diff --git a/CHANGELOG.md b/CHANGELOG.md new file mode 100644 --- /dev/null +++ b/CHANGELOG.md @@ -0,0 +1,6 @@ +# Changelog for `marching-cubes` + + +## 0.1.0.0 - 2023-20-02 + +First release diff --git a/LICENSE b/LICENSE new file mode 100644 --- /dev/null +++ b/LICENSE @@ -0,0 +1,30 @@ +Copyright Stéphane Laurent (c) 2023 + +All rights reserved. + +Redistribution and use in source and binary forms, with or without +modification, are permitted provided that the following conditions are met: + + * Redistributions of source code must retain the above copyright + notice, this list of conditions and the following disclaimer. + + * Redistributions in binary form must reproduce the above + copyright notice, this list of conditions and the following + disclaimer in the documentation and/or other materials provided + with the distribution. + + * Neither the name of Stéphane Laurent nor the names of other + contributors may be used to endorse or promote products derived + from this software without specific prior written permission. + +THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR +A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT +OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, +SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT +LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, +DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY +THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT +(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE +OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. diff --git a/README.md b/README.md new file mode 100644 --- /dev/null +++ b/README.md @@ -0,0 +1,10 @@ +# marching-cubes + + +[![Stack-lts](https://github.com/stla/marching-cubes/actions/workflows/Stack-lts.yml/badge.svg)](https://github.com/stla/marching-cubes/actions/workflows/Stack-lts.yml) +[![Stack-nightly](https://github.com/stla/marching-cubes/actions/workflows/Stack-nightly.yml/badge.svg)](https://github.com/stla/marching-cubes/actions/workflows/Stack-nightly.yml) + + + +Pure Haskell implementation of the marching cubes algorithm. +See [some examples here](https://github.com/stla/isosurfaces). diff --git a/Setup.hs b/Setup.hs new file mode 100644 --- /dev/null +++ b/Setup.hs @@ -0,0 +1,2 @@ +import Distribution.Simple +main = defaultMain diff --git a/marching-cubes.cabal b/marching-cubes.cabal new file mode 100644 --- /dev/null +++ b/marching-cubes.cabal @@ -0,0 +1,49 @@ +name: marching-cubes +version: 0.1.0.0 +synopsis: Marching Cubes +description: Pure Haskell implementation of the marching cubes algorithm. +homepage: https://github.com/stla/marching-cubes#readme +license: BSD3 +license-file: LICENSE +author: Stéphane Laurent +maintainer: laurent_step@outlook.fr +copyright: 2023 Stéphane Laurent +category: Computational geometry +build-type: Simple +extra-source-files: README.md + CHANGELOG.md +cabal-version: >=1.10 + +library + hs-source-dirs: src + exposed-modules: MarchingCubes + other-modules: MarchingCubes.Utils + , MarchingCubes.Tables + , MarchingCubes.Internal + , MarchingCubes.MarchingCubes + , MarchingCubes.Mesh + other-extensions: BangPatterns + , FlexibleContexts + , TupleSections + build-depends: base >= 4.7 && < 5 + , vector >= 0.12.3.1 + , matrix >= 0.3.6.1 + , array >= 0.5.4.0 + , extra >= 1.7.9 + , split >= 0.2.3.4 + , linear >= 1.21.6 + , containers >= 0.6.4.1 + default-language: Haskell2010 + ghc-options: -Wall + -Wcompat + -Widentities + -Wincomplete-record-updates + -Wincomplete-uni-patterns + -Wmissing-export-lists + -Wmissing-home-modules + -Wpartial-fields + -Wredundant-constraints + +source-repository head + type: git + location: https://github.com/stla/marching-cubes diff --git a/src/MarchingCubes.hs b/src/MarchingCubes.hs new file mode 100644 --- /dev/null +++ b/src/MarchingCubes.hs @@ -0,0 +1,12 @@ +module MarchingCubes + ( module X + ) where +import MarchingCubes.MarchingCubes as X + ( Voxel + , XYZ + , makeVoxel + ) +import MarchingCubes.Mesh as X + ( Mesh (..) + , makeMesh + ) diff --git a/src/MarchingCubes/Internal.hs b/src/MarchingCubes/Internal.hs new file mode 100644 --- /dev/null +++ b/src/MarchingCubes/Internal.hs @@ -0,0 +1,274 @@ +{-# LANGUAGE BangPatterns #-} +{-# LANGUAGE FlexibleContexts #-} +module MarchingCubes.Internal + ( module MarchingCubes.Internal + ) where +import Data.Array.Unboxed ( IArray(..) + , UArray + ) +import qualified