithull and qh_buildhull\n"));
+  if (qh->del_vertices)
+    qh_settruncate(qh, qh->del_vertices, 0);
+  if (allmem) {
+    while ((vertex= qh->vertex_list)) {
+      if (vertex->next)
+        qh_delvertex(qh, vertex);
+      else {
+        qh_memfree(qh, vertex, (int)sizeof(vertexT));
+        qh->newvertex_list= qh->vertex_list= NULL;
+      }
+    }
+  }else if (qh->VERTEXneighbors) {
+    FORALLvertices
+      qh_setfreelong(qh, &(vertex->neighbors));
+  }
+  qh->VERTEXneighbors= False;
+  qh->GOODclosest= NULL;
+  if (allmem) {
+    FORALLfacets {
+      FOREACHridge_(facet->ridges)
+        ridge->seen= False;
+    }
+    FORALLfacets {
+      if (facet->visible) {
+        FOREACHridge_(facet->ridges) {
+          if (!otherfacet_(ridge, facet)->visible)
+            ridge->seen= True;  /* an unattached ridge */
+        }
+      }
+    }
+    while ((facet= qh->facet_list)) {
+      FOREACHridge_(facet->ridges) {
+        if (ridge->seen) {
+          qh_setfree(qh, &(ridge->vertices));
+          qh_memfree(qh, ridge, (int)sizeof(ridgeT));
+        }else
+          ridge->seen= True;
+      }
+      qh_setfree(qh, &(facet->outsideset));
+      qh_setfree(qh, &(facet->coplanarset));
+      qh_setfree(qh, &(facet->neighbors));
+      qh_setfree(qh, &(facet->ridges));
+      qh_setfree(qh, &(facet->vertices));
+      if (facet->next)
+        qh_delfacet(qh, facet);
+      else {
+        qh_memfree(qh, facet, (int)sizeof(facetT));
+        qh->visible_list= qh->newfacet_list= qh->facet_list= NULL;
+      }
+    }
+  }else {
+    FORALLfacets {
+      qh_setfreelong(qh, &(facet->outsideset));
+      qh_setfreelong(qh, &(facet->coplanarset));
+      if (!facet->simplicial) {
+        qh_setfreelong(qh, &(facet->neighbors));
+        qh_setfreelong(qh, &(facet->ridges));
+        qh_setfreelong(qh, &(facet->vertices));
+      }
+    }
+  }
+  qh_setfree(qh, &(qh->hash_table));
+  qh_memfree(qh, qh->interior_point, qh->normal_size);
+  qh->interior_point= NULL;
+  FOREACHmerge_(qh->facet_mergeset)  /* usually empty */
+    qh_memfree(qh, merge, (int)sizeof(mergeT));
+  qh->facet_mergeset= NULL;  /* temp set */
+  qh->degen_mergeset= NULL;  /* temp set */
+  qh_settempfree_all(qh);
+} /* freebuild */
+
+/*---------------------------------
+
+  qh_freeqhull(qh, allmem )
+
+  free global memory and set qhT to 0
+  if !allmem,
+    does not free short memory (freed by qh_memfreeshort unless qh_NOmem)
+
+notes:
+  sets qh.NOerrexit in case caller forgets to
+  Does not throw errors
+
+see:
+  see qh_initqhull_start2()
+  For libqhull_r, qhstatT is part of qhT
+
+design:
+  free global and temporary memory from qh_initbuild and qh_buildhull
+  free buffers
+*/
+void qh_freeqhull(qhT *qh, boolT allmem) {
+
+  qh->NOerrexit= True;  /* no more setjmp since called at exit and ~QhullQh */
+  trace1((qh, qh->ferr, 1006, "qh_freeqhull: free global memory\n"));
+  qh_freebuild(qh, allmem);
+  qh_freebuffers(qh);
+  /* memset is the same in qh_freeqhull() and qh_initqhull_start2() */
+  memset((char *)qh, 0, sizeof(qhT)-sizeof(qhmemT)-sizeof(qhstatT));
+  qh->NOerrexit= True;
+} /* freeqhull2 */
+
+/*---------------------------------
+
+  qh_init_A(qh, infile, outfile, errfile, argc, argv )
+    initialize memory and stdio files
+    convert input options to option string (qh.qhull_command)
+
+  notes:
+    infile may be NULL if qh_readpoints() is not called
+
+    errfile should always be defined.  It is used for reporting
+    errors.  outfile is used for output and format options.
+
+    argc/argv may be 0/NULL
+
+    called before error handling initialized
+    qh_errexit() may not be used
+*/
+void qh_init_A(qhT *qh, FILE *infile, FILE *outfile, FILE *errfile, int argc, char *argv[]) {
+  qh_meminit(qh, errfile);
+  qh_initqhull_start(qh, infile, outfile, errfile);
+  qh_init_qhull_command(qh, argc, argv);
+} /* init_A */
+
+/*---------------------------------
+
+  qh_init_B(qh, points, numpoints, dim, ismalloc )
+    initialize globals for points array
+
+    points has numpoints dim-dimensional points
+      points[0] is the first coordinate of the first point
+      points[1] is the second coordinate of the first point
+      points[dim] is the first coordinate of the second point
+
+    ismalloc=True
+      Qhull will call qh_free(points) on exit or input transformation
+    ismalloc=False
+      Qhull will allocate a new point array if needed for input transformation
+
+    qh.qhull_command
+      is the option string.
+      It is defined by qh_init_B(), qh_qhull_command(), or qh_initflags
+
+  returns:
+    if qh.PROJECTinput or (qh.DELAUNAY and qh.PROJECTdelaunay)
+      projects the input to a new point array
+
+        if qh.DELAUNAY,
+          qh.hull_dim is increased by one
+        if qh.ATinfinity,
+          qh_projectinput adds point-at-infinity for Delaunay tri.
+
+    if qh.SCALEinput
+      changes the upper and lower bounds of the input, see qh_scaleinput(qh)
+
+    if qh.ROTATEinput
+      rotates the input by a random rotation, see qh_rotateinput()
+      if qh.DELAUNAY
+        rotates about the last coordinate
+
+  notes:
+    called after points are defined
+    qh_errexit() may be used
+*/
+void qh_init_B(qhT *qh, coordT *points, int numpoints, int dim, boolT ismalloc) {
+  qh_initqhull_globals(qh, points, numpoints, dim, ismalloc);
+  if (qh->qhmem.LASTsize == 0)
+    qh_initqhull_mem(qh);
+  /* mem_r.c and qset_r.c are initialized */
+  qh_initqhull_buffers(qh);
+  qh_initthresholds(qh, qh->qhull_command);
+  if (qh->PROJECTinput || (qh->DELAUNAY && qh->PROJECTdelaunay))
+    qh_projectinput(qh);
+  if (qh->SCALEinput)
+    qh_scaleinput(qh);
+  if (qh->ROTATErandom >= 0) {
+    qh_randommatrix(qh, qh->gm_matrix, qh->hull_dim, qh->gm_row);
+    if (qh->DELAUNAY) {
+      int k, lastk= qh->hull_dim-1;
+      for (k=0; k < lastk; k++) {
+        qh->gm_row[k][lastk]= 0.0;
+        qh->gm_row[lastk][k]= 0.0;
+      }
+      qh->gm_row[lastk][lastk]= 1.0;
+    }
+    qh_gram_schmidt(qh, qh->hull_dim, qh->gm_row);
+    qh_rotateinput(qh, qh->gm_row);
+  }
+} /* init_B */
+
+/*---------------------------------
+
+  qh_init_qhull_command(qh, argc, argv )
+    build qh.qhull_command from argc/argv
+    Calls qh_exit if qhull_command is too short
+
+  returns:
+    a space-delimited string of options (just as typed)
+
+  notes:
+    makes option string easy to input and output
+
+    argc/argv may be 0/NULL
+*/
+void qh_init_qhull_command(qhT *qh, int argc, char *argv[]) {
+
+  if (!qh_argv_to_command(argc, argv, qh->qhull_command, (int)sizeof(qh->qhull_command))){
+    /* Assumes qh.ferr is defined. */
+    qh_fprintf(qh, qh->ferr, 6033, "qhull input error: more than %d characters in command line.\n",
+          (int)sizeof(qh->qhull_command));
+    qh_exit(qh_ERRinput);  /* error reported, can not use qh_errexit */
+  }
+} /* init_qhull_command */
+
+/*---------------------------------
+
+  qh_initflags(qh, commandStr )
+    set flags and initialized constants from commandStr
+    calls qh_exit() if qh->NOerrexit
+
+  returns:
+    sets qh.qhull_command to command if needed
+
+  notes:
+    ignores first word (e.g., "qhull d")
+    use qh_strtol/strtod since strtol/strtod may or may not skip trailing spaces
+
+  see:
+    qh_initthresholds() continues processing of 'Pdn' and 'PDn'
+    'prompt' in unix_r.c for documentation
+
+  design:
+    for each space-delimited option group
+      if top-level option
+        check syntax
+        append appropriate option to option string
+        set appropriate global variable or append printFormat to print options
+      else
+        for each sub-option
+          check syntax
+          append appropriate option to option string
+          set appropriate global variable or append printFormat to print options
+*/
+void qh_initflags(qhT *qh, char *command) {
+  int k, i, lastproject;
+  char *s= command, *t, *prev_s, *start, key;
+  boolT isgeom= False, wasproject;
+  realT r;
+
+  if(qh->NOerrexit){
+    qh_fprintf(qh, qh->ferr, 6245, "qhull initflags error: qh.NOerrexit was not cleared before calling qh_initflags().  It should be cleared after setjmp().  Exit qhull.");
+    qh_exit(6245);
+  }
+  if (command <= &qh->qhull_command[0] || command > &qh->qhull_command[0] + sizeof(qh->qhull_command)) {
+    if (command != &qh->qhull_command[0]) {
+      *qh->qhull_command= '\0';
+      strncat(qh->qhull_command, command, sizeof(qh->qhull_command)-strlen(qh->qhull_command)-1);
+    }
+    while (*s && !isspace(*s))  /* skip program name */
+      s++;
+  }
+  while (*s) {
+    while (*s && isspace(*s))
+      s++;
+    if (*s == '-')
+      s++;
+    if (!*s)
+      break;
+    prev_s= s;
+    switch (*s++) {
+    case 'd':
+      qh_option(qh, "delaunay", NULL, NULL);
+      qh->DELAUNAY= True;
+      break;
+    case 'f':
+      qh_option(qh, "facets", NULL, NULL);
+      qh_appendprint(qh, qh_PRINTfacets);
+      break;
+    case 'i':
+      qh_option(qh, "incidence", NULL, NULL);
+      qh_appendprint(qh, qh_PRINTincidences);
+      break;
+    case 'm':
+      qh_option(qh, "mathematica", NULL, NULL);
+      qh_appendprint(qh, qh_PRINTmathematica);
+      break;
+    case 'n':
+      qh_option(qh, "normals", NULL, NULL);
+      qh_appendprint(qh, qh_PRINTnormals);
+      break;
+    case 'o':
+      qh_option(qh, "offFile", NULL, NULL);
+      qh_appendprint(qh, qh_PRINToff);
+      break;
+    case 'p':
+      qh_option(qh, "points", NULL, NULL);
+      qh_appendprint(qh, qh_PRINTpoints);
+      break;
+    case 's':
+      qh_option(qh, "summary", NULL, NULL);
+      qh->PRINTsummary= True;
+      break;
+    case 'v':
+      qh_option(qh, "voronoi", NULL, NULL);
+      qh->VORONOI= True;
+      qh->DELAUNAY= True;
+      break;
+    case 'A':
+      if (!isdigit(*s) && *s != '.' && *s != '-')
+        qh_fprintf(qh, qh->ferr, 7002, "qhull warning: no maximum cosine angle given for option 'An'.  Ignored.\n");
+      else {
+        if (*s == '-') {
+          qh->premerge_cos= -qh_strtod(s, &s);
+          qh_option(qh, "Angle-premerge-", NULL, &qh->premerge_cos);
+          qh->PREmerge= True;
+        }else {
+          qh->postmerge_cos= qh_strtod(s, &s);
+          qh_option(qh, "Angle-postmerge", NULL, &qh->postmerge_cos);
+          qh->POSTmerge= True;
+        }
+        qh->MERGING= True;
+      }
+      break;
+    case 'C':
+      if (!isdigit(*s) && *s != '.' && *s != '-')
+        qh_fprintf(qh, qh->ferr, 7003, "qhull warning: no centrum radius given for option 'Cn'.  Ignored.\n");
+      else {
+        if (*s == '-') {
+          qh->premerge_centrum= -qh_strtod(s, &s);
+          qh_option(qh, "Centrum-premerge-", NULL, &qh->premerge_centrum);
+          qh->PREmerge= True;
+        }else {
+          qh->postmerge_centrum= qh_strtod(s, &s);
+          qh_option(qh, "Centrum-postmerge", NULL, &qh->postmerge_centrum);
+          qh->POSTmerge= True;
+        }
+        qh->MERGING= True;
+      }
+      break;
+    case 'E':
+      if (*s == '-')
+        qh_fprintf(qh, qh->ferr, 7004, "qhull warning: negative maximum roundoff given for option 'An'.  Ignored.\n");
+      else if (!isdigit(*s))
+        qh_fprintf(qh, qh->ferr, 7005, "qhull warning: no maximum roundoff given for option 'En'.  Ignored.\n");
+      else {
+        qh->DISTround= qh_strtod(s, &s);
+        qh_option(qh, "Distance-roundoff", NULL, &qh->DISTround);
+        qh->SETroundoff= True;
+      }
+      break;
+    case 'H':
+      start= s;
+      qh->HALFspace= True;
+      qh_strtod(s, &t);
+      while (t > s)  {
+        if (*t && !isspace(*t)) {
+          if (*t == ',')
+            t++;
+          else
+            qh_fprintf(qh, qh->ferr, 7006, "qhull warning: origin for Halfspace intersection should be 'Hn,n,n,...'\n");
+        }
+        s= t;
+        qh_strtod(s, &t);
+      }
+      if (start < t) {
+        if (!(qh->feasible_string= (char*)calloc((size_t)(t-start+1), (size_t)1))) {
+          qh_fprintf(qh, qh->ferr, 6034, "qhull error: insufficient memory for 'Hn,n,n'\n");
+          qh_errexit(qh, qh_ERRmem, NULL, NULL);
+        }
+        strncpy(qh->feasible_string, start, (size_t)(t-start));
+        qh_option(qh, "Halfspace-about", NULL, NULL);
+        qh_option(qh, qh->feasible_string, NULL, NULL);
+      }else
+        qh_option(qh, "Halfspace", NULL, NULL);
+      break;
+    case 'R':
+      if (!isdigit(*s))
+        qh_fprintf(qh, qh->ferr, 7007, "qhull warning: missing random perturbation for option 'Rn'.  Ignored\n");
+      else {
+        qh->RANDOMfactor= qh_strtod(s, &s);
+        qh_option(qh, "Random_perturb", NULL, &qh->RANDOMfactor);
+        qh->RANDOMdist= True;
+      }
+      break;
+    case 'V':
+      if (!isdigit(*s) && *s != '-')
+        qh_fprintf(qh, qh->ferr, 7008, "qhull warning: missing visible distance for option 'Vn'.  Ignored\n");
+      else {
+        qh->MINvisible= qh_strtod(s, &s);
+        qh_option(qh, "Visible", NULL, &qh->MINvisible);
+      }
+      break;
+    case 'U':
+      if (!isdigit(*s) && *s != '-')
+        qh_fprintf(qh, qh->ferr, 7009, "qhull warning: missing coplanar distance for option 'Un'.  Ignored\n");
+      else {
+        qh->MAXcoplanar= qh_strtod(s, &s);
+        qh_option(qh, "U-coplanar", NULL, &qh->MAXcoplanar);
+      }
+      break;
+    case 'W':
+      if (*s == '-')
+        qh_fprintf(qh, qh->ferr, 7010, "qhull warning: negative outside width for option 'Wn'.  Ignored.\n");
+      else if (!isdigit(*s))
+        qh_fprintf(qh, qh->ferr, 7011, "qhull warning: missing outside width for option 'Wn'.  Ignored\n");
+      else {
+        qh->MINoutside= qh_strtod(s, &s);
+        qh_option(qh, "W-outside", NULL, &qh->MINoutside);
+        qh->APPROXhull= True;
+      }
+      break;
+    /************  sub menus ***************/
+    case 'F':
+      while (*s && !isspace(*s)) {
+        switch (*s++) {
+        case 'a':
+          qh_option(qh, "Farea", NULL, NULL);
+          qh_appendprint(qh, qh_PRINTarea);
+          qh->GETarea= True;
+          break;
+        case 'A':
+          qh_option(qh, "FArea-total", NULL, NULL);
+          qh->GETarea= True;
+          break;
+        case 'c':
+          qh_option(qh, "Fcoplanars", NULL, NULL);
+          qh_appendprint(qh, qh_PRINTcoplanars);
+          break;
+        case 'C':
+          qh_option(qh, "FCentrums", NULL, NULL);
+          qh_appendprint(qh, qh_PRINTcentrums);
+          break;
+        case 'd':
+          qh_option(qh, "Fd-cdd-in", NULL, NULL);
+          qh->CDDinput= True;
+          break;
+        case 'D':
+          qh_option(qh, "FD-cdd-out", NULL, NULL);
+          qh->CDDoutput= True;
+          break;
+        case 'F':
+          qh_option(qh, "FFacets-xridge", NULL, NULL);
+          qh_appendprint(qh, qh_PRINTfacets_xridge);
+          break;
+        case 'i':
+          qh_option(qh, "Finner", NULL, NULL);
+          qh_appendprint(qh, qh_PRINTinner);
+          break;
+        case 'I':
+          qh_option(qh, "FIDs", NULL, NULL);
+          qh_appendprint(qh, qh_PRINTids);
+          break;
+        case 'm':
+          qh_option(qh, "Fmerges", NULL, NULL);
+          qh_appendprint(qh, qh_PRINTmerges);
+          break;
+        case 'M':
+          qh_option(qh, "FMaple", NULL, NULL);
+          qh_appendprint(qh, qh_PRINTmaple);
+          break;
+        case 'n':
+          qh_option(qh, "Fneighbors", NULL, NULL);
+          qh_appendprint(qh, qh_PRINTneighbors);
+          break;
+        case 'N':
+          qh_option(qh, "FNeighbors-vertex", NULL, NULL);
+          qh_appendprint(qh, qh_PRINTvneighbors);
+          break;
+        case 'o':
+          qh_option(qh, "Fouter", NULL, NULL);
+          qh_appendprint(qh, qh_PRINTouter);
+          break;
+        case 'O':
+          if (qh->PRINToptions1st) {
+            qh_option(qh, "FOptions", NULL, NULL);
+            qh_appendprint(qh, qh_PRINToptions);
+          }else
+            qh->PRINToptions1st= True;
+          break;
+        case 'p':
+          qh_option(qh, "Fpoint-intersect", NULL, NULL);
+          qh_appendprint(qh, qh_PRINTpointintersect);
+          break;
+        case 'P':
+          qh_option(qh, "FPoint-nearest", NULL, NULL);
+          qh_appendprint(qh, qh_PRINTpointnearest);
+          break;
+        case 'Q':
+          qh_option(qh, "FQhull", NULL, NULL);
+          qh_appendprint(qh, qh_PRINTqhull);
+          break;
+        case 's':
+          qh_option(qh, "Fsummary", NULL, NULL);
+          qh_appendprint(qh, qh_PRINTsummary);
+          break;
+        case 'S':
+          qh_option(qh, "FSize", NULL, NULL);
+          qh_appendprint(qh, qh_PRINTsize);
+          qh->GETarea= True;
+          break;
+        case 't':
+          qh_option(qh, "Ftriangles", NULL, NULL);
+          qh_appendprint(qh, qh_PRINTtriangles);
+          break;
+        case 'v':
+          /* option set in qh_initqhull_globals */
+          qh_appendprint(qh, qh_PRINTvertices);
+          break;
+        case 'V':
+          qh_option(qh, "FVertex-average", NULL, NULL);
+          qh_appendprint(qh, qh_PRINTaverage);
+          break;
+        case 'x':
+          qh_option(qh, "Fxtremes", NULL, NULL);
+          qh_appendprint(qh, qh_PRINTextremes);
+          break;
+        default:
+          s--;
+          qh_fprintf(qh, qh->ferr, 7012, "qhull warning: unknown 'F' output option %c, rest ignored\n", (int)s[0]);
+          while (*++s && !isspace(*s));
+          break;
+        }
+      }
+      break;
+    case 'G':
+      isgeom= True;
+      qh_appendprint(qh, qh_PRINTgeom);
+      while (*s && !isspace(*s)) {
+        switch (*s++) {
+        case 'a':
+          qh_option(qh, "Gall-points", NULL, NULL);
+          qh->PRINTdots= True;
+          break;
+        case 'c':
+          qh_option(qh, "Gcentrums", NULL, NULL);
+          qh->PRINTcentrums= True;
+          break;
+        case 'h':
+          qh_option(qh, "Gintersections", NULL, NULL);
+          qh->DOintersections= True;
+          break;
+        case 'i':
+          qh_option(qh, "Ginner", NULL, NULL);
+          qh->PRINTinner= True;
+          break;
+        case 'n':
+          qh_option(qh, "Gno-planes", NULL, NULL);
+          qh->PRINTnoplanes= True;
+          break;
+        case 'o':
+          qh_option(qh, "Gouter", NULL, NULL);
+          qh->PRINTouter= True;
+          break;
+        case 'p':
+          qh_option(qh, "Gpoints", NULL, NULL);
+          qh->PRINTcoplanar= True;
+          break;
+        case 'r':
+          qh_option(qh, "Gridges", NULL, NULL);
+          qh->PRINTridges= True;
+          break;
+        case 't':
+          qh_option(qh, "Gtransparent", NULL, NULL);
+          qh->PRINTtransparent= True;
+          break;
+        case 'v':
+          qh_option(qh, "Gvertices", NULL, NULL);
+          qh->PRINTspheres= True;
+          break;
+        case 'D':
+          if (!isdigit(*s))
+            qh_fprintf(qh, qh->ferr, 6035, "qhull input error: missing dimension for option 'GDn'\n");
+          else {
+            if (qh->DROPdim >= 0)
+              qh_fprintf(qh, qh->ferr, 7013, "qhull warning: can only drop one dimension.  Previous 'GD%d' ignored\n",
+                   qh->DROPdim);
+            qh->DROPdim= qh_strtol(s, &s);
+            qh_option(qh, "GDrop-dim", &qh->DROPdim, NULL);
+          }
+          break;
+        default:
+          s--;
+          qh_fprintf(qh, qh->ferr, 7014, "qhull warning: unknown 'G' print option %c, rest ignored\n", (int)s[0]);
+          while (*++s && !isspace(*s));
+          break;
+        }
+      }
+      break;
+    case 'P':
+      while (*s && !isspace(*s)) {
+        switch (*s++) {
+        case 'd': case 'D':  /* see qh_initthresholds() */
+          key= s[-1];
+          i= qh_strtol(s, &s);
+          r= 0;
+          if (*s == ':') {
+            s++;
+            r= qh_strtod(s, &s);
+          }
+          if (key == 'd')
+            qh_option(qh, "Pdrop-facets-dim-less", &i, &r);
+          else
+            qh_option(qh, "PDrop-facets-dim-more", &i, &r);
+          break;
+        case 'g':
+          qh_option(qh, "Pgood-facets", NULL, NULL);
+          qh->PRINTgood= True;
+          break;
+        case 'G':
+          qh_option(qh, "PGood-facet-neighbors", NULL, NULL);
+          qh->PRINTneighbors= True;
+          break;
+        case 'o':
+          qh_option(qh, "Poutput-forced", NULL, NULL);
+          qh->FORCEoutput= True;
+          break;
+        case 'p':
+          qh_option(qh, "Pprecision-ignore", NULL, NULL);
+          qh->PRINTprecision= False;
+          break;
+        case 'A':
+          if (!isdigit(*s))
+            qh_fprintf(qh, qh->ferr, 6036, "qhull input error: missing facet count for keep area option 'PAn'\n");
+          else {
+            qh->KEEParea= qh_strtol(s, &s);
+            qh_option(qh, "PArea-keep", &qh->KEEParea, NULL);
+            qh->GETarea= True;
+          }
+          break;
+        case 'F':
+          if (!isdigit(*s))
+            qh_fprintf(qh, qh->ferr, 6037, "qhull input error: missing facet area for option 'PFn'\n");
+          else {
+            qh->KEEPminArea= qh_strtod(s, &s);
+            qh_option(qh, "PFacet-area-keep", NULL, &qh->KEEPminArea);
+            qh->GETarea= True;
+          }
+          break;
+        case 'M':
+          if (!isdigit(*s))
+            qh_fprintf(qh, qh->ferr, 6038, "qhull input error: missing merge count for option 'PMn'\n");
+          else {
+            qh->KEEPmerge= qh_strtol(s, &s);
+            qh_option(qh, "PMerge-keep", &qh->KEEPmerge, NULL);
+          }
+          break;
+        default:
+          s--;
+          qh_fprintf(qh, qh->ferr, 7015, "qhull warning: unknown 'P' print option %c, rest ignored\n", (int)s[0]);
+          while (*++s && !isspace(*s));
+          break;
+        }
+      }
+      break;
+    case 'Q':
+      lastproject= -1;
+      while (*s && !isspace(*s)) {
+        switch (*s++) {
+        case 'b': case 'B':  /* handled by qh_initthresholds */
+          key= s[-1];
+          if (key == 'b' && *s == 'B') {
+            s++;
+            r= qh_DEFAULTbox;
+            qh->SCALEinput= True;
+            qh_option(qh, "QbBound-unit-box", NULL, &r);
+            break;
+          }
+          if (key == 'b' && *s == 'b') {
+            s++;
+            qh->SCALElast= True;
+            qh_option(qh, "Qbbound-last", NULL, NULL);
+            break;
+          }
+          k= qh_strtol(s, &s);
+          r= 0.0;
+          wasproject= False;
+          if (*s == ':') {
+            s++;
+            if ((r= qh_strtod(s, &s)) == 0.0) {
+              t= s;            /* need true dimension for memory allocation */
+              while (*t && !isspace(*t)) {
+                if (toupper(*t++) == 'B'
+                 && k == qh_strtol(t, &t)
+                 && *t++ == ':'
+                 && qh_strtod(t, &t) == 0.0) {
+                  qh->PROJECTinput++;
+                  trace2((qh, qh->ferr, 2004, "qh_initflags: project dimension %d\n", k));
+                  qh_option(qh, "Qb-project-dim", &k, NULL);
+                  wasproject= True;
+                  lastproject= k;
+                  break;
+                }
+              }
+            }
+          }
+          if (!wasproject) {
+            if (lastproject == k && r == 0.0)
+              lastproject= -1;  /* doesn't catch all possible sequences */
+            else if (key == 'b') {
+              qh->SCALEinput= True;
+              if (r == 0.0)
+                r= -qh_DEFAULTbox;
+              qh_option(qh, "Qbound-dim-low", &k, &r);
+            }else {
+              qh->SCALEinput= True;
+              if (r == 0.0)
+                r= qh_DEFAULTbox;
+              qh_option(qh, "QBound-dim-high", &k, &r);
+            }
+          }
+          break;
+        case 'c':
+          qh_option(qh, "Qcoplanar-keep", NULL, NULL);
+          qh->KEEPcoplanar= True;
+          break;
+        case 'f':
+          qh_option(qh, "Qfurthest-outside", NULL, NULL);
+          qh->BESToutside= True;
+          break;
+        case 'g':
+          qh_option(qh, "Qgood-facets-only", NULL, NULL);
+          qh->ONLYgood= True;
+          break;
+        case 'i':
+          qh_option(qh, "Qinterior-keep", NULL, NULL);
+          qh->KEEPinside= True;
+          break;
+        case 'm':
+          qh_option(qh, "Qmax-outside-only", NULL, NULL);
+          qh->ONLYmax= True;
+          break;
+        case 'r':
+          qh_option(qh, "Qrandom-outside", NULL, NULL);
+          qh->RANDOMoutside= True;
+          break;
+        case 's':
+          qh_option(qh, "Qsearch-initial-simplex", NULL, NULL);
+          qh->ALLpoints= True;
+          break;
+        case 't':
+          qh_option(qh, "Qtriangulate", NULL, NULL);
+          qh->TRIangulate= True;
+          break;
+        case 'T':
+          qh_option(qh, "QTestPoints", NULL, NULL);
+          if (!isdigit(*s))
+            qh_fprintf(qh, qh->ferr, 6039, "qhull input error: missing number of test points for option 'QTn'\n");
+          else {
+            qh->TESTpoints= qh_strtol(s, &s);
+            qh_option(qh, "QTestPoints", &qh->TESTpoints, NULL);
+          }
+          break;
+        case 'u':
+          qh_option(qh, "QupperDelaunay", NULL, NULL);
+          qh->UPPERdelaunay= True;
+          break;
+        case 'v':
+          qh_option(qh, "Qvertex-neighbors-convex", NULL, NULL);
+          qh->TESTvneighbors= True;
+          break;
+        case 'x':
+          qh_option(qh, "Qxact-merge", NULL, NULL);
+          qh->MERGEexact= True;
+          break;
+        case 'z':
+          qh_option(qh, "Qz-infinity-point", NULL, NULL);
+          qh->ATinfinity= True;
+          break;
+        case '0':
+          qh_option(qh, "Q0-no-premerge", NULL, NULL);
+          qh->NOpremerge= True;
+          break;
+        case '1':
+          if (!isdigit(*s)) {
+            qh_option(qh, "Q1-no-angle-sort", NULL, NULL);
+            qh->ANGLEmerge= False;
+            break;
+          }
+          switch (*s++) {
+          case '0':
+            qh_option(qh, "Q10-no-narrow", NULL, NULL);
+            qh->NOnarrow= True;
+            break;
+          case '1':
+            qh_option(qh, "Q11-trinormals Qtriangulate", NULL, NULL);
+            qh->TRInormals= True;
+            qh->TRIangulate= True;
+            break;
+          case '2':
+              qh_option(qh, "Q12-no-wide-dup", NULL, NULL);
+              qh->NOwide= True;
+            break;
+          default:
+            s--;
+            qh_fprintf(qh, qh->ferr, 7016, "qhull warning: unknown 'Q' qhull option 1%c, rest ignored\n", (int)s[0]);
+            while (*++s && !isspace(*s));
+            break;
+          }
+          break;
+        case '2':
+          qh_option(qh, "Q2-no-merge-independent", NULL, NULL);
+          qh->MERGEindependent= False;
+          goto LABELcheckdigit;
+          break; /* no warnings */
+        case '3':
+          qh_option(qh, "Q3-no-merge-vertices", NULL, NULL);
+          qh->MERGEvertices= False;
+        LABELcheckdigit:
+          if (isdigit(*s))
+            qh_fprintf(qh, qh->ferr, 7017, "qhull warning: can not follow '1', '2', or '3' with a digit.  '%c' skipped.\n",
+                     *s++);
+          break;
+        case '4':
+          qh_option(qh, "Q4-avoid-old-into-new", NULL, NULL);
+          qh->AVOIDold= True;
+          break;
+        case '5':
+          qh_option(qh, "Q5-no-check-outer", NULL, NULL);
+          qh->SKIPcheckmax= True;
+          break;
+        case '6':
+          qh_option(qh, "Q6-no-concave-merge", NULL, NULL);
+          qh->SKIPconvex= True;
+          break;
+        case '7':
+          qh_option(qh, "Q7-no-breadth-first", NULL, NULL);
+          qh->VIRTUALmemory= True;
+          break;
+        case '8':
+          qh_option(qh, "Q8-no-near-inside", NULL, NULL);
+          qh->NOnearinside= True;
+          break;
+        case '9':
+          qh_option(qh, "Q9-pick-furthest", NULL, NULL);
+          qh->PICKfurthest= True;
+          break;
+        case 'G':
+          i= qh_strtol(s, &t);
+          if (qh->GOODpoint)
+            qh_fprintf(qh, qh->ferr, 7018, "qhull warning: good point already defined for option 'QGn'.  Ignored\n");
+          else if (s == t)
+            qh_fprintf(qh, qh->ferr, 7019, "qhull warning: missing good point id for option 'QGn'.  Ignored\n");
+          else if (i < 0 || *s == '-') {
+            qh->GOODpoint= i-1;
+            qh_option(qh, "QGood-if-dont-see-point", &i, NULL);
+          }else {
+            qh->GOODpoint= i+1;
+            qh_option(qh, "QGood-if-see-point", &i, NULL);
+          }
+          s= t;
+          break;
+        case 'J':
+          if (!isdigit(*s) && *s != '-')
+            qh->JOGGLEmax= 0.0;
+          else {
+            qh->JOGGLEmax= (realT) qh_strtod(s, &s);
+            qh_option(qh, "QJoggle", NULL, &qh->JOGGLEmax);
+          }
+          break;
+        case 'R':
+          if (!isdigit(*s) && *s != '-')
+            qh_fprintf(qh, qh->ferr, 7020, "qhull warning: missing random seed for option 'QRn'.  Ignored\n");
+          else {
+            qh->ROTATErandom= i= qh_strtol(s, &s);
+            if (i > 0)
+              qh_option(qh, "QRotate-id", &i, NULL );
+            else if (i < -1)
+              qh_option(qh, "QRandom-seed", &i, NULL );
+          }
+          break;
+        case 'V':
+          i= qh_strtol(s, &t);
+          if (qh->GOODvertex)
+            qh_fprintf(qh, qh->ferr, 7021, "qhull warning: good vertex already defined for option 'QVn'.  Ignored\n");
+          else if (s == t)
+            qh_fprintf(qh, qh->ferr, 7022, "qhull warning: no good point id given for option 'QVn'.  Ignored\n");
+          else if (i < 0) {
+            qh->GOODvertex= i - 1;
+            qh_option(qh, "QV-good-facets-not-point", &i, NULL);
+          }else {
+            qh_option(qh, "QV-good-facets-point", &i, NULL);
+            qh->GOODvertex= i + 1;
+          }
+          s= t;
+          break;
+        default:
+          s--;
+          qh_fprintf(qh, qh->ferr, 7023, "qhull warning: unknown 'Q' qhull option %c, rest ignored\n", (int)s[0]);
+          while (*++s && !isspace(*s));
+          break;
+        }
+      }
+      break;
+    case 'T':
+      while (*s && !isspace(*s)) {
+        if (isdigit(*s) || *s == '-')
+          qh->IStracing= qh_strtol(s, &s);
+        else switch (*s++) {
+        case 'a':
+          qh_option(qh, "Tannotate-output", NULL, NULL);
+          qh->ANNOTATEoutput= True;
+          break;
+        case 'c':
+          qh_option(qh, "Tcheck-frequently", NULL, NULL);
+          qh->CHECKfrequently= True;
+          break;
+        case 's':
+          qh_option(qh, "Tstatistics", NULL, NULL);
+          qh->PRINTstatistics= True;
+          break;
+        case 'v':
+          qh_option(qh, "Tverify", NULL, NULL);
+          qh->VERIFYoutput= True;
+          break;
+        case 'z':
+          if (qh->ferr == qh_FILEstderr) {
+            /* The C++ interface captures the output in qh_fprint_qhull() */
+            qh_option(qh, "Tz-stdout", NULL, NULL);
+            qh->USEstdout= True;
+          }else if (!qh->fout)
+            qh_fprintf(qh, qh->ferr, 7024, "qhull warning: output file undefined(stdout).  Option 'Tz' ignored.\n");
+          else {
+            qh_option(qh, "Tz-stdout", NULL, NULL);
+            qh->USEstdout= True;
+            qh->ferr= qh->fout;
+            qh->qhmem.ferr= qh->fout;
+          }
+          break;
+        case 'C':
+          if (!isdigit(*s))
+            qh_fprintf(qh, qh->ferr, 7025, "qhull warning: missing point id for cone for trace option 'TCn'.  Ignored\n");
+          else {
+            i= qh_strtol(s, &s);
+            qh_option(qh, "TCone-stop", &i, NULL);
+            qh->STOPcone= i + 1;
+          }
+          break;
+        case 'F':
+          if (!isdigit(*s))
+            qh_fprintf(qh, qh->ferr, 7026, "qhull warning: missing frequency count for trace option 'TFn'.  Ignored\n");
+          else {
+            qh->REPORTfreq= qh_strtol(s, &s);
+            qh_option(qh, "TFacet-log", &qh->REPORTfreq, NULL);
+            qh->REPORTfreq2= qh->REPORTfreq/2;  /* for tracemerging() */
+          }
+          break;
+        case 'I':
+          if (!isspace(*s))
+            qh_fprintf(qh, qh->ferr, 7027, "qhull warning: missing space between 'TI' and filename, %s\n", s);
+          while (isspace(*s))
+            s++;
+          t= qh_skipfilename(qh, s);
+          {
+            char filename[qh_FILENAMElen];
+
+            qh_copyfilename(qh, filename, (int)sizeof(filename), s, (int)(t-s));   /* WARN64 */
+            s= t;
+            if (!freopen(filename, "r", stdin)) {
+              qh_fprintf(qh, qh->ferr, 6041, "qhull error: could not open file \"%s\".", filename);
+              qh_errexit(qh, qh_ERRinput, NULL, NULL);
+            }else {
+              qh_option(qh, "TInput-file", NULL, NULL);
+              qh_option(qh, filename, NULL, NULL);
+            }
+          }
+          break;
+        case 'O':
+            if (!isspace(*s))
+                qh_fprintf(qh, qh->ferr, 7028, "qhull warning: missing space between 'TO' and filename, %s\n", s);
+            while (isspace(*s))
+                s++;
+            t= qh_skipfilename(qh, s);
+            {
+              char filename[qh_FILENAMElen];
+
+              qh_copyfilename(qh, filename, (int)sizeof(filename), s, (int)(t-s));  /* WARN64 */
+              s= t;
+              if (!qh->fout) {
+                qh_fprintf(qh, qh->ferr, 6266, "qhull input warning: qh.fout was not set by caller.  Cannot use option 'TO' to redirect output.  Ignoring option 'TO'\n");
+              }else if (!freopen(filename, "w", qh->fout)) {
+                qh_fprintf(qh, qh->ferr, 6044, "qhull error: could not open file \"%s\".", filename);
+                qh_errexit(qh, qh_ERRinput, NULL, NULL);
+              }else {
+                qh_option(qh, "TOutput-file", NULL, NULL);
+              qh_option(qh, filename, NULL, NULL);
+            }
+          }
+          break;
+        case 'P':
+          if (!isdigit(*s))
+            qh_fprintf(qh, qh->ferr, 7029, "qhull warning: missing point id for trace option 'TPn'.  Ignored\n");
+          else {
+            qh->TRACEpoint= qh_strtol(s, &s);
+            qh_option(qh, "Trace-point", &qh->TRACEpoint, NULL);
+          }
+          break;
+        case 'M':
+          if (!isdigit(*s))
+            qh_fprintf(qh, qh->ferr, 7030, "qhull warning: missing merge id for trace option 'TMn'.  Ignored\n");
+          else {
+            qh->TRACEmerge= qh_strtol(s, &s);
+            qh_option(qh, "Trace-merge", &qh->TRACEmerge, NULL);
+          }
+          break;
+        case 'R':
+          if (!isdigit(*s))
+            qh_fprintf(qh, qh->ferr, 7031, "qhull warning: missing rerun count for trace option 'TRn'.  Ignored\n");
+          else {
+            qh->RERUN= qh_strtol(s, &s);
+            qh_option(qh, "TRerun", &qh->RERUN, NULL);
+          }
+          break;
+        case 'V':
+          i= qh_strtol(s, &t);
+          if (s == t)
+            qh_fprintf(qh, qh->ferr, 7032, "qhull warning: missing furthest point id for trace option 'TVn'.  Ignored\n");
+          else if (i < 0) {
+            qh->STOPpoint= i - 1;
+            qh_option(qh, "TV-stop-before-point", &i, NULL);
+          }else {
+            qh->STOPpoint= i + 1;
+            qh_option(qh, "TV-stop-after-point", &i, NULL);
+          }
+          s= t;
+          break;
+        case 'W':
+          if (!isdigit(*s))
+            qh_fprintf(qh, qh->ferr, 7033, "qhull warning: missing max width for trace option 'TWn'.  Ignored\n");
+          else {
+            qh->TRACEdist= (realT) qh_strtod(s, &s);
+            qh_option(qh, "TWide-trace", NULL, &qh->TRACEdist);
+          }
+          break;
+        default:
+          s--;
+          qh_fprintf(qh, qh->ferr, 7034, "qhull warning: unknown 'T' trace option %c, rest ignored\n", (int)s[0]);
+          while (*++s && !isspace(*s));
+          break;
+        }
+      }
+      break;
+    default:
+      qh_fprintf(qh, qh->ferr, 7035, "qhull warning: unknown flag %c(%x)\n", (int)s[-1],
+               (int)s[-1]);
+      break;
+    }
+    if (s-1 == prev_s && *s && !isspace(*s)) {
+      qh_fprintf(qh, qh->ferr, 7036, "qhull warning: missing space after flag %c(%x); reserved for menu. Skipped.\n",
+               (int)*prev_s, (int)*prev_s);
+      while (*s && !isspace(*s))
+        s++;
+    }
+  }
+  if (qh->STOPcone && qh->JOGGLEmax < REALmax/2)
+    qh_fprintf(qh, qh->ferr, 7078, "qhull warning: 'TCn' (stopCone) ignored when used with 'QJn' (joggle)\n");
+  if (isgeom && !qh->FORCEoutput && qh->PRINTout[1])
+    qh_fprintf(qh, qh->ferr, 7037, "qhull warning: additional output formats are not compatible with Geomview\n");
+  /* set derived values in qh_initqhull_globals */
+} /* initflags */
+
+
+/*---------------------------------
+
+  qh_initqhull_buffers(qh)
+    initialize global memory buffers
+
+  notes:
+    must match qh_freebuffers()
+*/
+void qh_initqhull_buffers(qhT *qh) {
+  int k;
+
+  qh->TEMPsize= (qh->qhmem.LASTsize - sizeof(setT))/SETelemsize;
+  if (qh->TEMPsize <= 0 || qh->TEMPsize > qh->qhmem.LASTsize)
+    qh->TEMPsize= 8;  /* e.g., if qh_NOmem */
+  qh->other_points= qh_setnew(qh, qh->TEMPsize);
+  qh->del_vertices= qh_setnew(qh, qh->TEMPsize);
+  qh->coplanarfacetset= qh_setnew(qh, qh->TEMPsize);
+  qh->NEARzero= (realT *)qh_memalloc(qh, qh->hull_dim * sizeof(realT));
+  qh->lower_threshold= (realT *)qh_memalloc(qh, (qh->input_dim+1) * sizeof(realT));
+  qh->upper_threshold= (realT *)qh_memalloc(qh, (qh->input_dim+1) * sizeof(realT));
+  qh->lower_bound= (realT *)qh_memalloc(qh, (qh->input_dim+1) * sizeof(realT));
+  qh->upper_bound= (realT *)qh_memalloc(qh, (qh->input_dim+1) * sizeof(realT));
+  for (k=qh->input_dim+1; k--; ) {  /* duplicated in qh_initqhull_buffers and qh_clear_outputflags */
+    qh->lower_threshold[k]= -REALmax;
+    qh->upper_threshold[k]= REALmax;
+    qh->lower_bound[k]= -REALmax;
+    qh->upper_bound[k]= REALmax;
+  }
+  qh->gm_matrix= (coordT *)qh_memalloc(qh, (qh->hull_dim+1) * qh->hull_dim * sizeof(coordT));
+  qh->gm_row= (coordT **)qh_memalloc(qh, (qh->hull_dim+1) * sizeof(coordT *));
+} /* initqhull_buffers */
+
+/*---------------------------------
+
+  qh_initqhull_globals(qh, points, numpoints, dim, ismalloc )
+    initialize globals
+    if ismalloc
+      points were malloc'd and qhull should free at end
+
+  returns:
+    sets qh.first_point, num_points, input_dim, hull_dim and others
+    seeds random number generator (seed=1 if tracing)
+    modifies qh.hull_dim if ((qh.DELAUNAY and qh.PROJECTdelaunay) or qh.PROJECTinput)
+    adjust user flags as needed
+    also checks DIM3 dependencies and constants
+
+  notes:
+    do not use qh_point() since an input transformation may move them elsewhere
+
+  see:
+    qh_initqhull_start() sets default values for non-zero globals
+
+  design:
+    initialize points array from input arguments
+    test for qh.ZEROcentrum
+      (i.e., use opposite vertex instead of cetrum for convexity testing)
+    initialize qh.CENTERtype, qh.normal_size,
+      qh.center_size, qh.TRACEpoint/level,
+    initialize and test random numbers
+    qh_initqhull_outputflags() -- adjust and test output flags
+*/
+void qh_initqhull_globals(qhT *qh, coordT *points, int numpoints, int dim, boolT ismalloc) {
+  int seed, pointsneeded, extra= 0, i, randi, k;
+  realT randr;
+  realT factorial;
+
+  time_t timedata;
+
+  trace0((qh, qh->ferr, 13, "qh_initqhull_globals: for %s | %s\n", qh->rbox_command,
+      qh->qhull_command));
+  qh->POINTSmalloc= ismalloc;
+  qh->first_point= points;
+  qh->num_points= numpoints;
+  qh->hull_dim= qh->input_dim= dim;
+  if (!qh->NOpremerge && !qh->MERGEexact && !qh->PREmerge && qh->JOGGLEmax > REALmax/2) {
+    qh->MERGING= True;
+    if (qh->hull_dim <= 4) {
+      qh->PREmerge= True;
+      qh_option(qh, "_pre-merge", NULL, NULL);
+    }else {
+      qh->MERGEexact= True;
+      qh_option(qh, "Qxact_merge", NULL, NULL);
+    }
+  }else if (qh->MERGEexact)
+    qh->MERGING= True;
+  if (!qh->NOpremerge && qh->JOGGLEmax > REALmax/2) {
+#ifdef qh_NOmerge
+    qh->JOGGLEmax= 0.0;
+#endif
+  }
+  if (qh->TRIangulate && qh->JOGGLEmax < REALmax/2 && qh->PRINTprecision)
+    qh_fprintf(qh, qh->ferr, 7038, "qhull warning: joggle('QJ') always produces simplicial output.  Triangulated output('Qt') does nothing.\n");
+  if (qh->JOGGLEmax < REALmax/2 && qh->DELAUNAY && !qh->SCALEinput && !qh->SCALElast) {
+    qh->SCALElast= True;
+    qh_option(qh, "Qbbound-last-qj", NULL, NULL);
+  }
+  if (qh->MERGING && !qh->POSTmerge && qh->premerge_cos > REALmax/2
+  && qh->premerge_centrum == 0) {
+    qh->ZEROcentrum= True;
+    qh->ZEROall_ok= True;
+    qh_option(qh, "_zero-centrum", NULL, NULL);
+  }
+  if (qh->JOGGLEmax < REALmax/2 && REALepsilon > 2e-8 && qh->PRINTprecision)
+    qh_fprintf(qh, qh->ferr, 7039, "qhull warning: real epsilon, %2.2g, is probably too large for joggle('QJn')\nRecompile with double precision reals(see user.h).\n",
+          REALepsilon);
+#ifdef qh_NOmerge
+  if (qh->MERGING) {
+    qh_fprintf(qh, qh->ferr, 6045, "qhull input error: merging not installed(qh_NOmerge + 'Qx', 'Cn' or 'An')\n");
+    qh_errexit(qh, qh_ERRinput, NULL, NULL);
+  }
+#endif
+  if (qh->DELAUNAY && qh->KEEPcoplanar && !qh->KEEPinside) {
+    qh->KEEPinside= True;
+    qh_option(qh, "Qinterior-keep", NULL, NULL);
+  }
+  if (qh->DELAUNAY && qh->HALFspace) {
+    qh_fprintf(qh, qh->ferr, 6046, "qhull input error: can not use Delaunay('d') or Voronoi('v') with halfspace intersection('H')\n");
+    qh_errexit(qh, qh_ERRinput, NULL, NULL);
+  }
+  if (!qh->DELAUNAY && (qh->UPPERdelaunay || qh->ATinfinity)) {
+    qh_fprintf(qh, qh->ferr, 6047, "qhull input error: use upper-Delaunay('Qu') or infinity-point('Qz') with Delaunay('d') or Voronoi('v')\n");
+    qh_errexit(qh, qh_ERRinput, NULL, NULL);
+  }
+  if (qh->UPPERdelaunay && qh->ATinfinity) {
+    qh_fprintf(qh, qh->ferr, 6048, "qhull input error: can not use infinity-point('Qz') with upper-Delaunay('Qu')\n");
+    qh_errexit(qh, qh_ERRinput, NULL, NULL);
+  }
+  if (qh->SCALElast && !qh->DELAUNAY && qh->PRINTprecision)
+    qh_fprintf(qh, qh->ferr, 7040, "qhull input warning: option 'Qbb' (scale-last-coordinate) is normally used with 'd' or 'v'\n");
+  qh->DOcheckmax= (!qh->SKIPcheckmax && qh->MERGING );
+  qh->KEEPnearinside= (qh->DOcheckmax && !(qh->KEEPinside && qh->KEEPcoplanar)
+                          && !qh->NOnearinside);
+  if (qh->MERGING)
+    qh->CENTERtype= qh_AScentrum;
+  else if (qh->VORONOI)
+    qh->CENTERtype= qh_ASvoronoi;
+  if (qh->TESTvneighbors && !qh->MERGING) {
+    qh_fprintf(qh, qh->ferr, 6049, "qhull input error: test vertex neighbors('Qv') needs a merge option\n");
+    qh_errexit(qh, qh_ERRinput, NULL ,NULL);
+  }
+  if (qh->PROJECTinput || (qh->DELAUNAY && qh->PROJECTdelaunay)) {
+    qh->hull_dim -= qh->PROJECTinput;
+    if (qh->DELAUNAY) {
+      qh->hull_dim++;
+      if (qh->ATinfinity)
+        extra= 1;
+    }
+  }
+  if (qh->hull_dim <= 1) {
+    qh_fprintf(qh, qh->ferr, 6050, "qhull error: dimension %d must be > 1\n", qh->hull_dim);
+    qh_errexit(qh, qh_ERRinput, NULL, NULL);
+  }
+  for (k=2, factorial=1.0; k < qh->hull_dim; k++)
+    factorial *= k;
+  qh->AREAfactor= 1.0 / factorial;
+  trace2((qh, qh->ferr, 2005, "qh_initqhull_globals: initialize globals.  dim %d numpoints %d malloc? %d projected %d to hull_dim %d\n",
+        dim, numpoints, ismalloc, qh->PROJECTinput, qh->hull_dim));
+  qh->normal_size= qh->hull_dim * sizeof(coordT);
+  qh->center_size= qh->normal_size - sizeof(coordT);
+  pointsneeded= qh->hull_dim+1;
+  if (qh->hull_dim > qh_DIMmergeVertex) {
+    qh->MERGEvertices= False;
+    qh_option(qh, "Q3-no-merge-vertices-dim-high", NULL, NULL);
+  }
+  if (qh->GOODpoint)
+    pointsneeded++;
+#ifdef qh_NOtrace
+  if (qh->IStracing) {
+    qh_fprintf(qh, qh->ferr, 6051, "qhull input error: tracing is not installed(qh_NOtrace in user.h)");
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }
+#endif
+  if (qh->RERUN > 1) {
+    qh->TRACElastrun= qh->IStracing; /* qh_build_withrestart duplicates next conditional */
+    if (qh->IStracing != -1)
+      qh->IStracing= 0;
+  }else if (qh->TRACEpoint != qh_IDunknown || qh->TRACEdist < REALmax/2 || qh->TRACEmerge) {
+    qh->TRACElevel= (qh->IStracing? qh->IStracing : 3);
+    qh->IStracing= 0;
+  }
+  if (qh->ROTATErandom == 0 || qh->ROTATErandom == -1) {
+    seed= (int)time(&timedata);
+    if (qh->ROTATErandom  == -1) {
+      seed= -seed;
+      qh_option(qh, "QRandom-seed", &seed, NULL );
+    }else
+      qh_option(qh, "QRotate-random", &seed, NULL);
+    qh->ROTATErandom= seed;
+  }
+  seed= qh->ROTATErandom;
+  if (seed == INT_MIN)    /* default value */
+    seed= 1;
+  else if (seed < 0)
+    seed= -seed;
+  qh_RANDOMseed_(qh, seed);
+  randr= 0.0;
+  for (i=1000; i--; ) {
+    randi= qh_RANDOMint;
+    randr += randi;
+    if (randi > qh_RANDOMmax) {
+      qh_fprintf(qh, qh->ferr, 8036, "\
+qhull configuration error (qh_RANDOMmax in user.h):\n\
+   random integer %d > qh_RANDOMmax(qh, %.8g)\n",
+               randi, qh_RANDOMmax);
+      qh_errexit(qh, qh_ERRinput, NULL, NULL);
+    }
+  }
+  qh_RANDOMseed_(qh, seed);
+  randr = randr/1000;
+  if (randr < qh_RANDOMmax * 0.1
+  || randr > qh_RANDOMmax * 0.9)
+    qh_fprintf(qh, qh->ferr, 8037, "\
+qhull configuration warning (qh_RANDOMmax in user.h):\n\
+   average of 1000 random integers (%.2g) is much different than expected (%.2g).\n\
+   Is qh_RANDOMmax (%.2g) wrong?\n",
+             randr, qh_RANDOMmax * 0.5, qh_RANDOMmax);
+  qh->RANDOMa= 2.0 * qh->RANDOMfactor/qh_RANDOMmax;
+  qh->RANDOMb= 1.0 - qh->RANDOMfactor;
+  if (qh_HASHfactor < 1.1) {
+    qh_fprintf(qh, qh->ferr, 6052, "qhull internal error (qh_initqhull_globals): qh_HASHfactor %d must be at least 1.1.  Qhull uses linear hash probing\n",
+      qh_HASHfactor);
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }
+  if (numpoints+extra < pointsneeded) {
+    qh_fprintf(qh, qh->ferr, 6214, "qhull input error: not enough points(%d) to construct initial simplex (need %d)\n",
+            numpoints, pointsneeded);
+    qh_errexit(qh, qh_ERRinput, NULL, NULL);
+  }
+  qh_initqhull_outputflags(qh);
+} /* initqhull_globals */
+
+/*---------------------------------
+
+  qh_initqhull_mem(qh, )
+    initialize mem_r.c for qhull
+    qh.hull_dim and qh.normal_size determine some of the allocation sizes
+    if qh.MERGING,
+      includes ridgeT
+    calls qh_user_memsizes(qh) to add up to 10 additional sizes for quick allocation
+      (see numsizes below)
+
+  returns:
+    mem_r.c already for qh_memalloc/qh_memfree (errors if called beforehand)
+
+  notes:
+    qh_produceoutput() prints memsizes
+
+*/
+void qh_initqhull_mem(qhT *qh) {
+  int numsizes;
+  int i;
+
+  numsizes= 8+10;
+  qh_meminitbuffers(qh, qh->IStracing, qh_MEMalign, numsizes,
+                     qh_MEMbufsize, qh_MEMinitbuf);
+  qh_memsize(qh, (int)sizeof(vertexT));
+  if (qh->MERGING) {
+    qh_memsize(qh, (int)sizeof(ridgeT));
+    qh_memsize(qh, (int)sizeof(mergeT));
+  }
+  qh_memsize(qh, (int)sizeof(facetT));
+  i= sizeof(setT) + (qh->hull_dim - 1) * SETelemsize;  /* ridge.vertices */
+  qh_memsize(qh, i);
+  qh_memsize(qh, qh->normal_size);        /* normal */
+  i += SETelemsize;                 /* facet.vertices, .ridges, .neighbors */
+  qh_memsize(qh, i);
+  qh_user_memsizes(qh);
+  qh_memsetup(qh);
+} /* initqhull_mem */
+
+/*---------------------------------
+
+  qh_initqhull_outputflags
+    initialize flags concerned with output
+
+  returns:
+    adjust user flags as needed
+
+  see:
+    qh_clear_outputflags() resets the flags
+
+  design:
+    test for qh.PRINTgood (i.e., only print 'good' facets)
+    check for conflicting print output options
+*/
+void qh_initqhull_outputflags(qhT *qh) {
+  boolT printgeom= False, printmath= False, printcoplanar= False;
+  int i;
+
+  trace3((qh, qh->ferr, 3024, "qh_initqhull_outputflags: %s\n", qh->qhull_command));
+  if (!(qh->PRINTgood || qh->PRINTneighbors)) {
+    if (qh->KEEParea || qh->KEEPminArea < REALmax/2 || qh->KEEPmerge || qh->DELAUNAY
+        || (!qh->ONLYgood && (qh->GOODvertex || qh->GOODpoint))) {
+      qh->PRINTgood= True;
+      qh_option(qh, "Pgood", NULL, NULL);
+    }
+  }
+  if (qh->PRINTtransparent) {
+    if (qh->hull_dim != 4 || !qh->DELAUNAY || qh->VORONOI || qh->DROPdim >= 0) {
+      qh_fprintf(qh, qh->ferr, 6215, "qhull input error: transparent Delaunay('Gt') needs 3-d Delaunay('d') w/o 'GDn'\n");
+      qh_errexit(qh, qh_ERRinput, NULL, NULL);
+    }
+    qh->DROPdim = 3;
+    qh->PRINTridges = True;
+  }
+  for (i=qh_PRINTEND; i--; ) {
+    if (qh->PRINTout[i] == qh_PRINTgeom)
+      printgeom= True;
+    else if (qh->PRINTout[i] == qh_PRINTmathematica || qh->PRINTout[i] == qh_PRINTmaple)
+      printmath= True;
+    else if (qh->PRINTout[i] == qh_PRINTcoplanars)
+      printcoplanar= True;
+    else if (qh->PRINTout[i] == qh_PRINTpointnearest)
+      printcoplanar= True;
+    else if (qh->PRINTout[i] == qh_PRINTpointintersect && !qh->HALFspace) {
+      qh_fprintf(qh, qh->ferr, 6053, "qhull input error: option 'Fp' is only used for \nhalfspace intersection('Hn,n,n').\n");
+      qh_errexit(qh, qh_ERRinput, NULL, NULL);
+    }else if (qh->PRINTout[i] == qh_PRINTtriangles && (qh->HALFspace || qh->VORONOI)) {
+      qh_fprintf(qh, qh->ferr, 6054, "qhull input error: option 'Ft' is not available for Voronoi vertices or halfspace intersection\n");
+      qh_errexit(qh, qh_ERRinput, NULL, NULL);
+    }else if (qh->PRINTout[i] == qh_PRINTcentrums && qh->VORONOI) {
+      qh_fprintf(qh, qh->ferr, 6055, "qhull input error: option 'FC' is not available for Voronoi vertices('v')\n");
+      qh_errexit(qh, qh_ERRinput, NULL, NULL);
+    }else if (qh->PRINTout[i] == qh_PRINTvertices) {
+      if (qh->VORONOI)
+        qh_option(qh, "Fvoronoi", NULL, NULL);
+      else
+        qh_option(qh, "Fvertices", NULL, NULL);
+    }
+  }
+  if (printcoplanar && qh->DELAUNAY && qh->JOGGLEmax < REALmax/2) {
+    if (qh->PRINTprecision)
+      qh_fprintf(qh, qh->ferr, 7041, "qhull input warning: 'QJ' (joggle) will usually prevent coincident input sites for options 'Fc' and 'FP'\n");
+  }
+  if (printmath && (qh->hull_dim > 3 || qh->VORONOI)) {
+    qh_fprintf(qh, qh->ferr, 6056, "qhull input error: Mathematica and Maple output is only available for 2-d and 3-d convex hulls and 2-d Delaunay triangulations\n");
+    qh_errexit(qh, qh_ERRinput, NULL, NULL);
+  }
+  if (printgeom) {
+    if (qh->hull_dim > 4) {
+      qh_fprintf(qh, qh->ferr, 6057, "qhull input error: Geomview output is only available for 2-d, 3-d and 4-d\n");
+      qh_errexit(qh, qh_ERRinput, NULL, NULL);
+    }
+    if (qh->PRINTnoplanes && !(qh->PRINTcoplanar + qh->PRINTcentrums
+     + qh->PRINTdots + qh->PRINTspheres + qh->DOintersections + qh->PRINTridges)) {
+      qh_fprintf(qh, qh->ferr, 6058, "qhull input error: no output specified for Geomview\n");
+      qh_errexit(qh, qh_ERRinput, NULL, NULL);
+    }
+    if (qh->VORONOI && (qh->hull_dim > 3 || qh->DROPdim >= 0)) {
+      qh_fprintf(qh, qh->ferr, 6059, "qhull input error: Geomview output for Voronoi diagrams only for 2-d\n");
+      qh_errexit(qh, qh_ERRinput, NULL, NULL);
+    }
+    /* can not warn about furthest-site Geomview output: no lower_threshold */
+    if (qh->hull_dim == 4 && qh->DROPdim == -1 &&
+        (qh->PRINTcoplanar || qh->PRINTspheres || qh->PRINTcentrums)) {
+      qh_fprintf(qh, qh->ferr, 7042, "qhull input warning: coplanars, vertices, and centrums output not\n\
+available for 4-d output(ignored).  Could use 'GDn' instead.\n");
+      qh->PRINTcoplanar= qh->PRINTspheres= qh->PRINTcentrums= False;
+    }
+  }
+  if (!qh->KEEPcoplanar && !qh->KEEPinside && !qh->ONLYgood) {
+    if ((qh->PRINTcoplanar && qh->PRINTspheres) || printcoplanar) {
+      if (qh->QHULLfinished) {
+        qh_fprintf(qh, qh->ferr, 7072, "qhull output warning: ignoring coplanar points, option 'Qc' was not set for the first run of qhull.\n");
+      }else {
+        qh->KEEPcoplanar = True;
+        qh_option(qh, "Qcoplanar", NULL, NULL);
+      }
+    }
+  }
+  qh->PRINTdim= qh->hull_dim;
+  if (qh->DROPdim >=0) {    /* after Geomview checks */
+    if (qh->DROPdim < qh->hull_dim) {
+      qh->PRINTdim--;
+      if (!printgeom || qh->hull_dim < 3)
+        qh_fprintf(qh, qh->ferr, 7043, "qhull input warning: drop dimension 'GD%d' is only available for 3-d/4-d Geomview\n", qh->DROPdim);
+    }else
+      qh->DROPdim= -1;
+  }else if (qh->VORONOI) {
+    qh->DROPdim= qh->hull_dim-1;
+    qh->PRINTdim= qh->hull_dim-1;
+  }
+} /* qh_initqhull_outputflags */
+
+/*---------------------------------
+
+  qh_initqhull_start(qh, infile, outfile, errfile )
+    allocate memory if needed and call qh_initqhull_start2()
+*/
+void qh_initqhull_start(qhT *qh, FILE *infile, FILE *outfile, FILE *errfile) {
+
+  qh_initstatistics(qh);
+  qh_initqhull_start2(qh, infile, outfile, errfile);
+} /* initqhull_start */
+
+/*---------------------------------
+
+  qh_initqhull_start2(qh, infile, outfile, errfile )
+    start initialization of qhull
+    initialize statistics, stdio, default values for global variables
+    assumes qh is allocated
+  notes:
+    report errors elsewhere, error handling and g_qhull_output [Qhull.cpp, QhullQh()] not in initialized
+  see:
+    qh_maxmin() determines the precision constants
+    qh_freeqhull()
+*/
+void qh_initqhull_start2(qhT *qh, FILE *infile, FILE *outfile, FILE *errfile) {
+  time_t timedata;
+  int seed;
+
+  qh_CPUclock; /* start the clock(for qh_clock).  One-shot. */
+  /* memset is the same in qh_freeqhull() and qh_initqhull_start2() */
+  memset((char *)qh, 0, sizeof(qhT)-sizeof(qhmemT)-sizeof(qhstatT));   /* every field is 0, FALSE, NULL */
+  qh->NOerrexit= True;
+  qh->ANGLEmerge= True;
+  qh->DROPdim= -1;
+  qh->ferr= errfile;
+  qh->fin= infile;
+  qh->fout= outfile;
+  qh->furthest_id= qh_IDunknown;
+  qh->JOGGLEmax= REALmax;
+  qh->KEEPminArea = REALmax;
+  qh->last_low= REALmax;
+  qh->last_high= REALmax;
+  qh->last_newhigh= REALmax;
+  qh->last_random= 1;
+  qh->max_outside= 0.0;
+  qh->max_vertex= 0.0;
+  qh->MAXabs_coord= 0.0;
+  qh->MAXsumcoord= 0.0;
+  qh->MAXwidth= -REALmax;
+  qh->MERGEindependent= True;
+  qh->MINdenom_1= fmax_(1.0/REALmax, REALmin); /* used by qh_scalepoints */
+  qh->MINoutside= 0.0;
+  qh->MINvisible= REALmax;
+  qh->MAXcoplanar= REALmax;
+  qh->outside_err= REALmax;
+  qh->premerge_centrum= 0.0;
+  qh->premerge_cos= REALmax;
+  qh->PRINTprecision= True;
+  qh->PRINTradius= 0.0;
+  qh->postmerge_cos= REALmax;
+  qh->postmerge_centrum= 0.0;
+  qh->ROTATErandom= INT_MIN;
+  qh->MERGEvertices= True;
+  qh->totarea= 0.0;
+  qh->totvol= 0.0;
+  qh->TRACEdist= REALmax;
+  qh->TRACEpoint= qh_IDunknown; /* recompile or use 'TPn' */
+  qh->tracefacet_id= UINT_MAX;  /* recompile to trace a facet */
+  qh->tracevertex_id= UINT_MAX; /* recompile to trace a vertex */
+  seed= (int)time(&timedata);
+  qh_RANDOMseed_(qh, seed);
+  qh->run_id= qh_RANDOMint;
+  if(!qh->run_id)
+      qh->run_id++;  /* guarantee non-zero */
+  qh_option(qh, "run-id", &qh->run_id, NULL);
+  strcat(qh->qhull, "qhull");
+} /* initqhull_start2 */
+
+/*---------------------------------
+
+  qh_initthresholds(qh, commandString )
+    set thresholds for printing and scaling from commandString
+
+  returns:
+    sets qh.GOODthreshold or qh.SPLITthreshold if 'Pd0D1' used
+
+  see:
+    qh_initflags(), 'Qbk' 'QBk' 'Pdk' and 'PDk'
+    qh_inthresholds()
+
+  design:
+    for each 'Pdn' or 'PDn' option
+      check syntax
+      set qh.lower_threshold or qh.upper_threshold
+    set qh.GOODthreshold if an unbounded threshold is used
+    set qh.SPLITthreshold if a bounded threshold is used
+*/
+void qh_initthresholds(qhT *qh, char *command) {
+  realT value;
+  int idx, maxdim, k;
+  char *s= command; /* non-const due to strtol */
+  char key;
+
+  maxdim= qh->input_dim;
+  if (qh->DELAUNAY && (qh->PROJECTdelaunay || qh->PROJECTinput))
+    maxdim++;
+  while (*s) {
+    if (*s == '-')
+      s++;
+    if (*s == 'P') {
+      s++;
+      while (*s && !isspace(key= *s++)) {
+        if (key == 'd' || key == 'D') {
+          if (!isdigit(*s)) {
+            qh_fprintf(qh, qh->ferr, 7044, "qhull warning: no dimension given for Print option '%c' at: %s.  Ignored\n",
+                    key, s-1);
+            continue;
+          }
+          idx= qh_strtol(s, &s);
+          if (idx >= qh->hull_dim) {
+            qh_fprintf(qh, qh->ferr, 7045, "qhull warning: dimension %d for Print option '%c' is >= %d.  Ignored\n",
+                idx, key, qh->hull_dim);
+            continue;
+          }
+          if (*s == ':') {
+            s++;
+            value= qh_strtod(s, &s);
+            if (fabs((double)value) > 1.0) {
+              qh_fprintf(qh, qh->ferr, 7046, "qhull warning: value %2.4g for Print option %c is > +1 or < -1.  Ignored\n",
+                      value, key);
+              continue;
+            }
+          }else
+            value= 0.0;
+          if (key == 'd')
+            qh->lower_threshold[idx]= value;
+          else
+            qh->upper_threshold[idx]= value;
+        }
+      }
+    }else if (*s == 'Q') {
+      s++;
+      while (*s && !isspace(key= *s++)) {
+        if (key == 'b' && *s == 'B') {
+          s++;
+          for (k=maxdim; k--; ) {
+            qh->lower_bound[k]= -qh_DEFAULTbox;
+            qh->upper_bound[k]= qh_DEFAULTbox;
+          }
+        }else if (key == 'b' && *s == 'b')
+          s++;
+        else if (key == 'b' || key == 'B') {
+          if (!isdigit(*s)) {
+            qh_fprintf(qh, qh->ferr, 7047, "qhull warning: no dimension given for Qhull option %c.  Ignored\n",
+                    key);
+            continue;
+          }
+          idx= qh_strtol(s, &s);
+          if (idx >= maxdim) {
+            qh_fprintf(qh, qh->ferr, 7048, "qhull warning: dimension %d for Qhull option %c is >= %d.  Ignored\n",
+                idx, key, maxdim);
+            continue;
+          }
+          if (*s == ':') {
+            s++;
+            value= qh_strtod(s, &s);
+          }else if (key == 'b')
+            value= -qh_DEFAULTbox;
+          else
+            value= qh_DEFAULTbox;
+          if (key == 'b')
+            qh->lower_bound[idx]= value;
+          else
+            qh->upper_bound[idx]= value;
+        }
+      }
+    }else {
+      while (*s && !isspace(*s))
+        s++;
+    }
+    while (isspace(*s))
+      s++;
+  }
+  for (k=qh->hull_dim; k--; ) {
+    if (qh->lower_threshold[k] > -REALmax/2) {
+      qh->GOODthreshold= True;
+      if (qh->upper_threshold[k] < REALmax/2) {
+        qh->SPLITthresholds= True;
+        qh->GOODthreshold= False;
+        break;
+      }
+    }else if (qh->upper_threshold[k] < REALmax/2)
+      qh->GOODthreshold= True;
+  }
+} /* initthresholds */
+
+/*---------------------------------
+
+  qh_lib_check( qhullLibraryType, qhTsize, vertexTsize, ridgeTsize, facetTsize, setTsize, qhmemTsize )
+    Report error if library does not agree with caller
+
+  notes:
+    NOerrors -- qh_lib_check can not call qh_errexit()
+*/
+void qh_lib_check(int qhullLibraryType, int qhTsize, int vertexTsize, int ridgeTsize, int facetTsize, int setTsize, int qhmemTsize) {
+    boolT iserror= False;
+
+#if defined(_MSC_VER) && defined(_DEBUG) && defined(QHULL_CRTDBG)  /* user_r.h */
+    // _CrtSetBreakAlloc(744);  /* Break at memalloc {744}, or 'watch' _crtBreakAlloc */
+    _CrtSetDbgFlag( _CRTDBG_ALLOC_MEM_DF | _CRTDBG_DELAY_FREE_MEM_DF | _CRTDBG_LEAK_CHECK_DF | _CrtSetDbgFlag(_CRTDBG_REPORT_FLAG) );
+    _CrtSetReportMode( _CRT_ERROR, _CRTDBG_MODE_FILE | _CRTDBG_MODE_DEBUG );
+    _CrtSetReportFile( _CRT_ERROR, _CRTDBG_FILE_STDERR );
+    _CrtSetReportMode( _CRT_WARN, _CRTDBG_MODE_FILE | _CRTDBG_MODE_DEBUG );
+    _CrtSetReportFile( _CRT_WARN, _CRTDBG_FILE_STDERR );
+    _CrtSetReportMode( _CRT_ASSERT, _CRTDBG_MODE_FILE | _CRTDBG_MODE_DEBUG );
+    _CrtSetReportFile( _CRT_ASSERT, _CRTDBG_FILE_STDERR );
+#endif
+
+    if (qhullLibraryType==QHULL_NON_REENTRANT) { /* 0 */
+        qh_fprintf_stderr(6257, "qh_lib_check: Incorrect qhull library called.  Caller uses non-reentrant Qhull with a static qhT.  Library is reentrant.\n");
+        iserror= True;
+    }else if (qhullLibraryType==QHULL_QH_POINTER) { /* 1 */
+        qh_fprintf_stderr(6258, "qh_lib_check: Incorrect qhull library called.  Caller uses non-reentrant Qhull with a dynamic qhT via qh_QHpointer.  Library is reentrant.\n");
+        iserror= True;
+    }else if (qhullLibraryType!=QHULL_REENTRANT) { /* 2 */
+        qh_fprintf_stderr(6262, "qh_lib_check: Expecting qhullLibraryType QHULL_NON_REENTRANT(0), QHULL_QH_POINTER(1), or QHULL_REENTRANT(2).  Got %d\n", qhullLibraryType);
+        iserror= True;
+    }
+    if (qhTsize != sizeof(qhT)) {
+        qh_fprintf_stderr(6249, "qh_lib_check: Incorrect qhull library called.  Size of qhT for caller is %d, but for library is %d.\n", qhTsize, sizeof(qhT));
+        iserror= True;
+    }
+    if (vertexTsize != sizeof(vertexT)) {
+        qh_fprintf_stderr(6250, "qh_lib_check: Incorrect qhull library called.  Size of vertexT for caller is %d, but for library is %d.\n", vertexTsize, sizeof(vertexT));
+        iserror= True;
+    }
+    if (ridgeTsize != sizeof(ridgeT)) {
+        qh_fprintf_stderr(6251, "qh_lib_check: Incorrect qhull library called.  Size of ridgeT for caller is %d, but for library is %d.\n", ridgeTsize, sizeof(ridgeT));
+        iserror= True;
+    }
+    if (facetTsize != sizeof(facetT)) {
+        qh_fprintf_stderr(6252, "qh_lib_check: Incorrect qhull library called.  Size of facetT for caller is %d, but for library is %d.\n", facetTsize, sizeof(facetT));
+        iserror= True;
+    }
+    if (setTsize && setTsize != sizeof(setT)) {
+        qh_fprintf_stderr(6253, "qh_lib_check: Incorrect qhull library called.  Size of setT for caller is %d, but for library is %d.\n", setTsize, sizeof(setT));
+        iserror= True;
+    }
+    if (qhmemTsize && qhmemTsize != sizeof(qhmemT)) {
+        qh_fprintf_stderr(6254, "qh_lib_check: Incorrect qhull library called.  Size of qhmemT for caller is %d, but for library is %d.\n", qhmemTsize, sizeof(qhmemT));
+        iserror= True;
+    }
+    if (iserror) {
+        qh_fprintf_stderr(6259, "qh_lib_check: Cannot continue.  Library '%s' is reentrant (e.g., qhull_r.so)\n", qh_version2);
+        qh_exit(qh_ERRqhull);  /* can not use qh_errexit() */
+    }
+} /* lib_check */
+
+/*---------------------------------
+
+  qh_option(qh, option, intVal, realVal )
+    add an option description to qh.qhull_options
+
+  notes:
+    NOerrors -- qh_option can not call qh_errexit() [qh_initqhull_start2]
+    will be printed with statistics ('Ts') and errors
+    strlen(option) < 40
+*/
+void qh_option(qhT *qh, const char *option, int *i, realT *r) {
+  char buf[200];
+  int len, maxlen;
+
+  sprintf(buf, "  %s", option);
+  if (i)
+    sprintf(buf+strlen(buf), " %d", *i);
+  if (r)
+    sprintf(buf+strlen(buf), " %2.2g", *r);
+  len= (int)strlen(buf);  /* WARN64 */
+  qh->qhull_optionlen += len;
+  maxlen= sizeof(qh->qhull_options) - len -1;
+  maximize_(maxlen, 0);
+  if (qh->qhull_optionlen >= qh_OPTIONline && maxlen > 0) {
+    qh->qhull_optionlen= len;
+    strncat(qh->qhull_options, "\n", (size_t)(maxlen--));
+  }
+  strncat(qh->qhull_options, buf, (size_t)maxlen);
+} /* option */
+
+/*---------------------------------
+
+  qh_zero( qh, errfile )
+    Initialize and zero Qhull's memory for qh_new_qhull()
+
+  notes:
+    Not needed in global.c because static variables are initialized to zero
+*/
+void qh_zero(qhT *qh, FILE *errfile) {
+    memset((char *)qh, 0, sizeof(qhT));   /* every field is 0, FALSE, NULL */
+    qh->NOerrexit= True;
+    qh_meminit(qh, errfile);
+} /* zero */
+
diff --git a/Cdir/halfspaces.c b/Cdir/halfspaces.c
new file mode 100644
--- /dev/null
+++ b/Cdir/halfspaces.c
@@ -0,0 +1,68 @@
+#define qh_QHimport
+#include "qhull_ra.h"
+
+double** intersections(
+  double*   halfspaces,
+  double*   interiorpoint,
+  unsigned  dim,
+  unsigned  n,
+  unsigned* nintersections,
+  unsigned* exitcode,
+  unsigned  print
+)
+{
+  char opts[250];
+  sprintf(opts, "qhull s Fp FF H H%f", interiorpoint[0]); //, interiorpoint[1] , interiorpoint[2]);
+  for(unsigned i=1; i < dim; i++){
+    char x[20];
+    sprintf(x, ",%f", interiorpoint[i]);
+    strcat(opts, x);
+  }
+  printf(opts); printf("\n");
+
+  qhT qh_qh; /* Qhull's data structure */
+  qhT* qh= &qh_qh;
+  QHULL_LIB_CHECK
+  qh_meminit(qh, stderr);
+  boolT ismalloc  = False; /* True if qhull should free points in qh_freeqhull() or reallocation */
+  FILE *errfile   = NULL;
+  FILE* outfile = print ? stdout : NULL;
+  qh_zero(qh, errfile);
+  *exitcode = qh_new_qhull(qh, dim+1, n, halfspaces, ismalloc, opts, outfile,
+                           errfile);
+  printf("exitcode: %u\n", *exitcode);
+
+  double** out;
+  if(!(*exitcode)){
+    *nintersections = qh->num_facets;
+    out = malloc(*nintersections * sizeof(double*));
+    facetT *facet;
+    unsigned i_facet = 0;
+    FORALLfacets{
+      if(facet->offset != 0){
+        out[i_facet] = malloc(dim * sizeof(double));
+        for(unsigned i=0; i < dim; i++){
+          out[i_facet][i] = - facet->normal[i] / facet->offset +
+                            qh->feasible_point[i]; // = interiorpoint ? yes
+        }
+        i_facet++;
+      }else{
+        (*nintersections)--;
+      }
+    }
+
+  }
+
+  /* Do cleanup regardless of whether there is an error */
+  int curlong, totlong;
+  qh_freeqhull(qh, !qh_ALL);                /* free long memory */
+  qh_memfreeshort(qh, &curlong, &totlong);  /* free short memory and memory allocator */
+
+  if(*exitcode){
+    free(out);
+    return 0;
+  }else{
+    return out;
+  }
+
+}
diff --git a/Cdir/io_r.c b/Cdir/io_r.c
new file mode 100644
--- /dev/null
+++ b/Cdir/io_r.c
@@ -0,0 +1,4062 @@
+/*
  ---------------------------------
+
+   io_r.c
+   Input/Output routines of qhull application
+
+   see qh-io_r.htm and io_r.h
+
+   see user_r.c for qh_errprint and qh_printfacetlist
+
+   unix_r.c calls qh_readpoints and qh_produce_output
+
+   unix_r.c and user_r.c are the only callers of io_r.c functions
+   This allows the user to avoid loading io_r.o from qhull.a
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull_r/io_r.c#4 $$Change: 2064 $
+   $DateTime: 2016/01/18 12:36:08 $$Author: bbarber $
+*/
+
+#include "qhull_ra.h"
+
+/*========= -functions in alphabetical order after qh_produce_output(qh)  =====*/
+
+/*---------------------------------
+
+  qh_produce_output(qh)
+  qh_produce_output2(qh)
+    prints out the result of qhull in desired format
+    qh_produce_output2(qh) does not call qh_prepare_output(qh)
+    if qh.GETarea
+      computes and prints area and volume
+    qh.PRINTout[] is an array of output formats
+
+  notes:
+    prints output in qh.PRINTout order
+*/
+void qh_produce_output(qhT *qh) {
+    int tempsize= qh_setsize(qh, qh->qhmem.tempstack);
+
+    qh_prepare_output(qh);
+    qh_produce_output2(qh);
+    if (qh_setsize(qh, qh->qhmem.tempstack) != tempsize) {
+        qh_fprintf(qh, qh->ferr, 6206, "qhull internal error (qh_produce_output): temporary sets not empty(%d)\n",
+            qh_setsize(qh, qh->qhmem.tempstack));
+        qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+    }
+} /* produce_output */
+
+
+void qh_produce_output2(qhT *qh) {
+  int i, tempsize= qh_setsize(qh, qh->qhmem.tempstack), d_1;
+
+  if (qh->PRINTsummary)
+    qh_printsummary(qh, qh->ferr);
+  else if (qh->PRINTout[0] == qh_PRINTnone)
+    qh_printsummary(qh, qh->fout);
+  for (i=0; i < qh_PRINTEND; i++)
+    qh_printfacets(qh, qh->fout, qh->PRINTout[i], qh->facet_list, NULL, !qh_ALL);
+  qh_allstatistics(qh);
+  if (qh->PRINTprecision && !qh->MERGING && (qh->JOGGLEmax > REALmax/2 || qh->RERUN))
+    qh_printstats(qh, qh->ferr, qh->qhstat.precision, NULL);
+  if (qh->VERIFYoutput && (zzval_(Zridge) > 0 || zzval_(Zridgemid) > 0))
+    qh_printstats(qh, qh->ferr, qh->qhstat.vridges, NULL);
+  if (qh->PRINTstatistics) {
+    qh_printstatistics(qh, qh->ferr, "");
+    qh_memstatistics(qh, qh->ferr);
+    d_1= sizeof(setT) + (qh->hull_dim - 1) * SETelemsize;
+    qh_fprintf(qh, qh->ferr, 8040, "\
+    size in bytes: merge %d ridge %d vertex %d facet %d\n\
+         normal %d ridge vertices %d facet vertices or neighbors %d\n",
+            (int)sizeof(mergeT), (int)sizeof(ridgeT),
+            (int)sizeof(vertexT), (int)sizeof(facetT),
+            qh->normal_size, d_1, d_1 + SETelemsize);
+  }
+  if (qh_setsize(qh, qh->qhmem.tempstack) != tempsize) {
+    qh_fprintf(qh, qh->ferr, 6065, "qhull internal error (qh_produce_output2): temporary sets not empty(%d)\n",
+             qh_setsize(qh, qh->qhmem.tempstack));
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }
+} /* produce_output2 */
+
+/*---------------------------------
+
+  qh_dfacet(qh, id )
+    print facet by id, for debugging
+
+*/
+void qh_dfacet(qhT *qh, unsigned id) {
+  facetT *facet;
+
+  FORALLfacets {
+    if (facet->id == id) {
+      qh_printfacet(qh, qh->fout, facet);
+      break;
+    }
+  }
+} /* dfacet */
+
+
+/*---------------------------------
+
+  qh_dvertex(qh, id )
+    print vertex by id, for debugging
+*/
+void qh_dvertex(qhT *qh, unsigned id) {
+  vertexT *vertex;
+
+  FORALLvertices {
+    if (vertex->id == id) {
+      qh_printvertex(qh, qh->fout, vertex);
+      break;
+    }
+  }
+} /* dvertex */
+
+
+/*---------------------------------
+
+  qh_compare_facetarea(p1, p2 )
+    used by qsort() to order facets by area
+*/
+int qh_compare_facetarea(const void *p1, const void *p2) {
+  const facetT *a= *((facetT *const*)p1), *b= *((facetT *const*)p2);
+
+  if (!a->isarea)
+    return -1;
+  if (!b->isarea)
+    return 1;
+  if (a->f.area > b->f.area)
+    return 1;
+  else if (a->f.area == b->f.area)
+    return 0;
+  return -1;
+} /* compare_facetarea */
+
+/*---------------------------------
+
+  qh_compare_facetmerge(p1, p2 )
+    used by qsort() to order facets by number of merges
+*/
+int qh_compare_facetmerge(const void *p1, const void *p2) {
+  const facetT *a= *((facetT *const*)p1), *b= *((facetT *const*)p2);
+
+  return(a->nummerge - b->nummerge);
+} /* compare_facetvisit */
+
+/*---------------------------------
+
+  qh_compare_facetvisit(p1, p2 )
+    used by qsort() to order facets by visit id or id
+*/
+int qh_compare_facetvisit(const void *p1, const void *p2) {
+  const facetT *a= *((facetT *const*)p1), *b= *((facetT *const*)p2);
+  int i,j;
+
+  if (!(i= a->visitid))
+    i= 0 - a->id; /* do not convert to int, sign distinguishes id from visitid */
+  if (!(j= b->visitid))
+    j= 0 - b->id;
+  return(i - j);
+} /* compare_facetvisit */
+
+/*---------------------------------
+
+  qh_compare_vertexpoint( p1, p2 )
+    used by qsort() to order vertices by point id
+
+  Not usable in qhulllib_r since qh_pointid depends on qh
+
+  int qh_compare_vertexpoint(const void *p1, const void *p2) {
+  const vertexT *a= *((vertexT *const*)p1), *b= *((vertexT *const*)p2);
+
+  return((qh_pointid(qh, a->point) > qh_pointid(qh, b->point)?1:-1));
+}*/
+
+/*---------------------------------
+
+  qh_copyfilename(qh, dest, size, source, length )
+    copy filename identified by qh_skipfilename()
+
+  notes:
+    see qh_skipfilename() for syntax
+*/
+void qh_copyfilename(qhT *qh, char *filename, int size, const char* source, int length) {
+  char c= *source;
+
+  if (length > size + 1) {
+      qh_fprintf(qh, qh->ferr, 6040, "qhull error: filename is more than %d characters, %s\n",  size-1, source);
+      qh_errexit(qh, qh_ERRinput, NULL, NULL);
+  }
+  strncpy(filename, source, length);
+  filename[length]= '\0';
+  if (c == '\'' || c == '"') {
+    char *s= filename + 1;
+    char *t= filename;
+    while (*s) {
+      if (*s == c) {
+          if (s[-1] == '\\')
+              t[-1]= c;
+      }else
+          *t++= *s;
+      s++;
+    }
+    *t= '\0';
+  }
+} /* copyfilename */
+
+/*---------------------------------
+
+  qh_countfacets(qh, facetlist, facets, printall,
+          numfacets, numsimplicial, totneighbors, numridges, numcoplanar, numtricoplanars  )
+    count good facets for printing and set visitid
+    if allfacets, ignores qh_skipfacet()
+
+  notes:
+    qh_printsummary and qh_countfacets must match counts
+
+  returns:
+    numfacets, numsimplicial, total neighbors, numridges, coplanars
+    each facet with ->visitid indicating 1-relative position
+      ->visitid==0 indicates not good
+
+  notes
+    numfacets >= numsimplicial
+    if qh.NEWfacets,
+      does not count visible facets (matches qh_printafacet)
+
+  design:
+    for all facets on facetlist and in facets set
+      unless facet is skipped or visible (i.e., will be deleted)
+        mark facet->visitid
+        update counts
+*/
+void qh_countfacets(qhT *qh, facetT *facetlist, setT *facets, boolT printall,
+    int *numfacetsp, int *numsimplicialp, int *totneighborsp, int *numridgesp, int *numcoplanarsp, int *numtricoplanarsp) {
+  facetT *facet, **facetp;
+  int numfacets= 0, numsimplicial= 0, numridges= 0, totneighbors= 0, numcoplanars= 0, numtricoplanars= 0;
+
+  FORALLfacet_(facetlist) {
+    if ((facet->visible && qh->NEWfacets)
+    || (!printall && qh_skipfacet(qh, facet)))
+      facet->visitid= 0;
+    else {
+      facet->visitid= ++numfacets;
+      totneighbors += qh_setsize(qh, facet->neighbors);
+      if (facet->simplicial) {
+        numsimplicial++;
+        if (facet->keepcentrum && facet->tricoplanar)
+          numtricoplanars++;
+      }else
+        numridges += qh_setsize(qh, facet->ridges);
+      if (facet->coplanarset)
+        numcoplanars += qh_setsize(qh, facet->coplanarset);
+    }
+  }
+
+  FOREACHfacet_(facets) {
+    if ((facet->visible && qh->NEWfacets)
+    || (!printall && qh_skipfacet(qh, facet)))
+      facet->visitid= 0;
+    else {
+      facet->visitid= ++numfacets;
+      totneighbors += qh_setsize(qh, facet->neighbors);
+      if (facet->simplicial){
+        numsimplicial++;
+        if (facet->keepcentrum && facet->tricoplanar)
+          numtricoplanars++;
+      }else
+        numridges += qh_setsize(qh, facet->ridges);
+      if (facet->coplanarset)
+        numcoplanars += qh_setsize(qh, facet->coplanarset);
+    }
+  }
+  qh->visit_id += numfacets+1;
+  *numfacetsp= numfacets;
+  *numsimplicialp= numsimplicial;
+  *totneighborsp= totneighbors;
+  *numridgesp= numridges;
+  *numcoplanarsp= numcoplanars;
+  *numtricoplanarsp= numtricoplanars;
+} /* countfacets */
+
+/*---------------------------------
+
+  qh_detvnorm(qh, vertex, vertexA, centers, offset )
+    compute separating plane of the Voronoi diagram for a pair of input sites
+    centers= set of facets (i.e., Voronoi vertices)
+      facet->visitid= 0 iff vertex-at-infinity (i.e., unbounded)
+
+  assumes:
+    qh_ASvoronoi and qh_vertexneighbors() already set
+
+  returns:
+    norm
+      a pointer into qh.gm_matrix to qh.hull_dim-1 reals
+      copy the data before reusing qh.gm_matrix
+    offset
+      if 'QVn'
+        sign adjusted so that qh.GOODvertexp is inside
+      else
+        sign adjusted so that vertex is inside
+
+    qh.gm_matrix= simplex of points from centers relative to first center
+
+  notes:
+    in io_r.c so that code for 'v Tv' can be removed by removing io_r.c
+    returns pointer into qh.gm_matrix to avoid tracking of temporary memory
+
+  design:
+    determine midpoint of input sites
+    build points as the set of Voronoi vertices
+    select a simplex from points (if necessary)
+      include midpoint if the Voronoi region is unbounded
+    relocate the first vertex of the simplex to the origin
+    compute the normalized hyperplane through the simplex
+    orient the hyperplane toward 'QVn' or 'vertex'
+    if 'Tv' or 'Ts'
+      if bounded
+        test that hyperplane is the perpendicular bisector of the input sites
+      test that Voronoi vertices not in the simplex are still on the hyperplane
+    free up temporary memory
+*/
+pointT *qh_detvnorm(qhT *qh, vertexT *vertex, vertexT *vertexA, setT *centers, realT *offsetp) {
+  facetT *facet, **facetp;
+  int  i, k, pointid, pointidA, point_i, point_n;
+  setT *simplex= NULL;
+  pointT *point, **pointp, *point0, *midpoint, *normal, *inpoint;
+  coordT *coord, *gmcoord, *normalp;
+  setT *points= qh_settemp(qh, qh->TEMPsize);
+  boolT nearzero= False;
+  boolT unbounded= False;
+  int numcenters= 0;
+  int dim= qh->hull_dim - 1;
+  realT dist, offset, angle, zero= 0.0;
+
+  midpoint= qh->gm_matrix + qh->hull_dim * qh->hull_dim;  /* last row */
+  for (k=0; k < dim; k++)
+    midpoint[k]= (vertex->point[k] + vertexA->point[k])/2;
+  FOREACHfacet_(centers) {
+    numcenters++;
+    if (!facet->visitid)
+      unbounded= True;
+    else {
+      if (!facet->center)
+        facet->center= qh_facetcenter(qh, facet->vertices);
+      qh_setappend(qh, &points, facet->center);
+    }
+  }
+  if (numcenters > dim) {
+    simplex= qh_settemp(qh, qh->TEMPsize);
+    qh_setappend(qh, &simplex, vertex->point);
+    if (unbounded)
+      qh_setappend(qh, &simplex, midpoint);
+    qh_maxsimplex(qh, dim, points, NULL, 0, &simplex);
+    qh_setdelnth(qh, simplex, 0);
+  }else if (numcenters == dim) {
+    if (unbounded)
+      qh_setappend(qh, &points, midpoint);
+    simplex= points;
+  }else {
+    qh_fprintf(qh, qh->ferr, 6216, "qhull internal error (qh_detvnorm): too few points(%d) to compute separating plane\n", numcenters);
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }
+  i= 0;
+  gmcoord= qh->gm_matrix;
+  point0= SETfirstt_(simplex, pointT);
+  FOREACHpoint_(simplex) {
+    if (qh->IStracing >= 4)
+      qh_printmatrix(qh, qh->ferr, "qh_detvnorm: Voronoi vertex or midpoint",
+                              &point, 1, dim);
+    if (point != point0) {
+      qh->gm_row[i++]= gmcoord;
+      coord= point0;
+      for (k=dim; k--; )
+        *(gmcoord++)= *point++ - *coord++;
+    }
+  }
+  qh->gm_row[i]= gmcoord;  /* does not overlap midpoint, may be used later for qh_areasimplex */
+  normal= gmcoord;
+  qh_sethyperplane_gauss(qh, dim, qh->gm_row, point0, True,
+                normal, &offset, &nearzero);
+  if (qh->GOODvertexp == vertexA->point)
+    inpoint= vertexA->point;
+  else
+    inpoint= vertex->point;
+  zinc_(Zdistio);
+  dist= qh_distnorm(dim, inpoint, normal, &offset);
+  if (dist > 0) {
+    offset= -offset;
+    normalp= normal;
+    for (k=dim; k--; ) {
+      *normalp= -(*normalp);
+      normalp++;
+    }
+  }
+  if (qh->VERIFYoutput || qh->PRINTstatistics) {
+    pointid= qh_pointid(qh, vertex->point);
+    pointidA= qh_pointid(qh, vertexA->point);
+    if (!unbounded) {
+      zinc_(Zdiststat);
+      dist= qh_distnorm(dim, midpoint, normal, &offset);
+      if (dist < 0)
+        dist= -dist;
+      zzinc_(Zridgemid);
+      wwmax_(Wridgemidmax, dist);
+      wwadd_(Wridgemid, dist);
+      trace4((qh, qh->ferr, 4014, "qh_detvnorm: points %d %d midpoint dist %2.2g\n",
+                 pointid, pointidA, dist));
+      for (k=0; k < dim; k++)
+        midpoint[k]= vertexA->point[k] - vertex->point[k];  /* overwrites midpoint! */
+      qh_normalize(qh, midpoint, dim, False);
+      angle= qh_distnorm(dim, midpoint, normal, &zero); /* qh_detangle uses dim+1 */
+      if (angle < 0.0)
+        angle= angle + 1.0;
+      else
+        angle= angle - 1.0;
+      if (angle < 0.0)
+        angle -= angle;
+      trace4((qh, qh->ferr, 4015, "qh_detvnorm: points %d %d angle %2.2g nearzero %d\n",
+                 pointid, pointidA, angle, nearzero));
+      if (nearzero) {
+        zzinc_(Zridge0);
+        wwmax_(Wridge0max, angle);
+        wwadd_(Wridge0, angle);
+      }else {
+        zzinc_(Zridgeok)
+        wwmax_(Wridgeokmax, angle);
+        wwadd_(Wridgeok, angle);
+      }
+    }
+    if (simplex != points) {
+      FOREACHpoint_i_(qh, points) {
+        if (!qh_setin(simplex, point)) {
+          facet= SETelemt_(centers, point_i, facetT);
+          zinc_(Zdiststat);
+          dist= qh_distnorm(dim, point, normal, &offset);
+          if (dist < 0)
+            dist= -dist;
+          zzinc_(Zridge);
+          wwmax_(Wridgemax, dist);
+          wwadd_(Wridge, dist);
+          trace4((qh, qh->ferr, 4016, "qh_detvnorm: points %d %d Voronoi vertex %d dist %2.2g\n",
+                             pointid, pointidA, facet->visitid, dist));
+        }
+      }
+    }
+  }
+  *offsetp= offset;
+  if (simplex != points)
+    qh_settempfree(qh, &simplex);
+  qh_settempfree(qh, &points);
+  return normal;
+} /* detvnorm */
+
+/*---------------------------------
+
+  qh_detvridge(qh, vertexA )
+    determine Voronoi ridge from 'seen' neighbors of vertexA
+    include one vertex-at-infinite if an !neighbor->visitid
+
+  returns:
+    temporary set of centers (facets, i.e., Voronoi vertices)
+    sorted by center id
+*/
+setT *qh_detvridge(qhT *qh, vertexT *vertex) {
+  setT *centers= qh_settemp(qh, qh->TEMPsize);
+  setT *tricenters= qh_settemp(qh, qh->TEMPsize);
+  facetT *neighbor, **neighborp;
+  boolT firstinf= True;
+
+  FOREACHneighbor_(vertex) {
+    if (neighbor->seen) {
+      if (neighbor->visitid) {
+        if (!neighbor->tricoplanar || qh_setunique(qh, &tricenters, neighbor->center))
+          qh_setappend(qh, ¢ers, neighbor);
+      }else if (firstinf) {
+        firstinf= False;
+        qh_setappend(qh, ¢ers, neighbor);
+      }
+    }
+  }
+  qsort(SETaddr_(centers, facetT), (size_t)qh_setsize(qh, centers),
+             sizeof(facetT *), qh_compare_facetvisit);
+  qh_settempfree(qh, &tricenters);
+  return centers;
+} /* detvridge */
+
+/*---------------------------------
+
+  qh_detvridge3(qh, atvertex, vertex )
+    determine 3-d Voronoi ridge from 'seen' neighbors of atvertex and vertex
+    include one vertex-at-infinite for !neighbor->visitid
+    assumes all facet->seen2= True
+
+  returns:
+    temporary set of centers (facets, i.e., Voronoi vertices)
+    listed in adjacency order (!oriented)
+    all facet->seen2= True
+
+  design:
+    mark all neighbors of atvertex
+    for each adjacent neighbor of both atvertex and vertex
+      if neighbor selected
+        add neighbor to set of Voronoi vertices
+*/
+setT *qh_detvridge3(qhT *qh, vertexT *atvertex, vertexT *vertex) {
+  setT *centers= qh_settemp(qh, qh->TEMPsize);
+  setT *tricenters= qh_settemp(qh, qh->TEMPsize);
+  facetT *neighbor, **neighborp, *facet= NULL;
+  boolT firstinf= True;
+
+  FOREACHneighbor_(atvertex)
+    neighbor->seen2= False;
+  FOREACHneighbor_(vertex) {
+    if (!neighbor->seen2) {
+      facet= neighbor;
+      break;
+    }
+  }
+  while (facet) {
+    facet->seen2= True;
+    if (neighbor->seen) {
+      if (facet->visitid) {
+        if (!facet->tricoplanar || qh_setunique(qh, &tricenters, facet->center))
+          qh_setappend(qh, ¢ers, facet);
+      }else if (firstinf) {
+        firstinf= False;
+        qh_setappend(qh, ¢ers, facet);
+      }
+    }
+    FOREACHneighbor_(facet) {
+      if (!neighbor->seen2) {
+        if (qh_setin(vertex->neighbors, neighbor))
+          break;
+        else
+          neighbor->seen2= True;
+      }
+    }
+    facet= neighbor;
+  }
+  if (qh->CHECKfrequently) {
+    FOREACHneighbor_(vertex) {
+      if (!neighbor->seen2) {
+          qh_fprintf(qh, qh->ferr, 6217, "qhull internal error (qh_detvridge3): neighbors of vertex p%d are not connected at facet %d\n",
+                 qh_pointid(qh, vertex->point), neighbor->id);
+        qh_errexit(qh, qh_ERRqhull, neighbor, NULL);
+      }
+    }
+  }
+  FOREACHneighbor_(atvertex)
+    neighbor->seen2= True;
+  qh_settempfree(qh, &tricenters);
+  return centers;
+} /* detvridge3 */
+
+/*---------------------------------
+
+  qh_eachvoronoi(qh, fp, printvridge, vertex, visitall, innerouter, inorder )
+    if visitall,
+      visit all Voronoi ridges for vertex (i.e., an input site)
+    else
+      visit all unvisited Voronoi ridges for vertex
+      all vertex->seen= False if unvisited
+    assumes
+      all facet->seen= False
+      all facet->seen2= True (for qh_detvridge3)
+      all facet->visitid == 0 if vertex_at_infinity
+                         == index of Voronoi vertex
+                         >= qh.num_facets if ignored
+    innerouter:
+      qh_RIDGEall--  both inner (bounded) and outer(unbounded) ridges
+      qh_RIDGEinner- only inner
+      qh_RIDGEouter- only outer
+
+    if inorder
+      orders vertices for 3-d Voronoi diagrams
+
+  returns:
+    number of visited ridges (does not include previously visited ridges)
+
+    if printvridge,
+      calls printvridge( fp, vertex, vertexA, centers)
+        fp== any pointer (assumes FILE*)
+        vertex,vertexA= pair of input sites that define a Voronoi ridge
+        centers= set of facets (i.e., Voronoi vertices)
+                 ->visitid == index or 0 if vertex_at_infinity
+                 ordered for 3-d Voronoi diagram
+  notes:
+    uses qh.vertex_visit
