qhull-0.1.0.1: src/ConvexHull/Examples.hs
module ConvexHull.Examples
where
import Data.List hiding (permutations)
import Data.List.Split (chunksOf)
import Math.Combinat.Permutations
import System.Random
sixhundredCell :: [[Double]]
sixhundredCell =
[[i, j, k, l] | i <- pm, j <- pm, k <- pm, l <-pm] ++
[[0, 0, 0, i*2] | i <- pm] ++
[[0, 0, i*2, 0] | i <- pm] ++
[[0, i*2, 0, 0] | i <- pm] ++
[[i*2, 0, 0, 0] | i <- pm] ++
[ permuteList p [i*phi, j, k/phi, 0] |
p <- permutations4, isEvenPermutation p, i <- pm, j <- pm, k <- pm]
where
permutations4 = permutations 4
phi = (1 + sqrt 5) / 2
pm = [-1,1]
hexadecachoron :: [[Double]]
hexadecachoron =
[ [1,0,0,0]
, [-1,0,0,0]
, [0,1,0,0]
, [0,-1,0,0]
, [0,0,1,0]
, [0,0,-1,0]
, [0,0,0,1]
, [0,0,0,-1] ]
runcitruncated5cell :: [[Double]]
runcitruncated5cell =
[[2/sqrt 10, -2/sqrt 6, 1/sqrt 3, 3]
,[2/sqrt 10, 2/sqrt 6, -1/sqrt 3, 3]
,[2/sqrt 10, -2/sqrt 6, 4/sqrt 3, 2]
,[2/sqrt 10, 2/sqrt 6, -4/sqrt 3, 2]
,[2/sqrt 10, -2/sqrt 6, -5/sqrt 3, 1]
,[2/sqrt 10, 2/sqrt 6, 5/sqrt 3, 1]
,[2/sqrt 10, sqrt 6, 0, 2]
,[2/sqrt 10, -sqrt 6, 0, 2]
,[2/sqrt 10, sqrt 6, sqrt 3, 1]
,[2/sqrt 10, -sqrt 6, sqrt 3, 1]
,[7/sqrt 10, -1/sqrt 6, 2/sqrt 3, 2]
,[7/sqrt 10, -1/sqrt 6, -4/sqrt 3, 0]
,[7/sqrt 10, 3/sqrt 6, 0, 2]
,[7/sqrt 10, 3/sqrt 6, sqrt 3, 1]
,[7/sqrt 10, 3/sqrt 6, -sqrt 3, 1]
,[7/sqrt 10, -5/sqrt 6, 1/sqrt 3, 1]
,[7/sqrt 10, -5/sqrt 6, -2/sqrt 3, 0]
,[-3/sqrt 10, 1/sqrt 6, 1/sqrt 3, 3]
,[-3/sqrt 10, 1/sqrt 6, 4/sqrt 3, 2]
,[-3/sqrt 10, 1/sqrt 6, -5/sqrt 3, 1]
,[-3/sqrt 10, 5/sqrt 6, 2/sqrt 3, 2]
,[-3/sqrt 10, 5/sqrt 6, -4/sqrt 3, 0]
,[-3/sqrt 10, -7/sqrt 6, -1/sqrt 3, 1]
,[-3/sqrt 10, -7/sqrt 6, 2/sqrt 3, 0]
,[-8/sqrt 10, 0, 0, 2]
,[-8/sqrt 10, 0, sqrt 3, 1]
,[-8/sqrt 10, 0, -sqrt 3, 1]
,[-8/sqrt 10, -4/sqrt 6, -1/sqrt 3, 1]
,[-8/sqrt 10, 4/sqrt 6, 1/sqrt 3, 1]
,[-8/sqrt 10, -4/sqrt 6, 2/sqrt 3, 0]
,[-8/sqrt 10, 4/sqrt 6, -2/sqrt 3, 0]
,[2/sqrt 10, -2/sqrt 6, 1/sqrt 3, -3]
,[2/sqrt 10, 2/sqrt 6, -1/sqrt 3, -3]
,[2/sqrt 10, -2/sqrt 6, 4/sqrt 3, -2]
,[2/sqrt 10, 2/sqrt 6, -4/sqrt 3, -2]
,[2/sqrt 10, -2/sqrt 6, -5/sqrt 3, -1]
,[2/sqrt 10, 2/sqrt 6, 5/sqrt 3, -1]
,[2/sqrt 10, sqrt 6, 0, -2]
,[2/sqrt 10, -sqrt 6, 0, -2]
,[2/sqrt 10, sqrt 6, -sqrt 3, -1]
,[2/sqrt 10, -sqrt 6, -sqrt 3, -1]
,[7/sqrt 10, -1/sqrt 6, 2/sqrt 3, -2]
,[7/sqrt 10, 3/sqrt 6, 0, -2]
,[7/sqrt 10, 3/sqrt 6, sqrt 3, -1]
,[7/sqrt 10, 3/sqrt 6, -sqrt 3, -1]
,[7/sqrt 10, -5/sqrt 6, 1/sqrt 3, -1]
,[-3/sqrt 10, 1/sqrt 6, 1/sqrt 3, -3]
,[-3/sqrt 10, 1/sqrt 6, 4/sqrt 3, -2]
,[-3/sqrt 10, 1/sqrt 6, -5/sqrt 3, -1]
,[-3/sqrt 10, 5/sqrt 6, 2/sqrt 3, -2]
,[-3/sqrt 10, -7/sqrt 6, -1/sqrt 3, -1]
,[-8/sqrt 10, 0, 0, -2]
,[-8/sqrt 10, 0, sqrt 3, -1]
,[-8/sqrt 10, 0, -sqrt 3, -1]
,[-8/sqrt 10, -4/sqrt 6, -1/sqrt 3, -1]
,[-8/sqrt 10, 4/sqrt 6, 1/sqrt 3, -1] ]
cantellated5cell :: [[Double]]
cantellated5cell =
[[4/sqrt 10, 0, 0, 2]
,[4/sqrt 10, 0, 3/sqrt 3, 1]
,[4/sqrt 10, 0, -3/sqrt 3, 1]
,[4/sqrt 10, -4/sqrt 6, 2/sqrt 3, 0]
,[4/sqrt 10, 4/sqrt 6, -2/sqrt 3, 0]
,[4/sqrt 10, -4/sqrt 6, -1/sqrt 3, 1]
,[4/sqrt 10, 4/sqrt 6, 1/sqrt 3, 1]
,[-6/sqrt 10, -2/sqrt 6, -2/sqrt 3, 0]
,[-6/sqrt 10, 2/sqrt 6, 2/sqrt 3, 0]
,[-1/sqrt 10, -1/sqrt 6, -4/sqrt 3, 0]
,[-1/sqrt 10, -5/sqrt 6, -2/sqrt 3, 0]
,[-1/sqrt 10, 3/sqrt 6, 0, 2]
,[-1/sqrt 10, -1/sqrt 6, 2/sqrt 3, 2]
,[-1/sqrt 10, -5/sqrt 6, 1/sqrt 3, 1]
,[-1/sqrt 10, 3/sqrt 6, 3/sqrt 3, 1]
,[-1/sqrt 10, 3/sqrt 6, -3/sqrt 3, 1]
,[-6/sqrt 10, -2/sqrt 6, 1/sqrt 3, 1]
,[-6/sqrt 10, 2/sqrt 6, -1/sqrt 3, 1]
,[4/sqrt 10, 0, 0, -2]
,[4/sqrt 10, 0, 3/sqrt 3, -1]
,[4/sqrt 10, 0, -3/sqrt 3, -1]
,[4/sqrt 10, -4/sqrt 6, -1/sqrt 3, -1]
,[4/sqrt 10, 4/sqrt 6, 1/sqrt 3, -1]
,[-1/sqrt 10, 3/sqrt 6, 0, -2]
,[-1/sqrt 10, -1/sqrt 6, 2/sqrt 3, -2]
,[-1/sqrt 10, -5/sqrt 6, 1/sqrt 3, -1]
,[-1/sqrt 10, 3/sqrt 6, 3/sqrt 3, -1]
,[-1/sqrt 10, 3/sqrt 6, -3/sqrt 3, -1]
,[-6/sqrt 10, -2/sqrt 6, 1/sqrt 3, -1]
,[-6/sqrt 10, 2/sqrt 6, -1/sqrt 3, -1]]
bitruncated5cell :: [[Double]]
bitruncated5cell =
[ [0, 4/sqrt 6, 4/sqrt 3, 0]
, [0, -4/sqrt 6, -4/sqrt 3, 0]
, [0, 4/sqrt 6, -2/sqrt 3, 2]
, [0, 4/sqrt 6, -2/sqrt 3, -2]
, [0, -4/sqrt 6, 2/sqrt 3, -2]
, [0, -4/sqrt 6, 2/sqrt 3, 2]
, [5/sqrt 10, 1/sqrt 6, 4/sqrt 3, 0]
, [-5/sqrt 10, -1/sqrt 6, -4/sqrt 3, 0]
, [5/sqrt 10, 1/sqrt 6, -2/sqrt 3, 2]
, [5/sqrt 10, 1/sqrt 6, -2/sqrt 3, -2]
, [-5/sqrt 10, -1/sqrt 6, 2/sqrt 3, -2]
, [-5/sqrt 10, -1/sqrt 6, 2/sqrt 3, 2]
, [5/sqrt 10, 5/sqrt 6, 2/sqrt 3, 0]
, [-5/sqrt 10, -5/sqrt 6, -2/sqrt 3, 0]
, [5/sqrt 10, 5/sqrt 6, -1/sqrt 3, 1]
, [5/sqrt 10, 5/sqrt 6, -1/sqrt 3, -1]
, [-5/sqrt 10, -5/sqrt 6, 1/sqrt 3, -1]
, [-5/sqrt 10, -5/sqrt 6, 1/sqrt 3, 1]
, [5/sqrt 10, -3/sqrt 6, 0, 2]
, [5/sqrt 10, -3/sqrt 6, 0, -2]
, [-5/sqrt 10, 3/sqrt 6, 0, -2]
, [-5/sqrt 10, 3/sqrt 6, 0, 2]
, [5/sqrt 10, -3/sqrt 6, sqrt 3, 1]
, [5/sqrt 10, -3/sqrt 6, sqrt 3, -1]
, [5/sqrt 10, -3/sqrt 6, -sqrt 3, 1]
, [5/sqrt 10, -3/sqrt 6, -sqrt 3, -1]
, [-5/sqrt 10, 3/sqrt 6, -sqrt 3, -1]
, [-5/sqrt 10, 3/sqrt 6, -sqrt 3, 1]
, [-5/sqrt 10, 3/sqrt 6, sqrt 3, -1]
, [-5/sqrt 10, 3/sqrt 6, sqrt 3, 1] ]