Data.Array.Unboxed as A +import Data.Bits ( shiftL ) +import qualified Data.Foldable as F +import Data.List ( zipWith4 ) +import Data.Matrix ( Matrix(..) + , elementwiseUnsafe + , fromLists + , getElem + , getRow + , matrix + , minorMatrix + , scaleMatrix + ) +import qualified Data.Matrix as M +import Data.Sequence ( Seq + , (|>) + ) +import qualified Data.Sequence as S +import qualified Data.Vector as V +import Data.Vector.Unboxed ( (!) + , Unbox + , Vector + ) +import qualified Data.Vector.Unboxed as UV +import MarchingCubes.Tables ( crf + , facePoints + , indexArray + ) +import MarchingCubes.Utils ( arrayToMatrix + , kro1 + , kro2 + , levelMatrix + , whichIndicesAndItems + ) + +facesNo7 + :: (Num a, Ord a, Unbox a) + => Vector Int + -> Vector Int + -> Vector a + -> Int + -> Int + -> [Int] +facesNo7 faces p1 values l j = map fun [0 .. l - 1] + where + fun i = if temp == 1 then shiftL 1 (j - 1) else 0 + where + f = abs (faces ! i) - 1 + e = facePoints V.! f + e1 = e ! 1 + e2 = e ! 2 + e3 = e ! 3 + e4 = e ! 4 + p = p1 ! i - 2 + a = values ! (p + e1) + b = values ! (p + e2) + c = values ! (p + e3) + d = values ! (p + e4) + temp = + (if faces ! i > 0 then 1 :: Int else -1) + * (if a * b - c * d > 0 then 1 else -1) + +faces7 + :: (RealFloat a, Unbox a) + => Vector Int + -> Vector Int + -> Vector a + -> Int + -> Int + -> [Int] +faces7 faces p1 values l j = map fun [0 .. l - 1] + where + fun i = if temp == 1 then shiftL 1 (j - 1) else 0 + where + p = (p1 ! i) - 1 + a0 = values ! p + b0 = values ! (p + 3) + c0 = values ! (p + 2) + d0 = values ! (p + 1) + a1 = values ! (p + 4) + b1 = values ! (p + 7) + c1 = values ! (p + 6) + d1 = values ! (p + 5) + a = (a1 - a0) * (c1 - c0) - (b1 - b0) * (d1 - d0) + b = c0 * (a1 - a0) + a0 * (c1 - c0) - d0 * (b1 - b0) - b0 * (d1 - d0) + c = a0 * c0 - b0 * d0 + tmax = -b / 2 / a + mxmm = a * tmax * tmax + b * tmax + c + mxmm' = if isNaN mxmm then -1 else mxmm + cond1 = a < 0 + cond2 = tmax > 0 + cond3 = tmax < 1 + cond4 = mxmm' > 0 + totalcond = cond1 && cond2 && cond3 && cond4 + temp = + (if faces ! i > 0 then 1 :: Int else -1) * (if totalcond then 1 else -1) + +faceType :: Real a => Matrix a -> a -> a -> Matrix Int +faceType mtrx level mx = elementwiseUnsafe (+) sum1 sum2 + where + lm = levelMatrix mtrx level (level < mx) + m = nrows mtrx + n = ncols mtrx + minorMat = minorMatrix m n lm + sminorMat2 = scaleMatrix 2 (minorMatrix 1 n lm) + sminorMat4 = scaleMatrix 4 (minorMatrix 1 1 lm) + sminorMat8 = scaleMatrix 8 (minorMatrix m 1 lm) + sum1 = elementwiseUnsafe (+) minorMat sminorMat2 + sum2 = elementwiseUnsafe (+) sminorMat4 sminorMat8 + +levCells + :: (Real a, IArray UArray a) + => UArray (Int, Int, Int) a + -> a + -> a + -> Matrix Int +levCells a level mx = out + where + bottomTypes = faceType (arrayToMatrix a 0) level mx + (_, (nx', ny', nz')) = bounds a + -- nx = nx' + 1 + -- ny = ny' + 1 + -- nz = nz' + 1 + (lengths, cells, types) = go 0 S.empty bottomTypes S.empty S.empty + go + :: Int + -> Seq Int + -> Matrix Int + -> Seq (Seq Int) + -> Seq (Seq Int) + -> (Seq Int, Seq (Seq Int), Seq (Seq Int)) + go k !lngths !bTypes !clls !tps + | k == nz' = (lngths, clls, tps) + | otherwise = go (k + 1) (lngths |> l) tTypes (clls |> cll) (tps |> tp) + where + tTypes = faceType (arrayToMatrix a (k + 1)) level mx + cellTypes = elementwiseUnsafe (+) bTypes (scaleMatrix 16 tTypes) + goodcells = whichIndicesAndItems cellTypes + l = S.length goodcells + cll = fmap (\(i, _) -> i + nx' * ny' * k + 1) goodcells + tp = fmap snd goodcells + out = M.transpose (fromLists (concatMap f [0 .. nz' - 1])) + f k = map (g k) [0 .. S.index lengths k - 1] + g k l = + [ c `mod` nx' + 1 + , (c `div` nx') `mod` ny' + 1 + , c `div` (nx' * ny') + 1 + , S.index (S.index types k) l + ] + where c = S.index (S.index cells k) l - 1 + +getBasic1 :: Vector Int -> Matrix Int -> Matrix Int +getBasic1 r vivjvk = elementwiseUnsafe (+) k1 k2 + where + nR = UV.length r + cube1 = matrix nR 3 (\(i, j) -> getElem (r ! (i - 1) + 1) j vivjvk) + k1 = kro1 indexArray nR + k2 = kro2 cube1 8 + +getBasic2 + :: (Num a, Unbox a, IArray UArray a) + => UArray (Int, Int, Int) a + -> a + -> Matrix Int + -> Vector a +getBasic2 a level cubeco = UV.fromList values + where + f i j = getElem i j cubeco - 1 + values = + [ a A.! (f i 1, f i 2, f i 3) - level | i <- [1 .. nrows cubeco - 1] ] + ++ [0] + +getTcase :: V.Vector Int -> Vector Int +getTcase types = + UV.fromList [ crf ! (types V.! i) - 1 | i <- [0 .. V.length types - 1] ] + +getR :: Vector Int -> Vector Int +getR tcase = UV.fromList $ F.toList $ go 0 S.empty + where + n = UV.length tcase + go :: Int -> Seq Int -> Seq Int + go i !out + | i == n + = out + | otherwise + = if tc == 1 + || tc == 2 + || tc == 5 + || tc == 8 + || tc == 9 + || tc == 11 + || tc == 14 + then + go (i + 1) (out |> i) + else + go (i + 1) out + where tc = tcase ! i + +lambdaMu :: RealFrac a => [a] -> ([a], [a]) +lambdaMu x1 = (lambda, mu) + where + lambda = map (\x -> fromInteger $ floor (x / 9)) x1 + mu = map (1 -) lambda + +average :: Num a => ([a], [a]) -> [a] -> [a] -> [a] +average (lambda, mu) = zipWith4 (\a b c d -> b * c + a * d) lambda mu + +average7 :: Num a => ([a], [a]) -> [a] -> [a] +average7 (lambda, mu) = zipWith3 (\a b c -> b * c + a) lambda mu + +average8 :: Num a => ([a], [a]) -> [a] -> [a] +average8 (lambda, mu) = zipWith3 (\a b c -> b * c - a) lambda mu + +getPoints + :: (Unbox a, RealFrac a) + => Matrix Int + -> Vector a + -> [Int] + -> [Int] + -> [Int] + -> Matrix a +getPoints cubeco values p1 x1 x2 = fromLists + [out0, out1, out2, out3, out4, out5, out6, out7] + where + p1x1 = zipWith (+) p1 x1 + p1x2 = zipWith (+) p1 x2 + xx1 = map fromIntegral x1 + lambdamu = lambdaMu xx1 + v1 = map (\j -> fromIntegral $ getElem (j - 1) 1 cubeco) p1x1 + w1 = map (\j -> fromIntegral $ getElem j 1 cubeco) p1 + v2 = map (\j -> fromIntegral $ getElem (j - 1) 1 cubeco) p1x2 + w2 = map (\j -> fromIntegral $ getElem (j + 1) 1 cubeco) p1 + v3 = map (\j -> fromIntegral $ getElem (j - 1) 2 cubeco) p1x1 + w3 = map (\j -> fromIntegral $ getElem (j + 1) 2 cubeco) p1 + v4 = map (\j -> fromIntegral $ getElem (j - 1) 2 cubeco) p1x2 + w4 = map (\j -> fromIntegral $ getElem (j + 2) 2 cubeco) p1 + v5 = map (\j -> fromIntegral $ getElem (j - 1) 3 cubeco) p1x1 + w5 = map (\j -> fromIntegral $ getElem (j + 1) 3 cubeco) p1 + v6 = map (\j -> fromIntegral $ getElem (j - 1) 3 cubeco) p1x2 + w6 = map (\j -> fromIntegral $ getElem (j + 5) 3 cubeco) p1 + v7 = map (\j -> values ! (j - 2)) p1x1 + v8 = map (\j -> values ! (j - 2)) p1x2 + out0 = average lambdamu v1 w1 + out1 = average lambdamu v2 w2 + out2 = average lambdamu v3 w3 + out3 = average lambdamu v4 w4 + out4 = average lambdamu v5 w5 + out5 = average lambdamu v6 w6 + out6 = average7 lambdamu v7 + out7 = average8 lambdamu v8 + +calPoints :: Fractional a => Matrix a -> Matrix a +calPoints points = M.transpose $ fromLists [x, y, z] + where + x1 = getRow 1 points + x2 = getRow 2 points + y1 = getRow 3 points + y2 = getRow 4 points + z1 = getRow 5 points + z2 = getRow 6 points + v1 = getRow 7 points + v2 = getRow 8 points + s = V.zipWith (\a b -> a / (a - b)) v1 v2 + x = V.toList $ V.zipWith3 (\a b c -> a + c * (b - a)) x1 x2 s + y = V.toList $ V.zipWith3 (\a b c -> a + c * (b - a)) y1 y2 s + z = V.toList $ V.zipWith3 (\a b c -> a + c * (b - a)) z1 z2 s diff --git a/src/MarchingCubes/MarchingCubes.hs b/src/MarchingCubes/MarchingCubes.hs new file mode 100644 --- /dev/null +++ b/src/MarchingCubes/MarchingCubes.hs @@ -0,0 +1,179 @@ +{-# LANGUAGE BangPatterns #-} +{-# LANGUAGE FlexibleContexts #-} +module MarchingCubes.MarchingCubes + ( Voxel + , XYZ + , marchingCubes + , makeVoxel + ) where +import Data.Array.Unboxed ( IArray + , UArray + , listArray + ) +import qualified Data.Foldable as F +import Data.List ( elemIndices + , findIndices + ) +import Data.Matrix ( (<->) + , Matrix(ncols) + , getCol + , getRow + , mapCol + , submatrix + ) +import qualified Data.Matrix as M +import Data.Maybe ( catMaybes + , mapMaybe + ) +import qualified Data.Vector as V +import Data.Vector.Unboxed ( (!) + , Unbox + ) +import qualified Data.Vector.Unboxed as UV +import MarchingCubes.Internal ( calPoints + , faces7 + , facesNo7 + , getBasic1 + , getBasic2 + , getPoints + , getR + , getTcase + , levCells + ) +import MarchingCubes.Tables ( edgePoints + , edgesLengths + , edgesTable + , edgesTable2 + , facesTable + , specialInd + , specialName + , specialNedge + , specialNface + , specialPos + ) +import MarchingCubes.Utils ( cbind + , jthColumn + , matrix2listMinusFirstColumn + , replicateEach + , replicateEach' + , subMatrix + , vector2matrix + ) + +type Bounds a = ((a, a), (a, a), (a, a)) +type Dims = (Int, Int, Int) +type Voxel a = ((UArray Dims a, a), (Bounds a, Dims)) +type XYZ a = (a, a, a) + +-- | Make the voxel. +makeVoxel + :: (RealFloat