+
+  see:
+    qh_eachvoronoi_all()
+
+  design:
+    mark selected neighbors of atvertex
+    for each selected neighbor (either Voronoi vertex or vertex-at-infinity)
+      for each unvisited vertex
+        if atvertex and vertex share more than d-1 neighbors
+          bump totalcount
+          if printvridge defined
+            build the set of shared neighbors (i.e., Voronoi vertices)
+            call printvridge
+*/
+int qh_eachvoronoi(qhT *qh, FILE *fp, printvridgeT printvridge, vertexT *atvertex, boolT visitall, qh_RIDGE innerouter, boolT inorder) {
+  boolT unbounded;
+  int count;
+  facetT *neighbor, **neighborp, *neighborA, **neighborAp;
+  setT *centers;
+  setT *tricenters= qh_settemp(qh, qh->TEMPsize);
+
+  vertexT *vertex, **vertexp;
+  boolT firstinf;
+  unsigned int numfacets= (unsigned int)qh->num_facets;
+  int totridges= 0;
+
+  qh->vertex_visit++;
+  atvertex->seen= True;
+  if (visitall) {
+    FORALLvertices
+      vertex->seen= False;
+  }
+  FOREACHneighbor_(atvertex) {
+    if (neighbor->visitid < numfacets)
+      neighbor->seen= True;
+  }
+  FOREACHneighbor_(atvertex) {
+    if (neighbor->seen) {
+      FOREACHvertex_(neighbor->vertices) {
+        if (vertex->visitid != qh->vertex_visit && !vertex->seen) {
+          vertex->visitid= qh->vertex_visit;
+          count= 0;
+          firstinf= True;
+          qh_settruncate(qh, tricenters, 0);
+          FOREACHneighborA_(vertex) {
+            if (neighborA->seen) {
+              if (neighborA->visitid) {
+                if (!neighborA->tricoplanar || qh_setunique(qh, &tricenters, neighborA->center))
+                  count++;
+              }else if (firstinf) {
+                count++;
+                firstinf= False;
+              }
+            }
+          }
+          if (count >= qh->hull_dim - 1) {  /* e.g., 3 for 3-d Voronoi */
+            if (firstinf) {
+              if (innerouter == qh_RIDGEouter)
+                continue;
+              unbounded= False;
+            }else {
+              if (innerouter == qh_RIDGEinner)
+                continue;
+              unbounded= True;
+            }
+            totridges++;
+            trace4((qh, qh->ferr, 4017, "qh_eachvoronoi: Voronoi ridge of %d vertices between sites %d and %d\n",
+                  count, qh_pointid(qh, atvertex->point), qh_pointid(qh, vertex->point)));
+            if (printvridge && fp) {
+              if (inorder && qh->hull_dim == 3+1) /* 3-d Voronoi diagram */
+                centers= qh_detvridge3(qh, atvertex, vertex);
+              else
+                centers= qh_detvridge(qh, vertex);
+              (*printvridge)(qh, fp, atvertex, vertex, centers, unbounded);
+              qh_settempfree(qh, ¢ers);
+            }
+          }
+        }
+      }
+    }
+  }
+  FOREACHneighbor_(atvertex)
+    neighbor->seen= False;
+  qh_settempfree(qh, &tricenters);
+  return totridges;
+} /* eachvoronoi */
+
+
+/*---------------------------------
+
+  qh_eachvoronoi_all(qh, fp, printvridge, isUpper, innerouter, inorder )
+    visit all Voronoi ridges
+
+    innerouter:
+      see qh_eachvoronoi()
+
+    if inorder
+      orders vertices for 3-d Voronoi diagrams
+
+  returns
+    total number of ridges
+
+    if isUpper == facet->upperdelaunay  (i.e., a Vornoi vertex)
+      facet->visitid= Voronoi vertex index(same as 'o' format)
+    else
+      facet->visitid= 0
+
+    if printvridge,
+      calls printvridge( fp, vertex, vertexA, centers)
+      [see qh_eachvoronoi]
+
+  notes:
+    Not used for qhull.exe
+    same effect as qh_printvdiagram but ridges not sorted by point id
+*/
+int qh_eachvoronoi_all(qhT *qh, FILE *fp, printvridgeT printvridge, boolT isUpper, qh_RIDGE innerouter, boolT inorder) {
+  facetT *facet;
+  vertexT *vertex;
+  int numcenters= 1;  /* vertex 0 is vertex-at-infinity */
+  int totridges= 0;
+
+  qh_clearcenters(qh, qh_ASvoronoi);
+  qh_vertexneighbors(qh);
+  maximize_(qh->visit_id, (unsigned) qh->num_facets);
+  FORALLfacets {
+    facet->visitid= 0;
+    facet->seen= False;
+    facet->seen2= True;
+  }
+  FORALLfacets {
+    if (facet->upperdelaunay == isUpper)
+      facet->visitid= numcenters++;
+  }
+  FORALLvertices
+    vertex->seen= False;
+  FORALLvertices {
+    if (qh->GOODvertex > 0 && qh_pointid(qh, vertex->point)+1 != qh->GOODvertex)
+      continue;
+    totridges += qh_eachvoronoi(qh, fp, printvridge, vertex,
+                   !qh_ALL, innerouter, inorder);
+  }
+  return totridges;
+} /* eachvoronoi_all */
+
+/*---------------------------------
+
+  qh_facet2point(qh, facet, point0, point1, mindist )
+    return two projected temporary vertices for a 2-d facet
+    may be non-simplicial
+
+  returns:
+    point0 and point1 oriented and projected to the facet
+    returns mindist (maximum distance below plane)
+*/
+void qh_facet2point(qhT *qh, facetT *facet, pointT **point0, pointT **point1, realT *mindist) {
+  vertexT *vertex0, *vertex1;
+  realT dist;
+
+  if (facet->toporient ^ qh_ORIENTclock) {
+    vertex0= SETfirstt_(facet->vertices, vertexT);
+    vertex1= SETsecondt_(facet->vertices, vertexT);
+  }else {
+    vertex1= SETfirstt_(facet->vertices, vertexT);
+    vertex0= SETsecondt_(facet->vertices, vertexT);
+  }
+  zadd_(Zdistio, 2);
+  qh_distplane(qh, vertex0->point, facet, &dist);
+  *mindist= dist;
+  *point0= qh_projectpoint(qh, vertex0->point, facet, dist);
+  qh_distplane(qh, vertex1->point, facet, &dist);
+  minimize_(*mindist, dist);
+  *point1= qh_projectpoint(qh, vertex1->point, facet, dist);
+} /* facet2point */
+
+
+/*---------------------------------
+
+  qh_facetvertices(qh, facetlist, facets, allfacets )
+    returns temporary set of vertices in a set and/or list of facets
+    if allfacets, ignores qh_skipfacet()
+
+  returns:
+    vertices with qh.vertex_visit
+
+  notes:
+    optimized for allfacets of facet_list
+
+  design:
+    if allfacets of facet_list
+      create vertex set from vertex_list
+    else
+      for each selected facet in facets or facetlist
+        append unvisited vertices to vertex set
+*/
+setT *qh_facetvertices(qhT *qh, facetT *facetlist, setT *facets, boolT allfacets) {
+  setT *vertices;
+  facetT *facet, **facetp;
+  vertexT *vertex, **vertexp;
+
+  qh->vertex_visit++;
+  if (facetlist == qh->facet_list && allfacets && !facets) {
+    vertices= qh_settemp(qh, qh->num_vertices);
+    FORALLvertices {
+      vertex->visitid= qh->vertex_visit;
+      qh_setappend(qh, &vertices, vertex);
+    }
+  }else {
+    vertices= qh_settemp(qh, qh->TEMPsize);
+    FORALLfacet_(facetlist) {
+      if (!allfacets && qh_skipfacet(qh, facet))
+        continue;
+      FOREACHvertex_(facet->vertices) {
+        if (vertex->visitid != qh->vertex_visit) {
+          vertex->visitid= qh->vertex_visit;
+          qh_setappend(qh, &vertices, vertex);
+        }
+      }
+    }
+  }
+  FOREACHfacet_(facets) {
+    if (!allfacets && qh_skipfacet(qh, facet))
+      continue;
+    FOREACHvertex_(facet->vertices) {
+      if (vertex->visitid != qh->vertex_visit) {
+        vertex->visitid= qh->vertex_visit;
+        qh_setappend(qh, &vertices, vertex);
+      }
+    }
+  }
+  return vertices;
+} /* facetvertices */
+
+/*---------------------------------
+
+  qh_geomplanes(qh, facet, outerplane, innerplane )
+    return outer and inner planes for Geomview
+    qh.PRINTradius is size of vertices and points (includes qh.JOGGLEmax)
+
+  notes:
+    assume precise calculations in io.c with roundoff covered by qh_GEOMepsilon
+*/
+void qh_geomplanes(qhT *qh, facetT *facet, realT *outerplane, realT *innerplane) {
+  realT radius;
+
+  if (qh->MERGING || qh->JOGGLEmax < REALmax/2) {
+    qh_outerinner(qh, facet, outerplane, innerplane);
+    radius= qh->PRINTradius;
+    if (qh->JOGGLEmax < REALmax/2)
+      radius -= qh->JOGGLEmax * sqrt((realT)qh->hull_dim);  /* already accounted for in qh_outerinner() */
+    *outerplane += radius;
+    *innerplane -= radius;
+    if (qh->PRINTcoplanar || qh->PRINTspheres) {
+      *outerplane += qh->MAXabs_coord * qh_GEOMepsilon;
+      *innerplane -= qh->MAXabs_coord * qh_GEOMepsilon;
+    }
+  }else
+    *innerplane= *outerplane= 0;
+} /* geomplanes */
+
+
+/*---------------------------------
+
+  qh_markkeep(qh, facetlist )
+    mark good facets that meet qh.KEEParea, qh.KEEPmerge, and qh.KEEPminArea
+    ignores visible facets (!part of convex hull)
+
+  returns:
+    may clear facet->good
+    recomputes qh.num_good
+
+  design:
+    get set of good facets
+    if qh.KEEParea
+      sort facets by area
+      clear facet->good for all but n largest facets
+    if qh.KEEPmerge
+      sort facets by merge count
+      clear facet->good for all but n most merged facets
+    if qh.KEEPminarea
+      clear facet->good if area too small
+    update qh.num_good
+*/
+void qh_markkeep(qhT *qh, facetT *facetlist) {
+  facetT *facet, **facetp;
+  setT *facets= qh_settemp(qh, qh->num_facets);
+  int size, count;
+
+  trace2((qh, qh->ferr, 2006, "qh_markkeep: only keep %d largest and/or %d most merged facets and/or min area %.2g\n",
+          qh->KEEParea, qh->KEEPmerge, qh->KEEPminArea));
+  FORALLfacet_(facetlist) {
+    if (!facet->visible && facet->good)
+      qh_setappend(qh, &facets, facet);
+  }
+  size= qh_setsize(qh, facets);
+  if (qh->KEEParea) {
+    qsort(SETaddr_(facets, facetT), (size_t)size,
+             sizeof(facetT *), qh_compare_facetarea);
+    if ((count= size - qh->KEEParea) > 0) {
+      FOREACHfacet_(facets) {
+        facet->good= False;
+        if (--count == 0)
+          break;
+      }
+    }
+  }
+  if (qh->KEEPmerge) {
+    qsort(SETaddr_(facets, facetT), (size_t)size,
+             sizeof(facetT *), qh_compare_facetmerge);
+    if ((count= size - qh->KEEPmerge) > 0) {
+      FOREACHfacet_(facets) {
+        facet->good= False;
+        if (--count == 0)
+          break;
+      }
+    }
+  }
+  if (qh->KEEPminArea < REALmax/2) {
+    FOREACHfacet_(facets) {
+      if (!facet->isarea || facet->f.area < qh->KEEPminArea)
+        facet->good= False;
+    }
+  }
+  qh_settempfree(qh, &facets);
+  count= 0;
+  FORALLfacet_(facetlist) {
+    if (facet->good)
+      count++;
+  }
+  qh->num_good= count;
+} /* markkeep */
+
+
+/*---------------------------------
+
+  qh_markvoronoi(qh, facetlist, facets, printall, isLower, numcenters )
+    mark voronoi vertices for printing by site pairs
+
+  returns:
+    temporary set of vertices indexed by pointid
+    isLower set if printing lower hull (i.e., at least one facet is lower hull)
+    numcenters= total number of Voronoi vertices
+    bumps qh.printoutnum for vertex-at-infinity
+    clears all facet->seen and sets facet->seen2
+
+    if selected
+      facet->visitid= Voronoi vertex id
+    else if upper hull (or 'Qu' and lower hull)
+      facet->visitid= 0
+    else
+      facet->visitid >= qh->num_facets
+
+  notes:
+    ignores qh.ATinfinity, if defined
+*/
+setT *qh_markvoronoi(qhT *qh, facetT *facetlist, setT *facets, boolT printall, boolT *isLowerp, int *numcentersp) {
+  int numcenters=0;
+  facetT *facet, **facetp;
+  setT *vertices;
+  boolT isLower= False;
+
+  qh->printoutnum++;
+  qh_clearcenters(qh, qh_ASvoronoi);  /* in case, qh_printvdiagram2 called by user */
+  qh_vertexneighbors(qh);
+  vertices= qh_pointvertex(qh);
+  if (qh->ATinfinity)
+    SETelem_(vertices, qh->num_points-1)= NULL;
+  qh->visit_id++;
+  maximize_(qh->visit_id, (unsigned) qh->num_facets);
+  FORALLfacet_(facetlist) {
+    if (printall || !qh_skipfacet(qh, facet)) {
+      if (!facet->upperdelaunay) {
+        isLower= True;
+        break;
+      }
+    }
+  }
+  FOREACHfacet_(facets) {
+    if (printall || !qh_skipfacet(qh, facet)) {
+      if (!facet->upperdelaunay) {
+        isLower= True;
+        break;
+      }
+    }
+  }
+  FORALLfacets {
+    if (facet->normal && (facet->upperdelaunay == isLower))
+      facet->visitid= 0;  /* facetlist or facets may overwrite */
+    else
+      facet->visitid= qh->visit_id;
+    facet->seen= False;
+    facet->seen2= True;
+  }
+  numcenters++;  /* qh_INFINITE */
+  FORALLfacet_(facetlist) {
+    if (printall || !qh_skipfacet(qh, facet))
+      facet->visitid= numcenters++;
+  }
+  FOREACHfacet_(facets) {
+    if (printall || !qh_skipfacet(qh, facet))
+      facet->visitid= numcenters++;
+  }
+  *isLowerp= isLower;
+  *numcentersp= numcenters;
+  trace2((qh, qh->ferr, 2007, "qh_markvoronoi: isLower %d numcenters %d\n", isLower, numcenters));
+  return vertices;
+} /* markvoronoi */
+
+/*---------------------------------
+
+  qh_order_vertexneighbors(qh, vertex )
+    order facet neighbors of a 2-d or 3-d vertex by adjacency
+
+  notes:
+    does not orient the neighbors
+
+  design:
+    initialize a new neighbor set with the first facet in vertex->neighbors
+    while vertex->neighbors non-empty
+      select next neighbor in the previous facet's neighbor set
+    set vertex->neighbors to the new neighbor set
+*/
+void qh_order_vertexneighbors(qhT *qh, vertexT *vertex) {
+  setT *newset;
+  facetT *facet, *neighbor, **neighborp;
+
+  trace4((qh, qh->ferr, 4018, "qh_order_vertexneighbors: order neighbors of v%d for 3-d\n", vertex->id));
+  newset= qh_settemp(qh, qh_setsize(qh, vertex->neighbors));
+  facet= (facetT*)qh_setdellast(vertex->neighbors);
+  qh_setappend(qh, &newset, facet);
+  while (qh_setsize(qh, vertex->neighbors)) {
+    FOREACHneighbor_(vertex) {
+      if (qh_setin(facet->neighbors, neighbor)) {
+        qh_setdel(vertex->neighbors, neighbor);
+        qh_setappend(qh, &newset, neighbor);
+        facet= neighbor;
+        break;
+      }
+    }
+    if (!neighbor) {
+      qh_fprintf(qh, qh->ferr, 6066, "qhull internal error (qh_order_vertexneighbors): no neighbor of v%d for f%d\n",
+        vertex->id, facet->id);
+      qh_errexit(qh, qh_ERRqhull, facet, NULL);
+    }
+  }
+  qh_setfree(qh, &vertex->neighbors);
+  qh_settemppop(qh);
+  vertex->neighbors= newset;
+} /* order_vertexneighbors */
+
+/*---------------------------------
+
+  qh_prepare_output(qh, )
+    prepare for qh_produce_output2(qh) according to
+      qh.KEEPminArea, KEEParea, KEEPmerge, GOODvertex, GOODthreshold, GOODpoint, ONLYgood, SPLITthresholds
+    does not reset facet->good
+
+  notes
+    except for PRINTstatistics, no-op if previously called with same options
+*/
+void qh_prepare_output(qhT *qh) {
+  if (qh->VORONOI) {
+    qh_clearcenters(qh, qh_ASvoronoi);  /* must be before qh_triangulate */
+    qh_vertexneighbors(qh);
+  }
+  if (qh->TRIangulate && !qh->hasTriangulation) {
+    qh_triangulate(qh);
+    if (qh->VERIFYoutput && !qh->CHECKfrequently)
+      qh_checkpolygon(qh, qh->facet_list);
+  }
+  qh_findgood_all(qh, qh->facet_list);
+  if (qh->GETarea)
+    qh_getarea(qh, qh->facet_list);
+  if (qh->KEEParea || qh->KEEPmerge || qh->KEEPminArea < REALmax/2)
+    qh_markkeep(qh, qh->facet_list);
+  if (qh->PRINTstatistics)
+    qh_collectstatistics(qh);
+}
+
+/*---------------------------------
+
+  qh_printafacet(qh, fp, format, facet, printall )
+    print facet to fp in given output format (see qh.PRINTout)
+
+  returns:
+    nop if !printall and qh_skipfacet()
+    nop if visible facet and NEWfacets and format != PRINTfacets
+    must match qh_countfacets
+
+  notes
+    preserves qh.visit_id
+    facet->normal may be null if PREmerge/MERGEexact and STOPcone before merge
+
+  see
+    qh_printbegin() and qh_printend()
+
+  design:
+    test for printing facet
+    call appropriate routine for format
+    or output results directly
+*/
+void qh_printafacet(qhT *qh, FILE *fp, qh_PRINT format, facetT *facet, boolT printall) {
+  realT color[4], offset, dist, outerplane, innerplane;
+  boolT zerodiv;
+  coordT *point, *normp, *coordp, **pointp, *feasiblep;
+  int k;
+  vertexT *vertex, **vertexp;
+  facetT *neighbor, **neighborp;
+
+  if (!printall && qh_skipfacet(qh, facet))
+    return;
+  if (facet->visible && qh->NEWfacets && format != qh_PRINTfacets)
+    return;
+  qh->printoutnum++;
+  switch (format) {
+  case qh_PRINTarea:
+    if (facet->isarea) {
+      qh_fprintf(qh, fp, 9009, qh_REAL_1, facet->f.area);
+      qh_fprintf(qh, fp, 9010, "\n");
+    }else
+      qh_fprintf(qh, fp, 9011, "0\n");
+    break;
+  case qh_PRINTcoplanars:
+    qh_fprintf(qh, fp, 9012, "%d", qh_setsize(qh, facet->coplanarset));
+    FOREACHpoint_(facet->coplanarset)
+      qh_fprintf(qh, fp, 9013, " %d", qh_pointid(qh, point));
+    qh_fprintf(qh, fp, 9014, "\n");
+    break;
+  case qh_PRINTcentrums:
+    qh_printcenter(qh, fp, format, NULL, facet);
+    break;
+  case qh_PRINTfacets:
+    qh_printfacet(qh, fp, facet);
+    break;
+  case qh_PRINTfacets_xridge:
+    qh_printfacetheader(qh, fp, facet);
+    break;
+  case qh_PRINTgeom:  /* either 2 , 3, or 4-d by qh_printbegin */
+    if (!facet->normal)
+      break;
+    for (k=qh->hull_dim; k--; ) {
+      color[k]= (facet->normal[k]+1.0)/2.0;
+      maximize_(color[k], -1.0);
+      minimize_(color[k], +1.0);
+    }
+    qh_projectdim3(qh, color, color);
+    if (qh->PRINTdim != qh->hull_dim)
+      qh_normalize2(qh, color, 3, True, NULL, NULL);
+    if (qh->hull_dim <= 2)
+      qh_printfacet2geom(qh, fp, facet, color);
+    else if (qh->hull_dim == 3) {
+      if (facet->simplicial)
+        qh_printfacet3geom_simplicial(qh, fp, facet, color);
+      else
+        qh_printfacet3geom_nonsimplicial(qh, fp, facet, color);
+    }else {
+      if (facet->simplicial)
+        qh_printfacet4geom_simplicial(qh, fp, facet, color);
+      else
+        qh_printfacet4geom_nonsimplicial(qh, fp, facet, color);
+    }
+    break;
+  case qh_PRINTids:
+    qh_fprintf(qh, fp, 9015, "%d\n", facet->id);
+    break;
+  case qh_PRINTincidences:
+  case qh_PRINToff:
+  case qh_PRINTtriangles:
+    if (qh->hull_dim == 3 && format != qh_PRINTtriangles)
+      qh_printfacet3vertex(qh, fp, facet, format);
+    else if (facet->simplicial || qh->hull_dim == 2 || format == qh_PRINToff)
+      qh_printfacetNvertex_simplicial(qh, fp, facet, format);
+    else
+      qh_printfacetNvertex_nonsimplicial(qh, fp, facet, qh->printoutvar++, format);
+    break;
+  case qh_PRINTinner:
+    qh_outerinner(qh, facet, NULL, &innerplane);
+    offset= facet->offset - innerplane;
+    goto LABELprintnorm;
+    break; /* prevent warning */
+  case qh_PRINTmerges:
+    qh_fprintf(qh, fp, 9016, "%d\n", facet->nummerge);
+    break;
+  case qh_PRINTnormals:
+    offset= facet->offset;
+    goto LABELprintnorm;
+    break; /* prevent warning */
+  case qh_PRINTouter:
+    qh_outerinner(qh, facet, &outerplane, NULL);
+    offset= facet->offset - outerplane;
+  LABELprintnorm:
+    if (!facet->normal) {
+      qh_fprintf(qh, fp, 9017, "no normal for facet f%d\n", facet->id);
+      break;
+    }
+    if (qh->CDDoutput) {
+      qh_fprintf(qh, fp, 9018, qh_REAL_1, -offset);
+      for (k=0; k < qh->hull_dim; k++)
+        qh_fprintf(qh, fp, 9019, qh_REAL_1, -facet->normal[k]);
+    }else {
+      for (k=0; k < qh->hull_dim; k++)
+        qh_fprintf(qh, fp, 9020, qh_REAL_1, facet->normal[k]);
+      qh_fprintf(qh, fp, 9021, qh_REAL_1, offset);
+    }
+    qh_fprintf(qh, fp, 9022, "\n");
+    break;
+  case qh_PRINTmathematica:  /* either 2 or 3-d by qh_printbegin */
+  case qh_PRINTmaple:
+    if (qh->hull_dim == 2)
+      qh_printfacet2math(qh, fp, facet, format, qh->printoutvar++);
+    else
+      qh_printfacet3math(qh, fp, facet, format, qh->printoutvar++);
+    break;
+  case qh_PRINTneighbors:
+    qh_fprintf(qh, fp, 9023, "%d", qh_setsize(qh, facet->neighbors));
+    FOREACHneighbor_(facet)
+      qh_fprintf(qh, fp, 9024, " %d",
+               neighbor->visitid ? neighbor->visitid - 1: 0 - neighbor->id);
+    qh_fprintf(qh, fp, 9025, "\n");
+    break;
+  case qh_PRINTpointintersect:
+    if (!qh->feasible_point) {
+      qh_fprintf(qh, qh->ferr, 6067, "qhull input error (qh_printafacet): option 'Fp' needs qh->feasible_point\n");
+      qh_errexit(qh, qh_ERRinput, NULL, NULL);
+    }
+    if (facet->offset > 0)
+      goto LABELprintinfinite;
+    point= coordp= (coordT*)qh_memalloc(qh, qh->normal_size);
+    normp= facet->normal;
+    feasiblep= qh->feasible_point;
+    if (facet->offset < -qh->MINdenom) {
+      for (k=qh->hull_dim; k--; )
+        *(coordp++)= (*(normp++) / - facet->offset) + *(feasiblep++);
+    }else {
+      for (k=qh->hull_dim; k--; ) {
+        *(coordp++)= qh_divzero(*(normp++), facet->offset, qh->MINdenom_1,
+                                 &zerodiv) + *(feasiblep++);
+        if (zerodiv) {
+          qh_memfree(qh, point, qh->normal_size);
+          goto LABELprintinfinite;
+        }
+      }
+    }
+    qh_printpoint(qh, fp, NULL, point);
+    qh_memfree(qh, point, qh->normal_size);
+    break;
+  LABELprintinfinite:
+    for (k=qh->hull_dim; k--; )
+      qh_fprintf(qh, fp, 9026, qh_REAL_1, qh_INFINITE);
+    qh_fprintf(qh, fp, 9027, "\n");
+    break;
+  case qh_PRINTpointnearest:
+    FOREACHpoint_(facet->coplanarset) {
+      int id, id2;
+      vertex= qh_nearvertex(qh, facet, point, &dist);
+      id= qh_pointid(qh, vertex->point);
+      id2= qh_pointid(qh, point);
+      qh_fprintf(qh, fp, 9028, "%d %d %d " qh_REAL_1 "\n", id, id2, facet->id, dist);
+    }
+    break;
+  case qh_PRINTpoints:  /* VORONOI only by qh_printbegin */
+    if (qh->CDDoutput)
+      qh_fprintf(qh, fp, 9029, "1 ");
+    qh_printcenter(qh, fp, format, NULL, facet);
+    break;
+  case qh_PRINTvertices:
+    qh_fprintf(qh, fp, 9030, "%d", qh_setsize(qh, facet->vertices));
+    FOREACHvertex_(facet->vertices)
+      qh_fprintf(qh, fp, 9031, " %d", qh_pointid(qh, vertex->point));
+    qh_fprintf(qh, fp, 9032, "\n");
+    break;
+  default:
+    break;
+  }
+} /* printafacet */
+
+/*---------------------------------
+
+  qh_printbegin(qh, )
+    prints header for all output formats
+
+  returns:
+    checks for valid format
+
+  notes:
+    uses qh.visit_id for 3/4off
+    changes qh.interior_point if printing centrums
+    qh_countfacets clears facet->visitid for non-good facets
+
+  see
+    qh_printend() and qh_printafacet()
+
+  design:
+    count facets and related statistics
+    print header for format
+*/
+void qh_printbegin(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall) {
+  int numfacets, numsimplicial, numridges, totneighbors, numcoplanars, numtricoplanars;
+  int i, num;
+  facetT *facet, **facetp;
+  vertexT *vertex, **vertexp;
+  setT *vertices;
+  pointT *point, **pointp, *pointtemp;
+
+  qh->printoutnum= 0;
+  qh_countfacets(qh, facetlist, facets, printall, &numfacets, &numsimplicial,
+      &totneighbors, &numridges, &numcoplanars, &numtricoplanars);
+  switch (format) {
+  case qh_PRINTnone:
+    break;
+  case qh_PRINTarea:
+    qh_fprintf(qh, fp, 9033, "%d\n", numfacets);
+    break;
+  case qh_PRINTcoplanars:
+    qh_fprintf(qh, fp, 9034, "%d\n", numfacets);
+    break;
+  case qh_PRINTcentrums:
+    if (qh->CENTERtype == qh_ASnone)
+      qh_clearcenters(qh, qh_AScentrum);
+    qh_fprintf(qh, fp, 9035, "%d\n%d\n", qh->hull_dim, numfacets);
+    break;
+  case qh_PRINTfacets:
+  case qh_PRINTfacets_xridge:
+    if (facetlist)
+      qh_printvertexlist(qh, fp, "Vertices and facets:\n", facetlist, facets, printall);
+    break;
+  case qh_PRINTgeom:
+    if (qh->hull_dim > 4)  /* qh_initqhull_globals also checks */
+      goto LABELnoformat;
+    if (qh->VORONOI && qh->hull_dim > 3)  /* PRINTdim == DROPdim == hull_dim-1 */
+      goto LABELnoformat;
+    if (qh->hull_dim == 2 && (qh->PRINTridges || qh->DOintersections))
+      qh_fprintf(qh, qh->ferr, 7049, "qhull warning: output for ridges and intersections not implemented in 2-d\n");
+    if (qh->hull_dim == 4 && (qh->PRINTinner || qh->PRINTouter ||
+                             (qh->PRINTdim == 4 && qh->PRINTcentrums)))
+      qh_fprintf(qh, qh->ferr, 7050, "qhull warning: output for outer/inner planes and centrums not implemented in 4-d\n");
+    if (qh->PRINTdim == 4 && (qh->PRINTspheres))
+      qh_fprintf(qh, qh->ferr, 7051, "qhull warning: output for vertices not implemented in 4-d\n");
+    if (qh->PRINTdim == 4 && qh->DOintersections && qh->PRINTnoplanes)
+      qh_fprintf(qh, qh->ferr, 7052, "qhull warning: 'Gnh' generates no output in 4-d\n");
+    if (qh->PRINTdim == 2) {
+      qh_fprintf(qh, fp, 9036, "{appearance {linewidth 3} LIST # %s | %s\n",
+              qh->rbox_command, qh->qhull_command);
+    }else if (qh->PRINTdim == 3) {
+      qh_fprintf(qh, fp, 9037, "{appearance {+edge -evert linewidth 2} LIST # %s | %s\n",
+              qh->rbox_command, qh->qhull_command);
+    }else if (qh->PRINTdim == 4) {
+      qh->visit_id++;
+      num= 0;
+      FORALLfacet_(facetlist)    /* get number of ridges to be printed */
+        qh_printend4geom(qh, NULL, facet, &num, printall);
+      FOREACHfacet_(facets)
+        qh_printend4geom(qh, NULL, facet, &num, printall);
+      qh->ridgeoutnum= num;
+      qh->printoutvar= 0;  /* counts number of ridges in output */
+      qh_fprintf(qh, fp, 9038, "LIST # %s | %s\n", qh->rbox_command, qh->qhull_command);
+    }
+
+    if (qh->PRINTdots) {
+      qh->printoutnum++;
+      num= qh->num_points + qh_setsize(qh, qh->other_points);
+      if (qh->DELAUNAY && qh->ATinfinity)
+        num--;
+      if (qh->PRINTdim == 4)
+        qh_fprintf(qh, fp, 9039, "4VECT %d %d 1\n", num, num);
+      else
+        qh_fprintf(qh, fp, 9040, "VECT %d %d 1\n", num, num);
+
+      for (i=num; i--; ) {
+        if (i % 20 == 0)
+          qh_fprintf(qh, fp, 9041, "\n");
+        qh_fprintf(qh, fp, 9042, "1 ");
+      }
+      qh_fprintf(qh, fp, 9043, "# 1 point per line\n1 ");
+      for (i=num-1; i--; ) { /* num at least 3 for D2 */
+        if (i % 20 == 0)
+          qh_fprintf(qh, fp, 9044, "\n");
+        qh_fprintf(qh, fp, 9045, "0 ");
+      }
+      qh_fprintf(qh, fp, 9046, "# 1 color for all\n");
+      FORALLpoints {
+        if (!qh->DELAUNAY || !qh->ATinfinity || qh_pointid(qh, point) != qh->num_points-1) {
+          if (qh->PRINTdim == 4)
+            qh_printpoint(qh, fp, NULL, point);
+            else
+              qh_printpoint3(qh, fp, point);
+        }
+      }
+      FOREACHpoint_(qh->other_points) {
+        if (qh->PRINTdim == 4)
+          qh_printpoint(qh, fp, NULL, point);
+        else
+          qh_printpoint3(qh, fp, point);
+      }
+      qh_fprintf(qh, fp, 9047, "0 1 1 1  # color of points\n");
+    }
+
+    if (qh->PRINTdim == 4  && !qh->PRINTnoplanes)
+      /* 4dview loads up multiple 4OFF objects slowly */
+      qh_fprintf(qh, fp, 9048, "4OFF %d %d 1\n", 3*qh->ridgeoutnum, qh->ridgeoutnum);
+    qh->PRINTcradius= 2 * qh->DISTround;  /* include test DISTround */
+    if (qh->PREmerge) {
+      maximize_(qh->PRINTcradius, qh->premerge_centrum + qh->DISTround);
+    }else if (qh->POSTmerge)
+      maximize_(qh->PRINTcradius, qh->postmerge_centrum + qh->DISTround);
+    qh->PRINTradius= qh->PRINTcradius;
+    if (qh->PRINTspheres + qh->PRINTcoplanar)
+      maximize_(qh->PRINTradius, qh->MAXabs_coord * qh_MINradius);
+    if (qh->premerge_cos < REALmax/2) {
+      maximize_(qh->PRINTradius, (1- qh->premerge_cos) * qh->MAXabs_coord);
+    }else if (!qh->PREmerge && qh->POSTmerge && qh->postmerge_cos < REALmax/2) {
+      maximize_(qh->PRINTradius, (1- qh->postmerge_cos) * qh->MAXabs_coord);
+    }
+    maximize_(qh->PRINTradius, qh->MINvisible);
+    if (qh->JOGGLEmax < REALmax/2)
+      qh->PRINTradius += qh->JOGGLEmax * sqrt((realT)qh->hull_dim);
+    if (qh->PRINTdim != 4 &&
+        (qh->PRINTcoplanar || qh->PRINTspheres || qh->PRINTcentrums)) {
+      vertices= qh_facetvertices(qh, facetlist, facets, printall);
+      if (qh->PRINTspheres && qh->PRINTdim <= 3)
+        qh_printspheres(qh, fp, vertices, qh->PRINTradius);
+      if (qh->PRINTcoplanar || qh->PRINTcentrums) {
+        qh->firstcentrum= True;
+        if (qh->PRINTcoplanar&& !qh->PRINTspheres) {
+          FOREACHvertex_(vertices)
+            qh_printpointvect2(qh, fp, vertex->point, NULL, qh->interior_point, qh->PRINTradius);
+        }
+        FORALLfacet_(facetlist) {
+          if (!printall && qh_skipfacet(qh, facet))
+            continue;
+          if (!facet->normal)
+            continue;
+          if (qh->PRINTcentrums && qh->PRINTdim <= 3)
+            qh_printcentrum(qh, fp, facet, qh->PRINTcradius);
+          if (!qh->PRINTcoplanar)
+            continue;
+          FOREACHpoint_(facet->coplanarset)
+            qh_printpointvect2(qh, fp, point, facet->normal, NULL, qh->PRINTradius);
+          FOREACHpoint_(facet->outsideset)
+            qh_printpointvect2(qh, fp, point, facet->normal, NULL, qh->PRINTradius);
+        }
+        FOREACHfacet_(facets) {
+          if (!printall && qh_skipfacet(qh, facet))
+            continue;
+          if (!facet->normal)
+            continue;
+          if (qh->PRINTcentrums && qh->PRINTdim <= 3)
+            qh_printcentrum(qh, fp, facet, qh->PRINTcradius);
+          if (!qh->PRINTcoplanar)
+            continue;
+          FOREACHpoint_(facet->coplanarset)
+            qh_printpointvect2(qh, fp, point, facet->normal, NULL, qh->PRINTradius);
+          FOREACHpoint_(facet->outsideset)
+            qh_printpointvect2(qh, fp, point, facet->normal, NULL, qh->PRINTradius);
+        }
+      }
+      qh_settempfree(qh, &vertices);
+    }
+    qh->visit_id++; /* for printing hyperplane intersections */
+    break;
+  case qh_PRINTids:
+    qh_fprintf(qh, fp, 9049, "%d\n", numfacets);
+    break;
+  case qh_PRINTincidences:
+    if (qh->VORONOI && qh->PRINTprecision)
+      qh_fprintf(qh, qh->ferr, 7053, "qhull warning: writing Delaunay.  Use 'p' or 'o' for Voronoi centers\n");
+    qh->printoutvar= qh->vertex_id;  /* centrum id for non-simplicial facets */
+    if (qh->hull_dim <= 3)
+      qh_fprintf(qh, fp, 9050, "%d\n", numfacets);
+    else
+      qh_fprintf(qh, fp, 9051, "%d\n", numsimplicial+numridges);
+    break;
+  case qh_PRINTinner:
+  case qh_PRINTnormals:
+  case qh_PRINTouter:
+    if (qh->CDDoutput)
+      qh_fprintf(qh, fp, 9052, "%s | %s\nbegin\n    %d %d real\n", qh->rbox_command,
+            qh->qhull_command, numfacets, qh->hull_dim+1);
+    else
+      qh_fprintf(qh, fp, 9053, "%d\n%d\n", qh->hull_dim+1, numfacets);
+    break;
+  case qh_PRINTmathematica:
+  case qh_PRINTmaple:
+    if (qh->hull_dim > 3)  /* qh_initbuffers also checks */
+      goto LABELnoformat;
+    if (qh->VORONOI)
+      qh_fprintf(qh, qh->ferr, 7054, "qhull warning: output is the Delaunay triangulation\n");
+    if (format == qh_PRINTmaple) {
+      if (qh->hull_dim == 2)
+        qh_fprintf(qh, fp, 9054, "PLOT(CURVES(\n");
+      else
+        qh_fprintf(qh, fp, 9055, "PLOT3D(POLYGONS(\n");
+    }else
+      qh_fprintf(qh, fp, 9056, "{\n");
+    qh->printoutvar= 0;   /* counts number of facets for notfirst */
+    break;
+  case qh_PRINTmerges:
+    qh_fprintf(qh, fp, 9057, "%d\n", numfacets);
+    break;
+  case qh_PRINTpointintersect:
+    qh_fprintf(qh, fp, 9058, "%d\n%d\n", qh->hull_dim, numfacets);
+    break;
+  case qh_PRINTneighbors:
+    qh_fprintf(qh, fp, 9059, "%d\n", numfacets);
+    break;
+  case qh_PRINToff:
+  case qh_PRINTtriangles:
+    if (qh->VORONOI)
+      goto LABELnoformat;
+    num = qh->hull_dim;
+    if (format == qh_PRINToff || qh->hull_dim == 2)
+      qh_fprintf(qh, fp, 9060, "%d\n%d %d %d\n", num,
+        qh->num_points+qh_setsize(qh, qh->other_points), numfacets, totneighbors/2);
+    else { /* qh_PRINTtriangles */
+      qh->printoutvar= qh->num_points+qh_setsize(qh, qh->other_points); /* first centrum */
+      if (qh->DELAUNAY)
+        num--;  /* drop last dimension */
+      qh_fprintf(qh, fp, 9061, "%d\n%d %d %d\n", num, qh->printoutvar
+        + numfacets - numsimplicial, numsimplicial + numridges, totneighbors/2);
+    }
+    FORALLpoints
+      qh_printpointid(qh, qh->fout, NULL, num, point, qh_IDunknown);
+    FOREACHpoint_(qh->other_points)
+      qh_printpointid(qh, qh->fout, NULL, num, point, qh_IDunknown);
+    if (format == qh_PRINTtriangles && qh->hull_dim > 2) {
+      FORALLfacets {
+        if (!facet->simplicial && facet->visitid)
+          qh_printcenter(qh, qh->fout, format, NULL, facet);
+      }
+    }
+    break;
+  case qh_PRINTpointnearest:
+    qh_fprintf(qh, fp, 9062, "%d\n", numcoplanars);
+    break;
+  case qh_PRINTpoints:
+    if (!qh->VORONOI)
+      goto LABELnoformat;
+    if (qh->CDDoutput)
+      qh_fprintf(qh, fp, 9063, "%s | %s\nbegin\n%d %d real\n", qh->rbox_command,
+           qh->qhull_command, numfacets, qh->hull_dim);
+    else
+      qh_fprintf(qh, fp, 9064, "%d\n%d\n", qh->hull_dim-1, numfacets);
+    break;
+  case qh_PRINTvertices:
+    qh_fprintf(qh, fp, 9065, "%d\n", numfacets);
+    break;
+  case qh_PRINTsummary:
+  default:
+  LABELnoformat:
+    qh_fprintf(qh, qh->ferr, 6068, "qhull internal error (qh_printbegin): can not use this format for dimension %d\n",
+         qh->hull_dim);
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }
+} /* printbegin */
+
+/*---------------------------------
+
+  qh_printcenter(qh, fp, string, facet )
+    print facet->center as centrum or Voronoi center
+    string may be NULL.  Don't include '%' codes.
+    nop if qh->CENTERtype neither CENTERvoronoi nor CENTERcentrum
+    if upper envelope of Delaunay triangulation and point at-infinity
+      prints qh_INFINITE instead;
+
+  notes:
+    defines facet->center if needed
+    if format=PRINTgeom, adds a 0 if would otherwise be 2-d
+    Same as QhullFacet::printCenter
+*/
+void qh_printcenter(qhT *qh, FILE *fp, qh_PRINT format, const char *string, facetT *facet) {
+  int k, num;
+
+  if (qh->CENTERtype != qh_ASvoronoi && qh->CENTERtype != qh_AScentrum)
+    return;
+  if (string)
+    qh_fprintf(qh, fp, 9066, string);
+  if (qh->CENTERtype == qh_ASvoronoi) {
+    num= qh->hull_dim-1;
+    if (!facet->normal || !facet->upperdelaunay || !qh->ATinfinity) {
+      if (!facet->center)
+        facet->center= qh_facetcenter(qh, facet->vertices);
+      for (k=0; k < num; k++)
+        qh_fprintf(qh, fp, 9067, qh_REAL_1, facet->center[k]);
+    }else {
+      for (k=0; k < num; k++)
+        qh_fprintf(qh, fp, 9068, qh_REAL_1, qh_INFINITE);
+    }
+  }else /* qh->CENTERtype == qh_AScentrum */ {
+    num= qh->hull_dim;
+    if (format == qh_PRINTtriangles && qh->DELAUNAY)
+      num--;
+    if (!facet->center)
+      facet->center= qh_getcentrum(qh, facet);
+    for (k=0; k < num; k++)
+      qh_fprintf(qh, fp, 9069, qh_REAL_1, facet->center[k]);
+  }
+  if (format == qh_PRINTgeom && num == 2)
+    qh_fprintf(qh, fp, 9070, " 0\n");
+  else
+    qh_fprintf(qh, fp, 9071, "\n");
+} /* printcenter */
+
+/*---------------------------------
+
+  qh_printcentrum(qh, fp, facet, radius )
+    print centrum for a facet in OOGL format
+    radius defines size of centrum
+    2-d or 3-d only
+
+  returns:
+    defines facet->center if needed
+*/
+void qh_printcentrum(qhT *qh, FILE *fp, facetT *facet, realT radius) {
+  pointT *centrum, *projpt;
+  boolT tempcentrum= False;
+  realT xaxis[4], yaxis[4], normal[4], dist;
+  realT green[3]={0, 1, 0};
+  vertexT *apex;
+  int k;
+
+  if (qh->CENTERtype == qh_AScentrum) {
+    if (!facet->center)
+      facet->center= qh_getcentrum(qh, facet);
+    centrum= facet->center;
+  }else {
+    centrum= qh_getcentrum(qh, facet);
+    tempcentrum= True;
+  }
+  qh_fprintf(qh, fp, 9072, "{appearance {-normal -edge normscale 0} ");
+  if (qh->firstcentrum) {
+    qh->firstcentrum= False;
+    qh_fprintf(qh, fp, 9073, "{INST geom { define centrum CQUAD  # f%d\n\
+-0.3 -0.3 0.0001     0 0 1 1\n\
+ 0.3 -0.3 0.0001     0 0 1 1\n\
+ 0.3  0.3 0.0001     0 0 1 1\n\
+-0.3  0.3 0.0001     0 0 1 1 } transform { \n", facet->id);
+  }else
+    qh_fprintf(qh, fp, 9074, "{INST geom { : centrum } transform { # f%d\n", facet->id);
+  apex= SETfirstt_(facet->vertices, vertexT);
+  qh_distplane(qh, apex->point, facet, &dist);
+  projpt= qh_projectpoint(qh, apex->point, facet, dist);
+  for (k=qh->hull_dim; k--; ) {
+    xaxis[k]= projpt[k] - centrum[k];
+    normal[k]= facet->normal[k];
+  }
+  if (qh->hull_dim == 2) {
+    xaxis[2]= 0;
+    normal[2]= 0;
+  }else if (qh->hull_dim == 4) {
+    qh_projectdim3(qh, xaxis, xaxis);
+    qh_projectdim3(qh, normal, normal);
+    qh_normalize2(qh, normal, qh->PRINTdim, True, NULL, NULL);
+  }
+  qh_crossproduct(3, xaxis, normal, yaxis);
+  qh_fprintf(qh, fp, 9075, "%8.4g %8.4g %8.4g 0\n", xaxis[0], xaxis[1], xaxis[2]);
+  qh_fprintf(qh, fp, 9076, "%8.4g %8.4g %8.4g 0\n", yaxis[0], yaxis[1], yaxis[2]);
+  qh_fprintf(qh, fp, 9077, "%8.4g %8.4g %8.4g 0\n", normal[0], normal[1], normal[2]);
+  qh_printpoint3(qh, fp, centrum);
+  qh_fprintf(qh, fp, 9078, "1 }}}\n");
+  qh_memfree(qh, projpt, qh->normal_size);
+  qh_printpointvect(qh, fp, centrum, facet->normal, NULL, radius, green);
+  if (tempcentrum)
+    qh_memfree(qh, centrum, qh->normal_size);
+} /* printcentrum */
+
+/*---------------------------------
+
+  qh_printend(qh, fp, format )
+    prints trailer for all output formats
+
+  see:
+    qh_printbegin() and qh_printafacet()
+
+*/
+void qh_printend(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall) {
+  int num;
+  facetT *facet, **facetp;
+
+  if (!qh->printoutnum)
+    qh_fprintf(qh, qh->ferr, 7055, "qhull warning: no facets printed\n");
+  switch (format) {
+  case qh_PRINTgeom:
+    if (qh->hull_dim == 4 && qh->DROPdim < 0  && !qh->PRINTnoplanes) {
+      qh->visit_id++;
+      num= 0;
+      FORALLfacet_(facetlist)
+        qh_printend4geom(qh, fp, facet,&num, printall);
+      FOREACHfacet_(facets)
+        qh_printend4geom(qh, fp, facet, &num, printall);
+      if (num != qh->ridgeoutnum || qh->printoutvar != qh->ridgeoutnum) {
+        qh_fprintf(qh, qh->ferr, 6069, "qhull internal error (qh_printend): number of ridges %d != number printed %d and at end %d\n", qh->ridgeoutnum, qh->printoutvar, num);
+        qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+      }
+    }else
+      qh_fprintf(qh, fp, 9079, "}\n");
+    break;
+  case qh_PRINTinner:
+  case qh_PRINTnormals:
+  case qh_PRINTouter:
+    if (qh->CDDoutput)
+      qh_fprintf(qh, fp, 9080, "end\n");
+    break;
+  case qh_PRINTmaple:
+    qh_fprintf(qh, fp, 9081, "));\n");
+    break;
+  case qh_PRINTmathematica:
+    qh_fprintf(qh, fp, 9082, "}\n");
+    break;
+  case qh_PRINTpoints:
+    if (qh->CDDoutput)
+      qh_fprintf(qh, fp, 9083, "end\n");
+    break;
+  default:
+    break;
+  }
+} /* printend */
+
+/*---------------------------------
+
+  qh_printend4geom(qh, fp, facet, numridges, printall )
+    helper function for qh_printbegin/printend
+
+  returns:
+    number of printed ridges
+
+  notes:
+    just counts printed ridges if fp=NULL
+    uses facet->visitid
+    must agree with qh_printfacet4geom...
+
+  design:
+    computes color for facet from its normal
+    prints each ridge of facet
+*/
+void qh_printend4geom(qhT *qh, FILE *fp, facetT *facet, int *nump, boolT printall) {
+  realT color[3];
+  int i, num= *nump;
+  facetT *neighbor, **neighborp;
+  ridgeT *ridge, **ridgep;
+
+  if (!printall && qh_skipfacet(qh, facet))
+    return;
+  if (qh->PRINTnoplanes || (facet->visible && qh->NEWfacets))
+    return;
+  if (!facet->normal)
+    return;
+  if (fp) {
+    for (i=0; i < 3; i++) {
+      color[i]= (facet->normal[i]+1.0)/2.0;
+      maximize_(color[i], -1.0);
+      minimize_(color[i], +1.0);
+    }
+  }
+  facet->visitid= qh->visit_id;
+  if (facet->simplicial) {
+    FOREACHneighbor_(facet) {
+      if (neighbor->visitid != qh->visit_id) {
+        if (fp)
+          qh_fprintf(qh, fp, 9084, "3 %d %d %d %8.4g %8.4g %8.4g 1 # f%d f%d\n",
+                 3*num, 3*num+1, 3*num+2, color[0], color[1], color[2],
+                 facet->id, neighbor->id);
+        num++;
+      }
+    }
+  }else {
+    FOREACHridge_(facet->ridges) {
+      neighbor= otherfacet_(ridge, facet);
+      if (neighbor->visitid != qh->visit_id) {
+        if (fp)
+          qh_fprintf(qh, fp, 9085, "3 %d %d %d %8.4g %8.4g %8.4g 1 #r%d f%d f%d\n",
+                 3*num, 3*num+1, 3*num+2, color[0], color[1], color[2],
+                 ridge->id, facet->id, neighbor->id);
+        num++;
+      }
+    }
+  }
+  *nump= num;
+} /* printend4geom */
+
+/*---------------------------------
+
+  qh_printextremes(qh, fp, facetlist, facets, printall )
+    print extreme points for convex hulls or halfspace intersections
+
+  notes:
+    #points, followed by ids, one per line
+
+    sorted by id
+    same order as qh_printpoints_out if no coplanar/interior points
+*/
+void qh_printextremes(qhT *qh, FILE *fp, facetT *facetlist, setT *facets, boolT printall) {
+  setT *vertices, *points;
+  pointT *point;
+  vertexT *vertex, **vertexp;
+  int id;
+  int numpoints=0, point_i, point_n;
+  int allpoints= qh->num_points + qh_setsize(qh, qh->other_points);
+
+  points= qh_settemp(qh, allpoints);
+  qh_setzero(qh, points, 0, allpoints);
+  vertices= qh_facetvertices(qh, facetlist, facets, printall);
+  FOREACHvertex_(vertices) {
+    id= qh_pointid(qh, vertex->point);
+    if (id >= 0) {
+      SETelem_(points, id)= vertex->point;
+      numpoints++;
+    }
+  }
+  qh_settempfree(qh, &vertices);
+  qh_fprintf(qh, fp, 9086, "%d\n", numpoints);
+  FOREACHpoint_i_(qh, points) {
+    if (point)
+      qh_fprintf(qh, fp, 9087, "%d\n", point_i);
+  }
+  qh_settempfree(qh, &points);
+} /* printextremes */
+
+/*---------------------------------
+
+  qh_printextremes_2d(qh, fp, facetlist, facets, printall )
+    prints point ids for facets in qh_ORIENTclock order
+
+  notes:
+    #points, followed by ids, one per line
+    if facetlist/facets are disjoint than the output includes skips
+    errors if facets form a loop
+    does not print coplanar points
+*/
+void qh_printextremes_2d(qhT *qh, FILE *fp, facetT *facetlist, setT *facets, boolT printall) {
+  int numfacets, numridges, totneighbors, numcoplanars, numsimplicial, numtricoplanars;
+  setT *vertices;
+  facetT *facet, *startfacet, *nextfacet;
+  vertexT *vertexA, *vertexB;
+
+  qh_countfacets(qh, facetlist, facets, printall, &numfacets, &numsimplicial,
+      &totneighbors, &numridges, &numcoplanars, &numtricoplanars); /* marks qh->visit_id */
+  vertices= qh_facetvertices(qh, facetlist, facets, printall);
+  qh_fprintf(qh, fp, 9088, "%d\n", qh_setsize(qh, vertices));
+  qh_settempfree(qh, &vertices);
+  if (!numfacets)
+    return;
+  facet= startfacet= facetlist ? facetlist : SETfirstt_(facets, facetT);
+  qh->vertex_visit++;
+  qh->visit_id++;
+  do {
+    if (facet->toporient ^ qh_ORIENTclock) {
+      vertexA= SETfirstt_(facet->vertices, vertexT);
+      vertexB= SETsecondt_(facet->vertices, vertexT);
+      nextfacet= SETfirstt_(facet->neighbors, facetT);
+    }else {
+      vertexA= SETsecondt_(facet->vertices, vertexT);
+      vertexB= SETfirstt_(facet->vertices, vertexT);
+      nextfacet= SETsecondt_(facet->neighbors, facetT);
+    }
+    if (facet->visitid == qh->visit_id) {
+      qh_fprintf(qh, qh->ferr, 6218, "Qhull internal error (qh_printextremes_2d): loop in facet list.  facet %d nextfacet %d\n",
+                 facet->id, nextfacet->id);
+      qh_errexit2(qh, qh_ERRqhull, facet, nextfacet);
+    }
+    if (facet->visitid) {
+      if (vertexA->visitid != qh->vertex_visit) {
+        vertexA->visitid= qh->vertex_visit;
+        qh_fprintf(qh, fp, 9089, "%d\n", qh_pointid(qh, vertexA->point));
+      }
+      if (vertexB->visitid != qh->vertex_visit) {
+        vertexB->visitid= qh->vertex_visit;
+        qh_fprintf(qh, fp, 9090, "%d\n", qh_pointid(qh, vertexB->point));
+      }
+    }
+    facet->visitid= qh->visit_id;
+    facet= nextfacet;
+  }while (facet && facet != startfacet);
+} /* printextremes_2d */
+
+/*---------------------------------
+
+  qh_printextremes_d(qh, fp, facetlist, facets, printall )
+    print extreme points of input sites for Delaunay triangulations
+
+  notes:
+    #points, followed by ids, one per line
+
+    unordered
+*/
+void qh_printextremes_d(qhT *qh, FILE *fp, facetT *facetlist, setT *facets, boolT printall) {
+  setT *vertices;
+  vertexT *vertex, **vertexp;
+  boolT upperseen, lowerseen;
+  facetT *neighbor, **neighborp;
+  int numpoints=0;
+
+  vertices= qh_facetvertices(qh, facetlist, facets, printall);
+  qh_vertexneighbors(qh);
+  FOREACHvertex_(vertices) {
+    upperseen= lowerseen= False;
+    FOREACHneighbor_(vertex) {
+      if (neighbor->upperdelaunay)
+        upperseen= True;
+      else
+        lowerseen= True;
+    }
+    if (upperseen && lowerseen) {
+      vertex->seen= True;
+      numpoints++;
+    }else
+      vertex->seen= False;
+  }
+  qh_fprintf(qh, fp, 9091, "%d\n", numpoints);
+  FOREACHvertex_(vertices) {
+    if (vertex->seen)
+      qh_fprintf(qh, fp, 9092, "%d\n", qh_pointid(qh, vertex->point));
+  }
+  qh_settempfree(qh, &vertices);
+} /* printextremes_d */
+
+/*---------------------------------
+
+  qh_printfacet(qh, fp, facet )
+    prints all fields of a facet to fp
+
+  notes:
+    ridges printed in neighbor order
+*/
+void qh_printfacet(qhT *qh, FILE *fp, facetT *facet) {
+
+  qh_printfacetheader(qh, fp, facet);
+  if (facet->ridges)
+    qh_printfacetridges(qh, fp, facet);
+} /* printfacet */
+
+
+/*---------------------------------
+
+  qh_printfacet2geom(qh, fp, facet, color )
+    print facet as part of a 2-d VECT for Geomview
+
+    notes:
+      assume precise calculations in io_r.c with roundoff covered by qh_GEOMepsilon
+      mindist is calculated within io_r.c.  maxoutside is calculated elsewhere
+      so a DISTround error may have occurred.
+*/
+void qh_printfacet2geom(qhT *qh, FILE *fp, facetT *facet, realT color[3]) {
+  pointT *point0, *point1;
+  realT mindist, innerplane, outerplane;
+  int k;
+
+  qh_facet2point(qh, facet, &point0, &point1, &mindist);
+  qh_geomplanes(qh, facet, &outerplane, &innerplane);
+  if (qh->PRINTouter || (!qh->PRINTnoplanes && !qh->PRINTinner))
+    qh_printfacet2geom_points(qh, fp, point0, point1, facet, outerplane, color);
+  if (qh->PRINTinner || (!qh->PRINTnoplanes && !qh->PRINTouter &&
+                outerplane - innerplane > 2 * qh->MAXabs_coord * qh_GEOMepsilon)) {
+    for (k=3; k--; )
+      color[k]= 1.0 - color[k];
+    qh_printfacet2geom_points(qh, fp, point0, point1, facet, innerplane, color);
+  }
+  qh_memfree(qh, point1, qh->normal_size);
+  qh_memfree(qh, point0, qh->normal_size);
+} /* printfacet2geom */
+
+/*---------------------------------
+
+  qh_printfacet2geom_points(qh, fp, point1, point2, facet, offset, color )
+    prints a 2-d facet as a VECT with 2 points at some offset.
+    The points are on the facet's plane.
+*/
+void qh_printfacet2geom_points(qhT *qh, FILE *fp, pointT *point1, pointT *point2,
+                               facetT *facet, realT offset, realT color[3]) {
+  pointT *p1= point1, *p2= point2;
+
+  qh_fprintf(qh, fp, 9093, "VECT 1 2 1 2 1 # f%d\n", facet->id);
+  if (offset != 0.0) {
+    p1= qh_projectpoint(qh, p1, facet, -offset);
+    p2= qh_projectpoint(qh, p2, facet, -offset);
+  }
+  qh_fprintf(qh, fp, 9094, "%8.4g %8.4g %8.4g\n%8.4g %8.4g %8.4g\n",
+           p1[0], p1[1], 0.0, p2[0], p2[1], 0.0);
+  if (offset != 0.0) {
+    qh_memfree(qh, p1, qh->normal_size);
+    qh_memfree(qh, p2, qh->normal_size);
+  }
+  qh_fprintf(qh, fp, 9095, "%8.4g %8.4g %8.4g 1.0\n", color[0], color[1], color[2]);
+} /* printfacet2geom_points */
+
+
+/*---------------------------------
+
+  qh_printfacet2math(qh, fp, facet, format, notfirst )
+    print 2-d Maple or Mathematica output for a facet
+    may be non-simplicial
+
+  notes:
+    use %16.8f since Mathematica 2.2 does not handle exponential format
+    see qh_printfacet3math
+*/
+void qh_printfacet2math(qhT *qh, FILE *fp, facetT *facet, qh_PRINT format, int notfirst) {
+  pointT *point0, *point1;
+  realT mindist;
+  const char *pointfmt;
+
+  qh_facet2point(qh, facet, &point0, &point1, &mindist);
+  if (notfirst)
+    qh_fprintf(qh, fp, 9096, ",");
+  if (format == qh_PRINTmaple)
+    pointfmt= "[[%16.8f, %16.8f], [%16.8f, %16.8f]]\n";
+  else
+    pointfmt= "Line[{{%16.8f, %16.8f}, {%16.8f, %16.8f}}]\n";
+  qh_fprintf(qh, fp, 9097, pointfmt, point0[0], point0[1], point1[0], point1[1]);
+  qh_memfree(qh, point1, qh->normal_size);
+  qh_memfree(qh, point0, qh->normal_size);
+} /* printfacet2math */
+
+
+/*---------------------------------
+
+  qh_printfacet3geom_nonsimplicial(qh, fp, facet, color )
+    print Geomview OFF for a 3-d nonsimplicial facet.
+    if DOintersections, prints ridges to unvisited neighbors(qh->visit_id)
+
+  notes
+    uses facet->visitid for intersections and ridges
+*/
+void qh_printfacet3geom_nonsimplicial(qhT *qh, FILE *fp, facetT *facet, realT color[3]) {
+  ridgeT *ridge, **ridgep;
+  setT *projectedpoints, *vertices;
+  vertexT *vertex, **vertexp, *vertexA, *vertexB;
+  pointT *projpt, *point, **pointp;
+  facetT *neighbor;
+  realT dist, outerplane, innerplane;
+  int cntvertices, k;
+  realT black[3]={0, 0, 0}, green[3]={0, 1, 0};
+
+  qh_geomplanes(qh, facet, &outerplane, &innerplane);
+  vertices= qh_facet3vertex(qh, facet); /* oriented */
+  cntvertices= qh_setsize(qh, vertices);
+  projectedpoints= qh_settemp(qh, cntvertices);
+  FOREACHvertex_(vertices) {
+    zinc_(Zdistio);
+    qh_distplane(qh, vertex->point, facet, &dist);
+    projpt= qh_projectpoint(qh, vertex->point, facet, dist);
+    qh_setappend(qh, &projectedpoints, projpt);
+  }
+  if (qh->PRINTouter || (!qh->PRINTnoplanes && !qh->PRINTinner))
+    qh_printfacet3geom_points(qh, fp, projectedpoints, facet, outerplane, color);
+  if (qh->PRINTinner || (!qh->PRINTnoplanes && !qh->PRINTouter &&
+                outerplane - innerplane > 2 * qh->MAXabs_coord * qh_GEOMepsilon)) {
+    for (k=3; k--; )
+      color[k]= 1.0 - color[k];
+    qh_printfacet3geom_points(qh, fp, projectedpoints, facet, innerplane, color);
+  }
+  FOREACHpoint_(projectedpoints)
+    qh_memfree(qh, point, qh->normal_size);
+  qh_settempfree(qh, &projectedpoints);
+  qh_settempfree(qh, &vertices);
+  if ((qh->DOintersections || qh->PRINTridges)
+  && (!facet->visible || !qh->NEWfacets)) {
+    facet->visitid= qh->visit_id;
+    FOREACHridge_(facet->ridges) {
+      neighbor= otherfacet_(ridge, facet);
+      if (neighbor->visitid != qh->visit_id) {
+        if (qh->DOintersections)
+          qh_printhyperplaneintersection(qh, fp, facet, neighbor, ridge->vertices, black);
+        if (qh->PRINTridges) {
+          vertexA= SETfirstt_(ridge->vertices, vertexT);
+          vertexB= SETsecondt_(ridge->vertices, vertexT);
+          qh_printline3geom(qh, fp, vertexA->point, vertexB->point, green);
+        }
+      }
+    }
+  }
+} /* printfacet3geom_nonsimplicial */
+
+/*---------------------------------
+
+  qh_printfacet3geom_points(qh, fp, points, facet, offset )
+    prints a 3-d facet as OFF Geomview object.
+    offset is relative to the facet's hyperplane
+    Facet is determined as a list of points
+*/
+void qh_printfacet3geom_points(qhT *qh, FILE *fp, setT *points, facetT *facet, realT offset, realT color[3]) {
+  int k, n= qh_setsize(qh, points), i;
+  pointT *point, **pointp;
+  setT *printpoints;
+
+  qh_fprintf(qh, fp, 9098, "{ OFF %d 1 1 # f%d\n", n, facet->id);
+  if (offset != 0.0) {
+    printpoints= qh_settemp(qh, n);
+    FOREACHpoint_(points)
+      qh_setappend(qh, &printpoints, qh_projectpoint(qh, point, facet, -offset));
+  }else
+    printpoints= points;
+  FOREACHpoint_(printpoints) {
+    for (k=0; k < qh->hull_dim; k++) {
+      if (k == qh->DROPdim)
+        qh_fprintf(qh, fp, 9099, "0 ");
+      else
+        qh_fprintf(qh, fp, 9100, "%8.4g ", point[k]);
+    }
+    if (printpoints != points)
+      qh_memfree(qh, point, qh->normal_size);
+    qh_fprintf(qh, fp, 9101, "\n");
+  }
+  if (printpoints != points)
+    qh_settempfree(qh, &printpoints);
+  qh_fprintf(qh, fp, 9102, "%d ", n);
+  for (i=0; i < n; i++)
+    qh_fprintf(qh, fp, 9103, "%d ", i);
+  qh_fprintf(qh, fp, 9104, "%8.4g %8.4g %8.4g 1.0 }\n", color[0], color[1], color[2]);
+} /* printfacet3geom_points */
+
+
+/*---------------------------------
+
+  qh_printfacet3geom_simplicial(qh, )
+    print Geomview OFF for a 3-d simplicial facet.
+
+  notes:
+    may flip color
+    uses facet->visitid for intersections and ridges
+
+    assume precise calculations in io_r.c with roundoff covered by qh_GEOMepsilon
+    innerplane may be off by qh->DISTround.  Maxoutside is calculated elsewhere
+    so a DISTround error may have occurred.
+*/
+void qh_printfacet3geom_simplicial(qhT *qh, FILE *fp, facetT *facet, realT color[3]) {
+  setT *points, *vertices;
+  vertexT *vertex, **vertexp, *vertexA, *vertexB;
+  facetT *neighbor, **neighborp;
+  realT outerplane, innerplane;
+  realT black[3]={0, 0, 0}, green[3]={0, 1, 0};
+  int k;
+
+  qh_geomplanes(qh, facet, &outerplane, &innerplane);
+  vertices= qh_facet3vertex(qh, facet);
+  points= qh_settemp(qh, qh->TEMPsize);
+  FOREACHvertex_(vertices)
+    qh_setappend(qh, &points, vertex->point);
+  if (qh->PRINTouter || (!qh->PRINTnoplanes && !qh->PRINTinner))
+    qh_printfacet3geom_points(qh, fp, points, facet, outerplane, color);
+  if (qh->PRINTinner || (!qh->PRINTnoplanes && !qh->PRINTouter &&
+              outerplane - innerplane > 2 * qh->MAXabs_coord * qh_GEOMepsilon)) {
+    for (k=3; k--; )
+      color[k]= 1.0 - color[k];
+    qh_printfacet3geom_points(qh, fp, points, facet, innerplane, color);
+  }
+  qh_settempfree(qh, &points);
+  qh_settempfree(qh, &vertices);
+  if ((qh->DOintersections || qh->PRINTridges)
+  && (!facet->visible || !qh->NEWfacets)) {
+    facet->visitid= qh->visit_id;
+    FOREACHneighbor_(facet) {
+      if (neighbor->visitid != qh->visit_id) {
+        vertices= qh_setnew_delnthsorted(qh, facet->vertices, qh->hull_dim,
+                          SETindex_(facet->neighbors, neighbor), 0);
+        if (qh->DOintersections)
+           qh_printhyperplaneintersection(qh, fp, facet, neighbor, vertices, black);
+        if (qh->PRINTridges) {
+          vertexA= SETfirstt_(vertices, vertexT);
+          vertexB= SETsecondt_(vertices, vertexT);
+          qh_printline3geom(qh, fp, vertexA->point, vertexB->point, green);
+        }
+        qh_setfree(qh, &vertices);
+      }
+    }
+  }
+} /* printfacet3geom_simplicial */
+
+/*---------------------------------
+
+  qh_printfacet3math(qh, fp, facet, notfirst )
+    print 3-d Maple or Mathematica output for a facet
+
+  notes:
+    may be non-simplicial
+    use %16.8f since Mathematica 2.2 does not handle exponential format
+    see qh_printfacet2math
+*/
+void qh_printfacet3math(qhT *qh, FILE *fp, facetT *facet, qh_PRINT format, int notfirst) {
+  vertexT *vertex, **vertexp;
+  setT *points, *vertices;
+  pointT *point, **pointp;
+  boolT firstpoint= True;
+  realT dist;
+  const char *pointfmt, *endfmt;
+
+  if (notfirst)
+    qh_fprintf(qh, fp, 9105, ",\n");
+  vertices= qh_facet3vertex(qh, facet);
+  points= qh_settemp(qh, qh_setsize(qh, vertices));
+  FOREACHvertex_(vertices) {
+    zinc_(Zdistio);
+    qh_distplane(qh, vertex->point, facet, &dist);
+    point= qh_projectpoint(qh, vertex->point, facet, dist);
+    qh_setappend(qh, &points, point);
+  }
+  if (format == qh_PRINTmaple) {
+    qh_fprintf(qh, fp, 9106, "[");
+    pointfmt= "[%16.8f, %16.8f, %16.8f]";
+    endfmt= "]";
+  }else {
+    qh_fprintf(qh, fp, 9107, "Polygon[{");
+    pointfmt= "{%16.8f, %16.8f, %16.8f}";
+    endfmt= "}]";
+  }
+  FOREACHpoint_(points) {
+    if (firstpoint)
+      firstpoint= False;
+    else
+      qh_fprintf(qh, fp, 9108, ",\n");
+    qh_fprintf(qh, fp, 9109, pointfmt, point[0], point[1], point[2]);
+  }
+  FOREACHpoint_(points)
+    qh_memfree(qh, point, qh->normal_size);
+  qh_settempfree(qh, &points);
+  qh_settempfree(qh, &vertices);
+  qh_fprintf(qh, fp, 9110, "%s", endfmt);
+} /* printfacet3math */
+
+
+/*---------------------------------
+
+  qh_printfacet3vertex(qh, fp, facet, format )
+    print vertices in a 3-d facet as point ids
+
+  notes:
+    prints number of vertices first if format == qh_PRINToff
+    the facet may be non-simplicial
+*/
+void qh_printfacet3vertex(qhT *qh, FILE *fp, facetT *facet, qh_PRINT format) {
+  vertexT *vertex, **vertexp;
+  setT *vertices;
+
+  vertices= qh_facet3vertex(qh, facet);
+  if (format == qh_PRINToff)
+    qh_fprintf(qh, fp, 9111, "%d ", qh_setsize(qh, vertices));
+  FOREACHvertex_(vertices)
+    qh_fprintf(qh, fp, 9112, "%d ", qh_pointid(qh, vertex->point));
+  qh_fprintf(qh, fp, 9113, "\n");
+  qh_settempfree(qh, &vertices);
+} /* printfacet3vertex */
+
+
+/*---------------------------------
+
+  qh_printfacet4geom_nonsimplicial(qh, )
+    print Geomview 4OFF file for a 4d nonsimplicial facet
+    prints all ridges to unvisited neighbors (qh.visit_id)
+    if qh.DROPdim
+      prints in OFF format
+
+  notes:
+    must agree with printend4geom()
+*/
+void qh_printfacet4geom_nonsimplicial(qhT *qh, FILE *fp, facetT *facet, realT color[3]) {
+  facetT *neighbor;
+  ridgeT *ridge, **ridgep;
+  vertexT *vertex, **vertexp;
+  pointT *point;
+  int k;
+  realT dist;
+
+  facet->visitid= qh->visit_id;
+  if (qh->PRINTnoplanes || (facet->visible && qh->NEWfacets))
+    return;
+  FOREACHridge_(facet->ridges) {
+    neighbor= otherfacet_(ridge, facet);
+    if (neighbor->visitid == qh->visit_id)
+      continue;
+    if (qh->PRINTtransparent && !neighbor->good)
+      continue;
+    if (qh->DOintersections)
+      qh_printhyperplaneintersection(qh, fp, facet, neighbor, ridge->vertices, color);
+    else {
+      if (qh->DROPdim >= 0)
+        qh_fprintf(qh, fp, 9114, "OFF 3 1 1 # f%d\n", facet->id);
+      else {
+        qh->printoutvar++;
+        qh_fprintf(qh, fp, 9115, "# r%d between f%d f%d\n", ridge->id, facet->id, neighbor->id);
+      }
+      FOREACHvertex_(ridge->vertices) {
+        zinc_(Zdistio);
+        qh_distplane(qh, vertex->point,facet, &dist);
+        point=qh_projectpoint(qh, vertex->point,facet, dist);
+        for (k=0; k < qh->hull_dim; k++) {
+          if (k != qh->DROPdim)
+            qh_fprintf(qh, fp, 9116, "%8.4g ", point[k]);
+        }
+        qh_fprintf(qh, fp, 9117, "\n");
+        qh_memfree(qh, point, qh->normal_size);
+      }
+      if (qh->DROPdim >= 0)
+        qh_fprintf(qh, fp, 9118, "3 0 1 2 %8.4g %8.4g %8.4g\n", color[0], color[1], color[2]);
+    }
+  }
+} /* printfacet4geom_nonsimplicial */
+
+
+/*---------------------------------
+
+  qh_printfacet4geom_simplicial(qh, fp, facet, color )
+    print Geomview 4OFF file for a 4d simplicial facet
+    prints triangles for unvisited neighbors (qh.visit_id)
+
+  notes:
+    must agree with printend4geom()
+*/
+void qh_printfacet4geom_simplicial(qhT *qh, FILE *fp, facetT *facet, realT color[3]) {
+  setT *vertices;
+  facetT *neighbor, **neighborp;
+  vertexT *vertex, **vertexp;
+  int k;
+
+  facet->visitid= qh->visit_id;
+  if (qh->PRINTnoplanes || (facet->visible && qh->NEWfacets))
+    return;
+  FOREACHneighbor_(facet) {
+    if (neighbor->visitid == qh->visit_id)
+      continue;
+    if (qh->PRINTtransparent && !neighbor->good)
+      continue;
+    vertices= qh_setnew_delnthsorted(qh, facet->vertices, qh->hull_dim,
+                          SETindex_(facet->neighbors, neighbor), 0);
+    if (qh->DOintersections)
+      qh_printhyperplaneintersection(qh, fp, facet, neighbor, vertices, color);
+    else {
+      if (qh->DROPdim >= 0)
+        qh_fprintf(qh, fp, 9119, "OFF 3 1 1 # ridge between f%d f%d\n",
+                facet->id, neighbor->id);
+      else {
+        qh->printoutvar++;
+        qh_fprintf(qh, fp, 9120, "# ridge between f%d f%d\n", facet->id, neighbor->id);
+      }
+      FOREACHvertex_(vertices) {
+        for (k=0; k < qh->hull_dim; k++) {
+          if (k != qh->DROPdim)
+            qh_fprintf(qh, fp, 9121, "%8.4g ", vertex->point[k]);
+        }
+        qh_fprintf(qh, fp, 9122, "\n");
+      }
+      if (qh->DROPdim >= 0)
+        qh_fprintf(qh, fp, 9123, "3 0 1 2 %8.4g %8.4g %8.4g\n", color[0], color[1], color[2]);
+    }
+    qh_setfree(qh, &vertices);
+  }
+} /* printfacet4geom_simplicial */
+
+
+/*---------------------------------
+
+  qh_printfacetNvertex_nonsimplicial(qh, fp, facet, id, format )
+    print vertices for an N-d non-simplicial facet
+    triangulates each ridge to the id
+*/
+void qh_printfacetNvertex_nonsimplicial(qhT *qh, FILE *fp, facetT *facet, int id, qh_PRINT format) {
+  vertexT *vertex, **vertexp;
+  ridgeT *ridge, **ridgep;
+
+  if (facet->visible && qh->NEWfacets)
+    return;
+  FOREACHridge_(facet->ridges) {
+    if (format == qh_PRINTtriangles)
+      qh_fprintf(qh, fp, 9124, "%d ", qh->hull_dim);
+    qh_fprintf(qh, fp, 9125, "%d ", id);
+    if ((ridge->top == facet) ^ qh_ORIENTclock) {
+      FOREACHvertex_(ridge->vertices)
+        qh_fprintf(qh, fp, 9126, "%d ", qh_pointid(qh, vertex->point));
+    }else {
+      FOREACHvertexreverse12_(ridge->vertices)
+        qh_fprintf(qh, fp, 9127, "%d ", qh_pointid(qh, vertex->point));
+    }
+    qh_fprintf(qh, fp, 9128, "\n");
+  }
+} /* printfacetNvertex_nonsimplicial */
+
+
+/*---------------------------------
+
+  qh_printfacetNvertex_simplicial(qh, fp, facet, format )
+    print vertices for an N-d simplicial facet
+    prints vertices for non-simplicial facets
+      2-d facets (orientation preserved by qh_mergefacet2d)
+      PRINToff ('o') for 4-d and higher
+*/
+void qh_printfacetNvertex_simplicial(qhT *qh, FILE *fp, facetT *facet, qh_PRINT format) {
+  vertexT *vertex, **vertexp;
+
+  if (format == qh_PRINToff || format == qh_PRINTtriangles)
+    qh_fprintf(qh, fp, 9129, "%d ", qh_setsize(qh, facet->vertices));
+  if ((facet->toporient ^ qh_ORIENTclock)
+  || (qh->hull_dim > 2 && !facet->simplicial)) {
+    FOREACHvertex_(facet->vertices)
+      qh_fprintf(qh, fp, 9130, "%d ", qh_pointid(qh, vertex->point));
+  }else {
+    FOREACHvertexreverse12_(facet->vertices)
+      qh_fprintf(qh, fp, 9131, "%d ", qh_pointid(qh, vertex->point));
+  }
+  qh_fprintf(qh, fp, 9132, "\n");
+} /* printfacetNvertex_simplicial */
+
+
+/*---------------------------------
+
+  qh_printfacetheader(qh, fp, facet )
+    prints header fields of a facet to fp
+
+  notes:
+    for 'f' output and debugging
+    Same as QhullFacet::printHeader()
+*/
+void qh_printfacetheader(qhT *qh, FILE *fp, facetT *facet) {
+  pointT *point, **pointp, *furthest;
+  facetT *neighbor, **neighborp;
+  realT dist;
+
+  if (facet == qh_MERGEridge) {
+    qh_fprintf(qh, fp, 9133, " MERGEridge\n");
+    return;
+  }else if (facet == qh_DUPLICATEridge) {
+    qh_fprintf(qh, fp, 9134, " DUPLICATEridge\n");
+    return;
+  }else if (!facet) {
+    qh_fprintf(qh, fp, 9135, " NULLfacet\n");
+    return;
+  }
+  qh->old_randomdist= qh->RANDOMdist;
+  qh->RANDOMdist= False;
+  qh_fprintf(qh, fp, 9136, "- f%d\n", facet->id);
+  qh_fprintf(qh, fp, 9137, "    - flags:");
+  if (facet->toporient)
+    qh_fprintf(qh, fp, 9138, " top");
+  else
+    qh_fprintf(qh, fp, 9139, " bottom");
+  if (facet->simplicial)
+    qh_fprintf(qh, fp, 9140, " simplicial");
+  if (facet->tricoplanar)
+    qh_fprintf(qh, fp, 9141, " tricoplanar");
+  if (facet->upperdelaunay)
+    qh_fprintf(qh, fp, 9142, " upperDelaunay");
+  if (facet->visible)
+    qh_fprintf(qh, fp, 9143, " visible");
+  if (facet->newfacet)
+    qh_fprintf(qh, fp, 9144, " new");
+  if (facet->tested)
+    qh_fprintf(qh, fp, 9145, " tested");
+  if (!facet->good)
+    qh_fprintf(qh, fp, 9146, " notG");
+  if (facet->seen)
+    qh_fprintf(qh, fp, 9147, " seen");
+  if (facet->coplanar)
+    qh_fprintf(qh, fp, 9148, " coplanar");
+  if (facet->mergehorizon)
+    qh_fprintf(qh, fp, 9149, " mergehorizon");
+  if (facet->keepcentrum)
+    qh_fprintf(qh, fp, 9150, " keepcentrum");
+  if (facet->dupridge)
+    qh_fprintf(qh, fp, 9151, " dupridge");
+  if (facet->mergeridge && !facet->mergeridge2)
+    qh_fprintf(qh, fp, 9152, " mergeridge1");
+  if (facet->mergeridge2)
+    qh_fprintf(qh, fp, 9153, " mergeridge2");
+  if (facet->newmerge)
+    qh_fprintf(qh, fp, 9154, " newmerge");
+  if (facet->flipped)
+    qh_fprintf(qh, fp, 9155, " flipped");
+  if (facet->notfurthest)
+    qh_fprintf(qh, fp, 9156, " notfurthest");
+  if (facet->degenerate)
+    qh_fprintf(qh, fp, 9157, " degenerate");
+  if (facet->redundant)
+    qh_fprintf(qh, fp, 9158, " redundant");
+  qh_fprintf(qh, fp, 9159, "\n");
+  if (facet->isarea)
+    qh_fprintf(qh, fp, 9160, "    - area: %2.2g\n", facet->f.area);
+  else if (qh->NEWfacets && facet->visible && facet->f.replace)
+    qh_fprintf(qh, fp, 9161, "    - replacement: f%d\n", facet->f.replace->id);
+  else if (facet->newfacet) {
+    if (facet->f.samecycle && facet->f.samecycle != facet)
+      qh_fprintf(qh, fp, 9162, "    - shares same visible/horizon as f%d\n", facet->f.samecycle->id);
+  }else if (facet->tricoplanar /* !isarea */) {
+    if (facet->f.triowner)
+      qh_fprintf(qh, fp, 9163, "    - owner of normal & centrum is facet f%d\n", facet->f.triowner->id);
+  }else if (facet->f.newcycle)
+    qh_fprintf(qh, fp, 9164, "    - was horizon to f%d\n", facet->f.newcycle->id);
+  if (facet->nummerge)
+    qh_fprintf(qh, fp, 9165, "    - merges: %d\n", facet->nummerge);
+  qh_printpointid(qh, fp, "    - normal: ", qh->hull_dim, facet->normal, qh_IDunknown);
+  qh_fprintf(qh, fp, 9166, "    - offset: %10.7g\n", facet->offset);
+  if (qh->CENTERtype == qh_ASvoronoi || facet->center)
+    qh_printcenter(qh, fp, qh_PRINTfacets, "    - center: ", facet);
+#if qh_MAXoutside
+  if (facet->maxoutside > qh->DISTround)
+    qh_fprintf(qh, fp, 9167, "    - maxoutside: %10.7g\n", facet->maxoutside);
+#endif
+  if (!SETempty_(facet->outsideset)) {
+    furthest= (pointT*)qh_setlast(facet->outsideset);
+    if (qh_setsize(qh, facet->outsideset) < 6) {
+      qh_fprintf(qh, fp, 9168, "    - outside set(furthest p%d):\n", qh_pointid(qh, furthest));
+      FOREACHpoint_(facet->outsideset)
+        qh_printpoint(qh, fp, "     ", point);
+    }else if (qh_setsize(qh, facet->outsideset) < 21) {
+      qh_printpoints(qh, fp, "    - outside set:", facet->outsideset);
+    }else {
+      qh_fprintf(qh, fp, 9169, "    - outside set:  %d points.", qh_setsize(qh, facet->outsideset));
+      qh_printpoint(qh, fp, "  Furthest", furthest);
+    }
+#if !qh_COMPUTEfurthest
+    qh_fprintf(qh, fp, 9170, "    - furthest distance= %2.2g\n", facet->furthestdist);
+#endif
+  }
+  if (!SETempty_(facet->coplanarset)) {
+    furthest= (pointT*)qh_setlast(facet->coplanarset);
+    if (qh_setsize(qh, facet->coplanarset) < 6) {
+      qh_fprintf(qh, fp, 9171, "    - coplanar set(furthest p%d):\n", qh_pointid(qh, furthest));
+      FOREACHpoint_(facet->coplanarset)
+        qh_printpoint(qh, fp, "     ", point);
+    }else if (qh_setsize(qh, facet->coplanarset) < 21) {
+      qh_printpoints(qh, fp, "    - coplanar set:", facet->coplanarset);
+    }else {
+      qh_fprintf(qh, fp, 9172, "    - coplanar set:  %d points.", qh_setsize(qh, facet->coplanarset));
+      qh_printpoint(qh, fp, "  Furthest", furthest);
+    }
+    zinc_(Zdistio);
+    qh_distplane(qh, furthest, facet, &dist);
+    qh_fprintf(qh, fp, 9173, "      furthest distance= %2.2g\n", dist);
+  }
+  qh_printvertices(qh, fp, "    - vertices:", facet->vertices);
+  qh_fprintf(qh, fp, 9174, "    - neighboring facets:");
+  FOREACHneighbor_(facet) {
+    if (neighbor == qh_MERGEridge)
+      qh_fprintf(qh, fp, 9175, " MERGE");
+    else if (neighbor == qh_DUPLICATEridge)
+      qh_fprintf(qh, fp, 9176, " DUP");
+    else
+      qh_fprintf(qh, fp, 9177, " f%d", neighbor->id);
+  }
+  qh_fprintf(qh, fp, 9178, "\n");
+  qh->RANDOMdist= qh->old_randomdist;
+} /* printfacetheader */
+
+
+/*---------------------------------
+
+  qh_printfacetridges(qh, fp, facet )
+    prints ridges of a facet to fp
+
+  notes:
+    ridges printed in neighbor order
+    assumes the ridges exist
+    for 'f' output
+    same as QhullFacet::printRidges
+*/
+void qh_printfacetridges(qhT *qh, FILE *fp, facetT *facet) {
+  facetT *neighbor, **neighborp;
+  ridgeT *ridge, **ridgep;
+  int numridges= 0;
+
+
+  if (facet->visible && qh->NEWfacets) {
+    qh_fprintf(qh, fp, 9179, "    - ridges(ids may be garbage):");
+    FOREACHridge_(facet->ridges)
+      qh_fprintf(qh, fp, 9180, " r%d", ridge->id);
+    qh_fprintf(qh, fp, 9181, "\n");
+  }else {
+    qh_fprintf(qh, fp, 9182, "    - ridges:\n");
+    FOREACHridge_(facet->ridges)
+      ridge->seen= False;
+    if (qh->hull_dim == 3) {
+      ridge= SETfirstt_(facet->ridges, ridgeT);
+      while (ridge && !ridge->seen) {
+        ridge->seen= True;
+        qh_printridge(qh, fp, ridge);
+        numridges++;
+        ridge= qh_nextridge3d(ridge, facet, NULL);
+        }
+    }else {
+      FOREACHneighbor_(facet) {
+        FOREACHridge_(facet->ridges) {
+          if (otherfacet_(ridge,facet) == neighbor) {
+            ridge->seen= True;
+            qh_printridge(qh, fp, ridge);
+            numridges++;
+          }
+        }
+      }
+    }
+    if (numridges != qh_setsize(qh, facet->ridges)) {
+      qh_fprintf(qh, fp, 9183, "     - all ridges:");
+      FOREACHridge_(facet->ridges)
+        qh_fprintf(qh, fp, 9184, " r%d", ridge->id);
+        qh_fprintf(qh, fp, 9185, "\n");
+    }
+    FOREACHridge_(facet->ridges) {
+      if (!ridge->seen)
+        qh_printridge(qh, fp, ridge);
+    }
+  }
+} /* printfacetridges */
+
+/*---------------------------------
+
+  qh_printfacets(qh, fp, format, facetlist, facets, printall )
+    prints facetlist and/or facet set in output format
+
+  notes:
+    also used for specialized formats ('FO' and summary)
+    turns off 'Rn' option since want actual numbers
+*/
+void qh_printfacets(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall) {
+  int numfacets, numsimplicial, numridges, totneighbors, numcoplanars, numtricoplanars;
+  facetT *facet, **facetp;
+  setT *vertices;
+  coordT *center;
+  realT outerplane, innerplane;
+
+  qh->old_randomdist= qh->RANDOMdist;
+  qh->RANDOMdist= False;
+  if (qh->CDDoutput && (format == qh_PRINTcentrums || format == qh_PRINTpointintersect || format == qh_PRINToff))
+    qh_fprintf(qh, qh->ferr, 7056, "qhull warning: CDD format is not available for centrums, halfspace\nintersections, and OFF file format.\n");
+  if (format == qh_PRINTnone)
+    ; /* print nothing */
+  else if (format == qh_PRINTaverage) {
+    vertices= qh_facetvertices(qh, facetlist, facets, printall);
+    center= qh_getcenter(qh, vertices);
+    qh_fprintf(qh, fp, 9186, "%d 1\n", qh->hull_dim);
+    qh_printpointid(qh, fp, NULL, qh->hull_dim, center, qh_IDunknown);
+    qh_memfree(qh, center, qh->normal_size);
+    qh_settempfree(qh, &vertices);
+  }else if (format == qh_PRINTextremes) {
+    if (qh->DELAUNAY)
+      qh_printextremes_d(qh, fp, facetlist, facets, printall);
+    else if (qh->hull_dim == 2)
+      qh_printextremes_2d(qh, fp, facetlist, facets, printall);
+    else
+      qh_printextremes(qh, fp, facetlist, facets, printall);
+  }else if (format == qh_PRINToptions)
+    qh_fprintf(qh, fp, 9187, "Options selected for Qhull %s:\n%s\n", qh_version, qh->qhull_options);
+  else if (format == qh_PRINTpoints && !qh->VORONOI)
+    qh_printpoints_out(qh, fp, facetlist, facets, printall);
+  else if (format == qh_PRINTqhull)
+    qh_fprintf(qh, fp, 9188, "%s | %s\n", qh->rbox_command, qh->qhull_command);
+  else if (format == qh_PRINTsize) {
+    qh_fprintf(qh, fp, 9189, "0\n2 ");
+    qh_fprintf(qh, fp, 9190, qh_REAL_1, qh->totarea);
+    qh_fprintf(qh, fp, 9191, qh_REAL_1, qh->totvol);
+    qh_fprintf(qh, fp, 9192, "\n");
+  }else if (format == qh_PRINTsummary) {
+    qh_countfacets(qh, facetlist, facets, printall, &numfacets, &numsimplicial,
+      &totneighbors, &numridges, &numcoplanars, &numtricoplanars);
+    vertices= qh_facetvertices(qh, facetlist, facets, printall);
+    qh_fprintf(qh, fp, 9193, "10 %d %d %d %d %d %d %d %d %d %d\n2 ", qh->hull_dim,
+                qh->num_points + qh_setsize(qh, qh->other_points),
+                qh->num_vertices, qh->num_facets - qh->num_visible,
+                qh_setsize(qh, vertices), numfacets, numcoplanars,
+                numfacets - numsimplicial, zzval_(Zdelvertextot),
+                numtricoplanars);
+    qh_settempfree(qh, &vertices);
+    qh_outerinner(qh, NULL, &outerplane, &innerplane);
+    qh_fprintf(qh, fp, 9194, qh_REAL_2n, outerplane, innerplane);
+  }else if (format == qh_PRINTvneighbors)
+    qh_printvneighbors(qh, fp, facetlist, facets, printall);
+  else if (qh->VORONOI && format == qh_PRINToff)
+    qh_printvoronoi(qh, fp, format, facetlist, facets, printall);
+  else if (qh->VORONOI && format == qh_PRINTgeom) {
+    qh_printbegin(qh, fp, format, facetlist, facets, printall);
+    qh_printvoronoi(qh, fp, format, facetlist, facets, printall);
+    qh_printend(qh, fp, format, facetlist, facets, printall);
+  }else if (qh->VORONOI
+  && (format == qh_PRINTvertices || format == qh_PRINTinner || format == qh_PRINTouter))
+    qh_printvdiagram(qh, fp, format, facetlist, facets, printall);
+  else {
+    qh_printbegin(qh, fp, format, facetlist, facets, printall);
+    FORALLfacet_(facetlist)
+      qh_printafacet(qh, fp, format, facet, printall);
+    FOREACHfacet_(facets)
+      qh_printafacet(qh, fp, format, facet, printall);
+    qh_printend(qh, fp, format, facetlist, facets, printall);
+  }
+  qh->RANDOMdist= qh->old_randomdist;
+} /* printfacets */
+
+
+/*---------------------------------
+
+  qh_printhyperplaneintersection(qh, fp, facet1, facet2, vertices, color )
+    print Geomview OFF or 4OFF for the intersection of two hyperplanes in 3-d or 4-d
+*/
+void qh_printhyperplaneintersection(qhT *qh, FILE *fp, facetT *facet1, facetT *facet2,
+                   setT *vertices, realT color[3]) {
+  realT costheta, denominator, dist1, dist2, s, t, mindenom, p[4];
+  vertexT *vertex, **vertexp;
+  int i, k;
+  boolT nearzero1, nearzero2;
+
+  costheta= qh_getangle(qh, facet1->normal, facet2->normal);
+  denominator= 1 - costheta * costheta;
+  i= qh_setsize(qh, vertices);
+  if (qh->hull_dim == 3)
+    qh_fprintf(qh, fp, 9195, "VECT 1 %d 1 %d 1 ", i, i);
+  else if (qh->hull_dim == 4 && qh->DROPdim >= 0)
+    qh_fprintf(qh, fp, 9196, "OFF 3 1 1 ");
+  else
+    qh->printoutvar++;
+  qh_fprintf(qh, fp, 9197, "# intersect f%d f%d\n", facet1->id, facet2->id);
+  mindenom= 1 / (10.0 * qh->MAXabs_coord);
+  FOREACHvertex_(vertices) {
+    zadd_(Zdistio, 2);
+    qh_distplane(qh, vertex->point, facet1, &dist1);
+    qh_distplane(qh, vertex->point, facet2, &dist2);
+    s= qh_divzero(-dist1 + costheta * dist2, denominator,mindenom,&nearzero1);
+    t= qh_divzero(-dist2 + costheta * dist1, denominator,mindenom,&nearzero2);
+    if (nearzero1 || nearzero2)
+      s= t= 0.0;
+    for (k=qh->hull_dim; k--; )
+      p[k]= vertex->point[k] + facet1->normal[k] * s + facet2->normal[k] * t;
+    if (qh->PRINTdim <= 3) {
+      qh_projectdim3(qh, p, p);
+      qh_fprintf(qh, fp, 9198, "%8.4g %8.4g %8.4g # ", p[0], p[1], p[2]);
+    }else
+      qh_fprintf(qh, fp, 9199, "%8.4g %8.4g %8.4g %8.4g # ", p[0], p[1], p[2], p[3]);
+    if (nearzero1+nearzero2)
+      qh_fprintf(qh, fp, 9200, "p%d(coplanar facets)\n", qh_pointid(qh, vertex->point));
+    else
+      qh_fprintf(qh, fp, 9201, "projected p%d\n", qh_pointid(qh, vertex->point));
+  }
+  if (qh->hull_dim == 3)
+    qh_fprintf(qh, fp, 9202, "%8.4g %8.4g %8.4g 1.0\n", color[0], color[1], color[2]);
+  else if (qh->hull_dim == 4 && qh->DROPdim >= 0)
+    qh_fprintf(qh, fp, 9203, "3 0 1 2 %8.4g %8.4g %8.4g 1.0\n", color[0], color[1], color[2]);
+} /* printhyperplaneintersection */
+
+/*---------------------------------
+
+  qh_printline3geom(qh, fp, pointA, pointB, color )
+    prints a line as a VECT
+    prints 0's for qh.DROPdim
+
+  notes:
+    if pointA == pointB,
+      it's a 1 point VECT
+*/
+void qh_printline3geom(qhT *qh, FILE *fp, pointT *pointA, pointT *pointB, realT color[3]) {
+  int k;
+  realT pA[4], pB[4];
+
+  qh_projectdim3(qh, pointA, pA);
+  qh_projectdim3(qh, pointB, pB);
+  if ((fabs(pA[0] - pB[0]) > 1e-3) ||
+      (fabs(pA[1] - pB[1]) > 1e-3) ||
+      (fabs(pA[2] - pB[2]) > 1e-3)) {
+    qh_fprintf(qh, fp, 9204, "VECT 1 2 1 2 1\n");
+    for (k=0; k < 3; k++)
+       qh_fprintf(qh, fp, 9205, "%8.4g ", pB[k]);
+    qh_fprintf(qh, fp, 9206, " # p%d\n", qh_pointid(qh, pointB));
+  }else
+    qh_fprintf(qh, fp, 9207, "VECT 1 1 1 1 1\n");
+  for (k=0; k < 3; k++)
+    qh_fprintf(qh, fp, 9208, "%8.4g ", pA[k]);
+  qh_fprintf(qh, fp, 9209, " # p%d\n", qh_pointid(qh, pointA));
+  qh_fprintf(qh, fp, 9210, "%8.4g %8.4g %8.4g 1\n", color[0], color[1], color[2]);
+}
+
+/*---------------------------------
+
+  qh_printneighborhood(qh, fp, format, facetA, facetB, printall )
+    print neighborhood of one or two facets
+
+  notes:
+    calls qh_findgood_all()
+    bumps qh.visit_id
+*/
+void qh_printneighborhood(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetA, facetT *facetB, boolT printall) {
+  facetT *neighbor, **neighborp, *facet;
+  setT *facets;
+
+  if (format == qh_PRINTnone)
+    return;
+  qh_findgood_all(qh, qh->facet_list);
+  if (facetA == facetB)
+    facetB= NULL;
+  facets= qh_settemp(qh, 2*(qh_setsize(qh, facetA->neighbors)+1));
+  qh->visit_id++;
+  for (facet= facetA; facet; facet= ((facet == facetA) ? facetB : NULL)) {
+    if (facet->visitid != qh->visit_id) {
+      facet->visitid= qh->visit_id;
+      qh_setappend(qh, &facets, facet);
+    }
+    FOREACHneighbor_(facet) {
+      if (neighbor->visitid == qh->visit_id)
+        continue;
+      neighbor->visitid= qh->visit_id;
+      if (printall || !qh_skipfacet(qh, neighbor))
+        qh_setappend(qh, &facets, neighbor);
+    }
+  }
+  qh_printfacets(qh, fp, format, NULL, facets, printall);
+  qh_settempfree(qh, &facets);
+} /* printneighborhood */
+
+/*---------------------------------
+
+  qh_printpoint(qh, fp, string, point )
+  qh_printpointid(qh, fp, string, dim, point, id )
+    prints the coordinates of a point
+
+  returns:
+    if string is defined
+      prints 'string p%d'.  Skips p%d if id=qh_IDunknown(-1) or qh_IDnone(-3)
+
+  notes:
+    nop if point is NULL
+    Same as QhullPoint's printPoint
+*/
+void qh_printpoint(qhT *qh, FILE *fp, const char *string, pointT *point) {
+  int id= qh_pointid(qh, point);
+
+  qh_printpointid(qh, fp, string, qh->hull_dim, point, id);
+} /* printpoint */
+
+void qh_printpointid(qhT *qh, FILE *fp, const char *string, int dim, pointT *point, int id) {
+  int k;
+  realT r; /*bug fix*/
+
+  if (!point)
+    return;
+  if (string) {
+    qh_fprintf(qh, fp, 9211, "%s", string);
+    if (id != qh_IDunknown && id != qh_IDnone)
+      qh_fprintf(qh, fp, 9212, " p%d: ", id);
+  }
+  for (k=dim; k--; ) {
+    r= *point++;
+    if (string)
+      qh_fprintf(qh, fp, 9213, " %8.4g", r);
+    else
+      qh_fprintf(qh, fp, 9214, qh_REAL_1, r);
+  }
+  qh_fprintf(qh, fp, 9215, "\n");
+} /* printpointid */
+
+/*---------------------------------
+
+  qh_printpoint3(qh, fp, point )
+    prints 2-d, 3-d, or 4-d point as Geomview 3-d coordinates
+*/
+void qh_printpoint3(qhT *qh, FILE *fp, pointT *point) {
+  int k;
+  realT p[4];
+
+  qh_projectdim3(qh, point, p);
+  for (k=0; k < 3; k++)
+    qh_fprintf(qh, fp, 9216, "%8.4g ", p[k]);
+  qh_fprintf(qh, fp, 9217, " # p%d\n", qh_pointid(qh, point));
+} /* printpoint3 */
+
+/*----------------------------------------
+-printpoints- print pointids for a set of points starting at index
+   see geom_r.c
+*/
+
+/*---------------------------------
+
+  qh_printpoints_out(qh, fp, facetlist, facets, printall )
+    prints vertices, coplanar/inside points, for facets by their point coordinates
+    allows qh.CDDoutput
+
+  notes:
+    same format as qhull input
+    if no coplanar/interior points,
+      same order as qh_printextremes
+*/
+void qh_printpoints_out(qhT *qh, FILE *fp, facetT *facetlist, setT *facets, boolT printall) {
+  int allpoints= qh->num_points + qh_setsize(qh, qh->other_points);
+  int numpoints=0, point_i, point_n;
+  setT *vertices, *points;
+  facetT *facet, **facetp;
+  pointT *point, **pointp;
+  vertexT *vertex, **vertexp;
+  int id;
+
+  points= qh_settemp(qh, allpoints);
+  qh_setzero(qh, points, 0, allpoints);
+  vertices= qh_facetvertices(qh, facetlist, facets, printall);
+  FOREACHvertex_(vertices) {
+    id= qh_pointid(qh, vertex->point);
+    if (id >= 0)
+      SETelem_(points, id)= vertex->point;
+  }
+  if (qh->KEEPinside || qh->KEEPcoplanar || qh->KEEPnearinside) {
+    FORALLfacet_(facetlist) {
+      if (!printall && qh_skipfacet(qh, facet))
+        continue;
+      FOREACHpoint_(facet->coplanarset) {
+        id= qh_pointid(qh, point);
+        if (id >= 0)
+          SETelem_(points, id)= point;
+      }
+    }
+    FOREACHfacet_(facets) {
+      if (!printall && qh_skipfacet(qh, facet))
+        continue;
+      FOREACHpoint_(facet->coplanarset) {
+        id= qh_pointid(qh, point);
+        if (id >= 0)
+          SETelem_(points, id)= point;
+      }
+    }
+  }
+  qh_settempfree(qh, &vertices);
+  FOREACHpoint_i_(qh, points) {
+    if (point)
+      numpoints++;
+  }
+  if (qh->CDDoutput)
+    qh_fprintf(qh, fp, 9218, "%s | %s\nbegin\n%d %d real\n", qh->rbox_command,
+             qh->qhull_command, numpoints, qh->hull_dim + 1);
+  else
+    qh_fprintf(qh, fp, 9219, "%d\n%d\n", qh->hull_dim, numpoints);
+  FOREACHpoint_i_(qh, points) {
+    if (point) {
+      if (qh->CDDoutput)
+        qh_fprintf(qh, fp, 9220, "1 ");
+      qh_printpoint(qh, fp, NULL, point);
+    }
+  }
+  if (qh->CDDoutput)
+    qh_fprintf(qh, fp, 9221, "end\n");
+  qh_settempfree(qh, &points);
+} /* printpoints_out */
+
+
+/*---------------------------------
+
+  qh_printpointvect(qh, fp, point, normal, center, radius, color )
+    prints a 2-d, 3-d, or 4-d point as 3-d VECT's relative to normal or to center point
+*/
+void qh_printpointvect(qhT *qh, FILE *fp, pointT *point, coordT *normal, pointT *center, realT radius, realT color[3]) {
+  realT diff[4], pointA[4];
+  int k;
+
+  for (k=qh->hull_dim; k--; ) {
+    if (center)
+      diff[k]= point[k]-center[k];
+    else if (normal)
+      diff[k]= normal[k];
+    else
+      diff[k]= 0;
+  }
+  if (center)
+    qh_normalize2(qh, diff, qh->hull_dim, True, NULL, NULL);
+  for (k=qh->hull_dim; k--; )
+    pointA[k]= point[k]+diff[k] * radius;
+  qh_printline3geom(qh, fp, point, pointA, color);
+} /* printpointvect */
+
+/*---------------------------------
+
+  qh_printpointvect2(qh, fp, point, normal, center, radius )
+    prints a 2-d, 3-d, or 4-d point as 2 3-d VECT's for an imprecise point
+*/
+void qh_printpointvect2(qhT *qh, FILE *fp, pointT *point, coordT *normal, pointT *center, realT radius) {
+  realT red[3]={1, 0, 0}, yellow[3]={1, 1, 0};
+
+  qh_printpointvect(qh, fp, point, normal, center, radius, red);
+  qh_printpointvect(qh, fp, point, normal, center, -radius, yellow);
+} /* printpointvect2 */
+
+/*---------------------------------
+
+  qh_printridge(qh, fp, ridge )
+    prints the information in a ridge
+
+  notes:
+    for qh_printfacetridges()
+    same as operator<< [QhullRidge.cpp]
+*/
+void qh_printridge(qhT *qh, FILE *fp, ridgeT *ridge) {
+
+  qh_fprintf(qh, fp, 9222, "     - r%d", ridge->id);
+  if (ridge->tested)
+    qh_fprintf(qh, fp, 9223, " tested");
+  if (ridge->nonconvex)
+    qh_fprintf(qh, fp, 9224, " nonconvex");
+  qh_fprintf(qh, fp, 9225, "\n");
+  qh_printvertices(qh, fp, "           vertices:", ridge->vertices);
+  if (ridge->top && ridge->bottom)
+    qh_fprintf(qh, fp, 9226, "           between f%d and f%d\n",
+            ridge->top->id, ridge->bottom->id);
+} /* printridge */
+
+/*---------------------------------
+
+  qh_printspheres(qh, fp, vertices, radius )
+    prints 3-d vertices as OFF spheres
+
+  notes:
+    inflated octahedron from Stuart Levy earth/mksphere2
+*/
+void qh_printspheres(qhT *qh, FILE *fp, setT *vertices, realT radius) {
+  vertexT *vertex, **vertexp;
+
+  qh->printoutnum++;
+  qh_fprintf(qh, fp, 9227, "{appearance {-edge -normal normscale 0} {\n\
+INST geom {define vsphere OFF\n\
+18 32 48\n\
+\n\
+0 0 1\n\
+1 0 0\n\
+0 1 0\n\
+-1 0 0\n\
+0 -1 0\n\
+0 0 -1\n\
+0.707107 0 0.707107\n\
+0 -0.707107 0.707107\n\
+0.707107 -0.707107 0\n\
+-0.707107 0 0.707107\n\
+-0.707107 -0.707107 0\n\
+0 0.707107 0.707107\n\
+-0.707107 0.707107 0\n\
+0.707107 0.707107 0\n\
+0.707107 0 -0.707107\n\
+0 0.707107 -0.707107\n\
+-0.707107 0 -0.707107\n\
+0 -0.707107 -0.707107\n\
+\n\
+3 0 6 11\n\
+3 0 7 6 \n\
+3 0 9 7 \n\
+3 0 11 9\n\
+3 1 6 8 \n\
+3 1 8 14\n\
+3 1 13 6\n\
+3 1 14 13\n\
+3 2 11 13\n\
+3 2 12 11\n\
+3 2 13 15\n\
+3 2 15 12\n\
+3 3 9 12\n\
+3 3 10 9\n\
+3 3 12 16\n\
+3 3 16 10\n\
+3 4 7 10\n\
+3 4 8 7\n\
+3 4 10 17\n\
+3 4 17 8\n\
+3 5 14 17\n\
+3 5 15 14\n\
+3 5 16 15\n\
+3 5 17 16\n\
+3 6 13 11\n\
+3 7 8 6\n\
+3 9 10 7\n\
+3 11 12 9\n\
+3 14 8 17\n\
+3 15 13 14\n\
+3 16 12 15\n\
+3 17 10 16\n} transforms { TLIST\n");
+  FOREACHvertex_(vertices) {
+    qh_fprintf(qh, fp, 9228, "%8.4g 0 0 0 # v%d\n 0 %8.4g 0 0\n0 0 %8.4g 0\n",
+      radius, vertex->id, radius, radius);
+    qh_printpoint3(qh, fp, vertex->point);
+    qh_fprintf(qh, fp, 9229, "1\n");
+  }
+  qh_fprintf(qh, fp, 9230, "}}}\n");
+} /* printspheres */
+
+
+/*----------------------------------------------
+-printsummary-
+                see libqhull_r.c
+*/
+
+/*---------------------------------
+
+  qh_printvdiagram(qh, fp, format, facetlist, facets, printall )
+    print voronoi diagram
+      # of pairs of input sites
+      #indices site1 site2 vertex1 ...