rectified5cell :: [[Double]]
rectified5cell =
[ [-3/sqrt 10, -3/sqrt 6, 0, 0]
, [-3/sqrt 10, 1/sqrt 6, -2/sqrt 3, 0]
, [-3/sqrt 10, 1/sqrt 6, 1/sqrt 3, 1]
, [-3/sqrt 10, 1/sqrt 6, 1/sqrt 3, -1]
, [2/sqrt 10, 2/sqrt 6, 2/sqrt 3, 0]
, [2/sqrt 10, -2/sqrt 6, -2/sqrt 3, 0]
, [2/sqrt 10, 2/sqrt 6, -1/sqrt 3, 1]
, [2/sqrt 10, 2/sqrt 6, -1/sqrt 3, -1]
, [2/sqrt 10, -2/sqrt 6, 1/sqrt 3, 1]
, [2/sqrt 10, -2/sqrt 6, 1/sqrt 3, -1] ]
sircope :: [[Double]]
sircope =
let a = (1+ sqrt 2)/2 in
[
[-a, -0.5, -0.5, -0.5],
[a, -0.5, -0.5, -0.5],
[-a, 0.5, -0.5, -0.5],
[a, 0.5, -0.5, -0.5],
[-a, -0.5, 0.5, -0.5],
[a, -0.5, 0.5, -0.5],
[-a, 0.5, 0.5, -0.5],
[a, 0.5, 0.5, -0.5],
[-a, -0.5, -0.5, 0.5],
[a, -0.5, -0.5, 0.5],
[-a, 0.5, -0.5, 0.5],
[a, 0.5, -0.5, 0.5],
[-a, -0.5, 0.5, 0.5],
[a, -0.5, 0.5, 0.5],
[-a, 0.5, 0.5, 0.5],
[a, 0.5, 0.5, 0.5],
[-0.5, -a, -0.5, -0.5],
[0.5, -a, -0.5, -0.5],
[-0.5, a, -0.5, -0.5],
[0.5, a, -0.5, -0.5],
[-0.5, -a, 0.5, -0.5],
[0.5, -a, 0.5, -0.5],
[-0.5, a, 0.5, -0.5],
[0.5, a, 0.5, -0.5],
[-0.5, -a, -0.5, 0.5],
[0.5, -a, -0.5, 0.5],
[-0.5, a, -0.5, 0.5],
[0.5, a, -0.5, 0.5],
[-0.5, -a, 0.5, 0.5],
[0.5, -a, 0.5, 0.5],
[-0.5, a, 0.5, 0.5],
[0.5, a, 0.5, 0.5],
[-0.5, -0.5, -a, -0.5],
[0.5, -0.5, -a, -0.5],
[-0.5, 0.5, -a, -0.5],
[0.5, 0.5, -a, -0.5],
[-0.5, -0.5, a, -0.5],
[0.5, -0.5, a, -0.5],
[-0.5, 0.5, a, -0.5],
[0.5, 0.5, a, -0.5],
[-0.5, -0.5, -a, 0.5],
[0.5, -0.5, -a, 0.5],
[-0.5, 0.5, -a, 0.5],
[0.5, 0.5, -a, 0.5],
[-0.5, -0.5, a, 0.5],
[0.5, -0.5, a, 0.5],
[-0.5, 0.5, a, 0.5],
[0.5, 0.5, a, 0.5]
]
tutcup :: [[Double]]
tutcup =
[ [1, -1/sqrt 3, 5/sqrt 6, 1/sqrt 2]
, [-1, -1/sqrt 3, 5/sqrt 6, 1/sqrt 2]
, [0, 2/sqrt 3, 5/sqrt 6, 1/sqrt 2]
, [2, -2/sqrt 3, 1/sqrt 6, 1/sqrt 2]
, [-2, -2/sqrt 3, 1/sqrt 6, 1/sqrt 2]
, [0, 4/sqrt 3, 1/sqrt 6, 1/sqrt 2]
, [1, 3/sqrt 3, -3/sqrt 6, 1/sqrt 2]
, [1, -3/sqrt 3, -3/sqrt 6, 1/sqrt 2]
, [-1, 3/sqrt 3, -3/sqrt 6, 1/sqrt 2]
, [-1, -3/sqrt 3, -3/sqrt 6, 1/sqrt 2]
, [2, 0, -3/sqrt 6, 1/sqrt 2]
, [-2, 0, -3/sqrt 6, 1/sqrt 2]
, [1, 3/sqrt 3, 3/sqrt 6, -1/sqrt 2]
, [1, -3/sqrt 3, 3/sqrt 6, -1/sqrt 2]
, [-1, 3/sqrt 3, 3/sqrt 6, -1/sqrt 2]
, [-1, -3/sqrt 3, 3/sqrt 6, -1/sqrt 2]
, [2, 0, 3/sqrt 6, -1/sqrt 2]
, [-2, 0, 3/sqrt 6, -1/sqrt 2]
, [2, 2/sqrt 3, -1/sqrt 6, -1/sqrt 2]
, [-2, 2/sqrt 3, -1/sqrt 6, -1/sqrt 2]
, [0, -4/sqrt 3, -1/sqrt 6, -1/sqrt 2]
, [1, 1/sqrt 3, -5/sqrt 6, -1/sqrt 2]
, [-1, 1/sqrt 3, -5/sqrt 6, -1/sqrt 2]
, [0, -2/sqrt 3, -5/sqrt 6, -1/sqrt 2] ]
runcinatedTesseract :: [[Double]]
runcinatedTesseract =
[[i*a, j*b, k*c, l*d] | i <- pm, j <- pm, k <- pm, l <- pm, (a,b,c,d) <- s]
where
pm = [-1,1]
x = 1 + sqrt 2
s = [(1,1,1,x),(1,1,x,1),(1,x,1,1),(x,1,1,1)]
runcinated5cells :: [[Double]]
runcinated5cells = [ [sqrt(5/2), 1/sqrt 6, 1/sqrt 3, 1]
,[sqrt(5/2), 1/sqrt 6, 1/sqrt 3, -1]
,[-sqrt(5/2), -1/sqrt 6, -1/sqrt 3, -1]
,[-sqrt(5/2), -1/sqrt 6, -1/sqrt 3, 1]
,[sqrt(5/2), 1/sqrt 6, -2/sqrt 3, 0]
,[-sqrt(5/2), -1/sqrt 6, 2/sqrt 3, 0]
,[sqrt(5/2), -sqrt(3/2), 0, 0]
,[-sqrt(5/2), sqrt(3/2), 0, 0]
,[0, 2*sqrt(2/3), 1/sqrt 3, 1]
,[0, 2*sqrt(2/3), 1/sqrt 3, -1]
,[0, -2*sqrt(2/3), -1/sqrt 3, -1]
,[0, -2*sqrt(2/3), -1/sqrt 3, 1]
,[0, 2*sqrt(2/3), -2/sqrt 3, 0]
,[0, -2*sqrt(2/3), 2/sqrt 3, 0]
,[0, 0, sqrt 3, 1]
,[0, 0, sqrt 3, -1]
,[0, 0, -sqrt 3, 1]
,[0, 0, -sqrt 3, -1]
,[0, 0, 0, 2]
,[0, 0, 0, -2] ]
truncated5cells :: [[Double]]
truncated5cells = [ [3/sqrt 10, -1/sqrt 6, 2/sqrt 3, 2]
,[3/sqrt 10, -1/sqrt 6, 2/sqrt 3, -2]
,[3/sqrt 10, -1/sqrt 6, -4/sqrt 3, 0]
,[3/sqrt 10, 3/sqrt 6, 0, 2]
,[3/sqrt 10, 3/sqrt 6, 0, -2]
,[3/sqrt 10, 3/sqrt 6, sqrt 3, 1]
,[3/sqrt 10, 3/sqrt 6, sqrt 3, -1]
,[3/sqrt 10, 3/sqrt 6, -sqrt 3, 1]
,[3/sqrt 10, 3/sqrt 6, -sqrt 3, -1]
,[3/sqrt 10, -5/sqrt 6, 1/sqrt 3, 1]
,[3/sqrt 10, -5/sqrt 6, 1/sqrt 3, -1]
,[3/sqrt 10, -5/sqrt 6, -2/sqrt 3, 0]
,[-2/sqrt 10, 2/sqrt 6, 2/sqrt 3, 2]
,[-2/sqrt 10, 2/sqrt 6, 2/sqrt 3, -2]
,[-2/sqrt 10, 2/sqrt 6, -4/sqrt 3, 0]
,[-2/sqrt 10, -sqrt 6, 0, 0]
,[-7/sqrt 10, 1/sqrt 6, 1/sqrt 3, 1]
,[-7/sqrt 10, 1/sqrt 6, 1/sqrt 3, -1]
,[-7/sqrt 10, 1/sqrt 6, -2/sqrt 3, 0]
,[-7/sqrt 10, -3/sqrt 6, 0, 0] ]
truncated24cells :: [[Double]]
truncated24cells = [permuteList p [0,i,j*2,k*3] | p <- permutations 4, i <- pm, j <- pm , k <- pm]
where
pm = [-1,1]
thex :: [[Double]]
thex = nub [ permuteList p [0,0,i,j*2] | p <- permutations 4, i <- pm, j <- pm]
where
pm = [-1,1]
truncatedTetrahedron :: [[Double]]
truncatedTetrahedron = [ [1/sqrt 6, -2/sqrt 3, 2]
, [1/sqrt 6, -2/sqrt 3, -2]
, [1/sqrt 6, 4/ sqrt 3, 0]
, [-3/sqrt 6, 0, 2]
, [-3/sqrt 6, 0, -2]
, [-3/sqrt 6, sqrt 3, 1]
, [-3/sqrt 6, -sqrt 3, 1]
, [-3/sqrt 6, sqrt 3, -1]
, [-3/sqrt 6, -sqrt 3, -1]
, [5/sqrt 6, -1/sqrt 3, 1]
, [5/sqrt 6, -1/sqrt 3, -1]
, [5/sqrt 6, 2/sqrt 3, 0] ]
daVinci :: [[Double]]
daVinci = [ [1.61352, -0.43234, 1.1862],
[1.18118, -1.18118, 1.1862],
[0.43234, -1.61352, 1.1862],
[-0.43234, -1.61352, 1.1862],
[-1.18118, -1.18118, 1.1862],
[-1.61352, -0.43234, 1.1862],
[-1.61352, 0.43234, 1.1862],
[-1.18118, 1.18118, 1.1862],
[-0.43234, 1.61352, 1.1862],
[0.43234, 1.61352, 1.1862],