a, IArray UArray a) + => (XYZ a -> a) -- ^ the function defining the isosurface + -> Bounds a -- ^ bounds of the grid + -> Dims -- ^ numbers of subdivisions of the grid + -> Voxel a +makeVoxel fun bds@((xm, xM), (ym, yM), (zm, zM)) dims@(nx, ny, nz) = + ((listArray ((0, 0, 0), (nx - 1, ny - 1, nz - 1)) values, mxmm), (bds, dims)) + where + x_ = [ xm + (xM - xm) * fracx i | i <- [0 .. nx - 1] ] + fracx p = realToFrac p / (realToFrac nx - 1) + y_ = [ ym + (yM - ym) * fracy i | i <- [0 .. ny - 1] ] + fracy p = realToFrac p / (realToFrac ny - 1) + z_ = [ zm + (zM - zm) * fracz i | i <- [0 .. nz - 1] ] + fracz p = realToFrac p / (realToFrac nz - 1) + values = [ fun (x, y, z) | x <- x_, y <- y_, z <- z_ ] + mxmm = maximum (filter (not . isNaN) values) + +rescale :: Fractional a => (a, a) -> Int -> a -> a +rescale (minmm, maxmm) n w = minmm + (maxmm - minmm) * w / fromIntegral (n - 1) + +rescaleMatrix :: Fractional a => Matrix a -> Bounds a -> Dims -> Matrix a +rescaleMatrix mtrx (xbds, ybds, zbds) (nx, ny, nz) = mtrx''' + where + mtrx' = mapCol (\_ w -> rescale xbds nx (w - 1)) 1 mtrx + mtrx'' = mapCol (\_ w -> rescale ybds ny (w - 1)) 2 mtrx' + mtrx''' = mapCol (\_ w -> rescale zbds nz (w - 1)) 3 mtrx'' + +marchingCubes + :: (RealFloat a, Unbox a, IArray UArray a) => Voxel a -> a -> Matrix a +marchingCubes ((voxel, mx), (bds, dims)) level = rescaleMatrix + (maybe triangles1 (triangles1 <->) triangles2) + bds + dims + where + ijkt = levCells voxel level mx + vt = getRow 4 ijkt + tcase = getTcase vt + r = getR tcase + nR = UV.length r + ijk = submatrix 1 3 1 (ncols ijkt) ijkt + vivjvk = M.transpose ijk + cubeco = getBasic1 r vivjvk + values = getBasic2 voxel level cubeco + p1 = [ 8 * i + 1 | i <- [0 .. nR - 1] ] + cases = UV.map (\j -> vt V.! j - 1) r + edgeslengths = UV.map (edgesLengths UV.!) cases + p1rep = F.toList $ replicateEach p1 (UV.toList edgeslengths) + edges = + [ (edgesTable V.! (cases ! i)) ! j + | i <- [0 .. nR - 1] + , j <- [0 .. edgeslengths ! i - 1] + ] + epoints = map (\j -> edgePoints V.! (j - 1)) edges + x1 = map (! 1) epoints + x2 = map (! 2) epoints + points = getPoints cubeco values p1rep x1 x2 + triangles1 = calPoints points + -- ~~## special cases ##~~ + specialCases = map (`UV.elemIndices` tcase) specialName + r3s = filter (not . UV.null) specialCases + cs = findIndices (not . UV.null) specialCases + setOfTriangles = catMaybes (zipWith special cs r3s) + special c r3 = if null newtriangles + then Nothing + else Just $ foldl1 (<->) newtriangles + where + nR3 = UV.length r3 + cubeco3 = getBasic1 r3 vivjvk + values3 = getBasic2 voxel level cubeco3 + p13 = UV.map (\i -> 8 * i + 1) (UV.enumFromN 0 nR3) + cases3 = [ vt V.! (r3 ! i) - 1 | i <- [0 .. nR3 - 1] ] + nedge = specialNedge ! c + faces3 = UV.concat $ map (facesTable V.!) cases3 + index3 = case c of + 0 -> facesNo7 faces3 p13 values3 nR3 1 + 1 -> faces7 faces3 p13 values3 nR3 1 + _ -> index3' + where + nface = specialNface ! c + facelast = jthColumn faces3 nface (nface - 1) + index3' = loop 0 (faces7 facelast p13 values3 nR3 nface) + loop j !idx + | j == nface - 1 + = idx + | otherwise + = let facej = jthColumn faces3 nface j + in let temp = facesNo7 facej p13 values3 nR3 (j + 1) + in loop (j + 1) (zipWith (+) idx temp) + edges3' = UV.toList $ UV.concat $ map (edgesTable2 V.!) cases3 + edges3 = vector2matrix edges3' nedge + edgesp1index = cbind edges3 (UV.toList p13) index3 + ind3 = specialInd V.! c + newtriangles = mapMaybe f [0 .. UV.length ind3 - 1] + f j = triangles3 + where + wrows = elemIndices (ind3 ! j) index3 + triangles3 = if null wrows then Nothing else Just $ calPoints points3 + where + wcols = UV.cons nedge ((specialPos V.! c) V.! j) + ed = subMatrix edgesp1index wrows wcols + col0ed = V.toList $ getCol 1 ed + col0edrep = F.toList $ replicateEach' col0ed (UV.length wcols - 1) + edge1 = matrix2listMinusFirstColumn ed + epoints' = map (\k -> edgePoints V.! (k - 1)) edge1 + x1' = map (! 1) epoints' + x2' = map (! 