+
+    sites indexed by input point id
+      point 0 is the first input point
+    vertices indexed by 'o' and 'p' order
+      vertex 0 is the 'vertex-at-infinity'
+      vertex 1 is the first Voronoi vertex
+
+  see:
+    qh_printvoronoi()
+    qh_eachvoronoi_all()
+
+  notes:
+    if all facets are upperdelaunay,
+      prints upper hull (furthest-site Voronoi diagram)
+*/
+void qh_printvdiagram(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall) {
+  setT *vertices;
+  int totcount, numcenters;
+  boolT isLower;
+  qh_RIDGE innerouter= qh_RIDGEall;
+  printvridgeT printvridge= NULL;
+
+  if (format == qh_PRINTvertices) {
+    innerouter= qh_RIDGEall;
+    printvridge= qh_printvridge;
+  }else if (format == qh_PRINTinner) {
+    innerouter= qh_RIDGEinner;
+    printvridge= qh_printvnorm;
+  }else if (format == qh_PRINTouter) {
+    innerouter= qh_RIDGEouter;
+    printvridge= qh_printvnorm;
+  }else {
+    qh_fprintf(qh, qh->ferr, 6219, "Qhull internal error (qh_printvdiagram): unknown print format %d.\n", format);
+    qh_errexit(qh, qh_ERRinput, NULL, NULL);
+  }
+  vertices= qh_markvoronoi(qh, facetlist, facets, printall, &isLower, &numcenters);
+  totcount= qh_printvdiagram2(qh, NULL, NULL, vertices, innerouter, False);
+  qh_fprintf(qh, fp, 9231, "%d\n", totcount);
+  totcount= qh_printvdiagram2(qh, fp, printvridge, vertices, innerouter, True /* inorder*/);
+  qh_settempfree(qh, &vertices);
+#if 0  /* for testing qh_eachvoronoi_all */
+  qh_fprintf(qh, fp, 9232, "\n");
+  totcount= qh_eachvoronoi_all(qh, fp, printvridge, qh->UPPERdelaunay, innerouter, True /* inorder*/);
+  qh_fprintf(qh, fp, 9233, "%d\n", totcount);
+#endif
+} /* printvdiagram */
+
+/*---------------------------------
+
+  qh_printvdiagram2(qh, fp, printvridge, vertices, innerouter, inorder )
+    visit all pairs of input sites (vertices) for selected Voronoi vertices
+    vertices may include NULLs
+
+  innerouter:
+    qh_RIDGEall   print inner ridges(bounded) and outer ridges(unbounded)
+    qh_RIDGEinner print only inner ridges
+    qh_RIDGEouter print only outer ridges
+
+  inorder:
+    print 3-d Voronoi vertices in order
+
+  assumes:
+    qh_markvoronoi marked facet->visitid for Voronoi vertices
+    all facet->seen= False
+    all facet->seen2= True
+
+  returns:
+    total number of Voronoi ridges
+    if printvridge,
+      calls printvridge( fp, vertex, vertexA, centers) for each ridge
+      [see qh_eachvoronoi()]
+
+  see:
+    qh_eachvoronoi_all()
+*/
+int qh_printvdiagram2(qhT *qh, FILE *fp, printvridgeT printvridge, setT *vertices, qh_RIDGE innerouter, boolT inorder) {
+  int totcount= 0;
+  int vertex_i, vertex_n;
+  vertexT *vertex;
+
+  FORALLvertices
+    vertex->seen= False;
+  FOREACHvertex_i_(qh, vertices) {
+    if (vertex) {
+      if (qh->GOODvertex > 0 && qh_pointid(qh, vertex->point)+1 != qh->GOODvertex)
+        continue;
+      totcount += qh_eachvoronoi(qh, fp, printvridge, vertex, !qh_ALL, innerouter, inorder);
+    }
+  }
+  return totcount;
+} /* printvdiagram2 */
+
+/*---------------------------------
+
+  qh_printvertex(qh, fp, vertex )
+    prints the information in a vertex
+    Duplicated as operator<< [QhullVertex.cpp]
+*/
+void qh_printvertex(qhT *qh, FILE *fp, vertexT *vertex) {
+  pointT *point;
+  int k, count= 0;
+  facetT *neighbor, **neighborp;
+  realT r; /*bug fix*/
+
+  if (!vertex) {
+    qh_fprintf(qh, fp, 9234, "  NULLvertex\n");
+    return;
+  }
+  qh_fprintf(qh, fp, 9235, "- p%d(v%d):", qh_pointid(qh, vertex->point), vertex->id);
+  point= vertex->point;
+  if (point) {
+    for (k=qh->hull_dim; k--; ) {
+      r= *point++;
+      qh_fprintf(qh, fp, 9236, " %5.2g", r);
+    }
+  }
+  if (vertex->deleted)
+    qh_fprintf(qh, fp, 9237, " deleted");
+  if (vertex->delridge)
+    qh_fprintf(qh, fp, 9238, " ridgedeleted");
+  qh_fprintf(qh, fp, 9239, "\n");
+  if (vertex->neighbors) {
+    qh_fprintf(qh, fp, 9240, "  neighbors:");
+    FOREACHneighbor_(vertex) {
+      if (++count % 100 == 0)
+        qh_fprintf(qh, fp, 9241, "\n     ");
+      qh_fprintf(qh, fp, 9242, " f%d", neighbor->id);
+    }
+    qh_fprintf(qh, fp, 9243, "\n");
+  }
+} /* printvertex */
+
+
+/*---------------------------------
+
+  qh_printvertexlist(qh, fp, string, facetlist, facets, printall )
+    prints vertices used by a facetlist or facet set
+    tests qh_skipfacet() if !printall
+*/
+void qh_printvertexlist(qhT *qh, FILE *fp, const char* string, facetT *facetlist,
+                         setT *facets, boolT printall) {
+  vertexT *vertex, **vertexp;
+  setT *vertices;
+
+  vertices= qh_facetvertices(qh, facetlist, facets, printall);
+  qh_fprintf(qh, fp, 9244, "%s", string);
+  FOREACHvertex_(vertices)
+    qh_printvertex(qh, fp, vertex);
+  qh_settempfree(qh, &vertices);
+} /* printvertexlist */
+
+
+/*---------------------------------
+
+  qh_printvertices(qh, fp, string, vertices )
+    prints vertices in a set
+    duplicated as printVertexSet [QhullVertex.cpp]
+*/
+void qh_printvertices(qhT *qh, FILE *fp, const char* string, setT *vertices) {
+  vertexT *vertex, **vertexp;
+
+  qh_fprintf(qh, fp, 9245, "%s", string);
+  FOREACHvertex_(vertices)
+    qh_fprintf(qh, fp, 9246, " p%d(v%d)", qh_pointid(qh, vertex->point), vertex->id);
+  qh_fprintf(qh, fp, 9247, "\n");
+} /* printvertices */
+
+/*---------------------------------
+
+  qh_printvneighbors(qh, fp, facetlist, facets, printall )
+    print vertex neighbors of vertices in facetlist and facets ('FN')
+
+  notes:
+    qh_countfacets clears facet->visitid for non-printed facets
+
+  design:
+    collect facet count and related statistics
+    if necessary, build neighbor sets for each vertex
+    collect vertices in facetlist and facets
+    build a point array for point->vertex and point->coplanar facet
+    for each point
+      list vertex neighbors or coplanar facet
+*/
+void qh_printvneighbors(qhT *qh, FILE *fp, facetT* facetlist, setT *facets, boolT printall) {
+  int numfacets, numsimplicial, numridges, totneighbors, numneighbors, numcoplanars, numtricoplanars;
+  setT *vertices, *vertex_points, *coplanar_points;
+  int numpoints= qh->num_points + qh_setsize(qh, qh->other_points);
+  vertexT *vertex, **vertexp;
+  int vertex_i, vertex_n;
+  facetT *facet, **facetp, *neighbor, **neighborp;
+  pointT *point, **pointp;
+
+  qh_countfacets(qh, facetlist, facets, printall, &numfacets, &numsimplicial,
+      &totneighbors, &numridges, &numcoplanars, &numtricoplanars);  /* sets facet->visitid */
+  qh_fprintf(qh, fp, 9248, "%d\n", numpoints);
+  qh_vertexneighbors(qh);
+  vertices= qh_facetvertices(qh, facetlist, facets, printall);
+  vertex_points= qh_settemp(qh, numpoints);
+  coplanar_points= qh_settemp(qh, numpoints);
+  qh_setzero(qh, vertex_points, 0, numpoints);
+  qh_setzero(qh, coplanar_points, 0, numpoints);
+  FOREACHvertex_(vertices)
+    qh_point_add(qh, vertex_points, vertex->point, vertex);
+  FORALLfacet_(facetlist) {
+    FOREACHpoint_(facet->coplanarset)
+      qh_point_add(qh, coplanar_points, point, facet);
+  }
+  FOREACHfacet_(facets) {
+    FOREACHpoint_(facet->coplanarset)
+      qh_point_add(qh, coplanar_points, point, facet);
+  }
+  FOREACHvertex_i_(qh, vertex_points) {
+    if (vertex) {
+      numneighbors= qh_setsize(qh, vertex->neighbors);
+      qh_fprintf(qh, fp, 9249, "%d", numneighbors);
+      if (qh->hull_dim == 3)
+        qh_order_vertexneighbors(qh, vertex);
+      else if (qh->hull_dim >= 4)
+        qsort(SETaddr_(vertex->neighbors, facetT), (size_t)numneighbors,
+             sizeof(facetT *), qh_compare_facetvisit);
+      FOREACHneighbor_(vertex)
+        qh_fprintf(qh, fp, 9250, " %d",
+                 neighbor->visitid ? neighbor->visitid - 1 : 0 - neighbor->id);
+      qh_fprintf(qh, fp, 9251, "\n");
+    }else if ((facet= SETelemt_(coplanar_points, vertex_i, facetT)))
+      qh_fprintf(qh, fp, 9252, "1 %d\n",
+                  facet->visitid ? facet->visitid - 1 : 0 - facet->id);
+    else
+      qh_fprintf(qh, fp, 9253, "0\n");
+  }
+  qh_settempfree(qh, &coplanar_points);
+  qh_settempfree(qh, &vertex_points);
+  qh_settempfree(qh, &vertices);
+} /* printvneighbors */
+
+/*---------------------------------
+
+  qh_printvoronoi(qh, fp, format, facetlist, facets, printall )
+    print voronoi diagram in 'o' or 'G' format
+    for 'o' format
+      prints voronoi centers for each facet and for infinity
+      for each vertex, lists ids of printed facets or infinity
+      assumes facetlist and facets are disjoint
+    for 'G' format
+      prints an OFF object
+      adds a 0 coordinate to center
+      prints infinity but does not list in vertices
+
+  see:
+    qh_printvdiagram()
+
+  notes:
+    if 'o',
+      prints a line for each point except "at-infinity"
+    if all facets are upperdelaunay,
+      reverses lower and upper hull
+*/
+void qh_printvoronoi(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall) {
+  int k, numcenters, numvertices= 0, numneighbors, numinf, vid=1, vertex_i, vertex_n;
+  facetT *facet, **facetp, *neighbor, **neighborp;
+  setT *vertices;
+  vertexT *vertex;
+  boolT isLower;
+  unsigned int numfacets= (unsigned int) qh->num_facets;
+
+  vertices= qh_markvoronoi(qh, facetlist, facets, printall, &isLower, &numcenters);
+  FOREACHvertex_i_(qh, vertices) {
+    if (vertex) {
+      numvertices++;
+      numneighbors = numinf = 0;
+      FOREACHneighbor_(vertex) {
+        if (neighbor->visitid == 0)
+          numinf= 1;
+        else if (neighbor->visitid < numfacets)
+          numneighbors++;
+      }
+      if (numinf && !numneighbors) {
+        SETelem_(vertices, vertex_i)= NULL;
+        numvertices--;
+      }
+    }
+  }
+  if (format == qh_PRINTgeom)
+    qh_fprintf(qh, fp, 9254, "{appearance {+edge -face} OFF %d %d 1 # Voronoi centers and cells\n",
+                numcenters, numvertices);
+  else
+    qh_fprintf(qh, fp, 9255, "%d\n%d %d 1\n", qh->hull_dim-1, numcenters, qh_setsize(qh, vertices));
+  if (format == qh_PRINTgeom) {
+    for (k=qh->hull_dim-1; k--; )
+      qh_fprintf(qh, fp, 9256, qh_REAL_1, 0.0);
+    qh_fprintf(qh, fp, 9257, " 0 # infinity not used\n");
+  }else {
+    for (k=qh->hull_dim-1; k--; )
+      qh_fprintf(qh, fp, 9258, qh_REAL_1, qh_INFINITE);
+    qh_fprintf(qh, fp, 9259, "\n");
+  }
+  FORALLfacet_(facetlist) {
+    if (facet->visitid && facet->visitid < numfacets) {
+      if (format == qh_PRINTgeom)
+        qh_fprintf(qh, fp, 9260, "# %d f%d\n", vid++, facet->id);
+      qh_printcenter(qh, fp, format, NULL, facet);
+    }
+  }
+  FOREACHfacet_(facets) {
+    if (facet->visitid && facet->visitid < numfacets) {
+      if (format == qh_PRINTgeom)
+        qh_fprintf(qh, fp, 9261, "# %d f%d\n", vid++, facet->id);
+      qh_printcenter(qh, fp, format, NULL, facet);
+    }
+  }
+  FOREACHvertex_i_(qh, vertices) {
+    numneighbors= 0;
+    numinf=0;
+    if (vertex) {
+      if (qh->hull_dim == 3)
+        qh_order_vertexneighbors(qh, vertex);
+      else if (qh->hull_dim >= 4)
+        qsort(SETaddr_(vertex->neighbors, facetT),
+             (size_t)qh_setsize(qh, vertex->neighbors),
+             sizeof(facetT *), qh_compare_facetvisit);
+      FOREACHneighbor_(vertex) {
+        if (neighbor->visitid == 0)
+          numinf= 1;
+        else if (neighbor->visitid < numfacets)
+          numneighbors++;
+      }
+    }
+    if (format == qh_PRINTgeom) {
+      if (vertex) {
+        qh_fprintf(qh, fp, 9262, "%d", numneighbors);
+        FOREACHneighbor_(vertex) {
+          if (neighbor->visitid && neighbor->visitid < numfacets)
+            qh_fprintf(qh, fp, 9263, " %d", neighbor->visitid);
+        }
+        qh_fprintf(qh, fp, 9264, " # p%d(v%d)\n", vertex_i, vertex->id);
+      }else
+        qh_fprintf(qh, fp, 9265, " # p%d is coplanar or isolated\n", vertex_i);
+    }else {
+      if (numinf)
+        numneighbors++;
+      qh_fprintf(qh, fp, 9266, "%d", numneighbors);
+      if (vertex) {
+        FOREACHneighbor_(vertex) {
+          if (neighbor->visitid == 0) {
+            if (numinf) {
+              numinf= 0;
+              qh_fprintf(qh, fp, 9267, " %d", neighbor->visitid);
+            }
+          }else if (neighbor->visitid < numfacets)
+            qh_fprintf(qh, fp, 9268, " %d", neighbor->visitid);
+        }
+      }
+      qh_fprintf(qh, fp, 9269, "\n");
+    }
+  }
+  if (format == qh_PRINTgeom)
+    qh_fprintf(qh, fp, 9270, "}\n");
+  qh_settempfree(qh, &vertices);
+} /* printvoronoi */
+
+/*---------------------------------
+
+  qh_printvnorm(qh, fp, vertex, vertexA, centers, unbounded )
+    print one separating plane of the Voronoi diagram for a pair of input sites
+    unbounded==True if centers includes vertex-at-infinity
+
+  assumes:
+    qh_ASvoronoi and qh_vertexneighbors() already set
+
+  note:
+    parameter unbounded is UNUSED by this callback
+
+  see:
+    qh_printvdiagram()
+    qh_eachvoronoi()
+*/
+void qh_printvnorm(qhT *qh, FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded) {
+  pointT *normal;
+  realT offset;
+  int k;
+  QHULL_UNUSED(unbounded);
+
+  normal= qh_detvnorm(qh, vertex, vertexA, centers, &offset);
+  qh_fprintf(qh, fp, 9271, "%d %d %d ",
+      2+qh->hull_dim, qh_pointid(qh, vertex->point), qh_pointid(qh, vertexA->point));
+  for (k=0; k< qh->hull_dim-1; k++)
+    qh_fprintf(qh, fp, 9272, qh_REAL_1, normal[k]);
+  qh_fprintf(qh, fp, 9273, qh_REAL_1, offset);
+  qh_fprintf(qh, fp, 9274, "\n");
+} /* printvnorm */
+
+/*---------------------------------
+
+  qh_printvridge(qh, fp, vertex, vertexA, centers, unbounded )
+    print one ridge of the Voronoi diagram for a pair of input sites
+    unbounded==True if centers includes vertex-at-infinity
+
+  see:
+    qh_printvdiagram()
+
+  notes:
+    the user may use a different function
+    parameter unbounded is UNUSED
+*/
+void qh_printvridge(qhT *qh, FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded) {
+  facetT *facet, **facetp;
+  QHULL_UNUSED(unbounded);
+
+  qh_fprintf(qh, fp, 9275, "%d %d %d", qh_setsize(qh, centers)+2,
+       qh_pointid(qh, vertex->point), qh_pointid(qh, vertexA->point));
+  FOREACHfacet_(centers)
+    qh_fprintf(qh, fp, 9276, " %d", facet->visitid);
+  qh_fprintf(qh, fp, 9277, "\n");
+} /* printvridge */
+
+/*---------------------------------
+
+  qh_projectdim3(qh, source, destination )
+    project 2-d 3-d or 4-d point to a 3-d point
+    uses qh.DROPdim and qh.hull_dim
+    source and destination may be the same
+
+  notes:
+    allocate 4 elements to destination just in case
+*/
+void qh_projectdim3(qhT *qh, pointT *source, pointT *destination) {
+  int i,k;
+
+  for (k=0, i=0; k < qh->hull_dim; k++) {
+    if (qh->hull_dim == 4) {
+      if (k != qh->DROPdim)
+        destination[i++]= source[k];
+    }else if (k == qh->DROPdim)
+      destination[i++]= 0;
+    else
+      destination[i++]= source[k];
+  }
+  while (i < 3)
+    destination[i++]= 0.0;
+} /* projectdim3 */
+
+/*---------------------------------
+
+  qh_readfeasible(qh, dim, curline )
+    read feasible point from current line and qh.fin
+
+  returns:
+    number of lines read from qh.fin
+    sets qh.feasible_point with malloc'd coordinates
+
+  notes:
+    checks for qh.HALFspace
+    assumes dim > 1
+
+  see:
+    qh_setfeasible
+*/
+int qh_readfeasible(qhT *qh, int dim, const char *curline) {
+  boolT isfirst= True;
+  int linecount= 0, tokcount= 0;
+  const char *s;
+  char *t, firstline[qh_MAXfirst+1];
+  coordT *coords, value;
+
+  if (!qh->HALFspace) {
+    qh_fprintf(qh, qh->ferr, 6070, "qhull input error: feasible point(dim 1 coords) is only valid for halfspace intersection\n");
+    qh_errexit(qh, qh_ERRinput, NULL, NULL);
+  }
+  if (qh->feasible_string)
+    qh_fprintf(qh, qh->ferr, 7057, "qhull input warning: feasible point(dim 1 coords) overrides 'Hn,n,n' feasible point for halfspace intersection\n");
+  if (!(qh->feasible_point= (coordT*)qh_malloc(dim* sizeof(coordT)))) {
+    qh_fprintf(qh, qh->ferr, 6071, "qhull error: insufficient memory for feasible point\n");
+    qh_errexit(qh, qh_ERRmem, NULL, NULL);
+  }
+  coords= qh->feasible_point;
+  while ((s= (isfirst ?  curline : fgets(firstline, qh_MAXfirst, qh->fin)))) {
+    if (isfirst)
+      isfirst= False;
+    else
+      linecount++;
+    while (*s) {
+      while (isspace(*s))
+        s++;
+      value= qh_strtod(s, &t);
+      if (s == t)
+        break;
+      s= t;
+      *(coords++)= value;
+      if (++tokcount == dim) {
+        while (isspace(*s))
+          s++;
+        qh_strtod(s, &t);
+        if (s != t) {
+          qh_fprintf(qh, qh->ferr, 6072, "qhull input error: coordinates for feasible point do not finish out the line: %s\n",
+               s);
+          qh_errexit(qh, qh_ERRinput, NULL, NULL);
+        }
+        return linecount;
+      }
+    }
+  }
+  qh_fprintf(qh, qh->ferr, 6073, "qhull input error: only %d coordinates.  Could not read %d-d feasible point.\n",
+           tokcount, dim);
+  qh_errexit(qh, qh_ERRinput, NULL, NULL);
+  return 0;
+} /* readfeasible */
+
+/*---------------------------------
+
+  qh_readpoints(qh, numpoints, dimension, ismalloc )
+    read points from qh.fin into qh.first_point, qh.num_points
+    qh.fin is lines of coordinates, one per vertex, first line number of points
+    if 'rbox D4',
+      gives message
+    if qh.ATinfinity,
+      adds point-at-infinity for Delaunay triangulations
+
+  returns:
+    number of points, array of point coordinates, dimension, ismalloc True
+    if qh.DELAUNAY & !qh.PROJECTinput, projects points to paraboloid
+        and clears qh.PROJECTdelaunay
+    if qh.HALFspace, reads optional feasible point, reads halfspaces,
+        converts to dual.
+
+  for feasible point in "cdd format" in 3-d:
+    3 1
+    coordinates
+    comments
+    begin
+    n 4 real/integer
+    ...
+    end
+
+  notes:
+    dimension will change in qh_initqhull_globals if qh.PROJECTinput
+    uses malloc() since qh_mem not initialized
+    FIXUP QH11012: qh_readpoints needs rewriting, too long
+*/
+coordT *qh_readpoints(qhT *qh, int *numpoints, int *dimension, boolT *ismalloc) {
+  coordT *points, *coords, *infinity= NULL;
+  realT paraboloid, maxboloid= -REALmax, value;
+  realT *coordp= NULL, *offsetp= NULL, *normalp= NULL;
+  char *s= 0, *t, firstline[qh_MAXfirst+1];
+  int diminput=0, numinput=0, dimfeasible= 0, newnum, k, tempi;
+  int firsttext=0, firstshort=0, firstlong=0, firstpoint=0;
+  int tokcount= 0, linecount=0, maxcount, coordcount=0;
+  boolT islong, isfirst= True, wasbegin= False;
+  boolT isdelaunay= qh->DELAUNAY && !qh->PROJECTinput;
+
+  if (qh->CDDinput) {
+    while ((s= fgets(firstline, qh_MAXfirst, qh->fin))) {
+      linecount++;
+      if (qh->HALFspace && linecount == 1 && isdigit(*s)) {
+        dimfeasible= qh_strtol(s, &s);
+        while (isspace(*s))
+          s++;
+        if (qh_strtol(s, &s) == 1)
+          linecount += qh_readfeasible(qh, dimfeasible, s);
+        else
+          dimfeasible= 0;
+      }else if (!memcmp(firstline, "begin", (size_t)5) || !memcmp(firstline, "BEGIN", (size_t)5))
+        break;
+      else if (!*qh->rbox_command)
+        strncat(qh->rbox_command, s, sizeof(qh->rbox_command)-1);
+    }
+    if (!s) {
+      qh_fprintf(qh, qh->ferr, 6074, "qhull input error: missing \"begin\" for cdd-formated input\n");
+      qh_errexit(qh, qh_ERRinput, NULL, NULL);
+    }
+  }
+  while (!numinput && (s= fgets(firstline, qh_MAXfirst, qh->fin))) {
+    linecount++;
+    if (!memcmp(s, "begin", (size_t)5) || !memcmp(s, "BEGIN", (size_t)5))
+      wasbegin= True;
+    while (*s) {
+      while (isspace(*s))
+        s++;
+      if (!*s)
+        break;
+      if (!isdigit(*s)) {
+        if (!*qh->rbox_command) {
+          strncat(qh->rbox_command, s, sizeof(qh->rbox_command)-1);
+          firsttext= linecount;
+        }
+        break;
+      }
+      if (!diminput)
+        diminput= qh_strtol(s, &s);
+      else {
+        numinput= qh_strtol(s, &s);
+        if (numinput == 1 && diminput >= 2 && qh->HALFspace && !qh->CDDinput) {
+          linecount += qh_readfeasible(qh, diminput, s); /* checks if ok */
+          dimfeasible= diminput;
+          diminput= numinput= 0;
+        }else
+          break;
+      }
+    }
+  }
+  if (!s) {
+    qh_fprintf(qh, qh->ferr, 6075, "qhull input error: short input file.  Did not find dimension and number of points\n");
+    qh_errexit(qh, qh_ERRinput, NULL, NULL);
+  }
+  if (diminput > numinput) {
+    tempi= diminput;    /* exchange dim and n, e.g., for cdd input format */
+    diminput= numinput;
+    numinput= tempi;
+  }
+  if (diminput < 2) {
+    qh_fprintf(qh, qh->ferr, 6220,"qhull input error: dimension %d(first number) should be at least 2\n",
+            diminput);
+    qh_errexit(qh, qh_ERRinput, NULL, NULL);
+  }
+  if (isdelaunay) {
+    qh->PROJECTdelaunay= False;
+    if (qh->CDDinput)
+      *dimension= diminput;
+    else
+      *dimension= diminput+1;
+    *numpoints= numinput;
+    if (qh->ATinfinity)
+      (*numpoints)++;
+  }else if (qh->HALFspace) {
+    *dimension= diminput - 1;
+    *numpoints= numinput;
+    if (diminput < 3) {
+      qh_fprintf(qh, qh->ferr, 6221,"qhull input error: dimension %d(first number, includes offset) should be at least 3 for halfspaces\n",
+            diminput);
+      qh_errexit(qh, qh_ERRinput, NULL, NULL);
+    }
+    if (dimfeasible) {
+      if (dimfeasible != *dimension) {
+        qh_fprintf(qh, qh->ferr, 6222,"qhull input error: dimension %d of feasible point is not one less than dimension %d for halfspaces\n",
+          dimfeasible, diminput);
+        qh_errexit(qh, qh_ERRinput, NULL, NULL);
+      }
+    }else
+      qh_setfeasible(qh, *dimension);
+  }else {
+    if (qh->CDDinput)
+      *dimension= diminput-1;
+    else
+      *dimension= diminput;
+    *numpoints= numinput;
+  }
+  qh->normal_size= *dimension * sizeof(coordT); /* for tracing with qh_printpoint */
+  if (qh->HALFspace) {
+    qh->half_space= coordp= (coordT*)qh_malloc(qh->normal_size + sizeof(coordT));
+    if (qh->CDDinput) {
+      offsetp= qh->half_space;
+      normalp= offsetp + 1;
+    }else {
+      normalp= qh->half_space;
+      offsetp= normalp + *dimension;
+    }
+  }
+  qh->maxline= diminput * (qh_REALdigits + 5);
+  maximize_(qh->maxline, 500);
+  qh->line= (char*)qh_malloc((qh->maxline+1) * sizeof(char));
+  *ismalloc= True;  /* use malloc since memory not setup */
+  coords= points= qh->temp_malloc=  /* numinput and diminput >=2 by QH6220 */
+        (coordT*)qh_malloc((*numpoints)*(*dimension)*sizeof(coordT));
+  if (!coords || !qh->line || (qh->HALFspace && !qh->half_space)) {
+    qh_fprintf(qh, qh->ferr, 6076, "qhull error: insufficient memory to read %d points\n",
+            numinput);
+    qh_errexit(qh, qh_ERRmem, NULL, NULL);
+  }
+  if (isdelaunay && qh->ATinfinity) {
+    infinity= points + numinput * (*dimension);
+    for (k= (*dimension) - 1; k--; )
+      infinity[k]= 0.0;
+  }
+  maxcount= numinput * diminput;
+  paraboloid= 0.0;
+  while ((s= (isfirst ?  s : fgets(qh->line, qh->maxline, qh->fin)))) {
+    if (!isfirst) {
+      linecount++;
+      if (*s == 'e' || *s == 'E') {
+        if (!memcmp(s, "end", (size_t)3) || !memcmp(s, "END", (size_t)3)) {
+          if (qh->CDDinput )
+            break;
+          else if (wasbegin)
+            qh_fprintf(qh, qh->ferr, 7058, "qhull input warning: the input appears to be in cdd format.  If so, use 'Fd'\n");
+        }
+      }
+    }
+    islong= False;
+    while (*s) {
+      while (isspace(*s))
+        s++;
+      value= qh_strtod(s, &t);
+      if (s == t) {
+        if (!*qh->rbox_command)
+         strncat(qh->rbox_command, s, sizeof(qh->rbox_command)-1);
+        if (*s && !firsttext)
+          firsttext= linecount;
+        if (!islong && !firstshort && coordcount)
+          firstshort= linecount;
+        break;
+      }
+      if (!firstpoint)
+        firstpoint= linecount;
+      s= t;
+      if (++tokcount > maxcount)
+        continue;
+      if (qh->HALFspace) {
+        if (qh->CDDinput)
+          *(coordp++)= -value; /* both coefficients and offset */
+        else
+          *(coordp++)= value;
+      }else {
+        *(coords++)= value;
+        if (qh->CDDinput && !coordcount) {
+          if (value != 1.0) {
+            qh_fprintf(qh, qh->ferr, 6077, "qhull input error: for cdd format, point at line %d does not start with '1'\n",
+                   linecount);
+            qh_errexit(qh, qh_ERRinput, NULL, NULL);
+          }
+          coords--;
+        }else if (isdelaunay) {
+          paraboloid += value * value;
+          if (qh->ATinfinity) {
+            if (qh->CDDinput)
+              infinity[coordcount-1] += value;
+            else
+              infinity[coordcount] += value;
+          }
+        }
+      }
+      if (++coordcount == diminput) {
+        coordcount= 0;
+        if (isdelaunay) {
+          *(coords++)= paraboloid;
+          maximize_(maxboloid, paraboloid);
+          paraboloid= 0.0;
+        }else if (qh->HALFspace) {
+          if (!qh_sethalfspace(qh, *dimension, coords, &coords, normalp, offsetp, qh->feasible_point)) {
+            qh_fprintf(qh, qh->ferr, 8048, "The halfspace was on line %d\n", linecount);
+            if (wasbegin)
+              qh_fprintf(qh, qh->ferr, 8049, "The input appears to be in cdd format.  If so, you should use option 'Fd'\n");
+            qh_errexit(qh, qh_ERRinput, NULL, NULL);
+          }
+          coordp= qh->half_space;
+        }
+        while (isspace(*s))
+          s++;
+        if (*s) {
+          islong= True;
+          if (!firstlong)
+            firstlong= linecount;
+        }
+      }
+    }
+    if (!islong && !firstshort && coordcount)
+      firstshort= linecount;
+    if (!isfirst && s - qh->line >= qh->maxline) {
+      qh_fprintf(qh, qh->ferr, 6078, "qhull input error: line %d contained more than %d characters\n",
+              linecount, (int) (s - qh->line));   /* WARN64 */
+      qh_errexit(qh, qh_ERRinput, NULL, NULL);
+    }
+    isfirst= False;
+  }
+  if (tokcount != maxcount) {
+    newnum= fmin_(numinput, tokcount/diminput);
+    qh_fprintf(qh, qh->ferr, 7073,"\
+qhull warning: instead of %d %d-dimensional points, input contains\n\
+%d points and %d extra coordinates.  Line %d is the first\npoint",
+       numinput, diminput, tokcount/diminput, tokcount % diminput, firstpoint);
+    if (firsttext)
+      qh_fprintf(qh, qh->ferr, 8051, ", line %d is the first comment", firsttext);
+    if (firstshort)
+      qh_fprintf(qh, qh->ferr, 8052, ", line %d is the first short\nline", firstshort);
+    if (firstlong)
+      qh_fprintf(qh, qh->ferr, 8053, ", line %d is the first long line", firstlong);
+    qh_fprintf(qh, qh->ferr, 8054, ".  Continue with %d points.\n", newnum);
+    numinput= newnum;
+    if (isdelaunay && qh->ATinfinity) {
+      for (k= tokcount % diminput; k--; )
+        infinity[k] -= *(--coords);
+      *numpoints= newnum+1;
+    }else {
+      coords -= tokcount % diminput;
+      *numpoints= newnum;
+    }
+  }
+  if (isdelaunay && qh->ATinfinity) {
+    for (k= (*dimension) -1; k--; )
+      infinity[k] /= numinput;
+    if (coords == infinity)
+      coords += (*dimension) -1;
+    else {
+      for (k=0; k < (*dimension) -1; k++)
+        *(coords++)= infinity[k];
+    }
+    *(coords++)= maxboloid * 1.1;
+  }
+  if (qh->rbox_command[0]) {
+    qh->rbox_command[strlen(qh->rbox_command)-1]= '\0';
+    if (!strcmp(qh->rbox_command, "./rbox D4"))
+      qh_fprintf(qh, qh->ferr, 8055, "\n\
+This is the qhull test case.  If any errors or core dumps occur,\n\
+recompile qhull with 'make new'.  If errors still occur, there is\n\
+an incompatibility.  You should try a different compiler.  You can also\n\
+change the choices in user.h.  If you discover the source of the problem,\n\
+please send mail to qhull_bug@qhull.org.\n\
+\n\
+Type 'qhull' for a short list of options.\n");
+  }
+  qh_free(qh->line);
+  qh->line= NULL;
+  if (qh->half_space) {
+    qh_free(qh->half_space);
+    qh->half_space= NULL;
+  }
+  qh->temp_malloc= NULL;
+  trace1((qh, qh->ferr, 1008,"qh_readpoints: read in %d %d-dimensional points\n",
+          numinput, diminput));
+  return(points);
+} /* readpoints */
+
+
+/*---------------------------------
+
+  qh_setfeasible(qh, dim )
+    set qh.feasible_point from qh.feasible_string in "n,n,n" or "n n n" format
+
+  notes:
+    "n,n,n" already checked by qh_initflags()
+    see qh_readfeasible()
+    called only once from qh_new_qhull, otherwise leaks memory
+*/
+void qh_setfeasible(qhT *qh, int dim) {
+  int tokcount= 0;
+  char *s;
+  coordT *coords, value;
+
+  if (!(s= qh->feasible_string)) {
+    qh_fprintf(qh, qh->ferr, 6223, "\
+qhull input error: halfspace intersection needs a feasible point.\n\
+Either prepend the input with 1 point or use 'Hn,n,n'.  See manual.\n");
+    qh_errexit(qh, qh_ERRinput, NULL, NULL);
+  }
+  if (!(qh->feasible_point= (pointT*)qh_malloc(dim * sizeof(coordT)))) {
+    qh_fprintf(qh, qh->ferr, 6079, "qhull error: insufficient memory for 'Hn,n,n'\n");
+    qh_errexit(qh, qh_ERRmem, NULL, NULL);
+  }
+  coords= qh->feasible_point;
+  while (*s) {
+    value= qh_strtod(s, &s);
+    if (++tokcount > dim) {
+      qh_fprintf(qh, qh->ferr, 7059, "qhull input warning: more coordinates for 'H%s' than dimension %d\n",
+          qh->feasible_string, dim);
+      break;
+    }
+    *(coords++)= value;
+    if (*s)
+      s++;
+  }
+  while (++tokcount <= dim)
+    *(coords++)= 0.0;
+} /* setfeasible */
+
+/*---------------------------------
+
+  qh_skipfacet(qh, facet )
+    returns 'True' if this facet is not to be printed
+
+  notes:
+    based on the user provided slice thresholds and 'good' specifications
+*/
+boolT qh_skipfacet(qhT *qh, facetT *facet) {
+  facetT *neighbor, **neighborp;
+
+  if (qh->PRINTneighbors) {
+    if (facet->good)
+      return !qh->PRINTgood;
+    FOREACHneighbor_(facet) {
+      if (neighbor->good)
+        return False;
+    }
+    return True;
+  }else if (qh->PRINTgood)
+    return !facet->good;
+  else if (!facet->normal)
+    return True;
+  return(!qh_inthresholds(qh, facet->normal, NULL));
+} /* skipfacet */
+
+/*---------------------------------
+
+  qh_skipfilename(qh, string )
+    returns pointer to character after filename
+
+  notes:
+    skips leading spaces
+    ends with spacing or eol
+    if starts with ' or " ends with the same, skipping \' or \"
+    For qhull, qh_argv_to_command() only uses double quotes
+*/
+char *qh_skipfilename(qhT *qh, char *filename) {
+  char *s= filename;  /* non-const due to return */
+  char c;
+
+  while (*s && isspace(*s))
+    s++;
+  c= *s++;
+  if (c == '\0') {
+    qh_fprintf(qh, qh->ferr, 6204, "qhull input error: filename expected, none found.\n");
+    qh_errexit(qh, qh_ERRinput, NULL, NULL);
+  }
+  if (c == '\'' || c == '"') {
+    while (*s !=c || s[-1] == '\\') {
+      if (!*s) {
+        qh_fprintf(qh, qh->ferr, 6203, "qhull input error: missing quote after filename -- %s\n", filename);
+        qh_errexit(qh, qh_ERRinput, NULL, NULL);
+      }
+      s++;
+    }
+    s++;
+  }
+  else while (*s && !isspace(*s))
+      s++;
+  return s;
+} /* skipfilename */
+
diff --git a/Cdir/libqhull_r.c b/Cdir/libqhull_r.c
new file mode 100644
--- /dev/null
+++ b/Cdir/libqhull_r.c
@@ -0,0 +1,1403 @@
+/*
  ---------------------------------
+
+   libqhull_r.c
+   Quickhull algorithm for convex hulls
+
+   qhull() and top-level routines
+
+   see qh-qhull_r.htm, libqhull.h, unix_r.c
+
+   see qhull_ra.h for internal functions
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull_r/libqhull_r.c#2 $$Change: 2047 $
+   $DateTime: 2016/01/04 22:03:18 $$Author: bbarber $
+*/
+
+#include "qhull_ra.h"
+
+/*============= functions in alphabetic order after qhull() =======*/
+
+/*---------------------------------
+
+  qh_qhull(qh)
+    compute DIM3 convex hull of qh.num_points starting at qh.first_point
+    qh->contains all global options and variables
+
+  returns:
+    returns polyhedron
+      qh.facet_list, qh.num_facets, qh.vertex_list, qh.num_vertices,
+
+    returns global variables
+      qh.hulltime, qh.max_outside, qh.interior_point, qh.max_vertex, qh.min_vertex
+
+    returns precision constants
+      qh.ANGLEround, centrum_radius, cos_max, DISTround, MAXabs_coord, ONEmerge
+
+  notes:
+    unless needed for output
+      qh.max_vertex and qh.min_vertex are max/min due to merges
+
+  see:
+    to add individual points to either qh.num_points
+      use qh_addpoint()
+
+    if qh.GETarea
+      qh_produceoutput() returns qh.totarea and qh.totvol via qh_getarea()
+
+  design:
+    record starting time
+    initialize hull and partition points
+    build convex hull
+    unless early termination
+      update facet->maxoutside for vertices, coplanar, and near-inside points
+    error if temporary sets exist
+    record end time
+*/
+
+void qh_qhull(qhT *qh) {
+  int numoutside;
+
+  qh->hulltime= qh_CPUclock;
+  if (qh->RERUN || qh->JOGGLEmax < REALmax/2)
+    qh_build_withrestart(qh);
+  else {
+    qh_initbuild(qh);
+    qh_buildhull(qh);
+  }
+  if (!qh->STOPpoint && !qh->STOPcone) {
+    if (qh->ZEROall_ok && !qh->TESTvneighbors && qh->MERGEexact)
+      qh_checkzero(qh, qh_ALL);
+    if (qh->ZEROall_ok && !qh->TESTvneighbors && !qh->WAScoplanar) {
+      trace2((qh, qh->ferr, 2055, "qh_qhull: all facets are clearly convex and no coplanar points.  Post-merging and check of maxout not needed.\n"));
+      qh->DOcheckmax= False;
+    }else {
+      if (qh->MERGEexact || (qh->hull_dim > qh_DIMreduceBuild && qh->PREmerge))
+        qh_postmerge(qh, "First post-merge", qh->premerge_centrum, qh->premerge_cos,
+             (qh->POSTmerge ? False : qh->TESTvneighbors));
+      else if (!qh->POSTmerge && qh->TESTvneighbors)
+        qh_postmerge(qh, "For testing vertex neighbors", qh->premerge_centrum,
+             qh->premerge_cos, True);
+      if (qh->POSTmerge)
+        qh_postmerge(qh, "For post-merging", qh->postmerge_centrum,
+             qh->postmerge_cos, qh->TESTvneighbors);
+      if (qh->visible_list == qh->facet_list) { /* i.e., merging done */
+        qh->findbestnew= True;
+        qh_partitionvisible(qh /*qh.visible_list*/, !qh_ALL, &numoutside);
+        qh->findbestnew= False;
+        qh_deletevisible(qh /*qh.visible_list*/);
+        qh_resetlists(qh, False, qh_RESETvisible /*qh.visible_list newvertex_list newfacet_list */);
+      }
+    }
+    if (qh->DOcheckmax){
+      if (qh->REPORTfreq) {
+        qh_buildtracing(qh, NULL, NULL);
+        qh_fprintf(qh, qh->ferr, 8115, "\nTesting all coplanar points.\n");
+      }
+      qh_check_maxout(qh);
+    }
+    if (qh->KEEPnearinside && !qh->maxoutdone)
+      qh_nearcoplanar(qh);
+  }
+  if (qh_setsize(qh, qh->qhmem.tempstack) != 0) {
+    qh_fprintf(qh, qh->ferr, 6164, "qhull internal error (qh_qhull): temporary sets not empty(%d)\n",
+             qh_setsize(qh, qh->qhmem.tempstack));
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }
+  qh->hulltime= qh_CPUclock - qh->hulltime;
+  qh->QHULLfinished= True;
+  trace1((qh, qh->ferr, 1036, "Qhull: algorithm completed\n"));
+} /* qhull */
+
+/*---------------------------------
+
+  qh_addpoint(qh, furthest, facet, checkdist )
+    add point (usually furthest point) above facet to hull
+    if checkdist,
+      check that point is above facet.
+      if point is not outside of the hull, uses qh_partitioncoplanar()
+      assumes that facet is defined by qh_findbestfacet()
+    else if facet specified,
+      assumes that point is above facet (major damage if below)
+    for Delaunay triangulations,
+      Use qh_setdelaunay() to lift point to paraboloid and scale by 'Qbb' if needed
+      Do not use options 'Qbk', 'QBk', or 'QbB' since they scale the coordinates.
+
+  returns:
+    returns False if user requested an early termination
+     qh.visible_list, newfacet_list, delvertex_list, NEWfacets may be defined
+    updates qh.facet_list, qh.num_facets, qh.vertex_list, qh.num_vertices
+    clear qh.maxoutdone (will need to call qh_check_maxout() for facet->maxoutside)
+    if unknown point, adds a pointer to qh.other_points
+      do not deallocate the point's coordinates
+
+  notes:
+    assumes point is near its best facet and not at a local minimum of a lens
+      distributions.  Use qh_findbestfacet to avoid this case.
+    uses qh.visible_list, qh.newfacet_list, qh.delvertex_list, qh.NEWfacets
+
+  see also:
+    qh_triangulate() -- triangulate non-simplicial facets
+
+  design:
+    add point to other_points if needed
+    if checkdist
+      if point not above facet
+        partition coplanar point
+        exit
+    exit if pre STOPpoint requested
+    find horizon and visible facets for point
+    make new facets for point to horizon
+    make hyperplanes for point
+    compute balance statistics
+    match neighboring new facets
+    update vertex neighbors and delete interior vertices
+    exit if STOPcone requested
+    merge non-convex new facets
+    if merge found, many merges, or 'Qf'
+       use qh_findbestnew() instead of qh_findbest()
+    partition outside points from visible facets
+    delete visible facets
+    check polyhedron if requested
+    exit if post STOPpoint requested
+    reset working lists of facets and vertices
+*/
+boolT qh_addpoint(qhT *qh, pointT *furthest, facetT *facet, boolT checkdist) {
+  int goodvisible, goodhorizon;
+  vertexT *vertex;
+  facetT *newfacet;
+  realT dist, newbalance, pbalance;
+  boolT isoutside= False;
+  int numpart, numpoints, numnew, firstnew;
+
+  qh->maxoutdone= False;
+  if (qh_pointid(qh, furthest) == qh_IDunknown)
+    qh_setappend(qh, &qh->other_points, furthest);
+  if (!facet) {
+    qh_fprintf(qh, qh->ferr, 6213, "qhull internal error (qh_addpoint): NULL facet.  Need to call qh_findbestfacet first\n");
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }
+  if (checkdist) {
+    facet= qh_findbest(qh, furthest, facet, !qh_ALL, !qh_ISnewfacets, !qh_NOupper,
+                        &dist, &isoutside, &numpart);
+    zzadd_(Zpartition, numpart);
+    if (!isoutside) {
+      zinc_(Znotmax);  /* last point of outsideset is no longer furthest. */
+      facet->notfurthest= True;
+      qh_partitioncoplanar(qh, furthest, facet, &dist);
+      return True;
+    }
+  }
+  qh_buildtracing(qh, furthest, facet);
+  if (qh->STOPpoint < 0 && qh->furthest_id == -qh->STOPpoint-1) {
+    facet->notfurthest= True;
+    return False;
+  }
+  qh_findhorizon(qh, furthest, facet, &goodvisible, &goodhorizon);
+  if (qh->ONLYgood && !(goodvisible+goodhorizon) && !qh->GOODclosest) {
+    zinc_(Znotgood);
+    facet->notfurthest= True;
+    /* last point of outsideset is no longer furthest.  This is ok
+       since all points of the outside are likely to be bad */
+    qh_resetlists(qh, False, qh_RESETvisible /*qh.visible_list newvertex_list newfacet_list */);
+    return True;
+  }
+  zzinc_(Zprocessed);
+  firstnew= qh->facet_id;
+  vertex= qh_makenewfacets(qh, furthest /*visible_list, attaches if !ONLYgood */);
+  qh_makenewplanes(qh /* newfacet_list */);
+  numnew= qh->facet_id - firstnew;
+  newbalance= numnew - (realT) (qh->num_facets-qh->num_visible)
+                         * qh->hull_dim/qh->num_vertices;
+  wadd_(Wnewbalance, newbalance);
+  wadd_(Wnewbalance2, newbalance * newbalance);
+  if (qh->ONLYgood
+  && !qh_findgood(qh, qh->newfacet_list, goodhorizon) && !qh->GOODclosest) {
+    FORALLnew_facets
+      qh_delfacet(qh, newfacet);
+    qh_delvertex(qh, vertex);
+    qh_resetlists(qh, True, qh_RESETvisible /*qh.visible_list newvertex_list newfacet_list */);
+    zinc_(Znotgoodnew);
+    facet->notfurthest= True;
+    return True;
+  }
+  if (qh->ONLYgood)
+    qh_attachnewfacets(qh /*visible_list*/);
+  qh_matchnewfacets(qh);
+  qh_updatevertices(qh);
+  if (qh->STOPcone && qh->furthest_id == qh->STOPcone-1) {
+    facet->notfurthest= True;
+    return False;  /* visible_list etc. still defined */
+  }
+  qh->findbestnew= False;
+  if (qh->PREmerge || qh->MERGEexact) {
+    qh_premerge(qh, vertex, qh->premerge_centrum, qh->premerge_cos);
+    if (qh_USEfindbestnew)
+      qh->findbestnew= True;
+    else {
+      FORALLnew_facets {
+        if (!newfacet->simplicial) {
+          qh->findbestnew= True;  /* use qh_findbestnew instead of qh_findbest*/
+          break;
+        }
+      }
+    }
+  }else if (qh->BESToutside)
+    qh->findbestnew= True;
+  qh_partitionvisible(qh /*qh.visible_list*/, !qh_ALL, &numpoints);
+  qh->findbestnew= False;
+  qh->findbest_notsharp= False;
+  zinc_(Zpbalance);
+  pbalance= numpoints - (realT) qh->hull_dim /* assumes all points extreme */
+                * (qh->num_points - qh->num_vertices)/qh->num_vertices;
+  wadd_(Wpbalance, pbalance);
+  wadd_(Wpbalance2, pbalance * pbalance);
+  qh_deletevisible(qh /*qh.visible_list*/);
+  zmax_(Zmaxvertex, qh->num_vertices);
+  qh->NEWfacets= False;
+  if (qh->IStracing >= 4) {
+    if (qh->num_facets < 2000)
+      qh_printlists(qh);
+    qh_printfacetlist(qh, qh->newfacet_list, NULL, True);
+    qh_checkpolygon(qh, qh->facet_list);
+  }else if (qh->CHECKfrequently) {
+    if (qh->num_facets < 50)
+      qh_checkpolygon(qh, qh->facet_list);
+    else
+      qh_checkpolygon(qh, qh->newfacet_list);
+  }
+  if (qh->STOPpoint > 0 && qh->furthest_id == qh->STOPpoint-1)
+    return False;
+  qh_resetlists(qh, True, qh_RESETvisible /*qh.visible_list newvertex_list newfacet_list */);
+  /* qh_triangulate(qh); to test qh.TRInormals */
+  trace2((qh, qh->ferr, 2056, "qh_addpoint: added p%d new facets %d new balance %2.2g point balance %2.2g\n",
+    qh_pointid(qh, furthest), numnew, newbalance, pbalance));
+  return True;
+} /* addpoint */
+
+/*---------------------------------
+
+  qh_build_withrestart(qh)
+    allow restarts due to qh.JOGGLEmax while calling qh_buildhull()
+       qh_errexit always undoes qh_build_withrestart()
+    qh.FIRSTpoint/qh.NUMpoints is point array
+       it may be moved by qh_joggleinput(qh)
+*/
+void qh_build_withrestart(qhT *qh) {
+  int restart;
+
+  qh->ALLOWrestart= True;
+  while (True) {
+    restart= setjmp(qh->restartexit); /* simple statement for CRAY J916 */
+    if (restart) {       /* only from qh_precision() */
+      zzinc_(Zretry);
+      wmax_(Wretrymax, qh->JOGGLEmax);
+      /* QH7078 warns about using 'TCn' with 'QJn' */
+      qh->STOPcone= qh_IDunknown; /* if break from joggle, prevents normal output */
+    }
+    if (!qh->RERUN && qh->JOGGLEmax < REALmax/2) {
+      if (qh->build_cnt > qh_JOGGLEmaxretry) {
+        qh_fprintf(qh, qh->ferr, 6229, "qhull precision error: %d attempts to construct a convex hull\n\
+        with joggled input.  Increase joggle above 'QJ%2.2g'\n\
+        or modify qh_JOGGLE... parameters in user.h\n",
+           qh->build_cnt, qh->JOGGLEmax);
+        qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+      }
+      if (qh->build_cnt && !restart)
+        break;
+    }else if (qh->build_cnt && qh->build_cnt >= qh->RERUN)
+      break;
+    qh->STOPcone= 0;
+    qh_freebuild(qh, True);  /* first call is a nop */
+    qh->build_cnt++;
+    if (!qh->qhull_optionsiz)
+      qh->qhull_optionsiz= (int)strlen(qh->qhull_options);   /* WARN64 */
+    else {
+      qh->qhull_options [qh->qhull_optionsiz]= '\0';
+      qh->qhull_optionlen= qh_OPTIONline;  /* starts a new line */
+    }
+    qh_option(qh, "_run", &qh->build_cnt, NULL);
+    if (qh->build_cnt == qh->RERUN) {
+      qh->IStracing= qh->TRACElastrun;  /* duplicated from qh_initqhull_globals */
+      if (qh->TRACEpoint != qh_IDunknown || qh->TRACEdist < REALmax/2 || qh->TRACEmerge) {
+        qh->TRACElevel= (qh->IStracing? qh->IStracing : 3);
+        qh->IStracing= 0;
+      }
+      qh->qhmem.IStracing= qh->IStracing;
+    }
+    if (qh->JOGGLEmax < REALmax/2)
+      qh_joggleinput(qh);
+    qh_initbuild(qh);
+    qh_buildhull(qh);
+    if (qh->JOGGLEmax < REALmax/2 && !qh->MERGING)
+      qh_checkconvex(qh, qh->facet_list, qh_ALGORITHMfault);
+  }
+  qh->ALLOWrestart= False;
+} /* qh_build_withrestart */
+
+/*---------------------------------
+
+  qh_buildhull(qh)
+    construct a convex hull by adding outside points one at a time
+
+  returns:
+
+  notes:
+    may be called multiple times
+    checks facet and vertex lists for incorrect flags
+    to recover from STOPcone, call qh_deletevisible and qh_resetlists
+
+  design:
+    check visible facet and newfacet flags
+    check newlist vertex flags and qh.STOPcone/STOPpoint
+    for each facet with a furthest outside point
+      add point to facet
+      exit if qh.STOPcone or qh.STOPpoint requested
+    if qh.NARROWhull for initial simplex
+      partition remaining outside points to coplanar sets
+*/
+void qh_buildhull(qhT *qh) {
+  facetT *facet;
+  pointT *furthest;
+  vertexT *vertex;
+  int id;
+
+  trace1((qh, qh->ferr, 1037, "qh_buildhull: start build hull\n"));
+  FORALLfacets {
+    if (facet->visible || facet->newfacet) {
+      qh_fprintf(qh, qh->ferr, 6165, "qhull internal error (qh_buildhull): visible or new facet f%d in facet list\n",
+                   facet->id);
+      qh_errexit(qh, qh_ERRqhull, facet, NULL);
+    }
+  }
+  FORALLvertices {
+    if (vertex->newlist) {
+      qh_fprintf(qh, qh->ferr, 6166, "qhull internal error (qh_buildhull): new vertex f%d in vertex list\n",
+                   vertex->id);
+      qh_errprint(qh, "ERRONEOUS", NULL, NULL, NULL, vertex);
+      qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+    }
+    id= qh_pointid(qh, vertex->point);
+    if ((qh->STOPpoint>0 && id == qh->STOPpoint-1) ||
+        (qh->STOPpoint<0 && id == -qh->STOPpoint-1) ||
+        (qh->STOPcone>0 && id == qh->STOPcone-1)) {
+      trace1((qh, qh->ferr, 1038,"qh_buildhull: stop point or cone P%d in initial hull\n", id));
+      return;
+    }
+  }
+  qh->facet_next= qh->facet_list;      /* advance facet when processed */
+  while ((furthest= qh_nextfurthest(qh, &facet))) {
+    qh->num_outside--;  /* if ONLYmax, furthest may not be outside */
+    if (!qh_addpoint(qh, furthest, facet, qh->ONLYmax))
+      break;
+  }
+  if (qh->NARROWhull) /* move points from outsideset to coplanarset */
+    qh_outcoplanar(qh /* facet_list */ );
+  if (qh->num_outside && !furthest) {
+    qh_fprintf(qh, qh->ferr, 6167, "qhull internal error (qh_buildhull): %d outside points were never processed.\n", qh->num_outside);
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }
+  trace1((qh, qh->ferr, 1039, "qh_buildhull: completed the hull construction\n"));
+} /* buildhull */
+
+
+/*---------------------------------
+
+  qh_buildtracing(qh, furthest, facet )
+    trace an iteration of qh_buildhull() for furthest point and facet
+    if !furthest, prints progress message
+
+  returns:
+    tracks progress with qh.lastreport
+    updates qh.furthest_id (-3 if furthest is NULL)
+    also resets visit_id, vertext_visit on wrap around
+
+  see:
+    qh_tracemerging()
+
+  design:
+    if !furthest
+      print progress message
+      exit
+    if 'TFn' iteration
+      print progress message
+    else if tracing
+      trace furthest point and facet
+    reset qh.visit_id and qh.vertex_visit if overflow may occur
+    set qh.furthest_id for tracing
+*/
+void qh_buildtracing(qhT *qh, pointT *furthest, facetT *facet) {
+  realT dist= 0;
+  float cpu;
+  int total, furthestid;
+  time_t timedata;
+  struct tm *tp;
+  vertexT *vertex;
+
+  qh->old_randomdist= qh->RANDOMdist;
+  qh->RANDOMdist= False;
+  if (!furthest) {
+    time(&timedata);
+    tp= localtime(&timedata);
+    cpu= (float)qh_CPUclock - (float)qh->hulltime;
+    cpu /= (float)qh_SECticks;
+    total= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
+    qh_fprintf(qh, qh->ferr, 8118, "\n\
+At %02d:%02d:%02d & %2.5g CPU secs, qhull has created %d facets and merged %d.\n\
+ The current hull contains %d facets and %d vertices.  Last point was p%d\n",
+      tp->tm_hour, tp->tm_min, tp->tm_sec, cpu, qh->facet_id -1,
+      total, qh->num_facets, qh->num_vertices, qh->furthest_id);
+    return;
+  }
+  furthestid= qh_pointid(qh, furthest);
+  if (qh->TRACEpoint == furthestid) {
+    qh->IStracing= qh->TRACElevel;
+    qh->qhmem.IStracing= qh->TRACElevel;
+  }else if (qh->TRACEpoint != qh_IDunknown && qh->TRACEdist < REALmax/2) {
+    qh->IStracing= 0;
+    qh->qhmem.IStracing= 0;
+  }
+  if (qh->REPORTfreq && (qh->facet_id-1 > qh->lastreport+qh->REPORTfreq)) {
+    qh->lastreport= qh->facet_id-1;
+    time(&timedata);
+    tp= localtime(&timedata);
+    cpu= (float)qh_CPUclock - (float)qh->hulltime;
+    cpu /= (float)qh_SECticks;
+    total= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
+    zinc_(Zdistio);
+    qh_distplane(qh, furthest, facet, &dist);
+    qh_fprintf(qh, qh->ferr, 8119, "\n\
+At %02d:%02d:%02d & %2.5g CPU secs, qhull has created %d facets and merged %d.\n\
+ The current hull contains %d facets and %d vertices.  There are %d\n\
+ outside points.  Next is point p%d(v%d), %2.2g above f%d.\n",
+      tp->tm_hour, tp->tm_min, tp->tm_sec, cpu, qh->facet_id -1,
+      total, qh->num_facets, qh->num_vertices, qh->num_outside+1,
+      furthestid, qh->vertex_id, dist, getid_(facet));
+  }else if (qh->IStracing >=1) {
+    cpu= (float)qh_CPUclock - (float)qh->hulltime;
+    cpu /= (float)qh_SECticks;
+    qh_distplane(qh, furthest, facet, &dist);
+    qh_fprintf(qh, qh->ferr, 8120, "qh_addpoint: add p%d(v%d) to hull of %d facets(%2.2g above f%d) and %d outside at %4.4g CPU secs.  Previous was p%d.\n",
+      furthestid, qh->vertex_id, qh->num_facets, dist,
+      getid_(facet), qh->num_outside+1, cpu, qh->furthest_id);
+  }
+  zmax_(Zvisit2max, (int)qh->visit_id/2);
+  if (qh->visit_id > (unsigned) INT_MAX) { /* 31 bits */
+    zinc_(Zvisit);
+    qh->visit_id= 0;
+    FORALLfacets
+      facet->visitid= 0;
+  }
+  zmax_(Zvvisit2max, (int)qh->vertex_visit/2);
+  if (qh->vertex_visit > (unsigned) INT_MAX) { /* 31 bits */ 
+    zinc_(Zvvisit);
+    qh->vertex_visit= 0;
+    FORALLvertices
+      vertex->visitid= 0;
+  }
+  qh->furthest_id= furthestid;
+  qh->RANDOMdist= qh->old_randomdist;
+} /* buildtracing */
+
+/*---------------------------------
+
+  qh_errexit2(qh, exitcode, facet, otherfacet )
+    return exitcode to system after an error
+    report two facets
+
+  returns:
+    assumes exitcode non-zero
+
+  see:
+    normally use qh_errexit() in user.c(reports a facet and a ridge)
+*/
+void qh_errexit2(qhT *qh, int exitcode, facetT *facet, facetT *otherfacet) {
+
+  qh_errprint(qh, "ERRONEOUS", facet, otherfacet, NULL, NULL);
+  qh_errexit(qh, exitcode, NULL, NULL);
+} /* errexit2 */
+
+
+/*---------------------------------
+
+  qh_findhorizon(qh, point, facet, goodvisible, goodhorizon )
+    given a visible facet, find the point's horizon and visible facets
+    for all facets, !facet-visible
+
+  returns:
+    returns qh.visible_list/num_visible with all visible facets
+      marks visible facets with ->visible
+    updates count of good visible and good horizon facets
+    updates qh.max_outside, qh.max_vertex, facet->maxoutside
+
+  see:
+    similar to qh_delpoint()
+
+  design:
+    move facet to qh.visible_list at end of qh.facet_list
+    for all visible facets
+     for each unvisited neighbor of a visible facet
+       compute distance of point to neighbor
+       if point above neighbor
+         move neighbor to end of qh.visible_list
+       else if point is coplanar with neighbor
+         update qh.max_outside, qh.max_vertex, neighbor->maxoutside
+         mark neighbor coplanar (will create a samecycle later)
+         update horizon statistics
+*/
+void qh_findhorizon(qhT *qh, pointT *point, facetT *facet, int *goodvisible, int *goodhorizon) {
+  facetT *neighbor, **neighborp, *visible;
+  int numhorizon= 0, coplanar= 0;
+  realT dist;
+
+  trace1((qh, qh->ferr, 1040,"qh_findhorizon: find horizon for point p%d facet f%d\n",qh_pointid(qh, point),facet->id));
+  *goodvisible= *goodhorizon= 0;
+  zinc_(Ztotvisible);
+  qh_removefacet(qh, facet);  /* visible_list at end of qh->facet_list */
+  qh_appendfacet(qh, facet);
+  qh->num_visible= 1;
+  if (facet->good)
+    (*goodvisible)++;
+  qh->visible_list= facet;
+  facet->visible= True;
+  facet->f.replace= NULL;
+  if (qh->IStracing >=4)
+    qh_errprint(qh, "visible", facet, NULL, NULL, NULL);
+  qh->visit_id++;
+  FORALLvisible_facets {
+    if (visible->tricoplanar && !qh->TRInormals) {
+      qh_fprintf(qh, qh->ferr, 6230, "Qhull internal error (qh_findhorizon): does not work for tricoplanar facets.  Use option 'Q11'\n");
+      qh_errexit(qh, qh_ERRqhull, visible, NULL);
+    }
+    visible->visitid= qh->visit_id;
+    FOREACHneighbor_(visible) {
+      if (neighbor->visitid == qh->visit_id)
+        continue;
+      neighbor->visitid= qh->visit_id;
+      zzinc_(Znumvisibility);
+      qh_distplane(qh, point, neighbor, &dist);
+      if (dist > qh->MINvisible) {
+        zinc_(Ztotvisible);
+        qh_removefacet(qh, neighbor);  /* append to end of qh->visible_list */
+        qh_appendfacet(qh, neighbor);
+        neighbor->visible= True;
+        neighbor->f.replace= NULL;
+        qh->num_visible++;
+        if (neighbor->good)
+          (*goodvisible)++;
+        if (qh->IStracing >=4)
+          qh_errprint(qh, "visible", neighbor, NULL, NULL, NULL);
+      }else {
+        if (dist > - qh->MAXcoplanar) {
+          neighbor->coplanar= True;
+          zzinc_(Zcoplanarhorizon);
+          qh_precision(qh, "coplanar horizon");
+          coplanar++;
+          if (qh->MERGING) {
+            if (dist > 0) {
+              maximize_(qh->max_outside, dist);
+              maximize_(qh->max_vertex, dist);
+#if qh_MAXoutside
+              maximize_(neighbor->maxoutside, dist);
+#endif
+            }else
+              minimize_(qh->min_vertex, dist);  /* due to merge later */
+          }
+          trace2((qh, qh->ferr, 2057, "qh_findhorizon: point p%d is coplanar to horizon f%d, dist=%2.7g < qh->MINvisible(%2.7g)\n",
+              qh_pointid(qh, point), neighbor->id, dist, qh->MINvisible));
+        }else
+          neighbor->coplanar= False;
+        zinc_(Ztothorizon);
+        numhorizon++;
+        if (neighbor->good)
+          (*goodhorizon)++;
+        if (qh->IStracing >=4)
+          qh_errprint(qh, "horizon", neighbor, NULL, NULL, NULL);
+      }
+    }
+  }
+  if (!numhorizon) {
+    qh_precision(qh, "empty horizon");
+    qh_fprintf(qh, qh->ferr, 6168, "qhull precision error (qh_findhorizon): empty horizon\n\
+QhullPoint p%d was above all facets.\n", qh_pointid(qh, point));
+    qh_printfacetlist(qh, qh->facet_list, NULL, True);
+    qh_errexit(qh, qh_ERRprec, NULL, NULL);
+  }
+  trace1((qh, qh->ferr, 1041, "qh_findhorizon: %d horizon facets(good %d), %d visible(good %d), %d coplanar\n",
+       numhorizon, *goodhorizon, qh->num_visible, *goodvisible, coplanar));
+  if (qh->IStracing >= 4 && qh->num_facets < 50)
+    qh_printlists(qh);
+} /* findhorizon */
+
+/*---------------------------------
+
+  qh_nextfurthest(qh, visible )
+    returns next furthest point and visible facet for qh_addpoint()
+    starts search at qh.facet_next
+
+  returns:
+    removes furthest point from outside set
+    NULL if none available
+    advances qh.facet_next over facets with empty outside sets
+
+  design:
+    for each facet from qh.facet_next
+      if empty outside set
+        advance qh.facet_next
+      else if qh.NARROWhull
+        determine furthest outside point
+        if furthest point is not outside
+          advance qh.facet_next(point will be coplanar)
+    remove furthest point from outside set
+*/
+pointT *qh_nextfurthest(qhT *qh, facetT **visible) {
+  facetT *facet;
+  int size, idx;
+  realT randr, dist;
+  pointT *furthest;
+
+  while ((facet= qh->facet_next) != qh->facet_tail) {
+    if (!facet->outsideset) {
+      qh->facet_next= facet->next;
+      continue;
+    }
+    SETreturnsize_(facet->outsideset, size);
+    if (!size) {
+      qh_setfree(qh, &facet->outsideset);
+      qh->facet_next= facet->next;
+      continue;
+    }
+    if (qh->NARROWhull) {
+      if (facet->notfurthest)
+        qh_furthestout(qh, facet);
+      furthest= (pointT*)qh_setlast(facet->outsideset);
+#if qh_COMPUTEfurthest
+      qh_distplane(qh, furthest, facet, &dist);
+      zinc_(Zcomputefurthest);
+#else
+      dist= facet->furthestdist;
+#endif
+      if (dist < qh->MINoutside) { /* remainder of outside set is coplanar for qh_outcoplanar */
+        qh->facet_next= facet->next;
+        continue;
+      }
+    }
+    if (!qh->RANDOMoutside && !qh->VIRTUALmemory) {
+      if (qh->PICKfurthest) {
+        qh_furthestnext(qh /* qh->facet_list */);
+        facet= qh->facet_next;
+      }
+      *visible= facet;
+      return((pointT*)qh_setdellast(facet->outsideset));
+    }
+    if (qh->RANDOMoutside) {
+      int outcoplanar = 0;
+      if (qh->NARROWhull) {
+        FORALLfacets {
+          if (facet == qh->facet_next)
+            break;
+          if (facet->outsideset)
+            outcoplanar += qh_setsize(qh, facet->outsideset);
+        }
+      }
+      randr= qh_RANDOMint;
+      randr= randr/(qh_RANDOMmax+1);
+      idx= (int)floor((qh->num_outside - outcoplanar) * randr);
+      FORALLfacet_(qh->facet_next) {
+        if (facet->outsideset) {
+          SETreturnsize_(facet->outsideset, size);
+          if (!size)
+            qh_setfree(qh, &facet->outsideset);
+          else if (size > idx) {
+            *visible= facet;
+            return((pointT*)qh_setdelnth(qh, facet->outsideset, idx));
+          }else
+            idx -= size;
+        }
+      }
+      qh_fprintf(qh, qh->ferr, 6169, "qhull internal error (qh_nextfurthest): num_outside %d is too low\nby at least %d, or a random real %g >= 1.0\n",
+              qh->num_outside, idx+1, randr);
+      qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+    }else { /* VIRTUALmemory */
+      facet= qh->facet_tail->previous;
+      if (!(furthest= (pointT*)qh_setdellast(facet->outsideset))) {
+        if (facet->outsideset)
+          qh_setfree(qh, &facet->outsideset);
+        qh_removefacet(qh, facet);
+        qh_prependfacet(qh, facet, &qh->facet_list);
+        continue;
+      }
+      *visible= facet;
+      return furthest;
+    }
+  }
+  return NULL;
+} /* nextfurthest */
+
+/*---------------------------------
+
+  qh_partitionall(qh, vertices, points, numpoints )
+    partitions all points in points/numpoints to the outsidesets of facets
+    vertices= vertices in qh.facet_list(!partitioned)
+
+  returns:
+    builds facet->outsideset
+    does not partition qh.GOODpoint
+    if qh.ONLYgood && !qh.MERGING,
+      does not partition qh.GOODvertex
+
+  notes:
+    faster if qh.facet_list sorted by anticipated size of outside set
+
+  design:
+    initialize pointset with all points
+    remove vertices from pointset
+    remove qh.GOODpointp from pointset (unless it's qh.STOPcone or qh.STOPpoint)
+    for all facets
+      for all remaining points in pointset
+        compute distance from point to facet
+        if point is outside facet
+          remove point from pointset (by not reappending)
+          update bestpoint
+          append point or old bestpoint to facet's outside set
+      append bestpoint to facet's outside set (furthest)
+    for all points remaining in pointset
+      partition point into facets' outside sets and coplanar sets
+*/
+void qh_partitionall(qhT *qh, setT *vertices, pointT *points, int numpoints){
+  setT *pointset;
+  vertexT *vertex, **vertexp;
+  pointT *point, **pointp, *bestpoint;
+  int size, point_i, point_n, point_end, remaining, i, id;
+  facetT *facet;
+  realT bestdist= -REALmax, dist, distoutside;
+
+  trace1((qh, qh->ferr, 1042, "qh_partitionall: partition all points into outside sets\n"));
+  pointset= qh_settemp(qh, numpoints);
+  qh->num_outside= 0;
+  pointp= SETaddr_(pointset, pointT);
+  for (i=numpoints, point= points; i--; point += qh->hull_dim)
+    *(pointp++)= point;
+  qh_settruncate(qh, pointset, numpoints);
+  FOREACHvertex_(vertices) {
+    if ((id= qh_pointid(qh, vertex->point)) >= 0)
+      SETelem_(pointset, id)= NULL;
+  }
+  id= qh_pointid(qh, qh->GOODpointp);
+  if (id >=0 && qh->STOPcone-1 != id && -qh->STOPpoint-1 != id)
+    SETelem_(pointset, id)= NULL;
+  if (qh->GOODvertexp && qh->ONLYgood && !qh->MERGING) { /* matches qhull()*/
+    if ((id= qh_pointid(qh, qh->GOODvertexp)) >= 0)
+      SETelem_(pointset, id)= NULL;
+  }
+  if (!qh->BESToutside) {  /* matches conditional for qh_partitionpoint below */
+    distoutside= qh_DISToutside; /* multiple of qh.MINoutside & qh.max_outside, see user.h */
+    zval_(Ztotpartition)= qh->num_points - qh->hull_dim - 1; /*misses GOOD... */
+    remaining= qh->num_facets;
+    point_end= numpoints;
+    FORALLfacets {
+      size= point_end/(remaining--) + 100;
+      facet->outsideset= qh_setnew(qh, size);
+      bestpoint= NULL;
+      point_end= 0;
+      FOREACHpoint_i_(qh, pointset) {
+        if (point) {
+          zzinc_(Zpartitionall);
+          qh_distplane(qh, point, facet, &dist);
+          if (dist < distoutside)
+            SETelem_(pointset, point_end++)= point;
+          else {
+            qh->num_outside++;
+            if (!bestpoint) {
+              bestpoint= point;
+              bestdist= dist;
+            }else if (dist > bestdist) {
+              qh_setappend(qh, &facet->outsideset, bestpoint);
+              bestpoint= point;
+              bestdist= dist;
+            }else
+              qh_setappend(qh, &facet->outsideset, point);
+          }
+        }
+      }
+      if (bestpoint) {
+        qh_setappend(qh, &facet->outsideset, bestpoint);
+#if !qh_COMPUTEfurthest
+        facet->furthestdist= bestdist;
+#endif
+      }else
+        qh_setfree(qh, &facet->outsideset);
+      qh_settruncate(qh, pointset, point_end);
+    }
+  }
+  /* if !qh->BESToutside, pointset contains points not assigned to outsideset */
+  if (qh->BESToutside || qh->MERGING || qh->KEEPcoplanar || qh->KEEPinside) {
+    qh->findbestnew= True;
+    FOREACHpoint_i_(qh, pointset) {
+      if (point)
+        qh_partitionpoint(qh, point, qh->facet_list);
+    }
+    qh->findbestnew= False;
+  }
+  zzadd_(Zpartitionall, zzval_(Zpartition));
+  zzval_(Zpartition)= 0;
+  qh_settempfree(qh, &pointset);
+  if (qh->IStracing >= 4)
+    qh_printfacetlist(qh, qh->facet_list, NULL, True);
+} /* partitionall */
+
+
+/*---------------------------------
+
+  qh_partitioncoplanar(qh, point, facet, dist )
+    partition coplanar point to a facet
+    dist is distance from point to facet
+    if dist NULL,
+      searches for bestfacet and does nothing if inside
+    if qh.findbestnew set,
+      searches new facets instead of using qh_findbest()
+
+  returns:
+    qh.max_ouside updated
+    if qh.KEEPcoplanar or qh.KEEPinside
+      point assigned to best coplanarset
+
+  notes:
+    facet->maxoutside is updated at end by qh_check_maxout
+
+  design:
+    if dist undefined
+      find best facet for point
+      if point sufficiently below facet (depends on qh.NEARinside and qh.KEEPinside)
+        exit
+    if keeping coplanar/nearinside/inside points
+      if point is above furthest coplanar point
+        append point to coplanar set (it is the new furthest)
+        update qh.max_outside
+      else
+        append point one before end of coplanar set
+    else if point is clearly outside of qh.max_outside and bestfacet->coplanarset
+    and bestfacet is more than perpendicular to facet
+      repartition the point using qh_findbest() -- it may be put on an outsideset
+    else
+      update qh.max_outside
+*/
+void qh_partitioncoplanar(qhT *qh, pointT *point, facetT *facet, realT *dist) {
+  facetT *bestfacet;
+  pointT *oldfurthest;
+  realT bestdist, dist2= 0, angle;
+  int numpart= 0, oldfindbest;
+  boolT isoutside;
+
+  qh->WAScoplanar= True;
+  if (!dist) {
+    if (qh->findbestnew)
+      bestfacet= qh_findbestnew(qh, point, facet, &bestdist, qh_ALL, &isoutside, &numpart);
+    else
+      bestfacet= qh_findbest(qh, point, facet, qh_ALL, !qh_ISnewfacets, qh->DELAUNAY,
+                          &bestdist, &isoutside, &numpart);
+    zinc_(Ztotpartcoplanar);
+    zzadd_(Zpartcoplanar, numpart);
+    if (!qh->DELAUNAY && !qh->KEEPinside) { /*  for 'd', bestdist skips upperDelaunay facets */
+      if (qh->KEEPnearinside) {
+        if (bestdist < -qh->NEARinside) {
+          zinc_(Zcoplanarinside);
+          trace4((qh, qh->ferr, 4062, "qh_partitioncoplanar: point p%d is more than near-inside facet f%d dist %2.2g findbestnew %d\n",
+                  qh_pointid(qh, point), bestfacet->id, bestdist, qh->findbestnew));
+          return;
+        }
+      }else if (bestdist < -qh->MAXcoplanar) {
+          trace4((qh, qh->ferr, 4063, "qh_partitioncoplanar: point p%d is inside facet f%d dist %2.2g findbestnew %d\n",
+                  qh_pointid(qh, point), bestfacet->id, bestdist, qh->findbestnew));
+        zinc_(Zcoplanarinside);
+        return;
+      }
+    }
+  }else {
+    bestfacet= facet;
+    bestdist= *dist;
+  }
+  if (bestdist > qh->max_outside) {
+    if (!dist && facet != bestfacet) {
+      zinc_(Zpartangle);
+      angle= qh_getangle(qh, facet->normal, bestfacet->normal);
+      if (angle < 0) {
+        /* typically due to deleted vertex and coplanar facets, e.g.,
+             RBOX 1000 s Z1 G1e-13 t1001185205 | QHULL Tv */
+        zinc_(Zpartflip);
+        trace2((qh, qh->ferr, 2058, "qh_partitioncoplanar: repartition point p%d from f%d.  It is above flipped facet f%d dist %2.2g\n",
+                qh_pointid(qh, point), facet->id, bestfacet->id, bestdist));
+        oldfindbest= qh->findbestnew;
+        qh->findbestnew= False;
+        qh_partitionpoint(qh, point, bestfacet);
+        qh->findbestnew= oldfindbest;
+        return;
+      }
+    }
+    qh->max_outside= bestdist;
+    if (bestdist > qh->TRACEdist) {
+      qh_fprintf(qh, qh->ferr, 8122, "qh_partitioncoplanar: ====== p%d from f%d increases max_outside to %2.2g of f%d last p%d\n",
+                     qh_pointid(qh, point), facet->id, bestdist, bestfacet->id, qh->furthest_id);
+      qh_errprint(qh, "DISTANT", facet, bestfacet, NULL, NULL);
+    }
+  }
+  if (qh->KEEPcoplanar + qh->KEEPinside + qh->KEEPnearinside) {
+    oldfurthest= (pointT*)qh_setlast(bestfacet->coplanarset);
+    if (oldfurthest) {
+      zinc_(Zcomputefurthest);
+      qh_distplane(qh, oldfurthest, bestfacet, &dist2);
+    }
+    if (!oldfurthest || dist2 < bestdist)
+      qh_setappend(qh, &bestfacet->coplanarset, point);
+    else
+      qh_setappend2ndlast(qh, &bestfacet->coplanarset, point);
+  }
+  trace4((qh, qh->ferr, 4064, "qh_partitioncoplanar: point p%d is coplanar with facet f%d(or inside) dist %2.2g\n",
+          qh_pointid(qh, point), bestfacet->id, bestdist));
+} /* partitioncoplanar */
+
+/*---------------------------------
+
+  qh_partitionpoint(qh, point, facet )
+    assigns point to an outside set, coplanar set, or inside set (i.e., dropt)
+    if qh.findbestnew
+      uses qh_findbestnew() to search all new facets
+    else
+      uses qh_findbest()
+
+  notes:
+    after qh_distplane(), this and qh_findbest() are most expensive in 3-d
+
+  design:
+    find best facet for point
+      (either exhaustive search of new facets or directed search from facet)
+    if qh.NARROWhull
+      retain coplanar and nearinside points as outside points
+    if point is outside bestfacet
+      if point above furthest point for bestfacet
+        append point to outside set (it becomes the new furthest)
+        if outside set was empty
+          move bestfacet to end of qh.facet_list (i.e., after qh.facet_next)
+        update bestfacet->furthestdist
+      else
+        append point one before end of outside set
+    else if point is coplanar to bestfacet
+      if keeping coplanar points or need to update qh.max_outside
+        partition coplanar point into bestfacet
+    else if near-inside point
+      partition as coplanar point into bestfacet
+    else is an inside point
+      if keeping inside points
+        partition as coplanar point into bestfacet
+*/
+void qh_partitionpoint(qhT *qh, pointT *point, facetT *facet) {
+  realT bestdist;
+  boolT isoutside;
+  facetT *bestfacet;
+  int numpart;
+#if qh_COMPUTEfurthest
+  realT dist;
+#endif
+
+  if (qh->findbestnew)
+    bestfacet= qh_findbestnew(qh, point, facet, &bestdist, qh->BESToutside, &isoutside, &numpart);
+  else
+    bestfacet= qh_findbest(qh, point, facet, qh->BESToutside, qh_ISnewfacets, !qh_NOupper,
+                          &bestdist, &isoutside, &numpart);
+  zinc_(Ztotpartition);
+  zzadd_(Zpartition, numpart);
+  if (qh->NARROWhull) {
+    if (qh->DELAUNAY && !isoutside && bestdist >= -qh->MAXcoplanar)
+      qh_precision(qh, "nearly incident point(narrow hull)");
+    if (qh->KEEPnearinside) {
+      if (bestdist >= -qh->NEARinside)
+        isoutside= True;
+    }else if (bestdist >= -qh->MAXcoplanar)
+      isoutside= True;
+  }
+
+  if (isoutside) {
+    if (!bestfacet->outsideset
+    || !qh_setlast(bestfacet->outsideset)) {
+      qh_setappend(qh, &(bestfacet->outsideset), point);
+      if (!bestfacet->newfacet) {
+        qh_removefacet(qh, bestfacet);  /* make sure it's after qh->facet_next */
+        qh_appendfacet(qh, bestfacet);
+      }
+#if !qh_COMPUTEfurthest
+      bestfacet->furthestdist= bestdist;
+#endif
+    }else {
+#if qh_COMPUTEfurthest
+      zinc_(Zcomputefurthest);
+      qh_distplane(qh, oldfurthest, bestfacet, &dist);
+      if (dist < bestdist)
+        qh_setappend(qh, &(bestfacet->outsideset), point);
+      else
+        qh_setappend2ndlast(qh, &(bestfacet->outsideset), point);
+#else
+      if (bestfacet->furthestdist < bestdist) {
+        qh_setappend(qh, &(bestfacet->outsideset), point);
+        bestfacet->furthestdist= bestdist;
+      }else
+        qh_setappend2ndlast(qh, &(bestfacet->outsideset), point);
+#endif
+    }
+    qh->num_outside++;
+    trace4((qh, qh->ferr, 4065, "qh_partitionpoint: point p%d is outside facet f%d new? %d (or narrowhull)\n",
+          qh_pointid(qh, point), bestfacet->id, bestfacet->newfacet));
+  }else if (qh->DELAUNAY || bestdist >= -qh->MAXcoplanar) { /* for 'd', bestdist skips upperDelaunay facets */
+    zzinc_(Zcoplanarpart);
+    if (qh->DELAUNAY)
+      qh_precision(qh, "nearly incident point");
+    if ((qh->KEEPcoplanar + qh->KEEPnearinside) || bestdist > qh->max_outside)
+      qh_partitioncoplanar(qh, point, bestfacet, &bestdist);
+    else {
+      trace4((qh, qh->ferr, 4066, "qh_partitionpoint: point p%d is coplanar to facet f%d (dropped)\n",
+          qh_pointid(qh, point), bestfacet->id));
+    }
+  }else if (qh->KEEPnearinside && bestdist > -qh->NEARinside) {
+    zinc_(Zpartnear);
+    qh_partitioncoplanar(qh, point, bestfacet, &bestdist);
+  }else {
+    zinc_(Zpartinside);
+    trace4((qh, qh->ferr, 4067, "qh_partitionpoint: point p%d is inside all facets, closest to f%d dist %2.2g\n",
+          qh_pointid(qh, point), bestfacet->id, bestdist));
+    if (qh->KEEPinside)
+      qh_partitioncoplanar(qh, point, bestfacet, &bestdist);
+  }
+} /* partitionpoint */
+
+/*---------------------------------
+
+  qh_partitionvisible(qh, allpoints, numoutside )
+    partitions points in visible facets to qh.newfacet_list
+    qh.visible_list= visible facets
+    for visible facets
+      1st neighbor (if any) points to a horizon facet or a new facet
+    if allpoints(!used),
+      repartitions coplanar points
+
+  returns:
+    updates outside sets and coplanar sets of qh.newfacet_list
+    updates qh.num_outside (count of outside points)
+
+  notes:
+    qh.findbest_notsharp should be clear (extra work if set)
+
+  design:
+    for all visible facets with outside set or coplanar set
+      select a newfacet for visible facet
+      if outside set
+        partition outside set into new facets
+      if coplanar set and keeping coplanar/near-inside/inside points
+        if allpoints
+          partition coplanar set into new facets, may be assigned outside
+        else
+          partition coplanar set into coplanar sets of new facets
+    for each deleted vertex
+      if allpoints
+        partition vertex into new facets, may be assigned outside
+      else
+        partition vertex into coplanar sets of new facets
+*/
+void qh_partitionvisible(qhT *qh /*qh.visible_list*/, boolT allpoints, int *numoutside) {
+  facetT *visible, *newfacet;
+  pointT *point, **pointp;
+  int coplanar=0, size;
+  unsigned count;
+  vertexT *vertex, **vertexp;
+
+  if (qh->ONLYmax)
+    maximize_(qh->MINoutside, qh->max_vertex);
+  *numoutside= 0;
+  FORALLvisible_facets {
+    if (!visible->outsideset && !visible->coplanarset)
+      continue;
+    newfacet= visible->f.replace;
+    count= 0;
+    while (newfacet && newfacet->visible) {
+      newfacet= newfacet->f.replace;
+      if (count++ > qh->facet_id)
+        qh_infiniteloop(qh, visible);
+    }
+    if (!newfacet)
+      newfacet= qh->newfacet_list;
+    if (newfacet == qh->facet_tail) {
+      qh_fprintf(qh, qh->ferr, 6170, "qhull precision error (qh_partitionvisible): all new facets deleted as\n        degenerate facets. Can not continue.\n");
+      qh_errexit(qh, qh_ERRprec, NULL, NULL);
+    }
+    if (visible->outsideset) {
+      size= qh_setsize(qh, visible->outsideset);
+      *numoutside += size;
+      qh->num_outside -= size;
+      FOREACHpoint_(visible->outsideset)
+        qh_partitionpoint(qh, point, newfacet);
+    }
+    if (visible->coplanarset && (qh->KEEPcoplanar + qh->KEEPinside + qh->KEEPnearinside)) {
+      size= qh_setsize(qh, visible->coplanarset);
+      coplanar += size;
+      FOREACHpoint_(visible->coplanarset) {
+        if (allpoints) /* not used */
+          qh_partitionpoint(qh, point, newfacet);
+        else
+          qh_partitioncoplanar(qh, point, newfacet, NULL);
+      }
+    }
+  }
+  FOREACHvertex_(qh->del_vertices) {
+    if (vertex->point) {
+      if (allpoints) /* not used */
+        qh_partitionpoint(qh, vertex->point, qh->newfacet_list);
+      else
+        qh_partitioncoplanar(qh, vertex->point, qh->newfacet_list, NULL);
+    }
+  }
+  trace1((qh, qh->ferr, 1043,"qh_partitionvisible: partitioned %d points from outsidesets and %d points from coplanarsets\n", *numoutside, coplanar));
+} /* partitionvisible */
+
+
+
+/*---------------------------------
+
+  qh_precision(qh, reason )
+    restart on precision errors if not merging and if 'QJn'
+*/
+void qh_precision(qhT *qh, const char *reason) {
+
+  if (qh->ALLOWrestart && !qh->PREmerge && !qh->MERGEexact) {
+    if (qh->JOGGLEmax < REALmax/2) {
+      trace0((qh, qh->ferr, 26, "qh_precision: qhull restart because of %s\n", reason));
+      /* May be called repeatedly if qh->ALLOWrestart */
+      longjmp(qh->restartexit, qh_ERRprec);
+    }
+  }
+} /* qh_precision */
+
+/*---------------------------------
+
+  qh_printsummary(qh, fp )
+    prints summary to fp
+
+  notes:
+    not in io_r.c so that user_eg.c can prevent io_r.c from loading
+    qh_printsummary and qh_countfacets must match counts
+
+  design:
+    determine number of points, vertices, and coplanar points
+    print summary
+*/
+void qh_printsummary(qhT *qh, FILE *fp) {
+  realT ratio, outerplane, innerplane;
+  float cpu;
+  int size, id, nummerged, numvertices, numcoplanars= 0, nonsimplicial=0;
+  int goodused;
+  facetT *facet;
+  const char *s;
+  int numdel= zzval_(Zdelvertextot);
+  int numtricoplanars= 0;
+
+  size= qh->num_points + qh_setsize(qh, qh->other_points);
+  numvertices= qh->num_vertices - qh_setsize(qh, qh->del_vertices);
+  id= qh_pointid(qh, qh->GOODpointp);
+  FORALLfacets {
+    if (facet->coplanarset)
+      numcoplanars += qh_setsize(qh, facet->coplanarset);
+    if (facet->good) {
+      if (facet->simplicial) {
+        if (facet->keepcentrum && facet->tricoplanar)
+          numtricoplanars++;
+      }else if (qh_setsize(qh, facet->vertices) != qh->hull_dim)
+        nonsimplicial++;
+    }
+  }
+  if (id >=0 && qh->STOPcone-1 != id && -qh->STOPpoint-1 != id)
+    size--;
+  if (qh->STOPcone || qh->STOPpoint)
+      qh_fprintf(qh, fp, 9288, "\nAt a premature exit due to 'TVn', 'TCn', 'TRn', or precision error with 'QJn'.");
+  if (qh->UPPERdelaunay)
+    goodused= qh->GOODvertex + qh->GOODpoint + qh->SPLITthresholds;
+  else if (qh->DELAUNAY)
+    goodused= qh->GOODvertex + qh->GOODpoint + qh->GOODthreshold;
+  else
+    goodused= qh->num_good;
+  nummerged= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
+  if (qh->VORONOI) {
+    if (qh->UPPERdelaunay)
+      qh_fprintf(qh, fp, 9289, "\n\
+Furthest-site Voronoi vertices by the convex hull of %d points in %d-d:\n\n", size, qh->hull_dim);
+    else
+      qh_fprintf(qh, fp, 9290, "\n\
+Voronoi diagram by the convex hull of %d points in %d-d:\n\n", size, qh->hull_dim);
+    qh_fprintf(qh, fp, 9291, "  Number of Voronoi regions%s: %d\n",
+              qh->ATinfinity ? " and at-infinity" : "", numvertices);
+    if (numdel)
+      qh_fprintf(qh, fp, 9292, "  Total number of deleted points due to merging: %d\n", numdel);
+    if (numcoplanars - numdel > 0)
+      qh_fprintf(qh, fp, 9293, "  Number of nearly incident points: %d\n", numcoplanars - numdel);
+    else if (size - numvertices - numdel > 0)
+      qh_fprintf(qh, fp, 9294, "  Total number of nearly incident points: %d\n", size - numvertices - numdel);
+    qh_fprintf(qh, fp, 9295, "  Number of%s Voronoi vertices: %d\n",
+              goodused ? " 'good'" : "", qh->num_good);
+    if (nonsimplicial)
+      qh_fprintf(qh, fp, 9296, "  Number of%s non-simplicial Voronoi vertices: %d\n",
+              goodused ? " 'good'" : "", nonsimplicial);
+  }else if (qh->DELAUNAY) {
+    if (qh->UPPERdelaunay)
+      qh_fprintf(qh, fp, 9297, "\n\
+Furthest-site Delaunay triangulation by the convex hull of %d points in %d-d:\n\n", size, qh->hull_dim);
+    else
+      qh_fprintf(qh, fp, 9298, "\n\
+Delaunay triangulation by the convex hull of %d points in %d-d:\n\n", size, qh->hull_dim);
+    qh_fprintf(qh, fp, 9299, "  Number of input sites%s: %d\n",
+              qh->ATinfinity ? " and at-infinity" : "", numvertices);
+    if (numdel)
+      qh_fprintf(qh, fp, 9300, "  Total number of deleted points due to merging: %d\n", numdel);
+    if (numcoplanars - numdel > 0)
+      qh_fprintf(qh, fp, 9301, "  Number of nearly incident points: %d\n", numcoplanars - numdel);
+    else if (size - numvertices - numdel > 0)
+      qh_fprintf(qh, fp, 9302, "  Total number of nearly incident points: %d\n", size - numvertices - numdel);
+    qh_fprintf(qh, fp, 9303, "  Number of%s Delaunay regions: %d\n",
+              goodused ? " 'good'" : "", qh->num_good);
+    if (nonsimplicial)
+      qh_fprintf(qh, fp, 9304, "  Number of%s non-simplicial Delaunay regions: %d\n",
+              goodused ? " 'good'" : "", nonsimplicial);
+  }else if (qh->HALFspace) {
+    qh_fprintf(qh, fp, 9305, "\n\
+Halfspace intersection by the convex hull of %d points in %d-d:\n\n", size, qh->hull_dim);
+    qh_fprintf(qh, fp, 9306, "  Number of halfspaces: %d\n", size);
+    qh_fprintf(qh, fp, 9307, "  Number of non-redundant halfspaces: %d\n", numvertices);
+    if (numcoplanars) {
+      if (qh->KEEPinside && qh->KEEPcoplanar)
+        s= "similar and redundant";
+      else if (qh->KEEPinside)
+        s= "redundant";
+      else
+        s= "similar";
+      qh_fprintf(qh, fp, 9308, "  Number of %s halfspaces: %d\n", s, numcoplanars);
+    }
+    qh_fprintf(qh, fp, 9309, "  Number of intersection points: %d\n", qh->num_facets - qh->num_visible);
+    if (goodused)
+      qh_fprintf(qh, fp, 9310, "  Number of 'good' intersection points: %d\n", qh->num_good);
+    if (nonsimplicial)
+      qh_fprintf(qh, fp, 9311, "  Number of%s non-simplicial intersection points: %d\n",
+              goodused ? " 'good'" : "", nonsimplicial);
+  }else {
+    qh_fprintf(qh, fp, 9312, "\n\
+Convex hull of %d points in %d-d:\n\n", size, qh->hull_dim);
+    qh_fprintf(qh, fp, 9313, "  Number of vertices: %d\n", numvertices);
+    if (numcoplanars) {
+      if (qh->KEEPinside && qh->KEEPcoplanar)
+        s= "coplanar and interior";
+      else if (qh->KEEPinside)
+        s= "interior";
+      else
+        s= "coplanar";
+      qh_fprintf(qh, fp, 9314, "  Number of %s points: %d\n", s, numcoplanars);
+    }
+    qh_fprintf(qh, fp, 9315, "  Number of facets: %d\n", qh->num_facets - qh->num_visible);
+    if (goodused)
+      qh_fprintf(qh, fp, 9316, "  Number of 'good' facets: %d\n", qh->num_good);
+    if (nonsimplicial)
+      qh_fprintf(qh, fp, 9317, "  Number of%s non-simplicial facets: %d\n",
+              goodused ? " 'good'" : "", nonsimplicial);
+  }
+  if (numtricoplanars)
+      qh_fprintf(qh, fp, 9318, "  Number of triangulated facets: %d\n", numtricoplanars);
+  qh_fprintf(qh, fp, 9319, "\nStatistics for: %s | %s",
+                      qh->rbox_command, qh->qhull_command);
+  if (qh->ROTATErandom != INT_MIN)
+    qh_fprintf(qh, fp, 9320, " QR%d\n\n", qh->ROTATErandom);
+  else
+    qh_fprintf(qh, fp, 9321, "\n\n");
+  qh_fprintf(qh, fp, 9322, "  Number of points processed: %d\n", zzval_(Zprocessed));
+  qh_fprintf(qh, fp, 9323, "  Number of hyperplanes created: %d\n", zzval_(Zsetplane));
+  if (qh->DELAUNAY)
+    qh_fprintf(qh, fp, 9324, "  Number of facets in hull: %d\n", qh->num_facets - qh->num_visible);
+  qh_fprintf(qh, fp, 9325, "  Number of distance tests for qhull: %d\n", zzval_(Zpartition)+
+      zzval_(Zpartitionall)+zzval_(Znumvisibility)+zzval_(Zpartcoplanar));
+#if 0  /* NOTE: must print before printstatistics() */
+  {realT stddev, ave;
+  qh_fprintf(qh, fp, 9326, "  average new facet balance: %2.2g\n",
+          wval_(Wnewbalance)/zval_(Zprocessed));
+  stddev= qh_stddev(zval_(Zprocessed), wval_(Wnewbalance),
+                                 wval_(Wnewbalance2), &ave);
+  qh_fprintf(qh, fp, 9327, "  new facet standard deviation: %2.2g\n", stddev);
+  qh_fprintf(qh, fp, 9328, "  average partition balance: %2.2g\n",
+          wval_(Wpbalance)/zval_(Zpbalance));
+  stddev= qh_stddev(zval_(Zpbalance), wval_(Wpbalance),
+                                 wval_(Wpbalance2), &ave);
+  qh_fprintf(qh, fp, 9329, "  partition standard deviation: %2.2g\n", stddev);
+  }
+#endif
+  if (nummerged) {
+    qh_fprintf(qh, fp, 9330,"  Number of distance tests for merging: %d\n",zzval_(Zbestdist)+
+          zzval_(Zcentrumtests)+zzval_(Zdistconvex)+zzval_(Zdistcheck)+
+          zzval_(Zdistzero));
+    qh_fprintf(qh, fp, 9331,"  Number of distance tests for checking: %d\n",zzval_(Zcheckpart));
+    qh_fprintf(qh, fp, 9332,"  Number of merged facets: %d\n", nummerged);
+  }
+  if (!qh->RANDOMoutside && qh->QHULLfinished) {
+    cpu= (float)qh->hulltime;
+    cpu /= (float)qh_SECticks;
+    wval_(Wcpu)= cpu;
+    qh_fprintf(qh, fp, 9333, "  CPU seconds to compute hull (after input): %2.4g\n", cpu);
+  }
+  if (qh->RERUN) {
+    if (!qh->PREmerge && !qh->MERGEexact)
+      qh_fprintf(qh, fp, 9334, "  Percentage of runs with precision errors: %4.1f\n",
+           zzval_(Zretry)*100.0/qh->build_cnt);  /* careful of order */
+  }else if (qh->JOGGLEmax < REALmax/2) {
+    if (zzval_(Zretry))
+      qh_fprintf(qh, fp, 9335, "  After %d retries, input joggled by: %2.2g\n",
+         zzval_(Zretry), qh->JOGGLEmax);
+    else
+      qh_fprintf(qh, fp, 9336, "  Input joggled by: %2.2g\n", qh->JOGGLEmax);
+  }
+  if (qh->totarea != 0.0)
+    qh_fprintf(qh, fp, 9337, "  %s facet area:   %2.8g\n",
+            zzval_(Ztotmerge) ? "Approximate" : "Total", qh->totarea);
+  if (qh->totvol != 0.0)
+    qh_fprintf(qh, fp, 9338, "  %s volume:       %2.8g\n",
+            zzval_(Ztotmerge) ? "Approximate" : "Total", qh->totvol);
+  if (qh->MERGING) {
+    qh_outerinner(qh, NULL, &outerplane, &innerplane);
+    if (outerplane > 2 * qh->DISTround) {
+      qh_fprintf(qh, fp, 9339, "  Maximum distance of %spoint above facet: %2.2g",
+            (qh->QHULLfinished ? "" : "merged "), outerplane);
+      ratio= outerplane/(qh->ONEmerge + qh->DISTround);
+      /* don't report ratio if MINoutside is large */
+      if (ratio > 0.05 && 2* qh->ONEmerge > qh->MINoutside && qh->JOGGLEmax > REALmax/2)
+        qh_fprintf(qh, fp, 9340, " (%.1fx)\n", ratio);
+      else
+        qh_fprintf(qh, fp, 9341, "\n");
+    }
+    if (innerplane < -2 * qh->DISTround) {
+      qh_fprintf(qh, fp, 9342, "  Maximum distance of %svertex below facet: %2.2g",
+            (qh->QHULLfinished ? "" : "merged "), innerplane);
+      ratio= -innerplane/(qh->ONEmerge+qh->DISTround);
+      if (ratio > 0.05 && qh->JOGGLEmax > REALmax/2)
+        qh_fprintf(qh, fp, 9343, " (%.1fx)\n", ratio);
+      else
+        qh_fprintf(qh, fp, 9344, "\n");
+    }
+  }
+  qh_fprintf(qh, fp, 9345, "\n");
+} /* printsummary */
+
+
diff --git a/Cdir/mem_r.c b/Cdir/mem_r.c
new file mode 100644
--- /dev/null
+++ b/Cdir/mem_r.c
@@ -0,0 +1,562 @@
+/*
  ---------------------------------
+
+  mem_r.c
+    memory management routines for qhull
+
+  See libqhull/mem_r.c for a standalone program.