[1.18118, 1.18118, 1.1862],
[1.61352, 0.43234, 1.1862],
[1.61352, -0.43234, -1.1862],
[1.61352, 0.43234, -1.1862],
[1.18118, 1.18118, -1.1862],
[0.43234, 1.61352, -1.1862],
[-0.43234, 1.61352, -1.1862],
[-1.18118, 1.18118, -1.1862],
[-1.61352, 0.43234, -1.1862],
[-1.61352, -0.43234, -1.1862],
[-1.18118, -1.18118, -1.1862],
[-0.43234, -1.61352, -1.1862],
[0.43234, -1.61352, -1.1862],
[1.18118, -1.18118, -1.1862],
[2.0102, 0.53863, 0],
[1.47157, 1.47157, 0],
[0.53863, 2.0102, 0],
[-0.53863, 2.0102, 0],
[-1.47157, 1.47157, 0],
[-2.0102, 0.53863, 0],
[-2.0102, -0.53863, 0],
[-1.47157, -1.47157, 0],
[-0.53863, -2.0102, 0],
[0.53863, -2.0102, 0],
[1.47157, -1.47157, 0],
[2.0102, -0.53863, 0],
[0.89068, 0.23866, 1.77777],
[0.89068, -0.23866, 1.77777],
[0.65202, -0.65202, 1.77777],
[0.23866, -0.89068, 1.77777],
[-0.23866, -0.89068, 1.77777],
[-0.65202, -0.65202, 1.77777],
[-0.89068, -0.23866, 1.77777],
[-0.89068, 0.23866, 1.77777],
[-0.65202, 0.65202, 1.77777],
[-0.23866, 0.89068, 1.77777],
[0.23866, 0.89068, 1.77777],
[0.65202, 0.65202, 1.77777],
[0.65202, -0.65202, -1.77777],
[0.89068, -0.23866, -1.77777],
[0.89068, 0.23866, -1.77777],
[0.65202, 0.65202, -1.77777],
[0.23866, 0.89068, -1.77777],
[-0.23866, 0.89068, -1.77777],
[-0.65202, 0.65202, -1.77777],
[-0.89068, 0.23866, -1.77777],
[-0.89068, -0.23866, -1.77777],
[-0.65202, -0.65202, -1.77777],
[-0.23866, -0.89068, -1.77777],
[0.23866, -0.89068, -1.77777],
[0, 0, 2.04922],
[0, 0, -2.04922]]
-- Cuboctohadron4D - does not work
cuboctahedron4d :: [[Double]]
cuboctahedron4d = nub [ permuteList p [0,1,1,2] | p <- permutations 4]
-- OLOID --
twocircles :: [[Double]]
twocircles = circle1 `union` circle2
where
circle1 = [[cos (realToFrac i * 2*pi/30), sin (realToFrac i * 2*pi/30), 0] | i <- [0 .. 29]]
circle2 = [[0, cos (realToFrac i * 2*pi/30) - 1, sin (realToFrac i * 2*pi/30)] | i <- [0 .. 29]]
translate3 :: [[Double]] -> [Double] -> [[Double]]
translate3 points u = map (zipWith (+) u) points
duplicate3 :: [[Double]] -> [Double] -> [[Double]]
duplicate3 points u = nub $ points ++ translate3 points u
rgg :: [[Double]]
rgg = [[-5,-5, 16], [-5, 8, 3 ], [ 4,-1, 3 ], [ 4,-5, 7], [ 4,-1,-10],
[ 4,-5,-10], [-5, 8,-10], [-5,-5,-10]]
centricCube :: [[Double]]
centricCube = [[-1,-1,-1],[-1,-1, 1],[-1, 1,-1],[-1, 1, 1],[ 1,-1,-1],
[ 1,-1, 1],[ 1, 1,-1],[ 1, 1, 1],[ 0, 0, 0]]
squareLattice :: [[Double]]
squareLattice = [[0,0],[0,1],[0,2]
,[1,0],[1,1],[1,2]
,[2,0],[2,1],[2,2]]
centricSquare :: [[Double]]
centricSquare = [[0,0],[0,2],[2,0],[2,2],[1,1]]
cuboctahedron :: [[Double]]
cuboctahedron = [[i,j,0] | i <- [-1,1], j <- [-1,1]] ++
[[i,0,j] | i <- [-1,1], j <- [-1,1]] ++
[[0,i,j] | i <- [-1,1], j <- [-1,1]]
truncatedCuboctahedron :: [[Double]]
truncatedCuboctahedron =
[[i, j * (1 + sqrt 2), k * (1 + 2*sqrt 2)] | i <- pm, j <- pm, k <- pm] ++
[[j * (1 + sqrt 2), i, k * (1 + 2*sqrt 2)] | i <- pm, j <- pm, k <- pm] ++
[[j * (1 + sqrt 2), k * (1 + 2*sqrt 2), i] | i <- pm, j <- pm, k <- pm] ++
[[i, k * (1 + 2*sqrt 2), j * (1 + sqrt 2)] | i <- pm, j <- pm, k <- pm] ++
[[k * (1 + 2*sqrt 2), i, j * (1 + sqrt 2)] | i <- pm, j <- pm, k <- pm] ++
[[k * (1 + 2*sqrt 2), j * (1 + sqrt 2), i] | i <- pm, j <- pm, k <- pm]
where
pm = [-1,1]
rhombicDodecahedron :: [[Double]]
rhombicDodecahedron = [[-1.0, 0.0, 0.0], [-0.5,-0.5,-0.5], [-0.5,-0.5, 0.5],
[ 0.0,-1.0, 0.0], [-0.5, 0.5,-0.5], [-0.5, 0.5, 0.5],
[ 0.0, 1.0, 0.0], [ 1.0, 0.0, 0.0], [ 0.5,-0.5,-0.5],
[ 0.5,-0.5, 0.5], [ 0.5, 0.5,-0.5], [ 0.5, 0.5, 0.5],
[ 0.0, 0.0,-1.0], [ 0.0, 0.0, 1.0]]
faceCenteredCubic :: [[Double]]
faceCenteredCubic = [[-1,-1,-1],[-1,-1,1],[-1,1,-1],[-1,1,1]
,[1,-1,-1],[1,-1,1],[1,1,-1],[1,1,1]
,[1,0,0],[-1,0,0]
,[0,1,0],[0,-1,0]
,[0,0,1],[0,0,-1]]
waves :: [[Double]]
waves = [f u v | u <- seq_u, v <- seq_v]
where
f u v = [u, 0.05*(sin(v*4*pi)+sin(u*4*pi)), v]
frac p q = realToFrac p/ realToFrac q
n = 10
seq_u = [8 * frac i n - 4 | i <- [0 .. n]]
seq_v = [4 * frac i n - 2 | i <- [0 .. n]]
waves2D :: [[Double]]
waves2D = concatMap (\y' -> map (\[x,y] -> [x, y+y']) sinusoid) seq_y
where
seq_x = [realToFrac i * pi/2 | i <- [0 .. 20]]
sinusoid = map (\(x,y) -> [x,y]) (zip seq_x (map sin seq_x))
seq_y = [realToFrac 2*i | i <- [0 .. 20]]
type Vertex = [Double]
ncube :: Int -> [Vertex]
ncube n = concatMap (mapM (\x -> nub [x,-x])) [replicate n 1]
cube3 :: [[Double]]
cube3 = [[i,j,k] | i <- [-1,1], j <- [-1,1], k <- [-1,1]]
cube4 :: [[Double]]
cube4 = [[i,j,k,l] | i <- [-1,1], j <- [-1,1], k <- [-1,1], l <- [-1,1]]
cube5 :: [[Double]]
cube5 = [[i,j,k,l,m] | i <- [-1,1], j <- [-1,1], k <- [-1,1], l <- [-1,1],
m <- [-1,1]]
cube6 :: [[Double]]
cube6 = [[i,j,k,l,m,n] | i <- [-1,1], j <- [-1,1], k <- [-1,1], l <- [-1,1],
m <- [-1,1], n <- [-1,1]]
mobiusStrip :: [[Double]]
mobiusStrip = map (\(u,v) -> [ cos u * (1 + v/2 * cos(u/2))
, sin u * (1 + v/2 * cos(u/2))
, v/2 * sin(u/2) ]) uv
where
uv = [(u,v) | u <- u_, v <- v_]
u_ = [i/50 * 2 *pi | i <- [0 .. 50]]
v_ = [-1,1] -- [i/50 | i <- [-50 .. 50]]
irregularPolyhedron :: [[Double]]
irregularPolyhedron =