2) epoints' + points3 = getPoints cubeco3 values3 col0edrep x1' x2' + triangles2 = if null setOfTriangles + then Nothing + else Just $ foldl1 (<->) setOfTriangles diff --git a/src/MarchingCubes/Mesh.hs b/src/MarchingCubes/Mesh.hs new file mode 100644 --- /dev/null +++ b/src/MarchingCubes/Mesh.hs @@ -0,0 +1,124 @@ +{-# LANGUAGE FlexibleContexts #-} +{-# LANGUAGE TupleSections #-} +module MarchingCubes.Mesh + ( makeMesh + , Mesh (..) + ) where +import Data.Array.Unboxed ( IArray + , UArray + ) +import Data.Bifunctor ( bimap ) +import Data.Foldable ( foldl' ) +import Data.IntMap.Strict ( IntMap + , elems + , unionWith + ) +import qualified Data.IntMap.Strict as IM +import Data.List.Split ( chunksOf ) +import Data.Map.Strict ( insertLookupWithKey ) +import qualified Data.Map.Strict as M +import Data.Matrix ( Matrix + , nrows + , toLists + ) +import Data.Tuple.Extra ( (***) + , curry3 + , second + , thd3 + ) +import Data.Vector.Unboxed ( (!) + , Unbox + , Vector + , fromList + ) +import Linear ( V3(..) + , (^+^) + , (^-^) + , cross + , signorm + ) +import MarchingCubes.MarchingCubes ( Voxel + , marchingCubes + ) + +-- type Mesh a = ((Vector (a, a, a), [[Int]]), Vector (a, a, a)) + +data Mesh a = Mesh + { + _vertices :: Vector (a, a, a) + , _faces :: [(Int, Int, Int)] + , _normals :: Vector (a, a, a) + } + deriving Show + +matrix2listOfTriples :: Matrix a -> [(a, a, a)] +matrix2listOfTriples mtrx = + map (\row -> (row !! 0, row !! 1, row !! 2)) (toLists mtrx) + +uniqueWithIndices :: (Unbox a, Ord a) => [a] -> (Vector a, Vector Int) +uniqueWithIndices list = (fromList *** fromList) $ go 0 M.empty list + where + go _ _ [] = ([], []) + go i m (x : xs) = case insertLookupWithKey (curry3 thd3) x i m of + (Nothing, m') -> bimap (x :) (i :) (go (i + 1) m' xs) + (Just j , m') -> second (j :) (go i m' xs) + +undupMesh + :: (Unbox a, Ord a) => ([(a, a, a)], [[Int]]) -> (Vector (a, a, a), [[Int]]) +undupMesh (vertices, faces) = (vertices', faces') + where + (vertices', idx) = uniqueWithIndices vertices + faces' = map (map (idx !)) faces + +normal :: Floating a => (a, a, a) -> (a, a, a) -> (a, a, a) -> V3 a +normal v1 v2 v3 = signorm $ cross (v3' ^-^ v1') (v2' ^-^ v1') -- (NaN,NaN,NaN) if degenerate face + where + toV3 (x, y, z) = V3 x y z + v1' = toV3 v1 + v2' = toV3 v2 + v3' = toV3 v3 + +faceNormals + :: (Floating a, Unbox a) => Vector (a, a, a) -> [Int] -> IntMap (V3 a) +faceNormals vs face = IM.fromList nrmls + where + nrml = normal (vs ! (face !! 0)) (vs ! (face !! 1)) (vs ! (face !! 2)) + nrmls = map (, nrml) face + +normalsV3 + :: (Floating a, Unbox a) => (Vector (a, a, a), [[Int]]) -> IntMap (V3 a) +normalsV3 (vs, faces) = IM.map + signorm + (foldl' (unionWith (^+^)) IM.empty (map (faceNormals vs) faces)) + +normals + :: (Floating a, Unbox a) => (Vector (a, a, a), [[Int]]) -> Vector (a, a, a) +normals mesh = fromList $ map fromV3 (elems $ normalsV3 mesh) + where fromV3 (V3 x y z) = (x, y, z) + +degenerateFace :: (Unbox a, Eq a) => Vector (a, a, a) -> [Int] -> Bool +degenerateFace vertices face = v1 == v2 || v1 == v3 || v2 == v3 + where + v1 = vertices ! (face !! 0) + v2 = vertices ! (face !! 1) + v3 = vertices ! (face !! 2) + +-- | Make mesh of isosurface. +makeMesh :: + (Unbox a, RealFloat a, IArray UArray a) + => Voxel a -- ^ voxel obtained with `makeVoxel` + -> a -- ^ isovalue + -> Mesh a +makeMesh voxel level = Mesh + { + _vertices = vertices', _faces = faces''', _normals = normals mesh + } + where + mtrx = marchingCubes voxel level + vertices = matrix2listOfTriples mtrx + faces = chunksOf 3 [0 .. nrows mtrx - 1] + (vertices', faces') = undupMesh (vertices, faces) + faces'' = filter (not . degenerateFace vertices') faces' + faces''' = map toTriplet faces'' + mesh = (vertices', faces'') + toTriplet ikj = (ikj !! 0, ikj !! 2, ikj !! 1) diff --git a/src/MarchingCubes/Tables.hs b/src/MarchingCubes/Tables.hs new file mode 100644 --- /dev/null +++ b/src/MarchingCubes/Tables.hs @@ -0,0 +1,996 @@ +module MarchingCubes.Tables + ( module MarchingCubes.Tables + ) where +import Data.Matrix ( Matrix + , fromLists + ) +import qualified Data.Vector as V +import qualified Data.Vector.Unboxed as UV + + +indexArray :: Matrix Int +indexArray = fromLists + [ [0, 0, 0] + , [1, 0, 0] + , [1, 1, 0] + , [0, 1, 0] + , [0, 0, 1] + , [1, 0, 1] + , [1, 1, 1] + , [0, 1, 1] + ] + +edgesLengths :: UV.Vector Int +edgesLengths = UV.fromList + [3, 3, 6, 3, 0, 6, 9, 3, 6, 0, 9, 6, 9, 9, 6, 3, 6, 0, 9, 0, + 0, 0, 12, 0, 9, 0, 12, 0, 12, 0, 9, 3, 0, 6, 9, 0, 0, 9, 12, + 0, 0, 0, 12, 0, 0, 12, 9, 6, 9, 9, 6, 0, 0, 12, 9, 0, 12, 0, + 9, 0, 0, 0, 6, 3, 0, 0, 0, 6, 0, 9, 12, 0, 0, 0, 0, 9, 12, 12, + 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 9, 12, + 9, 0, 6, 9, 0, 0, 0, 0, 12, 0, 9, 6, 9, 12, 12, 9, 12, 0, 9, + 6, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 6, 9, 0, 12, + 