+
+  To initialize memory:
+
+    qh_meminit(qh, stderr);
+    qh_meminitbuffers(qh, qh->IStracing, qh_MEMalign, 7, qh_MEMbufsize,qh_MEMinitbuf);
+    qh_memsize(qh, (int)sizeof(facetT));
+    qh_memsize(qh, (int)sizeof(facetT));
+    ...
+    qh_memsetup(qh);
+
+  To free up all memory buffers:
+    qh_memfreeshort(qh, &curlong, &totlong);
+
+  if qh_NOmem,
+    malloc/free is used instead of mem.c
+
+  notes:
+    uses Quickfit algorithm (freelists for commonly allocated sizes)
+    assumes small sizes for freelists (it discards the tail of memory buffers)
+
+  see:
+    qh-mem_r.htm and mem_r.h
+    global_r.c (qh_initbuffers) for an example of using mem_r.c
+
+  Copyright (c) 1993-2015 The Geometry Center.
+  $Id: //main/2015/qhull/src/libqhull_r/mem_r.c#5 $$Change: 2065 $
+  $DateTime: 2016/01/18 13:51:04 $$Author: bbarber $
+*/
+
+#include "libqhull_r.h"  /* includes user_r.h and mem_r.h */
+
+#include 
+#include 
+#include 
+
+#ifndef qh_NOmem
+
+/*============= internal functions ==============*/
+
+static int qh_intcompare(const void *i, const void *j);
+
+/*========== functions in alphabetical order ======== */
+
+/*---------------------------------
+
+  qh_intcompare( i, j )
+    used by qsort and bsearch to compare two integers
+*/
+static int qh_intcompare(const void *i, const void *j) {
+  return(*((const int *)i) - *((const int *)j));
+} /* intcompare */
+
+
+/*----------------------------------
+
+  qh_memalloc( qh, insize )
+    returns object of insize bytes
+    qhmem is the global memory structure
+
+  returns:
+    pointer to allocated memory
+    errors if insufficient memory
+
+  notes:
+    use explicit type conversion to avoid type warnings on some compilers
+    actual object may be larger than insize
+    use qh_memalloc_() for inline code for quick allocations
+    logs allocations if 'T5'
+    caller is responsible for freeing the memory.
+    short memory is freed on shutdown by qh_memfreeshort unless qh_NOmem
+
+  design:
+    if size < qh->qhmem.LASTsize
+      if qh->qhmem.freelists[size] non-empty
+        return first object on freelist
+      else
+        round up request to size of qh->qhmem.freelists[size]
+        allocate new allocation buffer if necessary
+        allocate object from allocation buffer
+    else
+      allocate object with qh_malloc() in user.c
+*/
+void *qh_memalloc(qhT *qh, int insize) {
+  void **freelistp, *newbuffer;
+  int idx, size, n;
+  int outsize, bufsize;
+  void *object;
+
+  if (insize<0) {
+      qh_fprintf(qh, qh->qhmem.ferr, 6235, "qhull error (qh_memalloc): negative request size (%d).  Did int overflow due to high-D?\n", insize); /* WARN64 */
+      qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
+  }
+  if (insize>=0 && insize <= qh->qhmem.LASTsize) {
+    idx= qh->qhmem.indextable[insize];
+    outsize= qh->qhmem.sizetable[idx];
+    qh->qhmem.totshort += outsize;
+    freelistp= qh->qhmem.freelists+idx;
+    if ((object= *freelistp)) {
+      qh->qhmem.cntquick++;
+      qh->qhmem.totfree -= outsize;
+      *freelistp= *((void **)*freelistp);  /* replace freelist with next object */
+#ifdef qh_TRACEshort
+      n= qh->qhmem.cntshort+qh->qhmem.cntquick+qh->qhmem.freeshort;
+      if (qh->qhmem.IStracing >= 5)
+          qh_fprintf(qh, qh->qhmem.ferr, 8141, "qh_mem %p n %8d alloc quick: %d bytes (tot %d cnt %d)\n", object, n, outsize, qh->qhmem.totshort, qh->qhmem.cntshort+qh->qhmem.cntquick-qh->qhmem.freeshort);
+#endif
+      return(object);
+    }else {
+      qh->qhmem.cntshort++;
+      if (outsize > qh->qhmem.freesize) {
+        qh->qhmem.totdropped += qh->qhmem.freesize;
+        if (!qh->qhmem.curbuffer)
+          bufsize= qh->qhmem.BUFinit;
+        else
+          bufsize= qh->qhmem.BUFsize;
+        if (!(newbuffer= qh_malloc((size_t)bufsize))) {
+          qh_fprintf(qh, qh->qhmem.ferr, 6080, "qhull error (qh_memalloc): insufficient memory to allocate short memory buffer (%d bytes)\n", bufsize);
+          qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
+        }
+        *((void **)newbuffer)= qh->qhmem.curbuffer;  /* prepend newbuffer to curbuffer
+                                                    list.  newbuffer!=0 by QH6080 */
+        qh->qhmem.curbuffer= newbuffer;
+        size= (sizeof(void **) + qh->qhmem.ALIGNmask) & ~qh->qhmem.ALIGNmask;
+        qh->qhmem.freemem= (void *)((char *)newbuffer+size);
+        qh->qhmem.freesize= bufsize - size;
+        qh->qhmem.totbuffer += bufsize - size; /* easier to check */
+        /* Periodically test totbuffer.  It matches at beginning and exit of every call */
+        n = qh->qhmem.totshort + qh->qhmem.totfree + qh->qhmem.totdropped + qh->qhmem.freesize - outsize;
+        if (qh->qhmem.totbuffer != n) {
+            qh_fprintf(qh, qh->qhmem.ferr, 6212, "qh_memalloc internal error: short totbuffer %d != totshort+totfree... %d\n", qh->qhmem.totbuffer, n);
+            qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
+        }
+      }
+      object= qh->qhmem.freemem;
+      qh->qhmem.freemem= (void *)((char *)qh->qhmem.freemem + outsize);
+      qh->qhmem.freesize -= outsize;
+      qh->qhmem.totunused += outsize - insize;
+#ifdef qh_TRACEshort
+      n= qh->qhmem.cntshort+qh->qhmem.cntquick+qh->qhmem.freeshort;
+      if (qh->qhmem.IStracing >= 5)
+          qh_fprintf(qh, qh->qhmem.ferr, 8140, "qh_mem %p n %8d alloc short: %d bytes (tot %d cnt %d)\n", object, n, outsize, qh->qhmem.totshort, qh->qhmem.cntshort+qh->qhmem.cntquick-qh->qhmem.freeshort);
+#endif
+      return object;
+    }
+  }else {                     /* long allocation */
+    if (!qh->qhmem.indextable) {
+      qh_fprintf(qh, qh->qhmem.ferr, 6081, "qhull internal error (qh_memalloc): qhmem has not been initialized.\n");
+      qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
+    }
+    outsize= insize;
+    qh->qhmem.cntlong++;
+    qh->qhmem.totlong += outsize;
+    if (qh->qhmem.maxlong < qh->qhmem.totlong)
+      qh->qhmem.maxlong= qh->qhmem.totlong;
+    if (!(object= qh_malloc((size_t)outsize))) {
+      qh_fprintf(qh, qh->qhmem.ferr, 6082, "qhull error (qh_memalloc): insufficient memory to allocate %d bytes\n", outsize);
+      qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
+    }
+    if (qh->qhmem.IStracing >= 5)
+      qh_fprintf(qh, qh->qhmem.ferr, 8057, "qh_mem %p n %8d alloc long: %d bytes (tot %d cnt %d)\n", object, qh->qhmem.cntlong+qh->qhmem.freelong, outsize, qh->qhmem.totlong, qh->qhmem.cntlong-qh->qhmem.freelong);
+  }
+  return(object);
+} /* memalloc */
+
+
+/*----------------------------------
+
+  qh_memcheck(qh)
+*/
+void qh_memcheck(qhT *qh) {
+  int i, count, totfree= 0;
+  void *object;
+
+  if (!qh) {
+    qh_fprintf_stderr(6243, "qh_memcheck(qh) error: qh is 0.  It does not point to a qhT");
+    qh_exit(qhmem_ERRqhull);  /* can not use qh_errexit() */
+  }
+  if (qh->qhmem.ferr == 0 || qh->qhmem.IStracing < 0 || qh->qhmem.IStracing > 10 || (((qh->qhmem.ALIGNmask+1) & qh->qhmem.ALIGNmask) != 0)) {
+    qh_fprintf_stderr(6244, "qh_memcheck error: either qh->qhmem is overwritten or qh->qhmem is not initialized.  Call qh_mem_new() or qh_new_qhull() before calling qh_mem routines.  ferr 0x%x IsTracing %d ALIGNmask 0x%x", qh->qhmem.ferr, qh->qhmem.IStracing, qh->qhmem.ALIGNmask);
+    qh_exit(qhmem_ERRqhull);  /* can not use qh_errexit() */
+    return;
+  }
+  if (qh->qhmem.IStracing != 0)
+    qh_fprintf(qh, qh->qhmem.ferr, 8143, "qh_memcheck: check size of freelists on qh->qhmem\nqh_memcheck: A segmentation fault indicates an overwrite of qh->qhmem\n");
+  for (i=0; i < qh->qhmem.TABLEsize; i++) {
+    count=0;
+    for (object= qh->qhmem.freelists[i]; object; object= *((void **)object))
+      count++;
+    totfree += qh->qhmem.sizetable[i] * count;
+  }
+  if (totfree != qh->qhmem.totfree) {
+    qh_fprintf(qh, qh->qhmem.ferr, 6211, "Qhull internal error (qh_memcheck): totfree %d not equal to freelist total %d\n", qh->qhmem.totfree, totfree);
+    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
+  }
+  if (qh->qhmem.IStracing != 0)
+    qh_fprintf(qh, qh->qhmem.ferr, 8144, "qh_memcheck: total size of freelists totfree is the same as qh->qhmem.totfree\n", totfree);
+} /* memcheck */
+
+/*----------------------------------
+
+  qh_memfree(qh, object, insize )
+    free up an object of size bytes
+    size is insize from qh_memalloc
+
+  notes:
+    object may be NULL
+    type checking warns if using (void **)object
+    use qh_memfree_() for quick free's of small objects
+
+  design:
+    if size <= qh->qhmem.LASTsize
+      append object to corresponding freelist
+    else
+      call qh_free(object)
+*/
+void qh_memfree(qhT *qh, void *object, int insize) {
+  void **freelistp;
+  int idx, outsize;
+
+  if (!object)
+    return;
+  if (insize <= qh->qhmem.LASTsize) {
+    qh->qhmem.freeshort++;
+    idx= qh->qhmem.indextable[insize];
+    outsize= qh->qhmem.sizetable[idx];
+    qh->qhmem.totfree += outsize;
+    qh->qhmem.totshort -= outsize;
+    freelistp= qh->qhmem.freelists + idx;
+    *((void **)object)= *freelistp;
+    *freelistp= object;
+#ifdef qh_TRACEshort
+    idx= qh->qhmem.cntshort+qh->qhmem.cntquick+qh->qhmem.freeshort;
+    if (qh->qhmem.IStracing >= 5)
+        qh_fprintf(qh, qh->qhmem.ferr, 8142, "qh_mem %p n %8d free short: %d bytes (tot %d cnt %d)\n", object, idx, outsize, qh->qhmem.totshort, qh->qhmem.cntshort+qh->qhmem.cntquick-qh->qhmem.freeshort);
+#endif
+  }else {
+    qh->qhmem.freelong++;
+    qh->qhmem.totlong -= insize;
+    if (qh->qhmem.IStracing >= 5)
+      qh_fprintf(qh, qh->qhmem.ferr, 8058, "qh_mem %p n %8d free long: %d bytes (tot %d cnt %d)\n", object, qh->qhmem.cntlong+qh->qhmem.freelong, insize, qh->qhmem.totlong, qh->qhmem.cntlong-qh->qhmem.freelong);
+    qh_free(object);
+  }
+} /* memfree */
+
+
+/*---------------------------------
+
+  qh_memfreeshort(qh, curlong, totlong )
+    frees up all short and qhmem memory allocations
+
+  returns:
+    number and size of current long allocations
+
+  notes:
+    if qh_NOmem (qh_malloc() for all allocations),
+       short objects (e.g., facetT) are not recovered.
+       use qh_freeqhull(qh, qh_ALL) instead.
+
+  see:
+    qh_freeqhull(qh, allMem)
+    qh_memtotal(qh, curlong, totlong, curshort, totshort, maxlong, totbuffer);
+*/
+void qh_memfreeshort(qhT *qh, int *curlong, int *totlong) {
+  void *buffer, *nextbuffer;
+  FILE *ferr;
+
+  *curlong= qh->qhmem.cntlong - qh->qhmem.freelong;
+  *totlong= qh->qhmem.totlong;
+  for (buffer= qh->qhmem.curbuffer; buffer; buffer= nextbuffer) {
+    nextbuffer= *((void **) buffer);
+    qh_free(buffer);
+  }
+  qh->qhmem.curbuffer= NULL;
+  if (qh->qhmem.LASTsize) {
+    qh_free(qh->qhmem.indextable);
+    qh_free(qh->qhmem.freelists);
+    qh_free(qh->qhmem.sizetable);
+  }
+  ferr= qh->qhmem.ferr;
+  memset((char *)&qh->qhmem, 0, sizeof(qh->qhmem));  /* every field is 0, FALSE, NULL */
+  qh->qhmem.ferr= ferr;
+} /* memfreeshort */
+
+
+/*----------------------------------
+
+  qh_meminit(qh, ferr )
+    initialize qhmem and test sizeof( void*)
+    Does not throw errors.  qh_exit on failure
+*/
+void qh_meminit(qhT *qh, FILE *ferr) {
+
+  memset((char *)&qh->qhmem, 0, sizeof(qh->qhmem));  /* every field is 0, FALSE, NULL */
+  if (ferr)
+      qh->qhmem.ferr= ferr;
+  else
+      qh->qhmem.ferr= stderr;
+  if (sizeof(void*) < sizeof(int)) {
+    qh_fprintf(qh, qh->qhmem.ferr, 6083, "qhull internal error (qh_meminit): sizeof(void*) %d < sizeof(int) %d.  qset.c will not work\n", (int)sizeof(void*), (int)sizeof(int));
+    qh_exit(qhmem_ERRqhull);  /* can not use qh_errexit() */
+  }
+  if (sizeof(void*) > sizeof(ptr_intT)) {
+      qh_fprintf(qh, qh->qhmem.ferr, 6084, "qhull internal error (qh_meminit): sizeof(void*) %d > sizeof(ptr_intT) %d. Change ptr_intT in mem.h to 'long long'\n", (int)sizeof(void*), (int)sizeof(ptr_intT));
+      qh_exit(qhmem_ERRqhull);  /* can not use qh_errexit() */
+  }
+  qh_memcheck(qh);
+} /* meminit */
+
+/*---------------------------------
+
+  qh_meminitbuffers(qh, tracelevel, alignment, numsizes, bufsize, bufinit )
+    initialize qhmem
+    if tracelevel >= 5, trace memory allocations
+    alignment= desired address alignment for memory allocations
+    numsizes= number of freelists
+    bufsize=  size of additional memory buffers for short allocations
+    bufinit=  size of initial memory buffer for short allocations
+*/
+void qh_meminitbuffers(qhT *qh, int tracelevel, int alignment, int numsizes, int bufsize, int bufinit) {
+
+  qh->qhmem.IStracing= tracelevel;
+  qh->qhmem.NUMsizes= numsizes;
+  qh->qhmem.BUFsize= bufsize;
+  qh->qhmem.BUFinit= bufinit;
+  qh->qhmem.ALIGNmask= alignment-1;
+  if (qh->qhmem.ALIGNmask & ~qh->qhmem.ALIGNmask) {
+    qh_fprintf(qh, qh->qhmem.ferr, 6085, "qhull internal error (qh_meminit): memory alignment %d is not a power of 2\n", alignment);
+    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
+  }
+  qh->qhmem.sizetable= (int *) calloc((size_t)numsizes, sizeof(int));
+  qh->qhmem.freelists= (void **) calloc((size_t)numsizes, sizeof(void *));
+  if (!qh->qhmem.sizetable || !qh->qhmem.freelists) {
+    qh_fprintf(qh, qh->qhmem.ferr, 6086, "qhull error (qh_meminit): insufficient memory\n");
+    qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
+  }
+  if (qh->qhmem.IStracing >= 1)
+    qh_fprintf(qh, qh->qhmem.ferr, 8059, "qh_meminitbuffers: memory initialized with alignment %d\n", alignment);
+} /* meminitbuffers */
+
+/*---------------------------------
+
+  qh_memsetup(qh)
+    set up memory after running memsize()
+*/
+void qh_memsetup(qhT *qh) {
+  int k,i;
+
+  qsort(qh->qhmem.sizetable, (size_t)qh->qhmem.TABLEsize, sizeof(int), qh_intcompare);
+  qh->qhmem.LASTsize= qh->qhmem.sizetable[qh->qhmem.TABLEsize-1];
+  if(qh->qhmem.LASTsize >= qh->qhmem.BUFsize || qh->qhmem.LASTsize >= qh->qhmem.BUFinit) {
+    qh_fprintf(qh, qh->qhmem.ferr, 6087, "qhull error (qh_memsetup): largest mem size %d is >= buffer size %d or initial buffer size %d\n",
+            qh->qhmem.LASTsize, qh->qhmem.BUFsize, qh->qhmem.BUFinit);
+    qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
+  }
+  if (!(qh->qhmem.indextable= (int *)qh_malloc((qh->qhmem.LASTsize+1) * sizeof(int)))) {
+    qh_fprintf(qh, qh->qhmem.ferr, 6088, "qhull error (qh_memsetup): insufficient memory\n");
+    qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
+  }
+  for (k=qh->qhmem.LASTsize+1; k--; )
+    qh->qhmem.indextable[k]= k;
+  i= 0;
+  for (k=0; k <= qh->qhmem.LASTsize; k++) {
+    if (qh->qhmem.indextable[k] <= qh->qhmem.sizetable[i])
+      qh->qhmem.indextable[k]= i;
+    else
+      qh->qhmem.indextable[k]= ++i;
+  }
+} /* memsetup */
+
+/*---------------------------------
+
+  qh_memsize(qh, size )
+    define a free list for this size
+*/
+void qh_memsize(qhT *qh, int size) {
+  int k;
+
+  if(qh->qhmem.LASTsize) {
+    qh_fprintf(qh, qh->qhmem.ferr, 6089, "qhull error (qh_memsize): called after qhmem_setup\n");
+    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
+  }
+  size= (size + qh->qhmem.ALIGNmask) & ~qh->qhmem.ALIGNmask;
+  for (k=qh->qhmem.TABLEsize; k--; ) {
+    if (qh->qhmem.sizetable[k] == size)
+      return;
+  }
+  if (qh->qhmem.TABLEsize < qh->qhmem.NUMsizes)
+    qh->qhmem.sizetable[qh->qhmem.TABLEsize++]= size;
+  else
+    qh_fprintf(qh, qh->qhmem.ferr, 7060, "qhull warning (memsize): free list table has room for only %d sizes\n", qh->qhmem.NUMsizes);
+} /* memsize */
+
+
+/*---------------------------------
+
+  qh_memstatistics(qh, fp )
+    print out memory statistics
+
+    Verifies that qh->qhmem.totfree == sum of freelists
+*/
+void qh_memstatistics(qhT *qh, FILE *fp) {
+  int i;
+  int count;
+  void *object;
+
+  qh_memcheck(qh);
+  qh_fprintf(qh, fp, 9278, "\nmemory statistics:\n\
+%7d quick allocations\n\
+%7d short allocations\n\
+%7d long allocations\n\
+%7d short frees\n\
+%7d long frees\n\
+%7d bytes of short memory in use\n\
+%7d bytes of short memory in freelists\n\
+%7d bytes of dropped short memory\n\
+%7d bytes of unused short memory (estimated)\n\
+%7d bytes of long memory allocated (max, except for input)\n\
+%7d bytes of long memory in use (in %d pieces)\n\
+%7d bytes of short memory buffers (minus links)\n\
+%7d bytes per short memory buffer (initially %d bytes)\n",
+           qh->qhmem.cntquick, qh->qhmem.cntshort, qh->qhmem.cntlong,
+           qh->qhmem.freeshort, qh->qhmem.freelong,
+           qh->qhmem.totshort, qh->qhmem.totfree,
+           qh->qhmem.totdropped + qh->qhmem.freesize, qh->qhmem.totunused,
+           qh->qhmem.maxlong, qh->qhmem.totlong, qh->qhmem.cntlong - qh->qhmem.freelong,
+           qh->qhmem.totbuffer, qh->qhmem.BUFsize, qh->qhmem.BUFinit);
+  if (qh->qhmem.cntlarger) {
+    qh_fprintf(qh, fp, 9279, "%7d calls to qh_setlarger\n%7.2g     average copy size\n",
+           qh->qhmem.cntlarger, ((float)qh->qhmem.totlarger)/(float)qh->qhmem.cntlarger);
+    qh_fprintf(qh, fp, 9280, "  freelists(bytes->count):");
+  }
+  for (i=0; i < qh->qhmem.TABLEsize; i++) {
+    count=0;
+    for (object= qh->qhmem.freelists[i]; object; object= *((void **)object))
+      count++;
+    qh_fprintf(qh, fp, 9281, " %d->%d", qh->qhmem.sizetable[i], count);
+  }
+  qh_fprintf(qh, fp, 9282, "\n\n");
+} /* memstatistics */
+
+
+/*---------------------------------
+
+  qh_NOmem
+    turn off quick-fit memory allocation
+
+  notes:
+    uses qh_malloc() and qh_free() instead
+*/
+#else /* qh_NOmem */
+
+void *qh_memalloc(qhT *qh, int insize) {
+  void *object;
+
+  if (!(object= qh_malloc((size_t)insize))) {
+    qh_fprintf(qh, qh->qhmem.ferr, 6090, "qhull error (qh_memalloc): insufficient memory\n");
+    qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
+  }
+  qh->qhmem.cntlong++;
+  qh->qhmem.totlong += insize;
+  if (qh->qhmem.maxlong < qh->qhmem.totlong)
+      qh->qhmem.maxlong= qh->qhmem.totlong;
+  if (qh->qhmem.IStracing >= 5)
+    qh_fprintf(qh, qh->qhmem.ferr, 8060, "qh_mem %p n %8d alloc long: %d bytes (tot %d cnt %d)\n", object, qh->qhmem.cntlong+qh->qhmem.freelong, insize, qh->qhmem.totlong, qh->qhmem.cntlong-qh->qhmem.freelong);
+  return object;
+}
+
+void qh_memfree(qhT *qh, void *object, int insize) {
+
+  if (!object)
+    return;
+  qh_free(object);
+  qh->qhmem.freelong++;
+  qh->qhmem.totlong -= insize;
+  if (qh->qhmem.IStracing >= 5)
+    qh_fprintf(qh, qh->qhmem.ferr, 8061, "qh_mem %p n %8d free long: %d bytes (tot %d cnt %d)\n", object, qh->qhmem.cntlong+qh->qhmem.freelong, insize, qh->qhmem.totlong, qh->qhmem.cntlong-qh->qhmem.freelong);
+}
+
+void qh_memfreeshort(qhT *qh, int *curlong, int *totlong) {
+  *totlong= qh->qhmem.totlong;
+  *curlong= qh->qhmem.cntlong - qh->qhmem.freelong;
+  memset((char *)&qh->qhmem, 0, sizeof(qh->qhmem));  /* every field is 0, FALSE, NULL */
+}
+
+void qh_meminit(qhT *qh, FILE *ferr) {
+
+  memset((char *)&qh->qhmem, 0, sizeof(qh->qhmem));  /* every field is 0, FALSE, NULL */
+  if (ferr)
+      qh->qhmem.ferr= ferr;
+  else
+      qh->qhmem.ferr= stderr;
+  if (sizeof(void*) < sizeof(int)) {
+    qh_fprintf(qh, qh->qhmem.ferr, 6091, "qhull internal error (qh_meminit): sizeof(void*) %d < sizeof(int) %d.  qset.c will not work\n", (int)sizeof(void*), (int)sizeof(int));
+    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
+  }
+}
+
+void qh_meminitbuffers(qhT *qh, int tracelevel, int alignment, int numsizes, int bufsize, int bufinit) {
+
+  qh->qhmem.IStracing= tracelevel;
+}
+
+void qh_memsetup(qhT *qh) {
+
+}
+
+void qh_memsize(qhT *qh, int size) {
+
+}
+
+void qh_memstatistics(qhT *qh, FILE *fp) {
+
+  qh_fprintf(qh, fp, 9409, "\nmemory statistics:\n\
+%7d long allocations\n\
+%7d long frees\n\
+%7d bytes of long memory allocated (max, except for input)\n\
+%7d bytes of long memory in use (in %d pieces)\n",
+           qh->qhmem.cntlong,
+           qh->qhmem.freelong,
+           qh->qhmem.maxlong, qh->qhmem.totlong, qh->qhmem.cntlong - qh->qhmem.freelong);
+}
+
+#endif /* qh_NOmem */
+
+/*---------------------------------
+
+  qh_memtotal(qh, totlong, curlong, totshort, curshort, maxlong, totbuffer )
+    Return the total, allocated long and short memory
+
+  returns:
+    Returns the total current bytes of long and short allocations
+    Returns the current count of long and short allocations
+    Returns the maximum long memory and total short buffer (minus one link per buffer)
+    Does not error (for deprecated UsingLibQhull.cpp (libqhullpcpp))
+*/
+void qh_memtotal(qhT *qh, int *totlong, int *curlong, int *totshort, int *curshort, int *maxlong, int *totbuffer) {
+    *totlong= qh->qhmem.totlong;
+    *curlong= qh->qhmem.cntlong - qh->qhmem.freelong;
+    *totshort= qh->qhmem.totshort;
+    *curshort= qh->qhmem.cntshort + qh->qhmem.cntquick - qh->qhmem.freeshort;
+    *maxlong= qh->qhmem.maxlong;
+    *totbuffer= qh->qhmem.totbuffer;
+} /* memtotlong */
diff --git a/Cdir/merge_r.c b/Cdir/merge_r.c
new file mode 100644
--- /dev/null
+++ b/Cdir/merge_r.c
@@ -0,0 +1,3627 @@
+/*
  ---------------------------------
+
+   merge_r.c
+   merges non-convex facets
+
+   see qh-merge_r.htm and merge_r.h
+
+   other modules call qh_premerge() and qh_postmerge()
+
+   the user may call qh_postmerge() to perform additional merges.
+
+   To remove deleted facets and vertices (qhull() in libqhull_r.c):
+     qh_partitionvisible(qh, !qh_ALL, &numoutside);  // visible_list, newfacet_list
+     qh_deletevisible();         // qh.visible_list
+     qh_resetlists(qh, False, qh_RESETvisible);       // qh.visible_list newvertex_list newfacet_list
+
+   assumes qh.CENTERtype= centrum
+
+   merges occur in qh_mergefacet and in qh_mergecycle
+   vertex->neighbors not set until the first merge occurs
+
+   Copyright (c) 1993-2015 C.B. Barber.
+   $Id: //main/2015/qhull/src/libqhull_r/merge_r.c#5 $$Change: 2064 $
+   $DateTime: 2016/01/18 12:36:08 $$Author: bbarber $
+*/
+
+#include "qhull_ra.h"
+
+#ifndef qh_NOmerge
+
+/*===== functions(alphabetical after premerge and postmerge) ======*/
+
+/*---------------------------------
+
+  qh_premerge(qh, apex, maxcentrum )
+    pre-merge nonconvex facets in qh.newfacet_list for apex
+    maxcentrum defines coplanar and concave (qh_test_appendmerge)
+
+  returns:
+    deleted facets added to qh.visible_list with facet->visible set
+
+  notes:
+    uses globals, qh.MERGEexact, qh.PREmerge
+
+  design:
+    mark duplicate ridges in qh.newfacet_list
+    merge facet cycles in qh.newfacet_list
+    merge duplicate ridges and concave facets in qh.newfacet_list
+    check merged facet cycles for degenerate and redundant facets
+    merge degenerate and redundant facets
+    collect coplanar and concave facets
+    merge concave, coplanar, degenerate, and redundant facets
+*/
+void qh_premerge(qhT *qh, vertexT *apex, realT maxcentrum, realT maxangle) {
+  boolT othermerge= False;
+  facetT *newfacet;
+
+  if (qh->ZEROcentrum && qh_checkzero(qh, !qh_ALL))
+    return;
+  trace2((qh, qh->ferr, 2008, "qh_premerge: premerge centrum %2.2g angle %2.2g for apex v%d facetlist f%d\n",
+            maxcentrum, maxangle, apex->id, getid_(qh->newfacet_list)));
+  if (qh->IStracing >= 4 && qh->num_facets < 50)
+    qh_printlists(qh);
+  qh->centrum_radius= maxcentrum;
+  qh->cos_max= maxangle;
+  qh->degen_mergeset= qh_settemp(qh, qh->TEMPsize);
+  qh->facet_mergeset= qh_settemp(qh, qh->TEMPsize);
+  if (qh->hull_dim >=3) {
+    qh_mark_dupridges(qh, qh->newfacet_list); /* facet_mergeset */
+    qh_mergecycle_all(qh, qh->newfacet_list, &othermerge);
+    qh_forcedmerges(qh, &othermerge /* qh->facet_mergeset */);
+    FORALLnew_facets {  /* test samecycle merges */
+      if (!newfacet->simplicial && !newfacet->mergeridge)
+        qh_degen_redundant_neighbors(qh, newfacet, NULL);
+    }
+    if (qh_merge_degenredundant(qh))
+      othermerge= True;
+  }else /* qh->hull_dim == 2 */
+    qh_mergecycle_all(qh, qh->newfacet_list, &othermerge);
+  qh_flippedmerges(qh, qh->newfacet_list, &othermerge);
+  if (!qh->MERGEexact || zzval_(Ztotmerge)) {
+    zinc_(Zpremergetot);
+    qh->POSTmerging= False;
+    qh_getmergeset_initial(qh, qh->newfacet_list);
+    qh_all_merges(qh, othermerge, False);
+  }
+  qh_settempfree(qh, &qh->facet_mergeset);
+  qh_settempfree(qh, &qh->degen_mergeset);
+} /* premerge */
+
+/*---------------------------------
+
+  qh_postmerge(qh, reason, maxcentrum, maxangle, vneighbors )
+    post-merge nonconvex facets as defined by maxcentrum and maxangle
+    'reason' is for reporting progress
+    if vneighbors,
+      calls qh_test_vneighbors at end of qh_all_merge
+    if firstmerge,
+      calls qh_reducevertices before qh_getmergeset
+
+  returns:
+    if first call (qh.visible_list != qh.facet_list),
+      builds qh.facet_newlist, qh.newvertex_list
+    deleted facets added to qh.visible_list with facet->visible
+    qh.visible_list == qh.facet_list
+
+  notes:
+
+
+  design:
+    if first call
+      set qh.visible_list and qh.newfacet_list to qh.facet_list
+      add all facets to qh.newfacet_list
+      mark non-simplicial facets, facet->newmerge
+      set qh.newvertext_list to qh.vertex_list
+      add all vertices to qh.newvertex_list
+      if a pre-merge occured
+        set vertex->delridge {will retest the ridge}
+        if qh.MERGEexact
+          call qh_reducevertices()
+      if no pre-merging
+        merge flipped facets
+    determine non-convex facets
+    merge all non-convex facets
+*/
+void qh_postmerge(qhT *qh, const char *reason, realT maxcentrum, realT maxangle,
+                      boolT vneighbors) {
+  facetT *newfacet;
+  boolT othermerges= False;
+  vertexT *vertex;
+
+  if (qh->REPORTfreq || qh->IStracing) {
+    qh_buildtracing(qh, NULL, NULL);
+    qh_printsummary(qh, qh->ferr);
+    if (qh->PRINTstatistics)
+      qh_printallstatistics(qh, qh->ferr, "reason");
+    qh_fprintf(qh, qh->ferr, 8062, "\n%s with 'C%.2g' and 'A%.2g'\n",
+        reason, maxcentrum, maxangle);
+  }
+  trace2((qh, qh->ferr, 2009, "qh_postmerge: postmerge.  test vneighbors? %d\n",
+            vneighbors));
+  qh->centrum_radius= maxcentrum;
+  qh->cos_max= maxangle;
+  qh->POSTmerging= True;
+  qh->degen_mergeset= qh_settemp(qh, qh->TEMPsize);
+  qh->facet_mergeset= qh_settemp(qh, qh->TEMPsize);
+  if (qh->visible_list != qh->facet_list) {  /* first call */
+    qh->NEWfacets= True;
+    qh->visible_list= qh->newfacet_list= qh->facet_list;
+    FORALLnew_facets {
+      newfacet->newfacet= True;
+       if (!newfacet->simplicial)
+        newfacet->newmerge= True;
+     zinc_(Zpostfacets);
+    }
+    qh->newvertex_list= qh->vertex_list;
+    FORALLvertices
+      vertex->newlist= True;
+    if (qh->VERTEXneighbors) { /* a merge has occurred */
+      FORALLvertices
+        vertex->delridge= True; /* test for redundant, needed? */
+      if (qh->MERGEexact) {
+        if (qh->hull_dim <= qh_DIMreduceBuild)
+          qh_reducevertices(qh); /* was skipped during pre-merging */
+      }
+    }
+    if (!qh->PREmerge && !qh->MERGEexact)
+      qh_flippedmerges(qh, qh->newfacet_list, &othermerges);
+  }
+  qh_getmergeset_initial(qh, qh->newfacet_list);
+  qh_all_merges(qh, False, vneighbors);
+  qh_settempfree(qh, &qh->facet_mergeset);
+  qh_settempfree(qh, &qh->degen_mergeset);
+} /* post_merge */
+
+/*---------------------------------
+
+  qh_all_merges(qh, othermerge, vneighbors )
+    merge all non-convex facets
+
+    set othermerge if already merged facets (for qh_reducevertices)
+    if vneighbors
+      tests vertex neighbors for convexity at end
+    qh.facet_mergeset lists the non-convex ridges in qh_newfacet_list
+    qh.degen_mergeset is defined
+    if qh.MERGEexact && !qh.POSTmerging,
+      does not merge coplanar facets
+
+  returns:
+    deleted facets added to qh.visible_list with facet->visible
+    deleted vertices added qh.delvertex_list with vertex->delvertex
+
+  notes:
+    unless !qh.MERGEindependent,
+      merges facets in independent sets
+    uses qh.newfacet_list as argument since merges call qh_removefacet()
+
+  design:
+    while merges occur
+      for each merge in qh.facet_mergeset
+        unless one of the facets was already merged in this pass
+          merge the facets
+        test merged facets for additional merges
+        add merges to qh.facet_mergeset
+      if vertices record neighboring facets
+        rename redundant vertices
+          update qh.facet_mergeset
+    if vneighbors ??
+      tests vertex neighbors for convexity at end
+*/
+void qh_all_merges(qhT *qh, boolT othermerge, boolT vneighbors) {
+  facetT *facet1, *facet2;
+  mergeT *merge;
+  boolT wasmerge= True, isreduce;
+  void **freelistp;  /* used if !qh_NOmem by qh_memfree_() */
+  vertexT *vertex;
+  mergeType mergetype;
+  int numcoplanar=0, numconcave=0, numdegenredun= 0, numnewmerges= 0;
+
+  trace2((qh, qh->ferr, 2010, "qh_all_merges: starting to merge facets beginning from f%d\n",
+            getid_(qh->newfacet_list)));
+  while (True) {
+    wasmerge= False;
+    while (qh_setsize(qh, qh->facet_mergeset)) {
+      while ((merge= (mergeT*)qh_setdellast(qh->facet_mergeset))) {
+        facet1= merge->facet1;
+        facet2= merge->facet2;
+        mergetype= merge->type;
+        qh_memfree_(qh, merge, (int)sizeof(mergeT), freelistp);
+        if (facet1->visible || facet2->visible) /*deleted facet*/
+          continue;
+        if ((facet1->newfacet && !facet1->tested)
+                || (facet2->newfacet && !facet2->tested)) {
+          if (qh->MERGEindependent && mergetype <= MRGanglecoplanar)
+            continue;      /* perform independent sets of merges */
+        }
+        qh_merge_nonconvex(qh, facet1, facet2, mergetype);
+        numdegenredun += qh_merge_degenredundant(qh);
+        numnewmerges++;
+        wasmerge= True;
+        if (mergetype == MRGconcave)
+          numconcave++;
+        else /* MRGcoplanar or MRGanglecoplanar */
+          numcoplanar++;
+      } /* while setdellast */
+      if (qh->POSTmerging && qh->hull_dim <= qh_DIMreduceBuild
+      && numnewmerges > qh_MAXnewmerges) {
+        numnewmerges= 0;
+        qh_reducevertices(qh);  /* otherwise large post merges too slow */
+      }
+      qh_getmergeset(qh, qh->newfacet_list); /* facet_mergeset */
+    } /* while mergeset */
+    if (qh->VERTEXneighbors) {
+      isreduce= False;
+      if (qh->hull_dim >=4 && qh->POSTmerging) {
+        FORALLvertices
+          vertex->delridge= True;
+        isreduce= True;
+      }
+      if ((wasmerge || othermerge) && (!qh->MERGEexact || qh->POSTmerging)
+          && qh->hull_dim <= qh_DIMreduceBuild) {
+        othermerge= False;
+        isreduce= True;
+      }
+      if (isreduce) {
+        if (qh_reducevertices(qh)) {
+          qh_getmergeset(qh, qh->newfacet_list); /* facet_mergeset */
+          continue;
+        }
+      }
+    }
+    if (vneighbors && qh_test_vneighbors(qh /* qh->newfacet_list */))
+      continue;
+    break;
+  } /* while (True) */
+  if (qh->CHECKfrequently && !qh->MERGEexact) {
+    qh->old_randomdist= qh->RANDOMdist;
+    qh->RANDOMdist= False;
+    qh_checkconvex(qh, qh->newfacet_list, qh_ALGORITHMfault);
+    /* qh_checkconnect(qh); [this is slow and it changes the facet order] */
+    qh->RANDOMdist= qh->old_randomdist;
+  }
+  trace1((qh, qh->ferr, 1009, "qh_all_merges: merged %d coplanar facets %d concave facets and %d degen or redundant facets.\n",
+    numcoplanar, numconcave, numdegenredun));
+  if (qh->IStracing >= 4 && qh->num_facets < 50)
+    qh_printlists(qh);
+} /* all_merges */
+
+
+/*---------------------------------
+
+  qh_appendmergeset(qh, facet, neighbor, mergetype, angle )
+    appends an entry to qh.facet_mergeset or qh.degen_mergeset
+
+    angle ignored if NULL or !qh.ANGLEmerge
+
+  returns:
+    merge appended to facet_mergeset or degen_mergeset
+      sets ->degenerate or ->redundant if degen_mergeset
+
+  see:
+    qh_test_appendmerge()
+
+  design:
+    allocate merge entry
+    if regular merge
+      append to qh.facet_mergeset
+    else if degenerate merge and qh.facet_mergeset is all degenerate
+      append to qh.degen_mergeset
+    else if degenerate merge
+      prepend to qh.degen_mergeset
+    else if redundant merge
+      append to qh.degen_mergeset
+*/
+void qh_appendmergeset(qhT *qh, facetT *facet, facetT *neighbor, mergeType mergetype, realT *angle) {
+  mergeT *merge, *lastmerge;
+  void **freelistp; /* used if !qh_NOmem by qh_memalloc_() */
+
+  if (facet->redundant)
+    return;
+  if (facet->degenerate && mergetype == MRGdegen)
+    return;
+  qh_memalloc_(qh, (int)sizeof(mergeT), freelistp, merge, mergeT);
+  merge->facet1= facet;
+  merge->facet2= neighbor;
+  merge->type= mergetype;
+  if (angle && qh->ANGLEmerge)
+    merge->angle= *angle;
+  if (mergetype < MRGdegen)
+    qh_setappend(qh, &(qh->facet_mergeset), merge);
+  else if (mergetype == MRGdegen) {
+    facet->degenerate= True;
+    if (!(lastmerge= (mergeT*)qh_setlast(qh->degen_mergeset))
+    || lastmerge->type == MRGdegen)
+      qh_setappend(qh, &(qh->degen_mergeset), merge);
+    else
+      qh_setaddnth(qh, &(qh->degen_mergeset), 0, merge);
+  }else if (mergetype == MRGredundant) {
+    facet->redundant= True;
+    qh_setappend(qh, &(qh->degen_mergeset), merge);
+  }else /* mergetype == MRGmirror */ {
+    if (facet->redundant || neighbor->redundant) {
+      qh_fprintf(qh, qh->ferr, 6092, "qhull error (qh_appendmergeset): facet f%d or f%d is already a mirrored facet\n",
+           facet->id, neighbor->id);
+      qh_errexit2(qh, qh_ERRqhull, facet, neighbor);
+    }
+    if (!qh_setequal(facet->vertices, neighbor->vertices)) {
+      qh_fprintf(qh, qh->ferr, 6093, "qhull error (qh_appendmergeset): mirrored facets f%d and f%d do not have the same vertices\n",
+           facet->id, neighbor->id);
+      qh_errexit2(qh, qh_ERRqhull, facet, neighbor);
+    }
+    facet->redundant= True;
+    neighbor->redundant= True;
+    qh_setappend(qh, &(qh->degen_mergeset), merge);
+  }
+} /* appendmergeset */
+
+
+/*---------------------------------
+
+  qh_basevertices(qh, samecycle )
+    return temporary set of base vertices for samecycle
+    samecycle is first facet in the cycle
+    assumes apex is SETfirst_( samecycle->vertices )
+
+  returns:
+    vertices(settemp)
+    all ->seen are cleared
+
+  notes:
+    uses qh_vertex_visit;
+
+  design:
+    for each facet in samecycle
+      for each unseen vertex in facet->vertices
+        append to result
+*/
+setT *qh_basevertices(qhT *qh, facetT *samecycle) {
+  facetT *same;
+  vertexT *apex, *vertex, **vertexp;
+  setT *vertices= qh_settemp(qh, qh->TEMPsize);
+
+  apex= SETfirstt_(samecycle->vertices, vertexT);
+  apex->visitid= ++qh->vertex_visit;
+  FORALLsame_cycle_(samecycle) {
+    if (same->mergeridge)
+      continue;
+    FOREACHvertex_(same->vertices) {
+      if (vertex->visitid != qh->vertex_visit) {
+        qh_setappend(qh, &vertices, vertex);
+        vertex->visitid= qh->vertex_visit;
+        vertex->seen= False;
+      }
+    }
+  }
+  trace4((qh, qh->ferr, 4019, "qh_basevertices: found %d vertices\n",
+         qh_setsize(qh, vertices)));
+  return vertices;
+} /* basevertices */
+
+/*---------------------------------
+
+  qh_checkconnect(qh)
+    check that new facets are connected
+    new facets are on qh.newfacet_list
+
+  notes:
+    this is slow and it changes the order of the facets
+    uses qh.visit_id
+
+  design:
+    move first new facet to end of qh.facet_list
+    for all newly appended facets
+      append unvisited neighbors to end of qh.facet_list
+    for all new facets
+      report error if unvisited
+*/
+void qh_checkconnect(qhT *qh /* qh->newfacet_list */) {
+  facetT *facet, *newfacet, *errfacet= NULL, *neighbor, **neighborp;
+
+  facet= qh->newfacet_list;
+  qh_removefacet(qh, facet);
+  qh_appendfacet(qh, facet);
+  facet->visitid= ++qh->visit_id;
+  FORALLfacet_(facet) {
+    FOREACHneighbor_(facet) {
+      if (neighbor->visitid != qh->visit_id) {
+        qh_removefacet(qh, neighbor);
+        qh_appendfacet(qh, neighbor);
+        neighbor->visitid= qh->visit_id;
+      }
+    }
+  }
+  FORALLnew_facets {
+    if (newfacet->visitid == qh->visit_id)
+      break;
+    qh_fprintf(qh, qh->ferr, 6094, "qhull error: f%d is not attached to the new facets\n",
+         newfacet->id);
+    errfacet= newfacet;
+  }
+  if (errfacet)
+    qh_errexit(qh, qh_ERRqhull, errfacet, NULL);
+} /* checkconnect */
+
+/*---------------------------------
+
+  qh_checkzero(qh, testall )
+    check that facets are clearly convex for qh.DISTround with qh.MERGEexact
+
+    if testall,
+      test all facets for qh.MERGEexact post-merging
+    else
+      test qh.newfacet_list
+
+    if qh.MERGEexact,
+      allows coplanar ridges
+      skips convexity test while qh.ZEROall_ok
+
+  returns:
+    True if all facets !flipped, !dupridge, normal
+         if all horizon facets are simplicial
+         if all vertices are clearly below neighbor
+         if all opposite vertices of horizon are below
+    clears qh.ZEROall_ok if any problems or coplanar facets
+
+  notes:
+    uses qh.vertex_visit
+    horizon facets may define multiple new facets
+
+  design:
+    for all facets in qh.newfacet_list or qh.facet_list
+      check for flagged faults (flipped, etc.)
+    for all facets in qh.newfacet_list or qh.facet_list
+      for each neighbor of facet
+        skip horizon facets for qh.newfacet_list
+        test the opposite vertex
+      if qh.newfacet_list
+        test the other vertices in the facet's horizon facet
+*/
+boolT qh_checkzero(qhT *qh, boolT testall) {
+  facetT *facet, *neighbor, **neighborp;
+  facetT *horizon, *facetlist;
+  int neighbor_i;
+  vertexT *vertex, **vertexp;
+  realT dist;
+
+  if (testall)
+    facetlist= qh->facet_list;
+  else {
+    facetlist= qh->newfacet_list;
+    FORALLfacet_(facetlist) {
+      horizon= SETfirstt_(facet->neighbors, facetT);
+      if (!horizon->simplicial)
+        goto LABELproblem;
+      if (facet->flipped || facet->dupridge || !facet->normal)
+        goto LABELproblem;
+    }
+    if (qh->MERGEexact && qh->ZEROall_ok) {
+      trace2((qh, qh->ferr, 2011, "qh_checkzero: skip convexity check until first pre-merge\n"));
+      return True;
+    }
+  }
+  FORALLfacet_(facetlist) {
+    qh->vertex_visit++;
+    neighbor_i= 0;
+    horizon= NULL;
+    FOREACHneighbor_(facet) {
+      if (!neighbor_i && !testall) {
+        horizon= neighbor;
+        neighbor_i++;
+        continue; /* horizon facet tested in qh_findhorizon */
+      }
+      vertex= SETelemt_(facet->vertices, neighbor_i++, vertexT);
+      vertex->visitid= qh->vertex_visit;
+      zzinc_(Zdistzero);
+      qh_distplane(qh, vertex->point, neighbor, &dist);
+      if (dist >= -qh->DISTround) {
+        qh->ZEROall_ok= False;
+        if (!qh->MERGEexact || testall || dist > qh->DISTround)
+          goto LABELnonconvex;
+      }
+    }
+    if (!testall && horizon) {
+      FOREACHvertex_(horizon->vertices) {
+        if (vertex->visitid != qh->vertex_visit) {
+          zzinc_(Zdistzero);
+          qh_distplane(qh, vertex->point, facet, &dist);
+          if (dist >= -qh->DISTround) {
+            qh->ZEROall_ok= False;
+            if (!qh->MERGEexact || dist > qh->DISTround)
+              goto LABELnonconvex;
+          }
+          break;
+        }
+      }
+    }
+  }
+  trace2((qh, qh->ferr, 2012, "qh_checkzero: testall %d, facets are %s\n", testall,
+        (qh->MERGEexact && !testall) ?
+           "not concave, flipped, or duplicate ridged" : "clearly convex"));
+  return True;
+
+ LABELproblem:
+  qh->ZEROall_ok= False;
+  trace2((qh, qh->ferr, 2013, "qh_checkzero: facet f%d needs pre-merging\n",
+       facet->id));
+  return False;
+
+ LABELnonconvex:
+  trace2((qh, qh->ferr, 2014, "qh_checkzero: facet f%d and f%d are not clearly convex.  v%d dist %.2g\n",
+         facet->id, neighbor->id, vertex->id, dist));
+  return False;
+} /* checkzero */
+
+/*---------------------------------
+
+  qh_compareangle(angle1, angle2 )
+    used by qsort() to order merges by angle
+*/
+int qh_compareangle(const void *p1, const void *p2) {
+  const mergeT *a= *((mergeT *const*)p1), *b= *((mergeT *const*)p2);
+
+  return((a->angle > b->angle) ? 1 : -1);
+} /* compareangle */
+
+/*---------------------------------
+
+  qh_comparemerge(merge1, merge2 )
+    used by qsort() to order merges
+*/
+int qh_comparemerge(const void *p1, const void *p2) {
+  const mergeT *a= *((mergeT *const*)p1), *b= *((mergeT *const*)p2);
+
+  return(a->type - b->type);
+} /* comparemerge */
+
+/*---------------------------------
+
+  qh_comparevisit(vertex1, vertex2 )
+    used by qsort() to order vertices by their visitid
+*/
+int qh_comparevisit(const void *p1, const void *p2) {
+  const vertexT *a= *((vertexT *const*)p1), *b= *((vertexT *const*)p2);
+
+  return(a->visitid - b->visitid);
+} /* comparevisit */
+
+/*---------------------------------
+
+  qh_copynonconvex(qh, atridge )
+    set non-convex flag on other ridges (if any) between same neighbors
+
+  notes:
+    may be faster if use smaller ridge set
+
+  design:
+    for each ridge of atridge's top facet
+      if ridge shares the same neighbor
+        set nonconvex flag
+*/
+void qh_copynonconvex(qhT *qh, ridgeT *atridge) {
+  facetT *facet, *otherfacet;
+  ridgeT *ridge, **ridgep;
+
+  facet= atridge->top;
+  otherfacet= atridge->bottom;
+  FOREACHridge_(facet->ridges) {
+    if (otherfacet == otherfacet_(ridge, facet) && ridge != atridge) {
+      ridge->nonconvex= True;
+      trace4((qh, qh->ferr, 4020, "qh_copynonconvex: moved nonconvex flag from r%d to r%d\n",
+              atridge->id, ridge->id));
+      break;
+    }
+  }
+} /* copynonconvex */
+
+/*---------------------------------
+
+  qh_degen_redundant_facet(qh, facet )
+    check facet for degen. or redundancy
+
+  notes:
+    bumps vertex_visit
+    called if a facet was redundant but no longer is (qh_merge_degenredundant)
+    qh_appendmergeset() only appends first reference to facet (i.e., redundant)
+
+  see:
+    qh_degen_redundant_neighbors()
+
+  design:
+    test for redundant neighbor
+    test for degenerate facet
+*/
+void qh_degen_redundant_facet(qhT *qh, facetT *facet) {
+  vertexT *vertex, **vertexp;
+  facetT *neighbor, **neighborp;
+
+  trace4((qh, qh->ferr, 4021, "qh_degen_redundant_facet: test facet f%d for degen/redundant\n",
+          facet->id));
+  FOREACHneighbor_(facet) {
+    qh->vertex_visit++;
+    FOREACHvertex_(neighbor->vertices)
+      vertex->visitid= qh->vertex_visit;
+    FOREACHvertex_(facet->vertices) {
+      if (vertex->visitid != qh->vertex_visit)
+        break;
+    }
+    if (!vertex) {
+      qh_appendmergeset(qh, facet, neighbor, MRGredundant, NULL);
+      trace2((qh, qh->ferr, 2015, "qh_degen_redundant_facet: f%d is contained in f%d.  merge\n", facet->id, neighbor->id));
+      return;
+    }
+  }
+  if (qh_setsize(qh, facet->neighbors) < qh->hull_dim) {
+    qh_appendmergeset(qh, facet, facet, MRGdegen, NULL);
+    trace2((qh, qh->ferr, 2016, "qh_degen_redundant_neighbors: f%d is degenerate.\n", facet->id));
+  }
+} /* degen_redundant_facet */
+
+
+/*---------------------------------
+
+  qh_degen_redundant_neighbors(qh, facet, delfacet,  )
+    append degenerate and redundant neighbors to facet_mergeset
+    if delfacet,
+      only checks neighbors of both delfacet and facet
+    also checks current facet for degeneracy
+
+  notes:
+    bumps vertex_visit
+    called for each qh_mergefacet() and qh_mergecycle()
+    merge and statistics occur in merge_nonconvex
+    qh_appendmergeset() only appends first reference to facet (i.e., redundant)
+      it appends redundant facets after degenerate ones
+
+    a degenerate facet has fewer than hull_dim neighbors
+    a redundant facet's vertices is a subset of its neighbor's vertices
+    tests for redundant merges first (appendmergeset is nop for others)
+    in a merge, only needs to test neighbors of merged facet
+
+  see:
+    qh_merge_degenredundant() and qh_degen_redundant_facet()
+
+  design:
+    test for degenerate facet
+    test for redundant neighbor
+    test for degenerate neighbor
+*/
+void qh_degen_redundant_neighbors(qhT *qh, facetT *facet, facetT *delfacet) {
+  vertexT *vertex, **vertexp;
+  facetT *neighbor, **neighborp;
+  int size;
+
+  trace4((qh, qh->ferr, 4022, "qh_degen_redundant_neighbors: test neighbors of f%d with delfacet f%d\n",
+          facet->id, getid_(delfacet)));
+  if ((size= qh_setsize(qh, facet->neighbors)) < qh->hull_dim) {
+    qh_appendmergeset(qh, facet, facet, MRGdegen, NULL);
+    trace2((qh, qh->ferr, 2017, "qh_degen_redundant_neighbors: f%d is degenerate with %d neighbors.\n", facet->id, size));
+  }
+  if (!delfacet)
+    delfacet= facet;
+  qh->vertex_visit++;
+  FOREACHvertex_(facet->vertices)
+    vertex->visitid= qh->vertex_visit;
+  FOREACHneighbor_(delfacet) {
+    /* uses early out instead of checking vertex count */
+    if (neighbor == facet)
+      continue;
+    FOREACHvertex_(neighbor->vertices) {
+      if (vertex->visitid != qh->vertex_visit)
+        break;
+    }
+    if (!vertex) {
+      qh_appendmergeset(qh, neighbor, facet, MRGredundant, NULL);
+      trace2((qh, qh->ferr, 2018, "qh_degen_redundant_neighbors: f%d is contained in f%d.  merge\n", neighbor->id, facet->id));
+    }
+  }
+  FOREACHneighbor_(delfacet) {   /* redundant merges occur first */
+    if (neighbor == facet)
+      continue;
+    if ((size= qh_setsize(qh, neighbor->neighbors)) < qh->hull_dim) {
+      qh_appendmergeset(qh, neighbor, neighbor, MRGdegen, NULL);
+      trace2((qh, qh->ferr, 2019, "qh_degen_redundant_neighbors: f%d is degenerate with %d neighbors.  Neighbor of f%d.\n", neighbor->id, size, facet->id));
+    }
+  }
+} /* degen_redundant_neighbors */
+
+
+/*---------------------------------
+
+  qh_find_newvertex(qh, oldvertex, vertices, ridges )
+    locate new vertex for renaming old vertex
+    vertices is a set of possible new vertices
+      vertices sorted by number of deleted ridges
+
+  returns:
+    newvertex or NULL
+      each ridge includes both vertex and oldvertex
+    vertices sorted by number of deleted ridges
+
+  notes:
+    modifies vertex->visitid
+    new vertex is in one of the ridges
+    renaming will not cause a duplicate ridge
+    renaming will minimize the number of deleted ridges
+    newvertex may not be adjacent in the dual (though unlikely)
+
+  design:
+    for each vertex in vertices
+      set vertex->visitid to number of references in ridges
+    remove unvisited vertices
+    set qh.vertex_visit above all possible values
+    sort vertices by number of references in ridges
+    add each ridge to qh.hash_table
+    for each vertex in vertices
+      look for a vertex that would not cause a duplicate ridge after a rename
+*/
+vertexT *qh_find_newvertex(qhT *qh, vertexT *oldvertex, setT *vertices, setT *ridges) {
+  vertexT *vertex, **vertexp;
+  setT *newridges;
+  ridgeT *ridge, **ridgep;
+  int size, hashsize;
+  int hash;
+
+#ifndef qh_NOtrace
+  if (qh->IStracing >= 4) {
+    qh_fprintf(qh, qh->ferr, 8063, "qh_find_newvertex: find new vertex for v%d from ",
+             oldvertex->id);
+    FOREACHvertex_(vertices)
+      qh_fprintf(qh, qh->ferr, 8064, "v%d ", vertex->id);
+    FOREACHridge_(ridges)
+      qh_fprintf(qh, qh->ferr, 8065, "r%d ", ridge->id);
+    qh_fprintf(qh, qh->ferr, 8066, "\n");
+  }
+#endif
+  FOREACHvertex_(vertices)
+    vertex->visitid= 0;
+  FOREACHridge_(ridges) {
+    FOREACHvertex_(ridge->vertices)
+      vertex->visitid++;
+  }
+  FOREACHvertex_(vertices) {
+    if (!vertex->visitid) {
+      qh_setdelnth(qh, vertices, SETindex_(vertices,vertex));
+      vertexp--; /* repeat since deleted this vertex */
+    }
+  }
+  qh->vertex_visit += (unsigned int)qh_setsize(qh, ridges);
+  if (!qh_setsize(qh, vertices)) {
+    trace4((qh, qh->ferr, 4023, "qh_find_newvertex: vertices not in ridges for v%d\n",
+            oldvertex->id));
+    return NULL;
+  }
+  qsort(SETaddr_(vertices, vertexT), (size_t)qh_setsize(qh, vertices),
+                sizeof(vertexT *), qh_comparevisit);
+  /* can now use qh->vertex_visit */
+  if (qh->PRINTstatistics) {
+    size= qh_setsize(qh, vertices);
+    zinc_(Zintersect);
+    zadd_(Zintersecttot, size);
+    zmax_(Zintersectmax, size);
+  }
+  hashsize= qh_newhashtable(qh, qh_setsize(qh, ridges));
+  FOREACHridge_(ridges)
+    qh_hashridge(qh, qh->hash_table, hashsize, ridge, oldvertex);
+  FOREACHvertex_(vertices) {
+    newridges= qh_vertexridges(qh, vertex);
+    FOREACHridge_(newridges) {
+      if (qh_hashridge_find(qh, qh->hash_table, hashsize, ridge, vertex, oldvertex, &hash)) {
+        zinc_(Zdupridge);
+        break;
+      }
+    }
+    qh_settempfree(qh, &newridges);
+    if (!ridge)
+      break;  /* found a rename */
+  }
+  if (vertex) {
+    /* counted in qh_renamevertex */
+    trace2((qh, qh->ferr, 2020, "qh_find_newvertex: found v%d for old v%d from %d vertices and %d ridges.\n",
+      vertex->id, oldvertex->id, qh_setsize(qh, vertices), qh_setsize(qh, ridges)));
+  }else {
+    zinc_(Zfindfail);
+    trace0((qh, qh->ferr, 14, "qh_find_newvertex: no vertex for renaming v%d(all duplicated ridges) during p%d\n",
+      oldvertex->id, qh->furthest_id));
+  }
+  qh_setfree(qh, &qh->hash_table);
+  return vertex;
+} /* find_newvertex */
+
+/*---------------------------------
+
+  qh_findbest_test(qh, testcentrum, facet, neighbor, bestfacet, dist, mindist, maxdist )
+    test neighbor of facet for qh_findbestneighbor()
+    if testcentrum,
+      tests centrum (assumes it is defined)
+    else
+      tests vertices
+
+  returns:
+    if a better facet (i.e., vertices/centrum of facet closer to neighbor)
+      updates bestfacet, dist, mindist, and maxdist
+*/
+void qh_findbest_test(qhT *qh, boolT testcentrum, facetT *facet, facetT *neighbor,
+      facetT **bestfacet, realT *distp, realT *mindistp, realT *maxdistp) {
+  realT dist, mindist, maxdist;
+
+  if (testcentrum) {
+    zzinc_(Zbestdist);
+    qh_distplane(qh, facet->center, neighbor, &dist);
+    dist *= qh->hull_dim; /* estimate furthest vertex */
+    if (dist < 0) {
+      maxdist= 0;
+      mindist= dist;
+      dist= -dist;
+    }else {
+      mindist= 0;
+      maxdist= dist;
+    }
+  }else
+    dist= qh_getdistance(qh, facet, neighbor, &mindist, &maxdist);
+  if (dist < *distp) {
+    *bestfacet= neighbor;
+    *mindistp= mindist;
+    *maxdistp= maxdist;
+    *distp= dist;
+  }
+} /* findbest_test */
+
+/*---------------------------------
+
+  qh_findbestneighbor(qh, facet, dist, mindist, maxdist )
+    finds best neighbor (least dist) of a facet for merging
+
+  returns:
+    returns min and max distances and their max absolute value
+
+  notes:
+    error if qh_ASvoronoi
+    avoids merging old into new
+    assumes ridge->nonconvex only set on one ridge between a pair of facets
+    could use an early out predicate but not worth it
+
+  design:
+    if a large facet
+      will test centrum
+    else
+      will test vertices
+    if a large facet
+      test nonconvex neighbors for best merge
+    else
+      test all neighbors for the best merge
+    if testing centrum
+      get distance information
+*/
+facetT *qh_findbestneighbor(qhT *qh, facetT *facet, realT *distp, realT *mindistp, realT *maxdistp) {
+  facetT *neighbor, **neighborp, *bestfacet= NULL;
+  ridgeT *ridge, **ridgep;
+  boolT nonconvex= True, testcentrum= False;
+  int size= qh_setsize(qh, facet->vertices);
+
+  if(qh->CENTERtype==qh_ASvoronoi){
+    qh_fprintf(qh, qh->ferr, 6272, "qhull error: cannot call qh_findbestneighor for f%d while qh.CENTERtype is qh_ASvoronoi\n", facet->id);
+    qh_errexit(qh, qh_ERRqhull, facet, NULL);
+  }
+  *distp= REALmax;
+  if (size > qh_BESTcentrum2 * qh->hull_dim + qh_BESTcentrum) {
+    testcentrum= True;
+    zinc_(Zbestcentrum);
+    if (!facet->center)
+       facet->center= qh_getcentrum(qh, facet);
+  }
+  if (size > qh->hull_dim + qh_BESTnonconvex) {
+    FOREACHridge_(facet->ridges) {
+      if (ridge->nonconvex) {
+        neighbor= otherfacet_(ridge, facet);
+        qh_findbest_test(qh, testcentrum, facet, neighbor,
+                          &bestfacet, distp, mindistp, maxdistp);
+      }
+    }
+  }
+  if (!bestfacet) {
+    nonconvex= False;
+    FOREACHneighbor_(facet)
+      qh_findbest_test(qh, testcentrum, facet, neighbor,
+                        &bestfacet, distp, mindistp, maxdistp);
+  }
+  if (!bestfacet) {
+    qh_fprintf(qh, qh->ferr, 6095, "qhull internal error (qh_findbestneighbor): no neighbors for f%d\n", facet->id);
+    qh_errexit(qh, qh_ERRqhull, facet, NULL);
+  }
+  if (testcentrum)
+    qh_getdistance(qh, facet, bestfacet, mindistp, maxdistp);
+  trace3((qh, qh->ferr, 3002, "qh_findbestneighbor: f%d is best neighbor for f%d testcentrum? %d nonconvex? %d dist %2.2g min %2.2g max %2.2g\n",
+     bestfacet->id, facet->id, testcentrum, nonconvex, *distp, *mindistp, *maxdistp));
+  return(bestfacet);
+} /* findbestneighbor */
+
+
+/*---------------------------------
+
+  qh_flippedmerges(qh, facetlist, wasmerge )
+    merge flipped facets into best neighbor
+    assumes qh.facet_mergeset at top of temporary stack
+
+  returns:
+    no flipped facets on facetlist
+    sets wasmerge if merge occurred
+    degen/redundant merges passed through
+
+  notes:
+    othermerges not needed since qh.facet_mergeset is empty before & after
+      keep it in case of change
+
+  design:
+    append flipped facets to qh.facetmergeset
+    for each flipped merge
+      find best neighbor
+      merge facet into neighbor
+      merge degenerate and redundant facets
+    remove flipped merges from qh.facet_mergeset
+*/
+void qh_flippedmerges(qhT *qh, facetT *facetlist, boolT *wasmerge) {
+  facetT *facet, *neighbor, *facet1;
+  realT dist, mindist, maxdist;
+  mergeT *merge, **mergep;
+  setT *othermerges;
+  int nummerge=0;
+
+  trace4((qh, qh->ferr, 4024, "qh_flippedmerges: begin\n"));
+  FORALLfacet_(facetlist) {
+    if (facet->flipped && !facet->visible)
+      qh_appendmergeset(qh, facet, facet, MRGflip, NULL);
+  }
+  othermerges= qh_settemppop(qh); /* was facet_mergeset */
+  qh->facet_mergeset= qh_settemp(qh, qh->TEMPsize);
+  qh_settemppush(qh, othermerges);
+  FOREACHmerge_(othermerges) {
+    facet1= merge->facet1;
+    if (merge->type != MRGflip || facet1->visible)
+      continue;
+    if (qh->TRACEmerge-1 == zzval_(Ztotmerge))
+      qh->qhmem.IStracing= qh->IStracing= qh->TRACElevel;
+    neighbor= qh_findbestneighbor(qh, facet1, &dist, &mindist, &maxdist);
+    trace0((qh, qh->ferr, 15, "qh_flippedmerges: merge flipped f%d into f%d dist %2.2g during p%d\n",
+      facet1->id, neighbor->id, dist, qh->furthest_id));
+    qh_mergefacet(qh, facet1, neighbor, &mindist, &maxdist, !qh_MERGEapex);
+    nummerge++;
+    if (qh->PRINTstatistics) {
+      zinc_(Zflipped);
+      wadd_(Wflippedtot, dist);
+      wmax_(Wflippedmax, dist);
+    }
+    qh_merge_degenredundant(qh);
+  }
+  FOREACHmerge_(othermerges) {
+    if (merge->facet1->visible || merge->facet2->visible)
+      qh_memfree(qh, merge, (int)sizeof(mergeT));
+    else
+      qh_setappend(qh, &qh->facet_mergeset, merge);
+  }
+  qh_settempfree(qh, &othermerges);
+  if (nummerge)
+    *wasmerge= True;
+  trace1((qh, qh->ferr, 1010, "qh_flippedmerges: merged %d flipped facets into a good neighbor\n", nummerge));
+} /* flippedmerges */
+
+
+/*---------------------------------
+
+  qh_forcedmerges(qh, wasmerge )
+    merge duplicated ridges
+
+  returns:
+    removes all duplicate ridges on facet_mergeset
+    wasmerge set if merge
+    qh.facet_mergeset may include non-forced merges(none for now)
+    qh.degen_mergeset includes degen/redun merges
+
+  notes:
+    duplicate ridges occur when the horizon is pinched,
+        i.e. a subridge occurs in more than two horizon ridges.
+     could rename vertices that pinch the horizon
+    assumes qh_merge_degenredundant() has not be called
+    othermerges isn't needed since facet_mergeset is empty afterwards
+      keep it in case of change
+
+  design:
+    for each duplicate ridge
+      find current facets by chasing f.replace links
+      check for wide merge due to duplicate ridge
+      determine best direction for facet
+      merge one facet into the other
+      remove duplicate ridges from qh.facet_mergeset
+*/
+void qh_forcedmerges(qhT *qh, boolT *wasmerge) {
+  facetT *facet1, *facet2;
+  mergeT *merge, **mergep;
+  realT dist1, dist2, mindist1, mindist2, maxdist1, maxdist2;
+  setT *othermerges;
+  int nummerge=0, numflip=0;
+
+  if (qh->TRACEmerge-1 == zzval_(Ztotmerge))
+    qh->qhmem.IStracing= qh->IStracing= qh->TRACElevel;
+  trace4((qh, qh->ferr, 4025, "qh_forcedmerges: begin\n"));
+  othermerges= qh_settemppop(qh); /* was facet_mergeset */
+  qh->facet_mergeset= qh_settemp(qh, qh->TEMPsize);
+  qh_settemppush(qh, othermerges);
+  FOREACHmerge_(othermerges) {
+    if (merge->type != MRGridge)
+        continue;
+    if (qh->TRACEmerge-1 == zzval_(Ztotmerge))
+        qh->qhmem.IStracing= qh->IStracing= qh->TRACElevel;
+    facet1= merge->facet1;
+    facet2= merge->facet2;
+    while (facet1->visible)      /* must exist, no qh_merge_degenredunant */
+      facet1= facet1->f.replace; /* previously merged facet */
+    while (facet2->visible)
+      facet2= facet2->f.replace; /* previously merged facet */
+    if (facet1 == facet2)
+      continue;
+    if (!qh_setin(facet2->neighbors, facet1)) {
+      qh_fprintf(qh, qh->ferr, 6096, "qhull internal error (qh_forcedmerges): f%d and f%d had a duplicate ridge but as f%d and f%d they are no longer neighbors\n",
+               merge->facet1->id, merge->facet2->id, facet1->id, facet2->id);
+      qh_errexit2(qh, qh_ERRqhull, facet1, facet2);
+    }
+    dist1= qh_getdistance(qh, facet1, facet2, &mindist1, &maxdist1);
+    dist2= qh_getdistance(qh, facet2, facet1, &mindist2, &maxdist2);
+    qh_check_dupridge(qh, facet1, dist1, facet2, dist2);
+    if (dist1 < dist2)
+      qh_mergefacet(qh, facet1, facet2, &mindist1, &maxdist1, !qh_MERGEapex);
+    else {
+      qh_mergefacet(qh, facet2, facet1, &mindist2, &maxdist2, !qh_MERGEapex);
+      dist1= dist2;
+      facet1= facet2;
+    }
+    if (facet1->flipped) {
+      zinc_(Zmergeflipdup);
+      numflip++;
+    }else
+      nummerge++;
+    if (qh->PRINTstatistics) {
+      zinc_(Zduplicate);
+      wadd_(Wduplicatetot, dist1);
+      wmax_(Wduplicatemax, dist1);
+    }
+  }
+  FOREACHmerge_(othermerges) {
+    if (merge->type == MRGridge)
+      qh_memfree(qh, merge, (int)sizeof(mergeT));
+    else
+      qh_setappend(qh, &qh->facet_mergeset, merge);
+  }
+  qh_settempfree(qh, &othermerges);
+  if (nummerge)
+    *wasmerge= True;
+  trace1((qh, qh->ferr, 1011, "qh_forcedmerges: merged %d facets and %d flipped facets across duplicated ridges\n",
+                nummerge, numflip));
+} /* forcedmerges */
+
+
+/*---------------------------------
+
+  qh_getmergeset(qh, facetlist )
+    determines nonconvex facets on facetlist
+    tests !tested ridges and nonconvex ridges of !tested facets
+
+  returns:
+    returns sorted qh.facet_mergeset of facet-neighbor pairs to be merged
+    all ridges tested
+
+  notes:
+    assumes no nonconvex ridges with both facets tested
+    uses facet->tested/ridge->tested to prevent duplicate tests
+    can not limit tests to modified ridges since the centrum changed
+    uses qh.visit_id
+
+  see:
+    qh_getmergeset_initial()
+
+  design:
+    for each facet on facetlist
+      for each ridge of facet
+        if untested ridge
+          test ridge for convexity
+          if non-convex
+            append ridge to qh.facet_mergeset
+    sort qh.facet_mergeset by angle
+*/
+void qh_getmergeset(qhT *qh, facetT *facetlist) {
+  facetT *facet, *neighbor, **neighborp;
+  ridgeT *ridge, **ridgep;
+  int nummerges;
+
+  nummerges= qh_setsize(qh, qh->facet_mergeset);
+  trace4((qh, qh->ferr, 4026, "qh_getmergeset: started.\n"));
+  qh->visit_id++;
+  FORALLfacet_(facetlist) {
+    if (facet->tested)
+      continue;
+    facet->visitid= qh->visit_id;
+    facet->tested= True;  /* must be non-simplicial due to merge */
+    FOREACHneighbor_(facet)
+      neighbor->seen= False;
+    FOREACHridge_(facet->ridges) {
+      if (ridge->tested && !ridge->nonconvex)
+        continue;
+      /* if tested & nonconvex, need to append merge */
+      neighbor= otherfacet_(ridge, facet);
+      if (neighbor->seen) {
+        ridge->tested= True;
+        ridge->nonconvex= False;
+      }else if (neighbor->visitid != qh->visit_id) {
+        ridge->tested= True;
+        ridge->nonconvex= False;
+        neighbor->seen= True;      /* only one ridge is marked nonconvex */
+        if (qh_test_appendmerge(qh, facet, neighbor))
+          ridge->nonconvex= True;
+      }
+    }
+  }
+  nummerges= qh_setsize(qh, qh->facet_mergeset);
+  if (qh->ANGLEmerge)
+    qsort(SETaddr_(qh->facet_mergeset, mergeT), (size_t)nummerges, sizeof(mergeT *), qh_compareangle);
+  else
+    qsort(SETaddr_(qh->facet_mergeset, mergeT), (size_t)nummerges, sizeof(mergeT *), qh_comparemerge);
+  if (qh->POSTmerging) {
+    zadd_(Zmergesettot2, nummerges);
+  }else {
+    zadd_(Zmergesettot, nummerges);
+    zmax_(Zmergesetmax, nummerges);
+  }
+  trace2((qh, qh->ferr, 2021, "qh_getmergeset: %d merges found\n", nummerges));
+} /* getmergeset */
+
+
+/*---------------------------------
+
+  qh_getmergeset_initial(qh, facetlist )
+    determine initial qh.facet_mergeset for facets
+    tests all facet/neighbor pairs on facetlist
+
+  returns:
+    sorted qh.facet_mergeset with nonconvex ridges
+    sets facet->tested, ridge->tested, and ridge->nonconvex
+
+  notes:
+    uses visit_id, assumes ridge->nonconvex is False
+
+  see:
+    qh_getmergeset()
+
+  design:
+    for each facet on facetlist
+      for each untested neighbor of facet
+        test facet and neighbor for convexity
+        if non-convex
+          append merge to qh.facet_mergeset
+          mark one of the ridges as nonconvex
+    sort qh.facet_mergeset by angle
+*/
+void qh_getmergeset_initial(qhT *qh, facetT *facetlist) {
+  facetT *facet, *neighbor, **neighborp;
+  ridgeT *ridge, **ridgep;
+  int nummerges;
+
+  qh->visit_id++;
+  FORALLfacet_(facetlist) {
+    facet->visitid= qh->visit_id;
+    facet->tested= True;
+    FOREACHneighbor_(facet) {
+      if (neighbor->visitid != qh->visit_id) {
+        if (qh_test_appendmerge(qh, facet, neighbor)) {
+          FOREACHridge_(neighbor->ridges) {
+            if (facet == otherfacet_(ridge, neighbor)) {
+              ridge->nonconvex= True;
+              break;    /* only one ridge is marked nonconvex */
+            }
+          }
+        }
+      }
+    }
+    FOREACHridge_(facet->ridges)
+      ridge->tested= True;
+  }
+  nummerges= qh_setsize(qh, qh->facet_mergeset);
+  if (qh->ANGLEmerge)
+    qsort(SETaddr_(qh->facet_mergeset, mergeT), (size_t)nummerges, sizeof(mergeT *), qh_compareangle);
+  else
+    qsort(SETaddr_(qh->facet_mergeset, mergeT), (size_t)nummerges, sizeof(mergeT *), qh_comparemerge);
+  if (qh->POSTmerging) {
+    zadd_(Zmergeinittot2, nummerges);
+  }else {
+    zadd_(Zmergeinittot, nummerges);
+    zmax_(Zmergeinitmax, nummerges);
+  }
+  trace2((qh, qh->ferr, 2022, "qh_getmergeset_initial: %d merges found\n", nummerges));
+} /* getmergeset_initial */
+
+
+/*---------------------------------
+
+  qh_hashridge(qh, hashtable, hashsize, ridge, oldvertex )
+    add ridge to hashtable without oldvertex
+
+  notes:
+    assumes hashtable is large enough
+
+  design:
+    determine hash value for ridge without oldvertex
+    find next empty slot for ridge
+*/
+void qh_hashridge(qhT *qh, setT *hashtable, int hashsize, ridgeT *ridge, vertexT *oldvertex) {
+  int hash;
+  ridgeT *ridgeA;
+
+  hash= qh_gethash(qh, hashsize, ridge->vertices, qh->hull_dim-1, 0, oldvertex);
+  while (True) {
+    if (!(ridgeA= SETelemt_(hashtable, hash, ridgeT))) {
+      SETelem_(hashtable, hash)= ridge;
+      break;
+    }else if (ridgeA == ridge)
+      break;
+    if (++hash == hashsize)
+      hash= 0;
+  }
+} /* hashridge */
+
+
+/*---------------------------------
+
+  qh_hashridge_find(qh, hashtable, hashsize, ridge, vertex, oldvertex, hashslot )
+    returns matching ridge without oldvertex in hashtable
+      for ridge without vertex
+    if oldvertex is NULL
+      matches with any one skip
+
+  returns:
+    matching ridge or NULL
+    if no match,
+      if ridge already in   table
+        hashslot= -1
+      else
+        hashslot= next NULL index
+
+  notes:
+    assumes hashtable is large enough
+    can't match ridge to itself
+
+  design:
+    get hash value for ridge without vertex
+    for each hashslot
+      return match if ridge matches ridgeA without oldvertex
+*/
+ridgeT *qh_hashridge_find(qhT *qh, setT *hashtable, int hashsize, ridgeT *ridge,
+              vertexT *vertex, vertexT *oldvertex, int *hashslot) {
+  int hash;
+  ridgeT *ridgeA;
+
+  *hashslot= 0;
+  zinc_(Zhashridge);
+  hash= qh_gethash(qh, hashsize, ridge->vertices, qh->hull_dim-1, 0, vertex);
+  while ((ridgeA= SETelemt_(hashtable, hash, ridgeT))) {
+    if (ridgeA == ridge)
+      *hashslot= -1;
+    else {
+      zinc_(Zhashridgetest);
+      if (qh_setequal_except(ridge->vertices, vertex, ridgeA->vertices, oldvertex))
+        return ridgeA;
+    }
+    if (++hash == hashsize)
+      hash= 0;
+  }
+  if (!*hashslot)
+    *hashslot= hash;
+  return NULL;
+} /* hashridge_find */
+
+
+/*---------------------------------
+
+  qh_makeridges(qh, facet )
+    creates explicit ridges between simplicial facets
+
+  returns:
+    facet with ridges and without qh_MERGEridge
+    ->simplicial is False
+
+  notes:
+    allows qh_MERGEridge flag
+    uses existing ridges
+    duplicate neighbors ok if ridges already exist (qh_mergecycle_ridges)
+
+  see:
+    qh_mergecycle_ridges()
+
+  design:
+    look for qh_MERGEridge neighbors
+    mark neighbors that already have ridges
+    for each unprocessed neighbor of facet
+      create a ridge for neighbor and facet
+    if any qh_MERGEridge neighbors
+      delete qh_MERGEridge flags (already handled by qh_mark_dupridges)
+*/
+void qh_makeridges(qhT *qh, facetT *facet) {
+  facetT *neighbor, **neighborp;
+  ridgeT *ridge, **ridgep;
+  int neighbor_i, neighbor_n;
+  boolT toporient, mergeridge= False;
+
+  if (!facet->simplicial)
+    return;
+  trace4((qh, qh->ferr, 4027, "qh_makeridges: make ridges for f%d\n", facet->id));
+  facet->simplicial= False;
+  FOREACHneighbor_(facet) {
+    if (neighbor == qh_MERGEridge)
+      mergeridge= True;
+    else
+      neighbor->seen= False;
+  }
+  FOREACHridge_(facet->ridges)
+    otherfacet_(ridge, facet)->seen= True;
+  FOREACHneighbor_i_(qh, facet) {
+    if (neighbor == qh_MERGEridge)
+      continue;  /* fixed by qh_mark_dupridges */
+    else if (!neighbor->seen) {  /* no current ridges */
+      ridge= qh_newridge(qh);
+      ridge->vertices= qh_setnew_delnthsorted(qh, facet->vertices, qh->hull_dim,
+                                                          neighbor_i, 0);
+      toporient= facet->toporient ^ (neighbor_i & 0x1);
+      if (toporient) {
+        ridge->top= facet;
+        ridge->bottom= neighbor;
+      }else {
+        ridge->top= neighbor;
+        ridge->bottom= facet;
+      }
+#if 0 /* this also works */
+      flip= (facet->toporient ^ neighbor->toporient)^(skip1 & 0x1) ^ (skip2 & 0x1);
+      if (facet->toporient ^ (skip1 & 0x1) ^ flip) {
+        ridge->top= neighbor;
+        ridge->bottom= facet;
+      }else {
+        ridge->top= facet;
+        ridge->bottom= neighbor;
+      }
+#endif
+      qh_setappend(qh, &(facet->ridges), ridge);
+      qh_setappend(qh, &(neighbor->ridges), ridge);
+    }
+  }
+  if (mergeridge) {
+    while (qh_setdel(facet->neighbors, qh_MERGEridge))
+      ; /* delete each one */
+  }
+} /* makeridges */
+
+
+/*---------------------------------
+
+  qh_mark_dupridges(qh, facetlist )
+    add duplicated ridges to qh.facet_mergeset
+    facet->dupridge is true
+
+  returns:
+    duplicate ridges on qh.facet_mergeset
+    ->mergeridge/->mergeridge2 set
+    duplicate ridges marked by qh_MERGEridge and both sides facet->dupridge
+    no MERGEridges in neighbor sets
+
+  notes:
+    duplicate ridges occur when the horizon is pinched,
+        i.e. a subridge occurs in more than two horizon ridges.