[ [ -0.586233 , 0.192482 , -1.9732e-2 ]
, [ -0.344233 , 0.301871 , 0.358301 ]
, [ 0.344233 , -0.301871 , 0.358301 ]
, [ 0.179112 , -0.514398 , -0.290554 ]
, [ 1.1612e-2 , -0.564879 , 0.137037 ]
, [ -1.1612e-2 , 0.564879 , 0.137037 ]
, [ -0.179112 , 0.514398 , -0.290554 ]
, [ -0.151548 , -0.185001 , -0.529915 ]
, [ -5.5686e-2 , -0.430284 , -0.411612 ]
, [ -0.364663 , -0.382652 , -0.277601 ]
, [ -0.394163 , -0.151218 , -0.422176 ]
, [ 5.5686e-2 , 0.430284 , -0.411612 ]
, [ 0.364663 , 0.382652 , -0.277601 ]
, [ 0.394163 , 0.151218 , -0.422176 ]
, [ 0.151548 , 0.185001 , -0.529915 ]
, [ 0.361372 , 0.268614 , 0.393607 ]
, [ 0.246149 , 0.511456 , 0.185169 ]
, [ 0.417404 , 0.426728 , -1.1876e-2 ]
, [ 0.510787 , 0.234322 , 0.148969 ]
, [ -0.361372 , -0.268614 , 0.393608 ]
, [ -0.510787 , -0.234322 , 0.148969 ]
, [ -0.417404 , -0.426728 , -1.1876e-2 ]
, [ -0.246149 , -0.511456 , 0.185169 ]
, [ 0.430396 , -0.334808 , -0.249032 ]
, [ 0.586233 , -0.192482 , -1.9732e-2 ]
, [ 0.587567 , -0.188189 , -2.1408e-2 ]
, [ 0.509201 , -0.136702 , -0.282307 ]
, [ -0.430396 , 0.334808 , -0.249032 ]
, [ -0.509201 , 0.136702 , -0.282307 ]
, [ -0.587567 , 0.188189 , -2.1408e-2 ]
, [ -0.272269 , -0.118712 , 0.520703 ]
, [ -0.248355 , 9.5223e-2 , 0.535651 ]
, [ 0.272269 , 0.118712 , 0.520703 ]
, [ -2.22e-4 , 2.388e-3 , 0.617335 ]
, [ 2.22e-4 , -2.388e-3 , 0.617335 ]
, [ 0.248355 , -9.5223e-2 , 0.535651 ]
]
truncatedCube :: [[Double]]
truncatedCube =
let x = 1 + sqrt 2 in
[[i, j*x, k*x] | i <- [-1,1], j <- [-1,1], k <- [-1,1]] ++
[[i*x, j, k*x] | i <- [-1,1], j <- [-1,1], k <- [-1,1]] ++
[[i*x, j*x, k] | i <- [-1,1], j <- [-1,1], k <- [-1,1]]
truncatedTesseract :: [[Double]]
truncatedTesseract =
let x = 1 + sqrt 2 in
[[i, j*x, k*x, l*x] | i <- [-1,1], j <- [-1,1], k <- [-1,1], l <- [-1,1]] ++
[[i*x, j, k*x, l*x] | i <- [-1,1], j <- [-1,1], k <- [-1,1], l <- [-1,1]] ++
[[i*x, j*x, k, l*x] | i <- [-1,1], j <- [-1,1], k <- [-1,1], l <- [-1,1]] ++
[[i*x, j*x, k*x, l] | i <- [-1,1], j <- [-1,1], k <- [-1,1], l <- [-1,1]]
projectedTruncatedTesseract :: [[Double]]
projectedTruncatedTesseract =
[ [-x1,-x2,-x2],
[-x4,-x3,-x3],
[-x1,-x2, x2],
[-x4,-x3, x3],
[-x1, x2,-x2],
[-x4, x3,-x3],
[-x1, x2, x2],
[-x4, x3, x3],
[ x1,-x2,-x2],
[ x4,-x3,-x3],
[ x1,-x2, x2],
[ x4,-x3, x3],
[ x1, x2,-x2],
[ x4, x3,-x3],
[ x1, x2, x2],
[ x4, x3, x3],
[-x2,-x1,-x2],
[-x3,-x4,-x3],
[-x2,-x1, x2],
[-x3,-x4, x3],
[-x2, x1,-x2],
[-x3, x4,-x3],
[-x2, x1, x2],
[-x3, x4, x3],
[ x2,-x1,-x2],
[ x3,-x4,-x3],
[ x2,-x1, x2],
[ x3,-x4, x3],
[ x2, x1,-x2],
[ x3, x4,-x3],
[ x2, x1, x2],
[ x3, x4, x3],
[-x2,-x2,-x1],
[-x3,-x3,-x4],
[-x2,-x2, x1],
[-x3,-x3, x4],
[-x2, x2,-x1],
[-x3, x3,-x4],
[-x2, x2, x1],
[-x3, x3, x4],
[ x2,-x2,-x1],
[ x3,-x3,-x4],
[ x2,-x2, x1],
[ x3,-x3, x4],
[ x2, x2,-x1],
[ x3, x3,-x4],
[ x2, x2, x1],
[ x3, x3, x4],
[-x6,-x6,-x6],
[-x5,-x5,-x5],
[-x6,-x6, x6],
[-x5,-x5, x5],
[-x6, x6,-x6],
[-x5, x5,-x5],
[-x6, x6, x6],
[-x5, x5, x5],
[ x6,-x6,-x6],
[ x5,-x5,-x5],
[ x6,-x6, x6],
[ x5,-x5, x5],
[ x6, x6,-x6],
[ x5, x5,-x5],
[ x6, x6, x6],
[ x5, x5, x5]]
where
a = 1 + sqrt 2
x1 = 2 / (sqrt(1 + 3*a*a) + a) -- 0.29
x2 = 2*a / (sqrt(1 + 3*a*a) + a) -- 0.71
x3 = 2*a / (sqrt(1 + 3*a*a) - a) -- 2.56
x4 = 2 / (sqrt(1 + 3*a*a) - a) -- 1.06
x5 = 2*a / (sqrt(1 + 3*a*a) - 1) -- 1.46
x6 = 2*a / (sqrt(1 + 3*a*a) + 1) -- 0.91
rectifiedTesseract :: [[Double]]
rectifiedTesseract =
let x = sqrt 2 in
[[0, j*x, k*x, l*x] | j <- [-1,1], k <- [-1,1], l <- [-1,1]] ++
[[i*x, 0, k*x, l*x] | i <- [-1,1], k <- [-1,1], l <- [-1,1]] ++
[[i*x, j*x, 0, l*x] | i <- [-1,1], j <- [-1,1], l <- [-1,1]] ++
[[i*x, j*x, k*x, 0] | i <- [-1,1], j <- [-1,1], k <- [-1,1]]
cantellatedTesseract :: [[Double]]
cantellatedTesseract =
let x = 1 + sqrt 2 in
map (map (/ sqrt(2 + 2*x*x))) $
[[i, j, k*x, l*x] | i <- [-1,1], j <- [-1,1], k <- [-1,1], l <- [-1,1]] ++
[[i*x, j, k, l*x] | i <- [-1,1], j <- [-1,1], k <- [-1,1], l <- [-1,1]] ++
[[i*x, j*x, k, l] | i <- [-1,1], j <- [-1,1], k <- [-1,1], l <- [-1,1]] ++
[[i, j*x, k, l*x] | i <- [-1,1], j <- [-1,1], k <- [-1,1], l <- [-1,1]] ++
[[i, j*x, k*x, l] | i <- [-1,1], j <- [-1,1], k <- [-1,1], l <- [-1,1]] ++
[[i*x, j, k*x, l] | i <- [-1,1], j <- [-1,1], k <- [-1,1], l <- [-1,1]]
projectedCantellatedTesseract :: [[Double]]
projectedCantellatedTesseract = map stereographic cantellatedTesseract
where
stereographic x = map (/(1-x!!3)) [2 * x!!0, 2 * x!!1, 2 * x!!2]
octaplex :: [[Double]]
octaplex = map (map (/ sqrt 2)) $
[[i,j,0,0] | i <- pm, j <- pm] ++
[[i,0,j,0] | i <- pm, j <- pm] ++
[[i,0,0,j] | i <- pm, j <- pm] ++
[[0,0,i,j] | i <- pm, j <- pm] ++
[[0,i,0,j] | i <- pm, j <- pm] ++
[[0,i,j,0] | i <- pm, j <- pm]
where
pm = [-1,1]
nonConvexPolyhedron :: [[Double]]
nonConvexPolyhedron =
[[i*x, j*x, k*x] | i <- [-1,1], j <- [-1,1], k <- [-1,1]] ++
[[i*y, 0, 0] | i <- [-1,1]] ++
[[0, j*y, 0] | j <- [-1,1]] ++
[[0, 0, k*y] | k <- [-1,1]]
where x = 2.1806973249
y = 3.5617820682
-- tetrahedra: (i 2.18, j 2.18, k 2.18), (i 3.56, 0, 0), (0, j 3.56, 0), (0, 0, k 3.56)
dodecahedron :: [[Double]] -- it's icosahedron !