9, 12, 12, 9, 6, 9, 0, 12, 0, 0, 0, 0, 9, 6, 0, 9, 12, 9, 0, + 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 12, 12, + 9, 0, 0, 0, 0, 12, 9, 0, 6, 0, 0, 0, 3, 6, 0, 0, 0, 9, 0, 12, + 0, 9, 12, 0, 0, 6, 9, 9, 6, 9, 12, 0, 0, 12, 0, 0, 0, 12, 9, + 0, 0, 9, 6, 0, 3, 9, 0, 12, 0, 12, 0, 9, 0, 12, 0, 0, 0, 9, 0, + 6, 3, 6, 9, 9, 6, 9, 0, 6, 3, 9, 6, 0, 3, 6, 3, 3] + +edgePoints :: V.Vector (UV.Vector Int) +edgePoints = V.fromList + (map + UV.fromList + [ [1, 1, 2] + , [2, 2, 3] + , [3, 3, 4] + , [4, 4, 1] + , [5, 5, 6] + , [6, 6, 7] + , [7, 7, 8] + , [8, 8, 5] + , [9, 1, 5] + , [10, 2, 6] + , [11, 3, 7] + , [12, 4, 8] + , [13, 9, 9] + ] + ) + +edgesTable :: V.Vector (UV.Vector Int) +edgesTable = V.fromList + (map + UV.fromList + [ [4, 9, 1] + , [1, 10, 2] + , [9, 10, 4, 10, 2, 4] + , [2, 11, 3] + , [0] + , [10, 11, 1, 11, 3, 1] + , [4, 9, 3, 3, 9, 11, 9, 10, 11] + , [12, 4, 3] + , [12, 9, 3, 9, 1, 3] + , [0] + , [3, 12, 2, 2, 12, 10, 12, 9, 10] + , [4, 2, 12, 2, 11, 12] + , [2, 11, 1, 1, 11, 9, 11, 12, 9] + , [1, 10, 4, 4, 10, 12, 10, 11, 12] + , [11, 9, 10, 11, 12, 9] + , [8, 5, 9] + , [5, 1, 8, 1, 4, 8] + , [0] + , [10, 2, 5, 5, 2, 8, 2, 4, 8] + , [0] + , [0] + , [0] + , [3, 4, 8, 3, 8, 10, 3, 10, 11, 8, 5, 10] + , [0] + , [8, 5, 12, 12, 5, 3, 5, 1, 3] + , [0] + , [2, 5, 10, 2, 3, 8, 2, 8, 5, 8, 3, 12] + , [0] + , [2, 11, 12, 2, 12, 5, 2, 5, 1, 8, 12, 5] + , [0] + , [8, 5, 12, 5, 10, 12, 12, 10, 11] + , [6, 10, 5] + , [0] + , [1, 5, 2, 5, 6, 2] + , [5, 6, 9, 9, 6, 4, 6, 2, 4] + , [0] + , [0] + , [11, 3, 6, 6, 3, 5, 3, 1, 5] + , [6, 9, 5, 6, 11, 4, 6, 4, 9, 4, 11, 3] + , [0] + , [0] + , [0] + , [3, 6, 2, 3, 9, 6, 3, 12, 9, 5, 9, 6] + , [0] + , [0] + , [6, 1, 5, 6, 12, 1, 6, 11, 12, 1, 12, 4] + , [5, 6, 9, 6, 11, 9, 9, 11, 12] + , [8, 6, 9, 6, 10, 9] + , [1, 4, 10, 10, 4, 6, 4, 8, 6] + , [9, 8, 1, 1, 8, 2, 8, 6, 2] + , [4, 8, 6, 4, 6, 2] + , [0] + , [0] + , [9, 3, 1, 9, 6, 3, 9, 8, 6, 11, 6, 3] + , [11, 3, 6, 3, 4, 6, 6, 4, 8] + , [0] + , [10, 1, 3, 10, 3, 8, 10, 8, 6, 3, 12, 8] + , [0] + , [3, 12, 2, 12, 8, 2, 2, 8, 6] + , [0] + , [0] + , [0] + , [12, 8, 11, 11, 8, 6] + , [6, 7, 11] + , [0] + , [0] + , [0] + , [2, 6, 3, 6, 7, 3] + , [0] + , [6, 7, 10, 10, 7, 1, 7, 3, 1] + , [6, 7, 3, 6, 3, 9, 6, 9, 10, 4, 3, 9] + , [0] + , [0] + , [0] + , [0] + , [12, 4, 7, 7, 4, 6, 4, 2, 6] + , [1, 12, 9, 1, 6, 12, 1, 2, 6, 12, 6, 7] + , [4, 7, 12, 4, 1, 6, 4, 6, 7, 6, 1, 10] + , [6, 7, 10, 7, 12, 10, 10, 12, 9] + , [0] + , [0] + , [0] + , [0] + , [0] + , [0] + , [0] + , [0] + , [0] + , [0] + , [0] + , [0] + , [0] + , [0] + , [0] + , [0] + , [5, 7, 10, 7, 11, 10] + , [0] + , [2, 1, 11, 11, 1, 7, 1, 5, 7] + , [9, 5, 7, 9, 7, 2, 9, 2, 4, 7, 11, 2] + , [10, 5, 2, 2, 5, 3, 5, 7, 3] + , [0] + , [3, 1, 5, 3, 5, 7] + , [4, 9, 3, 9, 5, 3, 3, 5, 7] + , [0] + , [0] + , [0] + , [0] + , [10, 5, 7, 10, 7, 4, 10, 4, 2, 12, 7, 4] + , [0] + , [12, 4, 7, 4, 1, 7, 7, 1, 5] + , [9, 5, 12, 12, 5, 7] + , [7, 11, 8, 8, 11, 9, 11, 10, 9] + , [1, 11, 10, 1, 8, 11, 1, 4, 8, 7, 8, 11] + , [8, 1, 9, 8, 7, 2, 8, 2, 1, 2, 7, 11] + , [7, 11, 8, 11, 2, 8, 8, 2, 4] + , [2, 10, 9, 2, 9, 7, 2, 7, 3, 9, 8, 7] + , [0] + , [9, 8, 1, 8, 7, 1, 1, 7, 3] + , [8, 7, 4, 4, 7, 3] + , [0] + , [0] + , [0] + , [0] + , [0] + , [0] + , [0] + , [8, 7, 12] + , [8, 12, 7] + , [0] + , [0] + , [0] + , [0] + , [0] + , [0] + , [0] + , [8, 4, 7, 4, 3, 7] + , [9, 1, 8, 8, 1, 7, 1, 3, 7] + , [0] + , [2, 9, 10, 2, 7, 9, 2, 3, 7, 9, 7, 8] + , [7, 8, 11, 11, 8, 2, 8, 4, 2] + , [8, 9, 1, 8, 2, 7, 8, 1, 2, 2, 11, 7] + , [1, 10, 11, 1, 11, 8, 1, 8, 4, 7, 11, 8] + , [7, 8, 11, 8, 9, 11, 11, 9, 10] + , [9, 12, 5, 12, 7, 5] + , [12, 7, 4, 4, 7, 1, 7, 5, 1] + , [0] + , [10, 7, 5, 10, 4, 7, 10, 2, 4, 12, 4, 7] + , [0] + , [0] + , [0] + , [0] + , [4, 3, 9, 9, 3, 5, 3, 7, 5] + , [3, 5, 1, 3, 7, 5] + , [0] + , [10, 2, 5, 2, 3, 5, 5, 3, 7] + , [9, 7, 5, 9, 2, 7, 9, 4, 2, 7, 2, 11] + , [2, 11, 1, 11, 7, 1, 1, 7, 5] + , [0] + , [5, 10, 7, 7, 10, 11] + , [0] + , [0] + , [0] + , [0] + , [0] + , [0] + , [0] + , [0] + , [0] + , [0] + , [0] + , [0] + , [0] + , [0] + , [0] + , [0] + , [6, 10, 7, 7, 10, 12, 10, 9, 12] + , [4, 12, 7, 4, 6, 1, 4, 7, 6, 6, 10, 1] + , [1, 9, 12, 1, 12, 6, 1, 6, 2, 12, 7, 6] + , [12, 7, 4, 7, 6, 4, 4, 6, 2] + , [0] + , [0] + , [0] + , [0] + , [6, 3, 7, 6, 9, 3, 6, 10, 9, 4, 9, 3] + , [6, 10, 7, 10, 1, 7, 7, 1, 3] + , [0] + , [2, 3, 6, 6, 3, 7] + , [0] + , [0] + , [0] + , [6, 11, 