+    could rename vertices that pinch the horizon (thus removing subridge)
+    uses qh.visit_id
+
+  design:
+    for all facets on facetlist
+      if facet contains a duplicate ridge
+        for each neighbor of facet
+          if neighbor marked qh_MERGEridge (one side of the merge)
+            set facet->mergeridge
+          else
+            if neighbor contains a duplicate ridge
+            and the back link is qh_MERGEridge
+              append duplicate ridge to qh.facet_mergeset
+   for each duplicate ridge
+     make ridge sets in preparation for merging
+     remove qh_MERGEridge from neighbor set
+   for each duplicate ridge
+     restore the missing neighbor from the neighbor set that was qh_MERGEridge
+     add the missing ridge for this neighbor
+*/
+void qh_mark_dupridges(qhT *qh, facetT *facetlist) {
+  facetT *facet, *neighbor, **neighborp;
+  int nummerge=0;
+  mergeT *merge, **mergep;
+
+
+  trace4((qh, qh->ferr, 4028, "qh_mark_dupridges: identify duplicate ridges\n"));
+  FORALLfacet_(facetlist) {
+    if (facet->dupridge) {
+      FOREACHneighbor_(facet) {
+        if (neighbor == qh_MERGEridge) {
+          facet->mergeridge= True;
+          continue;
+        }
+        if (neighbor->dupridge
+        && !qh_setin(neighbor->neighbors, facet)) { /* qh_MERGEridge */
+          qh_appendmergeset(qh, facet, neighbor, MRGridge, NULL);
+          facet->mergeridge2= True;
+          facet->mergeridge= True;
+          nummerge++;
+        }
+      }
+    }
+  }
+  if (!nummerge)
+    return;
+  FORALLfacet_(facetlist) {            /* gets rid of qh_MERGEridge */
+    if (facet->mergeridge && !facet->mergeridge2)
+      qh_makeridges(qh, facet);
+  }
+  FOREACHmerge_(qh->facet_mergeset) {   /* restore the missing neighbors */
+    if (merge->type == MRGridge) {
+      qh_setappend(qh, &merge->facet2->neighbors, merge->facet1);
+      qh_makeridges(qh, merge->facet1);   /* and the missing ridges */
+    }
+  }
+  trace1((qh, qh->ferr, 1012, "qh_mark_dupridges: found %d duplicated ridges\n",
+                nummerge));
+} /* mark_dupridges */
+
+/*---------------------------------
+
+  qh_maydropneighbor(qh, facet )
+    drop neighbor relationship if no ridge between facet and neighbor
+
+  returns:
+    neighbor sets updated
+    appends degenerate facets to qh.facet_mergeset
+
+  notes:
+    won't cause redundant facets since vertex inclusion is the same
+    may drop vertex and neighbor if no ridge
+    uses qh.visit_id
+
+  design:
+    visit all neighbors with ridges
+    for each unvisited neighbor of facet
+      delete neighbor and facet from the neighbor sets
+      if neighbor becomes degenerate
+        append neighbor to qh.degen_mergeset
+    if facet is degenerate
+      append facet to qh.degen_mergeset
+*/
+void qh_maydropneighbor(qhT *qh, facetT *facet) {
+  ridgeT *ridge, **ridgep;
+  realT angledegen= qh_ANGLEdegen;
+  facetT *neighbor, **neighborp;
+
+  qh->visit_id++;
+  trace4((qh, qh->ferr, 4029, "qh_maydropneighbor: test f%d for no ridges to a neighbor\n",
+          facet->id));
+  FOREACHridge_(facet->ridges) {
+    ridge->top->visitid= qh->visit_id;
+    ridge->bottom->visitid= qh->visit_id;
+  }
+  FOREACHneighbor_(facet) {
+    if (neighbor->visitid != qh->visit_id) {
+      trace0((qh, qh->ferr, 17, "qh_maydropneighbor: facets f%d and f%d are no longer neighbors during p%d\n",
+            facet->id, neighbor->id, qh->furthest_id));
+      zinc_(Zdropneighbor);
+      qh_setdel(facet->neighbors, neighbor);
+      neighborp--;  /* repeat, deleted a neighbor */
+      qh_setdel(neighbor->neighbors, facet);
+      if (qh_setsize(qh, neighbor->neighbors) < qh->hull_dim) {
+        zinc_(Zdropdegen);
+        qh_appendmergeset(qh, neighbor, neighbor, MRGdegen, &angledegen);
+        trace2((qh, qh->ferr, 2023, "qh_maydropneighbors: f%d is degenerate.\n", neighbor->id));
+      }
+    }
+  }
+  if (qh_setsize(qh, facet->neighbors) < qh->hull_dim) {
+    zinc_(Zdropdegen);
+    qh_appendmergeset(qh, facet, facet, MRGdegen, &angledegen);
+    trace2((qh, qh->ferr, 2024, "qh_maydropneighbors: f%d is degenerate.\n", facet->id));
+  }
+} /* maydropneighbor */
+
+
+/*---------------------------------
+
+  qh_merge_degenredundant(qh)
+    merge all degenerate and redundant facets
+    qh.degen_mergeset contains merges from qh_degen_redundant_neighbors()
+
+  returns:
+    number of merges performed
+    resets facet->degenerate/redundant
+    if deleted (visible) facet has no neighbors
+      sets ->f.replace to NULL
+
+  notes:
+    redundant merges happen before degenerate ones
+    merging and renaming vertices can result in degen/redundant facets
+
+  design:
+    for each merge on qh.degen_mergeset
+      if redundant merge
+        if non-redundant facet merged into redundant facet
+          recheck facet for redundancy
+        else
+          merge redundant facet into other facet
+*/
+int qh_merge_degenredundant(qhT *qh) {
+  int size;
+  mergeT *merge;
+  facetT *bestneighbor, *facet1, *facet2;
+  realT dist, mindist, maxdist;
+  vertexT *vertex, **vertexp;
+  int nummerges= 0;
+  mergeType mergetype;
+
+  while ((merge= (mergeT*)qh_setdellast(qh->degen_mergeset))) {
+    facet1= merge->facet1;
+    facet2= merge->facet2;
+    mergetype= merge->type;
+    qh_memfree(qh, merge, (int)sizeof(mergeT));
+    if (facet1->visible)
+      continue;
+    facet1->degenerate= False;
+    facet1->redundant= False;
+    if (qh->TRACEmerge-1 == zzval_(Ztotmerge))
+      qh->qhmem.IStracing= qh->IStracing= qh->TRACElevel;
+    if (mergetype == MRGredundant) {
+      zinc_(Zneighbor);
+      while (facet2->visible) {
+        if (!facet2->f.replace) {
+          qh_fprintf(qh, qh->ferr, 6097, "qhull internal error (qh_merge_degenredunant): f%d redundant but f%d has no replacement\n",
+               facet1->id, facet2->id);
+          qh_errexit2(qh, qh_ERRqhull, facet1, facet2);
+        }
+        facet2= facet2->f.replace;
+      }
+      if (facet1 == facet2) {
+        qh_degen_redundant_facet(qh, facet1); /* in case of others */
+        continue;
+      }
+      trace2((qh, qh->ferr, 2025, "qh_merge_degenredundant: facet f%d is contained in f%d, will merge\n",
+            facet1->id, facet2->id));
+      qh_mergefacet(qh, facet1, facet2, NULL, NULL, !qh_MERGEapex);
+      /* merge distance is already accounted for */
+      nummerges++;
+    }else {  /* mergetype == MRGdegen, other merges may have fixed */
+      if (!(size= qh_setsize(qh, facet1->neighbors))) {
+        zinc_(Zdelfacetdup);
+        trace2((qh, qh->ferr, 2026, "qh_merge_degenredundant: facet f%d has no neighbors.  Deleted\n", facet1->id));
+        qh_willdelete(qh, facet1, NULL);
+        FOREACHvertex_(facet1->vertices) {
+          qh_setdel(vertex->neighbors, facet1);
+          if (!SETfirst_(vertex->neighbors)) {
+            zinc_(Zdegenvertex);
+            trace2((qh, qh->ferr, 2027, "qh_merge_degenredundant: deleted v%d because f%d has no neighbors\n",
+                 vertex->id, facet1->id));
+            vertex->deleted= True;
+            qh_setappend(qh, &qh->del_vertices, vertex);
+          }
+        }
+        nummerges++;
+      }else if (size < qh->hull_dim) {
+        bestneighbor= qh_findbestneighbor(qh, facet1, &dist, &mindist, &maxdist);
+        trace2((qh, qh->ferr, 2028, "qh_merge_degenredundant: facet f%d has %d neighbors, merge into f%d dist %2.2g\n",
+              facet1->id, size, bestneighbor->id, dist));
+        qh_mergefacet(qh, facet1, bestneighbor, &mindist, &maxdist, !qh_MERGEapex);
+        nummerges++;
+        if (qh->PRINTstatistics) {
+          zinc_(Zdegen);
+          wadd_(Wdegentot, dist);
+          wmax_(Wdegenmax, dist);
+        }
+      } /* else, another merge fixed the degeneracy and redundancy tested */
+    }
+  }
+  return nummerges;
+} /* merge_degenredundant */
+
+/*---------------------------------
+
+  qh_merge_nonconvex(qh, facet1, facet2, mergetype )
+    remove non-convex ridge between facet1 into facet2
+    mergetype gives why the facet's are non-convex
+
+  returns:
+    merges one of the facets into the best neighbor
+
+  design:
+    if one of the facets is a new facet
+      prefer merging new facet into old facet
+    find best neighbors for both facets
+    merge the nearest facet into its best neighbor
+    update the statistics
+*/
+void qh_merge_nonconvex(qhT *qh, facetT *facet1, facetT *facet2, mergeType mergetype) {
+  facetT *bestfacet, *bestneighbor, *neighbor;
+  realT dist, dist2, mindist, mindist2, maxdist, maxdist2;
+
+  if (qh->TRACEmerge-1 == zzval_(Ztotmerge))
+    qh->qhmem.IStracing= qh->IStracing= qh->TRACElevel;
+  trace3((qh, qh->ferr, 3003, "qh_merge_nonconvex: merge #%d for f%d and f%d type %d\n",
+      zzval_(Ztotmerge) + 1, facet1->id, facet2->id, mergetype));
+  /* concave or coplanar */
+  if (!facet1->newfacet) {
+    bestfacet= facet2;   /* avoid merging old facet if new is ok */
+    facet2= facet1;
+    facet1= bestfacet;
+  }else
+    bestfacet= facet1;
+  bestneighbor= qh_findbestneighbor(qh, bestfacet, &dist, &mindist, &maxdist);
+  neighbor= qh_findbestneighbor(qh, facet2, &dist2, &mindist2, &maxdist2);
+  if (dist < dist2) {
+    qh_mergefacet(qh, bestfacet, bestneighbor, &mindist, &maxdist, !qh_MERGEapex);
+  }else if (qh->AVOIDold && !facet2->newfacet
+  && ((mindist >= -qh->MAXcoplanar && maxdist <= qh->max_outside)
+       || dist * 1.5 < dist2)) {
+    zinc_(Zavoidold);
+    wadd_(Wavoidoldtot, dist);
+    wmax_(Wavoidoldmax, dist);
+    trace2((qh, qh->ferr, 2029, "qh_merge_nonconvex: avoid merging old facet f%d dist %2.2g.  Use f%d dist %2.2g instead\n",
+           facet2->id, dist2, facet1->id, dist2));
+    qh_mergefacet(qh, bestfacet, bestneighbor, &mindist, &maxdist, !qh_MERGEapex);
+  }else {
+    qh_mergefacet(qh, facet2, neighbor, &mindist2, &maxdist2, !qh_MERGEapex);
+    dist= dist2;
+  }
+  if (qh->PRINTstatistics) {
+    if (mergetype == MRGanglecoplanar) {
+      zinc_(Zacoplanar);
+      wadd_(Wacoplanartot, dist);
+      wmax_(Wacoplanarmax, dist);
+    }else if (mergetype == MRGconcave) {
+      zinc_(Zconcave);
+      wadd_(Wconcavetot, dist);
+      wmax_(Wconcavemax, dist);
+    }else { /* MRGcoplanar */
+      zinc_(Zcoplanar);
+      wadd_(Wcoplanartot, dist);
+      wmax_(Wcoplanarmax, dist);
+    }
+  }
+} /* merge_nonconvex */
+
+/*---------------------------------
+
+  qh_mergecycle(qh, samecycle, newfacet )
+    merge a cycle of facets starting at samecycle into a newfacet
+    newfacet is a horizon facet with ->normal
+    samecycle facets are simplicial from an apex
+
+  returns:
+    initializes vertex neighbors on first merge
+    samecycle deleted (placed on qh.visible_list)
+    newfacet at end of qh.facet_list
+    deleted vertices on qh.del_vertices
+
+  see:
+    qh_mergefacet()
+    called by qh_mergecycle_all() for multiple, same cycle facets
+
+  design:
+    make vertex neighbors if necessary
+    make ridges for newfacet
+    merge neighbor sets of samecycle into newfacet
+    merge ridges of samecycle into newfacet
+    merge vertex neighbors of samecycle into newfacet
+    make apex of samecycle the apex of newfacet
+    if newfacet wasn't a new facet
+      add its vertices to qh.newvertex_list
+    delete samecycle facets a make newfacet a newfacet
+*/
+void qh_mergecycle(qhT *qh, facetT *samecycle, facetT *newfacet) {
+  int traceonce= False, tracerestore= 0;
+  vertexT *apex;
+#ifndef qh_NOtrace
+  facetT *same;
+#endif
+
+  if (newfacet->tricoplanar) {
+    if (!qh->TRInormals) {
+      qh_fprintf(qh, qh->ferr, 6224, "Qhull internal error (qh_mergecycle): does not work for tricoplanar facets.  Use option 'Q11'\n");
+      qh_errexit(qh, qh_ERRqhull, newfacet, NULL);
+    }
+    newfacet->tricoplanar= False;
+    newfacet->keepcentrum= False;
+  }
+  if (!qh->VERTEXneighbors)
+    qh_vertexneighbors(qh);
+  zzinc_(Ztotmerge);
+  if (qh->REPORTfreq2 && qh->POSTmerging) {
+    if (zzval_(Ztotmerge) > qh->mergereport + qh->REPORTfreq2)
+      qh_tracemerging(qh);
+  }
+#ifndef qh_NOtrace
+  if (qh->TRACEmerge == zzval_(Ztotmerge))
+    qh->qhmem.IStracing= qh->IStracing= qh->TRACElevel;
+  trace2((qh, qh->ferr, 2030, "qh_mergecycle: merge #%d for facets from cycle f%d into coplanar horizon f%d\n",
+        zzval_(Ztotmerge), samecycle->id, newfacet->id));
+  if (newfacet == qh->tracefacet) {
+    tracerestore= qh->IStracing;
+    qh->IStracing= 4;
+    qh_fprintf(qh, qh->ferr, 8068, "qh_mergecycle: ========= trace merge %d of samecycle %d into trace f%d, furthest is p%d\n",
+               zzval_(Ztotmerge), samecycle->id, newfacet->id,  qh->furthest_id);
+    traceonce= True;
+  }
+  if (qh->IStracing >=4) {
+    qh_fprintf(qh, qh->ferr, 8069, "  same cycle:");
+    FORALLsame_cycle_(samecycle)
+      qh_fprintf(qh, qh->ferr, 8070, " f%d", same->id);
+    qh_fprintf(qh, qh->ferr, 8071, "\n");
+  }
+  if (qh->IStracing >=4)
+    qh_errprint(qh, "MERGING CYCLE", samecycle, newfacet, NULL, NULL);
+#endif /* !qh_NOtrace */
+  apex= SETfirstt_(samecycle->vertices, vertexT);
+  qh_makeridges(qh, newfacet);
+  qh_mergecycle_neighbors(qh, samecycle, newfacet);
+  qh_mergecycle_ridges(qh, samecycle, newfacet);
+  qh_mergecycle_vneighbors(qh, samecycle, newfacet);
+  if (SETfirstt_(newfacet->vertices, vertexT) != apex)
+    qh_setaddnth(qh, &newfacet->vertices, 0, apex);  /* apex has last id */
+  if (!newfacet->newfacet)
+    qh_newvertices(qh, newfacet->vertices);
+  qh_mergecycle_facets(qh, samecycle, newfacet);
+  qh_tracemerge(qh, samecycle, newfacet);
+  /* check for degen_redundant_neighbors after qh_forcedmerges() */
+  if (traceonce) {
+    qh_fprintf(qh, qh->ferr, 8072, "qh_mergecycle: end of trace facet\n");
+    qh->IStracing= tracerestore;
+  }
+} /* mergecycle */
+
+/*---------------------------------
+
+  qh_mergecycle_all(qh, facetlist, wasmerge )
+    merge all samecycles of coplanar facets into horizon
+    don't merge facets with ->mergeridge (these already have ->normal)
+    all facets are simplicial from apex
+    all facet->cycledone == False
+
+  returns:
+    all newfacets merged into coplanar horizon facets
+    deleted vertices on  qh.del_vertices
+    sets wasmerge if any merge
+
+  see:
+    calls qh_mergecycle for multiple, same cycle facets
+
+  design:
+    for each facet on facetlist
+      skip facets with duplicate ridges and normals
+      check that facet is in a samecycle (->mergehorizon)
+      if facet only member of samecycle
+        sets vertex->delridge for all vertices except apex
+        merge facet into horizon
+      else
+        mark all facets in samecycle
+        remove facets with duplicate ridges from samecycle
+        merge samecycle into horizon (deletes facets from facetlist)
+*/
+void qh_mergecycle_all(qhT *qh, facetT *facetlist, boolT *wasmerge) {
+  facetT *facet, *same, *prev, *horizon;
+  facetT *samecycle= NULL, *nextfacet, *nextsame;
+  vertexT *apex, *vertex, **vertexp;
+  int cycles=0, total=0, facets, nummerge;
+
+  trace2((qh, qh->ferr, 2031, "qh_mergecycle_all: begin\n"));
+  for (facet= facetlist; facet && (nextfacet= facet->next); facet= nextfacet) {
+    if (facet->normal)
+      continue;
+    if (!facet->mergehorizon) {
+      qh_fprintf(qh, qh->ferr, 6225, "Qhull internal error (qh_mergecycle_all): f%d without normal\n", facet->id);
+      qh_errexit(qh, qh_ERRqhull, facet, NULL);
+    }
+    horizon= SETfirstt_(facet->neighbors, facetT);
+    if (facet->f.samecycle == facet) {
+      zinc_(Zonehorizon);
+      /* merge distance done in qh_findhorizon */
+      apex= SETfirstt_(facet->vertices, vertexT);
+      FOREACHvertex_(facet->vertices) {
+        if (vertex != apex)
+          vertex->delridge= True;
+      }
+      horizon->f.newcycle= NULL;
+      qh_mergefacet(qh, facet, horizon, NULL, NULL, qh_MERGEapex);
+    }else {
+      samecycle= facet;
+      facets= 0;
+      prev= facet;
+      for (same= facet->f.samecycle; same;  /* FORALLsame_cycle_(facet) */
+           same= (same == facet ? NULL :nextsame)) { /* ends at facet */
+        nextsame= same->f.samecycle;
+        if (same->cycledone || same->visible)
+          qh_infiniteloop(qh, same);
+        same->cycledone= True;
+        if (same->normal) {
+          prev->f.samecycle= same->f.samecycle; /* unlink ->mergeridge */
+          same->f.samecycle= NULL;
+        }else {
+          prev= same;
+          facets++;
+        }
+      }
+      while (nextfacet && nextfacet->cycledone)  /* will delete samecycle */
+        nextfacet= nextfacet->next;
+      horizon->f.newcycle= NULL;
+      qh_mergecycle(qh, samecycle, horizon);
+      nummerge= horizon->nummerge + facets;
+      if (nummerge > qh_MAXnummerge)
+        horizon->nummerge= qh_MAXnummerge;
+      else
+        horizon->nummerge= (short unsigned int)nummerge;
+      zzinc_(Zcyclehorizon);
+      total += facets;
+      zzadd_(Zcyclefacettot, facets);
+      zmax_(Zcyclefacetmax, facets);
+    }
+    cycles++;
+  }
+  if (cycles)
+    *wasmerge= True;
+  trace1((qh, qh->ferr, 1013, "qh_mergecycle_all: merged %d same cycles or facets into coplanar horizons\n", cycles));
+} /* mergecycle_all */
+
+/*---------------------------------
+
+  qh_mergecycle_facets(qh, samecycle, newfacet )
+    finish merge of samecycle into newfacet
+
+  returns:
+    samecycle prepended to visible_list for later deletion and partitioning
+      each facet->f.replace == newfacet
+
+    newfacet moved to end of qh.facet_list
+      makes newfacet a newfacet (get's facet1->id if it was old)
+      sets newfacet->newmerge
+      clears newfacet->center (unless merging into a large facet)
+      clears newfacet->tested and ridge->tested for facet1
+
+    adds neighboring facets to facet_mergeset if redundant or degenerate
+
+  design:
+    make newfacet a new facet and set its flags
+    move samecycle facets to qh.visible_list for later deletion
+    unless newfacet is large
+      remove its centrum
+*/
+void qh_mergecycle_facets(qhT *qh, facetT *samecycle, facetT *newfacet) {
+  facetT *same, *next;
+
+  trace4((qh, qh->ferr, 4030, "qh_mergecycle_facets: make newfacet new and samecycle deleted\n"));
+  qh_removefacet(qh, newfacet);  /* append as a newfacet to end of qh->facet_list */
+  qh_appendfacet(qh, newfacet);
+  newfacet->newfacet= True;
+  newfacet->simplicial= False;
+  newfacet->newmerge= True;
+
+  for (same= samecycle->f.samecycle; same; same= (same == samecycle ?  NULL : next)) {
+    next= same->f.samecycle;  /* reused by willdelete */
+    qh_willdelete(qh, same, newfacet);
+  }
+  if (newfacet->center
+      && qh_setsize(qh, newfacet->vertices) <= qh->hull_dim + qh_MAXnewcentrum) {
+    qh_memfree(qh, newfacet->center, qh->normal_size);
+    newfacet->center= NULL;
+  }
+  trace3((qh, qh->ferr, 3004, "qh_mergecycle_facets: merged facets from cycle f%d into f%d\n",
+             samecycle->id, newfacet->id));
+} /* mergecycle_facets */
+
+/*---------------------------------
+
+  qh_mergecycle_neighbors(qh, samecycle, newfacet )
+    add neighbors for samecycle facets to newfacet
+
+  returns:
+    newfacet with updated neighbors and vice-versa
+    newfacet has ridges
+    all neighbors of newfacet marked with qh.visit_id
+    samecycle facets marked with qh.visit_id-1
+    ridges updated for simplicial neighbors of samecycle with a ridge
+
+  notes:
+    assumes newfacet not in samecycle
+    usually, samecycle facets are new, simplicial facets without internal ridges
+      not so if horizon facet is coplanar to two different samecycles
+
+  see:
+    qh_mergeneighbors()
+
+  design:
+    check samecycle
+    delete neighbors from newfacet that are also in samecycle
+    for each neighbor of a facet in samecycle
+      if neighbor is simplicial
+        if first visit
+          move the neighbor relation to newfacet
+          update facet links for its ridges
+        else
+          make ridges for neighbor
+          remove samecycle reference
+      else
+        update neighbor sets
+*/
+void qh_mergecycle_neighbors(qhT *qh, facetT *samecycle, facetT *newfacet) {
+  facetT *same, *neighbor, **neighborp;
+  int delneighbors= 0, newneighbors= 0;
+  unsigned int samevisitid;
+  ridgeT *ridge, **ridgep;
+
+  samevisitid= ++qh->visit_id;
+  FORALLsame_cycle_(samecycle) {
+    if (same->visitid == samevisitid || same->visible)
+      qh_infiniteloop(qh, samecycle);
+    same->visitid= samevisitid;
+  }
+  newfacet->visitid= ++qh->visit_id;
+  trace4((qh, qh->ferr, 4031, "qh_mergecycle_neighbors: delete shared neighbors from newfacet\n"));
+  FOREACHneighbor_(newfacet) {
+    if (neighbor->visitid == samevisitid) {
+      SETref_(neighbor)= NULL;  /* samecycle neighbors deleted */
+      delneighbors++;
+    }else
+      neighbor->visitid= qh->visit_id;
+  }
+  qh_setcompact(qh, newfacet->neighbors);
+
+  trace4((qh, qh->ferr, 4032, "qh_mergecycle_neighbors: update neighbors\n"));
+  FORALLsame_cycle_(samecycle) {
+    FOREACHneighbor_(same) {
+      if (neighbor->visitid == samevisitid)
+        continue;
+      if (neighbor->simplicial) {
+        if (neighbor->visitid != qh->visit_id) {
+          qh_setappend(qh, &newfacet->neighbors, neighbor);
+          qh_setreplace(qh, neighbor->neighbors, same, newfacet);
+          newneighbors++;
+          neighbor->visitid= qh->visit_id;
+          FOREACHridge_(neighbor->ridges) { /* update ridge in case of qh_makeridges */
+            if (ridge->top == same) {
+              ridge->top= newfacet;
+              break;
+            }else if (ridge->bottom == same) {
+              ridge->bottom= newfacet;
+              break;
+            }
+          }
+        }else {
+          qh_makeridges(qh, neighbor);
+          qh_setdel(neighbor->neighbors, same);
+          /* same can't be horizon facet for neighbor */
+        }
+      }else { /* non-simplicial neighbor */
+        qh_setdel(neighbor->neighbors, same);
+        if (neighbor->visitid != qh->visit_id) {
+          qh_setappend(qh, &neighbor->neighbors, newfacet);
+          qh_setappend(qh, &newfacet->neighbors, neighbor);
+          neighbor->visitid= qh->visit_id;
+          newneighbors++;
+        }
+      }
+    }
+  }
+  trace2((qh, qh->ferr, 2032, "qh_mergecycle_neighbors: deleted %d neighbors and added %d\n",
+             delneighbors, newneighbors));
+} /* mergecycle_neighbors */
+
+/*---------------------------------
+
+  qh_mergecycle_ridges(qh, samecycle, newfacet )
+    add ridges/neighbors for facets in samecycle to newfacet
+    all new/old neighbors of newfacet marked with qh.visit_id
+    facets in samecycle marked with qh.visit_id-1
+    newfacet marked with qh.visit_id
+
+  returns:
+    newfacet has merged ridges
+
+  notes:
+    ridge already updated for simplicial neighbors of samecycle with a ridge
+
+  see:
+    qh_mergeridges()
+    qh_makeridges()
+
+  design:
+    remove ridges between newfacet and samecycle
+    for each facet in samecycle
+      for each ridge in facet
+        update facet pointers in ridge
+        skip ridges processed in qh_mergecycle_neighors
+        free ridges between newfacet and samecycle
+        free ridges between facets of samecycle (on 2nd visit)
+        append remaining ridges to newfacet
+      if simpilicial facet
+        for each neighbor of facet
+          if simplicial facet
+          and not samecycle facet or newfacet
+            make ridge between neighbor and newfacet
+*/
+void qh_mergecycle_ridges(qhT *qh, facetT *samecycle, facetT *newfacet) {
+  facetT *same, *neighbor= NULL;
+  int numold=0, numnew=0;
+  int neighbor_i, neighbor_n;
+  unsigned int samevisitid;
+  ridgeT *ridge, **ridgep;
+  boolT toporient;
+  void **freelistp; /* used if !qh_NOmem by qh_memfree_() */
+
+  trace4((qh, qh->ferr, 4033, "qh_mergecycle_ridges: delete shared ridges from newfacet\n"));
+  samevisitid= qh->visit_id -1;
+  FOREACHridge_(newfacet->ridges) {
+    neighbor= otherfacet_(ridge, newfacet);
+    if (neighbor->visitid == samevisitid)
+      SETref_(ridge)= NULL; /* ridge free'd below */
+  }
+  qh_setcompact(qh, newfacet->ridges);
+
+  trace4((qh, qh->ferr, 4034, "qh_mergecycle_ridges: add ridges to newfacet\n"));
+  FORALLsame_cycle_(samecycle) {
+    FOREACHridge_(same->ridges) {
+      if (ridge->top == same) {
+        ridge->top= newfacet;
+        neighbor= ridge->bottom;
+      }else if (ridge->bottom == same) {
+        ridge->bottom= newfacet;
+        neighbor= ridge->top;
+      }else if (ridge->top == newfacet || ridge->bottom == newfacet) {
+        qh_setappend(qh, &newfacet->ridges, ridge);
+        numold++;  /* already set by qh_mergecycle_neighbors */
+        continue;
+      }else {
+        qh_fprintf(qh, qh->ferr, 6098, "qhull internal error (qh_mergecycle_ridges): bad ridge r%d\n", ridge->id);
+        qh_errexit(qh, qh_ERRqhull, NULL, ridge);
+      }
+      if (neighbor == newfacet) {
+        qh_setfree(qh, &(ridge->vertices));
+        qh_memfree_(qh, ridge, (int)sizeof(ridgeT), freelistp);
+        numold++;
+      }else if (neighbor->visitid == samevisitid) {
+        qh_setdel(neighbor->ridges, ridge);
+        qh_setfree(qh, &(ridge->vertices));
+        qh_memfree_(qh, ridge, (int)sizeof(ridgeT), freelistp);
+        numold++;
+      }else {
+        qh_setappend(qh, &newfacet->ridges, ridge);
+        numold++;
+      }
+    }
+    if (same->ridges)
+      qh_settruncate(qh, same->ridges, 0);
+    if (!same->simplicial)
+      continue;
+    FOREACHneighbor_i_(qh, same) {       /* note: !newfact->simplicial */
+      if (neighbor->visitid != samevisitid && neighbor->simplicial) {
+        ridge= qh_newridge(qh);
+        ridge->vertices= qh_setnew_delnthsorted(qh, same->vertices, qh->hull_dim,
+                                                          neighbor_i, 0);
+        toporient= same->toporient ^ (neighbor_i & 0x1);
+        if (toporient) {
+          ridge->top= newfacet;
+          ridge->bottom= neighbor;
+        }else {
+          ridge->top= neighbor;
+          ridge->bottom= newfacet;
+        }
+        qh_setappend(qh, &(newfacet->ridges), ridge);
+        qh_setappend(qh, &(neighbor->ridges), ridge);
+        numnew++;
+      }
+    }
+  }
+
+  trace2((qh, qh->ferr, 2033, "qh_mergecycle_ridges: found %d old ridges and %d new ones\n",
+             numold, numnew));
+} /* mergecycle_ridges */
+
+/*---------------------------------
+
+  qh_mergecycle_vneighbors(qh, samecycle, newfacet )
+    create vertex neighbors for newfacet from vertices of facets in samecycle
+    samecycle marked with visitid == qh.visit_id - 1
+
+  returns:
+    newfacet vertices with updated neighbors
+    marks newfacet with qh.visit_id-1
+    deletes vertices that are merged away
+    sets delridge on all vertices (faster here than in mergecycle_ridges)
+
+  see:
+    qh_mergevertex_neighbors()
+
+  design:
+    for each vertex of samecycle facet
+      set vertex->delridge
+      delete samecycle facets from vertex neighbors
+      append newfacet to vertex neighbors
+      if vertex only in newfacet
+        delete it from newfacet
+        add it to qh.del_vertices for later deletion
+*/
+void qh_mergecycle_vneighbors(qhT *qh, facetT *samecycle, facetT *newfacet) {
+  facetT *neighbor, **neighborp;
+  unsigned int mergeid;
+  vertexT *vertex, **vertexp, *apex;
+  setT *vertices;
+
+  trace4((qh, qh->ferr, 4035, "qh_mergecycle_vneighbors: update vertex neighbors for newfacet\n"));
+  mergeid= qh->visit_id - 1;
+  newfacet->visitid= mergeid;
+  vertices= qh_basevertices(qh, samecycle); /* temp */
+  apex= SETfirstt_(samecycle->vertices, vertexT);
+  qh_setappend(qh, &vertices, apex);
+  FOREACHvertex_(vertices) {
+    vertex->delridge= True;
+    FOREACHneighbor_(vertex) {
+      if (neighbor->visitid == mergeid)
+        SETref_(neighbor)= NULL;
+    }
+    qh_setcompact(qh, vertex->neighbors);
+    qh_setappend(qh, &vertex->neighbors, newfacet);
+    if (!SETsecond_(vertex->neighbors)) {
+      zinc_(Zcyclevertex);
+      trace2((qh, qh->ferr, 2034, "qh_mergecycle_vneighbors: deleted v%d when merging cycle f%d into f%d\n",
+        vertex->id, samecycle->id, newfacet->id));
+      qh_setdelsorted(newfacet->vertices, vertex);
+      vertex->deleted= True;
+      qh_setappend(qh, &qh->del_vertices, vertex);
+    }
+  }
+  qh_settempfree(qh, &vertices);
+  trace3((qh, qh->ferr, 3005, "qh_mergecycle_vneighbors: merged vertices from cycle f%d into f%d\n",
+             samecycle->id, newfacet->id));
+} /* mergecycle_vneighbors */
+
+/*---------------------------------
+
+  qh_mergefacet(qh, facet1, facet2, mindist, maxdist, mergeapex )
+    merges facet1 into facet2
+    mergeapex==qh_MERGEapex if merging new facet into coplanar horizon
+
+  returns:
+    qh.max_outside and qh.min_vertex updated
+    initializes vertex neighbors on first merge
+
+  returns:
+    facet2 contains facet1's vertices, neighbors, and ridges
+      facet2 moved to end of qh.facet_list
+      makes facet2 a newfacet
+      sets facet2->newmerge set
+      clears facet2->center (unless merging into a large facet)
+      clears facet2->tested and ridge->tested for facet1
+
+    facet1 prepended to visible_list for later deletion and partitioning
+      facet1->f.replace == facet2
+
+    adds neighboring facets to facet_mergeset if redundant or degenerate
+
+  notes:
+    mindist/maxdist may be NULL (only if both NULL)
+    traces merge if fmax_(maxdist,-mindist) > TRACEdist
+
+  see:
+    qh_mergecycle()
+
+  design:
+    trace merge and check for degenerate simplex
+    make ridges for both facets
+    update qh.max_outside, qh.max_vertex, qh.min_vertex
+    update facet2->maxoutside and keepcentrum
+    update facet2->nummerge
+    update tested flags for facet2
+    if facet1 is simplicial
+      merge facet1 into facet2
+    else
+      merge facet1's neighbors into facet2
+      merge facet1's ridges into facet2
+      merge facet1's vertices into facet2
+      merge facet1's vertex neighbors into facet2
+      add facet2's vertices to qh.new_vertexlist
+      unless qh_MERGEapex
+        test facet2 for degenerate or redundant neighbors
+      move facet1 to qh.visible_list for later deletion
+      move facet2 to end of qh.newfacet_list
+*/
+void qh_mergefacet(qhT *qh, facetT *facet1, facetT *facet2, realT *mindist, realT *maxdist, boolT mergeapex) {
+  boolT traceonce= False;
+  vertexT *vertex, **vertexp;
+  int tracerestore=0, nummerge;
+
+  if (facet1->tricoplanar || facet2->tricoplanar) {
+    if (!qh->TRInormals) {
+      qh_fprintf(qh, qh->ferr, 6226, "Qhull internal error (qh_mergefacet): does not work for tricoplanar facets.  Use option 'Q11'\n");
+      qh_errexit2(qh, qh_ERRqhull, facet1, facet2);
+    }
+    if (facet2->tricoplanar) {
+      facet2->tricoplanar= False;
+      facet2->keepcentrum= False;
+    }
+  }
+  zzinc_(Ztotmerge);
+  if (qh->REPORTfreq2 && qh->POSTmerging) {
+    if (zzval_(Ztotmerge) > qh->mergereport + qh->REPORTfreq2)
+      qh_tracemerging(qh);
+  }
+#ifndef qh_NOtrace
+  if (qh->build_cnt >= qh->RERUN) {
+    if (mindist && (-*mindist > qh->TRACEdist || *maxdist > qh->TRACEdist)) {
+      tracerestore= 0;
+      qh->IStracing= qh->TRACElevel;
+      traceonce= True;
+      qh_fprintf(qh, qh->ferr, 8075, "qh_mergefacet: ========= trace wide merge #%d(%2.2g) for f%d into f%d, last point was p%d\n", zzval_(Ztotmerge),
+             fmax_(-*mindist, *maxdist), facet1->id, facet2->id, qh->furthest_id);
+    }else if (facet1 == qh->tracefacet || facet2 == qh->tracefacet) {
+      tracerestore= qh->IStracing;
+      qh->IStracing= 4;
+      traceonce= True;
+      qh_fprintf(qh, qh->ferr, 8076, "qh_mergefacet: ========= trace merge #%d involving f%d, furthest is p%d\n",
+                 zzval_(Ztotmerge), qh->tracefacet_id,  qh->furthest_id);
+    }
+  }
+  if (qh->IStracing >= 2) {
+    realT mergemin= -2;
+    realT mergemax= -2;
+
+    if (mindist) {
+      mergemin= *mindist;
+      mergemax= *maxdist;
+    }
+    qh_fprintf(qh, qh->ferr, 8077, "qh_mergefacet: #%d merge f%d into f%d, mindist= %2.2g, maxdist= %2.2g\n",
+    zzval_(Ztotmerge), facet1->id, facet2->id, mergemin, mergemax);
+  }
+#endif /* !qh_NOtrace */
+  if (facet1 == facet2 || facet1->visible || facet2->visible) {
+    qh_fprintf(qh, qh->ferr, 6099, "qhull internal error (qh_mergefacet): either f%d and f%d are the same or one is a visible facet\n",
+             facet1->id, facet2->id);
+    qh_errexit2(qh, qh_ERRqhull, facet1, facet2);
+  }
+  if (qh->num_facets - qh->num_visible <= qh->hull_dim + 1) {
+    qh_fprintf(qh, qh->ferr, 6227, "\n\
+qhull precision error: Only %d facets remain.  Can not merge another\n\
+pair.  The input is too degenerate or the convexity constraints are\n\
+too strong.\n", qh->hull_dim+1);
+    if (qh->hull_dim >= 5 && !qh->MERGEexact)
+      qh_fprintf(qh, qh->ferr, 8079, "Option 'Qx' may avoid this problem.\n");
+    qh_errexit(qh, qh_ERRprec, NULL, NULL);
+  }
+  if (!qh->VERTEXneighbors)
+    qh_vertexneighbors(qh);
+  qh_makeridges(qh, facet1);
+  qh_makeridges(qh, facet2);
+  if (qh->IStracing >=4)
+    qh_errprint(qh, "MERGING", facet1, facet2, NULL, NULL);
+  if (mindist) {
+    maximize_(qh->max_outside, *maxdist);
+    maximize_(qh->max_vertex, *maxdist);
+#if qh_MAXoutside
+    maximize_(facet2->maxoutside, *maxdist);
+#endif
+    minimize_(qh->min_vertex, *mindist);
+    if (!facet2->keepcentrum
+    && (*maxdist > qh->WIDEfacet || *mindist < -qh->WIDEfacet)) {
+      facet2->keepcentrum= True;
+      zinc_(Zwidefacet);
+    }
+  }
+  nummerge= facet1->nummerge + facet2->nummerge + 1;
+  if (nummerge >= qh_MAXnummerge)
+    facet2->nummerge= qh_MAXnummerge;
+  else
+    facet2->nummerge= (short unsigned int)nummerge;
+  facet2->newmerge= True;
+  facet2->dupridge= False;
+  qh_updatetested(qh, facet1, facet2);
+  if (qh->hull_dim > 2 && qh_setsize(qh, facet1->vertices) == qh->hull_dim)
+    qh_mergesimplex(qh, facet1, facet2, mergeapex);
+  else {
+    qh->vertex_visit++;
+    FOREACHvertex_(facet2->vertices)
+      vertex->visitid= qh->vertex_visit;
+    if (qh->hull_dim == 2)
+      qh_mergefacet2d(qh, facet1, facet2);
+    else {
+      qh_mergeneighbors(qh, facet1, facet2);
+      qh_mergevertices(qh, facet1->vertices, &facet2->vertices);
+    }
+    qh_mergeridges(qh, facet1, facet2);
+    qh_mergevertex_neighbors(qh, facet1, facet2);
+    if (!facet2->newfacet)
+      qh_newvertices(qh, facet2->vertices);
+  }
+  if (!mergeapex)
+    qh_degen_redundant_neighbors(qh, facet2, facet1);
+  if (facet2->coplanar || !facet2->newfacet) {
+    zinc_(Zmergeintohorizon);
+  }else if (!facet1->newfacet && facet2->newfacet) {
+    zinc_(Zmergehorizon);
+  }else {
+    zinc_(Zmergenew);
+  }
+  qh_willdelete(qh, facet1, facet2);
+  qh_removefacet(qh, facet2);  /* append as a newfacet to end of qh->facet_list */
+  qh_appendfacet(qh, facet2);
+  facet2->newfacet= True;
+  facet2->tested= False;
+  qh_tracemerge(qh, facet1, facet2);
+  if (traceonce) {
+    qh_fprintf(qh, qh->ferr, 8080, "qh_mergefacet: end of wide tracing\n");
+    qh->IStracing= tracerestore;
+  }
+} /* mergefacet */
+
+
+/*---------------------------------
+
+  qh_mergefacet2d(qh, facet1, facet2 )
+    in 2d, merges neighbors and vertices of facet1 into facet2
+
+  returns:
+    build ridges for neighbors if necessary
+    facet2 looks like a simplicial facet except for centrum, ridges
+      neighbors are opposite the corresponding vertex
+      maintains orientation of facet2
+
+  notes:
+    qh_mergefacet() retains non-simplicial structures
+      they are not needed in 2d, but later routines may use them
+    preserves qh.vertex_visit for qh_mergevertex_neighbors()
+
+  design:
+    get vertices and neighbors
+    determine new vertices and neighbors
+    set new vertices and neighbors and adjust orientation
+    make ridges for new neighbor if needed
+*/
+void qh_mergefacet2d(qhT *qh, facetT *facet1, facetT *facet2) {
+  vertexT *vertex1A, *vertex1B, *vertex2A, *vertex2B, *vertexA, *vertexB;
+  facetT *neighbor1A, *neighbor1B, *neighbor2A, *neighbor2B, *neighborA, *neighborB;
+
+  vertex1A= SETfirstt_(facet1->vertices, vertexT);
+  vertex1B= SETsecondt_(facet1->vertices, vertexT);
+  vertex2A= SETfirstt_(facet2->vertices, vertexT);
+  vertex2B= SETsecondt_(facet2->vertices, vertexT);
+  neighbor1A= SETfirstt_(facet1->neighbors, facetT);
+  neighbor1B= SETsecondt_(facet1->neighbors, facetT);
+  neighbor2A= SETfirstt_(facet2->neighbors, facetT);
+  neighbor2B= SETsecondt_(facet2->neighbors, facetT);
+  if (vertex1A == vertex2A) {
+    vertexA= vertex1B;
+    vertexB= vertex2B;
+    neighborA= neighbor2A;
+    neighborB= neighbor1A;
+  }else if (vertex1A == vertex2B) {
+    vertexA= vertex1B;
+    vertexB= vertex2A;
+    neighborA= neighbor2B;
+    neighborB= neighbor1A;
+  }else if (vertex1B == vertex2A) {
+    vertexA= vertex1A;
+    vertexB= vertex2B;
+    neighborA= neighbor2A;
+    neighborB= neighbor1B;
+  }else { /* 1B == 2B */
+    vertexA= vertex1A;
+    vertexB= vertex2A;
+    neighborA= neighbor2B;
+    neighborB= neighbor1B;
+  }
+  /* vertexB always from facet2, neighborB always from facet1 */
+  if (vertexA->id > vertexB->id) {
+    SETfirst_(facet2->vertices)= vertexA;
+    SETsecond_(facet2->vertices)= vertexB;
+    if (vertexB == vertex2A)
+      facet2->toporient= !facet2->toporient;
+    SETfirst_(facet2->neighbors)= neighborA;
+    SETsecond_(facet2->neighbors)= neighborB;
+  }else {
+    SETfirst_(facet2->vertices)= vertexB;
+    SETsecond_(facet2->vertices)= vertexA;
+    if (vertexB == vertex2B)
+      facet2->toporient= !facet2->toporient;
+    SETfirst_(facet2->neighbors)= neighborB;
+    SETsecond_(facet2->neighbors)= neighborA;
+  }
+  qh_makeridges(qh, neighborB);
+  qh_setreplace(qh, neighborB->neighbors, facet1, facet2);
+  trace4((qh, qh->ferr, 4036, "qh_mergefacet2d: merged v%d and neighbor f%d of f%d into f%d\n",
+       vertexA->id, neighborB->id, facet1->id, facet2->id));
+} /* mergefacet2d */
+
+
+/*---------------------------------
+
+  qh_mergeneighbors(qh, facet1, facet2 )
+    merges the neighbors of facet1 into facet2
+
+  see:
+    qh_mergecycle_neighbors()
+
+  design:
+    for each neighbor of facet1
+      if neighbor is also a neighbor of facet2
+        if neighbor is simpilicial
+          make ridges for later deletion as a degenerate facet
+        update its neighbor set
+      else
+        move the neighbor relation to facet2
+    remove the neighbor relation for facet1 and facet2
+*/
+void qh_mergeneighbors(qhT *qh, facetT *facet1, facetT *facet2) {
+  facetT *neighbor, **neighborp;
+
+  trace4((qh, qh->ferr, 4037, "qh_mergeneighbors: merge neighbors of f%d and f%d\n",
+          facet1->id, facet2->id));
+  qh->visit_id++;
+  FOREACHneighbor_(facet2) {
+    neighbor->visitid= qh->visit_id;
+  }
+  FOREACHneighbor_(facet1) {
+    if (neighbor->visitid == qh->visit_id) {
+      if (neighbor->simplicial)    /* is degen, needs ridges */
+        qh_makeridges(qh, neighbor);
+      if (SETfirstt_(neighbor->neighbors, facetT) != facet1) /*keep newfacet->horizon*/
+        qh_setdel(neighbor->neighbors, facet1);
+      else {
+        qh_setdel(neighbor->neighbors, facet2);
+        qh_setreplace(qh, neighbor->neighbors, facet1, facet2);
+      }
+    }else if (neighbor != facet2) {
+      qh_setappend(qh, &(facet2->neighbors), neighbor);
+      qh_setreplace(qh, neighbor->neighbors, facet1, facet2);
+    }
+  }
+  qh_setdel(facet1->neighbors, facet2);  /* here for makeridges */
+  qh_setdel(facet2->neighbors, facet1);
+} /* mergeneighbors */
+
+
+/*---------------------------------
+
+  qh_mergeridges(qh, facet1, facet2 )
+    merges the ridge set of facet1 into facet2
+
+  returns:
+    may delete all ridges for a vertex
+    sets vertex->delridge on deleted ridges
+
+  see:
+    qh_mergecycle_ridges()
+
+  design:
+    delete ridges between facet1 and facet2
+      mark (delridge) vertices on these ridges for later testing
+    for each remaining ridge
+      rename facet1 to facet2
+*/
+void qh_mergeridges(qhT *qh, facetT *facet1, facetT *facet2) {
+  ridgeT *ridge, **ridgep;
+  vertexT *vertex, **vertexp;
+
+  trace4((qh, qh->ferr, 4038, "qh_mergeridges: merge ridges of f%d and f%d\n",
+          facet1->id, facet2->id));
+  FOREACHridge_(facet2->ridges) {
+    if ((ridge->top == facet1) || (ridge->bottom == facet1)) {
+      FOREACHvertex_(ridge->vertices)
+        vertex->delridge= True;
+      qh_delridge(qh, ridge);  /* expensive in high-d, could rebuild */
+      ridgep--; /*repeat*/
+    }
+  }
+  FOREACHridge_(facet1->ridges) {
+    if (ridge->top == facet1)
+      ridge->top= facet2;
+    else
+      ridge->bottom= facet2;
+    qh_setappend(qh, &(facet2->ridges), ridge);
+  }
+} /* mergeridges */
+
+
+/*---------------------------------
+
+  qh_mergesimplex(qh, facet1, facet2, mergeapex )
+    merge simplicial facet1 into facet2
+    mergeapex==qh_MERGEapex if merging samecycle into horizon facet
+      vertex id is latest (most recently created)
+    facet1 may be contained in facet2
+    ridges exist for both facets
+
+  returns:
+    facet2 with updated vertices, ridges, neighbors
+    updated neighbors for facet1's vertices
+    facet1 not deleted
+    sets vertex->delridge on deleted ridges
+
+  notes:
+    special case code since this is the most common merge
+    called from qh_mergefacet()
+
+  design:
+    if qh_MERGEapex
+      add vertices of facet2 to qh.new_vertexlist if necessary
+      add apex to facet2
+    else
+      for each ridge between facet1 and facet2
+        set vertex->delridge
+      determine the apex for facet1 (i.e., vertex to be merged)
+      unless apex already in facet2
+        insert apex into vertices for facet2
+      add vertices of facet2 to qh.new_vertexlist if necessary
+      add apex to qh.new_vertexlist if necessary
+      for each vertex of facet1
+        if apex
+          rename facet1 to facet2 in its vertex neighbors
+        else
+          delete facet1 from vertex neighors
+          if only in facet2
+            add vertex to qh.del_vertices for later deletion
+      for each ridge of facet1
+        delete ridges between facet1 and facet2
+        append other ridges to facet2 after renaming facet to facet2
+*/
+void qh_mergesimplex(qhT *qh, facetT *facet1, facetT *facet2, boolT mergeapex) {
+  vertexT *vertex, **vertexp, *apex;
+  ridgeT *ridge, **ridgep;
+  boolT issubset= False;
+  int vertex_i= -1, vertex_n;
+  facetT *neighbor, **neighborp, *otherfacet;
+
+  if (mergeapex) {
+    if (!facet2->newfacet)
+      qh_newvertices(qh, facet2->vertices);  /* apex is new */
+    apex= SETfirstt_(facet1->vertices, vertexT);
+    if (SETfirstt_(facet2->vertices, vertexT) != apex)
+      qh_setaddnth(qh, &facet2->vertices, 0, apex);  /* apex has last id */
+    else
+      issubset= True;
+  }else {
+    zinc_(Zmergesimplex);
+    FOREACHvertex_(facet1->vertices)
+      vertex->seen= False;
+    FOREACHridge_(facet1->ridges) {
+      if (otherfacet_(ridge, facet1) == facet2) {
+        FOREACHvertex_(ridge->vertices) {
+          vertex->seen= True;
+          vertex->delridge= True;
+        }
+        break;
+      }
+    }
+    FOREACHvertex_(facet1->vertices) {
+      if (!vertex->seen)
+        break;  /* must occur */
+    }
+    apex= vertex;
+    trace4((qh, qh->ferr, 4039, "qh_mergesimplex: merge apex v%d of f%d into facet f%d\n",
+          apex->id, facet1->id, facet2->id));
+    FOREACHvertex_i_(qh, facet2->vertices) {
+      if (vertex->id < apex->id) {
+        break;
+      }else if (vertex->id == apex->id) {
+        issubset= True;
+        break;
+      }
+    }
+    if (!issubset)
+      qh_setaddnth(qh, &facet2->vertices, vertex_i, apex);
+    if (!facet2->newfacet)
+      qh_newvertices(qh, facet2->vertices);
+    else if (!apex->newlist) {
+      qh_removevertex(qh, apex);
+      qh_appendvertex(qh, apex);
+    }
+  }
+  trace4((qh, qh->ferr, 4040, "qh_mergesimplex: update vertex neighbors of f%d\n",
+          facet1->id));
+  FOREACHvertex_(facet1->vertices) {
+    if (vertex == apex && !issubset)
+      qh_setreplace(qh, vertex->neighbors, facet1, facet2);
+    else {
+      qh_setdel(vertex->neighbors, facet1);
+      if (!SETsecond_(vertex->neighbors))
+        qh_mergevertex_del(qh, vertex, facet1, facet2);
+    }
+  }
+  trace4((qh, qh->ferr, 4041, "qh_mergesimplex: merge ridges and neighbors of f%d into f%d\n",
+          facet1->id, facet2->id));
+  qh->visit_id++;
+  FOREACHneighbor_(facet2)
+    neighbor->visitid= qh->visit_id;
+  FOREACHridge_(facet1->ridges) {
+    otherfacet= otherfacet_(ridge, facet1);
+    if (otherfacet == facet2) {
+      qh_setdel(facet2->ridges, ridge);
+      qh_setfree(qh, &(ridge->vertices));
+      qh_memfree(qh, ridge, (int)sizeof(ridgeT));
+      qh_setdel(facet2->neighbors, facet1);
+    }else {
+      qh_setappend(qh, &facet2->ridges, ridge);
+      if (otherfacet->visitid != qh->visit_id) {
+        qh_setappend(qh, &facet2->neighbors, otherfacet);
+        qh_setreplace(qh, otherfacet->neighbors, facet1, facet2);
+        otherfacet->visitid= qh->visit_id;
+      }else {
+        if (otherfacet->simplicial)    /* is degen, needs ridges */
+          qh_makeridges(qh, otherfacet);
+        if (SETfirstt_(otherfacet->neighbors, facetT) != facet1)
+          qh_setdel(otherfacet->neighbors, facet1);
+        else {   /*keep newfacet->neighbors->horizon*/
+          qh_setdel(otherfacet->neighbors, facet2);
+          qh_setreplace(qh, otherfacet->neighbors, facet1, facet2);
+        }
+      }
+      if (ridge->top == facet1) /* wait until after qh_makeridges */
+        ridge->top= facet2;
+      else
+        ridge->bottom= facet2;
+    }
+  }
+  SETfirst_(facet1->ridges)= NULL; /* it will be deleted */
+  trace3((qh, qh->ferr, 3006, "qh_mergesimplex: merged simplex f%d apex v%d into facet f%d\n",
+          facet1->id, getid_(apex), facet2->id));
+} /* mergesimplex */
+
+/*---------------------------------
+
+  qh_mergevertex_del(qh, vertex, facet1, facet2 )
+    delete a vertex because of merging facet1 into facet2
+
+  returns:
+    deletes vertex from facet2
+    adds vertex to qh.del_vertices for later deletion
+*/
+void qh_mergevertex_del(qhT *qh, vertexT *vertex, facetT *facet1, facetT *facet2) {
+
+  zinc_(Zmergevertex);
+  trace2((qh, qh->ferr, 2035, "qh_mergevertex_del: deleted v%d when merging f%d into f%d\n",
+          vertex->id, facet1->id, facet2->id));
+  qh_setdelsorted(facet2->vertices, vertex);
+  vertex->deleted= True;
+  qh_setappend(qh, &qh->del_vertices, vertex);
+} /* mergevertex_del */
+
+/*---------------------------------
+
+  qh_mergevertex_neighbors(qh, facet1, facet2 )
+    merge the vertex neighbors of facet1 to facet2
+
+  returns:
+    if vertex is current qh.vertex_visit
+      deletes facet1 from vertex->neighbors
+    else
+      renames facet1 to facet2 in vertex->neighbors
+    deletes vertices if only one neighbor
+
+  notes:
+    assumes vertex neighbor sets are good
+*/
+void qh_mergevertex_neighbors(qhT *qh, facetT *facet1, facetT *facet2) {
+  vertexT *vertex, **vertexp;
+
+  trace4((qh, qh->ferr, 4042, "qh_mergevertex_neighbors: merge vertex neighbors of f%d and f%d\n",
+          facet1->id, facet2->id));
+  if (qh->tracevertex) {
+    qh_fprintf(qh, qh->ferr, 8081, "qh_mergevertex_neighbors: of f%d and f%d at furthest p%d f0= %p\n",
+             facet1->id, facet2->id, qh->furthest_id, qh->tracevertex->neighbors->e[0].p);
+    qh_errprint(qh, "TRACE", NULL, NULL, NULL, qh->tracevertex);
+  }
+  FOREACHvertex_(facet1->vertices) {
+    if (vertex->visitid != qh->vertex_visit)
+      qh_setreplace(qh, vertex->neighbors, facet1, facet2);
+    else {
+      qh_setdel(vertex->neighbors, facet1);
+      if (!SETsecond_(vertex->neighbors))
+        qh_mergevertex_del(qh, vertex, facet1, facet2);
+    }
+  }
+  if (qh->tracevertex)
+    qh_errprint(qh, "TRACE", NULL, NULL, NULL, qh->tracevertex);
+} /* mergevertex_neighbors */
+
+
+/*---------------------------------
+
+  qh_mergevertices(qh, vertices1, vertices2 )
+    merges the vertex set of facet1 into facet2
+
+  returns:
+    replaces vertices2 with merged set
+    preserves vertex_visit for qh_mergevertex_neighbors
+    updates qh.newvertex_list
+
+  design:
+    create a merged set of both vertices (in inverse id order)
+*/
+void qh_mergevertices(qhT *qh, setT *vertices1, setT **vertices2) {
+  int newsize= qh_setsize(qh, vertices1)+qh_setsize(qh, *vertices2) - qh->hull_dim + 1;
+  setT *mergedvertices;
+  vertexT *vertex, **vertexp, **vertex2= SETaddr_(*vertices2, vertexT);
+
+  mergedvertices= qh_settemp(qh, newsize);
+  FOREACHvertex_(vertices1) {
+    if (!*vertex2 || vertex->id > (*vertex2)->id)
+      qh_setappend(qh, &mergedvertices, vertex);
+    else {
+      while (*vertex2 && (*vertex2)->id > vertex->id)
+        qh_setappend(qh, &mergedvertices, *vertex2++);
+      if (!*vertex2 || (*vertex2)->id < vertex->id)
+        qh_setappend(qh, &mergedvertices, vertex);
+      else
+        qh_setappend(qh, &mergedvertices, *vertex2++);
+    }
+  }
+  while (*vertex2)
+    qh_setappend(qh, &mergedvertices, *vertex2++);
+  if (newsize < qh_setsize(qh, mergedvertices)) {
+    qh_fprintf(qh, qh->ferr, 6100, "qhull internal error (qh_mergevertices): facets did not share a ridge\n");
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }
+  qh_setfree(qh, vertices2);
+  *vertices2= mergedvertices;
+  qh_settemppop(qh);
+} /* mergevertices */
+
+
+/*---------------------------------
+
+  qh_neighbor_intersections(qh, vertex )
+    return intersection of all vertices in vertex->neighbors except for vertex
+
+  returns:
+    returns temporary set of vertices
+    does not include vertex
+    NULL if a neighbor is simplicial
+    NULL if empty set
+
+  notes:
+    used for renaming vertices
+
+  design:
+    initialize the intersection set with vertices of the first two neighbors
+    delete vertex from the intersection
+    for each remaining neighbor
+      intersect its vertex set with the intersection set
+      return NULL if empty
+    return the intersection set
+*/
+setT *qh_neighbor_intersections(qhT *qh, vertexT *vertex) {
+  facetT *neighbor, **neighborp, *neighborA, *neighborB;
+  setT *intersect;
+  int neighbor_i, neighbor_n;
+
+  FOREACHneighbor_(vertex) {
+    if (neighbor->simplicial)
+      return NULL;
+  }
+  neighborA= SETfirstt_(vertex->neighbors, facetT);
+  neighborB= SETsecondt_(vertex->neighbors, facetT);
+  zinc_(Zintersectnum);
+  if (!neighborA)
+    return NULL;
+  if (!neighborB)
+    intersect= qh_setcopy(qh, neighborA->vertices, 0);
+  else
+    intersect= qh_vertexintersect_new(qh, neighborA->vertices, neighborB->vertices);
+  qh_settemppush(qh, intersect);
+  qh_setdelsorted(intersect, vertex);
+  FOREACHneighbor_i_(qh, vertex) {
+    if (neighbor_i >= 2) {
+      zinc_(Zintersectnum);
+      qh_vertexintersect(qh, &intersect, neighbor->vertices);
+      if (!SETfirst_(intersect)) {
+        zinc_(Zintersectfail);
+        qh_settempfree(qh, &intersect);
+        return NULL;
+      }
+    }
+  }
+  trace3((qh, qh->ferr, 3007, "qh_neighbor_intersections: %d vertices in neighbor intersection of v%d\n",
+          qh_setsize(qh, intersect), vertex->id));
+  return intersect;
+} /* neighbor_intersections */
+
+/*---------------------------------
+
+  qh_newvertices(qh, vertices )
+    add vertices to end of qh.vertex_list (marks as new vertices)
+
+  returns:
+    vertices on qh.newvertex_list
+    vertex->newlist set
+*/
+void qh_newvertices(qhT *qh, setT *vertices) {
+  vertexT *vertex, **vertexp;
+
+  FOREACHvertex_(vertices) {
+    if (!vertex->newlist) {
+      qh_removevertex(qh, vertex);
+      qh_appendvertex(qh, vertex);
+    }
+  }
+} /* newvertices */
+
+/*---------------------------------
+
+  qh_reducevertices(qh)
+    reduce extra vertices, shared vertices, and redundant vertices
+    facet->newmerge is set if merged since last call
+    if !qh.MERGEvertices, only removes extra vertices
+
+  returns:
+    True if also merged degen_redundant facets
+    vertices are renamed if possible
+    clears facet->newmerge and vertex->delridge
+
+  notes:
+    ignored if 2-d
+
+  design:
+    merge any degenerate or redundant facets
+    for each newly merged facet
+      remove extra vertices
+    if qh.MERGEvertices
+      for each newly merged facet
+        for each vertex
+          if vertex was on a deleted ridge
+            rename vertex if it is shared
+      remove delridge flag from new vertices
+*/
+boolT qh_reducevertices(qhT *qh) {
+  int numshare=0, numrename= 0;
+  boolT degenredun= False;
+  facetT *newfacet;
+  vertexT *vertex, **vertexp;
+
+  if (qh->hull_dim == 2)
+    return False;
+  if (qh_merge_degenredundant(qh))
+    degenredun= True;
+ LABELrestart:
+  FORALLnew_facets {
+    if (newfacet->newmerge) {
+      if (!qh->MERGEvertices)
+        newfacet->newmerge= False;
+      qh_remove_extravertices(qh, newfacet);
+    }
+  }
+  if (!qh->MERGEvertices)
+    return False;
+  FORALLnew_facets {
+    if (newfacet->newmerge) {
+      newfacet->newmerge= False;
+      FOREACHvertex_(newfacet->vertices) {
+        if (vertex->delridge) {
+          if (qh_rename_sharedvertex(qh, vertex, newfacet)) {
+            numshare++;
+            vertexp--; /* repeat since deleted vertex */
+          }
+        }
+      }
+    }
+  }
+  FORALLvertex_(qh->newvertex_list) {
+    if (vertex->delridge && !vertex->deleted) {
+      vertex->delridge= False;
+      if (qh->hull_dim >= 4 && qh_redundant_vertex(qh, vertex)) {
+        numrename++;
+        if (qh_merge_degenredundant(qh)) {
+          degenredun= True;
+          goto LABELrestart;
+        }
+      }
+    }
+  }
+  trace1((qh, qh->ferr, 1014, "qh_reducevertices: renamed %d shared vertices and %d redundant vertices. Degen? %d\n",
+          numshare, numrename, degenredun));
+  return degenredun;
+} /* reducevertices */
+
+/*---------------------------------
+
+  qh_redundant_vertex(qh, vertex )
+    detect and rename a redundant vertex
+    vertices have full vertex->neighbors
+
+  returns:
+    returns true if find a redundant vertex
+      deletes vertex(vertex->deleted)
+
+  notes:
+    only needed if vertex->delridge and hull_dim >= 4
+    may add degenerate facets to qh.facet_mergeset
+    doesn't change vertex->neighbors or create redundant facets
+
+  design:
+    intersect vertices of all facet neighbors of vertex
+    determine ridges for these vertices
+    if find a new vertex for vertex amoung these ridges and vertices
+      rename vertex to the new vertex
+*/
+vertexT *qh_redundant_vertex(qhT *qh, vertexT *vertex) {
+  vertexT *newvertex= NULL;
+  setT *vertices, *ridges;
+
+  trace3((qh, qh->ferr, 3008, "qh_redundant_vertex: check if v%d can be renamed\n", vertex->id));
+  if ((vertices= qh_neighbor_intersections(qh, vertex))) {
+    ridges= qh_vertexridges(qh, vertex);
+    if ((newvertex= qh_find_newvertex(qh, vertex, vertices, ridges)))
+      qh_renamevertex(qh, vertex, newvertex, ridges, NULL, NULL);
+    qh_settempfree(qh, &ridges);
+    qh_settempfree(qh, &vertices);
+  }
+  return newvertex;
+} /* redundant_vertex */
+
+/*---------------------------------
+
+  qh_remove_extravertices(qh, facet )
+    remove extra vertices from non-simplicial facets
+
+  returns:
+    returns True if it finds them
+
+  design:
+    for each vertex in facet
+      if vertex not in a ridge (i.e., no longer used)
+        delete vertex from facet
+        delete facet from vertice's neighbors
+        unless vertex in another facet
+          add vertex to qh.del_vertices for later deletion
+*/
+boolT qh_remove_extravertices(qhT *qh, facetT *facet) {
+  ridgeT *ridge, **ridgep;
+  vertexT *vertex, **vertexp;
+  boolT foundrem= False;
+
+  trace4((qh, qh->ferr, 4043, "qh_remove_extravertices: test f%d for extra vertices\n",
+          facet->id));
+  FOREACHvertex_(facet->vertices)
+    vertex->seen= False;
+  FOREACHridge_(facet->ridges) {
+    FOREACHvertex_(ridge->vertices)
+      vertex->seen= True;
+  }
+  FOREACHvertex_(facet->vertices) {
+    if (!vertex->seen) {
+      foundrem= True;
+      zinc_(Zremvertex);
+      qh_setdelsorted(facet->vertices, vertex);
+      qh_setdel(vertex->neighbors, facet);
+      if (!qh_setsize(qh, vertex->neighbors)) {
+        vertex->deleted= True;
+        qh_setappend(qh, &qh->del_vertices, vertex);
+        zinc_(Zremvertexdel);
+        trace2((qh, qh->ferr, 2036, "qh_remove_extravertices: v%d deleted because it's lost all ridges\n", vertex->id));
+      }else
+        trace3((qh, qh->ferr, 3009, "qh_remove_extravertices: v%d removed from f%d because it's lost all ridges\n", vertex->id, facet->id));
+      vertexp--; /*repeat*/
+    }
+  }
+  return foundrem;
+} /* remove_extravertices */
+
+/*---------------------------------
+
+  qh_rename_sharedvertex(qh, vertex, facet )
+    detect and rename if shared vertex in facet
+    vertices have full ->neighbors
+
+  returns:
+    newvertex or NULL
+    the vertex may still exist in other facets (i.e., a neighbor was pinched)
+    does not change facet->neighbors
+    updates vertex->neighbors
+
+  notes:
+    a shared vertex for a facet is only in ridges to one neighbor
+    this may undo a pinched facet
+
+    it does not catch pinches involving multiple facets.  These appear
+      to be difficult to detect, since an exhaustive search is too expensive.
+
+  design:
+    if vertex only has two neighbors
+      determine the ridges that contain the vertex
+      determine the vertices shared by both neighbors
+      if can find a new vertex in this set
+        rename the vertex to the new vertex
+*/
+vertexT *qh_rename_sharedvertex(qhT *qh, vertexT *vertex, facetT *facet) {
+  facetT *neighbor, **neighborp, *neighborA= NULL;
+  setT *vertices, *ridges;
+  vertexT *newvertex;
+
+  if (qh_setsize(qh, vertex->neighbors) == 2) {
+    neighborA= SETfirstt_(vertex->neighbors, facetT);
+    if (neighborA == facet)
+      neighborA= SETsecondt_(vertex->neighbors, facetT);
+  }else if (qh->hull_dim == 3)
+    return NULL;
+  else {
+    qh->visit_id++;
+    FOREACHneighbor_(facet)
+      neighbor->visitid= qh->visit_id;
+    FOREACHneighbor_(vertex) {
+      if (neighbor->visitid == qh->visit_id) {
+        if (neighborA)
+          return NULL;
+        neighborA= neighbor;
+      }
+    }
+    if (!neighborA) {
+      qh_fprintf(qh, qh->ferr, 6101, "qhull internal error (qh_rename_sharedvertex): v%d's neighbors not in f%d\n",
+        vertex->id, facet->id);
+      qh_errprint(qh, "ERRONEOUS", facet, NULL, NULL, vertex);
+      qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+    }
+  }
+  /* the vertex is shared by facet and neighborA */
+  ridges= qh_settemp(qh, qh->TEMPsize);
+  neighborA->visitid= ++qh->visit_id;
+  qh_vertexridges_facet(qh, vertex, facet, &ridges);
+  trace2((qh, qh->ferr, 2037, "qh_rename_sharedvertex: p%d(v%d) is shared by f%d(%d ridges) and f%d\n",
+    qh_pointid(qh, vertex->point), vertex->id, facet->id, qh_setsize(qh, ridges), neighborA->id));
+  zinc_(Zintersectnum);
+  vertices= qh_vertexintersect_new(qh, facet->vertices, neighborA->vertices);
+  qh_setdel(vertices, vertex);
+  qh_settemppush(qh, vertices);
+  if ((newvertex= qh_find_newvertex(qh, vertex, vertices, ridges)))
+    qh_renamevertex(qh, vertex, newvertex, ridges, facet, neighborA);
+  qh_settempfree(qh, &vertices);
+  qh_settempfree(qh, &ridges);
+  return newvertex;
+} /* rename_sharedvertex */
+
+/*---------------------------------
+
+  qh_renameridgevertex(qh, ridge, oldvertex, newvertex )
+    renames oldvertex as newvertex in ridge
+
+  returns:
+
+  design:
+    delete oldvertex from ridge
+    if newvertex already in ridge
+      copy ridge->noconvex to another ridge if possible
+      delete the ridge
+    else
+      insert newvertex into the ridge
+      adjust the ridge's orientation
+*/
+void qh_renameridgevertex(qhT *qh, ridgeT *ridge, vertexT *oldvertex, vertexT *newvertex) {
+  int nth= 0, oldnth;
+  facetT *temp;
+  vertexT *vertex, **vertexp;
+
+  oldnth= qh_setindex(ridge->vertices, oldvertex);
+  qh_setdelnthsorted(qh, ridge->vertices, oldnth);
+  FOREACHvertex_(ridge->vertices) {
+    if (vertex == newvertex) {
+      zinc_(Zdelridge);
+      if (ridge->nonconvex) /* only one ridge has nonconvex set */
+        qh_copynonconvex(qh, ridge);
+      trace2((qh, qh->ferr, 2038, "qh_renameridgevertex: ridge r%d deleted.  It contained both v%d and v%d\n",
+        ridge->id, oldvertex->id, newvertex->id));
+      qh_delridge(qh, ridge);
+      return;
+    }
+    if (vertex->id < newvertex->id)
+      break;
+    nth++;
+  }
+  qh_setaddnth(qh, &ridge->vertices, nth, newvertex);
+  if (abs(oldnth - nth)%2) {
+    trace3((qh, qh->ferr, 3010, "qh_renameridgevertex: swapped the top and bottom of ridge r%d\n",
+            ridge->id));
+    temp= ridge->top;
+    ridge->top= ridge->bottom;
+    ridge->bottom= temp;
+  }
+} /* renameridgevertex */
+
+
+/*---------------------------------
+
+  qh_renamevertex(qh, oldvertex, newvertex, ridges, oldfacet, neighborA )
+    renames oldvertex as newvertex in ridges
+    gives oldfacet/neighborA if oldvertex is shared between two facets
+
+  returns:
+    oldvertex may still exist afterwards
+
+
+  notes:
+    can not change neighbors of newvertex (since it's a subset)
+
+  design:
+    for each ridge in ridges
+      rename oldvertex to newvertex and delete degenerate ridges
+    if oldfacet not defined
+      for each neighbor of oldvertex
+        delete oldvertex from neighbor's vertices
+        remove extra vertices from neighbor
+      add oldvertex to qh.del_vertices
+    else if oldvertex only between oldfacet and neighborA
+      delete oldvertex from oldfacet and neighborA
+      add oldvertex to qh.del_vertices
+    else oldvertex is in oldfacet and neighborA and other facets (i.e., pinched)
+      delete oldvertex from oldfacet
+      delete oldfacet from oldvertice's neighbors
+      remove extra vertices (e.g., oldvertex) from neighborA
+*/
+void qh_renamevertex(qhT *qh, vertexT *oldvertex, vertexT *newvertex, setT *ridges, facetT *oldfacet, facetT *neighborA) {
+  facetT *neighbor, **neighborp;
+  ridgeT *ridge, **ridgep;
+  boolT istrace= False;
+
+  if (qh->IStracing >= 2 || oldvertex->id == qh->tracevertex_id ||
+        newvertex->id == qh->tracevertex_id)
+    istrace= True;
+  FOREACHridge_(ridges)
+    qh_renameridgevertex(qh, ridge, oldvertex, newvertex);
+  if (!oldfacet) {
+    zinc_(Zrenameall);
+    if (istrace)
+      qh_fprintf(qh, qh->ferr, 8082, "qh_renamevertex: renamed v%d to v%d in several facets\n",
+               oldvertex->id, newvertex->id);
+    FOREACHneighbor_(oldvertex) {
+      qh_maydropneighbor(qh, neighbor);
+      qh_setdelsorted(neighbor->vertices, oldvertex);
+      if (qh_remove_extravertices(qh, neighbor))
+        neighborp--; /* neighbor may be deleted */
+    }
+    if (!oldvertex->deleted) {
+      oldvertex->deleted= True;
+      qh_setappend(qh, &qh->del_vertices, oldvertex);
+    }
+  }else if (qh_setsize(qh, oldvertex->neighbors) == 2) {
+    zinc_(Zrenameshare);
+    if (istrace)
+      qh_fprintf(qh, qh->ferr, 8083, "qh_renamevertex: renamed v%d to v%d in oldfacet f%d\n",
+               oldvertex->id, newvertex->id, oldfacet->id);
+    FOREACHneighbor_(oldvertex)
+      qh_setdelsorted(neighbor->vertices, oldvertex);
+    oldvertex->deleted= True;
+    qh_setappend(qh, &qh->del_vertices, oldvertex);
+  }else {
+    zinc_(Zrenamepinch);
+    if (istrace || qh->IStracing)
+      qh_fprintf(qh, qh->ferr, 8084, "qh_renamevertex: renamed pinched v%d to v%d between f%d and f%d\n",
+               oldvertex->id, newvertex->id, oldfacet->id, neighborA->id);
+    qh_setdelsorted(oldfacet->vertices, oldvertex);
+    qh_setdel(oldvertex->neighbors, oldfacet);
+    qh_remove_extravertices(qh, neighborA);
+  }
+} /* renamevertex */
+
+
+/*---------------------------------
+
+  qh_test_appendmerge(qh, facet, neighbor )
+    tests facet/neighbor for convexity
+    appends to mergeset if non-convex
+    if pre-merging,
+      nop if qh.SKIPconvex, or qh.MERGEexact and coplanar
+
+  returns:
+    true if appends facet/neighbor to mergeset
+    sets facet->center as needed
+    does not change facet->seen
+
+  design:
+    if qh.cos_max is defined
+      if the angle between facet normals is too shallow
+        append an angle-coplanar merge to qh.mergeset
+        return True
+    make facet's centrum if needed
+    if facet's centrum is above the neighbor
+      set isconcave
+    else
+      if facet's centrum is not below the neighbor
+        set iscoplanar
+      make neighbor's centrum if needed
+      if neighbor's centrum is above the facet
+        set isconcave
+      else if neighbor's centrum is not below the facet
+        set iscoplanar
+   if isconcave or iscoplanar
+     get angle if needed
+     append concave or coplanar merge to qh.mergeset
+*/
+boolT qh_test_appendmerge(qhT *qh, facetT *facet, facetT *neighbor) {
+  realT dist, dist2= -REALmax, angle= -REALmax;
+  boolT isconcave= False, iscoplanar= False, okangle= False;
+
+  if (qh->SKIPconvex && !qh->POSTmerging)
+    return False;
+  if ((!qh->MERGEexact || qh->POSTmerging) && qh->cos_max < REALmax/2) {
+    angle= qh_getangle(qh, facet->normal, neighbor->normal);
+    zinc_(Zangletests);
+    if (angle > qh->cos_max) {
+      zinc_(Zcoplanarangle);
+      qh_appendmergeset(qh, facet, neighbor, MRGanglecoplanar, &angle);
+      trace2((qh, qh->ferr, 2039, "qh_test_appendmerge: coplanar angle %4.4g between f%d and f%d\n",
+         angle, facet->id, neighbor->id));
+      return True;
+    }else
+      okangle= True;
+  }
+  if (!facet->center)
+    facet->center= qh_getcentrum(qh, facet);
+  zzinc_(Zcentrumtests);
+  qh_distplane(qh, facet->center, neighbor, &dist);
+  if (dist > qh->centrum_radius)
+    isconcave= True;
+  else {
+    if (dist > -qh->centrum_radius)
+      iscoplanar= True;
+    if (!neighbor->center)
+      neighbor->center= qh_getcentrum(qh, neighbor);
+    zzinc_(Zcentrumtests);
+    qh_distplane(qh, neighbor->center, facet, &dist2);
+    if (dist2 > qh->centrum_radius)
+      isconcave= True;
+    else if (!iscoplanar && dist2 > -qh->centrum_radius)
+      iscoplanar= True;
+  }
+  if (!isconcave && (!iscoplanar || (qh->MERGEexact && !qh->POSTmerging)))
+    return False;
+  if (!okangle && qh->ANGLEmerge) {
+    angle= qh_getangle(qh, facet->normal, neighbor->normal);
+    zinc_(Zangletests);
+  }
+  if (isconcave) {
+    zinc_(Zconcaveridge);
+    if (qh->ANGLEmerge)
+      angle += qh_ANGLEconcave + 0.5;
+    qh_appendmergeset(qh, facet, neighbor, MRGconcave, &angle);
+    trace0((qh, qh->ferr, 18, "qh_test_appendmerge: concave f%d to f%d dist %4.4g and reverse dist %4.4g angle %4.4g during p%d\n",
+           facet->id, neighbor->id, dist, dist2, angle, qh->furthest_id));
+  }else /* iscoplanar */ {
+    zinc_(Zcoplanarcentrum);
+    qh_appendmergeset(qh, facet, neighbor, MRGcoplanar, &angle);
+    trace2((qh, qh->ferr, 2040, "qh_test_appendmerge: coplanar f%d to f%d dist %4.4g, reverse dist %4.4g angle %4.4g\n",
+              facet->id, neighbor->id, dist, dist2, angle));
+  }
+  return True;
+} /* test_appendmerge */
+
+/*---------------------------------
+
+  qh_test_vneighbors(qh)
+    test vertex neighbors for convexity
+    tests all facets on qh.newfacet_list
+
+  returns:
+    true if non-convex vneighbors appended to qh.facet_mergeset
+    initializes vertex neighbors if needed
+
+  notes:
+    assumes all facet neighbors have been tested
+    this can be expensive
+    this does not guarantee that a centrum is below all facets
+      but it is unlikely
+    uses qh.visit_id
+
+  design:
+    build vertex neighbors if necessary
+    for all new facets
+      for all vertices
+        for each unvisited facet neighbor of the vertex
+          test new facet and neighbor for convexity
+*/
+boolT qh_test_vneighbors(qhT *qh /* qh->newfacet_list */) {
+  facetT *newfacet, *neighbor, **neighborp;
+  vertexT *vertex, **vertexp;
+  int nummerges= 0;
+
+  trace1((qh, qh->ferr, 1015, "qh_test_vneighbors: testing vertex neighbors for convexity\n"));
+  if (!qh->VERTEXneighbors)
+    qh_vertexneighbors(qh);
+  FORALLnew_facets
+    newfacet->seen= False;
+  FORALLnew_facets {
+    newfacet->seen= True;
+    newfacet->visitid= qh->visit_id++;
+    FOREACHneighbor_(newfacet)
+      newfacet->visitid= qh->visit_id;
+    FOREACHvertex_(newfacet->vertices) {
+      FOREACHneighbor_(vertex) {
+        if (neighbor->seen || neighbor->visitid == qh->visit_id)
+          continue;
+        if (qh_test_appendmerge(qh, newfacet, neighbor))
+          nummerges++;
+      }
+    }
+  }
+  zadd_(Ztestvneighbor, nummerges);
+  trace1((qh, qh->ferr, 1016, "qh_test_vneighbors: found %d non-convex, vertex neighbors\n",
+           nummerges));
+  return (nummerges > 0);
+} /* test_vneighbors */
+
+/*---------------------------------
+
+  qh_tracemerge(qh, facet1, facet2 )
+    print trace message after merge
+*/
+void qh_tracemerge(qhT *qh, facetT *facet1, facetT *facet2) {
+  boolT waserror= False;
+
+#ifndef qh_NOtrace
+  if (qh->IStracing >= 4)
+    qh_errprint(qh, "MERGED", facet2, NULL, NULL, NULL);
+  if (facet2 == qh->tracefacet || (qh->tracevertex && qh->tracevertex->newlist)) {
+    qh_fprintf(qh, qh->ferr, 8085, "qh_tracemerge: trace facet and vertex after merge of f%d and f%d, furthest p%d\n", facet1->id, facet2->id, qh->furthest_id);
+    if (facet2 != qh->tracefacet)
+      qh_errprint(qh, "TRACE", qh->tracefacet,
+        (qh->tracevertex && qh->tracevertex->neighbors) ?
+           SETfirstt_(qh->tracevertex->neighbors, facetT) : NULL,
+        NULL, qh->tracevertex);
+  }
+  if (qh->tracevertex) {
+    if (qh->tracevertex->deleted)
+      qh_fprintf(qh, qh->ferr, 8086, "qh_tracemerge: trace vertex deleted at furthest p%d\n",
+            qh->furthest_id);
+    else
+      qh_checkvertex(qh, qh->tracevertex);
+  }
+  if (qh->tracefacet) {
+    qh_checkfacet(qh, qh->tracefacet, True, &waserror);
+    if (waserror)
+      qh_errexit(qh, qh_ERRqhull, qh->tracefacet, NULL);
+  }
+#endif /* !qh_NOtrace */
+  if (qh->CHECKfrequently || qh->IStracing >= 4) { /* can't check polygon here */
+    qh_checkfacet(qh, facet2, True, &waserror);
+    if (waserror)
+      qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }
+} /* tracemerge */
+
+/*---------------------------------
+
+  qh_tracemerging(qh)
+    print trace message during POSTmerging
+
+  returns:
+    updates qh.mergereport
+
+  notes:
+    called from qh_mergecycle() and qh_mergefacet()
+
+  see:
+    qh_buildtracing()
+*/
+void qh_tracemerging(qhT *qh) {
+  realT cpu;
+  int total;
+  time_t timedata;
+  struct tm *tp;
+
+  qh->mergereport= zzval_(Ztotmerge);
+  time(&timedata);
+  tp= localtime(&timedata);
+  cpu= qh_CPUclock;
+  cpu /= qh_SECticks;
+  total= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
+  qh_fprintf(qh, qh->ferr, 8087, "\n\
+At %d:%d:%d & %2.5g CPU secs, qhull has merged %d facets.  The hull\n\
+  contains %d facets and %d vertices.\n",
+      tp->tm_hour, tp->tm_min, tp->tm_sec, cpu,
+      total, qh->num_facets - qh->num_visible,
+      qh->num_vertices-qh_setsize(qh, qh->del_vertices));
+} /* tracemerging */
+
+/*---------------------------------
+
+  qh_updatetested(qh, facet1, facet2 )
+    clear facet2->tested and facet1->ridge->tested for merge
+
+  returns:
+    deletes facet2->center unless it's already large
+      if so, clears facet2->ridge->tested
+
+  design:
+    clear facet2->tested
+    clear ridge->tested for facet1's ridges
+    if facet2 has a centrum
+      if facet2 is large
+        set facet2->keepcentrum
+      else if facet2 has 3 vertices due to many merges, or not large and post merging
+        clear facet2->keepcentrum
+      unless facet2->keepcentrum
+        clear facet2->center to recompute centrum later
+        clear ridge->tested for facet2's ridges
+*/
+void qh_updatetested(qhT *qh, facetT *facet1, facetT *facet2) {
+  ridgeT *ridge, **ridgep;
+  int size;
+
+  facet2->tested= False;
+  FOREACHridge_(facet1->ridges)
+    ridge->tested= False;
+  if (!facet2->center)
+    return;
+  size= qh_setsize(qh, facet2->vertices);
+  if (!facet2->keepcentrum) {
+    if (size > qh->hull_dim + qh_MAXnewcentrum) {
+      facet2->keepcentrum= True;
+      zinc_(Zwidevertices);
+    }
+  }else if (size <= qh->hull_dim + qh_MAXnewcentrum) {
+    /* center and keepcentrum was set */
+    if (size == qh->hull_dim || qh->POSTmerging)
+      facet2->keepcentrum= False; /* if many merges need to recompute centrum */
+  }
+  if (!facet2->keepcentrum) {
+    qh_memfree(qh, facet2->center, qh->normal_size);
+    facet2->center= NULL;
+    FOREACHridge_(facet2->ridges)
+      ridge->tested= False;
+  }
+} /* updatetested */
+
+/*---------------------------------
+
+  qh_vertexridges(qh, vertex )
+    return temporary set of ridges adjacent to a vertex
+    vertex->neighbors defined
+
+  ntoes:
+    uses qh.visit_id
+    does not include implicit ridges for simplicial facets
+
+  design:
+    for each neighbor of vertex
+      add ridges that include the vertex to ridges
+*/
+setT *qh_vertexridges(qhT *qh, vertexT *vertex) {
+  facetT *neighbor, **neighborp;
+  setT *ridges= qh_settemp(qh, qh->TEMPsize);
+  int size;
+
+  qh->visit_id++;
+  FOREACHneighbor_(vertex)
+    neighbor->visitid= qh->visit_id;
+  FOREACHneighbor_(vertex) {
+    if (*neighborp)   /* no new ridges in last neighbor */
+      qh_vertexridges_facet(qh, vertex, neighbor, &ridges);
+  }
+  if (qh->PRINTstatistics || qh->IStracing) {
+    size= qh_setsize(qh, ridges);
+    zinc_(Zvertexridge);
+    zadd_(Zvertexridgetot, size);
+    zmax_(Zvertexridgemax, size);
+    trace3((qh, qh->ferr, 3011, "qh_vertexridges: found %d ridges for v%d\n",
+             size, vertex->id));
+  }
+  return ridges;
+} /* vertexridges */
+
+/*---------------------------------
+
+  qh_vertexridges_facet(qh, vertex, facet, ridges )
+    add adjacent ridges for vertex in facet
+    neighbor->visitid==qh.visit_id if it hasn't been visited
+
+  returns:
+    ridges updated
+    sets facet->visitid to qh.visit_id-1
+
+  design:
+    for each ridge of facet
+      if ridge of visited neighbor (i.e., unprocessed)
+        if vertex in ridge
+          append ridge to vertex
+    mark facet processed
+*/
+void qh_vertexridges_facet(qhT *qh, vertexT *vertex, facetT *facet, setT **ridges) {
+  ridgeT *ridge, **ridgep;
+  facetT *neighbor;
+
+  FOREACHridge_(facet->ridges) {
+    neighbor= otherfacet_(ridge, facet);
+    if (neighbor->visitid == qh->visit_id
+    && qh_setin(ridge->vertices, vertex))
+      qh_setappend(qh, ridges, ridge);
+  }
+  facet->visitid= qh->visit_id-1;
+} /* vertexridges_facet */
+
+/*---------------------------------
+
+  qh_willdelete(qh, facet, replace )
+    moves facet to visible list
+    sets facet->f.replace to replace (may be NULL)
+
+  returns:
+    bumps qh.num_visible
+*/
+void qh_willdelete(qhT *qh, facetT *facet, facetT *replace) {
+
+  qh_removefacet(qh, facet);
+  qh_prependfacet(qh, facet, &qh->visible_list);
+  qh->num_visible++;
+  facet->visible= True;
+  facet->f.replace= replace;
+} /* willdelete */
+
+#else /* qh_NOmerge */
+void qh_premerge(qhT *qh, vertexT *apex, realT maxcentrum, realT maxangle) {
+}
+void qh_postmerge(qhT *qh, const char *reason, realT maxcentrum, realT maxangle,
+                      boolT vneighbors) {
+}
+boolT qh_checkzero(qhT *qh, boolT testall) {
+   }
+#endif /* qh_NOmerge */
+
diff --git a/Cdir/poly2_r.c b/Cdir/poly2_r.c
new file mode 100644
--- /dev/null
+++ b/Cdir/poly2_r.c
@@ -0,0 +1,3222 @@
+/*
  ---------------------------------
+
+   poly2_r.c
+   implements polygons and simplicies
+
+   see qh-poly_r.htm, poly_r.h and libqhull_r.h
+
+   frequently used code is in poly_r.c
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull_r/poly2_r.c#10 $$Change: 2069 $
+   $DateTime: 2016/01/18 22:05:03 $$Author: bbarber $
+*/
+
+#include "qhull_ra.h"
+
+/*======== functions in alphabetical order ==========*/
+
+/*---------------------------------
+
+  qh_addhash( newelem, hashtable, hashsize, hash )
+    add newelem to linear hash table at hash if not already there
+*/
+void qh_addhash(void *newelem, setT *hashtable, int hashsize, int hash) {
+  int scan;
+  void *elem;
+
+  for (scan= (int)hash; (elem= SETelem_(hashtable, scan));
+       scan= (++scan >= hashsize ? 0 : scan)) {
+    if (elem == newelem)
+      break;
+  }
+  /* loop terminates because qh_HASHfactor >= 1.1 by qh_initbuffers */
+  if (!elem)
+    SETelem_(hashtable, scan)= newelem;
+} /* addhash */
+
+/*---------------------------------
+
+  qh_check_bestdist(qh)
+    check that all points are within max_outside of the nearest facet
+    if qh.ONLYgood,
+      ignores !good facets
+
+  see:
+    qh_check_maxout(), qh_outerinner()
+
+  notes:
+    only called from qh_check_points()
+      seldom used since qh.MERGING is almost always set
+    if notverified>0 at end of routine
+      some points were well inside the hull.  If the hull contains
+      a lens-shaped component, these points were not verified.  Use
+      options 'Qi Tv' to verify all points.  (Exhaustive check also verifies)
+
+  design:
+    determine facet for each point (if any)
+    for each point
+      start with the assigned facet or with the first facet
+      find the best facet for the point and check all coplanar facets
+      error if point is outside of facet
+*/
+void qh_check_bestdist(qhT *qh) {
+  boolT waserror= False, unassigned;
+  facetT *facet, *bestfacet, *errfacet1= NULL, *errfacet2= NULL;
+  facetT *facetlist;
+  realT dist, maxoutside, maxdist= -REALmax;
+  pointT *point;
+  int numpart= 0, facet_i, facet_n, notgood= 0, notverified= 0;
+  setT *facets;
+
+  trace1((qh, qh->ferr, 1020, "qh_check_bestdist: check points below nearest facet.  Facet_list f%d\n",
+      qh->facet_list->id));
+  maxoutside= qh_maxouter(qh);
+  maxoutside += qh->DISTround;
+  /* one more qh.DISTround for check computation */
+  trace1((qh, qh->ferr, 1021, "qh_check_bestdist: check that all points are within %2.2g of best facet\n", maxoutside));
+  facets= qh_pointfacet(qh /*qh.facet_list*/);
+  if (!qh_QUICKhelp && qh->PRINTprecision)
+    qh_fprintf(qh, qh->ferr, 8091, "\n\
+qhull output completed.  Verifying that %d points are\n\
+below %2.2g of the nearest %sfacet.\n",
+             qh_setsize(qh, facets), maxoutside, (qh->ONLYgood ?  "good " : ""));
+  FOREACHfacet_i_(qh, facets) {  /* for each point with facet assignment */
+    if (facet)
+      unassigned= False;
+    else {
+      unassigned= True;
+      facet= qh->facet_list;
+    }
+    point= qh_point(qh, facet_i);
+    if (point == qh->GOODpointp)
+      continue;
+    qh_distplane(qh, point, facet, &dist);
+    numpart++;
+    bestfacet= qh_findbesthorizon(qh, !qh_IScheckmax, point, facet, qh_NOupper, &dist, &numpart);
+    /* occurs after statistics reported */
+    maximize_(maxdist, dist);
+    if (dist > maxoutside) {
+      if (qh->ONLYgood && !bestfacet->good
+          && !((bestfacet= qh_findgooddist(qh, point, bestfacet, &dist, &facetlist))
+               && dist > maxoutside))
+        notgood++;
+      else {
+        waserror= True;
+        qh_fprintf(qh, qh->ferr, 6109, "qhull precision error: point p%d is outside facet f%d, distance= %6.8g maxoutside= %6.8g\n",
+                facet_i, bestfacet->id, dist, maxoutside);
+        if (errfacet1 != bestfacet) {
+          errfacet2= errfacet1;
+          errfacet1= bestfacet;
+        }
+      }
+    }else if (unassigned && dist < -qh->MAXcoplanar)
+      notverified++;
+  }
+  qh_settempfree(qh, &facets);
+  if (notverified && !qh->DELAUNAY && !qh_QUICKhelp && qh->PRINTprecision)
+    qh_fprintf(qh, qh->ferr, 8092, "\n%d points were well inside the hull.  If the hull contains\n\
+a lens-shaped component, these points were not verified.  Use\n\
+options 'Qci Tv' to verify all points.\n", notverified);
+  if (maxdist > qh->outside_err) {
+    qh_fprintf(qh, qh->ferr, 6110, "qhull precision error (qh_check_bestdist): a coplanar point is %6.2g from convex hull.  The maximum value(qh.outside_err) is %6.2g\n",
+              maxdist, qh->outside_err);
+    qh_errexit2(qh, qh_ERRprec, errfacet1, errfacet2);
+  }else if (waserror && qh->outside_err > REALmax/2)
+    qh_errexit2(qh, qh_ERRprec, errfacet1, errfacet2);
+  /* else if waserror, the error was logged to qh.ferr but does not effect the output */
+  trace0((qh, qh->ferr, 20, "qh_check_bestdist: max distance outside %2.2g\n", maxdist));
+} /* check_bestdist */
+
+/*---------------------------------
+
+  qh_check_dupridge(qh, facet1, dist1, facet2, dist2)
+    Check duplicate ridge between facet1 and facet2 for wide merge
+    dist1 is the maximum distance of facet1's vertices to facet2
+    dist2 is the maximum distance of facet2's vertices to facet1
+
+  Returns
+    Level 1 log of the duplicate ridge with the minimum distance between vertices
+    Throws error if the merge will increase the maximum facet width by qh_WIDEduplicate (100x)
+
+  called from:
+    qh_forcedmerges()
+*/
+#ifndef qh_NOmerge
+void qh_check_dupridge(qhT *qh, facetT *facet1, realT dist1, facetT *facet2, realT dist2) {
+  vertexT *vertex, **vertexp, *vertexA, **vertexAp;
+  realT dist, innerplane, mergedist, outerplane, prevdist, ratio;
+  realT minvertex= REALmax;
+
+  mergedist= fmin_(dist1, dist2);
+  qh_outerinner(qh, NULL, &outerplane, &innerplane);  /* ratio from qh_printsummary */
+  prevdist= fmax_(outerplane, innerplane);
+  maximize_(prevdist, qh->ONEmerge + qh->DISTround);
+  maximize_(prevdist, qh->MINoutside + qh->DISTround);
+  ratio= mergedist/prevdist;
+  FOREACHvertex_(facet1->vertices) {     /* The duplicate ridge is between facet1 and facet2, so either facet can be tested */
+    FOREACHvertexA_(facet1->vertices) {
+      if (vertex > vertexA){   /* Test each pair once */
+        dist= qh_pointdist(vertex->point, vertexA->point, qh->hull_dim);
+        minimize_(minvertex, dist);
+      }
+    }
+  }
+  trace0((qh, qh->ferr, 16, "qh_check_dupridge: duplicate ridge between f%d and f%d due to nearly-coincident vertices (%2.2g), dist %2.2g, reverse dist %2.2g, ratio %2.2g while processing p%d\n",
+        facet1->id, facet2->id, minvertex, dist1, dist2, ratio, qh->furthest_id));
+  if (ratio > qh_WIDEduplicate) {
+    qh_fprintf(qh, qh->ferr, 6271, "qhull precision error (qh_check_dupridge): wide merge (%.0f times wider) due to duplicate ridge with nearly coincident points (%2.2g) between f%d and f%d, merge dist %2.2g, while processing p%d\n- Ignore error with option 'Q12'\n- To be fixed in a later version of Qhull\n",
+          ratio, minvertex, facet1->id, facet2->id, mergedist, qh->furthest_id);
+    if (qh->DELAUNAY)
+      qh_fprintf(qh, qh->ferr, 8145, "- A bounding box for the input sites may alleviate this error.\n");
+    if(minvertex > qh_WIDEduplicate*prevdist)
+      qh_fprintf(qh, qh->ferr, 8146, "- Vertex distance %2.2g is greater than %d times maximum distance %2.2g\n  Please report to bradb@shore.net with steps to reproduce and all output\n",
+          minvertex, qh_WIDEduplicate, prevdist);
+    if (!qh->NOwide)
+      qh_errexit2(qh, qh_ERRqhull, facet1, facet2);
+  }
+} /* check_dupridge */
+#endif
+
+/*---------------------------------
+
+  qh_check_maxout(qh)
+    updates qh.max_outside by checking all points against bestfacet
+    if qh.ONLYgood, ignores !good facets
+
+  returns:
+    updates facet->maxoutside via qh_findbesthorizon()
+    sets qh.maxoutdone
+    if printing qh.min_vertex (qh_outerinner),
+      it is updated to the current vertices
+    removes inside/coplanar points from coplanarset as needed
+
+  notes:
+    defines coplanar as min_vertex instead of MAXcoplanar
+    may not need to check near-inside points because of qh.MAXcoplanar
+      and qh.KEEPnearinside (before it was -DISTround)
+
+  see also:
+    qh_check_bestdist()
+
+  design:
+    if qh.min_vertex is needed
+      for all neighbors of all vertices
+        test distance from vertex to neighbor
+    determine facet for each point (if any)
+    for each point with an assigned facet
+      find the best facet for the point and check all coplanar facets
+        (updates outer planes)
+    remove near-inside points from coplanar sets
+*/
+#ifndef qh_NOmerge
+void qh_check_maxout(qhT *qh) {
+  facetT *facet, *bestfacet, *neighbor, **neighborp, *facetlist;
+  realT dist, maxoutside, minvertex, old_maxoutside;
+  pointT *point;
+  int numpart= 0, facet_i, facet_n, notgood= 0;
+  setT *facets, *vertices;
+  vertexT *vertex;
+
+  trace1((qh, qh->ferr, 1022, "qh_check_maxout: check and update maxoutside for each facet.\n"));
+  maxoutside= minvertex= 0;
+  if (qh->VERTEXneighbors
+  && (qh->PRINTsummary || qh->KEEPinside || qh->KEEPcoplanar
+        || qh->TRACElevel || qh->PRINTstatistics
+        || qh->PRINTout[0] == qh_PRINTsummary || qh->PRINTout[0] == qh_PRINTnone)) {
+    trace1((qh, qh->ferr, 1023, "qh_check_maxout: determine actual maxoutside and minvertex\n"));
+    vertices= qh_pointvertex(qh /*qh.facet_list*/);
+    FORALLvertices {
+      FOREACHneighbor_(vertex) {
+        zinc_(Zdistvertex);  /* distance also computed by main loop below */
+        qh_distplane(qh, vertex->point, neighbor, &dist);
+        minimize_(minvertex, dist);
+        if (-dist > qh->TRACEdist || dist > qh->TRACEdist
+        || neighbor == qh->tracefacet || vertex == qh->tracevertex)
+          qh_fprintf(qh, qh->ferr, 8093, "qh_check_maxout: p%d(v%d) is %.2g from f%d\n",
+                    qh_pointid(qh, vertex->point), vertex->id, dist, neighbor->id);
+      }
+    }
+    if (qh->MERGING) {
+      wmin_(Wminvertex, qh->min_vertex);
+    }
+    qh->min_vertex= minvertex;
+    qh_settempfree(qh, &vertices);
+  }
+  facets= qh_pointfacet(qh /*qh.facet_list*/);
+  do {
+    old_maxoutside= fmax_(qh->max_outside, maxoutside);
+    FOREACHfacet_i_(qh, facets) {     /* for each point with facet assignment */
+      if (facet) {
+        point= qh_point(qh, facet_i);
+        if (point == qh->GOODpointp)
+          continue;
+        zzinc_(Ztotcheck);
+        qh_distplane(qh, point, facet, &dist);
+        numpart++;
+        bestfacet= qh_findbesthorizon(qh, qh_IScheckmax, point, facet, !qh_NOupper, &dist, &numpart);
+        if (bestfacet && dist > maxoutside) {
+          if (qh->ONLYgood && !bestfacet->good
+          && !((bestfacet= qh_findgooddist(qh, point, bestfacet, &dist, &facetlist))
+               && dist > maxoutside))
+            notgood++;
+          else
+            maxoutside= dist;
+        }
+        if (dist > qh->TRACEdist || (bestfacet && bestfacet == qh->tracefacet))
+          qh_fprintf(qh, qh->ferr, 8094, "qh_check_maxout: p%d is %.2g above f%d\n",
+          qh_pointid(qh, point), dist, (bestfacet ? bestfacet->id : UINT_MAX));
+      }
+    }
+  }while
+    (maxoutside > 2*old_maxoutside);
+    /* if qh.maxoutside increases substantially, qh_SEARCHdist is not valid
+          e.g., RBOX 5000 s Z1 G1e-13 t1001200614 | qhull */
+  zzadd_(Zcheckpart, numpart);
+  qh_settempfree(qh, &facets);
+  wval_(Wmaxout)= maxoutside - qh->max_outside;
+  wmax_(Wmaxoutside, qh->max_outside);
+  qh->max_outside= maxoutside;
+  qh_nearcoplanar(qh /*qh.facet_list*/);
+  qh->maxoutdone= True;
+  trace1((qh, qh->ferr, 1024, "qh_check_maxout: maxoutside %2.2g, min_vertex %2.2g, outside of not good %d\n",
+       maxoutside, qh->min_vertex, notgood));
+} /* check_maxout */
+#else /* qh_NOmerge */
+void qh_check_maxout(qhT *qh) {
+}
+#endif
+
+/*---------------------------------
+
+  qh_check_output(qh)
+    performs the checks at the end of qhull algorithm
+    Maybe called after voronoi output.  Will recompute otherwise centrums are Voronoi centers instead
+*/
+void qh_check_output(qhT *qh) {
+  int i;
+
+  if (qh->STOPcone)
+    return;
+  if (qh->VERIFYoutput | qh->IStracing | qh->CHECKfrequently) {
+    qh_checkpolygon(qh, qh->facet_list);
+    qh_checkflipped_all(qh, qh->facet_list);
+    qh_checkconvex(qh, qh->facet_list, qh_ALGORITHMfault);
+  }else if (!qh->MERGING && qh_newstats(qh, qh->qhstat.precision, &i)) {
+    qh_checkflipped_all(qh, qh->facet_list);
+    qh_checkconvex(qh, qh->facet_list, qh_ALGORITHMfault);
+  }
+} /* check_output */
+
+
+
+/*---------------------------------
+
+  qh_check_point(qh, point, facet, maxoutside, maxdist, errfacet1, errfacet2 )
+    check that point is less than maxoutside from facet
+*/
+void qh_check_point(qhT *qh, pointT *point, facetT *facet, realT *maxoutside, realT *maxdist, facetT **errfacet1, facetT **errfacet2) {
+  realT dist;
+
+  /* occurs after statistics reported */
+  qh_distplane(qh, point, facet, &dist);
+  if (dist > *maxoutside) {
+    if (*errfacet1 != facet) {
+      *errfacet2= *errfacet1;
+      *errfacet1= facet;
+    }
+    qh_fprintf(qh, qh->ferr, 6111, "qhull precision error: point p%d is outside facet f%d, distance= %6.8g maxoutside= %6.8g\n",
+              qh_pointid(qh, point), facet->id, dist, *maxoutside);
+  }
+  maximize_(*maxdist, dist);
+} /* qh_check_point */
+
+
+/*---------------------------------
+
+  qh_check_points(qh)
+    checks that all points are inside all facets
+
+  notes:
+    if many points and qh_check_maxout not called (i.e., !qh.MERGING),
+       calls qh_findbesthorizon (seldom done).