dodecahedron = let phi = (1 + sqrt 5)/2 in
[[0,i,j] | i <- [-1,1], j <- [-phi, phi]] ++
[[j,0,i] | i <- [-1,1], j <- [-phi, phi]] ++
[[i,j,0] | i <- [-1,1], j <- [-phi, phi]]
icosahedron :: [[Double]]
icosahedron = dodecahedron
duoprism330 :: [[Double]]
duoprism330 = [a ++ b | a <- triangle, b <- p30]
where
triangle = [[cos (realToFrac i * 2*pi/3), sin (realToFrac i * 2*pi/3)] | i <- [0 .. 2]]
p30 = [[cos (realToFrac i * 2*pi/30), sin (realToFrac i * 2*pi/30)] | i <- [0 .. 29]]
duoprism35 :: [[Double]]
duoprism35 = [a ++ b | a <- triangle, b <- pentagon]
where
triangle = [ [sqrt 3 / 2 , 0.5]
, [-sqrt 3 / 2, 0.5]
, [0 , -1 ] ]
pentagon = [ [1 , 0 ]
, [cos(2*pi/5), sin(2*pi/5)]
, [cos(4*pi/5), sin(4*pi/5)]
, [cos(6*pi/5), sin(6*pi/5)]
, [cos(8*pi/5), sin(8*pi/5)] ]
duoprism34 :: [[Double]]
duoprism34 = [a ++ b | a <- triangle, b <- square]
where
triangle = [ [sqrt 3 / 2 , 0.5]
, [-sqrt 3 / 2, 0.5]
, [0 , -1 ] ]
square = [[i * sqrt 2 / 2, j * sqrt 2 / 2] | i <- [-1,1], j <- [-1,1]]
triangularDuoprism :: [[Double]]
triangularDuoprism = [a ++ b | a <- triangle, b <- triangle]
where
triangle = [ [sqrt 3 / 2 , 0.5]
, [-sqrt 3 / 2, 0.5]
, [0 , -1 ] ]
hexagonalDuoprism :: [[Double]]
hexagonalDuoprism = [a ++ b | a <- hexagon, b <- hexagon]
where
hexagon = [ [sqrt 3 / 2, 0.5]
, [0 , 1 ]
, [-sqrt 3 / 2, 0.5]
, [-sqrt 3 / 2, -0.5]
, [0 , -1 ]
, [sqrt 3 / 2 , -0.5] ]
projectedHexagonalDuoprims :: [[Double]]
projectedHexagonalDuoprims =
[ [ 1.8945800837529239 , 1.0938363213560542 , 1.8945800837529239 ]
, [ 4.181540550352056 , 2.414213562373096 , 0.0 ]
, [ 1.8945800837529239 , 1.0938363213560542 , -1.8945800837529239 ]
, [ 0.904836765142137 , 0.522407749927483 , -0.904836765142137 ]
, [ 0.7174389352143009 , 0.4142135623730951 , 0.0 ]
, [ 0.904836765142137 , 0.522407749927483 , 0.904836765142137 ]
, [ 0.0 , 2.1876726427121085 , 1.8945800837529239 ]
, [ 0.0 , 4.828427124746192 , 0.0 ]
, [ 0.0 , 2.1876726427121085 , -1.8945800837529239 ]
, [ 0.0 , 1.044815499854966 , -0.904836765142137 ]
, [ 0.0 , 0.8284271247461902 , 0.0 ]
, [ 0.0 , 1.044815499854966 , 0.904836765142137 ]
, [ -1.8945800837529239 , 1.0938363213560542 , 1.8945800837529239 ]
, [ -4.181540550352056 , 2.414213562373096 , 0.0 ]
, [ -1.8945800837529239
, 1.0938363213560542
, -1.8945800837529239
]
, [ -0.904836765142137 , 0.522407749927483 , -0.904836765142137 ]
, [ -0.7174389352143009 , 0.4142135623730951 , 0.0 ]
, [ -0.904836765142137 , 0.522407749927483 , 0.904836765142137 ]
, [ -1.8945800837529239
, -1.0938363213560542
, 1.8945800837529239
]
, [ -4.181540550352056 , -2.414213562373096 , 0.0 ]
, [ -1.8945800837529239
, -1.0938363213560542
, -1.8945800837529239
]
, [ -0.904836765142137 , -0.522407749927483 , -0.904836765142137 ]
, [ -0.7174389352143009 , -0.4142135623730951 , 0.0 ]
, [ -0.904836765142137 , -0.522407749927483 , 0.904836765142137 ]
, [ 0.0 , -2.1876726427121085 , 1.8945800837529239 ]
, [ 0.0 , -4.828427124746192 , 0.0 ]
, [ 0.0 , -2.1876726427121085 , -1.8945800837529239 ]
, [ 0.0 , -1.044815499854966 , -0.904836765142137 ]
, [ 0.0 , -0.8284271247461902 , 0.0 ]
, [ 0.0 , -1.044815499854966 , 0.904836765142137 ]
, [ 1.8945800837529239 , -1.0938363213560542 , 1.8945800837529239 ]
, [ 4.181540550352056 , -2.414213562373096 , 0.0 ]
, [ 1.8945800837529239
, -1.0938363213560542
, -1.8945800837529239
]
, [ 0.904836765142137 , -0.522407749927483 , -0.904836765142137 ]
, [ 0.7174389352143009 , -0.4142135623730951 , 0.0 ]
, [ 0.904836765142137 , -0.522407749927483 , 0.904836765142137 ]
]
hexaSquare :: [[Double]]
hexaSquare = [a ++ b | a <- hexagon, b <- square]
where
hexagon = [ [sqrt 3 / 2, 0.5]
, [0 , 1 ]
, [-sqrt 3 / 2, 0.5]
, [-sqrt 3 / 2, -0.5]
, [0 , -1 ]
, [sqrt 3 / 2 , -0.5] ]
square = [[i * sqrt 2 / 2, j * sqrt 2 / 2] | i <- [-1,1], j <- [-1,1]]
cubinder :: [[Double]]
cubinder = [a ++ b | a <- circle, b <- square]
where
circle = [[cos (realToFrac i * 2*pi/30), sin (realToFrac i * 2*pi/30)] | i <- [0 .. 29]]
square = [[i * sqrt 2 / 2, j * sqrt 2 / 2] | i <- [-1,1], j <- [-1,1]]
duoprism1616 :: [[Double]]
duoprism1616 = [a ++ b | a <- p16, b <- p16]
where
p16 = [[cos (realToFrac i * 2*pi/16), sin (realToFrac i * 2*pi/16)] | i <- [0 .. 15]]
duocylinder :: [[Double]]
duocylinder = [a ++ b | a <- circle, b <- circle]
where
circle = [[cos (realToFrac i * 2*pi/30), sin (realToFrac i * 2*pi/30)] | i <- [0 .. 29]]
reuleuxTetrahedron :: [[Double]]
reuleuxTetrahedron =
[ [0.5 / sqrt 3, -0.5, 0.5 / sqrt 6]
, [sqrt 3 / 3, 0, -0.5 / sqrt 6]
, [0.5 / sqrt 3, 0.5, -0.5 / sqrt 6]
, [0, 0, 0.5 * sqrt 3 / sqrt 2] ]
hexacosichoron :: [[Double]]
hexacosichoron =
[[i*0.5, j*0.5, k*0.5, l*0.5] | i <- pm, j <- pm, k <- pm, l <-pm] ++
[[0, 0, 0, i] | i <- pm] ++
[[0, 0, i, 0] | i <- pm] ++
[[0, i, 0, 0] | i <- pm] ++
[[i, 0, 0, 0] | i <- pm] ++
[ permuteList p [phi/2, 1/2, 1/2/phi, 0] | p <- permutations4, isEvenPermutation p] ++
[ permuteList p [phi/2, 1/2, -1/2/phi, 0] | p <- permutations4, isEvenPermutation p] ++
[ permuteList p [phi/2, -1/2, 1/2/phi, 0] | p <- permutations4, isEvenPermutation p] ++
[ permuteList p [phi/2, -1/2, -1/2/phi, 0] | p <- permutations4, isEvenPermutation p] ++
[ permuteList p [-phi/2, 1/2, 1/2/phi, 0] | p <- permutations4, isEvenPermutation p] ++
[ permuteList p [-phi/2, 1/2, -1/2/phi, 0] | p <- permutations4, isEvenPermutation p] ++
[ permuteList p [-phi/2, -1/2, 1/2/phi, 0] | p <- permutations4, isEvenPermutation p] ++
[ permuteList p [-phi/2, -1/2, -1/2/phi, 0] | p <- permutations4, isEvenPermutation p]
where
permutations4 = permutations 4
phi = (1 + sqrt 5) / 2
pm = [-1,1]
snub24cell :: [[Double]]
snub24cell =
[ permuteList p [0, i, i'*phi, i''*phi*phi] | i <- pm, i' <- pm, i'' <- pm, p <- permutations4, isEvenPermutation p]
where
permutations4 = permutations 4
phi = (1 + sqrt 5) / 2
pm = [-1,1]
dodecaplex :: [[Double]]
dodecaplex = nub $
[permuteList p [0.0, 0.0, i, j] | i <- pm2 , j <- pm2, p <- perms4] ++
[permuteList p [i, j, k, l] | i <- pm, j <- pm, k <-pm, l <- pmsqrt5, p <- perms4] ++
[permuteList p [i ,j ,k ,l] | i <- pmphipowminus2, j <- pmphi, k <- pmphi, l <- pmphi, p <- perms4] ++