+    ignores flipped facets
+    maxoutside includes 2 qh.DISTrounds
+      one qh.DISTround for the computed distances in qh_check_points
+    qh_printafacet and qh_printsummary needs only one qh.DISTround
+    the computation for qh.VERIFYdirect does not account for qh.other_points
+
+  design:
+    if many points
+      use qh_check_bestdist()
+    else
+      for all facets
+        for all points
+          check that point is inside facet
+*/
+void qh_check_points(qhT *qh) {
+  facetT *facet, *errfacet1= NULL, *errfacet2= NULL;
+  realT total, maxoutside, maxdist= -REALmax;
+  pointT *point, **pointp, *pointtemp;
+  boolT testouter;
+
+  maxoutside= qh_maxouter(qh);
+  maxoutside += qh->DISTround;
+  /* one more qh.DISTround for check computation */
+  trace1((qh, qh->ferr, 1025, "qh_check_points: check all points below %2.2g of all facet planes\n",
+          maxoutside));
+  if (qh->num_good)   /* miss counts other_points and !good facets */
+     total= (float)qh->num_good * (float)qh->num_points;
+  else
+     total= (float)qh->num_facets * (float)qh->num_points;
+  if (total >= qh_VERIFYdirect && !qh->maxoutdone) {
+    if (!qh_QUICKhelp && qh->SKIPcheckmax && qh->MERGING)
+      qh_fprintf(qh, qh->ferr, 7075, "qhull input warning: merging without checking outer planes('Q5' or 'Po').\n\
+Verify may report that a point is outside of a facet.\n");
+    qh_check_bestdist(qh);
+  }else {
+    if (qh_MAXoutside && qh->maxoutdone)
+      testouter= True;
+    else
+      testouter= False;
+    if (!qh_QUICKhelp) {
+      if (qh->MERGEexact)
+        qh_fprintf(qh, qh->ferr, 7076, "qhull input warning: exact merge ('Qx').  Verify may report that a point\n\
+is outside of a facet.  See qh-optq.htm#Qx\n");
+      else if (qh->SKIPcheckmax || qh->NOnearinside)
+        qh_fprintf(qh, qh->ferr, 7077, "qhull input warning: no outer plane check ('Q5') or no processing of\n\
+near-inside points ('Q8').  Verify may report that a point is outside\n\
+of a facet.\n");
+    }
+    if (qh->PRINTprecision) {
+      if (testouter)
+        qh_fprintf(qh, qh->ferr, 8098, "\n\
+Output completed.  Verifying that all points are below outer planes of\n\
+all %sfacets.  Will make %2.0f distance computations.\n",
+              (qh->ONLYgood ?  "good " : ""), total);
+      else
+        qh_fprintf(qh, qh->ferr, 8099, "\n\
+Output completed.  Verifying that all points are below %2.2g of\n\
+all %sfacets.  Will make %2.0f distance computations.\n",
+              maxoutside, (qh->ONLYgood ?  "good " : ""), total);
+    }
+    FORALLfacets {
+      if (!facet->good && qh->ONLYgood)
+        continue;
+      if (facet->flipped)
+        continue;
+      if (!facet->normal) {
+        qh_fprintf(qh, qh->ferr, 7061, "qhull warning (qh_check_points): missing normal for facet f%d\n", facet->id);
+        continue;
+      }
+      if (testouter) {
+#if qh_MAXoutside
+        maxoutside= facet->maxoutside + 2* qh->DISTround;
+        /* one DISTround to actual point and another to computed point */
+#endif
+      }
+      FORALLpoints {
+        if (point != qh->GOODpointp)
+          qh_check_point(qh, point, facet, &maxoutside, &maxdist, &errfacet1, &errfacet2);
+      }
+      FOREACHpoint_(qh->other_points) {
+        if (point != qh->GOODpointp)
+          qh_check_point(qh, point, facet, &maxoutside, &maxdist, &errfacet1, &errfacet2);
+      }
+    }
+    if (maxdist > qh->outside_err) {
+      qh_fprintf(qh, qh->ferr, 6112, "qhull precision error (qh_check_points): a coplanar point is %6.2g from convex hull.  The maximum value(qh.outside_err) is %6.2g\n",
+                maxdist, qh->outside_err );
+      qh_errexit2(qh, qh_ERRprec, errfacet1, errfacet2 );
+    }else if (errfacet1 && qh->outside_err > REALmax/2)
+        qh_errexit2(qh, qh_ERRprec, errfacet1, errfacet2 );
+    /* else if errfacet1, the error was logged to qh.ferr but does not effect the output */
+    trace0((qh, qh->ferr, 21, "qh_check_points: max distance outside %2.2g\n", maxdist));
+  }
+} /* check_points */
+
+
+/*---------------------------------
+
+  qh_checkconvex(qh, facetlist, fault )
+    check that each ridge in facetlist is convex
+    fault = qh_DATAfault if reporting errors
+          = qh_ALGORITHMfault otherwise
+
+  returns:
+    counts Zconcaveridges and Zcoplanarridges
+    errors if concaveridge or if merging an coplanar ridge
+
+  note:
+    if not merging,
+      tests vertices for neighboring simplicial facets
+    else if ZEROcentrum,
+      tests vertices for neighboring simplicial   facets
+    else
+      tests centrums of neighboring facets
+
+  design:
+    for all facets
+      report flipped facets
+      if ZEROcentrum and simplicial neighbors
+        test vertices for neighboring simplicial facets
+      else
+        test centrum against all neighbors
+*/
+void qh_checkconvex(qhT *qh, facetT *facetlist, int fault) {
+  facetT *facet, *neighbor, **neighborp, *errfacet1=NULL, *errfacet2=NULL;
+  vertexT *vertex;
+  realT dist;
+  pointT *centrum;
+  boolT waserror= False, centrum_warning= False, tempcentrum= False, allsimplicial;
+  int neighbor_i;
+
+  trace1((qh, qh->ferr, 1026, "qh_checkconvex: check all ridges are convex\n"));
+  if (!qh->RERUN) {
+    zzval_(Zconcaveridges)= 0;
+    zzval_(Zcoplanarridges)= 0;
+  }
+  FORALLfacet_(facetlist) {
+    if (facet->flipped) {
+      qh_precision(qh, "flipped facet");
+      qh_fprintf(qh, qh->ferr, 6113, "qhull precision error: f%d is flipped(interior point is outside)\n",
+               facet->id);
+      errfacet1= facet;
+      waserror= True;
+      continue;
+    }
+    if (qh->MERGING && (!qh->ZEROcentrum || !facet->simplicial || facet->tricoplanar))
+      allsimplicial= False;
+    else {
+      allsimplicial= True;
+      neighbor_i= 0;
+      FOREACHneighbor_(facet) {
+        vertex= SETelemt_(facet->vertices, neighbor_i++, vertexT);
+        if (!neighbor->simplicial || neighbor->tricoplanar) {
+          allsimplicial= False;
+          continue;
+        }
+        qh_distplane(qh, vertex->point, neighbor, &dist);
+        if (dist > -qh->DISTround) {
+          if (fault == qh_DATAfault) {
+            qh_precision(qh, "coplanar or concave ridge");
+            qh_fprintf(qh, qh->ferr, 6114, "qhull precision error: initial simplex is not convex. Distance=%.2g\n", dist);
+            qh_errexit(qh, qh_ERRsingular, NULL, NULL);
+          }
+          if (dist > qh->DISTround) {
+            zzinc_(Zconcaveridges);
+            qh_precision(qh, "concave ridge");
+            qh_fprintf(qh, qh->ferr, 6115, "qhull precision error: f%d is concave to f%d, since p%d(v%d) is %6.4g above\n",
+              facet->id, neighbor->id, qh_pointid(qh, vertex->point), vertex->id, dist);
+            errfacet1= facet;
+            errfacet2= neighbor;
+            waserror= True;
+          }else if (qh->ZEROcentrum) {
+            if (dist > 0) {     /* qh_checkzero checks that dist < - qh->DISTround */
+              zzinc_(Zcoplanarridges);
+              qh_precision(qh, "coplanar ridge");
+              qh_fprintf(qh, qh->ferr, 6116, "qhull precision error: f%d is clearly not convex to f%d, since p%d(v%d) is %6.4g above\n",
+                facet->id, neighbor->id, qh_pointid(qh, vertex->point), vertex->id, dist);
+              errfacet1= facet;
+              errfacet2= neighbor;
+              waserror= True;
+            }
+          }else {
+            zzinc_(Zcoplanarridges);
+            qh_precision(qh, "coplanar ridge");
+            trace0((qh, qh->ferr, 22, "qhull precision error: f%d may be coplanar to f%d, since p%d(v%d) is within %6.4g during p%d\n",
+              facet->id, neighbor->id, qh_pointid(qh, vertex->point), vertex->id, dist, qh->furthest_id));
+          }
+        }
+      }
+    }
+    if (!allsimplicial) {
+      if (qh->CENTERtype == qh_AScentrum) {
+        if (!facet->center)
+          facet->center= qh_getcentrum(qh, facet);
+        centrum= facet->center;
+      }else {
+        if (!centrum_warning && (!facet->simplicial || facet->tricoplanar)) {
+           centrum_warning= True;
+           qh_fprintf(qh, qh->ferr, 7062, "qhull warning: recomputing centrums for convexity test.  This may lead to false, precision errors.\n");
+        }
+        centrum= qh_getcentrum(qh, facet);
+        tempcentrum= True;
+      }
+      FOREACHneighbor_(facet) {
+        if (qh->ZEROcentrum && facet->simplicial && neighbor->simplicial)
+          continue;
+        if (facet->tricoplanar || neighbor->tricoplanar)
+          continue;
+        zzinc_(Zdistconvex);
+        qh_distplane(qh, centrum, neighbor, &dist);
+        if (dist > qh->DISTround) {
+          zzinc_(Zconcaveridges);
+          qh_precision(qh, "concave ridge");
+          qh_fprintf(qh, qh->ferr, 6117, "qhull precision error: f%d is concave to f%d.  Centrum of f%d is %6.4g above f%d\n",
+            facet->id, neighbor->id, facet->id, dist, neighbor->id);
+          errfacet1= facet;
+          errfacet2= neighbor;
+          waserror= True;
+        }else if (dist >= 0.0) {   /* if arithmetic always rounds the same,
+                                     can test against centrum radius instead */
+          zzinc_(Zcoplanarridges);
+          qh_precision(qh, "coplanar ridge");
+          qh_fprintf(qh, qh->ferr, 6118, "qhull precision error: f%d is coplanar or concave to f%d.  Centrum of f%d is %6.4g above f%d\n",
+            facet->id, neighbor->id, facet->id, dist, neighbor->id);
+          errfacet1= facet;
+          errfacet2= neighbor;
+          waserror= True;
+        }
+      }
+      if (tempcentrum)
+        qh_memfree(qh, centrum, qh->normal_size);
+    }
+  }
+  if (waserror && !qh->FORCEoutput)
+    qh_errexit2(qh, qh_ERRprec, errfacet1, errfacet2);
+} /* checkconvex */
+
+
+/*---------------------------------
+
+  qh_checkfacet(qh, facet, newmerge, waserror )
+    checks for consistency errors in facet
+    newmerge set if from merge_r.c
+
+  returns:
+    sets waserror if any error occurs
+
+  checks:
+    vertex ids are inverse sorted
+    unless newmerge, at least hull_dim neighbors and vertices (exactly if simplicial)
+    if non-simplicial, at least as many ridges as neighbors
+    neighbors are not duplicated
+    ridges are not duplicated
+    in 3-d, ridges=verticies
+    (qh.hull_dim-1) ridge vertices
+    neighbors are reciprocated
+    ridge neighbors are facet neighbors and a ridge for every neighbor
+    simplicial neighbors match facetintersect
+    vertex intersection matches vertices of common ridges
+    vertex neighbors and facet vertices agree
+    all ridges have distinct vertex sets
+
+  notes:
+    uses neighbor->seen
+
+  design:
+    check sets
+    check vertices
+    check sizes of neighbors and vertices
+    check for qh_MERGEridge and qh_DUPLICATEridge flags
+    check neighbor set
+    check ridge set
+    check ridges, neighbors, and vertices
+*/
+void qh_checkfacet(qhT *qh, facetT *facet, boolT newmerge, boolT *waserrorp) {
+  facetT *neighbor, **neighborp, *errother=NULL;
+  ridgeT *ridge, **ridgep, *errridge= NULL, *ridge2;
+  vertexT *vertex, **vertexp;
+  unsigned previousid= INT_MAX;
+  int numneighbors, numvertices, numridges=0, numRvertices=0;
+  boolT waserror= False;
+  int skipA, skipB, ridge_i, ridge_n, i;
+  setT *intersection;
+
+  if (facet->visible) {
+    qh_fprintf(qh, qh->ferr, 6119, "qhull internal error (qh_checkfacet): facet f%d is on the visible_list\n",
+      facet->id);
+    qh_errexit(qh, qh_ERRqhull, facet, NULL);
+  }
+  if (!facet->normal) {
+    qh_fprintf(qh, qh->ferr, 6120, "qhull internal error (qh_checkfacet): facet f%d does not have  a normal\n",
+      facet->id);
+    waserror= True;
+  }
+  qh_setcheck(qh, facet->vertices, "vertices for f", facet->id);
+  qh_setcheck(qh, facet->ridges, "ridges for f", facet->id);
+  qh_setcheck(qh, facet->outsideset, "outsideset for f", facet->id);
+  qh_setcheck(qh, facet->coplanarset, "coplanarset for f", facet->id);
+  qh_setcheck(qh, facet->neighbors, "neighbors for f", facet->id);
+  FOREACHvertex_(facet->vertices) {
+    if (vertex->deleted) {
+      qh_fprintf(qh, qh->ferr, 6121, "qhull internal error (qh_checkfacet): deleted vertex v%d in f%d\n", vertex->id, facet->id);
+      qh_errprint(qh, "ERRONEOUS", NULL, NULL, NULL, vertex);
+      waserror= True;
+    }
+    if (vertex->id >= previousid) {
+      qh_fprintf(qh, qh->ferr, 6122, "qhull internal error (qh_checkfacet): vertices of f%d are not in descending id order at v%d\n", facet->id, vertex->id);
+      waserror= True;
+      break;
+    }
+    previousid= vertex->id;
+  }
+  numneighbors= qh_setsize(qh, facet->neighbors);
+  numvertices= qh_setsize(qh, facet->vertices);
+  numridges= qh_setsize(qh, facet->ridges);
+  if (facet->simplicial) {
+    if (numvertices+numneighbors != 2*qh->hull_dim
+    && !facet->degenerate && !facet->redundant) {
+      qh_fprintf(qh, qh->ferr, 6123, "qhull internal error (qh_checkfacet): for simplicial facet f%d, #vertices %d + #neighbors %d != 2*qh->hull_dim\n",
+                facet->id, numvertices, numneighbors);
+      qh_setprint(qh, qh->ferr, "", facet->neighbors);
+      waserror= True;
+    }
+  }else { /* non-simplicial */
+    if (!newmerge
+    &&(numvertices < qh->hull_dim || numneighbors < qh->hull_dim)
+    && !facet->degenerate && !facet->redundant) {
+      qh_fprintf(qh, qh->ferr, 6124, "qhull internal error (qh_checkfacet): for facet f%d, #vertices %d or #neighbors %d < qh->hull_dim\n",
+         facet->id, numvertices, numneighbors);
+       waserror= True;
+    }
+    /* in 3-d, can get a vertex twice in an edge list, e.g., RBOX 1000 s W1e-13 t995849315 D2 | QHULL d Tc Tv TP624 TW1e-13 T4 */
+    if (numridges < numneighbors
+    ||(qh->hull_dim == 3 && numvertices > numridges && !qh->NEWfacets)
+    ||(qh->hull_dim == 2 && numridges + numvertices + numneighbors != 6)) {
+      if (!facet->degenerate && !facet->redundant) {
+        qh_fprintf(qh, qh->ferr, 6125, "qhull internal error (qh_checkfacet): for facet f%d, #ridges %d < #neighbors %d or(3-d) > #vertices %d or(2-d) not all 2\n",
+            facet->id, numridges, numneighbors, numvertices);
+        waserror= True;
+      }
+    }
+  }
+  FOREACHneighbor_(facet) {
+    if (neighbor == qh_MERGEridge || neighbor == qh_DUPLICATEridge) {
+      qh_fprintf(qh, qh->ferr, 6126, "qhull internal error (qh_checkfacet): facet f%d still has a MERGE or DUP neighbor\n", facet->id);
+      qh_errexit(qh, qh_ERRqhull, facet, NULL);
+    }
+    neighbor->seen= True;
+  }
+  FOREACHneighbor_(facet) {
+    if (!qh_setin(neighbor->neighbors, facet)) {
+      qh_fprintf(qh, qh->ferr, 6127, "qhull internal error (qh_checkfacet): facet f%d has neighbor f%d, but f%d does not have neighbor f%d\n",
+              facet->id, neighbor->id, neighbor->id, facet->id);
+      errother= neighbor;
+      waserror= True;
+    }
+    if (!neighbor->seen) {
+      qh_fprintf(qh, qh->ferr, 6128, "qhull internal error (qh_checkfacet): facet f%d has a duplicate neighbor f%d\n",
+              facet->id, neighbor->id);
+      errother= neighbor;
+      waserror= True;
+    }
+    neighbor->seen= False;
+  }
+  FOREACHridge_(facet->ridges) {
+    qh_setcheck(qh, ridge->vertices, "vertices for r", ridge->id);
+    ridge->seen= False;
+  }
+  FOREACHridge_(facet->ridges) {
+    if (ridge->seen) {
+      qh_fprintf(qh, qh->ferr, 6129, "qhull internal error (qh_checkfacet): facet f%d has a duplicate ridge r%d\n",
+              facet->id, ridge->id);
+      errridge= ridge;
+      waserror= True;
+    }
+    ridge->seen= True;
+    numRvertices= qh_setsize(qh, ridge->vertices);
+    if (numRvertices != qh->hull_dim - 1) {
+      qh_fprintf(qh, qh->ferr, 6130, "qhull internal error (qh_checkfacet): ridge between f%d and f%d has %d vertices\n",
+                ridge->top->id, ridge->bottom->id, numRvertices);
+      errridge= ridge;
+      waserror= True;
+    }
+    neighbor= otherfacet_(ridge, facet);
+    neighbor->seen= True;
+    if (!qh_setin(facet->neighbors, neighbor)) {
+      qh_fprintf(qh, qh->ferr, 6131, "qhull internal error (qh_checkfacet): for facet f%d, neighbor f%d of ridge r%d not in facet\n",
+           facet->id, neighbor->id, ridge->id);
+      errridge= ridge;
+      waserror= True;
+    }
+  }
+  if (!facet->simplicial) {
+    FOREACHneighbor_(facet) {
+      if (!neighbor->seen) {
+        qh_fprintf(qh, qh->ferr, 6132, "qhull internal error (qh_checkfacet): facet f%d does not have a ridge for neighbor f%d\n",
+              facet->id, neighbor->id);
+        errother= neighbor;
+        waserror= True;
+      }
+      intersection= qh_vertexintersect_new(qh, facet->vertices, neighbor->vertices);
+      qh_settemppush(qh, intersection);
+      FOREACHvertex_(facet->vertices) {
+        vertex->seen= False;
+        vertex->seen2= False;
+      }
+      FOREACHvertex_(intersection)
+        vertex->seen= True;
+      FOREACHridge_(facet->ridges) {
+        if (neighbor != otherfacet_(ridge, facet))
+            continue;
+        FOREACHvertex_(ridge->vertices) {
+          if (!vertex->seen) {
+            qh_fprintf(qh, qh->ferr, 6133, "qhull internal error (qh_checkfacet): vertex v%d in r%d not in f%d intersect f%d\n",
+                  vertex->id, ridge->id, facet->id, neighbor->id);
+            qh_errexit(qh, qh_ERRqhull, facet, ridge);
+          }
+          vertex->seen2= True;
+        }
+      }
+      if (!newmerge) {
+        FOREACHvertex_(intersection) {
+          if (!vertex->seen2) {
+            if (qh->IStracing >=3 || !qh->MERGING) {
+              qh_fprintf(qh, qh->ferr, 6134, "qhull precision error (qh_checkfacet): vertex v%d in f%d intersect f%d but\n\
+ not in a ridge.  This is ok under merging.  Last point was p%d\n",
+                     vertex->id, facet->id, neighbor->id, qh->furthest_id);
+              if (!qh->FORCEoutput && !qh->MERGING) {
+                qh_errprint(qh, "ERRONEOUS", facet, neighbor, NULL, vertex);
+                if (!qh->MERGING)
+                  qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+              }
+            }
+          }
+        }
+      }
+      qh_settempfree(qh, &intersection);
+    }
+  }else { /* simplicial */
+    FOREACHneighbor_(facet) {
+      if (neighbor->simplicial) {
+        skipA= SETindex_(facet->neighbors, neighbor);
+        skipB= qh_setindex(neighbor->neighbors, facet);
+        if (skipA<0 || skipB<0 || !qh_setequal_skip(facet->vertices, skipA, neighbor->vertices, skipB)) {
+          qh_fprintf(qh, qh->ferr, 6135, "qhull internal error (qh_checkfacet): facet f%d skip %d and neighbor f%d skip %d do not match \n",
+                   facet->id, skipA, neighbor->id, skipB);
+          errother= neighbor;
+          waserror= True;
+        }
+      }
+    }
+  }
+  if (qh->hull_dim < 5 && (qh->IStracing > 2 || qh->CHECKfrequently)) {
+    FOREACHridge_i_(qh, facet->ridges) {           /* expensive */
+      for (i=ridge_i+1; i < ridge_n; i++) {
+        ridge2= SETelemt_(facet->ridges, i, ridgeT);
+        if (qh_setequal(ridge->vertices, ridge2->vertices)) {
+          qh_fprintf(qh, qh->ferr, 6227, "Qhull internal error (qh_checkfacet): ridges r%d and r%d have the same vertices\n",
+                  ridge->id, ridge2->id);
+          errridge= ridge;
+          waserror= True;
+        }
+      }
+    }
+  }
+  if (waserror) {
+    qh_errprint(qh, "ERRONEOUS", facet, errother, errridge, NULL);
+    *waserrorp= True;
+  }
+} /* checkfacet */
+
+
+/*---------------------------------
+
+  qh_checkflipped_all(qh, facetlist )
+    checks orientation of facets in list against interior point
+*/
+void qh_checkflipped_all(qhT *qh, facetT *facetlist) {
+  facetT *facet;
+  boolT waserror= False;
+  realT dist;
+
+  if (facetlist == qh->facet_list)
+    zzval_(Zflippedfacets)= 0;
+  FORALLfacet_(facetlist) {
+    if (facet->normal && !qh_checkflipped(qh, facet, &dist, !qh_ALL)) {
+      qh_fprintf(qh, qh->ferr, 6136, "qhull precision error: facet f%d is flipped, distance= %6.12g\n",
+              facet->id, dist);
+      if (!qh->FORCEoutput) {
+        qh_errprint(qh, "ERRONEOUS", facet, NULL, NULL, NULL);
+        waserror= True;
+      }
+    }
+  }
+  if (waserror) {
+    qh_fprintf(qh, qh->ferr, 8101, "\n\
+A flipped facet occurs when its distance to the interior point is\n\
+greater than %2.2g, the maximum roundoff error.\n", -qh->DISTround);
+    qh_errexit(qh, qh_ERRprec, NULL, NULL);
+  }
+} /* checkflipped_all */
+
+/*---------------------------------
+
+  qh_checkpolygon(qh, facetlist )
+    checks the correctness of the structure
+
+  notes:
+    call with either qh.facet_list or qh.newfacet_list
+    checks num_facets and num_vertices if qh.facet_list
+
+  design:
+    for each facet
+      checks facet and outside set
+    initializes vertexlist
+    for each facet
+      checks vertex set
+    if checking all facets(qh.facetlist)
+      check facet count
+      if qh.VERTEXneighbors
+        check vertex neighbors and count
+      check vertex count
+*/
+void qh_checkpolygon(qhT *qh, facetT *facetlist) {
+  facetT *facet;
+  vertexT *vertex, **vertexp, *vertexlist;
+  int numfacets= 0, numvertices= 0, numridges= 0;
+  int totvneighbors= 0, totvertices= 0;
+  boolT waserror= False, nextseen= False, visibleseen= False;
+
+  trace1((qh, qh->ferr, 1027, "qh_checkpolygon: check all facets from f%d\n", facetlist->id));
+  if (facetlist != qh->facet_list || qh->ONLYgood)
+    nextseen= True;
+  FORALLfacet_(facetlist) {
+    if (facet == qh->visible_list)
+      visibleseen= True;
+    if (!facet->visible) {
+      if (!nextseen) {
+        if (facet == qh->facet_next)
+          nextseen= True;
+        else if (qh_setsize(qh, facet->outsideset)) {
+          if (!qh->NARROWhull
+#if !qh_COMPUTEfurthest
+               || facet->furthestdist >= qh->MINoutside
+#endif
+                        ) {
+            qh_fprintf(qh, qh->ferr, 6137, "qhull internal error (qh_checkpolygon): f%d has outside points before qh->facet_next\n",
+                     facet->id);
+            qh_errexit(qh, qh_ERRqhull, facet, NULL);
+          }
+        }
+      }
+      numfacets++;
+      qh_checkfacet(qh, facet, False, &waserror);
+    }
+  }
+  if (qh->visible_list && !visibleseen && facetlist == qh->facet_list) {
+    qh_fprintf(qh, qh->ferr, 6138, "qhull internal error (qh_checkpolygon): visible list f%d no longer on facet list\n", qh->visible_list->id);
+    qh_printlists(qh);
+    qh_errexit(qh, qh_ERRqhull, qh->visible_list, NULL);
+  }
+  if (facetlist == qh->facet_list)
+    vertexlist= qh->vertex_list;
+  else if (facetlist == qh->newfacet_list)
+    vertexlist= qh->newvertex_list;
+  else
+    vertexlist= NULL;
+  FORALLvertex_(vertexlist) {
+    vertex->seen= False;
+    vertex->visitid= 0;
+  }
+  FORALLfacet_(facetlist) {
+    if (facet->visible)
+      continue;
+    if (facet->simplicial)
+      numridges += qh->hull_dim;
+    else
+      numridges += qh_setsize(qh, facet->ridges);
+    FOREACHvertex_(facet->vertices) {
+      vertex->visitid++;
+      if (!vertex->seen) {
+        vertex->seen= True;
+        numvertices++;
+        if (qh_pointid(qh, vertex->point) == qh_IDunknown) {
+          qh_fprintf(qh, qh->ferr, 6139, "qhull internal error (qh_checkpolygon): unknown point %p for vertex v%d first_point %p\n",
+                   vertex->point, vertex->id, qh->first_point);
+          waserror= True;
+        }
+      }
+    }
+  }
+  qh->vertex_visit += (unsigned int)numfacets;
+  if (facetlist == qh->facet_list) {
+    if (numfacets != qh->num_facets - qh->num_visible) {
+      qh_fprintf(qh, qh->ferr, 6140, "qhull internal error (qh_checkpolygon): actual number of facets is %d, cumulative facet count is %d - %d visible facets\n",
+              numfacets, qh->num_facets, qh->num_visible);
+      waserror= True;
+    }
+    qh->vertex_visit++;
+    if (qh->VERTEXneighbors) {
+      FORALLvertices {
+        qh_setcheck(qh, vertex->neighbors, "neighbors for v", vertex->id);
+        if (vertex->deleted)
+          continue;
+        totvneighbors += qh_setsize(qh, vertex->neighbors);
+      }
+      FORALLfacet_(facetlist)
+        totvertices += qh_setsize(qh, facet->vertices);
+      if (totvneighbors != totvertices) {
+        qh_fprintf(qh, qh->ferr, 6141, "qhull internal error (qh_checkpolygon): vertex neighbors inconsistent.  Totvneighbors %d, totvertices %d\n",
+                totvneighbors, totvertices);
+        waserror= True;
+      }
+    }
+    if (numvertices != qh->num_vertices - qh_setsize(qh, qh->del_vertices)) {
+      qh_fprintf(qh, qh->ferr, 6142, "qhull internal error (qh_checkpolygon): actual number of vertices is %d, cumulative vertex count is %d\n",
+              numvertices, qh->num_vertices - qh_setsize(qh, qh->del_vertices));
+      waserror= True;
+    }
+    if (qh->hull_dim == 2 && numvertices != numfacets) {
+      qh_fprintf(qh, qh->ferr, 6143, "qhull internal error (qh_checkpolygon): #vertices %d != #facets %d\n",
+        numvertices, numfacets);
+      waserror= True;
+    }
+    if (qh->hull_dim == 3 && numvertices + numfacets - numridges/2 != 2) {
+      qh_fprintf(qh, qh->ferr, 7063, "qhull warning: #vertices %d + #facets %d - #edges %d != 2\n\
+        A vertex appears twice in a edge list.  May occur during merging.",
+        numvertices, numfacets, numridges/2);
+      /* occurs if lots of merging and a vertex ends up twice in an edge list.  e.g., RBOX 1000 s W1e-13 t995849315 D2 | QHULL d Tc Tv */
+    }
+  }
+  if (waserror)
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+} /* checkpolygon */
+
+
+/*---------------------------------
+
+  qh_checkvertex(qh, vertex )
+    check vertex for consistency
+    checks vertex->neighbors
+
+  notes:
+    neighbors checked efficiently in checkpolygon
+*/
+void qh_checkvertex(qhT *qh, vertexT *vertex) {
+  boolT waserror= False;
+  facetT *neighbor, **neighborp, *errfacet=NULL;
+
+  if (qh_pointid(qh, vertex->point) == qh_IDunknown) {
+    qh_fprintf(qh, qh->ferr, 6144, "qhull internal error (qh_checkvertex): unknown point id %p\n", vertex->point);
+    waserror= True;
+  }
+  if (vertex->id >= qh->vertex_id) {
+    qh_fprintf(qh, qh->ferr, 6145, "qhull internal error (qh_checkvertex): unknown vertex id %d\n", vertex->id);
+    waserror= True;
+  }
+  if (!waserror && !vertex->deleted) {
+    if (qh_setsize(qh, vertex->neighbors)) {
+      FOREACHneighbor_(vertex) {
+        if (!qh_setin(neighbor->vertices, vertex)) {
+          qh_fprintf(qh, qh->ferr, 6146, "qhull internal error (qh_checkvertex): neighbor f%d does not contain v%d\n", neighbor->id, vertex->id);
+          errfacet= neighbor;
+          waserror= True;
+        }
+      }
+    }
+  }
+  if (waserror) {
+    qh_errprint(qh, "ERRONEOUS", NULL, NULL, NULL, vertex);
+    qh_errexit(qh, qh_ERRqhull, errfacet, NULL);
+  }
+} /* checkvertex */
+
+/*---------------------------------
+
+  qh_clearcenters(qh, type )
+    clear old data from facet->center
+
+  notes:
+    sets new centertype
+    nop if CENTERtype is the same
+*/
+void qh_clearcenters(qhT *qh, qh_CENTER type) {
+  facetT *facet;
+
+  if (qh->CENTERtype != type) {
+    FORALLfacets {
+      if (facet->tricoplanar && !facet->keepcentrum)
+          facet->center= NULL;  /* center is owned by the ->keepcentrum facet */
+      else if (qh->CENTERtype == qh_ASvoronoi){
+        if (facet->center) {
+          qh_memfree(qh, facet->center, qh->center_size);
+          facet->center= NULL;
+        }
+      }else /* qh->CENTERtype == qh_AScentrum */ {
+        if (facet->center) {
+          qh_memfree(qh, facet->center, qh->normal_size);
+          facet->center= NULL;
+        }
+      }
+    }
+    qh->CENTERtype= type;
+  }
+  trace2((qh, qh->ferr, 2043, "qh_clearcenters: switched to center type %d\n", type));
+} /* clearcenters */
+
+/*---------------------------------
+
+  qh_createsimplex(qh, vertices )
+    creates a simplex from a set of vertices
+
+  returns:
+    initializes qh.facet_list to the simplex
+    initializes qh.newfacet_list, .facet_tail
+    initializes qh.vertex_list, .newvertex_list, .vertex_tail
+
+  design:
+    initializes lists
+    for each vertex
+      create a new facet
+    for each new facet
+      create its neighbor set
+*/
+void qh_createsimplex(qhT *qh, setT *vertices) {
+  facetT *facet= NULL, *newfacet;
+  boolT toporient= True;
+  int vertex_i, vertex_n, nth;
+  setT *newfacets= qh_settemp(qh, qh->hull_dim+1);
+  vertexT *vertex;
+
+  qh->facet_list= qh->newfacet_list= qh->facet_tail= qh_newfacet(qh);
+  qh->num_facets= qh->num_vertices= qh->num_visible= 0;
+  qh->vertex_list= qh->newvertex_list= qh->vertex_tail= qh_newvertex(qh, NULL);
+  FOREACHvertex_i_(qh, vertices) {
+    newfacet= qh_newfacet(qh);
+    newfacet->vertices= qh_setnew_delnthsorted(qh, vertices, vertex_n,
+                                                vertex_i, 0);
+    newfacet->toporient= (unsigned char)toporient;
+    qh_appendfacet(qh, newfacet);
+    newfacet->newfacet= True;
+    qh_appendvertex(qh, vertex);
+    qh_setappend(qh, &newfacets, newfacet);
+    toporient ^= True;
+  }
+  FORALLnew_facets {
+    nth= 0;
+    FORALLfacet_(qh->newfacet_list) {
+      if (facet != newfacet)
+        SETelem_(newfacet->neighbors, nth++)= facet;
+    }
+    qh_settruncate(qh, newfacet->neighbors, qh->hull_dim);
+  }
+  qh_settempfree(qh, &newfacets);
+  trace1((qh, qh->ferr, 1028, "qh_createsimplex: created simplex\n"));
+} /* createsimplex */
+
+/*---------------------------------
+
+  qh_delridge(qh, ridge )
+    deletes ridge from data structures it belongs to
+    frees up its memory
+
+  notes:
+    in merge_r.c, caller sets vertex->delridge for each vertex
+    ridges also freed in qh_freeqhull
+*/
+void qh_delridge(qhT *qh, ridgeT *ridge) {
+  void **freelistp; /* used if !qh_NOmem by qh_memfree_() */
+
+  qh_setdel(ridge->top->ridges, ridge);
+  qh_setdel(ridge->bottom->ridges, ridge);
+  qh_setfree(qh, &(ridge->vertices));
+  qh_memfree_(qh, ridge, (int)sizeof(ridgeT), freelistp);
+} /* delridge */
+
+
+/*---------------------------------
+
+  qh_delvertex(qh, vertex )
+    deletes a vertex and frees its memory
+
+  notes:
+    assumes vertex->adjacencies have been updated if needed
+    unlinks from vertex_list
+*/
+void qh_delvertex(qhT *qh, vertexT *vertex) {
+
+  if (vertex == qh->tracevertex)
+    qh->tracevertex= NULL;
+  qh_removevertex(qh, vertex);
+  qh_setfree(qh, &vertex->neighbors);
+  qh_memfree(qh, vertex, (int)sizeof(vertexT));
+} /* delvertex */
+
+
+/*---------------------------------
+
+  qh_facet3vertex(qh, )
+    return temporary set of 3-d vertices in qh_ORIENTclock order
+
+  design:
+    if simplicial facet
+      build set from facet->vertices with facet->toporient
+    else
+      for each ridge in order
+        build set from ridge's vertices
+*/
+setT *qh_facet3vertex(qhT *qh, facetT *facet) {
+  ridgeT *ridge, *firstridge;
+  vertexT *vertex;
+  int cntvertices, cntprojected=0;
+  setT *vertices;
+
+  cntvertices= qh_setsize(qh, facet->vertices);
+  vertices= qh_settemp(qh, cntvertices);
+  if (facet->simplicial) {
+    if (cntvertices != 3) {
+      qh_fprintf(qh, qh->ferr, 6147, "qhull internal error (qh_facet3vertex): only %d vertices for simplicial facet f%d\n",
+                  cntvertices, facet->id);
+      qh_errexit(qh, qh_ERRqhull, facet, NULL);
+    }
+    qh_setappend(qh, &vertices, SETfirst_(facet->vertices));
+    if (facet->toporient ^ qh_ORIENTclock)
+      qh_setappend(qh, &vertices, SETsecond_(facet->vertices));
+    else
+      qh_setaddnth(qh, &vertices, 0, SETsecond_(facet->vertices));
+    qh_setappend(qh, &vertices, SETelem_(facet->vertices, 2));
+  }else {
+    ridge= firstridge= SETfirstt_(facet->ridges, ridgeT);   /* no infinite */
+    while ((ridge= qh_nextridge3d(ridge, facet, &vertex))) {
+      qh_setappend(qh, &vertices, vertex);
+      if (++cntprojected > cntvertices || ridge == firstridge)
+        break;
+    }
+    if (!ridge || cntprojected != cntvertices) {
+      qh_fprintf(qh, qh->ferr, 6148, "qhull internal error (qh_facet3vertex): ridges for facet %d don't match up.  got at least %d\n",
+                  facet->id, cntprojected);
+      qh_errexit(qh, qh_ERRqhull, facet, ridge);
+    }
+  }
+  return vertices;
+} /* facet3vertex */
+
+/*---------------------------------
+
+  qh_findbestfacet(qh, point, bestoutside, bestdist, isoutside )
+    find facet that is furthest below a point
+
+    for Delaunay triangulations,
+      Use qh_setdelaunay() to lift point to paraboloid and scale by 'Qbb' if needed
+      Do not use options 'Qbk', 'QBk', or 'QbB' since they scale the coordinates.
+
+  returns:
+    if bestoutside is set (e.g., qh_ALL)
+      returns best facet that is not upperdelaunay
+      if Delaunay and inside, point is outside circumsphere of bestfacet
+    else
+      returns first facet below point
+      if point is inside, returns nearest, !upperdelaunay facet
+    distance to facet
+    isoutside set if outside of facet
+
+  notes:
+    For tricoplanar facets, this finds one of the tricoplanar facets closest
+    to the point.  For Delaunay triangulations, the point may be inside a
+    different tricoplanar facet. See locate a facet with qh_findbestfacet()
+
+    If inside, qh_findbestfacet performs an exhaustive search
+       this may be too conservative.  Sometimes it is clearly required.
+
+    qh_findbestfacet is not used by qhull.
+    uses qh.visit_id and qh.coplanarset
+
+  see:
+    qh_findbest
+*/
+facetT *qh_findbestfacet(qhT *qh, pointT *point, boolT bestoutside,
+           realT *bestdist, boolT *isoutside) {
+  facetT *bestfacet= NULL;
+  int numpart, totpart= 0;
+
+  bestfacet= qh_findbest(qh, point, qh->facet_list,
+                            bestoutside, !qh_ISnewfacets, bestoutside /* qh_NOupper */,
+                            bestdist, isoutside, &totpart);
+  if (*bestdist < -qh->DISTround) {
+    bestfacet= qh_findfacet_all(qh, point, bestdist, isoutside, &numpart);
+    totpart += numpart;
+    if ((isoutside && *isoutside && bestoutside)
+    || (isoutside && !*isoutside && bestfacet->upperdelaunay)) {
+      bestfacet= qh_findbest(qh, point, bestfacet,
+                            bestoutside, False, bestoutside,
+                            bestdist, isoutside, &totpart);
+      totpart += numpart;
+    }
+  }
+  trace3((qh, qh->ferr, 3014, "qh_findbestfacet: f%d dist %2.2g isoutside %d totpart %d\n",
+          bestfacet->id, *bestdist, (isoutside ? *isoutside : UINT_MAX), totpart));
+  return bestfacet;
+} /* findbestfacet */
+
+/*---------------------------------
+
+  qh_findbestlower(qh, facet, point, bestdist, numpart )
+    returns best non-upper, non-flipped neighbor of facet for point
+    if needed, searches vertex neighbors
+
+  returns:
+    returns bestdist and updates numpart
+
+  notes:
+    if Delaunay and inside, point is outside of circumsphere of bestfacet
+    called by qh_findbest() for points above an upperdelaunay facet
+
+*/
+facetT *qh_findbestlower(qhT *qh, facetT *upperfacet, pointT *point, realT *bestdistp, int *numpart) {
+  facetT *neighbor, **neighborp, *bestfacet= NULL;
+  realT bestdist= -REALmax/2 /* avoid underflow */;
+  realT dist;
+  vertexT *vertex;
+  boolT isoutside= False;  /* not used */
+
+  zinc_(Zbestlower);
+  FOREACHneighbor_(upperfacet) {
+    if (neighbor->upperdelaunay || neighbor->flipped)
+      continue;
+    (*numpart)++;
+    qh_distplane(qh, point, neighbor, &dist);
+    if (dist > bestdist) {
+      bestfacet= neighbor;
+      bestdist= dist;
+    }
+  }
+  if (!bestfacet) {
+    zinc_(Zbestlowerv);
+    /* rarely called, numpart does not count nearvertex computations */
+    vertex= qh_nearvertex(qh, upperfacet, point, &dist);
+    qh_vertexneighbors(qh);
+    FOREACHneighbor_(vertex) {
+      if (neighbor->upperdelaunay || neighbor->flipped)
+        continue;
+      (*numpart)++;
+      qh_distplane(qh, point, neighbor, &dist);
+      if (dist > bestdist) {
+        bestfacet= neighbor;
+        bestdist= dist;
+      }
+    }
+  }
+  if (!bestfacet) {
+    zinc_(Zbestlowerall);  /* invoked once per point in outsideset */
+    zmax_(Zbestloweralln, qh->num_facets);
+    /* [dec'15] Previously reported as QH6228 */
+    trace3((qh, qh->ferr, 3025, "qh_findbestlower: all neighbors of facet %d are flipped or upper Delaunay.  Search all facets\n",
+       upperfacet->id));
+    /* rarely called */
+    bestfacet= qh_findfacet_all(qh, point, &bestdist, &isoutside, numpart);
+  }
+  *bestdistp= bestdist;
+  trace3((qh, qh->ferr, 3015, "qh_findbestlower: f%d dist %2.2g for f%d p%d\n",
+          bestfacet->id, bestdist, upperfacet->id, qh_pointid(qh, point)));
+  return bestfacet;
+} /* findbestlower */
+
+/*---------------------------------
+
+  qh_findfacet_all(qh, point, bestdist, isoutside, numpart )
+    exhaustive search for facet below a point
+
+    for Delaunay triangulations,
+      Use qh_setdelaunay() to lift point to paraboloid and scale by 'Qbb' if needed
+      Do not use options 'Qbk', 'QBk', or 'QbB' since they scale the coordinates.
+
+  returns:
+    returns first facet below point
+    if point is inside,
+      returns nearest facet
+    distance to facet
+    isoutside if point is outside of the hull
+    number of distance tests
+
+  notes:
+    primarily for library users, rarely used by Qhull
+*/
+facetT *qh_findfacet_all(qhT *qh, pointT *point, realT *bestdist, boolT *isoutside,
+                          int *numpart) {
+  facetT *bestfacet= NULL, *facet;
+  realT dist;
+  int totpart= 0;
+
+  *bestdist= -REALmax;
+  *isoutside= False;
+  FORALLfacets {
+    if (facet->flipped || !facet->normal)
+      continue;
+    totpart++;
+    qh_distplane(qh, point, facet, &dist);
+    if (dist > *bestdist) {
+      *bestdist= dist;
+      bestfacet= facet;
+      if (dist > qh->MINoutside) {
+        *isoutside= True;
+        break;
+      }
+    }
+  }
+  *numpart= totpart;
+  trace3((qh, qh->ferr, 3016, "qh_findfacet_all: f%d dist %2.2g isoutside %d totpart %d\n",
+          getid_(bestfacet), *bestdist, *isoutside, totpart));
+  return bestfacet;
+} /* findfacet_all */
+
+/*---------------------------------
+
+  qh_findgood(qh, facetlist, goodhorizon )
+    identify good facets for qh.PRINTgood
+    if qh.GOODvertex>0
+      facet includes point as vertex
+      if !match, returns goodhorizon
+      inactive if qh.MERGING
+    if qh.GOODpoint
+      facet is visible or coplanar (>0) or not visible (<0)
+    if qh.GOODthreshold
+      facet->normal matches threshold
+    if !goodhorizon and !match,
+      selects facet with closest angle
+      sets GOODclosest
+
+  returns:
+    number of new, good facets found
+    determines facet->good
+    may update qh.GOODclosest
+
+  notes:
+    qh_findgood_all further reduces the good region
+
+  design:
+    count good facets
+    mark good facets for qh.GOODpoint
+    mark good facets for qh.GOODthreshold
+    if necessary
+      update qh.GOODclosest
+*/
+int qh_findgood(qhT *qh, facetT *facetlist, int goodhorizon) {
+  facetT *facet, *bestfacet= NULL;
+  realT angle, bestangle= REALmax, dist;
+  int  numgood=0;
+
+  FORALLfacet_(facetlist) {
+    if (facet->good)
+      numgood++;
+  }
+  if (qh->GOODvertex>0 && !qh->MERGING) {
+    FORALLfacet_(facetlist) {
+      if (!qh_isvertex(qh->GOODvertexp, facet->vertices)) {
+        facet->good= False;
+        numgood--;
+      }
+    }
+  }
+  if (qh->GOODpoint && numgood) {
+    FORALLfacet_(facetlist) {
+      if (facet->good && facet->normal) {
+        zinc_(Zdistgood);
+        qh_distplane(qh, qh->GOODpointp, facet, &dist);
+        if ((qh->GOODpoint > 0) ^ (dist > 0.0)) {
+          facet->good= False;
+          numgood--;
+        }
+      }
+    }
+  }
+  if (qh->GOODthreshold && (numgood || goodhorizon || qh->GOODclosest)) {
+    FORALLfacet_(facetlist) {
+      if (facet->good && facet->normal) {
+        if (!qh_inthresholds(qh, facet->normal, &angle)) {
+          facet->good= False;
+          numgood--;
+          if (angle < bestangle) {
+            bestangle= angle;
+            bestfacet= facet;
+          }
+        }
+      }
+    }
+    if (!numgood && (!goodhorizon || qh->GOODclosest)) {
+      if (qh->GOODclosest) {
+        if (qh->GOODclosest->visible)
+          qh->GOODclosest= NULL;
+        else {
+          qh_inthresholds(qh, qh->GOODclosest->normal, &angle);
+          if (angle < bestangle)
+            bestfacet= qh->GOODclosest;
+        }
+      }
+      if (bestfacet && bestfacet != qh->GOODclosest) {
+        if (qh->GOODclosest)
+          qh->GOODclosest->good= False;
+        qh->GOODclosest= bestfacet;
+        bestfacet->good= True;
+        numgood++;
+        trace2((qh, qh->ferr, 2044, "qh_findgood: f%d is closest(%2.2g) to thresholds\n",
+           bestfacet->id, bestangle));
+        return numgood;
+      }
+    }else if (qh->GOODclosest) { /* numgood > 0 */
+      qh->GOODclosest->good= False;
+      qh->GOODclosest= NULL;
+    }
+  }
+  zadd_(Zgoodfacet, numgood);
+  trace2((qh, qh->ferr, 2045, "qh_findgood: found %d good facets with %d good horizon\n",
+               numgood, goodhorizon));
+  if (!numgood && qh->GOODvertex>0 && !qh->MERGING)
+    return goodhorizon;
+  return numgood;
+} /* findgood */
+
+/*---------------------------------
+
+  qh_findgood_all(qh, facetlist )
+    apply other constraints for good facets (used by qh.PRINTgood)
+    if qh.GOODvertex
+      facet includes (>0) or doesn't include (<0) point as vertex
+      if last good facet and ONLYgood, prints warning and continues
+    if qh.SPLITthresholds
+      facet->normal matches threshold, or if none, the closest one
+    calls qh_findgood
+    nop if good not used
+
+  returns:
+    clears facet->good if not good
+    sets qh.num_good
+
+  notes:
+    this is like qh_findgood but more restrictive
+
+  design:
+    uses qh_findgood to mark good facets
+    marks facets for qh.GOODvertex
+    marks facets for qh.SPLITthreholds
+*/
+void qh_findgood_all(qhT *qh, facetT *facetlist) {
+  facetT *facet, *bestfacet=NULL;
+  realT angle, bestangle= REALmax;
+  int  numgood=0, startgood;
+
+  if (!qh->GOODvertex && !qh->GOODthreshold && !qh->GOODpoint
+  && !qh->SPLITthresholds)
+    return;
+  if (!qh->ONLYgood)
+    qh_findgood(qh, qh->facet_list, 0);
+  FORALLfacet_(facetlist) {
+    if (facet->good)
+      numgood++;
+  }
+  if (qh->GOODvertex <0 || (qh->GOODvertex > 0 && qh->MERGING)) {
+    FORALLfacet_(facetlist) {
+      if (facet->good && ((qh->GOODvertex > 0) ^ !!qh_isvertex(qh->GOODvertexp, facet->vertices))) {
+        if (!--numgood) {
+          if (qh->ONLYgood) {
+            qh_fprintf(qh, qh->ferr, 7064, "qhull warning: good vertex p%d does not match last good facet f%d.  Ignored.\n",
+               qh_pointid(qh, qh->GOODvertexp), facet->id);
+            return;
+          }else if (qh->GOODvertex > 0)
+            qh_fprintf(qh, qh->ferr, 7065, "qhull warning: point p%d is not a vertex('QV%d').\n",
+                qh->GOODvertex-1, qh->GOODvertex-1);
+          else
+            qh_fprintf(qh, qh->ferr, 7066, "qhull warning: point p%d is a vertex for every facet('QV-%d').\n",
+                -qh->GOODvertex - 1, -qh->GOODvertex - 1);
+        }
+        facet->good= False;
+      }
+    }
+  }
+  startgood= numgood;
+  if (qh->SPLITthresholds) {
+    FORALLfacet_(facetlist) {
+      if (facet->good) {
+        if (!qh_inthresholds(qh, facet->normal, &angle)) {
+          facet->good= False;
+          numgood--;
+          if (angle < bestangle) {
+            bestangle= angle;
+            bestfacet= facet;
+          }
+        }
+      }
+    }
+    if (!numgood && bestfacet) {
+      bestfacet->good= True;
+      numgood++;
+      trace0((qh, qh->ferr, 23, "qh_findgood_all: f%d is closest(%2.2g) to thresholds\n",
+           bestfacet->id, bestangle));
+      return;
+    }
+  }
+  qh->num_good= numgood;
+  trace0((qh, qh->ferr, 24, "qh_findgood_all: %d good facets remain out of %d facets\n",
+        numgood, startgood));
+} /* findgood_all */
+
+/*---------------------------------
+
+  qh_furthestnext()
+    set qh.facet_next to facet with furthest of all furthest points
+    searches all facets on qh.facet_list
+
+  notes:
+    this may help avoid precision problems
+*/
+void qh_furthestnext(qhT *qh /* qh->facet_list */) {
+  facetT *facet, *bestfacet= NULL;
+  realT dist, bestdist= -REALmax;
+
+  FORALLfacets {
+    if (facet->outsideset) {
+#if qh_COMPUTEfurthest
+      pointT *furthest;
+      furthest= (pointT*)qh_setlast(facet->outsideset);
+      zinc_(Zcomputefurthest);
+      qh_distplane(qh, furthest, facet, &dist);
+#else
+      dist= facet->furthestdist;
+#endif
+      if (dist > bestdist) {
+        bestfacet= facet;
+        bestdist= dist;
+      }
+    }
+  }
+  if (bestfacet) {
+    qh_removefacet(qh, bestfacet);
+    qh_prependfacet(qh, bestfacet, &qh->facet_next);
+    trace1((qh, qh->ferr, 1029, "qh_furthestnext: made f%d next facet(dist %.2g)\n",
+            bestfacet->id, bestdist));
+  }
+} /* furthestnext */
+
+/*---------------------------------
+
+  qh_furthestout(qh, facet )
+    make furthest outside point the last point of outsideset
+
+  returns:
+    updates facet->outsideset
+    clears facet->notfurthest
+    sets facet->furthestdist
+
+  design:
+    determine best point of outsideset
+    make it the last point of outsideset
+*/
+void qh_furthestout(qhT *qh, facetT *facet) {
+  pointT *point, **pointp, *bestpoint= NULL;
+  realT dist, bestdist= -REALmax;
+
+  FOREACHpoint_(facet->outsideset) {
+    qh_distplane(qh, point, facet, &dist);
+    zinc_(Zcomputefurthest);
+    if (dist > bestdist) {
+      bestpoint= point;
+      bestdist= dist;
+    }
+  }
+  if (bestpoint) {
+    qh_setdel(facet->outsideset, point);
+    qh_setappend(qh, &facet->outsideset, point);
+#if !qh_COMPUTEfurthest
+    facet->furthestdist= bestdist;
+#endif
+  }
+  facet->notfurthest= False;
+  trace3((qh, qh->ferr, 3017, "qh_furthestout: p%d is furthest outside point of f%d\n",
+          qh_pointid(qh, point), facet->id));
+} /* furthestout */
+
+
+/*---------------------------------
+
+  qh_infiniteloop(qh, facet )
+    report infinite loop error due to facet
+*/
+void qh_infiniteloop(qhT *qh, facetT *facet) {
+
+  qh_fprintf(qh, qh->ferr, 6149, "qhull internal error (qh_infiniteloop): potential infinite loop detected\n");
+  qh_errexit(qh, qh_ERRqhull, facet, NULL);
+} /* qh_infiniteloop */
+
+/*---------------------------------
+
+  qh_initbuild()
+    initialize hull and outside sets with point array
+    qh.FIRSTpoint/qh.NUMpoints is point array
+    if qh.GOODpoint
+      adds qh.GOODpoint to initial hull
+
+  returns:
+    qh_facetlist with initial hull
+    points partioned into outside sets, coplanar sets, or inside
+    initializes qh.GOODpointp, qh.GOODvertexp,
+
+  design:
+    initialize global variables used during qh_buildhull
+    determine precision constants and points with max/min coordinate values
+      if qh.SCALElast, scale last coordinate(for 'd')
+    build initial simplex
+    partition input points into facets of initial simplex
+    set up lists
+    if qh.ONLYgood
+      check consistency
+      add qh.GOODvertex if defined
+*/
+void qh_initbuild(qhT *qh) {
+  setT *maxpoints, *vertices;
+  facetT *facet;
+  int i, numpart;
+  realT dist;
+  boolT isoutside;
+
+  qh->furthest_id= qh_IDunknown;
+  qh->lastreport= 0;
+  qh->facet_id= qh->vertex_id= qh->ridge_id= 0;
+  qh->visit_id= qh->vertex_visit= 0;
+  qh->maxoutdone= False;
+
+  if (qh->GOODpoint > 0)
+    qh->GOODpointp= qh_point(qh, qh->GOODpoint-1);
+  else if (qh->GOODpoint < 0)
+    qh->GOODpointp= qh_point(qh, -qh->GOODpoint-1);
+  if (qh->GOODvertex > 0)
+    qh->GOODvertexp= qh_point(qh, qh->GOODvertex-1);
+  else if (qh->GOODvertex < 0)
+    qh->GOODvertexp= qh_point(qh, -qh->GOODvertex-1);
+  if ((qh->GOODpoint
+       && (qh->GOODpointp < qh->first_point  /* also catches !GOODpointp */
+           || qh->GOODpointp > qh_point(qh, qh->num_points-1)))
+    || (qh->GOODvertex
+        && (qh->GOODvertexp < qh->first_point  /* also catches !GOODvertexp */
+            || qh->GOODvertexp > qh_point(qh, qh->num_points-1)))) {
+    qh_fprintf(qh, qh->ferr, 6150, "qhull input error: either QGn or QVn point is > p%d\n",
+             qh->num_points-1);
+    qh_errexit(qh, qh_ERRinput, NULL, NULL);
+  }
+  maxpoints= qh_maxmin(qh, qh->first_point, qh->num_points, qh->hull_dim);
+  if (qh->SCALElast)
+    qh_scalelast(qh, qh->first_point, qh->num_points, qh->hull_dim,
+               qh->MINlastcoord, qh->MAXlastcoord, qh->MAXwidth);
+  qh_detroundoff(qh);
+  if (qh->DELAUNAY && qh->upper_threshold[qh->hull_dim-1] > REALmax/2
+                  && qh->lower_threshold[qh->hull_dim-1] < -REALmax/2) {
+    for (i=qh_PRINTEND; i--; ) {
+      if (qh->PRINTout[i] == qh_PRINTgeom && qh->DROPdim < 0
+          && !qh->GOODthreshold && !qh->SPLITthresholds)
+        break;  /* in this case, don't set upper_threshold */
+    }
+    if (i < 0) {
+      if (qh->UPPERdelaunay) { /* matches qh.upperdelaunay in qh_setfacetplane */
+        qh->lower_threshold[qh->hull_dim-1]= qh->ANGLEround * qh_ZEROdelaunay;
+        qh->GOODthreshold= True;
+      }else {
+        qh->upper_threshold[qh->hull_dim-1]= -qh->ANGLEround * qh_ZEROdelaunay;
+        if (!qh->GOODthreshold)
+          qh->SPLITthresholds= True; /* build upper-convex hull even if Qg */
+          /* qh_initqhull_globals errors if Qg without Pdk/etc. */
+      }
+    }
+  }
+  vertices= qh_initialvertices(qh, qh->hull_dim, maxpoints, qh->first_point, qh->num_points);
+  qh_initialhull(qh, vertices);  /* initial qh->facet_list */
+  qh_partitionall(qh, vertices, qh->first_point, qh->num_points);
+  if (qh->PRINToptions1st || qh->TRACElevel || qh->IStracing) {
+    if (qh->TRACElevel || qh->IStracing)
+      qh_fprintf(qh, qh->ferr, 8103, "\nTrace level %d for %s | %s\n",
+         qh->IStracing ? qh->IStracing : qh->TRACElevel, qh->rbox_command, qh->qhull_command);
+    qh_fprintf(qh, qh->ferr, 8104, "Options selected for Qhull %s:\n%s\n", qh_version, qh->qhull_options);
+  }
+  qh_resetlists(qh, False, qh_RESETvisible /*qh.visible_list newvertex_list newfacet_list */);
+  qh->facet_next= qh->facet_list;
+  qh_furthestnext(qh /* qh->facet_list */);
+  if (qh->PREmerge) {
+    qh->cos_max= qh->premerge_cos;
+    qh->centrum_radius= qh->premerge_centrum;
+  }
+  if (qh->ONLYgood) {
+    if (qh->GOODvertex > 0 && qh->MERGING) {
+      qh_fprintf(qh, qh->ferr, 6151, "qhull input error: 'Qg QVn' (only good vertex) does not work with merging.\nUse 'QJ' to joggle the input or 'Q0' to turn off merging.\n");
+      qh_errexit(qh, qh_ERRinput, NULL, NULL);
+    }
+    if (!(qh->GOODthreshold || qh->GOODpoint
+         || (!qh->MERGEexact && !qh->PREmerge && qh->GOODvertexp))) {
+      qh_fprintf(qh, qh->ferr, 6152, "qhull input error: 'Qg' (ONLYgood) needs a good threshold('Pd0D0'), a\n\
+good point(QGn or QG-n), or a good vertex with 'QJ' or 'Q0' (QVn).\n");
+      qh_errexit(qh, qh_ERRinput, NULL, NULL);
+    }
+    if (qh->GOODvertex > 0  && !qh->MERGING  /* matches qh_partitionall */
+        && !qh_isvertex(qh->GOODvertexp, vertices)) {
+      facet= qh_findbestnew(qh, qh->GOODvertexp, qh->facet_list,
+                          &dist, !qh_ALL, &isoutside, &numpart);
+      zadd_(Zdistgood, numpart);
+      if (!isoutside) {
+        qh_fprintf(qh, qh->ferr, 6153, "qhull input error: point for QV%d is inside initial simplex.  It can not be made a vertex.\n",
+               qh_pointid(qh, qh->GOODvertexp));
+        qh_errexit(qh, qh_ERRinput, NULL, NULL);
+      }
+      if (!qh_addpoint(qh, qh->GOODvertexp, facet, False)) {
+        qh_settempfree(qh, &vertices);
+        qh_settempfree(qh, &maxpoints);
+        return;
+      }
+    }
+    qh_findgood(qh, qh->facet_list, 0);
+  }
+  qh_settempfree(qh, &vertices);
+  qh_settempfree(qh, &maxpoints);
+  trace1((qh, qh->ferr, 1030, "qh_initbuild: initial hull created and points partitioned\n"));
+} /* initbuild */
+
+/*---------------------------------
+
+  qh_initialhull(qh, vertices )
+    constructs the initial hull as a DIM3 simplex of vertices
+
+  design:
+    creates a simplex (initializes lists)
+    determines orientation of simplex
+    sets hyperplanes for facets
+    doubles checks orientation (in case of axis-parallel facets with Gaussian elimination)
+    checks for flipped facets and qh.NARROWhull
+    checks the result
+*/
+void qh_initialhull(qhT *qh, setT *vertices) {
+  facetT *facet, *firstfacet, *neighbor, **neighborp;
+  realT dist, angle, minangle= REALmax;
+#ifndef qh_NOtrace
+  int k;
+#endif
+
+  qh_createsimplex(qh, vertices);  /* qh->facet_list */
+  qh_resetlists(qh, False, qh_RESETvisible);
+  qh->facet_next= qh->facet_list;      /* advance facet when processed */
+  qh->interior_point= qh_getcenter(qh, vertices);
+  firstfacet= qh->facet_list;
+  qh_setfacetplane(qh, firstfacet);
+  zinc_(Znumvisibility); /* needs to be in printsummary */
+  qh_distplane(qh, qh->interior_point, firstfacet, &dist);
+  if (dist > 0) {
+    FORALLfacets
+      facet->toporient ^= (unsigned char)True;
+  }
+  FORALLfacets
+    qh_setfacetplane(qh, facet);
+  FORALLfacets {
+    if (!qh_checkflipped(qh, facet, NULL, qh_ALL)) {/* due to axis-parallel facet */
+      trace1((qh, qh->ferr, 1031, "qh_initialhull: initial orientation incorrect.  Correct all facets\n"));
+      facet->flipped= False;
+      FORALLfacets {
+        facet->toporient ^= (unsigned char)True;
+        qh_orientoutside(qh, facet);
+      }
+      break;
+    }
+  }
+  FORALLfacets {
+    if (!qh_checkflipped(qh, facet, NULL, !qh_ALL)) {  /* can happen with 'R0.1' */
+      if (qh->DELAUNAY && ! qh->ATinfinity) {
+        if (qh->UPPERdelaunay)
+          qh_fprintf(qh, qh->ferr, 6240, "Qhull precision error: Initial simplex is cocircular or cospherical.  Option 'Qs' searches all points.  Can not compute the upper Delaunay triangulation or upper Voronoi diagram of cocircular/cospherical points.\n");
+        else
+          qh_fprintf(qh, qh->ferr, 6239, "Qhull precision error: Initial simplex is cocircular or cospherical.  Use option 'Qz' for the Delaunay triangulation or Voronoi diagram of cocircular/cospherical points.  Option 'Qz' adds a point \"at infinity\".  Use option 'Qs' to search all points for the initial simplex.\n");
+        qh_errexit(qh, qh_ERRinput, NULL, NULL);
+      }
+      qh_precision(qh, "initial simplex is flat");
+      qh_fprintf(qh, qh->ferr, 6154, "Qhull precision error: Initial simplex is flat (facet %d is coplanar with the interior point)\n",
+                   facet->id);
+      qh_errexit(qh, qh_ERRsingular, NULL, NULL);  /* calls qh_printhelp_singular */
+    }
+    FOREACHneighbor_(facet) {
+      angle= qh_getangle(qh, facet->normal, neighbor->normal);
+      minimize_( minangle, angle);
+    }
+  }
+  if (minangle < qh_MAXnarrow && !qh->NOnarrow) {
+    realT diff= 1.0 + minangle;
+
+    qh->NARROWhull= True;
+    qh_option(qh, "_narrow-hull", NULL, &diff);
+    if (minangle < qh_WARNnarrow && !qh->RERUN && qh->PRINTprecision)
+      qh_printhelp_narrowhull(qh, qh->ferr, minangle);
+  }
+  zzval_(Zprocessed)= qh->hull_dim+1;
+  qh_checkpolygon(qh, qh->facet_list);
+  qh_checkconvex(qh, qh->facet_list,   qh_DATAfault);
+#ifndef qh_NOtrace
+  if (qh->IStracing >= 1) {
+    qh_fprintf(qh, qh->ferr, 8105, "qh_initialhull: simplex constructed, interior point:");
+    for (k=0; k < qh->hull_dim; k++)
+      qh_fprintf(qh, qh->ferr, 8106, " %6.4g", qh->interior_point[k]);
+    qh_fprintf(qh, qh->ferr, 8107, "\n");
+  }
+#endif
+} /* initialhull */
+
+/*---------------------------------
+
+  qh_initialvertices(qh, dim, maxpoints, points, numpoints )
+    determines a non-singular set of initial vertices
+    maxpoints may include duplicate points
+
+  returns:
+    temporary set of dim+1 vertices in descending order by vertex id
+    if qh.RANDOMoutside && !qh.ALLpoints
+      picks random points
+    if dim >= qh_INITIALmax,
+      uses min/max x and max points with non-zero determinants
+
+  notes:
+    unless qh.ALLpoints,
+      uses maxpoints as long as determinate is non-zero
+*/
+setT *qh_initialvertices(qhT *qh, int dim, setT *maxpoints, pointT *points, int numpoints) {
+  pointT *point, **pointp;
+  setT *vertices, *simplex, *tested;
+  realT randr;
+  int idx, point_i, point_n, k;
+  boolT nearzero= False;
+
+  vertices= qh_settemp(qh, dim + 1);
+  simplex= qh_settemp(qh, dim+1);
+  if (qh->ALLpoints)
+    qh_maxsimplex(qh, dim, NULL, points, numpoints, &simplex);
+  else if (qh->RANDOMoutside) {
+    while (qh_setsize(qh, simplex) != dim+1) {
+      randr= qh_RANDOMint;
+      randr= randr/(qh_RANDOMmax+1);
+      idx= (int)floor(qh->num_points * randr);
+      while (qh_setin(simplex, qh_point(qh, idx))) {
+            idx++; /* in case qh_RANDOMint always returns the same value */
+        idx= idx < qh->num_points ? idx : 0;
+      }
+      qh_setappend(qh, &simplex, qh_point(qh, idx));
+    }
+  }else if (qh->hull_dim >= qh_INITIALmax) {
+    tested= qh_settemp(qh, dim+1);
+    qh_setappend(qh, &simplex, SETfirst_(maxpoints));   /* max and min X coord */
+    qh_setappend(qh, &simplex, SETsecond_(maxpoints));
+    qh_maxsimplex(qh, fmin_(qh_INITIALsearch, dim), maxpoints, points, numpoints, &simplex);
+    k= qh_setsize(qh, simplex);
+    FOREACHpoint_i_(qh, maxpoints) {
+      if (point_i & 0x1) {     /* first pick up max. coord. points */
+        if (!qh_setin(simplex, point) && !qh_setin(tested, point)){
+          qh_detsimplex(qh, point, simplex, k, &nearzero);
+          if (nearzero)
+            qh_setappend(qh, &tested, point);
+          else {
+            qh_setappend(qh, &simplex, point);
+            if (++k == dim)  /* use search for last point */
+              break;
+          }
+        }
+      }
+    }
+    while (k != dim && (point= (pointT*)qh_setdellast(maxpoints))) {
+      if (!qh_setin(simplex, point) && !qh_setin(tested, point)){
+        qh_detsimplex(qh, point, simplex, k, &nearzero);
+        if (nearzero)
+          qh_setappend(qh, &tested, point);
+        else {
+          qh_setappend(qh, &simplex, point);
+          k++;
+        }
+      }
+    }
+    idx= 0;
+    while (k != dim && (point= qh_point(qh, idx++))) {
+      if (!qh_setin(simplex, point) && !qh_setin(tested, point)){
+        qh_detsimplex(qh, point, simplex, k, &nearzero);
+        if (!nearzero){
+          qh_setappend(qh, &simplex, point);
+          k++;
+        }
+      }
+    }
+    qh_settempfree(qh, &tested);
+    qh_maxsimplex(qh, dim, maxpoints, points, numpoints, &simplex);
+  }else
+    qh_maxsimplex(qh, dim, maxpoints, points, numpoints, &simplex);
+  FOREACHpoint_(simplex)
+    qh_setaddnth(qh, &vertices, 0, qh_newvertex(qh, point)); /* descending order */
+  qh_settempfree(qh, &simplex);
+  return vertices;
+} /* initialvertices */
+
+
+/*---------------------------------
+
+  qh_isvertex( point, vertices )
+    returns vertex if point is in vertex set, else returns NULL
+
+  notes:
+    for qh.GOODvertex
+*/
+vertexT *qh_isvertex(pointT *point, setT *vertices) {
+  vertexT *vertex, **vertexp;
+
+  FOREACHvertex_(vertices) {
+    if (vertex->point == point)
+      return vertex;
+  }
+  return NULL;
+} /* isvertex */
+
+/*---------------------------------
+
+  qh_makenewfacets(qh, point )
+    make new facets from point and qh.visible_list
+
+  returns:
+    qh.newfacet_list= list of new facets with hyperplanes and ->newfacet
+    qh.newvertex_list= list of vertices in new facets with ->newlist set
+
+    if (qh.ONLYgood)
+      newfacets reference horizon facets, but not vice versa
+      ridges reference non-simplicial horizon ridges, but not vice versa
+      does not change existing facets
+    else
+      sets qh.NEWfacets
+      new facets attached to horizon facets and ridges
+      for visible facets,
+        visible->r.replace is corresponding new facet
+
+  see also:
+    qh_makenewplanes() -- make hyperplanes for facets
+    qh_attachnewfacets() -- attachnewfacets if not done here(qh->ONLYgood)
+    qh_matchnewfacets() -- match up neighbors
+    qh_updatevertices() -- update vertex neighbors and delvertices
+    qh_deletevisible() -- delete visible facets
+    qh_checkpolygon() --check the result
+    qh_triangulate() -- triangulate a non-simplicial facet
+
+  design:
+    for each visible facet
+      make new facets to its horizon facets
+      update its f.replace
+      clear its neighbor set
+*/
+vertexT *qh_makenewfacets(qhT *qh, pointT *point /*visible_list*/) {
+  facetT *visible, *newfacet= NULL, *newfacet2= NULL, *neighbor, **neighborp;
+  vertexT *apex;
+  int numnew=0;
+
+  qh->newfacet_list= qh->facet_tail;
+  qh->newvertex_list= qh->vertex_tail;
+  apex= qh_newvertex(qh, point);
+  qh_appendvertex(qh, apex);
+  qh->visit_id++;
+  if (!qh->ONLYgood)
+    qh->NEWfacets= True;
+  FORALLvisible_facets {
+    FOREACHneighbor_(visible)
+      neighbor->seen= False;
+    if (visible->ridges) {
+      visible->visitid= qh->visit_id;
+      newfacet2= qh_makenew_nonsimplicial(qh, visible, apex, &numnew);
+    }
+    if (visible->simplicial)
+      newfacet= qh_makenew_simplicial(qh, visible, apex, &numnew);
+    if (!qh->ONLYgood) {
+      if (newfacet2)  /* newfacet is null if all ridges defined */
+        newfacet= newfacet2;
+      if (newfacet)
+        visible->f.replace= newfacet;
+      else
+        zinc_(Zinsidevisible);
+      SETfirst_(visible->neighbors)= NULL;
+    }
+  }
+  trace1((qh, qh->ferr, 1032, "qh_makenewfacets: created %d new facets from point p%d to horizon\n",
+          numnew, qh_pointid(qh, point)));
+  if (qh->IStracing >= 4)
+    qh_printfacetlist(qh, qh->newfacet_list, NULL, qh_ALL);
+  return apex;
+} /* makenewfacets */
+
+/*---------------------------------
+
+  qh_matchduplicates(qh, atfacet, atskip, hashsize, hashcount )
+    match duplicate ridges in qh.hash_table for atfacet/atskip
+    duplicates marked with ->dupridge and qh_DUPLICATEridge
+
+  returns:
+    picks match with worst merge (min distance apart)
+    updates hashcount
+
+  see also:
+    qh_matchneighbor
+
+  notes:
+
+  design:
+    compute hash value for atfacet and atskip
+    repeat twice -- once to make best matches, once to match the rest
+      for each possible facet in qh.hash_table
+        if it is a matching facet and pass 2
+          make match
+          unless tricoplanar, mark match for merging (qh_MERGEridge)
+          [e.g., tricoplanar RBOX s 1000 t993602376 | QHULL C-1e-3 d Qbb FA Qt]
+        if it is a matching facet and pass 1
+          test if this is a better match
+      if pass 1,
+        make best match (it will not be merged)
+*/
+#ifndef qh_NOmerge
+void qh_matchduplicates(qhT *qh, facetT *atfacet, int atskip, int hashsize, int *hashcount) {
+  boolT same, ismatch;
+  int hash, scan;
+  facetT *facet, *newfacet, *maxmatch= NULL, *maxmatch2= NULL, *nextfacet;
+  int skip, newskip, nextskip= 0, maxskip= 0, maxskip2= 0, makematch;
+  realT maxdist= -REALmax, mindist, dist2, low, high;
+
+  hash= qh_gethash(qh, hashsize, atfacet->vertices, qh->hull_dim, 1,
+                     SETelem_(atfacet->vertices, atskip));
+  trace2((qh, qh->ferr, 2046, "qh_matchduplicates: find duplicate matches for f%d skip %d hash %d hashcount %d\n",
+          atfacet->id, atskip, hash, *hashcount));
+  for (makematch= 0; makematch < 2; makematch++) {
+    qh->visit_id++;
+    for (newfacet= atfacet, newskip= atskip; newfacet; newfacet= nextfacet, newskip= nextskip) {
+      zinc_(Zhashlookup);
+      nextfacet= NULL;
+      newfacet->visitid= qh->visit_id;
+      for (scan= hash; (facet= SETelemt_(qh->hash_table, scan, facetT));
+           scan= (++scan >= hashsize ? 0 : scan)) {
+        if (!facet->dupridge || facet->visitid == qh->visit_id)
+          continue;
+        zinc_(Zhashtests);
+        if (qh_matchvertices(qh, 1, newfacet->vertices, newskip, facet->vertices, &skip, &same)) {
+          ismatch= (same == (boolT)(newfacet->toporient ^ facet->toporient));
+          if (SETelemt_(facet->neighbors, skip, facetT) != qh_DUPLICATEridge) {
+            if (!makematch) {
+              qh_fprintf(qh, qh->ferr, 6155, "qhull internal error (qh_matchduplicates): missing dupridge at f%d skip %d for new f%d skip %d hash %d\n",
+                     facet->id, skip, newfacet->id, newskip, hash);
+              qh_errexit2(qh, qh_ERRqhull, facet, newfacet);
+            }
+          }else if (ismatch && makematch) {
+            if (SETelemt_(newfacet->neighbors, newskip, facetT) == qh_DUPLICATEridge) {
+              SETelem_(facet->neighbors, skip)= newfacet;
+              if (newfacet->tricoplanar)
+                SETelem_(newfacet->neighbors, newskip)= facet;
+              else
+                SETelem_(newfacet->neighbors, newskip)= qh_MERGEridge;
+              *hashcount -= 2; /* removed two unmatched facets */
+              trace4((qh, qh->ferr, 4059, "qh_matchduplicates: duplicate f%d skip %d matched with new f%d skip %d merge\n",
+                    facet->id, skip, newfacet->id, newskip));
+            }
+          }else if (ismatch) {
+            mindist= qh_getdistance(qh, facet, newfacet, &low, &high);
+            dist2= qh_getdistance(qh, newfacet, facet, &low, &high);
+            minimize_(mindist, dist2);
+            if (mindist > maxdist) {
+              maxdist= mindist;
+              maxmatch= facet;
+              maxskip= skip;
+              maxmatch2= newfacet;
+              maxskip2= newskip;
+            }
+            trace3((qh, qh->ferr, 3018, "qh_matchduplicates: duplicate f%d skip %d new f%d skip %d at dist %2.2g, max is now f%d f%d\n",
+                    facet->id, skip, newfacet->id, newskip, mindist,
+                    maxmatch->id, maxmatch2->id));
+          }else { /* !ismatch */
+            nextfacet= facet;
+            nextskip= skip;
+          }
+        }
+        if (makematch && !facet
+        && SETelemt_(facet->neighbors, skip, facetT) == qh_DUPLICATEridge) {
+          qh_fprintf(qh, qh->ferr, 6156, "qhull internal error (qh_matchduplicates): no MERGEridge match for duplicate f%d skip %d at hash %d\n",
+                     newfacet->id, newskip, hash);
+          qh_errexit(qh, qh_ERRqhull, newfacet, NULL);
+        }
+      }
+    } /* end of for each new facet at hash */
+    if (!makematch) {
+      if (!maxmatch) {
+        qh_fprintf(qh, qh->ferr, 6157, "qhull internal error (qh_matchduplicates): no maximum match at duplicate f%d skip %d at hash %d\n",
+                     atfacet->id, atskip, hash);
+        qh_errexit(qh, qh_ERRqhull, atfacet, NULL);
+      }
+      SETelem_(maxmatch->neighbors, maxskip)= maxmatch2; /* maxmatch!=0 by QH6157 */
+      SETelem_(maxmatch2->neighbors, maxskip2)= maxmatch;
+      *hashcount -= 2; /* removed two unmatched facets */
+      zzinc_(Zmultiridge);
+      trace0((qh, qh->ferr, 25, "qh_matchduplicates: duplicate f%d skip %d matched with new f%d skip %d keep\n",
+              maxmatch->id, maxskip, maxmatch2->id, maxskip2));
+      qh_precision(qh, "ridge with multiple neighbors");
+      if (qh->IStracing >= 4)
+        qh_errprint(qh, "DUPLICATED/MATCH", maxmatch, maxmatch2, NULL, NULL);
+    }
+  }
+} /* matchduplicates */
+
+/*---------------------------------
+
+  qh_nearcoplanar()
+    for all facets, remove near-inside points from facet->coplanarset
+    coplanar points defined by innerplane from qh_outerinner()
+
+  returns:
+    if qh->KEEPcoplanar && !qh->KEEPinside
+      facet->coplanarset only contains coplanar points
+    if qh.JOGGLEmax
+      drops inner plane by another qh.JOGGLEmax diagonal since a
+        vertex could shift out while a coplanar point shifts in
+
+  notes:
+    used for qh.PREmerge and qh.JOGGLEmax
+    must agree with computation of qh.NEARcoplanar in qh_detroundoff(qh)
+  design:
+    if not keeping coplanar or inside points
+      free all coplanar sets
+    else if not keeping both coplanar and inside points
+      remove !coplanar or !inside points from coplanar sets
+*/
+void qh_nearcoplanar(qhT *qh /* qh.facet_list */) {
+  facetT *facet;
+  pointT *point, **pointp;
+  int numpart;
+  realT dist, innerplane;
+
+  if (!qh->KEEPcoplanar && !qh->KEEPinside) {
+    FORALLfacets {
+      if (facet->coplanarset)
+        qh_setfree(qh, &facet->coplanarset);
+    }
+  }else if (!qh->KEEPcoplanar || !qh->KEEPinside) {
+    qh_outerinner(qh, NULL, NULL, &innerplane);
+    if (qh->JOGGLEmax < REALmax/2)
+      innerplane -= qh->JOGGLEmax * sqrt((realT)qh->hull_dim);
+    numpart= 0;
+    FORALLfacets {
+      if (facet->coplanarset) {
+        FOREACHpoint_(facet->coplanarset) {
+          numpart++;
+          qh_distplane(qh, point, facet, &dist);
+          if (dist < innerplane) {
+            if (!qh->KEEPinside)
+              SETref_(point)= NULL;
+          }else if (!qh->KEEPcoplanar)
+            SETref_(point)= NULL;
+        }
+        qh_setcompact(qh, facet->coplanarset);
+      }
+    }
+    zzadd_(Zcheckpart, numpart);
+  }
+} /* nearcoplanar */
+
+/*---------------------------------
+
+  qh_nearvertex(qh, facet, point, bestdist )
+    return nearest vertex in facet to point
+
+  returns:
+    vertex and its distance
+
+  notes:
+    if qh.DELAUNAY
+      distance is measured in the input set
+    searches neighboring tricoplanar facets (requires vertexneighbors)
+      Slow implementation.  Recomputes vertex set for each point.
+    The vertex set could be stored in the qh.keepcentrum facet.
+*/
+vertexT *qh_nearvertex(qhT *qh, facetT *facet, pointT *point, realT *bestdistp) {
+  realT bestdist= REALmax, dist;
+  vertexT *bestvertex= NULL, *vertex, **vertexp, *apex;
+  coordT *center;
+  facetT *neighbor, **neighborp;
+  setT *vertices;
+  int dim= qh->hull_dim;
+
+  if (qh->DELAUNAY)
+    dim--;
+  if (facet->tricoplanar) {
+    if (!qh->VERTEXneighbors || !facet->center) {
+      qh_fprintf(qh, qh->ferr, 6158, "qhull internal error (qh_nearvertex): qh.VERTEXneighbors and facet->center required for tricoplanar facets\n");
+      qh_errexit(qh, qh_ERRqhull, facet, NULL);
+    }
+    vertices= qh_settemp(qh, qh->TEMPsize);
+    apex= SETfirstt_(facet->vertices, vertexT);
+    center= facet->center;
+    FOREACHneighbor_(apex) {
+      if (neighbor->center == center) {
+        FOREACHvertex_(neighbor->vertices)
+          qh_setappend(qh, &vertices, vertex);
+      }
+    }
+  }else
+    vertices= facet->vertices;
+  FOREACHvertex_(vertices) {
+    dist= qh_pointdist(vertex->point, point, -dim);
+    if (dist < bestdist) {
+      bestdist= dist;
+      bestvertex= vertex;
+    }
+  }
+  if (facet->tricoplanar)
+    qh_settempfree(qh, &vertices);
+  *bestdistp= sqrt(bestdist);
+  if (!bestvertex) {
+      qh_fprintf(qh, qh->ferr, 6261, "qhull internal error (qh_nearvertex): did not find bestvertex for f%d p%d\n", facet->id, qh_pointid(qh, point));
+      qh_errexit(qh, qh_ERRqhull, facet, NULL);
+  }
+  trace3((qh, qh->ferr, 3019, "qh_nearvertex: v%d dist %2.2g for f%d p%d\n",
+        bestvertex->id, *bestdistp, facet->id, qh_pointid(qh, point))); /* bestvertex!=0 by QH2161 */
+  return bestvertex;
+} /* nearvertex */
+
+/*---------------------------------
+
+  qh_newhashtable(qh, newsize )
+    returns size of qh.hash_table of at least newsize slots
+
+  notes:
+    assumes qh.hash_table is NULL
+    qh_HASHfactor determines the number of extra slots
+    size is not divisible by 2, 3, or 5
+*/
+int qh_newhashtable(qhT *qh, int newsize) {
+  int size;
+
+  size= ((newsize+1)*qh_HASHfactor) | 0x1;  /* odd number */
+  while (True) {
+    if (newsize<0 || size<0) {
+        qh_fprintf(qh, qh->qhmem.ferr, 6236, "qhull error (qh_newhashtable): negative request (%d) or size (%d).  Did int overflow due to high-D?\n", newsize, size); /* WARN64 */
+        qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
+    }
+    if ((size%3) && (size%5))
+      break;
+    size += 2;
+    /* loop terminates because there is an infinite number of primes */
+  }
+  qh->hash_table= qh_setnew(qh, size);
+  qh_setzero(qh, qh->hash_table, 0, size);
+  return size;
+} /* newhashtable */
+
+/*---------------------------------
+
+  qh_newvertex(qh, point )
+    returns a new vertex for point
+*/
+vertexT *qh_newvertex(qhT *qh, pointT *point) {
+  vertexT *vertex;
+
+  zinc_(Ztotvertices);
+  vertex= (vertexT *)qh_memalloc(qh, (int)sizeof(vertexT));
+  memset((char *) vertex, (size_t)0, sizeof(vertexT));
+  if (qh->vertex_id == UINT_MAX) {
+    qh_memfree(qh, vertex, (int)sizeof(vertexT));
+    qh_fprintf(qh, qh->ferr, 6159, "qhull error: more than 2^32 vertices.  vertexT.id field overflows.  Vertices would not be sorted correctly.\n");
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }
+  if (qh->vertex_id == qh->tracevertex_id)
+    qh->tracevertex= vertex;
+  vertex->id= qh->vertex_id++;
+  vertex->point= point;
+  trace4((qh, qh->ferr, 4060, "qh_newvertex: vertex p%d(v%d) created\n", qh_pointid(qh, vertex->point),
+          vertex->id));
+  return(vertex);
+} /* newvertex */
+
+/*---------------------------------
+
+  qh_nextridge3d( atridge, facet, vertex )
+    return next ridge and vertex for a 3d facet
+    returns NULL on error
+    [for QhullFacet::nextRidge3d] Does not call qh_errexit nor access qhT.
+
+  notes:
+    in qh_ORIENTclock order
+    this is a O(n^2) implementation to trace all ridges
+    be sure to stop on any 2nd visit
+    same as QhullRidge::nextRidge3d
+    does not use qhT or qh_errexit [QhullFacet.cpp]
+
+  design:
+    for each ridge
+      exit if it is the ridge after atridge
+*/
+ridgeT *qh_nextridge3d(ridgeT *atridge, facetT *facet, vertexT **vertexp) {
+  vertexT *atvertex, *vertex, *othervertex;
+  ridgeT *ridge, **ridgep;
+
+  if ((atridge->top == facet) ^ qh_ORIENTclock)
+    atvertex= SETsecondt_(atridge->vertices, vertexT);
+  else
+    atvertex= SETfirstt_(atridge->vertices, vertexT);
+  FOREACHridge_(facet->ridges) {
+    if (ridge == atridge)
+      continue;
+    if ((ridge->top == facet) ^ qh_ORIENTclock) {
+      othervertex= SETsecondt_(ridge->vertices, vertexT);
+      vertex= SETfirstt_(ridge->vertices, vertexT);
+    }else {
+      vertex= SETsecondt_(ridge->vertices, vertexT);
+      othervertex= SETfirstt_(ridge->vertices, vertexT);
+    }
+    if (vertex == atvertex) {
+      if (vertexp)
+        *vertexp= othervertex;
+      return ridge;
+    }
+  }
+  return NULL;
+} /* nextridge3d */
+#else /* qh_NOmerge */
+void qh_matchduplicates(qhT *qh, facetT *atfacet, int atskip, int hashsize, int *hashcount) {
+}
+ridgeT *qh_nextridge3d(ridgeT *atridge, facetT *facet, vertexT **vertexp) {
+
+  return NULL;
+}
+#endif /* qh_NOmerge */
+
+/*---------------------------------
+
+  qh_outcoplanar()
+    move points from all facets' outsidesets to their coplanarsets
+
+  notes:
+    for post-processing under qh.NARROWhull
+
+  design:
+    for each facet
+      for each outside point for facet
+        partition point into coplanar set
+*/
+void qh_outcoplanar(qhT *qh /* facet_list */) {
+  pointT *point, **pointp;
+  facetT *facet;
+  realT dist;
+
+  trace1((qh, qh->ferr, 1033, "qh_outcoplanar: move outsideset to coplanarset for qh->NARROWhull\n"));
+  FORALLfacets {
+    FOREACHpoint_(facet->outsideset) {
+      qh->num_outside--;
+      if (qh->KEEPcoplanar || qh->KEEPnearinside) {
+        qh_distplane(qh, point, facet, &dist);
+        zinc_(Zpartition);
+        qh_partitioncoplanar(qh, point, facet, &dist);
+      }
+    }
+    qh_setfree(qh, &facet->outsideset);
+  }
+} /* outcoplanar */
+
+/*---------------------------------
+
+  qh_point(qh, id )
+    return point for a point id, or NULL if unknown
+
+  alternative code:
+    return((pointT *)((unsigned   long)qh.first_point
+           + (unsigned long)((id)*qh.normal_size)));
+*/
+pointT *qh_point(qhT *qh, int id) {
+
+  if (id < 0)
+    return NULL;
+  if (id < qh->num_points)
+    return qh->first_point + id * qh->hull_dim;
+  id -= qh->num_points;
+  if (id < qh_setsize(qh, qh->other_points))
+    return SETelemt_(qh->other_points, id, pointT);
+  return NULL;
+} /* point */
+
+/*---------------------------------
+
+  qh_point_add(qh, set, point, elem )
+    stores elem at set[point.id]
+
+  returns:
+    access function for qh_pointfacet and qh_pointvertex
+
+  notes:
+    checks point.id
+*/
+void qh_point_add(qhT *qh, setT *set, pointT *point, void *elem) {
+  int id, size;
+
+  SETreturnsize_(set, size);
+  if ((id= qh_pointid(qh, point)) < 0)
+    qh_fprintf(qh, qh->ferr, 7067, "qhull internal warning (point_add): unknown point %p id %d\n",
+      point, id);
+  else if (id >= size) {
+    qh_fprintf(qh, qh->ferr, 6160, "qhull internal errror(point_add): point p%d is out of bounds(%d)\n",
+             id, size);
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }else
+    SETelem_(set, id)= elem;
+} /* point_add */
+
+
+/*---------------------------------
+
+  qh_pointfacet()
+    return temporary set of facet for each point
+    the set is indexed by point id
+
+  notes:
+    vertices assigned to one of the facets
+    coplanarset assigned to the facet
+    outside set assigned to the facet
+    NULL if no facet for point (inside)
+      includes qh.GOODpointp
+
+  access:
+    FOREACHfacet_i_(qh, facets) { ... }
+    SETelem_(facets, i)
+
+  design:
+    for each facet
+      add each vertex
+      add each coplanar point
+      add each outside point
+*/
+setT *qh_pointfacet(qhT *qh /*qh.facet_list*/) {
+  int numpoints= qh->num_points + qh_setsize(qh, qh->other_points);
+  setT *facets;
+  facetT *facet;
+  vertexT *vertex, **vertexp;
+  pointT *point, **pointp;
+
+  facets= qh_settemp(qh, numpoints);
+  qh_setzero(qh, facets, 0, numpoints);
+  qh->vertex_visit++;
+  FORALLfacets {
+    FOREACHvertex_(facet->vertices) {
+      if (vertex->visitid != qh->vertex_visit) {
+        vertex->visitid= qh->vertex_visit;
+        qh_point_add(qh, facets, vertex->point, facet);
+      }
+    }
+    FOREACHpoint_(facet->coplanarset)
+      qh_point_add(qh, facets, point, facet);
+    FOREACHpoint_(facet->outsideset)
+      qh_point_add(qh, facets, point, facet);
+  }
+  return facets;
+} /* pointfacet */
+
+/*---------------------------------
+
+  qh_pointvertex(qh, )
+    return temporary set of vertices indexed by point id
+    entry is NULL if no vertex for a point
+      this will include qh.GOODpointp
+
+  access:
+    FOREACHvertex_i_(qh, vertices) { ... }
+    SETelem_(vertices, i)
+*/
+setT *qh_pointvertex(qhT *qh /*qh.facet_list*/) {
+  int numpoints= qh->num_points + qh_setsize(qh, qh->other_points);
+  setT *vertices;
+  vertexT *vertex;
+
+  vertices= qh_settemp(qh, numpoints);
+  qh_setzero(qh, vertices, 0, numpoints);
+  FORALLvertices
+    qh_point_add(qh, vertices, vertex->point, vertex);
+  return vertices;
+} /* pointvertex */
+
+
+/*---------------------------------
+
+  qh_prependfacet(qh, facet, facetlist )
+    prepend facet to the start of a facetlist
+
+  returns:
+    increments qh.numfacets
+    updates facetlist, qh.facet_list, facet_next
+
+  notes:
+    be careful of prepending since it can lose a pointer.
+      e.g., can lose _next by deleting and then prepending before _next
+*/
+void qh_prependfacet(qhT *qh, facetT *facet, facetT **facetlist) {
+  facetT *prevfacet, *list;
+
+
+  trace4((qh, qh->ferr, 4061, "qh_prependfacet: prepend f%d before f%d\n",
+          facet->id, getid_(*facetlist)));
+  if (!*facetlist)
+    (*facetlist)= qh->facet_tail;
+  list= *facetlist;
+  prevfacet= list->previous;
+  facet->previous= prevfacet;
+  if (prevfacet)
+    prevfacet->next= facet;
+  list->previous= facet;
+  facet->next= *facetlist;
+  if (qh->facet_list == list)  /* this may change *facetlist */
+    qh->facet_list= facet;
+  if (qh->facet_next == list)
+    qh->facet_next= facet;
+  *facetlist= facet;
+  qh->num_facets++;
+} /* prependfacet */
+
+
+/*---------------------------------
+
+  qh_printhashtable(qh, fp )
+    print hash table to fp
+
+  notes:
+    not in I/O to avoid bringing io_r.c in
+
+  design:
+    for each hash entry
+      if defined
+        if unmatched or will merge (NULL, qh_MERGEridge, qh_DUPLICATEridge)
+          print entry and neighbors
+*/
+void qh_printhashtable(qhT *qh, FILE *fp) {
+  facetT *facet, *neighbor;
+  int id, facet_i, facet_n, neighbor_i= 0, neighbor_n= 0;
+  vertexT *vertex, **vertexp;
+
+  FOREACHfacet_i_(qh, qh->hash_table) {
+    if (facet) {
+      FOREACHneighbor_i_(qh, facet) {
+        if (!neighbor || neighbor == qh_MERGEridge || neighbor == qh_DUPLICATEridge)
+          break;
+      }
+      if (neighbor_i == neighbor_n)
+        continue;
+      qh_fprintf(qh, fp, 9283, "hash %d f%d ", facet_i, facet->id);
+      FOREACHvertex_(facet->vertices)
+        qh_fprintf(qh, fp, 9284, "v%d ", vertex->id);
+      qh_fprintf(qh, fp, 9285, "\n neighbors:");
+      FOREACHneighbor_i_(qh, facet) {
+        if (neighbor == qh_MERGEridge)
+          id= -3;
+        else if (neighbor == qh_DUPLICATEridge)
+          id= -2;
+        else
+          id= getid_(neighbor);
+        qh_fprintf(qh, fp, 9286, " %d", id);
+      }
+      qh_fprintf(qh, fp, 9287, "\n");
+    }
+  }
+} /* printhashtable */
+
+
+/*---------------------------------
+
+  qh_printlists(qh, fp )
+    print out facet and vertex list for debugging (without 'f/v' tags)
+*/
+void qh_printlists(qhT *qh) {
+  facetT *facet;
+  vertexT *vertex;
+  int count= 0;
+
+  qh_fprintf(qh, qh->ferr, 8108, "qh_printlists: facets:");
+  FORALLfacets {
+    if (++count % 100 == 0)
+      qh_fprintf(qh, qh->ferr, 8109, "\n     ");
+    qh_fprintf(qh, qh->ferr, 8110, " %d", facet->id);
+  }
+  qh_fprintf(qh, qh->ferr, 8111, "\n  new facets %d visible facets %d next facet for qh_addpoint %d\n  vertices(new %d):",
+     getid_(qh->newfacet_list), getid_(qh->visible_list), getid_(qh->facet_next),
+     getid_(qh->newvertex_list));
+  count = 0;
+  FORALLvertices {
+    if (++count % 100 == 0)
+      qh_fprintf(qh, qh->ferr, 8112, "\n     ");
+    qh_fprintf(qh, qh->ferr, 8113, " %d", vertex->id);
+  }
+  qh_fprintf(qh, qh->ferr, 8114, "\n");
+} /* printlists */
+
+/*---------------------------------
+
+  qh_resetlists(qh, stats, qh_RESETvisible )
+    reset newvertex_list, newfacet_list, visible_list
+    if stats,
+      maintains statistics
+
+  returns:
+    visible_list is empty if qh_deletevisible was called
+*/
+void qh_resetlists(qhT *qh, boolT stats, boolT resetVisible /*qh.newvertex_list newfacet_list visible_list*/) {
+  vertexT *vertex;
+  facetT *newfacet, *visible;
+  int totnew=0, totver=0;
+
+  if (stats) {
+    FORALLvertex_(qh->newvertex_list)
+      totver++;
+    FORALLnew_facets
+      totnew++;
+    zadd_(Zvisvertextot, totver);
+    zmax_(Zvisvertexmax, totver);
+    zadd_(Znewfacettot, totnew);
+    zmax_(Znewfacetmax, totnew);
+  }
+  FORALLvertex_(qh->newvertex_list)
+    vertex->newlist= False;
+  qh->newvertex_list= NULL;
+  FORALLnew_facets
+    newfacet->newfacet= False;
+  qh->newfacet_list= NULL;
+  if (resetVisible) {
+    FORALLvisible_facets {
+      visible->f.replace= NULL;
+      visible->visible= False;
+    }
+    qh->num_visible= 0;
+  }
+  qh->visible_list= NULL; /* may still have visible facets via qh_triangulate */
+  qh->NEWfacets= False;
+} /* resetlists */
+
+/*---------------------------------
+
+  qh_setvoronoi_all(qh)
+    compute Voronoi centers for all facets
+    includes upperDelaunay facets if qh.UPPERdelaunay ('Qu')
+
+  returns:
+    facet->center is the Voronoi center
+
+  notes:
+    this is unused/untested code
+      please email bradb@shore.net if this works ok for you
+
+  use:
+    FORALLvertices {...} to locate the vertex for a point.
+    FOREACHneighbor_(vertex) {...} to visit the Voronoi centers for a Voronoi cell.
+*/
+void qh_setvoronoi_all(qhT *qh) {
+  facetT *facet;
+
+  qh_clearcenters(qh, qh_ASvoronoi);
+  qh_vertexneighbors(qh);
+
+  FORALLfacets {
+    if (!facet->normal || !facet->upperdelaunay || qh->UPPERdelaunay) {
+      if (!facet->center)
+        facet->center= qh_facetcenter(qh, facet->vertices);
+    }
+  }
+} /* setvoronoi_all */
+
+#ifndef qh_NOmerge
+
+/*---------------------------------
+
+  qh_triangulate()
+    triangulate non-simplicial facets on qh.facet_list,
+    if qh->VORONOI, sets Voronoi centers of non-simplicial facets
+    nop if hasTriangulation
+
+  returns:
+    all facets simplicial
+    each tricoplanar facet has ->f.triowner == owner of ->center,normal,etc.
+
+  notes:
+    call after qh_check_output since may switch to Voronoi centers
+    Output may overwrite ->f.triowner with ->f.area
+*/
+void qh_triangulate(qhT *qh /*qh.facet_list*/) {
+  facetT *facet, *nextfacet, *owner;
+  int onlygood= qh->ONLYgood;
+  facetT *neighbor, *visible= NULL, *facet1, *facet2, *new_facet_list= NULL;
+  facetT *orig_neighbor= NULL, *otherfacet;
+  vertexT *new_vertex_list= NULL;
+  mergeT *merge;
+  mergeType mergetype;
+  int neighbor_i, neighbor_n;
+
+  if (qh->hasTriangulation)
+      return;
+  trace1((qh, qh->ferr, 1034, "qh_triangulate: triangulate non-simplicial facets\n"));
+  if (qh->hull_dim == 2)
+    return;
+  if (qh->VORONOI) {  /* otherwise lose Voronoi centers [could rebuild vertex set from tricoplanar] */
+    qh_clearcenters(qh, qh_ASvoronoi);
+    qh_vertexneighbors(qh);
+  }
+  qh->ONLYgood= False; /* for makenew_nonsimplicial */
+  qh->visit_id++;
+  qh->NEWfacets= True;
+  qh->degen_mergeset= qh_settemp(qh, qh->TEMPsize);
+  qh->newvertex_list= qh->vertex_tail;
+  for (facet= qh->facet_list; facet && facet->next; facet= nextfacet) { /* non-simplicial facets moved to end */
+    nextfacet= facet->next;
+    if (facet->visible || facet->simplicial)
+      continue;
+    /* triangulate all non-simplicial facets, otherwise merging does not work, e.g., RBOX c P-0.1 P+0.1 P+0.1 D3 | QHULL d Qt Tv */
+    if (!new_facet_list)
+      new_facet_list= facet;  /* will be moved to end */
+    qh_triangulate_facet(qh, facet, &new_vertex_list);
+  }
+  trace2((qh, qh->ferr, 2047, "qh_triangulate: delete null facets from f%d -- apex same as second vertex\n", getid_(new_facet_list)));
+  for (facet= new_facet_list; facet && facet->next; facet= nextfacet) { /* null facets moved to end */
+    nextfacet= facet->next;
+    if (facet->visible)
+      continue;
+    if (facet->ridges) {
+      if (qh_setsize(qh, facet->ridges) > 0) {
+        qh_fprintf(qh, qh->ferr, 6161, "qhull error (qh_triangulate): ridges still defined for f%d\n", facet->id);
+        qh_errexit(qh, qh_ERRqhull, facet, NULL);
+      }
+      qh_setfree(qh, &facet->ridges);
+    }
+    if (SETfirst_(facet->vertices) == SETsecond_(facet->vertices)) {
+      zinc_(Ztrinull);
+      qh_triangulate_null(qh, facet);
+    }
+  }
+  trace2((qh, qh->ferr, 2048, "qh_triangulate: delete %d or more mirror facets -- same vertices and neighbors\n", qh_setsize(qh, qh->degen_mergeset)));
+  qh->visible_list= qh->facet_tail;
+  while ((merge= (mergeT*)qh_setdellast(qh->degen_mergeset))) {
+    facet1= merge->facet1;
+    facet2= merge->facet2;
+    mergetype= merge->type;
+    qh_memfree(qh, merge, (int)sizeof(mergeT));
+    if (mergetype == MRGmirror) {
+      zinc_(Ztrimirror);
+      qh_triangulate_mirror(qh, facet1, facet2);
+    }
+  }
+  qh_settempfree(qh, &qh->degen_mergeset);
+  trace2((qh, qh->ferr, 2049, "qh_triangulate: update neighbor lists for vertices from v%d\n", getid_(new_vertex_list)));
+  qh->newvertex_list= new_vertex_list;  /* all vertices of new facets */
+  qh->visible_list= NULL;
+  qh_updatevertices(qh /*qh.newvertex_list, empty newfacet_list and visible_list*/);
+  qh_resetlists(qh, False, !qh_RESETvisible /*qh.newvertex_list, empty newfacet_list and visible_list*/);
+
+  trace2((qh, qh->ferr, 2050, "qh_triangulate: identify degenerate tricoplanar facets from f%d\n", getid_(new_facet_list)));
+  trace2((qh, qh->ferr, 2051, "qh_triangulate: and replace facet->f.triowner with tricoplanar facets that own center, normal, etc.\n"));
+  FORALLfacet_(new_facet_list) {
+    if (facet->tricoplanar && !facet->visible) {
+      FOREACHneighbor_i_(qh, facet) {
+        if (neighbor_i == 0) {  /* first iteration */
+          if (neighbor->tricoplanar)
+            orig_neighbor= neighbor->f.triowner;
+          else
+            orig_neighbor= neighbor;
+        }else {
+          if (neighbor->tricoplanar)
+            otherfacet= neighbor->f.triowner;
+          else
+            otherfacet= neighbor;
+          if (orig_neighbor == otherfacet) {
+            zinc_(Ztridegen);
+            facet->degenerate= True;
+            break;
+          }
+        }
+      }
+    }
+  }
+
+  trace2((qh, qh->ferr, 2052, "qh_triangulate: delete visible facets -- non-simplicial, null, and mirrored facets\n"));
+  owner= NULL;
+  visible= NULL;
+  for (facet= new_facet_list; facet && facet->next; facet= nextfacet) { /* may delete facet */
+    nextfacet= facet->next;
+    if (facet->visible) {
+      if (facet->tricoplanar) { /* a null or mirrored facet */
+        qh_delfacet(qh, facet);
+        qh->num_visible--;
+      }else {  /* a non-simplicial facet followed by its tricoplanars */
+        if (visible && !owner) {
+          /*  RBOX 200 s D5 t1001471447 | QHULL Qt C-0.01 Qx Qc Tv Qt -- f4483 had 6 vertices/neighbors and 8 ridges */
+          trace2((qh, qh->ferr, 2053, "qh_triangulate: all tricoplanar facets degenerate for non-simplicial facet f%d\n",
+                       visible->id));
+          qh_delfacet(qh, visible);
+          qh->num_visible--;
+        }
+        visible= facet;
+        owner= NULL;
+      }
+    }else if (facet->tricoplanar) {
+      if (facet->f.triowner != visible || visible==NULL) {
+        qh_fprintf(qh, qh->ferr, 6162, "qhull error (qh_triangulate): tricoplanar facet f%d not owned by its visible, non-simplicial facet f%d\n", facet->id, getid_(visible));
+        qh_errexit2(qh, qh_ERRqhull, facet, visible);
+      }
+      if (owner)
+        facet->f.triowner= owner;
+      else if (!facet->degenerate) {
+        owner= facet;
+        nextfacet= visible->next; /* rescan tricoplanar facets with owner, visible!=0 by QH6162 */
+        facet->keepcentrum= True;  /* one facet owns ->normal, etc. */
+        facet->coplanarset= visible->coplanarset;
+        facet->outsideset= visible->outsideset;
+        visible->coplanarset= NULL;
+        visible->outsideset= NULL;
+        if (!qh->TRInormals) { /* center and normal copied to tricoplanar facets */
+          visible->center= NULL;
+          visible->normal= NULL;
+        }
+        qh_delfacet(qh, visible);
+        qh->num_visible--;
+      }
+    }
+  }
+  if (visible && !owner) {
+    trace2((qh, qh->ferr, 2054, "qh_triangulate: all tricoplanar facets degenerate for last non-simplicial facet f%d\n",
+                 visible->id));
+    qh_delfacet(qh, visible);
+    qh->num_visible--;
+  }
+  qh->NEWfacets= False;
+  qh->ONLYgood= onlygood; /* restore value */
+  if (qh->CHECKfrequently)
+    qh_checkpolygon(qh, qh->facet_list);
+  qh->hasTriangulation= True;
+} /* triangulate */
+
+
+/*---------------------------------
+
+  qh_triangulate_facet(qh, facetA, &firstVertex )
+    triangulate a non-simplicial facet
+      if qh.CENTERtype=qh_ASvoronoi, sets its Voronoi center
+  returns:
+    qh.newfacet_list == simplicial facets
+      facet->tricoplanar set and ->keepcentrum false
+      facet->degenerate set if duplicated apex
+      facet->f.trivisible set to facetA
+      facet->center copied from facetA (created if qh_ASvoronoi)
+        qh_eachvoronoi, qh_detvridge, qh_detvridge3 assume centers copied
+      facet->normal,offset,maxoutside copied from facetA
+
+  notes:
+      only called by qh_triangulate
+      qh_makenew_nonsimplicial uses neighbor->seen for the same
+      if qh.TRInormals, newfacet->normal will need qh_free
+        if qh.TRInormals and qh_AScentrum, newfacet->center will need qh_free
+        keepcentrum is also set on Zwidefacet in qh_mergefacet
+        freed by qh_clearcenters
+
+  see also:
+      qh_addpoint() -- add a point
+      qh_makenewfacets() -- construct a cone of facets for a new vertex
+
+  design:
+      if qh_ASvoronoi,
+         compute Voronoi center (facet->center)
+      select first vertex (highest ID to preserve ID ordering of ->vertices)
+      triangulate from vertex to ridges
+      copy facet->center, normal, offset
+      update vertex neighbors
+*/
+void qh_triangulate_facet(qhT *qh, facetT *facetA, vertexT **first_vertex) {
+  facetT *newfacet;
+  facetT *neighbor, **neighborp;
+  vertexT *apex;
+  int numnew=0;
+
+  trace3((qh, qh->ferr, 3020, "qh_triangulate_facet: triangulate facet f%d\n", facetA->id));
+
+  if (qh->IStracing >= 4)
+    qh_printfacet(qh, qh->ferr, facetA);
+  FOREACHneighbor_(facetA) {
+    neighbor->seen= False;
+    neighbor->coplanar= False;
+  }
+  if (qh->CENTERtype == qh_ASvoronoi && !facetA->center  /* matches upperdelaunay in qh_setfacetplane() */
+        && fabs_(facetA->normal[qh->hull_dim -1]) >= qh->ANGLEround * qh_ZEROdelaunay) {
+    facetA->center= qh_facetcenter(qh, facetA->vertices);
+  }
+  qh_willdelete(qh, facetA, NULL);
+  qh->newfacet_list= qh->facet_tail;
+  facetA->visitid= qh->visit_id;
+  apex= SETfirstt_(facetA->vertices, vertexT);
+  qh_makenew_nonsimplicial(qh, facetA, apex, &numnew);
+  SETfirst_(facetA->neighbors)= NULL;
+  FORALLnew_facets {
+    newfacet->tricoplanar= True;
+    newfacet->f.trivisible= facetA;
+    newfacet->degenerate= False;
+    newfacet->upperdelaunay= facetA->upperdelaunay;
+    newfacet->good= facetA->good;
+    if (qh->TRInormals) { /* 'Q11' triangulate duplicates ->normal and ->center */
+      newfacet->keepcentrum= True;
+      if(facetA->normal){
+        newfacet->normal= qh_memalloc(qh, qh->normal_size);
+        memcpy((char *)newfacet->normal, facetA->normal, qh->normal_size);
+      }
+      if (qh->CENTERtype == qh_AScentrum)
+        newfacet->center= qh_getcentrum(qh, newfacet);
+      else if (qh->CENTERtype == qh_ASvoronoi && facetA->center){
+        newfacet->center= qh_memalloc(qh, qh->center_size);
+        memcpy((char *)newfacet->center, facetA->center, qh->center_size);
+      }
+    }else {
+      newfacet->keepcentrum= False;
+      /* one facet will have keepcentrum=True at end of qh_triangulate */
+      newfacet->normal= facetA->normal;
+      newfacet->center= facetA->center;
+    }
+    newfacet->offset= facetA->offset;
+#if qh_MAXoutside
+    newfacet->maxoutside= facetA->maxoutside;
+#endif
+  }
+  qh_matchnewfacets(qh /*qh.newfacet_list*/);
+  zinc_(Ztricoplanar);
+  zadd_(Ztricoplanartot, numnew);
+  zmax_(Ztricoplanarmax, numnew);
+  qh->visible_list= NULL;
+  if (!(*first_vertex))
+    (*first_vertex)= qh->newvertex_list;
+  qh->newvertex_list= NULL;
+  qh_updatevertices(qh /*qh.newfacet_list, qh.empty visible_list and qh.newvertex_list*/);
+  qh_resetlists(qh, False, !qh_RESETvisible /*qh.newfacet_list, qh.empty visible_list and qh.newvertex_list*/);
+} /* triangulate_facet */
+
+/*---------------------------------
+
+  qh_triangulate_link(qh, oldfacetA, facetA, oldfacetB, facetB)
+    relink facetA to facetB via oldfacets
+  returns:
+    adds mirror facets to qh->degen_mergeset (4-d and up only)
+  design:
+    if they are already neighbors, the opposing neighbors become MRGmirror facets
+*/
+void qh_triangulate_link(qhT *qh, facetT *oldfacetA, facetT *facetA, facetT *oldfacetB, facetT *facetB) {
+  int errmirror= False;
+
+  trace3((qh, qh->ferr, 3021, "qh_triangulate_link: relink old facets f%d and f%d between neighbors f%d and f%d\n",
+         oldfacetA->id, oldfacetB->id, facetA->id, facetB->id));
+  if (qh_setin(facetA->neighbors, facetB)) {
+    if (!qh_setin(facetB->neighbors, facetA))
+      errmirror= True;
+    else
+      qh_appendmergeset(qh, facetA, facetB, MRGmirror, NULL);
+  }else if (qh_setin(facetB->neighbors, facetA))
+    errmirror= True;
+  if (errmirror) {
+    qh_fprintf(qh, qh->ferr, 6163, "qhull error (qh_triangulate_link): mirror facets f%d and f%d do not match for old facets f%d and f%d\n",
+       facetA->id, facetB->id, oldfacetA->id, oldfacetB->id);
+    qh_errexit2(qh, qh_ERRqhull, facetA, facetB);
+  }
+  qh_setreplace(qh, facetB->neighbors, oldfacetB, facetA);
+  qh_setreplace(qh, facetA->neighbors, oldfacetA, facetB);
+} /* triangulate_link */
+
+/*---------------------------------
+
+  qh_triangulate_mirror(qh, facetA, facetB)
+    delete mirrored facets from qh_triangulate_null() and qh_triangulate_mirror
+      a mirrored facet shares the same vertices of a logical ridge
+  design:
+    since a null facet duplicates the first two vertices, the opposing neighbors absorb the null facet
+    if they are already neighbors, the opposing neighbors become MRGmirror facets
+*/
+void qh_triangulate_mirror(qhT *qh, facetT *facetA, facetT *facetB) {
+  facetT *neighbor, *neighborB;
+  int neighbor_i, neighbor_n;
+
+  trace3((qh, qh->ferr, 3022, "qh_triangulate_mirror: delete mirrored facets f%d and f%d\n",
+         facetA->id, facetB->id));
+  FOREACHneighbor_i_(qh, facetA) {
+    neighborB= SETelemt_(facetB->neighbors, neighbor_i, facetT);
+    if (neighbor == neighborB)
+      continue; /* occurs twice */
+    qh_triangulate_link(qh, facetA, neighbor, facetB, neighborB);
+  }
+  qh_willdelete(qh, facetA, NULL);
+  qh_willdelete(qh, facetB, NULL);
+} /* triangulate_mirror */
+
+/*---------------------------------
+
+  qh_triangulate_null(qh, facetA)
+    remove null facetA from qh_triangulate_facet()
+      a null facet has vertex #1 (apex) == vertex #2
+  returns:
+    adds facetA to ->visible for deletion after qh_updatevertices
+    qh->degen_mergeset contains mirror facets (4-d and up only)
+  design:
+    since a null facet duplicates the first two vertices, the opposing neighbors absorb the null facet
+    if they are already neighbors, the opposing neighbors become MRGmirror facets
+*/
+void qh_triangulate_null(qhT *qh, facetT *facetA) {
+  facetT *neighbor, *otherfacet;
+
+  trace3((qh, qh->ferr, 3023, "qh_triangulate_null: delete null facet f%d\n", facetA->id));
+  neighbor= SETfirstt_(facetA->neighbors, facetT);
+  otherfacet= SETsecondt_(facetA->neighbors, facetT);
+  qh_triangulate_link(qh, facetA, neighbor, facetA, otherfacet);
+  qh_willdelete(qh, facetA, NULL);
+} /* triangulate_null */
+
+#else /* qh_NOmerge */
+void qh_triangulate(qhT *qh) {
+}
+#endif /* qh_NOmerge */
+
+   /*---------------------------------
+
+  qh_vertexintersect(qh, vertexsetA, vertexsetB )
+    intersects two vertex sets (inverse id ordered)
+    vertexsetA is a temporary set at the top of qh->qhmem.tempstack
+
+  returns:
+    replaces vertexsetA with the intersection
+
+  notes:
+    could overwrite vertexsetA if currently too slow
+*/
+void qh_vertexintersect(qhT *qh, setT **vertexsetA,setT *vertexsetB) {
+  setT *intersection;
+
+  intersection= qh_vertexintersect_new(qh, *vertexsetA, vertexsetB);
+  qh_settempfree(qh, vertexsetA);
+  *vertexsetA= intersection;
+  qh_settemppush(qh, intersection);
+} /* vertexintersect */
+
+/*---------------------------------
+
+  qh_vertexintersect_new(qh, )
+    intersects two vertex sets (inverse id ordered)
+
+  returns:
+    a new set
+*/
+setT *qh_vertexintersect_new(qhT *qh, setT *vertexsetA,setT *vertexsetB) {
+  setT *intersection= qh_setnew(qh, qh->hull_dim - 1);
+  vertexT **vertexA= SETaddr_(vertexsetA, vertexT);
+  vertexT **vertexB= SETaddr_(vertexsetB, vertexT);
+
+  while (*vertexA && *vertexB) {
+    if (*vertexA  == *vertexB) {
+      qh_setappend(qh, &intersection, *vertexA);
+      vertexA++; vertexB++;
+    }else {
+      if ((*vertexA)->id > (*vertexB)->id)
+        vertexA++;
+      else
+        vertexB++;
+    }
+  }
+  return intersection;
+} /* vertexintersect_new */
+
+/*---------------------------------
+
+  qh_vertexneighbors(qh)
+    for each vertex in qh.facet_list,
+      determine its neighboring facets
+
+  returns:
+    sets qh.VERTEXneighbors
+      nop if qh.VERTEXneighbors already set
+      qh_addpoint() will maintain them
+
+  notes:
+    assumes all vertex->neighbors are NULL
+
+  design:
+    for each facet
+      for each vertex
+        append facet to vertex->neighbors
+*/
+void qh_vertexneighbors(qhT *qh /*qh.facet_list*/) {
+  facetT *facet;
+  vertexT *vertex, **vertexp;
+
+  if (qh->VERTEXneighbors)
+    return;
+  trace1((qh, qh->ferr, 1035, "qh_vertexneighbors: determining neighboring facets for each vertex\n"));
+  qh->vertex_visit++;
+  FORALLfacets {
+    if (facet->visible)
+      continue;
+    FOREACHvertex_(facet->vertices) {
+      if (vertex->visitid != qh->vertex_visit) {
+        vertex->visitid= qh->vertex_visit;
+        vertex->neighbors= qh_setnew(qh, qh->hull_dim);
+      }
+      qh_setappend(qh, &vertex->neighbors, facet);
+    }
+  }
+  qh->VERTEXneighbors= True;
+} /* vertexneighbors */
+
+/*---------------------------------
+
+  qh_vertexsubset( vertexsetA, vertexsetB )
+    returns True if vertexsetA is a subset of vertexsetB
+    assumes vertexsets are sorted
+
+  note:
+    empty set is a subset of any other set
+*/
+boolT qh_vertexsubset(setT *vertexsetA, setT *vertexsetB) {
+  vertexT **vertexA= (vertexT **) SETaddr_(vertexsetA, vertexT);
+  vertexT **vertexB= (vertexT **) SETaddr_(vertexsetB, vertexT);
+
+  while (True) {
+    if (!*vertexA)
+      return True;
+    if (!*vertexB)
+      return False;
+    if ((*vertexA)->id > (*vertexB)->id)
+      return False;
+    if (*vertexA  == *vertexB)
+      vertexA++;
+    vertexB++;
+  }
+  return False; /* avoid warnings */
+} /* vertexsubset */
diff --git a/Cdir/poly_r.c b/Cdir/poly_r.c
new file mode 100644
--- /dev/null
+++ b/Cdir/poly_r.c
@@ -0,0 +1,1205 @@
+/*
  ---------------------------------
+
+   poly_r.c
+   implements polygons and simplices
+
+   see qh-poly_r.htm, poly_r.h and libqhull_r.h
+
+   infrequent code is in poly2_r.c
+   (all but top 50 and their callers 12/3/95)
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull_r/poly_r.c#3 $$Change: 2064 $
+   $DateTime: 2016/01/18 12:36:08 $$Author: bbarber $
+*/
+
+#include "qhull_ra.h"
+
+/*======== functions in alphabetical order ==========*/
+
+/*---------------------------------
+
+  qh_appendfacet(qh, facet )
+    appends facet to end of qh.facet_list,
+
+  returns:
+    updates qh.newfacet_list, facet_next, facet_list
+    increments qh.numfacets
+
+  notes:
+    assumes qh.facet_list/facet_tail is defined (createsimplex)
+
+  see:
+    qh_removefacet()
+
+*/
+void qh_appendfacet(qhT *qh, facetT *facet) {
+  facetT *tail= qh->facet_tail;
+
+  if (tail == qh->newfacet_list)
+    qh->newfacet_list= facet;
+  if (tail == qh->facet_next)
+    qh->facet_next= facet;
+  facet->previous= tail->previous;
+  facet->next= tail;
+  if (tail->previous)
+    tail->previous->next= facet;
+  else
+    qh->facet_list= facet;
+  tail->previous= facet;
+  qh->num_facets++;
+  trace4((qh, qh->ferr, 4044, "qh_appendfacet: append f%d to facet_list\n", facet->id));
+} /* appendfacet */
+
+
+/*---------------------------------
+
+  qh_appendvertex(qh, vertex )
+    appends vertex to end of qh.vertex_list,
+
+  returns:
+    sets vertex->newlist
+    updates qh.vertex_list, newvertex_list
+    increments qh.num_vertices
+
+  notes:
+    assumes qh.vertex_list/vertex_tail is defined (createsimplex)
+
+*/
+void qh_appendvertex(qhT *qh, vertexT *vertex) {
+  vertexT *tail= qh->vertex_tail;
+
+  if (tail == qh->newvertex_list)
+    qh->newvertex_list= vertex;
+  vertex->newlist= True;
+  vertex->previous= tail->previous;
+  vertex->next= tail;
+  if (tail->previous)
+    tail->previous->next= vertex;
+  else
+    qh->vertex_list= vertex;
+  tail->previous= vertex;
+  qh->num_vertices++;
+  trace4((qh, qh->ferr, 4045, "qh_appendvertex: append v%d to vertex_list\n", vertex->id));
+} /* appendvertex */
+
+
+/*---------------------------------
+
+  qh_attachnewfacets(qh, )
+    attach horizon facets to new facets in qh.newfacet_list
+    newfacets have neighbor and ridge links to horizon but not vice versa
+    only needed for qh.ONLYgood
+
+  returns:
+    set qh.NEWfacets
+    horizon facets linked to new facets
+      ridges changed from visible facets to new facets
+      simplicial ridges deleted
+    qh.visible_list, no ridges valid
+    facet->f.replace is a newfacet (if any)
+
+  design:
+    delete interior ridges and neighbor sets by
+      for each visible, non-simplicial facet
+        for each ridge
+          if last visit or if neighbor is simplicial
+            if horizon neighbor
+              delete ridge for horizon's ridge set
+            delete ridge
+        erase neighbor set
+    attach horizon facets and new facets by
+      for all new facets
+        if corresponding horizon facet is simplicial
+          locate corresponding visible facet {may be more than one}
+          link visible facet to new facet
+          replace visible facet with new facet in horizon
+        else it's non-simplicial
+          for all visible neighbors of the horizon facet
+            link visible neighbor to new facet
+            delete visible neighbor from horizon facet
+          append new facet to horizon's neighbors
+          the first ridge of the new facet is the horizon ridge
+          link the new facet into the horizon ridge
+*/
+void qh_attachnewfacets(qhT *qh /* qh.visible_list, newfacet_list */) {
+  facetT *newfacet= NULL, *neighbor, **neighborp, *horizon, *visible;
+  ridgeT *ridge, **ridgep;
+
+  qh->NEWfacets= True;
+  trace3((qh, qh->ferr, 3012, "qh_attachnewfacets: delete interior ridges\n"));
+  qh->visit_id++;
+  FORALLvisible_facets {
+    visible->visitid= qh->visit_id;
+    if (visible->ridges) {
+      FOREACHridge_(visible->ridges) {
+        neighbor= otherfacet_(ridge, visible);
+        if (neighbor->visitid == qh->visit_id
+            || (!neighbor->visible && neighbor->simplicial)) {
+          if (!neighbor->visible)  /* delete ridge for simplicial horizon */
+            qh_setdel(neighbor->ridges, ridge);
+          qh_setfree(qh, &(ridge->vertices)); /* delete on 2nd visit */
+          qh_memfree(qh, ridge, (int)sizeof(ridgeT));
+        }
+      }
+      SETfirst_(visible->ridges)= NULL;
+    }
+    SETfirst_(visible->neighbors)= NULL;
+  }
+  trace1((qh, qh->ferr, 1017, "qh_attachnewfacets: attach horizon facets to new facets\n"));
+  FORALLnew_facets {
+    horizon= SETfirstt_(newfacet->neighbors, facetT);
+    if (horizon->simplicial) {
+      visible= NULL;
+      FOREACHneighbor_(horizon) {   /* may have more than one horizon ridge */
+        if (neighbor->visible) {
+          if (visible) {
+            if (qh_setequal_skip(newfacet->vertices, 0, horizon->vertices,
+                                  SETindex_(horizon->neighbors, neighbor))) {
+              visible= neighbor;
+              break;
+            }
+          }else
+            visible= neighbor;
+        }
+      }
+      if (visible) {
+        visible->f.replace= newfacet;
+        qh_setreplace(qh, horizon->neighbors, visible, newfacet);
+      }else {
+        qh_fprintf(qh, qh->ferr, 6102, "qhull internal error (qh_attachnewfacets): couldn't find visible facet for horizon f%d of newfacet f%d\n",
+                 horizon->id, newfacet->id);
+        qh_errexit2(qh, qh_ERRqhull, horizon, newfacet);
+      }
+    }else { /* non-simplicial, with a ridge for newfacet */
+      FOREACHneighbor_(horizon) {    /* may hold for many new facets */
+        if (neighbor->visible) {
+          neighbor->f.replace= newfacet;
+          qh_setdelnth(qh, horizon->neighbors,
+                        SETindex_(horizon->neighbors, neighbor));
+          neighborp--; /* repeat */
+        }
+      }
+      qh_setappend(qh, &horizon->neighbors, newfacet);
+      ridge= SETfirstt_(newfacet->ridges, ridgeT);
+      if (ridge->top == horizon)
+        ridge->bottom= newfacet;
+      else
+        ridge->top= newfacet;
+      }
+  } /* newfacets */
+  if (qh->PRINTstatistics) {
+    FORALLvisible_facets {
+      if (!visible->f.replace)
+        zinc_(Zinsidevisible);
+    }
+  }
+} /* attachnewfacets */
+
+/*---------------------------------
+
+  qh_checkflipped(qh, facet, dist, allerror )
+    checks facet orientation to interior point
+
+    if allerror set,
+      tests against qh.DISTround
+    else
+      tests against 0 since tested against DISTround before
+
+  returns:
+    False if it flipped orientation (sets facet->flipped)
+    distance if non-NULL
+*/
+boolT qh_checkflipped(qhT *qh, facetT *facet, realT *distp, boolT allerror) {
+  realT dist;
+
+  if (facet->flipped && !distp)
+    return False;
+  zzinc_(Zdistcheck);
+  qh_distplane(qh, qh->interior_point, facet, &dist);
+  if (distp)
+    *distp= dist;
+  if ((allerror && dist > -qh->DISTround)|| (!allerror && dist >= 0.0)) {
+    facet->flipped= True;
+    zzinc_(Zflippedfacets);
+    trace0((qh, qh->ferr, 19, "qh_checkflipped: facet f%d is flipped, distance= %6.12g during p%d\n",
+              facet->id, dist, qh->furthest_id));
+    qh_precision(qh, "flipped facet");
+    return False;
+  }
+  return True;
+} /* checkflipped */
+
+/*---------------------------------
+
+  qh_delfacet(qh, facet )
+    removes facet from facet_list and frees up its memory
+
+  notes:
+    assumes vertices and ridges already freed
+*/
+void qh_delfacet(qhT *qh, facetT *facet) {
+  void **freelistp; /* used if !qh_NOmem by qh_memfree_() */
+
+  trace4((qh, qh->ferr, 4046, "qh_delfacet: delete f%d\n", facet->id));
+  if (facet == qh->tracefacet)
+    qh->tracefacet= NULL;
+  if (facet == qh->GOODclosest)
+    qh->GOODclosest= NULL;
+  qh_removefacet(qh, facet);
+  if (!facet->tricoplanar || facet->keepcentrum) {
+    qh_memfree_(qh, facet->normal, qh->normal_size, freelistp);
+    if (qh->CENTERtype == qh_ASvoronoi) {   /* braces for macro calls */
+      qh_memfree_(qh, facet->center, qh->center_size, freelistp);
+    }else /* AScentrum */ {
+      qh_memfree_(qh, facet->center, qh->normal_size, freelistp);
+    }
+  }
+  qh_setfree(qh, &(facet->neighbors));
+  if (facet->ridges)
+    qh_setfree(qh, &(facet->ridges));
+  qh_setfree(qh, &(facet->vertices));
+  if (facet->outsideset)
+    qh_setfree(qh, &(facet->outsideset));
+  if (facet->coplanarset)
+    qh_setfree(qh, &(facet->coplanarset));
+  qh_memfree_(qh, facet, (int)sizeof(facetT), freelistp);
+} /* delfacet */
+
+
+/*---------------------------------
+
+  qh_deletevisible()
+    delete visible facets and vertices
+
+  returns:
+    deletes each facet and removes from facetlist
+    at exit, qh.visible_list empty (== qh.newfacet_list)
+
+  notes:
+    ridges already deleted
+    horizon facets do not reference facets on qh.visible_list
+    new facets in qh.newfacet_list
+    uses   qh.visit_id;
+*/
+void qh_deletevisible(qhT *qh /*qh.visible_list*/) {
+  facetT *visible, *nextfacet;
+  vertexT *vertex, **vertexp;
+  int numvisible= 0, numdel= qh_setsize(qh, qh->del_vertices);
+
+  trace1((qh, qh->ferr, 1018, "qh_deletevisible: delete %d visible facets and %d vertices\n",
+         qh->num_visible, numdel));
+  for (visible= qh->visible_list; visible && visible->visible;
+                visible= nextfacet) { /* deleting current */
+    nextfacet= visible->next;
+    numvisible++;
+    qh_delfacet(qh, visible);
+  }
+  if (numvisible != qh->num_visible) {
+    qh_fprintf(qh, qh->ferr, 6103, "qhull internal error (qh_deletevisible): qh->num_visible %d is not number of visible facets %d\n",
+             qh->num_visible, numvisible);
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }
+  qh->num_visible= 0;
+  zadd_(Zvisfacettot, numvisible);
+  zmax_(Zvisfacetmax, numvisible);
+  zzadd_(Zdelvertextot, numdel);
+  zmax_(Zdelvertexmax, numdel);
+  FOREACHvertex_(qh->del_vertices)
+    qh_delvertex(qh, vertex);
+  qh_settruncate(qh, qh->del_vertices, 0);
+} /* deletevisible */
+
+/*---------------------------------
+
+  qh_facetintersect(qh, facetA, facetB, skipa, skipB, prepend )
+    return vertices for intersection of two simplicial facets
+    may include 1 prepended entry (if more, need to settemppush)
+
+  returns:
+    returns set of qh.hull_dim-1 + prepend vertices
+    returns skipped index for each test and checks for exactly one
+
+  notes:
+    does not need settemp since set in quick memory
+
+  see also:
+    qh_vertexintersect and qh_vertexintersect_new
+    use qh_setnew_delnthsorted to get nth ridge (no skip information)
+
+  design:
+    locate skipped vertex by scanning facet A's neighbors
+    locate skipped vertex by scanning facet B's neighbors
+    intersect the vertex sets
+*/
+setT *qh_facetintersect(qhT *qh, facetT *facetA, facetT *facetB,
+                         int *skipA,int *skipB, int prepend) {
+  setT *intersect;
+  int dim= qh->hull_dim, i, j;
+  facetT **neighborsA, **neighborsB;
+
+  neighborsA= SETaddr_(facetA->neighbors, facetT);
+  neighborsB= SETaddr_(facetB->neighbors, facetT);
+  i= j= 0;
+  if (facetB == *neighborsA++)
+    *skipA= 0;
+  else if (facetB == *neighborsA++)
+    *skipA= 1;
+  else if (facetB == *neighborsA++)
+    *skipA= 2;
+  else {
+    for (i=3; i < dim; i++) {
+      if (facetB == *neighborsA++) {
+        *skipA= i;
+        break;
+      }
+    }
+  }
+  if (facetA == *neighborsB++)
+    *skipB= 0;
+  else if (facetA == *neighborsB++)
+    *skipB= 1;
+  else if (facetA == *neighborsB++)
+    *skipB= 2;
+  else {
+    for (j=3; j < dim; j++) {
+      if (facetA == *neighborsB++) {
+        *skipB= j;
+        break;
+      }
+    }
+  }
+  if (i >= dim || j >= dim) {
+    qh_fprintf(qh, qh->ferr, 6104, "qhull internal error (qh_facetintersect): f%d or f%d not in others neighbors\n",
+            facetA->id, facetB->id);
+    qh_errexit2(qh, qh_ERRqhull, facetA, facetB);
+  }
+  intersect= qh_setnew_delnthsorted(qh, facetA->vertices, qh->hull_dim, *skipA, prepend);
+  trace4((qh, qh->ferr, 4047, "qh_facetintersect: f%d skip %d matches f%d skip %d\n",
+          facetA->id, *skipA, facetB->id, *skipB));
+  return(intersect);
+} /* facetintersect */
+
+/*---------------------------------
+
+  qh_gethash(qh, hashsize, set, size, firstindex, skipelem )
+    return hashvalue for a set with firstindex and skipelem
+
+  notes:
+    returned hash is in [0,hashsize)
+    assumes at least firstindex+1 elements
+    assumes skipelem is NULL, in set, or part of hash
+
+    hashes memory addresses which may change over different runs of the same data
+    using sum for hash does badly in high d
+*/
+int qh_gethash(qhT *qh, int hashsize, setT *set, int size, int firstindex, void *skipelem) {
+  void **elemp= SETelemaddr_(set, firstindex, void);
+  ptr_intT hash = 0, elem;
+  unsigned result;
+  int i;
+#ifdef _MSC_VER                   /* Microsoft Visual C++ -- warn about 64-bit issues */
+#pragma warning( push)            /* WARN64 -- ptr_intT holds a 64-bit pointer */
+#pragma warning( disable : 4311)  /* 'type cast': pointer truncation from 'void*' to 'ptr_intT' */
+#endif
+
+  switch (size-firstindex) {
+  case 1:
+    hash= (ptr_intT)(*elemp) - (ptr_intT) skipelem;
+    break;
+  case 2:
+    hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] - (ptr_intT) skipelem;
+    break;
+  case 3:
+    hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] + (ptr_intT)elemp[2]
+      - (ptr_intT) skipelem;
+    break;
+  case 4:
+    hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] + (ptr_intT)elemp[2]
+      + (ptr_intT)elemp[3] - (ptr_intT) skipelem;
+    break;
+  case 5:
+    hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] + (ptr_intT)elemp[2]
+      + (ptr_intT)elemp[3] + (ptr_intT)elemp[4] - (ptr_intT) skipelem;
+    break;
+  case 6:
+    hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] + (ptr_intT)elemp[2]
+      + (ptr_intT)elemp[3] + (ptr_intT)elemp[4]+ (ptr_intT)elemp[5]
+      - (ptr_intT) skipelem;
+    break;
+  default:
+    hash= 0;
+    i= 3;
+    do {     /* this is about 10% in 10-d */
+      if ((elem= (ptr_intT)*elemp++) != (ptr_intT)skipelem) {
+        hash ^= (elem << i) + (elem >> (32-i));
+        i += 3;
+        if (i >= 32)
+          i -= 32;
+      }
+    }while (*elemp);
+    break;
+  }
+  if (hashsize<0) {
+    qh_fprintf(qh, qh->ferr, 6202, "qhull internal error: negative hashsize %d passed to qh_gethash [poly.c]\n", hashsize);
+    qh_errexit2(qh, qh_ERRqhull, NULL, NULL);
+  }
+  result= (unsigned)hash;
+  result %= (unsigned)hashsize;
+  /* result= 0; for debugging */
+  return result;
+#ifdef _MSC_VER
+#pragma warning( pop)
+#endif
+} /* gethash */
+
+/*---------------------------------
+
+  qh_makenewfacet(qh, vertices, toporient, horizon )
+    creates a toporient? facet from vertices
+
+  returns:
+    returns newfacet
+      adds newfacet to qh.facet_list
+      newfacet->vertices= vertices
+      if horizon
+        newfacet->neighbor= horizon, but not vice versa
+    newvertex_list updated with vertices
+*/
+facetT *qh_makenewfacet(qhT *qh, setT *vertices, boolT toporient,facetT *horizon) {
+  facetT *newfacet;
+  vertexT *vertex, **vertexp;
+
+  FOREACHvertex_(vertices) {
+    if (!vertex->newlist) {
+      qh_removevertex(qh, vertex);
+      qh_appendvertex(qh, vertex);
+    }
+  }
+  newfacet= qh_newfacet(qh);
+  newfacet->vertices= vertices;
+  newfacet->toporient= (unsigned char)toporient;
+  if (horizon)
+    qh_setappend(qh, &(newfacet->neighbors), horizon);
+  qh_appendfacet(qh, newfacet);
+  return(newfacet);
+} /* makenewfacet */
+
+
+/*---------------------------------
+
+  qh_makenewplanes()
+    make new hyperplanes for facets on qh.newfacet_list
+
+  returns:
+    all facets have hyperplanes or are marked for   merging
+    doesn't create hyperplane if horizon is coplanar (will merge)
+    updates qh.min_vertex if qh.JOGGLEmax
+
+  notes:
+    facet->f.samecycle is defined for facet->mergehorizon facets
+*/
+void qh_makenewplanes(qhT *qh /* qh.newfacet_list */) {
+  facetT *newfacet;
+
+  FORALLnew_facets {
+    if (!newfacet->mergehorizon)
+      qh_setfacetplane(qh, newfacet);
+  }
+  if (qh->JOGGLEmax < REALmax/2)
+    minimize_(qh->min_vertex, -wwval_(Wnewvertexmax));
+} /* makenewplanes */
+
+/*---------------------------------
+
+  qh_makenew_nonsimplicial(qh, visible, apex, numnew )
+    make new facets for ridges of a visible facet
+
+  returns:
+    first newfacet, bumps numnew as needed
+    attaches new facets if !qh.ONLYgood
+    marks ridge neighbors for simplicial visible
+    if (qh.ONLYgood)
+      ridges on newfacet, horizon, and visible
+    else
+      ridge and neighbors between newfacet and   horizon
+      visible facet's ridges are deleted
+
+  notes:
+    qh.visit_id if visible has already been processed
+    sets neighbor->seen for building f.samecycle
+      assumes all 'seen' flags initially false
+
+  design:
+    for each ridge of visible facet
+      get neighbor of visible facet
+      if neighbor was already processed
+        delete the ridge (will delete all visible facets later)
+      if neighbor is a horizon facet
+        create a new facet
+        if neighbor coplanar
+          adds newfacet to f.samecycle for later merging
+        else
+          updates neighbor's neighbor set
+          (checks for non-simplicial facet with multiple ridges to visible facet)
+        updates neighbor's ridge set
+        (checks for simplicial neighbor to non-simplicial visible facet)
+        (deletes ridge if neighbor is simplicial)
+
+*/
+#ifndef qh_NOmerge
+facetT *qh_makenew_nonsimplicial(qhT *qh, facetT *visible, vertexT *apex, int *numnew) {
+  void **freelistp; /* used if !qh_NOmem by qh_memfree_() */
+  ridgeT *ridge, **ridgep;
+  facetT *neighbor, *newfacet= NULL, *samecycle;
+  setT *vertices;
+  boolT toporient;
+  int ridgeid;
+
+  FOREACHridge_(visible->ridges) {
+    ridgeid= ridge->id;
+    neighbor= otherfacet_(ridge, visible);
+    if (neighbor->visible) {
+      if (!qh->ONLYgood) {
+        if (neighbor->visitid == qh->visit_id) {
+          qh_setfree(qh, &(ridge->vertices));  /* delete on 2nd visit */
+          qh_memfree_(qh, ridge, (int)sizeof(ridgeT), freelistp);
+        }
+      }
+    }else {  /* neighbor is an horizon facet */
+      toporient= (ridge->top == visible);
+      vertices= qh_setnew(qh, qh->hull_dim); /* makes sure this is quick */
+      qh_setappend(qh, &vertices, apex);
+      qh_setappend_set(qh, &vertices, ridge->vertices);
+      newfacet= qh_makenewfacet(qh, vertices, toporient, neighbor);
+      (*numnew)++;
+      if (neighbor->coplanar) {
+        newfacet->mergehorizon= True;
+        if (!neighbor->seen) {
+          newfacet->f.samecycle= newfacet;
+          neighbor->f.newcycle= newfacet;
+        }else {
+          samecycle= neighbor->f.newcycle;
+          newfacet->f.samecycle= samecycle->f.samecycle;
+          samecycle->f.samecycle= newfacet;
+        }
+      }
+      if (qh->ONLYgood) {
+        if (!neighbor->simplicial)
+          qh_setappend(qh, &(newfacet->ridges), ridge);
+      }else {  /* qh_attachnewfacets */
+        if (neighbor->seen) {
+          if (neighbor->simplicial) {
+            qh_fprintf(qh, qh->ferr, 6105, "qhull internal error (qh_makenew_nonsimplicial): simplicial f%d sharing two ridges with f%d\n",
+                   neighbor->id, visible->id);
+            qh_errexit2(qh, qh_ERRqhull, neighbor, visible);
+          }
+          qh_setappend(qh, &(neighbor->neighbors), newfacet);
+        }else
+          qh_setreplace(qh, neighbor->neighbors, visible, newfacet);
+        if (neighbor->simplicial) {
+          qh_setdel(neighbor->ridges, ridge);
+          qh_setfree(qh, &(ridge->vertices));
+          qh_memfree(qh, ridge, (int)sizeof(ridgeT));
+        }else {
+          qh_setappend(qh, &(newfacet->ridges), ridge);
+          if (toporient)
+            ridge->top= newfacet;
+          else
+            ridge->bottom= newfacet;
+        }
+      trace4((qh, qh->ferr, 4048, "qh_makenew_nonsimplicial: created facet f%d from v%d and r%d of horizon f%d\n",
+            newfacet->id, apex->id, ridgeid, neighbor->id));
+      }
+    }
+    neighbor->seen= True;
+  } /* for each ridge */
+  if (!qh->ONLYgood)
+    SETfirst_(visible->ridges)= NULL;
+  return newfacet;
+} /* makenew_nonsimplicial */
+#else /* qh_NOmerge */
+facetT *qh_makenew_nonsimplicial(qhT *qh, facetT *visible, vertexT *apex, int *numnew) {
+  return NULL;
+}
+#endif /* qh_NOmerge */
+
+/*---------------------------------
+
+  qh_makenew_simplicial(qh, visible, apex, numnew )
+    make new facets for simplicial visible facet and apex
+
+  returns:
+    attaches new facets if (!qh.ONLYgood)
+      neighbors between newfacet and horizon
+
+  notes:
+    nop if neighbor->seen or neighbor->visible(see qh_makenew_nonsimplicial)
+
+  design:
+    locate neighboring horizon facet for visible facet
+    determine vertices and orientation
+    create new facet
+    if coplanar,
+      add new facet to f.samecycle
+    update horizon facet's neighbor list
+*/
+facetT *qh_makenew_simplicial(qhT *qh, facetT *visible, vertexT *apex, int *numnew) {
+  facetT *neighbor, **neighborp, *newfacet= NULL;
+  setT *vertices;
+  boolT flip, toporient;
+  int horizonskip= 0, visibleskip= 0;
+
+  FOREACHneighbor_(visible) {
+    if (!neighbor->seen && !neighbor->visible) {
+      vertices= qh_facetintersect(qh, neighbor,visible, &horizonskip, &visibleskip, 1);
+      SETfirst_(vertices)= apex;
+      flip= ((horizonskip & 0x1) ^ (visibleskip & 0x1));
+      if (neighbor->toporient)
+        toporient= horizonskip & 0x1;
+      else
+        toporient= (horizonskip & 0x1) ^ 0x1;
+      newfacet= qh_makenewfacet(qh, vertices, toporient, neighbor);
+      (*numnew)++;
+      if (neighbor->coplanar && (qh->PREmerge || qh->MERGEexact)) {
+#ifndef qh_NOmerge
+        newfacet->f.samecycle= newfacet;
+        newfacet->mergehorizon= True;
+#endif
+      }
+      if (!qh->ONLYgood)
+        SETelem_(neighbor->neighbors, horizonskip)= newfacet;
+      trace4((qh, qh->ferr, 4049, "qh_makenew_simplicial: create facet f%d top %d from v%d and horizon f%d skip %d top %d and visible f%d skip %d, flip? %d\n",
+            newfacet->id, toporient, apex->id, neighbor->id, horizonskip,
+              neighbor->toporient, visible->id, visibleskip, flip));
+    }
+  }
+  return newfacet;
+} /* makenew_simplicial */
+
+/*---------------------------------
+
+  qh_matchneighbor(qh, newfacet, newskip, hashsize, hashcount )
+    either match subridge of newfacet with neighbor or add to hash_table
+
+  returns:
+    duplicate ridges are unmatched and marked by qh_DUPLICATEridge
+
+  notes:
+    ridge is newfacet->vertices w/o newskip vertex
+    do not allocate memory (need to free hash_table cleanly)
+    uses linear hash chains
+
+  see also:
+    qh_matchduplicates
+
+  design:
+    for each possible matching facet in qh.hash_table
+      if vertices match
+        set ismatch, if facets have opposite orientation
+        if ismatch and matching facet doesn't have a match
+          match the facets by updating their neighbor sets
+        else
+          indicate a duplicate ridge
+          set facet hyperplane for later testing
+          add facet to hashtable
+          unless the other facet was already a duplicate ridge
+            mark both facets with a duplicate ridge
+            add other facet (if defined) to hash table
+*/
+void qh_matchneighbor(qhT *qh, facetT *newfacet, int newskip, int hashsize, int *hashcount) {
+  boolT newfound= False;   /* True, if new facet is already in hash chain */
+  boolT same, ismatch;
+  int hash, scan;
+  facetT *facet, *matchfacet;
+  int skip, matchskip;
+
+  hash= qh_gethash(qh, hashsize, newfacet->vertices, qh->hull_dim, 1,
+                     SETelem_(newfacet->vertices, newskip));
+  trace4((qh, qh->ferr, 4050, "qh_matchneighbor: newfacet f%d skip %d hash %d hashcount %d\n",
+          newfacet->id, newskip, hash, *hashcount));
+  zinc_(Zhashlookup);
+  for (scan= hash; (facet= SETelemt_(qh->hash_table, scan, facetT));
+       scan= (++scan >= hashsize ? 0 : scan)) {
+    if (facet == newfacet) {
+      newfound= True;
+      continue;
+    }
+    zinc_(Zhashtests);
+    if (qh_matchvertices(qh, 1, newfacet->vertices, newskip, facet->vertices, &skip, &same)) {
+      if (SETelem_(newfacet->vertices, newskip) ==
+          SETelem_(facet->vertices, skip)) {
+        qh_precision(qh, "two facets with the same vertices");
+        qh_fprintf(qh, qh->ferr, 6106, "qhull precision error: Vertex sets are the same for f%d and f%d.  Can not force output.\n",
+          facet->id, newfacet->id);
+        qh_errexit2(qh, qh_ERRprec, facet, newfacet);
+      }
+      ismatch= (same == (boolT)((newfacet->toporient ^ facet->toporient)));
+      matchfacet= SETelemt_(facet->neighbors, skip, facetT);
+      if (ismatch && !matchfacet) {
+        SETelem_(facet->neighbors, skip)= newfacet;
+        SETelem_(newfacet->neighbors, newskip)= facet;
+        (*hashcount)--;
+        trace4((qh, qh->ferr, 4051, "qh_matchneighbor: f%d skip %d matched with new f%d skip %d\n",
+           facet->id, skip, newfacet->id, newskip));
+        return;
+      }
+      if (!qh->PREmerge && !qh->MERGEexact) {
+        qh_precision(qh, "a ridge with more than two neighbors");
+        qh_fprintf(qh, qh->ferr, 6107, "qhull precision error: facets f%d, f%d and f%d meet at a ridge with more than 2 neighbors.  Can not continue.\n",
+                 facet->id, newfacet->id, getid_(matchfacet));
+        qh_errexit2(qh, qh_ERRprec, facet, newfacet);
+      }
+      SETelem_(newfacet->neighbors, newskip)= qh_DUPLICATEridge;
+      newfacet->dupridge= True;
+      if (!newfacet->normal)
+        qh_setfacetplane(qh, newfacet);
+      qh_addhash(newfacet, qh->hash_table, hashsize, hash);
+      (*hashcount)++;
+      if (!facet->normal)
+        qh_setfacetplane(qh, facet);
+      if (matchfacet != qh_DUPLICATEridge) {
+        SETelem_(facet->neighbors, skip)= qh_DUPLICATEridge;
+        facet->dupridge= True;
+        if (!facet->normal)
+          qh_setfacetplane(qh, facet);
+        if (matchfacet) {
+          matchskip= qh_setindex(matchfacet->neighbors, facet);
+          if (matchskip<0) {
+              qh_fprintf(qh, qh->ferr, 6260, "qhull internal error (qh_matchneighbor): matchfacet f%d is in f%d neighbors but not vice versa.  Can not continue.\n",
+                  matchfacet->id, facet->id);
+              qh_errexit2(qh, qh_ERRqhull, matchfacet, facet);
+          }
+          SETelem_(matchfacet->neighbors, matchskip)= qh_DUPLICATEridge; /* matchskip>=0 by QH6260 */
+          matchfacet->dupridge= True;
+          if (!matchfacet->normal)
+            qh_setfacetplane(qh, matchfacet);
+          qh_addhash(matchfacet, qh->hash_table, hashsize, hash);
+          *hashcount += 2;
+        }
+      }
+      trace4((qh, qh->ferr, 4052, "qh_matchneighbor: new f%d skip %d duplicates ridge for f%d skip %d matching f%d ismatch %d at hash %d\n",
+           newfacet->id, newskip, facet->id, skip,
+           (matchfacet == qh_DUPLICATEridge ? -2 : getid_(matchfacet)),
+           ismatch, hash));
+      return; /* end of duplicate ridge */
+    }
+  }
+  if (!newfound)
+    SETelem_(qh->hash_table, scan)= newfacet;  /* same as qh_addhash */
+  (*hashcount)++;
+  trace4((qh, qh->ferr, 4053, "qh_matchneighbor: no match for f%d skip %d at hash %d\n",
+           newfacet->id, newskip, hash));
+} /* matchneighbor */
+
+
+/*---------------------------------
+
+  qh_matchnewfacets()
+    match newfacets in qh.newfacet_list to their newfacet neighbors
+
+  returns:
+    qh.newfacet_list with full neighbor sets
+      get vertices with nth neighbor by deleting nth vertex
+    if qh.PREmerge/MERGEexact or qh.FORCEoutput
+      sets facet->flippped if flipped normal (also prevents point partitioning)
+    if duplicate ridges and qh.PREmerge/MERGEexact
+      sets facet->dupridge
+      missing neighbor links identifies extra ridges to be merging (qh_MERGEridge)
+
+  notes:
+    newfacets already have neighbor[0] (horizon facet)
+    assumes qh.hash_table is NULL
+    vertex->neighbors has not been updated yet
+    do not allocate memory after qh.hash_table (need to free it cleanly)
+
+  design:
+    delete neighbor sets for all new facets
+    initialize a hash table
+    for all new facets
+      match facet with neighbors
+    if unmatched facets (due to duplicate ridges)
+      for each new facet with a duplicate ridge
+        match it with a facet
+    check for flipped facets
+*/
+void qh_matchnewfacets(qhT *qh /* qh.newfacet_list */) {
+  int numnew=0, hashcount=0, newskip;
+  facetT *newfacet, *neighbor;
+  int dim= qh->hull_dim, hashsize, neighbor_i, neighbor_n;
+  setT *neighbors;
+#ifndef qh_NOtrace
+  int facet_i, facet_n, numfree= 0;
+  facetT *facet;
+#endif
+
+  trace1((qh, qh->ferr, 1019, "qh_matchnewfacets: match neighbors for new facets.\n"));
+  FORALLnew_facets {
+    numnew++;
+    {  /* inline qh_setzero(qh, newfacet->neighbors, 1, qh->hull_dim); */
+      neighbors= newfacet->neighbors;
+      neighbors->e[neighbors->maxsize].i= dim+1; /*may be overwritten*/
+      memset((char *)SETelemaddr_(neighbors, 1, void), 0, dim * SETelemsize);
+    }
+  }
+
+  qh_newhashtable(qh, numnew*(qh->hull_dim-1)); /* twice what is normally needed,
+                                     but every ridge could be DUPLICATEridge */
+  hashsize= qh_setsize(qh, qh->hash_table);
+  FORALLnew_facets {
+    for (newskip=1; newskiphull_dim; newskip++) /* furthest/horizon already matched */
+      /* hashsize>0 because hull_dim>1 and numnew>0 */
+      qh_matchneighbor(qh, newfacet, newskip, hashsize, &hashcount);
+#if 0   /* use the following to trap hashcount errors */
+    {
+      int count= 0, k;
+      facetT *facet, *neighbor;
+
+      count= 0;
+      FORALLfacet_(qh->newfacet_list) {  /* newfacet already in use */
+        for (k=1; k < qh->hull_dim; k++) {
+          neighbor= SETelemt_(facet->neighbors, k, facetT);
+          if (!neighbor || neighbor == qh_DUPLICATEridge)
+            count++;
+        }
+        if (facet == newfacet)
+          break;
+      }
+      if (count != hashcount) {
+        qh_fprintf(qh, qh->ferr, 8088, "qh_matchnewfacets: after adding facet %d, hashcount %d != count %d\n",
+                 newfacet->id, hashcount, count);
+        qh_errexit(qh, qh_ERRqhull, newfacet, NULL);
+      }
+    }
+#endif  /* end of trap code */
+  }
+  if (hashcount) {
+    FORALLnew_facets {
+      if (newfacet->dupridge) {
+        FOREACHneighbor_i_(qh, newfacet) {
+          if (neighbor == qh_DUPLICATEridge) {
+            qh_matchduplicates(qh, newfacet, neighbor_i, hashsize, &hashcount);
+                    /* this may report MERGEfacet */
+          }
+        }
+      }
+    }
+  }
+  if (hashcount) {
+    qh_fprintf(qh, qh->ferr, 6108, "qhull internal error (qh_matchnewfacets): %d neighbors did not match up\n",
+        hashcount);
+    qh_printhashtable(qh, qh->ferr);
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }
+#ifndef qh_NOtrace
+  if (qh->IStracing >= 2) {
+    FOREACHfacet_i_(qh, qh->hash_table) {
+      if (!facet)
+        numfree++;
+    }
+    qh_fprintf(qh, qh->ferr, 8089, "qh_matchnewfacets: %d new facets, %d unused hash entries .  hashsize %d\n",
+             numnew, numfree, qh_setsize(qh, qh->hash_table));
+  }
+#endif /* !qh_NOtrace */
+  qh_setfree(qh, &qh->hash_table);
+  if (qh->PREmerge || qh->MERGEexact) {
+    if (qh->IStracing >= 4)
+      qh_printfacetlist(qh, qh->newfacet_list, NULL, qh_ALL);
+    FORALLnew_facets {
+      if (newfacet->normal)
+        qh_checkflipped(qh, newfacet, NULL, qh_ALL);
+    }
+  }else if (qh->FORCEoutput)
+    qh_checkflipped_all(qh, qh->newfacet_list);  /* prints warnings for flipped */
+} /* matchnewfacets */
+
+
+/*---------------------------------
+
+  qh_matchvertices(qh, firstindex, verticesA, skipA, verticesB, skipB, same )
+    tests whether vertices match with a single skip
+    starts match at firstindex since all new facets have a common vertex
+
+  returns:
+    true if matched vertices
+    skip index for each set
+    sets same iff vertices have the same orientation
+
+  notes:
+    assumes skipA is in A and both sets are the same size
+
+  design:
+    set up pointers
+    scan both sets checking for a match
+    test orientation
+*/
+boolT qh_matchvertices(qhT *qh, int firstindex, setT *verticesA, int skipA,
+       setT *verticesB, int *skipB, boolT *same) {
+  vertexT **elemAp, **elemBp, **skipBp=NULL, **skipAp;
+
+  elemAp= SETelemaddr_(verticesA, firstindex, vertexT);
+  elemBp= SETelemaddr_(verticesB, firstindex, vertexT);
+  skipAp= SETelemaddr_(verticesA, skipA, vertexT);
+  do if (elemAp != skipAp) {
+    while (*elemAp != *elemBp++) {
+      if (skipBp)
+        return False;
+      skipBp= elemBp;  /* one extra like FOREACH */
+    }
+  }while (*(++elemAp));
+  if (!skipBp)
+    skipBp= ++elemBp;
+  *skipB= SETindex_(verticesB, skipB); /* i.e., skipBp - verticesB */
+  *same= !((skipA & 0x1) ^ (*skipB & 0x1)); /* result is 0 or 1 */
+  trace4((qh, qh->ferr, 4054, "qh_matchvertices: matched by skip %d(v%d) and skip %d(v%d) same? %d\n",
+          skipA, (*skipAp)->id, *skipB, (*(skipBp-1))->id, *same));
+  return(True);
+} /* matchvertices */
+
+/*---------------------------------
+
+  qh_newfacet(qh)
+    return a new facet
+
+  returns:
+    all fields initialized or cleared   (NULL)
+    preallocates neighbors set
+*/
+facetT *qh_newfacet(qhT *qh) {
+  facetT *facet;
+  void **freelistp; /* used if !qh_NOmem by qh_memalloc_() */
+
+  qh_memalloc_(qh, (int)sizeof(facetT), freelistp, facet, facetT);
+  memset((char *)facet, (size_t)0, sizeof(facetT));
+  if (qh->facet_id == qh->tracefacet_id)
+    qh->tracefacet= facet;
+  facet->id= qh->facet_id++;
+  facet->neighbors= qh_setnew(qh, qh->hull_dim);
+#if !qh_COMPUTEfurthest
+  facet->furthestdist= 0.0;
+#endif
+#if qh_MAXoutside
+  if (qh->FORCEoutput && qh->APPROXhull)
+    facet->maxoutside= qh->MINoutside;
+  else
+    facet->maxoutside= qh->DISTround;
+#endif
+  facet->simplicial= True;
+  facet->good= True;
+  facet->newfacet= True;
+  trace4((qh, qh->ferr, 4055, "qh_newfacet: created facet f%d\n", facet->id));
+  return(facet);
+} /* newfacet */
+
+
+/*---------------------------------
+
+  qh_newridge()
+    return a new ridge
+*/
+ridgeT *qh_newridge(qhT *qh) {
+  ridgeT *ridge;
+  void **freelistp;   /* used if !qh_NOmem by qh_memalloc_() */
+
+  qh_memalloc_(qh, (int)sizeof(ridgeT), freelistp, ridge, ridgeT);
+  memset((char *)ridge, (size_t)0, sizeof(ridgeT));
+  zinc_(Ztotridges);
+  if (qh->ridge_id == UINT_MAX) {
+    qh_fprintf(qh, qh->ferr, 7074, "\
+qhull warning: more than 2^32 ridges.  Qhull results are OK.  Since the ridge ID wraps around to 0, two ridges may have the same identifier.\n");
+  }
+  ridge->id= qh->ridge_id++;
+  trace4((qh, qh->ferr, 4056, "qh_newridge: created ridge r%d\n", ridge->id));
+  return(ridge);
+} /* newridge */
+
+
+/*---------------------------------
+
+  qh_pointid(qh, point )
+    return id for a point,
+    returns qh_IDnone(-3) if null, qh_IDinterior(-2) if interior, or qh_IDunknown(-1) if not known
+
+  alternative code if point is in qh.first_point...
+    unsigned long id;
+    id= ((unsigned long)point - (unsigned long)qh.first_point)/qh.normal_size;
+
+  notes:
+    Valid points are non-negative
+    WARN64 -- id truncated to 32-bits, at most 2G points
+    NOerrors returned (QhullPoint::id)
+    if point not in point array
+      the code does a comparison of unrelated pointers.
+*/
+int qh_pointid(qhT *qh, pointT *point) {
+  ptr_intT offset, id;
+
+  if (!point || !qh)
+    return qh_IDnone;
+  else if (point == qh->interior_point)
+    return qh_IDinterior;
+  else if (point >= qh->first_point
+  && point < qh->first_point + qh->num_points * qh->hull_dim) {
+    offset= (ptr_intT)(point - qh->first_point);
+    id= offset / qh->hull_dim;
+  }else if ((id= qh_setindex(qh->other_points, point)) != -1)
+    id += qh->num_points;
+  else
+    return qh_IDunknown;
+  return (int)id;
+} /* pointid */
+
+/*---------------------------------
+
+  qh_removefacet(qh, facet )
+    unlinks facet from qh.facet_list,
+
+  returns:
+    updates qh.facet_list .newfacet_list .facet_next visible_list
+    decrements qh.num_facets
+
+  see:
+    qh_appendfacet
+*/
+void qh_removefacet(qhT *qh, facetT *facet) {
+  facetT *next= facet->next, *previous= facet->previous;
+
+  if (facet == qh->newfacet_list)
+    qh->newfacet_list= next;
+  if (facet == qh->facet_next)
+    qh->facet_next= next;
+  if (facet == qh->visible_list)
+    qh->visible_list= next;
+  if (previous) {
+    previous->next= next;
+    next->previous= previous;
+  }else {  /* 1st facet in qh->facet_list */
+    qh->facet_list= next;
+    qh->facet_list->previous= NULL;
+  }
+  qh->num_facets--;
+  trace4((qh, qh->ferr, 4057, "qh_removefacet: remove f%d from facet_list\n", facet->id));
+} /* removefacet */
+
+
+/*---------------------------------
+
+  qh_removevertex(qh, vertex )
+    unlinks vertex from qh.vertex_list,
+
+  returns:
+    updates qh.vertex_list .newvertex_list
+    decrements qh.num_vertices
+*/
+void qh_removevertex(qhT *qh, vertexT *vertex) {
+  vertexT *next= vertex->next, *previous= vertex->previous;
+
+  if (vertex == qh->newvertex_list)
+    qh->newvertex_list= next;
+  if (previous) {
+    previous->next= next;
+    next->previous= previous;
+  }else {  /* 1st vertex in qh->vertex_list */
+    qh->vertex_list= vertex->next;
+    qh->vertex_list->previous= NULL;
+  }
+  qh->num_vertices--;
+  trace4((qh, qh->ferr, 4058, "qh_removevertex: remove v%d from vertex_list\n", vertex->id));
+} /* removevertex */
+
+
+/*---------------------------------
+
+  qh_updatevertices()
+    update vertex neighbors and delete interior vertices
+
+  returns:
+    if qh.VERTEXneighbors, updates neighbors for each vertex
+      if qh.newvertex_list,
+         removes visible neighbors  from vertex neighbors
+      if qh.newfacet_list
+         adds new facets to vertex neighbors
+    if qh.visible_list
+       interior vertices added to qh.del_vertices for later partitioning
+
+  design:
+    if qh.VERTEXneighbors
+      deletes references to visible facets from vertex neighbors
+      appends new facets to the neighbor list for each vertex
+      checks all vertices of visible facets
+        removes visible facets from neighbor lists
+        marks unused vertices for deletion
+*/
+void qh_updatevertices(qhT *qh /*qh.newvertex_list, newfacet_list, visible_list*/) {
+  facetT *newfacet= NULL, *neighbor, **neighborp, *visible;
+  vertexT *vertex, **vertexp;
+
+  trace3((qh, qh->ferr, 3013, "qh_updatevertices: delete interior vertices and update vertex->neighbors\n"));
+  if (qh->VERTEXneighbors) {
+    FORALLvertex_(qh->newvertex_list) {
+      FOREACHneighbor_(vertex) {
+        if (neighbor->visible)
+          SETref_(neighbor)= NULL;
+      }
+      qh_setcompact(qh, vertex->neighbors);
+    }
+    FORALLnew_facets {
+      FOREACHvertex_(newfacet->vertices)
+        qh_setappend(qh, &vertex->neighbors, newfacet);
+    }
+    FORALLvisible_facets {
+      FOREACHvertex_(visible->vertices) {
+        if (!vertex->newlist && !vertex->deleted) {
+          FOREACHneighbor_(vertex) { /* this can happen under merging */
+            if (!neighbor->visible)
+              break;
+          }
+          if (neighbor)
+            qh_setdel(vertex->neighbors, visible);
+          else {
+            vertex->deleted= True;
+            qh_setappend(qh, &qh->del_vertices, vertex);
+            trace2((qh, qh->ferr, 2041, "qh_updatevertices: delete vertex p%d(v%d) in f%d\n",
+                  qh_pointid(qh, vertex->point), vertex->id, visible->id));
+          }
+        }
+      }
+    }
+  }else {  /* !VERTEXneighbors */
+    FORALLvisible_facets {
+      FOREACHvertex_(visible->vertices) {
+        if (!vertex->newlist && !vertex->deleted) {
+          vertex->deleted= True;
+          qh_setappend(qh, &qh->del_vertices, vertex);
+          trace2((qh, qh->ferr, 2042, "qh_updatevertices: delete vertex p%d(v%d) in f%d\n",
+                  qh_pointid(qh, vertex->point), vertex->id, visible->id));
+        }
+      }
+    }
+  }
+} /* updatevertices */
+
+
+
diff --git a/Cdir/qset_r.c b/Cdir/qset_r.c
new file mode 100644
--- /dev/null
+++ b/Cdir/qset_r.c
@@ -0,0 +1,1340 @@
+/*
  ---------------------------------
+
+   qset_r.c
+   implements set manipulations needed for quickhull
+
+   see qh-set_r.htm and qset_r.h
+
+   Be careful of strict aliasing (two pointers of different types
+   that reference the same location).  The last slot of a set is
+   either the actual size of the set plus 1, or the NULL terminator
+   of the set (i.e., setelemT).
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull_r/qset_r.c#3 $$Change: 2062 $
+   $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
+*/
+
+#include "libqhull_r.h" /* for qhT and QHULL_CRTDBG */
+#include "qset_r.h"
+#include "mem_r.h"
+#include 
+#include 
+/*** uncomment here and qhull_ra.h
+     if string.h does not define memcpy()
+#include 
+*/
+
+#ifndef qhDEFlibqhull
+typedef struct ridgeT ridgeT;
+typedef struct facetT facetT;
+void    qh_errexit(qhT *qh, int exitcode, facetT *, ridgeT *);
+void    qh_fprintf(qhT *qh, FILE *fp, int msgcode, const char *fmt, ... );
+#  ifdef _MSC_VER  /* Microsoft Visual C++ -- warning level 4 */
+#  pragma warning( disable : 4127)  /* conditional expression is constant */
+#  pragma warning( disable : 4706)  /* assignment within conditional function */
+#  endif
+#endif
+
+/*=============== internal macros ===========================*/
+
+/*============ functions in alphabetical order ===================*/
+
+/*----------------------------------
+
+  qh_setaddnth(qh, setp, nth, newelem)
+    adds newelem as n'th element of sorted or unsorted *setp
+
+  notes:
+    *setp and newelem must be defined
+    *setp may be a temp set
+    nth=0 is first element
+    errors if nth is out of bounds
+
+  design:
+    expand *setp if empty or full
+    move tail of *setp up one
+    insert newelem
+*/
+void qh_setaddnth(qhT *qh, setT **setp, int nth, void *newelem) {
+  int oldsize, i;
+  setelemT *sizep;          /* avoid strict aliasing */
+  setelemT *oldp, *newp;
+
+  if (!*setp || (sizep= SETsizeaddr_(*setp))->i==0) {
+    qh_setlarger(qh, setp);
+    sizep= SETsizeaddr_(*setp);
+  }
+  oldsize= sizep->i - 1;
+  if (nth < 0 || nth > oldsize) {
+    qh_fprintf(qh, qh->qhmem.ferr, 6171, "qhull internal error (qh_setaddnth): nth %d is out-of-bounds for set:\n", nth);
+    qh_setprint(qh, qh->qhmem.ferr, "", *setp);
+    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
+  }
+  sizep->i++;
+  oldp= (setelemT *)SETelemaddr_(*setp, oldsize, void);   /* NULL */
+  newp= oldp+1;
+  for (i=oldsize-nth+1; i--; )  /* move at least NULL  */
+    (newp--)->p= (oldp--)->p;       /* may overwrite *sizep */
+  newp->p= newelem;
+} /* setaddnth */
+
+
+/*----------------------------------
+
+  setaddsorted( setp, newelem )
+    adds an newelem into sorted *setp
+
+  notes:
+    *setp and newelem must be defined
+    *setp may be a temp set
+    nop if newelem already in set
+
+  design:
+    find newelem's position in *setp
+    insert newelem
+*/
+void qh_setaddsorted(qhT *qh, setT **setp, void *newelem) {
+  int newindex=0;
+  void *elem, **elemp;
+
+  FOREACHelem_(*setp) {          /* could use binary search instead */
+    if (elem < newelem)
+      newindex++;
+    else if (elem == newelem)
+      return;
+    else
+      break;
+  }
+  qh_setaddnth(qh, setp, newindex, newelem);
+} /* setaddsorted */
+
+
+/*---------------------------------
+
+  qh_setappend(qh, setp, newelem)
+    append newelem to *setp
+
+  notes:
+    *setp may be a temp set
+    *setp and newelem may be NULL
+
+  design:
+    expand *setp if empty or full
+    append newelem to *setp
+
+*/
+void qh_setappend(qhT *qh, setT **setp, void *newelem) {
+  setelemT *sizep;  /* Avoid strict aliasing.  Writing to *endp may overwrite *sizep */
+  setelemT *endp;
+  int count;
+
+  if (!newelem)
+    return;
+  if (!*setp || (sizep= SETsizeaddr_(*setp))->i==0) {
+    qh_setlarger(qh, setp);
+    sizep= SETsizeaddr_(*setp);
+  }
+  count= (sizep->i)++ - 1;
+  endp= (setelemT *)SETelemaddr_(*setp, count, void);
+  (endp++)->p= newelem;
+  endp->p= NULL;
+} /* setappend */
+
+/*---------------------------------
+
+  qh_setappend_set(qh, setp, setA)
+    appends setA to *setp
+
+  notes:
+    *setp can not be a temp set
+    *setp and setA may be NULL
+
+  design:
+    setup for copy
+    expand *setp if it is too small
+    append all elements of setA to *setp
+*/
+void qh_setappend_set(qhT *qh, setT **setp, setT *setA) {
+  int sizeA, size;
+  setT *oldset;
+  setelemT *sizep;
+
+  if (!setA)
+    return;
+  SETreturnsize_(setA, sizeA);
+  if (!*setp)
+    *setp= qh_setnew(qh, sizeA);
+  sizep= SETsizeaddr_(*setp);
+  if (!(size= sizep->i))
+    size= (*setp)->maxsize;
+  else
+    size--;
+  if (size + sizeA > (*setp)->maxsize) {
+    oldset= *setp;
+    *setp= qh_setcopy(qh, oldset, sizeA);
+    qh_setfree(qh, &oldset);
+    sizep= SETsizeaddr_(*setp);
+  }
+  if (sizeA > 0) {
+    sizep->i= size+sizeA+1;   /* memcpy may overwrite */
+    memcpy((char *)&((*setp)->e[size].p), (char *)&(setA->e[0].p), (size_t)(sizeA+1) * SETelemsize);
+  }
+} /* setappend_set */
+
+
+/*---------------------------------
+
+  qh_setappend2ndlast(qh, setp, newelem )
+    makes newelem the next to the last element in *setp
+
+  notes:
+    *setp must have at least one element
+    newelem must be defined
+    *setp may be a temp set
+
+  design:
+    expand *setp if empty or full
+    move last element of *setp up one
+    insert newelem
+*/
+void qh_setappend2ndlast(qhT *qh, setT **setp, void *newelem) {
+    setelemT *sizep;  /* Avoid strict aliasing.  Writing to *endp may overwrite *sizep */
+    setelemT *endp, *lastp;
+    int count;
+
+    if (!*setp || (sizep= SETsizeaddr_(*setp))->i==0) {
+        qh_setlarger(qh, setp);
+        sizep= SETsizeaddr_(*setp);
+    }
+    count= (sizep->i)++ - 1;
+    endp= (setelemT *)SETelemaddr_(*setp, count, void); /* NULL */
+    lastp= endp-1;
+    *(endp++)= *lastp;
+    endp->p= NULL;    /* may overwrite *sizep */
+    lastp->p= newelem;
+} /* setappend2ndlast */
+
+/*---------------------------------
+
+  qh_setcheck(qh, set, typename, id )
+    check set for validity
+    report errors with typename and id
+
+  design:
+    checks that maxsize, actual size, and NULL terminator agree
+*/
+void qh_setcheck(qhT *qh, setT *set, const char *tname, unsigned id) {
+  int maxsize, size;
+  int waserr= 0;
+
+  if (!set)
+    return;
+  SETreturnsize_(set, size);
+  maxsize= set->maxsize;
+  if (size > maxsize || !maxsize) {
+    qh_fprintf(qh, qh->qhmem.ferr, 6172, "qhull internal error (qh_setcheck): actual size %d of %s%d is greater than max size %d\n",
+             size, tname, id, maxsize);
+    waserr= 1;
+  }else if (set->e[size].p) {
+    qh_fprintf(qh, qh->qhmem.ferr, 6173, "qhull internal error (qh_setcheck): %s%d(size %d max %d) is not null terminated.\n",
+             tname, id, size-1, maxsize);
+    waserr= 1;
+  }
+  if (waserr) {
+    qh_setprint(qh, qh->qhmem.ferr, "ERRONEOUS", set);
+    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
+  }
+} /* setcheck */
+
+
+/*---------------------------------
+
+  qh_setcompact(qh, set )
+    remove internal NULLs from an unsorted set
+
+  returns:
+    updated set
+
+  notes:
+    set may be NULL
+    it would be faster to swap tail of set into holes, like qh_setdel
+
+  design:
+    setup pointers into set
+    skip NULLs while copying elements to start of set
+    update the actual size
+*/
+void qh_setcompact(qhT *qh, setT *set) {
+  int size;
+  void **destp, **elemp, **endp, **firstp;
+
+  if (!set)
+    return;
+  SETreturnsize_(set, size);
+  destp= elemp= firstp= SETaddr_(set, void);
+  endp= destp + size;
+  while (1) {
+    if (!(*destp++ = *elemp++)) {
+      destp--;
+      if (elemp > endp)
+        break;
+    }
+  }
+  qh_settruncate(qh, set, (int)(destp-firstp));   /* WARN64 */
+} /* setcompact */
+
+
+/*---------------------------------
+
+  qh_setcopy(qh, set, extra )
+    make a copy of a sorted or unsorted set with extra slots
+
+  returns:
+    new set
+
+  design:
+    create a newset with extra slots
+    copy the elements to the newset
+
+*/
+setT *qh_setcopy(qhT *qh, setT *set, int extra) {
+  setT *newset;
+  int size;
+
+  if (extra < 0)
+    extra= 0;
+  SETreturnsize_(set, size);
+  newset= qh_setnew(qh, size+extra);
+  SETsizeaddr_(newset)->i= size+1;    /* memcpy may overwrite */
+  memcpy((char *)&(newset->e[0].p), (char *)&(set->e[0].p), (size_t)(size+1) * SETelemsize);
+  return(newset);
+} /* setcopy */
+
+
+/*---------------------------------
+
+  qh_setdel(set, oldelem )
+    delete oldelem from an unsorted set
+
+  returns:
+    returns oldelem if found
+    returns NULL otherwise
+
+  notes:
+    set may be NULL
+    oldelem must not be NULL;
+    only deletes one copy of oldelem in set
+
+  design:
+    locate oldelem
+    update actual size if it was full
+    move the last element to the oldelem's location
+*/
+void *qh_setdel(setT *set, void *oldelem) {
+  setelemT *sizep;
+  setelemT *elemp;
+  setelemT *lastp;
+
+  if (!set)
+    return NULL;
+  elemp= (setelemT *)SETaddr_(set, void);
+  while (elemp->p != oldelem && elemp->p)
+    elemp++;
+  if (elemp->p) {
+    sizep= SETsizeaddr_(set);
+    if (!(sizep->i)--)         /*  if was a full set */
+      sizep->i= set->maxsize;  /*     *sizep= (maxsize-1)+ 1 */
+    lastp= (setelemT *)SETelemaddr_(set, sizep->i-1, void);
+    elemp->p= lastp->p;      /* may overwrite itself */
+    lastp->p= NULL;
+    return oldelem;
+  }
+  return NULL;
+} /* setdel */
+
+
+/*---------------------------------
+
+  qh_setdellast(set)
+    return last element of set or NULL
+
+  notes:
+    deletes element from set
+    set may be NULL
+
+  design:
+    return NULL if empty
+    if full set
+      delete last element and set actual size
+    else
+      delete last element and update actual size
+*/
+void *qh_setdellast(setT *set) {
+  int setsize;  /* actually, actual_size + 1 */
+  int maxsize;
+  setelemT *sizep;
+  void *returnvalue;
+
+  if (!set || !(set->e[0].p))
+    return NULL;
+  sizep= SETsizeaddr_(set);
+  if ((setsize= sizep->i)) {
+    returnvalue= set->e[setsize - 2].p;
+    set->e[setsize - 2].p= NULL;
+    sizep->i--;
+  }else {
+    maxsize= set->maxsize;
+    returnvalue= set->e[maxsize - 1].p;
+    set->e[maxsize - 1].p= NULL;
+    sizep->i= maxsize;
+  }
+  return returnvalue;
+} /* setdellast */
+
+
+/*---------------------------------
+
+  qh_setdelnth(qh, set, nth )
+    deletes nth element from unsorted set
+    0 is first element
+
+  returns:
+    returns the element (needs type conversion)
+
+  notes:
+    errors if nth invalid
+
+  design:
+    setup points and check nth
+    delete nth element and overwrite with last element
+*/
+void *qh_setdelnth(qhT *qh, setT *set, int nth) {
+  void *elem;
+  setelemT *sizep;
+  setelemT *elemp, *lastp;
+
+  sizep= SETsizeaddr_(set);
+  if ((sizep->i--)==0)         /*  if was a full set */
+    sizep->i= set->maxsize;  /*     *sizep= (maxsize-1)+ 1 */
+  if (nth < 0 || nth >= sizep->i) {
+    qh_fprintf(qh, qh->qhmem.ferr, 6174, "qhull internal error (qh_setdelnth): nth %d is out-of-bounds for set:\n", nth);
+    qh_setprint(qh, qh->qhmem.ferr, "", set);
+    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
+  }
+  elemp= (setelemT *)SETelemaddr_(set, nth, void); /* nth valid by QH6174 */
+  lastp= (setelemT *)SETelemaddr_(set, sizep->i-1, void);
+  elem= elemp->p;
+  elemp->p= lastp->p;      /* may overwrite itself */
+  lastp->p= NULL;
+  return elem;
+} /* setdelnth */
+
+/*---------------------------------
+
+  qh_setdelnthsorted(qh, set, nth )
+    deletes nth element from sorted set
+
+  returns:
+    returns the element (use type conversion)
+
+  notes:
+    errors if nth invalid
+
+  see also:
+    setnew_delnthsorted
+
+  design:
+    setup points and check nth
+    copy remaining elements down one
+    update actual size
+*/
+void *qh_setdelnthsorted(qhT *qh, setT *set, int nth) {
+  void *elem;
+  setelemT *sizep;
+  setelemT *newp, *oldp;
+
+  sizep= SETsizeaddr_(set);
+  if (nth < 0 || (sizep->i && nth >= sizep->i-1) || nth >= set->maxsize) {
+    qh_fprintf(qh, qh->qhmem.ferr, 6175, "qhull internal error (qh_setdelnthsorted): nth %d is out-of-bounds for set:\n", nth);
+    qh_setprint(qh, qh->qhmem.ferr, "", set);
+    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
+  }
+  newp= (setelemT *)SETelemaddr_(set, nth, void);
+  elem= newp->p;
+  oldp= newp+1;
+  while (((newp++)->p= (oldp++)->p))
+    ; /* copy remaining elements and NULL */
+  if ((sizep->i--)==0)         /*  if was a full set */
+    sizep->i= set->maxsize;  /*     *sizep= (max size-1)+ 1 */
+  return elem;
+} /* setdelnthsorted */
+
+
+/*---------------------------------
+
+  qh_setdelsorted(set, oldelem )
+    deletes oldelem from sorted set
+
+  returns:
+    returns oldelem if it was deleted
+
+  notes:
+    set may be NULL
+
+  design:
+    locate oldelem in set
+    copy remaining elements down one
+    update actual size
+*/
+void *qh_setdelsorted(setT *set, void *oldelem) {
+  setelemT *sizep;
+  setelemT *newp, *oldp;
+
+  if (!set)
+    return NULL;
+  newp= (setelemT *)SETaddr_(set, void);
+  while(newp->p != oldelem && newp->p)
+    newp++;
+  if (newp->p) {
+    oldp= newp+1;
+    while (((newp++)->p= (oldp++)->p))
+      ; /* copy remaining elements */
+    sizep= SETsizeaddr_(set);
+    if ((sizep->i--)==0)    /*  if was a full set */
+      sizep->i= set->maxsize;  /*     *sizep= (max size-1)+ 1 */
+    return oldelem;
+  }
+  return NULL;
+} /* setdelsorted */
+
+
+/*---------------------------------
+
+  qh_setduplicate(qh, set, elemsize )
+    duplicate a set of elemsize elements
+
+  notes:
+    use setcopy if retaining old elements
+
+  design:
+    create a new set
+    for each elem of the old set
+      create a newelem
+      append newelem to newset
+*/
+setT *qh_setduplicate(qhT *qh, setT *set, int elemsize) {
+  void          *elem, **elemp, *newElem;
+  setT          *newSet;
+  int           size;
+
+  if (!(size= qh_setsize(qh, set)))
+    return NULL;
+  newSet= qh_setnew(qh, size);
+  FOREACHelem_(set) {
+    newElem= qh_memalloc(qh, elemsize);
+    memcpy(newElem, elem, (size_t)elemsize);
+    qh_setappend(qh, &newSet, newElem);
+  }
+  return newSet;
+} /* setduplicate */
+
+
+/*---------------------------------
+
+  qh_setendpointer( set )
+    Returns pointer to NULL terminator of a set's elements
+    set can not be NULL
+
+*/
+void **qh_setendpointer(setT *set) {
+
+  setelemT *sizep= SETsizeaddr_(set);
+  int n= sizep->i;
+  return (n ? &set->e[n-1].p : &sizep->p);
+} /* qh_setendpointer */
+
+/*---------------------------------
+
+  qh_setequal( setA, setB )
+    returns 1 if two sorted sets are equal, otherwise returns 0
+
+  notes:
+    either set may be NULL
+
+  design:
+    check size of each set
+    setup pointers
+    compare elements of each set
+*/
+int qh_setequal(setT *setA, setT *setB) {
+  void **elemAp, **elemBp;
+  int sizeA= 0, sizeB= 0;
+
+  if (setA) {
+    SETreturnsize_(setA, sizeA);
+  }
+  if (setB) {
+    SETreturnsize_(setB, sizeB);
+  }
+  if (sizeA != sizeB)
+    return 0;
+  if (!sizeA)
+    return 1;
+  elemAp= SETaddr_(setA, void);
+  elemBp= SETaddr_(setB, void);
+  if (!memcmp((char *)elemAp, (char *)elemBp, sizeA*SETelemsize))
+    return 1;
+  return 0;
+} /* setequal */
+
+
+/*---------------------------------
+
+  qh_setequal_except( setA, skipelemA, setB, skipelemB )
+    returns 1 if sorted setA and setB are equal except for skipelemA & B
+
+  returns:
+    false if either skipelemA or skipelemB are missing
+
+  notes:
+    neither set may be NULL
+
+    if skipelemB is NULL,
+      can skip any one element of setB
+
+  design:
+    setup pointers
+    search for skipelemA, skipelemB, and mismatches
+    check results
+*/
+int qh_setequal_except(setT *setA, void *skipelemA, setT *setB, void *skipelemB) {
+  void **elemA, **elemB;
+  int skip=0;
+
+  elemA= SETaddr_(setA, void);
+  elemB= SETaddr_(setB, void);
+  while (1) {
+    if (*elemA == skipelemA) {
+      skip++;
+      elemA++;
+    }
+    if (skipelemB) {
+      if (*elemB == skipelemB) {
+        skip++;
+        elemB++;
+      }
+    }else if (*elemA != *elemB) {
+      skip++;
+      if (!(skipelemB= *elemB++))
+        return 0;
+    }
+    if (!*elemA)
+      break;
+    if (*elemA++ != *elemB++)
+      return 0;
+  }
+  if (skip != 2 || *elemB)
+    return 0;
+  return 1;
+} /* setequal_except */
+
+
+/*---------------------------------
+
+  qh_setequal_skip( setA, skipA, setB, skipB )
+    returns 1 if sorted setA and setB are equal except for elements skipA & B
+
+  returns:
+    false if different size
+
+  notes:
+    neither set may be NULL
+
+  design:
+    setup pointers
+    search for mismatches while skipping skipA and skipB
+*/
+int qh_setequal_skip(setT *setA, int skipA, setT *setB, int skipB) {
+  void **elemA, **elemB, **skipAp, **skipBp;
+
+  elemA= SETaddr_(setA, void);
+  elemB= SETaddr_(setB, void);
+  skipAp= SETelemaddr_(setA, skipA, void);
+  skipBp= SETelemaddr_(setB, skipB, void);
+  while (1) {
+    if (elemA == skipAp)
+      elemA++;
+    if (elemB == skipBp)
+      elemB++;
+    if (!*elemA)
+      break;
+    if (*elemA++ != *elemB++)
+      return 0;
+  }
+  if (*elemB)
+    return 0;
+  return 1;
+} /* setequal_skip */
+
+
+/*---------------------------------
+
+  qh_setfree(qh, setp )
+    frees the space occupied by a sorted or unsorted set
+
+  returns:
+    sets setp to NULL
+
+  notes:
+    set may be NULL
+
+  design:
+    free array
+    free set
+*/
+void qh_setfree(qhT *qh, setT **setp) {
+  int size;
+  void **freelistp;  /* used if !qh_NOmem by qh_memfree_() */
+
+  if (*setp) {
+    size= sizeof(setT) + ((*setp)->maxsize)*SETelemsize;
+    if (size <= qh->qhmem.LASTsize) {
+      qh_memfree_(qh, *setp, size, freelistp);
+    }else
+      qh_memfree(qh, *setp, size);
+    *setp= NULL;
+  }
+} /* setfree */
+
+
+/*---------------------------------
+
+  qh_setfree2(qh, setp, elemsize )
+    frees the space occupied by a set and its elements
+
+  notes:
+    set may be NULL
+
+  design:
+    free each element
+    free set
+*/
+void qh_setfree2(qhT *qh, setT **setp, int elemsize) {
+  void          *elem, **elemp;
+
+  FOREACHelem_(*setp)
+    qh_memfree(qh, elem, elemsize);
+  qh_setfree(qh, setp);
+} /* setfree2 */
+
+
+
+/*---------------------------------
+
+  qh_setfreelong(qh, setp )
+    frees a set only if it's in long memory
+
+  returns:
+    sets setp to NULL if it is freed
+
+  notes:
+    set may be NULL
+
+  design:
+    if set is large
+      free it
+*/
+void qh_setfreelong(qhT *qh, setT **setp) {
+  int size;
+
+  if (*setp) {
+    size= sizeof(setT) + ((*setp)->maxsize)*SETelemsize;
+    if (size > qh->qhmem.LASTsize) {
+      qh_memfree(qh, *setp, size);
+      *setp= NULL;
+    }
+  }
+} /* setfreelong */
+
+
+/*---------------------------------
+
+  qh_setin(set, setelem )
+    returns 1 if setelem is in a set, 0 otherwise
+
+  notes:
+    set may be NULL or unsorted
+
+  design:
+    scans set for setelem
+*/
+int qh_setin(setT *set, void *setelem) {
+  void *elem, **elemp;
+
+  FOREACHelem_(set) {
+    if (elem == setelem)
+      return 1;
+  }
+  return 0;
+} /* setin */
+
+
+/*---------------------------------
+
+  qh_setindex(set, atelem )
+    returns the index of atelem in set.