[permuteList p [i ,j ,k ,l] | i <- pmphipowminus1, j <- pmphipowminus1, k <- pmphipowminus1, l <- pmphipow2, p <- perms4] ++
[permuteList p [0, i, j, k] | i <- pmphipowminus2, j <- pm, k <- pmphipow2, p <- perms4, isEvenPermutation p] ++
[permuteList p [0, i, j, k] | i <- pmphipowminus1, j <- pmphi, k <- pmsqrt5, p <- perms4, isEvenPermutation p] ++
[permuteList p [i, j, k, l] | i <- pmphipowminus1, j <- pm, k <- pmphi, l <- pm2, p <- perms4, isEvenPermutation p]
where
pm = [-1.0,1.0]
pm2 = [-2, 2]
perms4 = permutations 4
pmsqrt5 = [-sqrt 5, sqrt 5]
pmphipowminus2 = [-1/phi/phi, 1/phi/phi]
pmphipow2 = [-phi*phi, phi*phi]
phi = (1 + sqrt 5) / 2
-- pmphiminus1 = phi-1
pmphi = [phi, -phi]
pmphipowminus1 = [-1/phi, 1/phi]
spheresPack :: [[Double]]
spheresPack = [ [2,1,1], [4,1,1]
, [1, 1 + sqrt 3, 1], [3, 1 + sqrt 3, 1], [5, 1 + sqrt 3, 1]
, [2, 1 + 2*sqrt 3, 1], [4, 1 + 2*sqrt 3, 1]
, [3, 1 + sqrt 3 / 3, 1 + 2*sqrt 6 / 3]
, [2, 1 + 4*sqrt 3 / 3, 1 + 2*sqrt 6 / 3], [4, 1 + 4*sqrt 3 / 3, 1 + 2*sqrt 6 / 3]
, [3, 1 + sqrt 3, 1 + 4*sqrt 6 /3]
, [3, 1 + sqrt 3 / 3, 1 - 2*sqrt 6 / 3]
, [2, 1 + 4*sqrt 3 / 3, 1 - 2*sqrt 6 / 3], [4, 1 + 4*sqrt 3 / 3, 1 - 2*sqrt 6 / 3]
, [3, 1 + sqrt 3, 1 - 4*sqrt 6 /3] ]
randomInCircle :: Int -> IO [[Double]]
randomInCircle n = do
g1 <- newStdGen
let theta = map (*(2*pi)) (take n (randoms g1 :: [Double]))
g2 <- newStdGen
let rho = map (/2) (take n (randoms g2 :: [Double]))
return $ zipWith (\r a -> [(r+0.5) * cos a, (r+0.5) * sin a]) rho theta
randomInSquare :: Int -> IO [[Double]]
randomInSquare n = do
g <- newStdGen
return $ chunksOf 2 (take (2*n) (randoms g :: [Double]))
randomInSphere :: Int -> IO [[Double]]
randomInSphere n = do
g1 <- newStdGen
let theta = map (*(2*pi)) (take n (randoms g1 :: [Double]))
g2 <- newStdGen
let phi = map (*pi) (take n (randoms g2 :: [Double]))
g3 <- newStdGen
let rho = take n (randoms g3 :: [Double])
return $ zipWith3 (\r a b -> [r * cos a * sin b,
r * sin a * sin b,
r * cos b ])
rho theta phi
regularSphere :: Int -> [[Double]]
regularSphere n =
concatMap (\a -> map (s2c a) phi) theta
where
theta = map (*(2*pi)) [frac i n | i <- [0 .. n-1]]
phi = map (*pi) [frac i n | i <- [1 .. n-1]]
frac :: Int -> Int -> Double
frac p q = realToFrac p / realToFrac q
s2c :: Double -> Double -> [Double]
s2c th ph = [cos th * sin ph, sin th * sin ph, cos ph]
randomOnSphere :: Int -> Double -> IO [[Double]]
randomOnSphere n r = do
g <- newStdGen
let x = take (2*n) (randoms g :: [Double])
let u_ = map (*(2*pi)) (take n x)
let v_ = drop n x
return $ zipWith (\u v -> [r * cos u * sin (acos (2*v-1)),
r * sin u * sin (acos (2*v-1)),
r * (2*v-1) ]) u_ v_
randomInCube :: Int -> IO [[Double]]
randomInCube n = do
g <- newStdGen
return $ chunksOf 3 (take (3*n) (randoms g :: [Double]))
randomOnTorus :: Int -> Double -> Double -> IO [[Double]]
randomOnTorus n c a = do
g <- newStdGen
let x = take (2*n) (randoms g :: [Double])
let u_ = map (*(2*pi)) (take n x)
let v_ = map (*(2*pi)) (drop n x)
return $ zipWith (\u v -> [cos u * (c + a * cos v),
sin u * (c + a * cos v),
a * sin v ]) u_ v_
qcube1,qcube2,qcube3,qcube4,qcube5 :: [[Double]]
qcube1 =
[ [ 0.0 , 0.6180339887498949 , 1.618033988749895 ]
, [ -0.6180339887498949 , 1.618033988749895 , 0.0 ]
, [ 1.618033988749895 , 0.0 , 0.6180339887498949 ]
, [ 1.0 , 1.0 , -1.0 ]
, [ 0.6180339887498949 , -1.618033988749895 , 0.0 ]
, [ -1.0 , -1.0 , 1.0 ]
, [ -1.618033988749895 , 0.0 , -0.6180339887498949 ]
, [ 0.0 , -0.6180339887498949 , -1.618033988749895 ]
]
qcube2 =
[ [ -1.0 , 1.0 , 1.0 ]
, [ 0.6180339887498949 , 1.618033988749895 , 0.0 ]
, [ 0.0 , 0.6180339887498949 , -1.618033988749895 ]
, [ 0.0 , -0.6180339887498949 , 1.618033988749895 ]
, [ 1.618033988749895 , 0.0 , 0.6180339887498949 ]
, [ 1.0 , -1.0 , -1.0 ]
, [ -1.618033988749895 , 0.0 , -0.6180339887498949 ]
, [ -0.6180339887498949 , -1.618033988749895 , 0.0 ]
]
qcube3 =
[ [ -0.6180339887498949 , 1.618033988749895 , 0.0 ]
, [ 0.0 , 0.6180339887498949 , -1.618033988749895 ]
, [ 0.0 , -0.6180339887498949 , 1.618033988749895 ]
, [ 1.0 , 1.0 , 1.0 ]
, [ 1.618033988749895 , 0.0 , -0.6180339887498949 ]
, [ 0.6180339887498949 , -1.618033988749895 , 0.0 ]
, [ -1.618033988749895 , 0.0 , 0.6180339887498949 ]
, [ -1.0 , -1.0 , -1.0 ]
]
qcube4 =
[ [ -1.0 , 1.0 , 1.0 ]
, [ 1.0 , -1.0 , 1.0 ]
, [ 1.0 , 1.0 , 1.0 ]
, [ 1.0 , 1.0 , -1.0 ]
, [ 1.0 , -1.0 , -1.0 ]
, [ -1.0 , -1.0 , 1.0 ]
, [ -1.0 , 1.0 , -1.0 ]
, [ -1.0 , -1.0 , -1.0 ]
]
qcube5 =
[ [ 0.0 , 0.6180339887498949 , 1.618033988749895 ]
, [ 0.6180339887498949 , 1.618033988749895 , 0.0 ]
, [ 1.0 , -1.0 , 1.0 ]
, [ 1.618033988749895 , 0.0 , -0.6180339887498949 ]
, [ -1.618033988749895 , 0.0 , 0.6180339887498949 ]
, [ -1.0 , 1.0 , -1.0 ]
, [ -0.6180339887498949 , -1.618033988749895 , 0.0 ]
, [ 0.0 , -0.6180339887498949 , -1.618033988749895 ]
]
teapot :: [[Double]]
teapot =
[ [-3, 1.64999997615814, 0]
, [-2.98710989952087, 1.64999997615814, -0.0984380021691322]
, [-2.98710989952087, 1.64999997615814, 0.0984380021691322]
, [-2.98537993431091, 1.56731998920441, -0.0492190010845661]
, [-2.98537993431091, 1.56731998920441, 0.0492190010845661]
, [-2.9835000038147, 1.48308002948761, 0]
, [-2.98188996315002, 1.72346997261047, -0.0492190010845661]
, [-2.98188996315002, 1.72346997261047, 0.0492190010845661]
, [-2.97656011581421, 1.79852998256683, 0]
, [-2.97090005874634, 1.48620998859406, -0.0984380021691322]
, [-2.97090005874634, 1.48620998859406, 0.0984380021691322]
, [-2.96388006210327, 1.79533994197845, -0.0984380021691322]
, [-2.96388006210327, 1.79533994197845, 0.0984380021691322]
, [-2.96220993995667, 1.57017004489899, -0.133594006299973]
, [-2.96220993995667, 1.57017004489899, 0.133594006299973]
, [-2.95864009857178, 1.72056996822357, -0.133594006299973]
, [-2.95864009857178, 1.72056996822357, 0.133594006299973]
, [-2.95313000679016, 1.64999997615814, -0.168750002980232]
, [-2.95313000679016, 1.64999997615814, 0.168750002980232]
, [-2.95247006416321, 1.40374004840851, -0.0492190010845661]
, [-2.95247006416321, 1.40374004840851, 0.0492190010845661]
, [-2.93770003318787, 1.49447000026703, -0.168750002980232]