+    returns -1, if not in set or maxsize wrong
+
+  notes:
+    set may be NULL and may contain nulls.
+    NOerrors returned (qh_pointid, QhullPoint::id)
+
+  design:
+    checks maxsize
+    scans set for atelem
+*/
+int qh_setindex(setT *set, void *atelem) {
+  void **elem;
+  int size, i;
+
+  if (!set)
+    return -1;
+  SETreturnsize_(set, size);
+  if (size > set->maxsize)
+    return -1;
+  elem= SETaddr_(set, void);
+  for (i=0; i < size; i++) {
+    if (*elem++ == atelem)
+      return i;
+  }
+  return -1;
+} /* setindex */
+
+
+/*---------------------------------
+
+  qh_setlarger(qh, oldsetp )
+    returns a larger set that contains all elements of *oldsetp
+
+  notes:
+    the set is at least twice as large
+    if temp set, updates qh->qhmem.tempstack
+
+  design:
+    creates a new set
+    copies the old set to the new set
+    updates pointers in tempstack
+    deletes the old set
+*/
+void qh_setlarger(qhT *qh, setT **oldsetp) {
+  int size= 1;
+  setT *newset, *set, **setp, *oldset;
+  setelemT *sizep;
+  setelemT *newp, *oldp;
+
+  if (*oldsetp) {
+    oldset= *oldsetp;
+    SETreturnsize_(oldset, size);
+    qh->qhmem.cntlarger++;
+    qh->qhmem.totlarger += size+1;
+    newset= qh_setnew(qh, 2 * size);
+    oldp= (setelemT *)SETaddr_(oldset, void);
+    newp= (setelemT *)SETaddr_(newset, void);
+    memcpy((char *)newp, (char *)oldp, (size_t)(size+1) * SETelemsize);
+    sizep= SETsizeaddr_(newset);
+    sizep->i= size+1;
+    FOREACHset_((setT *)qh->qhmem.tempstack) {
+      if (set == oldset)
+        *(setp-1)= newset;
+    }
+    qh_setfree(qh, oldsetp);
+  }else
+    newset= qh_setnew(qh, 3);
+  *oldsetp= newset;
+} /* setlarger */
+
+
+/*---------------------------------
+
+  qh_setlast( set )
+    return last element of set or NULL (use type conversion)
+
+  notes:
+    set may be NULL
+
+  design:
+    return last element
+*/
+void *qh_setlast(setT *set) {
+  int size;
+
+  if (set) {
+    size= SETsizeaddr_(set)->i;
+    if (!size)
+      return SETelem_(set, set->maxsize - 1);
+    else if (size > 1)
+      return SETelem_(set, size - 2);
+  }
+  return NULL;
+} /* setlast */
+
+
+/*---------------------------------
+
+  qh_setnew(qh, setsize )
+    creates and allocates space for a set
+
+  notes:
+    setsize means the number of elements (!including the NULL terminator)
+    use qh_settemp/qh_setfreetemp if set is temporary
+
+  design:
+    allocate memory for set
+    roundup memory if small set
+    initialize as empty set
+*/
+setT *qh_setnew(qhT *qh, int setsize) {
+  setT *set;
+  int sizereceived; /* used if !qh_NOmem */
+  int size;
+  void **freelistp; /* used if !qh_NOmem by qh_memalloc_() */
+
+  if (!setsize)
+    setsize++;
+  size= sizeof(setT) + setsize * SETelemsize;
+  if (size>0 && size <= qh->qhmem.LASTsize) {
+    qh_memalloc_(qh, size, freelistp, set, setT);
+#ifndef qh_NOmem
+    sizereceived= qh->qhmem.sizetable[ qh->qhmem.indextable[size]];
+    if (sizereceived > size)
+      setsize += (sizereceived - size)/SETelemsize;
+#endif
+  }else
+    set= (setT*)qh_memalloc(qh, size);
+  set->maxsize= setsize;
+  set->e[setsize].i= 1;
+  set->e[0].p= NULL;
+  return(set);
+} /* setnew */
+
+
+/*---------------------------------
+
+  qh_setnew_delnthsorted(qh, set, size, nth, prepend )
+    creates a sorted set not containing nth element
+    if prepend, the first prepend elements are undefined
+
+  notes:
+    set must be defined
+    checks nth
+    see also: setdelnthsorted
+
+  design:
+    create new set
+    setup pointers and allocate room for prepend'ed entries
+    append head of old set to new set
+    append tail of old set to new set
+*/
+setT *qh_setnew_delnthsorted(qhT *qh, setT *set, int size, int nth, int prepend) {
+  setT *newset;
+  void **oldp, **newp;
+  int tailsize= size - nth -1, newsize;
+
+  if (tailsize < 0) {
+    qh_fprintf(qh, qh->qhmem.ferr, 6176, "qhull internal error (qh_setnew_delnthsorted): nth %d is out-of-bounds for set:\n", nth);
+    qh_setprint(qh, qh->qhmem.ferr, "", set);
+    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
+  }
+  newsize= size-1 + prepend;
+  newset= qh_setnew(qh, newsize);
+  newset->e[newset->maxsize].i= newsize+1;  /* may be overwritten */
+  oldp= SETaddr_(set, void);
+  newp= SETaddr_(newset, void) + prepend;
+  switch (nth) {
+  case 0:
+    break;
+  case 1:
+    *(newp++)= *oldp++;
+    break;
+  case 2:
+    *(newp++)= *oldp++;
+    *(newp++)= *oldp++;
+    break;
+  case 3:
+    *(newp++)= *oldp++;
+    *(newp++)= *oldp++;
+    *(newp++)= *oldp++;
+    break;
+  case 4:
+    *(newp++)= *oldp++;
+    *(newp++)= *oldp++;
+    *(newp++)= *oldp++;
+    *(newp++)= *oldp++;
+    break;
+  default:
+    memcpy((char *)newp, (char *)oldp, (size_t)nth * SETelemsize);
+    newp += nth;
+    oldp += nth;
+    break;
+  }
+  oldp++;
+  switch (tailsize) {
+  case 0:
+    break;
+  case 1:
+    *(newp++)= *oldp++;
+    break;
+  case 2:
+    *(newp++)= *oldp++;
+    *(newp++)= *oldp++;
+    break;
+  case 3:
+    *(newp++)= *oldp++;
+    *(newp++)= *oldp++;
+    *(newp++)= *oldp++;
+    break;
+  case 4:
+    *(newp++)= *oldp++;
+    *(newp++)= *oldp++;
+    *(newp++)= *oldp++;
+    *(newp++)= *oldp++;
+    break;
+  default:
+    memcpy((char *)newp, (char *)oldp, (size_t)tailsize * SETelemsize);
+    newp += tailsize;
+  }
+  *newp= NULL;
+  return(newset);
+} /* setnew_delnthsorted */
+
+
+/*---------------------------------
+
+  qh_setprint(qh, fp, string, set )
+    print set elements to fp with identifying string
+
+  notes:
+    never errors
+*/
+void qh_setprint(qhT *qh, FILE *fp, const char* string, setT *set) {
+  int size, k;
+
+  if (!set)
+    qh_fprintf(qh, fp, 9346, "%s set is null\n", string);
+  else {
+    SETreturnsize_(set, size);
+    qh_fprintf(qh, fp, 9347, "%s set=%p maxsize=%d size=%d elems=",
+             string, set, set->maxsize, size);
+    if (size > set->maxsize)
+      size= set->maxsize+1;
+    for (k=0; k < size; k++)
+      qh_fprintf(qh, fp, 9348, " %p", set->e[k].p);
+    qh_fprintf(qh, fp, 9349, "\n");
+  }
+} /* setprint */
+
+/*---------------------------------
+
+  qh_setreplace(qh, set, oldelem, newelem )
+    replaces oldelem in set with newelem
+
+  notes:
+    errors if oldelem not in the set
+    newelem may be NULL, but it turns the set into an indexed set (no FOREACH)
+
+  design:
+    find oldelem
+    replace with newelem
+*/
+void qh_setreplace(qhT *qh, setT *set, void *oldelem, void *newelem) {
+  void **elemp;
+
+  elemp= SETaddr_(set, void);
+  while (*elemp != oldelem && *elemp)
+    elemp++;
+  if (*elemp)
+    *elemp= newelem;
+  else {
+    qh_fprintf(qh, qh->qhmem.ferr, 6177, "qhull internal error (qh_setreplace): elem %p not found in set\n",
+       oldelem);
+    qh_setprint(qh, qh->qhmem.ferr, "", set);
+    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
+  }
+} /* setreplace */
+
+
+/*---------------------------------
+
+  qh_setsize(qh, set )
+    returns the size of a set
+
+  notes:
+    errors if set's maxsize is incorrect
+    same as SETreturnsize_(set)
+    same code for qh_setsize [qset_r.c] and QhullSetBase::count
+
+  design:
+    determine actual size of set from maxsize
+*/
+int qh_setsize(qhT *qh, setT *set) {
+  int size;
+  setelemT *sizep;
+
+  if (!set)
+    return(0);
+  sizep= SETsizeaddr_(set);
+  if ((size= sizep->i)) {
+    size--;
+    if (size > set->maxsize) {
+      qh_fprintf(qh, qh->qhmem.ferr, 6178, "qhull internal error (qh_setsize): current set size %d is greater than maximum size %d\n",
+               size, set->maxsize);
+      qh_setprint(qh, qh->qhmem.ferr, "set: ", set);
+      qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
+    }
+  }else
+    size= set->maxsize;
+  return size;
+} /* setsize */
+
+/*---------------------------------
+
+  qh_settemp(qh, setsize )
+    return a stacked, temporary set of upto setsize elements
+
+  notes:
+    use settempfree or settempfree_all to release from qh->qhmem.tempstack
+    see also qh_setnew
+
+  design:
+    allocate set
+    append to qh->qhmem.tempstack
+
+*/
+setT *qh_settemp(qhT *qh, int setsize) {
+  setT *newset;
+
+  newset= qh_setnew(qh, setsize);
+  qh_setappend(qh, &qh->qhmem.tempstack, newset);
+  if (qh->qhmem.IStracing >= 5)
+    qh_fprintf(qh, qh->qhmem.ferr, 8123, "qh_settemp: temp set %p of %d elements, depth %d\n",
+       newset, newset->maxsize, qh_setsize(qh, qh->qhmem.tempstack));
+  return newset;
+} /* settemp */
+
+/*---------------------------------
+
+  qh_settempfree(qh, set )
+    free temporary set at top of qh->qhmem.tempstack
+
+  notes:
+    nop if set is NULL
+    errors if set not from previous   qh_settemp
+
+  to locate errors:
+    use 'T2' to find source and then find mis-matching qh_settemp
+
+  design:
+    check top of qh->qhmem.tempstack
+    free it
+*/
+void qh_settempfree(qhT *qh, setT **set) {
+  setT *stackedset;
+
+  if (!*set)
+    return;
+  stackedset= qh_settemppop(qh);
+  if (stackedset != *set) {
+    qh_settemppush(qh, stackedset);
+    qh_fprintf(qh, qh->qhmem.ferr, 6179, "qhull internal error (qh_settempfree): set %p(size %d) was not last temporary allocated(depth %d, set %p, size %d)\n",
+             *set, qh_setsize(qh, *set), qh_setsize(qh, qh->qhmem.tempstack)+1,
+             stackedset, qh_setsize(qh, stackedset));
+    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
+  }
+  qh_setfree(qh, set);
+} /* settempfree */
+
+/*---------------------------------
+
+  qh_settempfree_all(qh)
+    free all temporary sets in qh->qhmem.tempstack
+
+  design:
+    for each set in tempstack
+      free set
+    free qh->qhmem.tempstack
+*/
+void qh_settempfree_all(qhT *qh) {
+  setT *set, **setp;
+
+  FOREACHset_(qh->qhmem.tempstack)
+    qh_setfree(qh, &set);
+  qh_setfree(qh, &qh->qhmem.tempstack);
+} /* settempfree_all */
+
+/*---------------------------------
+
+  qh_settemppop(qh)
+    pop and return temporary set from qh->qhmem.tempstack
+
+  notes:
+    the returned set is permanent
+
+  design:
+    pop and check top of qh->qhmem.tempstack
+*/
+setT *qh_settemppop(qhT *qh) {
+  setT *stackedset;
+
+  stackedset= (setT*)qh_setdellast(qh->qhmem.tempstack);
+  if (!stackedset) {
+    qh_fprintf(qh, qh->qhmem.ferr, 6180, "qhull internal error (qh_settemppop): pop from empty temporary stack\n");
+    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
+  }
+  if (qh->qhmem.IStracing >= 5)
+    qh_fprintf(qh, qh->qhmem.ferr, 8124, "qh_settemppop: depth %d temp set %p of %d elements\n",
+       qh_setsize(qh, qh->qhmem.tempstack)+1, stackedset, qh_setsize(qh, stackedset));
+  return stackedset;
+} /* settemppop */
+
+/*---------------------------------
+
+  qh_settemppush(qh, set )
+    push temporary set unto qh->qhmem.tempstack (makes it temporary)
+
+  notes:
+    duplicates settemp() for tracing
+
+  design:
+    append set to tempstack
+*/
+void qh_settemppush(qhT *qh, setT *set) {
+  if (!set) {
+    qh_fprintf(qh, qh->qhmem.ferr, 6267, "qhull error (qh_settemppush): can not push a NULL temp\n");
+    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
+  }
+  qh_setappend(qh, &qh->qhmem.tempstack, set);
+  if (qh->qhmem.IStracing >= 5)
+    qh_fprintf(qh, qh->qhmem.ferr, 8125, "qh_settemppush: depth %d temp set %p of %d elements\n",
+      qh_setsize(qh, qh->qhmem.tempstack), set, qh_setsize(qh, set));
+} /* settemppush */
+
+
+/*---------------------------------
+
+  qh_settruncate(qh, set, size )
+    truncate set to size elements
+
+  notes:
+    set must be defined
+
+  see:
+    SETtruncate_
+
+  design:
+    check size
+    update actual size of set
+*/
+void qh_settruncate(qhT *qh, setT *set, int size) {
+
+  if (size < 0 || size > set->maxsize) {
+    qh_fprintf(qh, qh->qhmem.ferr, 6181, "qhull internal error (qh_settruncate): size %d out of bounds for set:\n", size);
+    qh_setprint(qh, qh->qhmem.ferr, "", set);
+    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
+  }
+  set->e[set->maxsize].i= size+1;   /* maybe overwritten */
+  set->e[size].p= NULL;
+} /* settruncate */
+
+/*---------------------------------
+
+  qh_setunique(qh, set, elem )
+    add elem to unsorted set unless it is already in set
+
+  notes:
+    returns 1 if it is appended
+
+  design:
+    if elem not in set
+      append elem to set
+*/
+int qh_setunique(qhT *qh, setT **set, void *elem) {
+
+  if (!qh_setin(*set, elem)) {
+    qh_setappend(qh, set, elem);
+    return 1;
+  }
+  return 0;
+} /* setunique */
+
+/*---------------------------------
+
+  qh_setzero(qh, set, index, size )
+    zero elements from index on
+    set actual size of set to size
+
+  notes:
+    set must be defined
+    the set becomes an indexed set (can not use FOREACH...)
+
+  see also:
+    qh_settruncate
+
+  design:
+    check index and size
+    update actual size
+    zero elements starting at e[index]
+*/
+void qh_setzero(qhT *qh, setT *set, int idx, int size) {
+  int count;
+
+  if (idx < 0 || idx >= size || size > set->maxsize) {
+    qh_fprintf(qh, qh->qhmem.ferr, 6182, "qhull internal error (qh_setzero): index %d or size %d out of bounds for set:\n", idx, size);
+    qh_setprint(qh, qh->qhmem.ferr, "", set);
+    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
+  }
+  set->e[set->maxsize].i=  size+1;  /* may be overwritten */
+  count= size - idx + 1;   /* +1 for NULL terminator */
+  memset((char *)SETelemaddr_(set, idx, void), 0, (size_t)count * SETelemsize);
+} /* setzero */
+
+
diff --git a/Cdir/random_r.c b/Cdir/random_r.c
new file mode 100644
--- /dev/null
+++ b/Cdir/random_r.c
@@ -0,0 +1,247 @@
+/*
  ---------------------------------
+
+   random_r.c and utilities
+     Park & Miller's minimimal standard random number generator
+     argc/argv conversion
+
+     Used by rbox.  Do not use 'qh' 
+*/
+
+#include "libqhull_r.h"
+#include "random_r.h"
+
+#include 
+#include 
+#include 
+
+#ifdef _MSC_VER  /* Microsoft Visual C++ -- warning level 4 */
+#pragma warning( disable : 4706)  /* assignment within conditional function */
+#pragma warning( disable : 4996)  /* function was declared deprecated(strcpy, localtime, etc.) */
+#endif
+
+/*---------------------------------
+
+ qh_argv_to_command(argc, argv, command, max_size )
+
+    build command from argc/argv
+    max_size is at least
+
+ returns:
+    a space-delimited string of options (just as typed)
+    returns false if max_size is too short
+
+ notes:
+    silently removes
+    makes option string easy to input and output
+    matches qh_argv_to_command_size()
+
+    argc may be 0
+*/
+int qh_argv_to_command(int argc, char *argv[], char* command, int max_size) {
+  int i, remaining;
+  char *s;
+  *command= '\0';  /* max_size > 0 */
+
+  if (argc) {
+    if ((s= strrchr( argv[0], '\\')) /* get filename w/o .exe extension */
+    || (s= strrchr( argv[0], '/')))
+        s++;
+    else
+        s= argv[0];
+    if ((int)strlen(s) < max_size)   /* WARN64 */
+        strcpy(command, s);
+    else
+        goto error_argv;
+    if ((s= strstr(command, ".EXE"))
+    ||  (s= strstr(command, ".exe")))
+        *s= '\0';
+  }
+  for (i=1; i < argc; i++) {
+    s= argv[i];
+    remaining= max_size - (int)strlen(command) - (int)strlen(s) - 2;   /* WARN64 */
+    if (!*s || strchr(s, ' ')) {
+      char *t= command + strlen(command);
+      remaining -= 2;
+      if (remaining < 0) {
+        goto error_argv;
+      }
+      *t++= ' ';
+      *t++= '"';
+      while (*s) {
+        if (*s == '"') {
+          if (--remaining < 0)
+            goto error_argv;
+          *t++= '\\';
+        }
+        *t++= *s++;
+      }
+      *t++= '"';
+      *t= '\0';
+    }else if (remaining < 0) {
+      goto error_argv;
+    }else
+      strcat(command, " ");
+      strcat(command, s);
+  }
+  return 1;
+
+error_argv:
+  return 0;
+} /* argv_to_command */
+
+/*---------------------------------
+
+qh_argv_to_command_size(argc, argv )
+
+    return size to allocate for qh_argv_to_command()
+
+notes:
+    argc may be 0
+    actual size is usually shorter
+*/
+int qh_argv_to_command_size(int argc, char *argv[]) {
+    unsigned int count= 1; /* null-terminator if argc==0 */
+    int i;
+    char *s;
+
+    for (i=0; i0 && strchr(argv[i], ' ')) {
+        count += 2;  /* quote delimiters */
+        for (s=argv[i]; *s; s++) {
+          if (*s == '"') {
+            count++;
+          }
+        }
+      }
+    }
+    return count;
+} /* argv_to_command_size */
+
+/*---------------------------------
+
+  qh_rand()
+  qh_srand(qh, seed )
+    generate pseudo-random number between 1 and 2^31 -2
+
+  notes:
+    For qhull and rbox, called from qh_RANDOMint(),etc. [user.h]
+
+    From Park & Miller's minimal standard random number generator
+      Communications of the ACM, 31:1192-1201, 1988.
+    Does not use 0 or 2^31 -1
+      this is silently enforced by qh_srand()
+    Can make 'Rn' much faster by moving qh_rand to qh_distplane
+*/
+
+/* Global variables and constants */
+
+#define qh_rand_a 16807
+#define qh_rand_m 2147483647
+#define qh_rand_q 127773  /* m div a */
+#define qh_rand_r 2836    /* m mod a */
+
+int qh_rand(qhT *qh) {
+    int lo, hi, test;
+    int seed = qh->last_random;
+
+    hi = seed / qh_rand_q;  /* seed div q */
+    lo = seed % qh_rand_q;  /* seed mod q */
+    test = qh_rand_a * lo - qh_rand_r * hi;
+    if (test > 0)
+        seed= test;
+    else
+        seed= test + qh_rand_m;
+    qh->last_random= seed;
+    /* seed = seed < qh_RANDOMmax/2 ? 0 : qh_RANDOMmax;  for testing */
+    /* seed = qh_RANDOMmax;  for testing */
+    return seed;
+} /* rand */
+
+void qh_srand(qhT *qh, int seed) {
+    if (seed < 1)
+        qh->last_random= 1;
+    else if (seed >= qh_rand_m)
+        qh->last_random= qh_rand_m - 1;
+    else
+        qh->last_random= seed;
+} /* qh_srand */
+
+/*---------------------------------
+
+qh_randomfactor(qh, scale, offset )
+  return a random factor r * scale + offset
+
+notes:
+  qh.RANDOMa/b are defined in global_r.c
+  qh_RANDOMint requires 'qh'
+*/
+realT qh_randomfactor(qhT *qh, realT scale, realT offset) {
+    realT randr;
+
+    randr= qh_RANDOMint;
+    return randr * scale + offset;
+} /* randomfactor */
+
+/*---------------------------------
+
+qh_randommatrix(qh, buffer, dim, rows )
+  generate a random dim X dim matrix in range [-1,1]
+  assumes buffer is [dim+1, dim]
+
+  returns:
+    sets buffer to random numbers
+    sets rows to rows of buffer
+    sets row[dim] as scratch row
+
+  notes:
+    qh_RANDOMint requires 'qh'
+*/
+void qh_randommatrix(qhT *qh, realT *buffer, int dim, realT **rows) {
+    int i, k;
+    realT **rowi, *coord, realr;
+
+    coord= buffer;
+    rowi= rows;
+    for (i=0; i < dim; i++) {
+        *(rowi++)= coord;
+        for (k=0; k < dim; k++) {
+            realr= qh_RANDOMint;
+            *(coord++)= 2.0 * realr/(qh_RANDOMmax+1) - 1.0;
+        }
+    }
+    *rowi= coord;
+} /* randommatrix */
+
+/*---------------------------------
+
+  qh_strtol( s, endp) qh_strtod( s, endp)
+    internal versions of strtol() and strtod()
+    does not skip trailing spaces
+  notes:
+    some implementations of strtol()/strtod() skip trailing spaces
+*/
+double qh_strtod(const char *s, char **endp) {
+  double result;
+
+  result= strtod(s, endp);
+  if (s < (*endp) && (*endp)[-1] == ' ')
+    (*endp)--;
+  return result;
+} /* strtod */
+
+int qh_strtol(const char *s, char **endp) {
+  int result;
+
+  result= (int) strtol(s, endp, 10);     /* WARN64 */
+  if (s< (*endp) && (*endp)[-1] == ' ')
+    (*endp)--;
+  return result;
+} /* strtol */
diff --git a/Cdir/stat_r.c b/Cdir/stat_r.c
new file mode 100644
--- /dev/null
+++ b/Cdir/stat_r.c
@@ -0,0 +1,682 @@
+/*
  ---------------------------------
+
+   stat_r.c
+   contains all statistics that are collected for qhull
+
+   see qh-stat_r.htm and stat_r.h
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull_r/stat_r.c#5 $$Change: 2062 $
+   $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
+*/
+
+#include "qhull_ra.h"
+
+/*========== functions in alphabetic order ================*/
+
+/*---------------------------------
+
+  qh_allstatA()
+    define statistics in groups of 20
+
+  notes:
+    (otherwise, 'gcc -O2' uses too much memory)
+    uses qhstat.next
+*/
+void qh_allstatA(qhT *qh) {
+
+   /* zdef_(type,name,doc,average) */
+  zzdef_(zdoc, Zdoc2, "precision statistics", -1);
+  zdef_(zinc, Znewvertex, NULL, -1);
+  zdef_(wadd, Wnewvertex, "ave. distance of a new vertex to a facet(!0s)", Znewvertex);
+  zzdef_(wmax, Wnewvertexmax, "max. distance of a new vertex to a facet", -1);
+  zdef_(wmax, Wvertexmax, "max. distance of an output vertex to a facet", -1);
+  zdef_(wmin, Wvertexmin, "min. distance of an output vertex to a facet", -1);
+  zdef_(wmin, Wmindenom, "min. denominator in hyperplane computation", -1);
+
+  qh->qhstat.precision= qh->qhstat.next;  /* call qh_precision for each of these */
+  zzdef_(zdoc, Zdoc3, "precision problems (corrected unless 'Q0' or an error)", -1);
+  zzdef_(zinc, Zcoplanarridges, "coplanar half ridges in output", -1);
+  zzdef_(zinc, Zconcaveridges, "concave half ridges in output", -1);
+  zzdef_(zinc, Zflippedfacets, "flipped facets", -1);
+  zzdef_(zinc, Zcoplanarhorizon, "coplanar horizon facets for new vertices", -1);
+  zzdef_(zinc, Zcoplanarpart, "coplanar points during partitioning", -1);
+  zzdef_(zinc, Zminnorm, "degenerate hyperplanes recomputed with gaussian elimination", -1);
+  zzdef_(zinc, Znearlysingular, "nearly singular or axis-parallel hyperplanes", -1);
+  zzdef_(zinc, Zback0, "zero divisors during back substitute", -1);
+  zzdef_(zinc, Zgauss0, "zero divisors during gaussian elimination", -1);
+  zzdef_(zinc, Zmultiridge, "ridges with multiple neighbors", -1);
+}
+void qh_allstatB(qhT *qh) {
+  zzdef_(zdoc, Zdoc1, "summary information", -1);
+  zdef_(zinc, Zvertices, "number of vertices in output", -1);
+  zdef_(zinc, Znumfacets, "number of facets in output", -1);
+  zdef_(zinc, Znonsimplicial, "number of non-simplicial facets in output", -1);
+  zdef_(zinc, Znowsimplicial, "number of simplicial facets that were merged", -1);
+  zdef_(zinc, Znumridges, "number of ridges in output", -1);
+  zdef_(zadd, Znumridges, "average number of ridges per facet", Znumfacets);
+  zdef_(zmax, Zmaxridges, "maximum number of ridges", -1);
+  zdef_(zadd, Znumneighbors, "average number of neighbors per facet", Znumfacets);
+  zdef_(zmax, Zmaxneighbors, "maximum number of neighbors", -1);
+  zdef_(zadd, Znumvertices, "average number of vertices per facet", Znumfacets);
+  zdef_(zmax, Zmaxvertices, "maximum number of vertices", -1);
+  zdef_(zadd, Znumvneighbors, "average number of neighbors per vertex", Zvertices);
+  zdef_(zmax, Zmaxvneighbors, "maximum number of neighbors", -1);
+  zdef_(wadd, Wcpu, "cpu seconds for qhull after input", -1);
+  zdef_(zinc, Ztotvertices, "vertices created altogether", -1);
+  zzdef_(zinc, Zsetplane, "facets created altogether", -1);
+  zdef_(zinc, Ztotridges, "ridges created altogether", -1);
+  zdef_(zinc, Zpostfacets, "facets before post merge", -1);
+  zdef_(zadd, Znummergetot, "average merges per facet(at most 511)", Znumfacets);
+  zdef_(zmax, Znummergemax, "  maximum merges for a facet(at most 511)", -1);
+  zdef_(zinc, Zangle, NULL, -1);
+  zdef_(wadd, Wangle, "average angle(cosine) of facet normals for all ridges", Zangle);
+  zdef_(wmax, Wanglemax, "  maximum angle(cosine) of facet normals across a ridge", -1);
+  zdef_(wmin, Wanglemin, "  minimum angle(cosine) of facet normals across a ridge", -1);
+  zdef_(wadd, Wareatot, "total area of facets", -1);
+  zdef_(wmax, Wareamax, "  maximum facet area", -1);
+  zdef_(wmin, Wareamin, "  minimum facet area", -1);
+}
+void qh_allstatC(qhT *qh) {
+  zdef_(zdoc, Zdoc9, "build hull statistics", -1);
+  zzdef_(zinc, Zprocessed, "points processed", -1);
+  zzdef_(zinc, Zretry, "retries due to precision problems", -1);
+  zdef_(wmax, Wretrymax, "  max. random joggle", -1);
+  zdef_(zmax, Zmaxvertex, "max. vertices at any one time", -1);
+  zdef_(zinc, Ztotvisible, "ave. visible facets per iteration", Zprocessed);
+  zdef_(zinc, Zinsidevisible, "  ave. visible facets without an horizon neighbor", Zprocessed);
+  zdef_(zadd, Zvisfacettot,  "  ave. facets deleted per iteration", Zprocessed);
+  zdef_(zmax, Zvisfacetmax,  "    maximum", -1);
+  zdef_(zadd, Zvisvertextot, "ave. visible vertices per iteration", Zprocessed);
+  zdef_(zmax, Zvisvertexmax, "    maximum", -1);
+  zdef_(zinc, Ztothorizon, "ave. horizon facets per iteration", Zprocessed);
+  zdef_(zadd, Znewfacettot,  "ave. new or merged facets per iteration", Zprocessed);
+  zdef_(zmax, Znewfacetmax,  "    maximum(includes initial simplex)", -1);
+  zdef_(wadd, Wnewbalance, "average new facet balance", Zprocessed);
+  zdef_(wadd, Wnewbalance2, "  standard deviation", -1);
+  zdef_(wadd, Wpbalance, "average partition balance", Zpbalance);
+  zdef_(wadd, Wpbalance2, "  standard deviation", -1);
+  zdef_(zinc, Zpbalance, "  number of trials", -1);
+  zdef_(zinc, Zsearchpoints, "searches of all points for initial simplex", -1);
+  zdef_(zinc, Zdetsimplex, "determinants computed(area & initial hull)", -1);
+  zdef_(zinc, Znoarea, "determinants not computed because vertex too low", -1);
+  zdef_(zinc, Znotmax, "points ignored(!above max_outside)", -1);
+  zdef_(zinc, Znotgood, "points ignored(!above a good facet)", -1);
+  zdef_(zinc, Znotgoodnew, "points ignored(didn't create a good new facet)", -1);
+  zdef_(zinc, Zgoodfacet, "good facets found", -1);
+  zzdef_(zinc, Znumvisibility, "distance tests for facet visibility", -1);
+  zdef_(zinc, Zdistvertex, "distance tests to report minimum vertex", -1);
+  zzdef_(zinc, Ztotcheck, "points checked for facets' outer planes", -1);
+  zzdef_(zinc, Zcheckpart, "  ave. distance tests per check", Ztotcheck);
+}
+void qh_allstatD(qhT *qh) {
+  zdef_(zinc, Zvisit, "resets of visit_id", -1);
+  zdef_(zinc, Zvvisit, "  resets of vertex_visit", -1);
+  zdef_(zmax, Zvisit2max, "  max visit_id/2", -1);
+  zdef_(zmax, Zvvisit2max, "  max vertex_visit/2", -1);
+
+  zdef_(zdoc, Zdoc4, "partitioning statistics(see previous for outer planes)", -1);
+  zzdef_(zadd, Zdelvertextot, "total vertices deleted", -1);
+  zdef_(zmax, Zdelvertexmax, "    maximum vertices deleted per iteration", -1);
+  zdef_(zinc, Zfindbest, "calls to findbest", -1);
+  zdef_(zadd, Zfindbesttot, " ave. facets tested", Zfindbest);
+  zdef_(zmax, Zfindbestmax, " max. facets tested", -1);
+  zdef_(zadd, Zfindcoplanar, " ave. coplanar search", Zfindbest);
+  zdef_(zinc, Zfindnew, "calls to findbestnew", -1);
+  zdef_(zadd, Zfindnewtot, " ave. facets tested", Zfindnew);
+  zdef_(zmax, Zfindnewmax, " max. facets tested", -1);
+  zdef_(zinc, Zfindnewjump, " ave. clearly better", Zfindnew);
+  zdef_(zinc, Zfindnewsharp, " calls due to qh_sharpnewfacets", -1);
+  zdef_(zinc, Zfindhorizon, "calls to findhorizon", -1);
+  zdef_(zadd, Zfindhorizontot, " ave. facets tested", Zfindhorizon);
+  zdef_(zmax, Zfindhorizonmax, " max. facets tested", -1);
+  zdef_(zinc, Zfindjump,       " ave. clearly better", Zfindhorizon);
+  zdef_(zinc, Zparthorizon, " horizon facets better than bestfacet", -1);
+  zdef_(zinc, Zpartangle, "angle tests for repartitioned coplanar points", -1);
+  zdef_(zinc, Zpartflip, "  repartitioned coplanar points for flipped orientation", -1);
+}
+void qh_allstatE(qhT *qh) {
+  zdef_(zinc, Zpartinside, "inside points", -1);
+  zdef_(zinc, Zpartnear, "  inside points kept with a facet", -1);
+  zdef_(zinc, Zcoplanarinside, "  inside points that were coplanar with a facet", -1);
+  zdef_(zinc, Zbestlower, "calls to findbestlower", -1);
+  zdef_(zinc, Zbestlowerv, "  with search of vertex neighbors", -1);
+  zdef_(zinc, Zbestlowerall, "  with rare search of all facets", -1);
+  zdef_(zmax, Zbestloweralln, "  facets per search of all facets", -1);
+  zdef_(wadd, Wmaxout, "difference in max_outside at final check", -1);
+  zzdef_(zinc, Zpartitionall, "distance tests for initial partition", -1);
+  zdef_(zinc, Ztotpartition, "partitions of a point", -1);
+  zzdef_(zinc, Zpartition, "distance tests for partitioning", -1);
+  zzdef_(zinc, Zdistcheck, "distance tests for checking flipped facets", -1);
+  zzdef_(zinc, Zdistconvex, "distance tests for checking convexity", -1);
+  zdef_(zinc, Zdistgood, "distance tests for checking good point", -1);
+  zdef_(zinc, Zdistio, "distance tests for output", -1);
+  zdef_(zinc, Zdiststat, "distance tests for statistics", -1);
+  zdef_(zinc, Zdistplane, "total number of distance tests", -1);
+  zdef_(zinc, Ztotpartcoplanar, "partitions of coplanar points or deleted vertices", -1);
+  zzdef_(zinc, Zpartcoplanar, "   distance tests for these partitions", -1);
+  zdef_(zinc, Zcomputefurthest, "distance tests for computing furthest", -1);
+}
+void qh_allstatE2(qhT *qh) {
+  zdef_(zdoc, Zdoc5, "statistics for matching ridges", -1);
+  zdef_(zinc, Zhashlookup, "total lookups for matching ridges of new facets", -1);
+  zdef_(zinc, Zhashtests, "average number of tests to match a ridge", Zhashlookup);
+  zdef_(zinc, Zhashridge, "total lookups of subridges(duplicates and boundary)", -1);
+  zdef_(zinc, Zhashridgetest, "average number of tests per subridge", Zhashridge);
+  zdef_(zinc, Zdupsame, "duplicated ridges in same merge cycle", -1);
+  zdef_(zinc, Zdupflip, "duplicated ridges with flipped facets", -1);
+
+  zdef_(zdoc, Zdoc6, "statistics for determining merges", -1);
+  zdef_(zinc, Zangletests, "angles computed for ridge convexity", -1);
+  zdef_(zinc, Zbestcentrum, "best merges used centrum instead of vertices",-1);
+  zzdef_(zinc, Zbestdist, "distance tests for best merge", -1);
+  zzdef_(zinc, Zcentrumtests, "distance tests for centrum convexity", -1);
+  zzdef_(zinc, Zdistzero, "distance tests for checking simplicial convexity", -1);
+  zdef_(zinc, Zcoplanarangle, "coplanar angles in getmergeset", -1);
+  zdef_(zinc, Zcoplanarcentrum, "coplanar centrums in getmergeset", -1);
+  zdef_(zinc, Zconcaveridge, "concave ridges in getmergeset", -1);
+}
+void qh_allstatF(qhT *qh) {
+  zdef_(zdoc, Zdoc7, "statistics for merging", -1);
+  zdef_(zinc, Zpremergetot, "merge iterations", -1);
+  zdef_(zadd, Zmergeinittot, "ave. initial non-convex ridges per iteration", Zpremergetot);
+  zdef_(zadd, Zmergeinitmax, "  maximum", -1);
+  zdef_(zadd, Zmergesettot, "  ave. additional non-convex ridges per iteration", Zpremergetot);
+  zdef_(zadd, Zmergesetmax, "  maximum additional in one pass", -1);
+  zdef_(zadd, Zmergeinittot2, "initial non-convex ridges for post merging", -1);
+  zdef_(zadd, Zmergesettot2, "  additional non-convex ridges", -1);
+  zdef_(wmax, Wmaxoutside, "max distance of vertex or coplanar point above facet(w/roundoff)", -1);
+  zdef_(wmin, Wminvertex, "max distance of merged vertex below facet(or roundoff)", -1);
+  zdef_(zinc, Zwidefacet, "centrums frozen due to a wide merge", -1);
+  zdef_(zinc, Zwidevertices, "centrums frozen due to extra vertices", -1);
+  zzdef_(zinc, Ztotmerge, "total number of facets or cycles of facets merged", -1);
+  zdef_(zinc, Zmergesimplex, "merged a simplex", -1);
+  zdef_(zinc, Zonehorizon, "simplices merged into coplanar horizon", -1);
+  zzdef_(zinc, Zcyclehorizon, "cycles of facets merged into coplanar horizon", -1);
+  zzdef_(zadd, Zcyclefacettot, "  ave. facets per cycle", Zcyclehorizon);
+  zdef_(zmax, Zcyclefacetmax, "  max. facets", -1);
+  zdef_(zinc, Zmergeintohorizon, "new facets merged into horizon", -1);
+  zdef_(zinc, Zmergenew, "new facets merged", -1);
+  zdef_(zinc, Zmergehorizon, "horizon facets merged into new facets", -1);
+  zdef_(zinc, Zmergevertex, "vertices deleted by merging", -1);
+  zdef_(zinc, Zcyclevertex, "vertices deleted by merging into coplanar horizon", -1);
+  zdef_(zinc, Zdegenvertex, "vertices deleted by degenerate facet", -1);
+  zdef_(zinc, Zmergeflipdup, "merges due to flipped facets in duplicated ridge", -1);
+  zdef_(zinc, Zneighbor, "merges due to redundant neighbors", -1);
+  zdef_(zadd, Ztestvneighbor, "non-convex vertex neighbors", -1);
+}
+void qh_allstatG(qhT *qh) {
+  zdef_(zinc, Zacoplanar, "merges due to angle coplanar facets", -1);
+  zdef_(wadd, Wacoplanartot, "  average merge distance", Zacoplanar);
+  zdef_(wmax, Wacoplanarmax, "  maximum merge distance", -1);
+  zdef_(zinc, Zcoplanar, "merges due to coplanar facets", -1);
+  zdef_(wadd, Wcoplanartot, "  average merge distance", Zcoplanar);
+  zdef_(wmax, Wcoplanarmax, "  maximum merge distance", -1);
+  zdef_(zinc, Zconcave, "merges due to concave facets", -1);
+  zdef_(wadd, Wconcavetot, "  average merge distance", Zconcave);
+  zdef_(wmax, Wconcavemax, "  maximum merge distance", -1);
+  zdef_(zinc, Zavoidold, "coplanar/concave merges due to avoiding old merge", -1);
+  zdef_(wadd, Wavoidoldtot, "  average merge distance", Zavoidold);
+  zdef_(wmax, Wavoidoldmax, "  maximum merge distance", -1);
+  zdef_(zinc, Zdegen, "merges due to degenerate facets", -1);
+  zdef_(wadd, Wdegentot, "  average merge distance", Zdegen);
+  zdef_(wmax, Wdegenmax, "  maximum merge distance", -1);
+  zdef_(zinc, Zflipped, "merges due to removing flipped facets", -1);
+  zdef_(wadd, Wflippedtot, "  average merge distance", Zflipped);
+  zdef_(wmax, Wflippedmax, "  maximum merge distance", -1);
+  zdef_(zinc, Zduplicate, "merges due to duplicated ridges", -1);
+  zdef_(wadd, Wduplicatetot, "  average merge distance", Zduplicate);
+  zdef_(wmax, Wduplicatemax, "  maximum merge distance", -1);
+}
+void qh_allstatH(qhT *qh) {
+  zdef_(zdoc, Zdoc8, "renamed vertex statistics", -1);
+  zdef_(zinc, Zrenameshare, "renamed vertices shared by two facets", -1);
+  zdef_(zinc, Zrenamepinch, "renamed vertices in a pinched facet", -1);
+  zdef_(zinc, Zrenameall, "renamed vertices shared by multiple facets", -1);
+  zdef_(zinc, Zfindfail, "rename failures due to duplicated ridges", -1);
+  zdef_(zinc, Zdupridge, "  duplicate ridges detected", -1);
+  zdef_(zinc, Zdelridge, "deleted ridges due to renamed vertices", -1);
+  zdef_(zinc, Zdropneighbor, "dropped neighbors due to renamed vertices", -1);
+  zdef_(zinc, Zdropdegen, "degenerate facets due to dropped neighbors", -1);
+  zdef_(zinc, Zdelfacetdup, "  facets deleted because of no neighbors", -1);
+  zdef_(zinc, Zremvertex, "vertices removed from facets due to no ridges", -1);
+  zdef_(zinc, Zremvertexdel, "  deleted", -1);
+  zdef_(zinc, Zintersectnum, "vertex intersections for locating redundant vertices", -1);
+  zdef_(zinc, Zintersectfail, "intersections failed to find a redundant vertex", -1);
+  zdef_(zinc, Zintersect, "intersections found redundant vertices", -1);
+  zdef_(zadd, Zintersecttot, "   ave. number found per vertex", Zintersect);
+  zdef_(zmax, Zintersectmax, "   max. found for a vertex", -1);
+  zdef_(zinc, Zvertexridge, NULL, -1);
+  zdef_(zadd, Zvertexridgetot, "  ave. number of ridges per tested vertex", Zvertexridge);
+  zdef_(zmax, Zvertexridgemax, "  max. number of ridges per tested vertex", -1);
+
+  zdef_(zdoc, Zdoc10, "memory usage statistics(in bytes)", -1);
+  zdef_(zadd, Zmemfacets, "for facets and their normals, neighbor and vertex sets", -1);
+  zdef_(zadd, Zmemvertices, "for vertices and their neighbor sets", -1);
+  zdef_(zadd, Zmempoints, "for input points, outside and coplanar sets, and qhT",-1);
+  zdef_(zadd, Zmemridges, "for ridges and their vertex sets", -1);
+} /* allstat */
+
+void qh_allstatI(qhT *qh) {
+  qh->qhstat.vridges= qh->qhstat.next;
+  zzdef_(zdoc, Zdoc11, "Voronoi ridge statistics", -1);
+  zzdef_(zinc, Zridge, "non-simplicial Voronoi vertices for all ridges", -1);
+  zzdef_(wadd, Wridge, "  ave. distance to ridge", Zridge);
+  zzdef_(wmax, Wridgemax, "  max. distance to ridge", -1);
+  zzdef_(zinc, Zridgemid, "bounded ridges", -1);
+  zzdef_(wadd, Wridgemid, "  ave. distance of midpoint to ridge", Zridgemid);
+  zzdef_(wmax, Wridgemidmax, "  max. distance of midpoint to ridge", -1);
+  zzdef_(zinc, Zridgeok, "bounded ridges with ok normal", -1);
+  zzdef_(wadd, Wridgeok, "  ave. angle to ridge", Zridgeok);
+  zzdef_(wmax, Wridgeokmax, "  max. angle to ridge", -1);
+  zzdef_(zinc, Zridge0, "bounded ridges with near-zero normal", -1);
+  zzdef_(wadd, Wridge0, "  ave. angle to ridge", Zridge0);
+  zzdef_(wmax, Wridge0max, "  max. angle to ridge", -1);
+
+  zdef_(zdoc, Zdoc12, "Triangulation statistics(Qt)", -1);
+  zdef_(zinc, Ztricoplanar, "non-simplicial facets triangulated", -1);
+  zdef_(zadd, Ztricoplanartot, "  ave. new facets created(may be deleted)", Ztricoplanar);
+  zdef_(zmax, Ztricoplanarmax, "  max. new facets created", -1);
+  zdef_(zinc, Ztrinull, "null new facets deleted(duplicated vertex)", -1);
+  zdef_(zinc, Ztrimirror, "mirrored pairs of new facets deleted(same vertices)", -1);
+  zdef_(zinc, Ztridegen, "degenerate new facets in output(same ridge)", -1);
+} /* allstat */
+
+/*---------------------------------
+
+  qh_allstatistics()
+    reset printed flag for all statistics
+*/
+void qh_allstatistics(qhT *qh) {
+  int i;
+
+  for(i=ZEND; i--; )
+    qh->qhstat.printed[i]= False;
+} /* allstatistics */
+
+#if qh_KEEPstatistics
+/*---------------------------------
+
+  qh_collectstatistics()
+    collect statistics for qh.facet_list
+
+*/
+void qh_collectstatistics(qhT *qh) {
+  facetT *facet, *neighbor, **neighborp;
+  vertexT *vertex, **vertexp;
+  realT dotproduct, dist;
+  int sizneighbors, sizridges, sizvertices, i;
+
+  qh->old_randomdist= qh->RANDOMdist;
+  qh->RANDOMdist= False;
+  zval_(Zmempoints)= qh->num_points * qh->normal_size + sizeof(qhT);
+  zval_(Zmemfacets)= 0;
+  zval_(Zmemridges)= 0;
+  zval_(Zmemvertices)= 0;
+  zval_(Zangle)= 0;
+  wval_(Wangle)= 0.0;
+  zval_(Znumridges)= 0;
+  zval_(Znumfacets)= 0;
+  zval_(Znumneighbors)= 0;
+  zval_(Znumvertices)= 0;
+  zval_(Znumvneighbors)= 0;
+  zval_(Znummergetot)= 0;
+  zval_(Znummergemax)= 0;
+  zval_(Zvertices)= qh->num_vertices - qh_setsize(qh, qh->del_vertices);
+  if (qh->MERGING || qh->APPROXhull || qh->JOGGLEmax < REALmax/2)
+    wmax_(Wmaxoutside, qh->max_outside);
+  if (qh->MERGING)
+    wmin_(Wminvertex, qh->min_vertex);
+  FORALLfacets
+    facet->seen= False;
+  if (qh->DELAUNAY) {
+    FORALLfacets {
+      if (facet->upperdelaunay != qh->UPPERdelaunay)
+        facet->seen= True; /* remove from angle statistics */
+    }
+  }
+  FORALLfacets {
+    if (facet->visible && qh->NEWfacets)
+      continue;
+    sizvertices= qh_setsize(qh, facet->vertices);
+    sizneighbors= qh_setsize(qh, facet->neighbors);
+    sizridges= qh_setsize(qh, facet->ridges);
+    zinc_(Znumfacets);
+    zadd_(Znumvertices, sizvertices);
+    zmax_(Zmaxvertices, sizvertices);
+    zadd_(Znumneighbors, sizneighbors);
+    zmax_(Zmaxneighbors, sizneighbors);
+    zadd_(Znummergetot, facet->nummerge);
+    i= facet->nummerge; /* avoid warnings */
+    zmax_(Znummergemax, i);
+    if (!facet->simplicial) {
+      if (sizvertices == qh->hull_dim) {
+        zinc_(Znowsimplicial);
+      }else {
+        zinc_(Znonsimplicial);
+      }
+    }
+    if (sizridges) {
+      zadd_(Znumridges, sizridges);
+      zmax_(Zmaxridges, sizridges);
+    }
+    zadd_(Zmemfacets, sizeof(facetT) + qh->normal_size + 2*sizeof(setT)
+       + SETelemsize * (sizneighbors + sizvertices));
+    if (facet->ridges) {
+      zadd_(Zmemridges,
+         sizeof(setT) + SETelemsize * sizridges + sizridges *
+         (sizeof(ridgeT) + sizeof(setT) + SETelemsize * (qh->hull_dim-1))/2);
+    }
+    if (facet->outsideset)
+      zadd_(Zmempoints, sizeof(setT) + SETelemsize * qh_setsize(qh, facet->outsideset));
+    if (facet->coplanarset)
+      zadd_(Zmempoints, sizeof(setT) + SETelemsize * qh_setsize(qh, facet->coplanarset));
+    if (facet->seen) /* Delaunay upper envelope */
+      continue;
+    facet->seen= True;
+    FOREACHneighbor_(facet) {
+      if (neighbor == qh_DUPLICATEridge || neighbor == qh_MERGEridge
+          || neighbor->seen || !facet->normal || !neighbor->normal)
+        continue;
+      dotproduct= qh_getangle(qh, facet->normal, neighbor->normal);
+      zinc_(Zangle);
+      wadd_(Wangle, dotproduct);
+      wmax_(Wanglemax, dotproduct)
+      wmin_(Wanglemin, dotproduct)
+    }
+    if (facet->normal) {
+      FOREACHvertex_(facet->vertices) {
+        zinc_(Zdiststat);
+        qh_distplane(qh, vertex->point, facet, &dist);
+        wmax_(Wvertexmax, dist);
+        wmin_(Wvertexmin, dist);
+      }
+    }
+  }
+  FORALLvertices {
+    if (vertex->deleted)
+      continue;
+    zadd_(Zmemvertices, sizeof(vertexT));
+    if (vertex->neighbors) {
+      sizneighbors= qh_setsize(qh, vertex->neighbors);
+      zadd_(Znumvneighbors, sizneighbors);
+      zmax_(Zmaxvneighbors, sizneighbors);
+      zadd_(Zmemvertices, sizeof(vertexT) + SETelemsize * sizneighbors);
+    }
+  }
+  qh->RANDOMdist= qh->old_randomdist;
+} /* collectstatistics */
+#endif /* qh_KEEPstatistics */
+
+/*---------------------------------
+
+  qh_initstatistics(qh)
+    initialize statistics
+
+  notes:
+  NOerrors -- qh_initstatistics can not use qh_errexit(), qh_fprintf, or qh.ferr
+  On first call, only qhmem.ferr is defined.  qh_memalloc is not setup.
+  Also invoked by QhullQh().
+*/
+void qh_initstatistics(qhT *qh) {
+  int i;
+  realT realx;
+  int intx;
+
+  qh->qhstat.next= 0;
+  qh_allstatA(qh);
+  qh_allstatB(qh);
+  qh_allstatC(qh);
+  qh_allstatD(qh);
+  qh_allstatE(qh);
+  qh_allstatE2(qh);
+  qh_allstatF(qh);
+  qh_allstatG(qh);
+  qh_allstatH(qh);
+  qh_allstatI(qh);
+  if (qh->qhstat.next > (int)sizeof(qh->qhstat.id)) {
+    qh_fprintf(qh, qh->qhmem.ferr, 6184, "qhull error (qh_initstatistics): increase size of qhstat.id[].\n\
+      qhstat.next %d should be <= sizeof(qh->qhstat.id) %d\n", qh->qhstat.next, (int)sizeof(qh->qhstat.id));
+#if 0 /* for locating error, Znumridges should be duplicated */
+    for(i=0; i < ZEND; i++) {
+      int j;
+      for(j=i+1; j < ZEND; j++) {
+        if (qh->qhstat.id[i] == qh->qhstat.id[j]) {
+          qh_fprintf(qh, qh->qhmem.ferr, 6185, "qhull error (qh_initstatistics): duplicated statistic %d at indices %d and %d\n",
+              qh->qhstat.id[i], i, j);
+        }
+      }
+    }
+#endif
+    qh_exit(qh_ERRqhull);  /* can not use qh_errexit() */
+  }
+  qh->qhstat.init[zinc].i= 0;
+  qh->qhstat.init[zadd].i= 0;
+  qh->qhstat.init[zmin].i= INT_MAX;
+  qh->qhstat.init[zmax].i= INT_MIN;
+  qh->qhstat.init[wadd].r= 0;
+  qh->qhstat.init[wmin].r= REALmax;
+  qh->qhstat.init[wmax].r= -REALmax;
+  for(i=0; i < ZEND; i++) {
+    if (qh->qhstat.type[i] > ZTYPEreal) {
+      realx= qh->qhstat.init[(unsigned char)(qh->qhstat.type[i])].r;
+      qh->qhstat.stats[i].r= realx;
+    }else if (qh->qhstat.type[i] != zdoc) {
+      intx= qh->qhstat.init[(unsigned char)(qh->qhstat.type[i])].i;
+      qh->qhstat.stats[i].i= intx;
+    }
+  }
+} /* initstatistics */
+
+/*---------------------------------
+
+  qh_newstats(qh, )
+    returns True if statistics for zdoc
+
+  returns:
+    next zdoc
+*/
+boolT qh_newstats(qhT *qh, int idx, int *nextindex) {
+  boolT isnew= False;
+  int start, i;
+
+  if (qh->qhstat.type[qh->qhstat.id[idx]] == zdoc)
+    start= idx+1;
+  else
+    start= idx;
+  for(i= start; i < qh->qhstat.next && qh->qhstat.type[qh->qhstat.id[i]] != zdoc; i++) {
+    if (!qh_nostatistic(qh, qh->qhstat.id[i]) && !qh->qhstat.printed[qh->qhstat.id[i]])
+        isnew= True;
+  }
+  *nextindex= i;
+  return isnew;
+} /* newstats */
+
+/*---------------------------------
+
+  qh_nostatistic(qh, index )
+    true if no statistic to print
+*/
+boolT qh_nostatistic(qhT *qh, int i) {
+
+  if ((qh->qhstat.type[i] > ZTYPEreal
+       &&qh->qhstat.stats[i].r == qh->qhstat.init[(unsigned char)(qh->qhstat.type[i])].r)
+      || (qh->qhstat.type[i] < ZTYPEreal
+          &&qh->qhstat.stats[i].i == qh->qhstat.init[(unsigned char)(qh->qhstat.type[i])].i))
+    return True;
+  return False;
+} /* nostatistic */
+
+#if qh_KEEPstatistics
+/*---------------------------------
+
+  qh_printallstatistics(qh, fp, string )
+    print all statistics with header 'string'
+*/
+void qh_printallstatistics(qhT *qh, FILE *fp, const char *string) {
+
+  qh_allstatistics(qh);
+  qh_collectstatistics(qh);
+  qh_printstatistics(qh, fp, string);
+  qh_memstatistics(qh, fp);
+}
+
+
+/*---------------------------------
+
+  qh_printstatistics(qh, fp, string )
+    print statistics to a file with header 'string'
+    skips statistics with qhstat.printed[] (reset with qh_allstatistics)
+
+  see:
+    qh_printallstatistics()
+*/
+void qh_printstatistics(qhT *qh, FILE *fp, const char *string) {
+  int i, k;
+  realT ave;
+
+  if (qh->num_points != qh->num_vertices) {
+    wval_(Wpbalance)= 0;
+    wval_(Wpbalance2)= 0;
+  }else
+    wval_(Wpbalance2)= qh_stddev(zval_(Zpbalance), wval_(Wpbalance),
+                                 wval_(Wpbalance2), &ave);
+  wval_(Wnewbalance2)= qh_stddev(zval_(Zprocessed), wval_(Wnewbalance),
+                                 wval_(Wnewbalance2), &ave);
+  qh_fprintf(qh, fp, 9350, "\n\
+%s\n\
+ qhull invoked by: %s | %s\n%s with options:\n%s\n", string, qh->rbox_command,
+     qh->qhull_command, qh_version, qh->qhull_options);
+  qh_fprintf(qh, fp, 9351, "\nprecision constants:\n\
+ %6.2g max. abs. coordinate in the (transformed) input('Qbd:n')\n\
+ %6.2g max. roundoff error for distance computation('En')\n\
+ %6.2g max. roundoff error for angle computations\n\
+ %6.2g min. distance for outside points ('Wn')\n\
+ %6.2g min. distance for visible facets ('Vn')\n\
+ %6.2g max. distance for coplanar facets ('Un')\n\
+ %6.2g max. facet width for recomputing centrum and area\n\
+",
+  qh->MAXabs_coord, qh->DISTround, qh->ANGLEround, qh->MINoutside,
+        qh->MINvisible, qh->MAXcoplanar, qh->WIDEfacet);
+  if (qh->KEEPnearinside)
+    qh_fprintf(qh, fp, 9352, "\
+ %6.2g max. distance for near-inside points\n", qh->NEARinside);
+  if (qh->premerge_cos < REALmax/2) qh_fprintf(qh, fp, 9353, "\
+ %6.2g max. cosine for pre-merge angle\n", qh->premerge_cos);
+  if (qh->PREmerge) qh_fprintf(qh, fp, 9354, "\
+ %6.2g radius of pre-merge centrum\n", qh->premerge_centrum);
+  if (qh->postmerge_cos < REALmax/2) qh_fprintf(qh, fp, 9355, "\
+ %6.2g max. cosine for post-merge angle\n", qh->postmerge_cos);
+  if (qh->POSTmerge) qh_fprintf(qh, fp, 9356, "\
+ %6.2g radius of post-merge centrum\n", qh->postmerge_centrum);
+  qh_fprintf(qh, fp, 9357, "\
+ %6.2g max. distance for merging two simplicial facets\n\
+ %6.2g max. roundoff error for arithmetic operations\n\
+ %6.2g min. denominator for divisions\n\
+  zero diagonal for Gauss: ", qh->ONEmerge, REALepsilon, qh->MINdenom);
+  for(k=0; k < qh->hull_dim; k++)
+    qh_fprintf(qh, fp, 9358, "%6.2e ", qh->NEARzero[k]);
+  qh_fprintf(qh, fp, 9359, "\n\n");
+  for(i=0 ; i < qh->qhstat.next; )
+    qh_printstats(qh, fp, i, &i);
+} /* printstatistics */
+#endif /* qh_KEEPstatistics */
+
+/*---------------------------------
+
+  qh_printstatlevel(qh, fp, id )
+    print level information for a statistic
+
+  notes:
+    nop if id >= ZEND, printed, or same as initial value
+*/
+void qh_printstatlevel(qhT *qh, FILE *fp, int id) {
+#define NULLfield "       "
+
+  if (id >= ZEND || qh->qhstat.printed[id])
+    return;
+  if (qh->qhstat.type[id] == zdoc) {
+    qh_fprintf(qh, fp, 9360, "%s\n", qh->qhstat.doc[id]);
+    return;
+  }
+  if (qh_nostatistic(qh, id) || !qh->qhstat.doc[id])
+    return;
+  qh->qhstat.printed[id]= True;
+  if (qh->qhstat.count[id] != -1
+      && qh->qhstat.stats[(unsigned char)(qh->qhstat.count[id])].i == 0)
+    qh_fprintf(qh, fp, 9361, " *0 cnt*");
+  else if (qh->qhstat.type[id] >= ZTYPEreal && qh->qhstat.count[id] == -1)
+    qh_fprintf(qh, fp, 9362, "%7.2g", qh->qhstat.stats[id].r);
+  else if (qh->qhstat.type[id] >= ZTYPEreal && qh->qhstat.count[id] != -1)
+    qh_fprintf(qh, fp, 9363, "%7.2g", qh->qhstat.stats[id].r/ qh->qhstat.stats[(unsigned char)(qh->qhstat.count[id])].i);
+  else if (qh->qhstat.type[id] < ZTYPEreal && qh->qhstat.count[id] == -1)
+    qh_fprintf(qh, fp, 9364, "%7d", qh->qhstat.stats[id].i);
+  else if (qh->qhstat.type[id] < ZTYPEreal && qh->qhstat.count[id] != -1)
+    qh_fprintf(qh, fp, 9365, "%7.3g", (realT) qh->qhstat.stats[id].i / qh->qhstat.stats[(unsigned char)(qh->qhstat.count[id])].i);
+  qh_fprintf(qh, fp, 9366, " %s\n", qh->qhstat.doc[id]);
+} /* printstatlevel */
+
+
+/*---------------------------------
+
+  qh_printstats(qh, fp, index, nextindex )
+    print statistics for a zdoc group
+
+  returns:
+    next zdoc if non-null
+*/
+void qh_printstats(qhT *qh, FILE *fp, int idx, int *nextindex) {
+  int j, nexti;
+
+  if (qh_newstats(qh, idx, &nexti)) {
+    qh_fprintf(qh, fp, 9367, "\n");
+    for (j=idx; jqhstat.id[j]);
+  }
+  if (nextindex)
+    *nextindex= nexti;
+} /* printstats */
+
+#if qh_KEEPstatistics
+
+/*---------------------------------
+
+  qh_stddev(num, tot, tot2, ave )
+    compute the standard deviation and average from statistics
+
+    tot2 is the sum of the squares
+  notes:
+    computes r.m.s.:
+      (x-ave)^2
+      == x^2 - 2x tot/num +   (tot/num)^2
+      == tot2 - 2 tot tot/num + tot tot/num
+      == tot2 - tot ave
+*/
+realT qh_stddev(int num, realT tot, realT tot2, realT *ave) {
+  realT stddev;
+
+  *ave= tot/num;
+  stddev= sqrt(tot2/num - *ave * *ave);
+  return stddev;
+} /* stddev */
+
+#endif /* qh_KEEPstatistics */
+
+#if !qh_KEEPstatistics
+void    qh_collectstatistics(qhT *qh) {}
+void    qh_printallstatistics(qhT *qh, FILE *fp, char *string) {};
+void    qh_printstatistics(qhT *qh, FILE *fp, char *string) {}
+#endif
+
diff --git a/Cdir/user_r.c b/Cdir/user_r.c
new file mode 100644
--- /dev/null
+++ b/Cdir/user_r.c
@@ -0,0 +1,527 @@
+/*
  ---------------------------------
+
+   user.c
+   user redefinable functions
+
+   see user2_r.c for qh_fprintf, qh_malloc, qh_free
+
+   see README.txt  see COPYING.txt for copyright information.
+
+   see libqhull_r.h for data structures, macros, and user-callable functions.
+
+   see user_eg.c, user_eg2.c, and unix.c for examples.
+
+   see user.h for user-definable constants
+
+      use qh_NOmem in mem_r.h to turn off memory management
+      use qh_NOmerge in user.h to turn off facet merging
+      set qh_KEEPstatistics in user.h to 0 to turn off statistics
+
+   This is unsupported software.  You're welcome to make changes,
+   but you're on your own if something goes wrong.  Use 'Tc' to
+   check frequently.  Usually qhull will report an error if
+   a data structure becomes inconsistent.  If so, it also reports
+   the last point added to the hull, e.g., 102.  You can then trace
+   the execution of qhull with "T4P102".
+
+   Please report any errors that you fix to qhull@qhull.org
+
+   Qhull-template is a template for calling qhull from within your application
+
+   if you recompile and load this module, then user.o will not be loaded
+   from qhull.a
+
+   you can add additional quick allocation sizes in qh_user_memsizes
+
+   if the other functions here are redefined to not use qh_print...,
+   then io.o will not be loaded from qhull.a.  See user_eg_r.c for an
+   example.  We recommend keeping io.o for the extra debugging
+   information it supplies.
+*/
+
+#include "qhull_ra.h"
+
+#include 
+
+/*---------------------------------
+
+  Qhull-template
+    Template for calling qhull from inside your program
+
+  returns:
+    exit code(see qh_ERR... in libqhull_r.h)
+    all memory freed
+
+  notes:
+    This can be called any number of times.
+
+*/
+#if 0
+{
+  int dim;                  /* dimension of points */
+  int numpoints;            /* number of points */
+  coordT *points;           /* array of coordinates for each point */
+  boolT ismalloc;           /* True if qhull should free points in qh_freeqhull() or reallocation */
+  char flags[]= "qhull Tv"; /* option flags for qhull, see qh_opt.htm */
+  FILE *outfile= stdout;    /* output from qh_produce_output(qh)
+                               use NULL to skip qh_produce_output(qh) */
+  FILE *errfile= stderr;    /* error messages from qhull code */
+  int exitcode;             /* 0 if no error from qhull */
+  facetT *facet;            /* set by FORALLfacets */
+  int curlong, totlong;     /* memory remaining after qh_memfreeshort */
+
+  qhT qh_qh;                /* Qhull's data structure.  First argument of most calls */
+  qhT *qh= &qh_qh;          /* Alternatively -- qhT *qh= (qhT*)malloc(sizeof(qhT)) */
+
+  QHULL_LIB_CHECK /* Check for compatible library */
+
+  qh_zero(qh, errfile);
+
+  /* initialize dim, numpoints, points[], ismalloc here */
+  exitcode= qh_new_qhull(qh, dim, numpoints, points, ismalloc,
+                      flags, outfile, errfile);
+  if (!exitcode) {                  /* if no error */
+    /* 'qh->facet_list' contains the convex hull */
+    FORALLfacets {
+       /* ... your code ... */
+    }
+  }
+  qh_freeqhull(qh, !qh_ALL);
+  qh_memfreeshort(qh, &curlong, &totlong);
+  if (curlong || totlong)
+    qh_fprintf(qh, errfile, 7068, "qhull internal warning (main): did not free %d bytes of long memory(%d pieces)\n", totlong, curlong);
+}
+#endif
+
+/*---------------------------------
+
+  qh_new_qhull(qh, dim, numpoints, points, ismalloc, qhull_cmd, outfile, errfile )
+    Run qhull and return results in qh.
+    Returns exitcode (0 if no errors).
+    Before first call, either call qh_zero(qh, errfile), or set qh to all zero.
+
+  notes:
+    do not modify points until finished with results.
+      The qhull data structure contains pointers into the points array.
+    do not call qhull functions before qh_new_qhull().
+      The qhull data structure is not initialized until qh_new_qhull().
+    do not call qh_init_A (global_r.c)
+
+    Default errfile is stderr, outfile may be null
+    qhull_cmd must start with "qhull "
+    projects points to a new point array for Delaunay triangulations ('d' and 'v')
+    transforms points into a new point array for halfspace intersection ('H')
+
+  see:
+    Qhull-template at the beginning of this file.
+    An example of using qh_new_qhull is user_eg_r.c
+*/
+int qh_new_qhull(qhT *qh, int dim, int numpoints, coordT *points, boolT ismalloc,
+                char *qhull_cmd, FILE *outfile, FILE *errfile) {
+  /* gcc may issue a "might be clobbered" warning for dim, points, and ismalloc [-Wclobbered].
+     These parameters are not referenced after a longjmp() and hence not clobbered.
+     See http://stackoverflow.com/questions/7721854/what-sense-do-these-clobbered-variable-warnings-make */
+  int exitcode, hulldim;
+  boolT new_ismalloc;
+  coordT *new_points;
+
+  if(!errfile){
+    errfile= stderr;
+  }
+  if (!qh->qhmem.ferr) {
+    qh_meminit(qh, errfile);
+  } else {
+    qh_memcheck(qh);
+  }
+  if (strncmp(qhull_cmd, "qhull ", (size_t)6)) {
+    qh_fprintf(qh, errfile, 6186, "qhull error (qh_new_qhull): start qhull_cmd argument with \"qhull \"\n");
+    return qh_ERRinput;
+  }
+  qh_initqhull_start(qh, NULL, outfile, errfile);
+  trace1((qh, qh->ferr, 1044, "qh_new_qhull: build new Qhull for %d %d-d points with %s\n", numpoints, dim, qhull_cmd));
+  exitcode = setjmp(qh->errexit);
+  if (!exitcode)
+  {
+    qh->NOerrexit = False;
+    qh_initflags(qh, qhull_cmd);
+    if (qh->DELAUNAY)
+      qh->PROJECTdelaunay= True;
+    if (qh->HALFspace) {
+      /* points is an array of halfspaces,
+         the last coordinate of each halfspace is its offset */
+      hulldim= dim-1;
+      qh_setfeasible(qh, hulldim);
+      new_points= qh_sethalfspace_all(qh, dim, numpoints, points, qh->feasible_point);
+      new_ismalloc= True;
+      if (ismalloc)
+        qh_free(points);
+    }else {
+      hulldim= dim;
+      new_points= points;
+      new_ismalloc= ismalloc;
+    }
+    qh_init_B(qh, new_points, numpoints, hulldim, new_ismalloc);
+    qh_qhull(qh);
+    qh_check_output(qh);
+    if (outfile) {
+      qh_produce_output(qh);
+    }else {
+      qh_prepare_output(qh);
+    }
+    if (qh->VERIFYoutput && !qh->STOPpoint && !qh->STOPcone)
+      qh_check_points(qh);
+  }
+  qh->NOerrexit = True;
+  return exitcode;
+} /* new_qhull */
+
+/*---------------------------------
+
+  qh_errexit(qh, exitcode, facet, ridge )
+    report and exit from an error
+    report facet and ridge if non-NULL
+    reports useful information such as last point processed
+    set qh.FORCEoutput to print neighborhood of facet
+
+  see:
+    qh_errexit2() in libqhull_r.c for printing 2 facets
+
+  design:
+    check for error within error processing
+    compute qh.hulltime
+    print facet and ridge (if any)
+    report commandString, options, qh.furthest_id
+    print summary and statistics (including precision statistics)
+    if qh_ERRsingular
+      print help text for singular data set
+    exit program via long jump (if defined) or exit()
+*/
+void qh_errexit(qhT *qh, int exitcode, facetT *facet, ridgeT *ridge) {
+
+  if (qh->ERREXITcalled) {
+    qh_fprintf(qh, qh->ferr, 8126, "\nqhull error while processing previous error.  Exit program\n");
+    qh_exit(qh_ERRqhull);
+  }
+  qh->ERREXITcalled= True;
+  if (!qh->QHULLfinished)
+    qh->hulltime= qh_CPUclock - qh->hulltime;
+  qh_errprint(qh, "ERRONEOUS", facet, NULL, ridge, NULL);
+  qh_fprintf(qh, qh->ferr, 8127, "\nWhile executing: %s | %s\n", qh->rbox_command, qh->qhull_command);
+  qh_fprintf(qh, qh->ferr, 8128, "Options selected for Qhull %s:\n%s\n", qh_version, qh->qhull_options);
+  if (qh->furthest_id >= 0) {
+    qh_fprintf(qh, qh->ferr, 8129, "Last point added to hull was p%d.", qh->furthest_id);
+    if (zzval_(Ztotmerge))
+      qh_fprintf(qh, qh->ferr, 8130, "  Last merge was #%d.", zzval_(Ztotmerge));
+    if (qh->QHULLfinished)
+      qh_fprintf(qh, qh->ferr, 8131, "\nQhull has finished constructing the hull.");
+    else if (qh->POSTmerging)
+      qh_fprintf(qh, qh->ferr, 8132, "\nQhull has started post-merging.");
+    qh_fprintf(qh, qh->ferr, 8133, "\n");
+  }
+  if (qh->FORCEoutput && (qh->QHULLfinished || (!facet && !ridge)))
+    qh_produce_output(qh);
+  else if (exitcode != qh_ERRinput) {
+    if (exitcode != qh_ERRsingular && zzval_(Zsetplane) > qh->hull_dim+1) {
+      qh_fprintf(qh, qh->ferr, 8134, "\nAt error exit:\n");
+      qh_printsummary(qh, qh->ferr);
+      if (qh->PRINTstatistics) {
+        qh_collectstatistics(qh);
+        qh_printstatistics(qh, qh->ferr, "at error exit");
+        qh_memstatistics(qh, qh->ferr);
+      }
+    }
+    if (qh->PRINTprecision)
+      qh_printstats(qh, qh->ferr, qh->qhstat.precision, NULL);
+  }
+  if (!exitcode)
+    exitcode= qh_ERRqhull;
+  else if (exitcode == qh_ERRsingular)
+    qh_printhelp_singular(qh, qh->ferr);
+  else if (exitcode == qh_ERRprec && !qh->PREmerge)
+    qh_printhelp_degenerate(qh, qh->ferr);
+  if (qh->NOerrexit) {
+    qh_fprintf(qh, qh->ferr, 6187, "qhull error while ending program, or qh->NOerrexit not cleared after setjmp(). Exit program with error.\n");
+    qh_exit(qh_ERRqhull);
+  }
+  qh->ERREXITcalled= False;
+  qh->NOerrexit= True;
+  qh->ALLOWrestart= False;  /* longjmp will undo qh_build_withrestart */
+  longjmp(qh->errexit, exitcode);
+} /* errexit */
+
+
+/*---------------------------------
+
+  qh_errprint(qh, fp, string, atfacet, otherfacet, atridge, atvertex )
+    prints out the information of facets and ridges to fp
+    also prints neighbors and geomview output
+
+  notes:
+    except for string, any parameter may be NULL
+*/
+void qh_errprint(qhT *qh, const char *string, facetT *atfacet, facetT *otherfacet, ridgeT *atridge, vertexT *atvertex) {
+  int i;
+
+  if (atfacet) {
+    qh_fprintf(qh, qh->ferr, 8135, "%s FACET:\n", string);
+    qh_printfacet(qh, qh->ferr, atfacet);
+  }
+  if (otherfacet) {
+    qh_fprintf(qh, qh->ferr, 8136, "%s OTHER FACET:\n", string);
+    qh_printfacet(qh, qh->ferr, otherfacet);
+  }
+  if (atridge) {
+    qh_fprintf(qh, qh->ferr, 8137, "%s RIDGE:\n", string);
+    qh_printridge(qh, qh->ferr, atridge);
+    if (atridge->top && atridge->top != atfacet && atridge->top != otherfacet)
+      qh_printfacet(qh, qh->ferr, atridge->top);
+    if (atridge->bottom
+        && atridge->bottom != atfacet && atridge->bottom != otherfacet)
+      qh_printfacet(qh, qh->ferr, atridge->bottom);
+    if (!atfacet)
+      atfacet= atridge->top;
+    if (!otherfacet)
+      otherfacet= otherfacet_(atridge, atfacet);
+  }
+  if (atvertex) {
+    qh_fprintf(qh, qh->ferr, 8138, "%s VERTEX:\n", string);
+    qh_printvertex(qh, qh->ferr, atvertex);
+  }
+  if (qh->fout && qh->FORCEoutput && atfacet && !qh->QHULLfinished && !qh->IStracing) {
+    qh_fprintf(qh, qh->ferr, 8139, "ERRONEOUS and NEIGHBORING FACETS to output\n");
+    for (i=0; i < qh_PRINTEND; i++)  /* use fout for geomview output */
+      qh_printneighborhood(qh, qh->fout, qh->PRINTout[i], atfacet, otherfacet,
+                            !qh_ALL);
+  }
+} /* errprint */
+
+
+/*---------------------------------
+
+  qh_printfacetlist(qh, fp, facetlist, facets, printall )
+    print all fields for a facet list and/or set of facets to fp
+    if !printall,
+      only prints good facets
+
+  notes:
+    also prints all vertices
+*/
+void qh_printfacetlist(qhT *qh, facetT *facetlist, setT *facets, boolT printall) {
+  facetT *facet, **facetp;
+
+  qh_printbegin(qh, qh->ferr, qh_PRINTfacets, facetlist, facets, printall);
+  FORALLfacet_(facetlist)
+    qh_printafacet(qh, qh->ferr, qh_PRINTfacets, facet, printall);
+  FOREACHfacet_(facets)
+    qh_printafacet(qh, qh->ferr, qh_PRINTfacets, facet, printall);
+  qh_printend(qh, qh->ferr, qh_PRINTfacets, facetlist, facets, printall);
+} /* printfacetlist */
+
+
+/*---------------------------------
+
+  qh_printhelp_degenerate(qh, fp )
+    prints descriptive message for precision error
+
+  notes:
+    no message if qh_QUICKhelp
+*/
+void qh_printhelp_degenerate(qhT *qh, FILE *fp) {
+
+  if (qh->MERGEexact || qh->PREmerge || qh->JOGGLEmax < REALmax/2)
+    qh_fprintf(qh, fp, 9368, "\n\
+A Qhull error has occurred.  Qhull should have corrected the above\n\
+precision error.  Please send the input and all of the output to\n\
+qhull_bug@qhull.org\n");
+  else if (!qh_QUICKhelp) {
+    qh_fprintf(qh, fp, 9369, "\n\
+Precision problems were detected during construction of the convex hull.\n\
+This occurs because convex hull algorithms assume that calculations are\n\
+exact, but floating-point arithmetic has roundoff errors.\n\
+\n\
+To correct for precision problems, do not use 'Q0'.  By default, Qhull\n\
+selects 'C-0' or 'Qx' and merges non-convex facets.  With option 'QJ',\n\
+Qhull joggles the input to prevent precision problems.  See \"Imprecision\n\
+in Qhull\" (qh-impre.htm).\n\
+\n\
+If you use 'Q0', the output may include\n\
+coplanar ridges, concave ridges, and flipped facets.  In 4-d and higher,\n\
+Qhull may produce a ridge with four neighbors or two facets with the same \n\
+vertices.  Qhull reports these events when they occur.  It stops when a\n\
+concave ridge, flipped facet, or duplicate facet occurs.\n");
+#if REALfloat
+    qh_fprintf(qh, fp, 9370, "\
+\n\
+Qhull is currently using single precision arithmetic.  The following\n\
+will probably remove the precision problems:\n\
+  - recompile qhull for realT precision(#define REALfloat 0 in user.h).\n");
+#endif
+    if (qh->DELAUNAY && !qh->SCALElast && qh->MAXabs_coord > 1e4)
+      qh_fprintf(qh, fp, 9371, "\
+\n\
+When computing the Delaunay triangulation of coordinates > 1.0,\n\
+  - use 'Qbb' to scale the last coordinate to [0,m] (max previous coordinate)\n");
+    if (qh->DELAUNAY && !qh->ATinfinity)
+      qh_fprintf(qh, fp, 9372, "\
+When computing the Delaunay triangulation:\n\
+  - use 'Qz' to add a point at-infinity.  This reduces precision problems.\n");
+
+    qh_fprintf(qh, fp, 9373, "\
+\n\
+If you need triangular output:\n\
+  - use option 'Qt' to triangulate the output\n\
+  - use option 'QJ' to joggle the input points and remove precision errors\n\
+  - use option 'Ft'.  It triangulates non-simplicial facets with added points.\n\
+\n\
+If you must use 'Q0',\n\
+try one or more of the following options.  They can not guarantee an output.\n\
+  - use 'QbB' to scale the input to a cube.\n\
+  - use 'Po' to produce output and prevent partitioning for flipped facets\n\
+  - use 'V0' to set min. distance to visible facet as 0 instead of roundoff\n\
+  - use 'En' to specify a maximum roundoff error less than %2.2g.\n\
+  - options 'Qf', 'Qbb', and 'QR0' may also help\n",
+               qh->DISTround);
+    qh_fprintf(qh, fp, 9374, "\
+\n\
+To guarantee simplicial output:\n\
+  - use option 'Qt' to triangulate the output\n\
+  - use option 'QJ' to joggle the input points and remove precision errors\n\
+  - use option 'Ft' to triangulate the output by adding points\n\
+  - use exact arithmetic (see \"Imprecision in Qhull\", qh-impre.htm)\n\
+");
+  }
+} /* printhelp_degenerate */
+
+
+/*---------------------------------
+
+  qh_printhelp_narrowhull(qh, minangle )
+    Warn about a narrow hull
+
+  notes:
+    Alternatively, reduce qh_WARNnarrow in user.h
+
+*/
+void qh_printhelp_narrowhull(qhT *qh, FILE *fp, realT minangle) {
+
+    qh_fprintf(qh, fp, 9375, "qhull precision warning: \n\
+The initial hull is narrow (cosine of min. angle is %.16f).\n\
+Is the input lower dimensional (e.g., on a plane in 3-d)?  Qhull may\n\
+produce a wide facet.  Options 'QbB' (scale to unit box) or 'Qbb' (scale\n\
+last coordinate) may remove this warning.  Use 'Pp' to skip this warning.\n\
+See 'Limitations' in qh-impre.htm.\n",
+          -minangle);   /* convert from angle between normals to angle between facets */
+} /* printhelp_narrowhull */
+
+/*---------------------------------
+
+  qh_printhelp_singular(qh, fp )
+    prints descriptive message for singular input
+*/
+void qh_printhelp_singular(qhT *qh, FILE *fp) {
+  facetT *facet;
+  vertexT *vertex, **vertexp;
+  realT min, max, *coord, dist;
+  int i,k;
+
+  qh_fprintf(qh, fp, 9376, "\n\
+The input to qhull appears to be less than %d dimensional, or a\n\
+computation has overflowed.\n\n\
+Qhull could not construct a clearly convex simplex from points:\n",
+           qh->hull_dim);
+  qh_printvertexlist(qh, fp, "", qh->facet_list, NULL, qh_ALL);
+  if (!qh_QUICKhelp)
+    qh_fprintf(qh, fp, 9377, "\n\
+The center point is coplanar with a facet, or a vertex is coplanar\n\
+with a neighboring facet.  The maximum round off error for\n\
+computing distances is %2.2g.  The center point, facets and distances\n\
+to the center point are as follows:\n\n", qh->DISTround);
+  qh_printpointid(qh, fp, "center point", qh->hull_dim, qh->interior_point, qh_IDunknown);
+  qh_fprintf(qh, fp, 9378, "\n");
+  FORALLfacets {
+    qh_fprintf(qh, fp, 9379, "facet");
+    FOREACHvertex_(facet->vertices)
+      qh_fprintf(qh, fp, 9380, " p%d", qh_pointid(qh, vertex->point));
+    zinc_(Zdistio);
+    qh_distplane(qh, qh->interior_point, facet, &dist);
+    qh_fprintf(qh, fp, 9381, " distance= %4.2g\n", dist);
+  }
+  if (!qh_QUICKhelp) {
+    if (qh->HALFspace)
+      qh_fprintf(qh, fp, 9382, "\n\
+These points are the dual of the given halfspaces.  They indicate that\n\
+the intersection is degenerate.\n");
+    qh_fprintf(qh, fp, 9383,"\n\
+These points either have a maximum or minimum x-coordinate, or\n\
+they maximize the determinant for k coordinates.  Trial points\n\
+are first selected from points that maximize a coordinate.\n");
+    if (qh->hull_dim >= qh_INITIALmax)
+      qh_fprintf(qh, fp, 9384, "\n\
+Because of the high dimension, the min x-coordinate and max-coordinate\n\
+points are used if the determinant is non-zero.  Option 'Qs' will\n\
+do a better, though much slower, job.  Instead of 'Qs', you can change\n\
+the points by randomly rotating the input with 'QR0'.\n");
+  }
+  qh_fprintf(qh, fp, 9385, "\nThe min and max coordinates for each dimension are:\n");
+  for (k=0; k < qh->hull_dim; k++) {
+    min= REALmax;
+    max= -REALmin;
+    for (i=qh->num_points, coord= qh->first_point+k; i--; coord += qh->hull_dim) {
+      maximize_(max, *coord);
+      minimize_(min, *coord);
+    }
+    qh_fprintf(qh, fp, 9386, "  %d:  %8.4g  %8.4g  difference= %4.4g\n", k, min, max, max-min);
+  }
+  if (!qh_QUICKhelp) {
+    qh_fprintf(qh, fp, 9387, "\n\
+If the input should be full dimensional, you have several options that\n\
+may determine an initial simplex:\n\
+  - use 'QJ'  to joggle the input and make it full dimensional\n\
+  - use 'QbB' to scale the points to the unit cube\n\
+  - use 'QR0' to randomly rotate the input for different maximum points\n\
+  - use 'Qs'  to search all points for the initial simplex\n\
+  - use 'En'  to specify a maximum roundoff error less than %2.2g.\n\
+  - trace execution with 'T3' to see the determinant for each point.\n",
+                     qh->DISTround);
+#if REALfloat
+    qh_fprintf(qh, fp, 9388, "\
+  - recompile qhull for realT precision(#define REALfloat 0 in libqhull_r.h).\n");
+#endif
+    qh_fprintf(qh, fp, 9389, "\n\
+If the input is lower dimensional:\n\
+  - use 'QJ' to joggle the input and make it full dimensional\n\
+  - use 'Qbk:0Bk:0' to delete coordinate k from the input.  You should\n\
+    pick the coordinate with the least range.  The hull will have the\n\
+    correct topology.\n\
+  - determine the flat containing the points, rotate the points\n\
+    into a coordinate plane, and delete the other coordinates.\n\
+  - add one or more points to make the input full dimensional.\n\
+");
+  }
+} /* printhelp_singular */
+
+/*---------------------------------
+
+  qh_user_memsizes(qh)
+    allocate up to 10 additional, quick allocation sizes
+
+  notes:
+    increase maximum number of allocations in qh_initqhull_mem()
+*/
+void qh_user_memsizes(qhT *qh) {
+
+  QHULL_UNUSED(qh)
+  /* qh_memsize(qh, size); */
+} /* user_memsizes */
+
+
diff --git a/Cdir/usermem_r.c b/Cdir/usermem_r.c
new file mode 100644
--- /dev/null
+++ b/Cdir/usermem_r.c
@@ -0,0 +1,94 @@
+/*
  ---------------------------------
+
+   usermem_r.c
+   qh_exit(), qh_free(), and qh_malloc()
+
+   See README.txt.
+
+   If you redefine one of these functions you must redefine all of them.
+   If you recompile and load this file, then usermem.o will not be loaded
+   from qhull.a or qhull.lib
+
+   See libqhull_r.h for data structures, macros, and user-callable functions.
+   See user_r.c for qhull-related, redefinable functions
+   see user_r.h for user-definable constants
+   See userprintf_r.c for qh_fprintf and userprintf_rbox_r.c for qh_fprintf_rbox
+
+   Please report any errors that you fix to qhull@qhull.org
+*/
+
+#include "libqhull_r.h"
+
+#include 
+#include 
+
+/*---------------------------------
+
+  qh_exit( exitcode )
+    exit program
+
+  notes:
+    qh_exit() is called when qh_errexit() and longjmp() are not available.
+
+    This is the only use of exit() in Qhull
+    To replace qh_exit with 'throw', see libqhullcpp/usermem_r-cpp.cpp
+*/
+void qh_exit(int exitcode) {
+    exit(exitcode);
+} /* exit */
+
+/*---------------------------------
+
+  qh_fprintf_stderr( msgcode, format, list of args )
+    fprintf to stderr with msgcode (non-zero)
+
+  notes:
+    qh_fprintf_stderr() is called when qh->ferr is not defined, usually due to an initialization error
+    
+    It is typically followed by qh_errexit().
+
+    Redefine this function to avoid using stderr
+
+    Use qh_fprintf [userprintf_r.c] for normal printing
+*/
+void qh_fprintf_stderr(int msgcode, const char *fmt, ... ) {
+    va_list args;
+
+    va_start(args, fmt);
+    if(msgcode)
+      fprintf(stderr, "QH%.4d ", msgcode);
+    vfprintf(stderr, fmt, args);
+    va_end(args);
+} /* fprintf_stderr */
+
+/*---------------------------------
+
+  qh_free(qhT *qh, mem )
+    free memory
+
+  notes:
+    same as free()
+    No calls to qh_errexit() 
+*/
+void qh_free(void *mem) {
+    free(mem);
+} /* free */
+
+/*---------------------------------
+
+    qh_malloc( mem )
+      allocate memory
+
+    notes:
+      same as malloc()
+*/
+void *qh_malloc(size_t size) {
+    return malloc(size);
+} /* malloc */
+
+
diff --git a/Cdir/userprintf_r.c b/Cdir/userprintf_r.c
new file mode 100644
--- /dev/null
+++ b/Cdir/userprintf_r.c
@@ -0,0 +1,65 @@
+/*
  ---------------------------------
+
+   userprintf_r.c
+   qh_fprintf()
+
+   see README.txt  see COPYING.txt for copyright information.
+
+   If you recompile and load this file, then userprintf_r.o will not be loaded
+   from qhull.a or qhull.lib
+
+   See libqhull_r.h for data structures, macros, and user-callable functions.
+   See user_r.c for qhull-related, redefinable functions
+   see user_r.h for user-definable constants
+   See usermem_r.c for qh_exit(), qh_free(), and qh_malloc()
+   see Qhull.cpp and RboxPoints.cpp for examples.
+
+   Please report any errors that you fix to qhull@qhull.org
+*/
+
+#include "libqhull_r.h"
+
+#include 
+#include 
+#include 
+
+/*---------------------------------
+
+   qh_fprintf(qh, fp, msgcode, format, list of args )
+     print arguments to *fp according to format
+     Use qh_fprintf_rbox() for rboxlib_r.c
+
+   notes:
+     same as fprintf()
+     fgets() is not trapped like fprintf()
+     exit qh_fprintf via qh_errexit()
+     may be called for errors in qh_initstatistics and qh_meminit
+*/
+
+void qh_fprintf(qhT *qh, FILE *fp, int msgcode, const char *fmt, ... ) {
+    va_list args;
+
+    if (!fp) {
+        if(!qh){
+            qh_fprintf_stderr(6241, "userprintf_r.c: fp and qh not defined for qh_fprintf '%s'", fmt);
+            qh_exit(qhmem_ERRqhull);  /* can not use qh_errexit() */
+        }
+        /* could use qh->qhmem.ferr, but probably better to be cautious */
+        qh_fprintf_stderr(6232, "Qhull internal error (userprintf_r.c): fp is 0.  Wrong qh_fprintf called.\n");
+        qh_errexit(qh, 6232, NULL, NULL);
+    }
+    va_start(args, fmt);
+    if (qh && qh->ANNOTATEoutput) {
+      fprintf(fp, "[QH%.4d]", msgcode);
+    }else if (msgcode >= MSG_ERROR && msgcode < MSG_STDERR ) {
+      fprintf(fp, "QH%.4d ", msgcode);
+    }
+    vfprintf(fp, fmt, args);
+    va_end(args);
+
+    /* Place debugging traps here. Use with option 'Tn' */
+
+} /* qh_fprintf */
+
diff --git a/Cdir/utils.c b/Cdir/utils.c
new file mode 100644
--- /dev/null
+++ b/Cdir/utils.c
@@ -0,0 +1,91 @@
+#include  // to use realloc
+#include  // to use NAN
+#include  // to use printf
+
+double* getpoint(double* points, unsigned dim, unsigned id){
+  double* out = malloc(dim * sizeof(double));
+  for(unsigned i=0; i < dim; i++){
+    out[i] = points[id*dim+i];
+  }
+  return out;
+}
+
+/* dot product of two vectors */
+double dotproduct(double* p1, double* p2, unsigned dim){
+  double out = 0;
+  for(unsigned i=0; i < dim; i++){
+    out += p1[i] * p2[i];
+  }
+  return out;
+}
+
+/* middle of segment [p1,p2] */
+double* middle(double* p1, double* p2, unsigned dim){
+  double* out = malloc(dim * sizeof(double));
+  for(unsigned i=0; i 0 ? 1 : -1);
+}
+void qsortu(unsigned* vector, unsigned length){
+  qsort(vector, length, sizeof(unsigned), cmpfunc);
+}
+
+
+double square(double x){
+  return x*x;
+}
+
+/* append to a vector of unsigned */
+void appendu(unsigned x, unsigned** array, unsigned length, unsigned* flag){
+  *flag = 1;
+  for(unsigned i=0; i instead of ""
+    change both include-dir and C-dir to ./Cdir
+    there was a hint on stackoverflow that single char dirs do not work well in cabal
+    works with stack once, after stack install uniform-geometry can use it.
+-     cannot go to hpack, trying stack init - not working either
diff --git a/qhull.cabal b/qhull.cabal
--- a/qhull.cabal
+++ b/qhull.cabal
@@ -1,5 +1,5 @@
 name:                qhull
-version:             0.1.0.1
+version:             0.1.0.3
 synopsis:       Delaunay triangulation, Voronoi diagrams and convex hulls. 
 description:    Based on the qhull C library. 
 
@@ -12,9 +12,13 @@
 copyright:           2018 Stéphane Laurent
 category:            Math
 build-type:          Simple
-extra-source-files:  README.md
+extra-source-files:  README.md ChangeLog.md
 cabal-version:       >=1.10
 
+source-repository head
+  type:     git
+  location: https://github.com/stla/qhull
+
 flag exe
   description:
     Build the executables.
@@ -87,26 +91,28 @@
   other-extensions:    ForeignFunctionInterface
                      , TypeFamilies
   default-language:    Haskell2010
-  include-dirs:        C
-  C-sources:           ./C/libqhull_r.c
-                     , ./C/geom_r.c
-                     , ./C/geom2_r.c
-                     , ./C/global_r.c
-                     , ./C/io_r.c
-                     , ./C/mem_r.c
-                     , ./C/merge_r.c
-                     , ./C/poly_r.c
-                     , ./C/poly2_r.c
-                     , ./C/qset_r.c
-                     , ./C/random_r.c
-                     , ./C/usermem_r.c
-                     , ./C/userprintf_r.c
-                     , ./C/user_r.c
-                     , ./C/stat_r.c
-                     , ./C/delaunay.c
-                     , ./C/convexhull.c
-                     , ./C/utils.c
-                     , ./C/halfspaces.c
+
+  include-dirs:        ./Cdir
+  C-sources:           ./Cdir/libqhull_r.c
+                     , ./Cdir/geom_r.c
+                     , ./Cdir/geom2_r.c
+                     , ./Cdir/global_r.c
+                     , ./Cdir/io_r.c
+                     , ./Cdir/mem_r.c
+                     , ./Cdir/merge_r.c
+                     , ./Cdir/poly_r.c
+                     , ./Cdir/poly2_r.c
+                     , ./Cdir/qset_r.c
+                     , ./Cdir/random_r.c
+                     , ./Cdir/usermem_r.c
+                     , ./Cdir/userprintf_r.c
+                     , ./Cdir/user_r.c
+                     , ./Cdir/stat_r.c
+                     , ./Cdir/delaunay.c
+                     , ./Cdir/convexhull.c
+                     , ./Cdir/utils.c
+                     , ./Cdir/halfspaces.c
+
   ghc-options:         -O0 -Wall
 
 executable test_delaunay
@@ -185,6 +191,4 @@
                      , containers
   ghc-options:         -main-is Adjacency.AdjacencyMatrix
 
-source-repository head
-  type:     git
-  location: https://github.com/stla/qhull
+