, [-2.93770003318787, 1.49447000026703, 0.168750002980232]
, [-2.93523001670837, 1.85214996337891, -0.0492190010845661]
, [-2.93523001670837, 1.85214996337891, 0.0492190010845661]
, [-2.93358993530273, 1.32011997699738, 0]
, [-2.93044996261597, 1.78692996501923, -0.168750002980232]
, [-2.93044996261597, 1.78692996501923, 0.168750002980232]
, [-2.93037009239197, 1.41149997711182, -0.133594006299973]
, [-2.93037009239197, 1.41149997711182, 0.133594006299973]
, [-2.92188000679016, 1.32553005218506, -0.0984380021691322]
, [-2.92188000679016, 1.32553005218506, 0.0984380021691322]
, [-2.91278004646301, 1.84416997432709, -0.133594006299973]
, [-2.91278004646301, 1.84416997432709, 0.133594006299973]
, [-2.90625, 1.91015994548798, 0]
, [-2.89422988891602, 1.90456998348236, -0.0984380021691322]
, [-2.89422988891602, 1.90456998348236, 0.0984380021691322]
, [-2.89138007164001, 1.57910001277924, -0.196875005960464]
, [-2.89138007164001, 1.57910001277924, 0.196875005960464]
, [-2.8909900188446, 1.33980000019073, -0.168750002980232]
, [-2.8909900188446, 1.33980000019073, 0.168750002980232]
, [-2.89065003395081, 1.71208000183105, -0.196875005960464]
, [-2.89065003395081, 1.71208000183105, 0.196875005960464]
, [-2.88346004486084, 1.24579000473022, -0.0483429990708828]
, [-2.88346004486084, 1.24579000473022, 0.0483429990708828]
, [-2.86346006393433, 1.25713002681732, -0.132717996835709]
, [-2.86346006393433, 1.25713002681732, 0.132717996835709]
, [-2.86265993118286, 1.43482995033264, -0.196875005960464]
, [-2.86265993118286, 1.43482995033264, 0.196875005960464]
, [-2.8625500202179, 1.88982999324799, -0.168750002980232]
, [-2.8625500202179, 1.88982999324799, 0.168750002980232]
, [-2.84999990463257, 1.64999997615814, -0.224999994039536]
, [-2.84999990463257, 1.64999997615814, 0.224999994039536]
, [-2.84970998764038, 1.16155004501343, 0]
, [-2.84710001945496, 1.82081997394562, -0.196875005960464]
, [-2.84710001945496, 1.82081997394562, 0.196875005960464]
, [-2.84193992614746, 1.94692003726959, -0.0492190010845661]
, [-2.84193992614746, 1.94692003726959, 0.0492190010845661]
, [-2.8289999961853, 1.76139998435974, -0.224999994039536]
, [-2.8289999961853, 1.76139998435974, 0.224999994039536]
, [-2.82867002487183, 1.17597997188568, -0.0949330031871796]
, [-2.82867002487183, 1.17597997188568, 0.0949330031871796]
, [-2.82470011711121, 1.52193999290466, -0.224999994039536]
, [-2.82470011711121, 1.52193999290466, 0.224999994039536]
, [-2.82115006446838, 1.93519997596741, -0.133594006299973]
, [-2.82115006446838, 1.93519997596741, 0.133594006299973]
, [-2.81230998039246, 1.18719005584717, -0.168750002980232]
, [-2.81230998039246, 1.18719005584717, 0.168750002980232]
, [-2.80501008033752, 1.28997004032135, -0.196875005960464]
, [-2.80501008033752, 1.28997004032135, 0.196875005960464]
, [-2.79727005958557, 1.38311004638672, -0.224999994039536]
, [-2.79727005958557, 1.38311004638672, 0.224999994039536]
, [-2.78906011581421, 1.99013996124268, 0]
, [-2.78836011886597, 1.69931995868683, -0.196875005960464]
, [-2.78836011886597, 1.69931995868683, 0.196875005960464]
, [-2.77820992469788, 1.98283004760742, -0.0984380021691322]
, [-2.77820992469788, 1.98283004760742, 0.0984380021691322]
, [-2.77442002296448, 1.52737998962402, -0.196875005960464]
, [-2.77442002296448, 1.52737998962402, 0.196875005960464]
, [-2.77356004714966, 1.09860002994537, -0.0843750014901161]
, [-2.77356004714966, 1.09860002994537, 0.0843750014901161]
, [-2.76641011238098, 1.84511995315552, -0.224999994039536]
, [-2.76641011238098, 1.84511995315552, 0.224999994039536]
, [-2.76033997535706, 1.90090000629425, -0.196875005960464]
, [-2.76033997535706, 1.90090000629425, 0.196875005960464]
, [-2.74959993362427, 1.96355998516083, -0.168750002980232]
, [-2.74959993362427, 1.96355998516083, 0.168750002980232]
, [-2.74831008911133, 1.78569996356964, -0.196875005960464]
, [-2.74831008911133, 1.78569996356964, 0.196875005960464]
, [-2.74688005447388, 1.64999997615814, -0.168750002980232]
, [-2.74688005447388, 1.64999997615814, 0.168750002980232]
, [-2.73125004768372, 1.00780999660492, 0]
, [-2.72756004333496, 1.73587000370026, -0.168750002980232]
, [-2.72756004333496, 1.73587000370026, 0.168750002980232]
, [-2.72036004066467, 1.69082999229431, -0.133594006299973]
, [-2.72036004066467, 1.69082999229431, 0.133594006299973]
, [-2.71948003768921, 1.24977004528046, -0.224999994039536]
, [-2.71948003768921, 1.24977004528046, 0.224999994039536]
, [-2.71677994728088, 1.14468002319336, -0.196875005960464]
, [-2.71677994728088, 1.14468002319336, 0.196875005960464]
, [-2.71288990974426, 1.64999997615814, -0.0984380021691322]
, [-2.71288990974426, 1.64999997615814, 0.0984380021691322]
, [-2.7089900970459, 1.54176998138428, -0.133594006299973]
, [-2.7089900970459, 1.54176998138428, 0.133594006299973]
, [-2.70354008674622, 1.42640995979309, -0.168750002980232]
, [-2.70354008674622, 1.42640995979309, 0.168750002980232]
, [-2.70097994804382, 1.03784000873566, -0.168750002980232]
, [-2.70097994804382, 1.03784000873566, 0.168750002980232]
, [-2.70000004768372, 1.64999997615814, 0]
, [-2.69965004920959, 2.0107901096344, -0.0483460016548634]
, [-2.69965004920959, 2.0107901096344, 0.0483460016548634]
, [-2.69711995124817, 1.68792998790741, -0.0492190010845661]
, [-2.69711995124817, 1.68792998790741, 0.0492190010845661]
, [-2.69412994384766, 1.72746002674103, -0.0984380021691322]
, [-2.69412994384766, 1.72746002674103, 0.0984380021691322]
, [-2.68661999702454, 1.54668998718262, -0.0492190010845661]
, [-2.68661999702454, 1.54668998718262, 0.0492190010845661]
, [-2.68263006210327, 1.76234996318817, -0.133594006299973]
, [-2.68263006210327, 1.76234996318817, 0.133594006299973]
, [-2.68147993087769, 1.9964599609375, -0.13272100687027]
, [-2.68147993087769, 1.9964599609375, 0.13272100687027]
, [-2.68144011497498, 1.72426998615265, 0]
, [-2.67574000358582, 1.27084994316101, -0.196875005960464]
, [-2.67574000358582, 1.27084994316101, 0.196875005960464]
, [-2.67265009880066, 1.44068002700806, -0.0984380021691322]
, [-2.67265009880066, 1.44068002700806, 0.0984380021691322]
, [-2.67025995254517, 1.80040001869202, -0.168750002980232]
, [-2.67025995254517, 1.80040001869202, 0.168750002980232]
, [-2.667799949646, 1.84623003005981, -0.196875005960464]
, [-2.667799949646, 1.84623003005981, 0.196875005960464]
, [-2.66279006004333, 1.9050999879837, -0.224999994039536]
, [-2.66279006004333, 1.9050999879837, 0.224999994039536]
, [-2.66093993186951, 1.44608998298645, 0]
, [-2.66018009185791, 1.75436997413635, -0.0492190010845661]
, [-2.66018009185791, 1.75436997413635, 0.0492190010845661]
, [-2.63858008384705, 1.78567004203796, -0.0984380021691322]
, [-2.63858008384705, 1.78567004203796, 0.0984380021691322]
, [-2.63438010215759, 1.10390996932983, -0.224999994039536]
, [-2.63438010215759, 1.10390996932983, 0.224999994039536]
, [-2.63073992729187, 1.95674002170563, -0.196875005960464]
, [-2.63073992729187, 1.95674002170563, 0.196875005960464]
, [-2.62655997276306, 1.78007996082306, 0]
, [-2.625, 2.04375004768372, 0]
, [-2.62463998794556, 1.30501997470856, -0.132813006639481]
, [-2.62463998794556, 1.30501997470856, 0.132813006639481]
, [-2.60642004013062, 1.31745004653931, -0.0484380014240742]
, [-2.60642004013062, 1.31745004653931, 0.0484380014240742]
, [-2.60631990432739, 2.02643990516663, -0.0949449986219406]
, [-2.60631990432739, 2.02643990516663, 0.0949449986219406]
, [-2.59179997444153, 2.01298999786377, -0.168750002980232]
, [-2.59179997444153, 2.01298999786377, 0.168750002980232]
, [-2.57172989845276, 1.83429002761841, -0.168750002980232]
, [-2.57172989845276, 1.83429002761841, 0.168750002980232]
, [-2.56777000427246, 1.16997003555298, -0.168750002980232]
, [-2.56777000427246, 1.16997003555298, 0.168750002980232]
, [-2.55460000038147, 1.18304002285004, -0.0953150019049644]
, [-2.55460000038147, 1.18304002285004, 0.0953150019049644]
, [-2.54975008964539, 1.89058995246887, -0.196875005960464]
, [-2.54975008964539, 1.89058995246887, 0.196875005960464]
, [-2.5495400428772, 0.878983974456787, -0.0843750014901161]
, [-2.5495400428772, 0.878983974456787, 0.0843750014901161]
, [-2.5464301109314, 1.83196997642517, -0.13272100687027]
, [-2.5464301109314, 1.83196997642517, 0.13272100687027]
, [-2.53749990463257, 1.20000004768372, 0]
, [-2.52720999717712, 1.81920003890991, -0.0483460016548634]
, [-2.52720999717712, 1.81920003890991, 0.0483460016548634]
, [-2.51874995231628, 1.94530999660492, -0.224999994039536]
, [-2.51874995231628, 1.94530999660492, 0.224999994039536]
, [-2.51682996749878, 0.932671010494232, -0.196875005960464]
, [-2.51682996749878, 0.932671010494232, 0.196875005960464]
, [-2.47183990478516, 1.00648999214172, -0.196875005960464]
, [-2.47183990478516, 1.00648999214172, 0.196875005960464]
, [-2.44569993019104, 1.87764000892639, -0.168750002980232]
, [-2.44569993019104, 1.87764000892639, 0.168750002980232]
, [-2.43913006782532, 1.06017994880676, -0.0843750014901161]
, [-2.43913006782532, 1.06017994880676, 0.0843750014901161]
, [-2.43118000030518, 1.86417996883392, -0.0949449986219406]
, [-2.43118000030518, 1.86417996883392, 0.0949449986219406]
, [-2.41249990463257, 1.84686994552612, 0]
, [-2.38827991485596, 0.716602027416229, 0]
, [-2.3822500705719, 0.737662971019745, -0.0958539992570877]
, [-2.3822500705719, 0.737662971019745, 0.0958539992570877]
, [-2.37883996963501, 2.05202007293701, -0.0843750014901161]
, [-2.37883996963501, 2.05202007293701, 0.0843750014901161]
, [-2.37766003608704, 0.753679990768433, -0.168750002980232]
, [-2.37766003608704, 0.753679990768433, 0.168750002980232]
, [-2.36474990844727, 0.798761010169983, -0.199836000800133]
, [-2.36474990844727, 0.798761010169983, 0.199836000800133]
, [-2.35430002212524, 0.835254013538361, -0.224999994039536]
, [-2.35430002212524, 0.835254013538361, 0.224999994039536]
, [-2.34383988380432, 0.871747016906738, -0.199836000800133]
, [-2.34383988380432, 0.871747016906738, 0.199836000800133]
, [-2.3411500453949, 1.99971997737885, -0.196875005960464]
, [-2.3411500453949, 1.99971997737885, 0.196875005960464]
, [-2.33092999458313, 0.916827023029327, -0.168750002980232]
, [-2.33092999458313, 0.916827023029327, 0.168750002980232]
, [-2.32031011581421, 0.953905999660492, 0]
, [-2.28931999206543, 1.9278199672699, -0.196875005960464]
, [-2.28931999206543, 1.9278199672699, 0.196875005960464]
, [-2.251620054245, 1.87551999092102, -0.0843750014901161]
, [-2.251620054245, 1.87551999092102, 0.0843750014901161]
, [-2.24741005897522, 0.882284998893738, -0.0843750014901161]
, [-2.24741005897522, 0.882284998893738, 0.0843750014901161]
, [-2.17362999916077, 0.844043016433716, 0]
, [-2.16852998733521, 0.826951026916504, -0.0971840023994446]
, [-2.16852998733521, 0.826951026916504, 0.0971840023994446]
, [-2.16476988792419, 0.814364016056061, -0.168750002980232]
, [-2.16476988792419, 0.814364016056061, 0.168750002980232]
, [-2.15687990188599, 0.78669399023056, -0.187068000435829]
, [-2.15687990188599, 0.78669399023056, 0.187068000435829]
, [-2.15625, 2.09296989440918, 0]
, [-2.15411996841431, 0.740520000457764, -0.215193003416061]
, [-2.15411996841431, 0.740520000457764, 0.215193003416061]
, [-2.15017008781433, 0.69473397731781, -0.215193003416061]
, [-2.15017008781433, 0.69473397731781, 0.215193003416061]
, [-2.14741992950439, 0.648559987545013, -0.187068000435829]
, [-2.14741992950439, 0.648559987545013, 0.187068000435829]
, [-2.14495992660522, 0.6127769947052, -0.132947996258736]
, [-2.14495992660522, 0.6127769947052, 0.132947996258736]
, [-2.143709897995, 0.59178900718689, -0.0485729984939098]
, [-2.143709897995, 0.59178900718689, 0.0485729984939098]
, [-2.14232993125916, 2.05836009979248, -0.168750002980232]
, [-2.14232993125916, 2.05836009979248, 0.168750002980232]
, [-2.11172008514404, 1.98222994804382, -0.224999994039536]
, [-2.11172008514404, 1.98222994804382, 0.224999994039536]
, [-2.08447003364563, 0.789525985717773, -0.0489050000905991]
, [-2.08447003364563, 0.789525985717773, 0.0489050000905991]
, [-2.08109998703003, 1.90609002113342, -0.168750002980232]
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voronoiCellTeapot :: [[Double]]
voronoiCellTeapot =
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