7] + , [12, 11, 8, 11, 6, 8] + , [0] + , [0] + , [0] + , [3, 2, 12, 12, 2, 8, 2, 6, 8] + , [0] + , [10, 3, 1, 10, 8, 3, 10, 6, 8, 3, 8, 12] + , [0] + , [11, 6, 3, 3, 6, 4, 6, 8, 4] + , [9, 1, 3, 9, 3, 6, 9, 6, 8, 11, 3, 6] + , [0] + , [0] + , [4, 6, 8, 4, 2, 6] + , [9, 1, 8, 1, 2, 8, 8, 2, 6] + , [1, 10, 4, 10, 6, 4, 4, 6, 8] + , [8, 9, 6, 6, 9, 10] + , [5, 9, 6, 6, 9, 11, 9, 12, 11] + , [6, 5, 1, 6, 1, 12, 6, 12, 11, 1, 4, 12] + , [0] + , [0] + , [3, 2, 6, 3, 6, 9, 3, 9, 12, 5, 6, 9] + , [0] + , [0] + , [0] + , [6, 5, 9, 6, 4, 11, 6, 9, 4, 4, 3, 11] + , [11, 6, 3, 6, 5, 3, 3, 5, 1] + , [0] + , [0] + , [5, 9, 6, 9, 4, 6, 6, 4, 2] + , [1, 2, 5, 5, 2, 6] + , [0] + , [6, 5, 10] + , [8, 12, 5, 5, 12, 10, 12, 11, 10] + , [0] + , [2, 12, 11, 2, 5, 12, 2, 1, 5, 8, 5, 12] + , [0] + , [2, 10, 5, 2, 8, 3, 2, 5, 8, 8, 12, 3] + , [0] + , [8, 12, 5, 12, 3, 5, 5, 3, 1] + , [0] + , [3, 8, 4, 3, 10, 8, 3, 11, 10, 8, 10, 5] + , [0] + , [0] + , [0] + , [10, 5, 2, 5, 8, 2, 2, 8, 4] + , [0] + , [5, 8, 1, 1, 8, 4] + , [8, 9, 5] + , [11, 10, 9, 11, 9, 12] + , [1, 4, 10, 4, 12, 10, 10, 12, 11] + , [2, 1, 11, 1, 9, 11, 11, 9, 12] + , [4, 12, 2, 2, 12, 11] + , [3, 2, 12, 2, 10, 12, 12, 10, 9] + , [0] + , [12, 3, 9, 9, 3, 1] + , [12, 3, 4] + , [4, 3, 9, 3, 11, 9, 9, 11, 10] + , [10, 1, 11, 11, 1, 3] + , [0] + , [2, 3, 11] + , [9, 4, 10, 10, 4, 2] + , [1, 2, 10] + , [4, 1, 9] + ] + ) + +facesTable :: V.Vector (UV.Vector Int) +facesTable = V.fromList + (map + UV.fromList + [ [0] + , [0] + , [0] + , [0] + , [5] + , [0] + , [0] + , [0] + , [0] + , [-5] + , [0] + , [0] + , [0] + , [0] + , [0] + , [0] + , [0] + , [-1] + , [0] + , [7] + , [5, 7] + , [-1, 7] + , [0] + , [-4] + , [0] + , [-5, -1, -4, 7] + , [0] + , [-4, 7] + , [0] + , [-4, -1, 7] + , [0] + , [0] + , [1] + , [0] + , [0] + , [-2] + , [-2, 1, 5, -7] + , [0] + , [0] + , [-7] + , [1, -7] + , [-5, -7] + , [0] + , [-2, -7] + , [-2, 1, -7] + , [0] + , [0] + , [0] + , [0] + , [0] + , [0] + , [-2, 7] + , [5, -2, 7] + , [0] + , [0] + , [-4, -7] + , [0] + , [-4, -5, -7] + , [0] + , [-2, -4, 7] + , [2, -7] + , [4, 7] + , [0] + , [0] + , [7] + , [2] + , [2, 7] + , [0] + , [5, 7] + , [0] + , [0] + , [3] + , [3, 7] + , [-5, 3, 2, 7] + , [2, 3, 7] + , [0] + , [0] + , [0] + , [0] + , [6] + , [6, 7] + , [6, -1, 2, -7] + , [2, 6, 7] + , [6, 7] + , [6, 5, 7] + , [6, -1, 7] + , [-6, -7] + , [6, 3, -4, -7] + , [6, 3, 7] + , [-5, -1, 6, 3, 2, -4, 7] + , [-3, -6, -2, 7] + , [-4, 6, 7] + , [-6, -7] + , [-6, 4, 1, 7] + , [-6] + , [0] + , [1, 7] + , [0] + , [0] + , [0] + , [5, 1, 7] + , [0] + , [0] + , [3, -7] + , [1, 3, 7] + , [-5, 3, -7] + , [-3, 7] + , [0] + , [-1, -7] + , [0] + , [0] + , [0] + , [0] + , [0] + , [0] + , [0] + , [-5, -7] + , [0] + , [0] + , [-4, 3, -7] + , [-3, -7] + , [4, -3, 5, -7] + , [-3] + , [4, -7] + , [-7] + , [4] + , [0] + , [0] + , [4] + , [-7] + , [4, -7] + , [-3] + , [4, -3, 5, -7] + , [-3, -7] + , [4, -3, -7] + , [0] + , [0] + , [-5, -7] + , [0] + , [0] + , [0] + , [0] + , [0] + , [0] + , [0] + , [-1, -7] + , [0] + , [-3, 7] + , [5, -3, 7] + , [-1, -3, 7] + , [3, -7] + , [0] + , [0] + , [-5, -1, -7] + , [0] + , [0] + , [0] + , [1, 7] + , [0] + , [-6] + , [-6, 4, 1, 7] + , [-6, -7] + , [4, -6, -7] + , [-3, -6, -2, 7] + , [5, 1, -6, -3, -2, 4, 7] + , [-6, -3, -7] + , [6, 3, -4, -7] + , [-6, -7] + , [-6, 1, -7] + , [-6, -5, -7] + , [6, 7] + , [-2, -6, -7] + , [6, -1, 2, -7] + , [6, 7] + , [6] + , [0] + , [0] + , [0] + , [0] + , [-2, -3, 7] + , [-5, 3, 2, 7] + , [3, 7] + , [3] + , [0] + , [0] + , [5, 7] + , [0] + , [2, 7] + , [2] + , [7] + , [0] + , [0] + , [4, 7] + , [2, -7] + , [2, 4, 7] + , [0] + , [4, 5, 7] + , [0] + , [-4, -7] + , [0] + , [0] + , [-5, 2, -7] + , [-2, 7] + , [0] + , [0] + , [0] + , [0] + , [0] + , [0] + , [2, -1, -7] + , [-2, -7] + , [0] + , [-5, -7] + , [1, -7] + , [-7] + , [0] + , [0] + , [-2, 1, 5, -7] + , [-2] + , [0] + , [0] + , [1] + , [0] + , [0] + , [4, 1, 7] + , [0] + , [-4, 7] + , [0] + , [-5, -1, -4, 7] + , [0] + , [-4] + , [0] + , [-1, 7] + , [5, 7] + , [7] + , [0] + , [-1] + , [0] + , [0] + , [0] + , [0] + , [0] + , [0] + , [0] + , [-5] + , [0] + , [0] + , [0] + , [0] + , [5] + , [0] + , [0] + , [0] + , [0] + ] + ) + +facePoints :: V.Vector (UV.Vector Int) +facePoints = V.fromList + (map + UV.fromList + [ [1, 1, 6, 2, 5, 60] + , [2, 2, 7, 3, 6, 252] + , [3, 4, 7, 3, 8, 672] + , [4, 1, 8, 4, 5, 160] + , [5, 1, 3, 2, 4, 24] + , [6, 5, 7, 6, 8, 1680] + ] + ) + +edgesTable2 :: V.Vector (UV.Vector Int) +edgesTable2 = V.fromList + (map + UV.fromList + [ + [0], + [0], + [0], + [0], + [2, 11, 3, 4, 9, 1, 2, 11, 1, 11, 9, 1, 11, 4, 9, 11, 3, 4], + [0], + [0], + [0], + [0], + [1, 10, 2, 3, 12, 4, 1, 10, 4, 10, 12, 4, 10, 3, 12, 10, 2, 3], + [0], + [0], + [0], + [0], + [0], + [0], + [0], + [10, 2, 1, 9, 8, 5, 10, 2, 5, 2, 8, 5, 2, 9, 8, 2, 1, 9], + [0], + [2, 11, 3, 9, 8, 5, 2, 9, 3, 9, 8, 3, 11, 3, 8, 2, 11, 5, 2, 5, 9, 11, 8, 5], + [4, 8, 1, 8, 5, 1, 2, 11, 3, 4, 8, 3, 8, 11, 3, 8, 5, 11, 2, 11, 5, 2, 5, 1, 4, 1, 2, 4, 2, 3, 3, 2, 11, 4, 8, 3, 8, 11, 3, 8, 5, 11, 2, 11, 5, 2, 5, 1], + [10, 11, 1, 11, 3, 1, 9, 8, 5, 10, 11, 5, 11, 8, 5, 11, 3, 8, 9, 8, 3, 9, 3, 1, 10, 1, 9, 10, 9, 5, 5, 9, 8, 10, 11, 5, 11, 8, 5, 11, 3, 8, 9, 8, 3, 9, 3, 1], + [0], + [8, 5, 9, 4, 3, 12, 8, 5, 12, 5, 3, 12, 5, 4, 3, 5, 9, 4], + [0], + [2, 1, 10, 4, 3, 12, 9, 8, 5, 2, 1, 10, 4, 5, 9, 4, 3, 5, 8, 5, 3, 8, 3, 12, 4, 3, 12, 2, 1, 9, 2, 9, 8, 2, 5, 10, 2, 8, 5, 9, 8, 5, 2, 3, 12, 2, 12, 10, 10, 12, 4, 10, 4, 1, 2, 13, 10, 10, 13, 5, 8, 5, 13, 8, 13, 12, 12, 13, 3, 4, 3, 13, 4, 13, 9, 9, 13, 1, 2, 1, 13, 2, 13, 10, 2, 13, 3, 12, 13, 3, 8, 13, 12, 8, 5, 13, 9, 5, 13, 4, 13, 9, 4, 1, 13, 10, 13, 1, 8, 5, 13, 10, 13, 5, 2, 13, 10, 2, 3, 13, 12, 13, 3, 4, 13, 12, 4, 1, 13, 9, 13, 1, 9, 8, 13, 2, 3, 12, 2, 12, 5, 2, 5, 10, 8, 5, 12, 4, + 1, 9, 2, 3, 1, 4, 1, 3, 4, 3, 12, 4, 12, 8, 4, 8, 9, 9, 8, 5, 9, 5, 1, 10, 1, 5, 2, 1, 10], + [0], + [4, 2, 12, 2, 11, 12, 8, 5, 9, 4, 2, 9, 2, 5, 9, 2, 11, 5, 8, 5, 11, 8, 11, 12, 4, 12, 8, 4, 8, 9, 9, 8, 5, 4, 2, 9, 2, 5, 9, 2, 11, 5, 8, 5, 11, 8, 11, 12], + [0], + [8, 5, 12, 5, 10, 12, 4, 1, 9, 12, 10, 11, 8, 4, 9, 8, 12, 4, 4, 11, 12, 4, 1, 11, 5, 10, 1, 5, 1, 9, 8, 5, 9, 1, 10, 11, 8, 5, 13, 5, 9, 13, 4, 13, 9, 1, 10, 13, 4, 1, 13, 11, 13, 10, 12, 13, 11, 8, 12, 13, 1, 9, 13, 8, 13, 9, 8, 5, 13, 5, 10, 13, 11, 13, 10, 12, 11, 13, 4, 13, 12, 4, 1, 13, 8, 5, 9, 4, 1, 10, 4, 10, 12, 12, 10, 11], + [0], + [0], + [5, 6, 10, 1, 4, 9, 5, 6, 9, 6, 4, 9, 6, 1, 4, 6, 10, 1], + [0], + [0], + [10, 5, 6, 11, 3, 2, 10, 5, 2, 5, 3, 2, 5, 11, 3, 5, 6, 11], + [6, 10, 5, 2, 11, 3, 1, 4, 9, 6, 10, 5, 2, 9, 1, 2, 11, 9, 4, 9, 11, 4, 11, 3, 2, 11, 3, 6, 10, 1, 6, 1, 4, 6, 9, 5, 6, 4, 9, 1, 4, 9, 6, 11, 3, 6, 3, 5, 5, 3, 2, 5, 2, 10, 6, 13, 5, 5, 13, 9, 4, 9, 13, 4, 13, 3, 3, 13, 11, 2, 11, 13, 2, 13, 1, 1, 13, 10, 6, 10, 13, 6, 13, 5, 6, 13, 11, 3, 13, 11, 4, 13, 3, 4, 9, 13, 1, 9, 13, 2, 13, 1, 2, 10, 13, 5, 13, 10, 4, 9, 13, 5, 13, 9, 6, 13, 5, 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5, 3, 8, 3, 5, 8, 12, 3, 4, 12, 3, 2, 9, 1, 2, 8, 9, 2, 10, 5, 2, 5, 8, 9, 5, 8, 2, 12, 3, 2, 10, 12, 10, 4, 12, 10, 1, 4, 2, 10, 13, 10, 5, 13, 8, 13, 5, 8, 12, 13, 12, 3, 13, 4, 13, 3, 4, 9, 13, 9, 1, 13, 2, 13, 1, 2, 10, 13, 2, 3, 13, 12, 3, 13, 8, 12, 13, 8, 13, 5, 9, 13, 5, 4, 9, 13, 4, 13, 1, 10, 1, 13, 8, 13, 5, 10, 5, 13, 2, 10, 13, 2, 13, 3, 12, 3, 13, 4, 12, 13, 4, 13, 1, 9, 1, 13, 9, 13, 8, 2, 12, 3, 2, 5, 12, 2, 10, 5, 8, 12, 5, 4, + 9, 1, 2, 1, 3, 4, 3, 1, 4, 12, 3, 4, 8, 12, 4, 9, 8, 9, 5, 8, 9, 1, 5, 10, 5, 1, 2, 10, 1], + [0], + [8, 9, 5, 4, 12, 3, 8, 12, 5, 5, 12, 3, 5, 3, 4, 5, 4, 9], + [0], + [10, 1, 11, 11, 1, 3, 9, 5, 8, 10, 5, 11, 11, 5, 8, 11, 8, 3, 9, 3, 8, 9, 1, 3, 10, 9, 1, 10, 5, 9, 5, 8, 9, 10, 5, 11, 11, 5, 8, 11, 8, 3, 9, 3, 8, 9, 1, 3], + [4, 1, 8, 8, 1, 5, 2, 3, 11, 4, 3, 8, 8, 3, 11, 8, 11, 5, 2, 5, 11, 2, 1, 5, 4, 2, 1, 4, 3, 2, 3, 11, 2, 4, 3, 8, 8, 3, 11, 8, 11, 5, 2, 5, 11, 2, 1, 5], + [2, 3, 11, 9, 5, 8, 2, 3, 9, 9, 3, 8, 11, 8, 3, 2, 5, 11, 2, 9, 5, 11, 5, 8], + [0], + [10, 1, 2, 9, 5, 8, 10, 5, 2, 2, 5, 8, 2, 8, 9, 2, 9, 1], + [0], + [0], + [0], + [0], + [0], + [0], + [0], + [1, 2, 10, 3, 4, 12, 1, 4, 10, 10, 4, 12, 10, 12, 3, 10, 3, 2], + [0], + [0], + [0], + [0], + [2, 3, 11, 4, 1, 9, 2, 1, 11, 11, 1, 9, 11, 9, 4, 11, 4, 3], + [0], + [0], + [0], + [0] + ] + ) + +specialName :: [Int] +specialName = [3, 4, 6, 7, 10, 12, 13] + +specialNface, specialNedge :: UV.Vector Int +specialNface = UV.fromList [1, 1, 2, 4, 3, 3, 7] +specialNedge = UV.fromList [18, 24, 48, 177, 96, 96, 816] + +specialInd :: V.Vector (UV.Vector Int) +specialInd = V.fromList + (map + UV.fromList + [ + [0, 1], + [0, 1], + [0, 2, 1, 3], + [0, 8, 4, 12, 2, 10, 1, 9, 6, 14, 5, 13, 3, 11, 15, 7], + [0, 4, 1, 5, 2, 6, 3, 7], + [0, 4, 2, 6, 1, 5, 3, 7], + [0, 1, 2, 4, 8, 16, 32, 3, 9, 17, 33, 6, 18, 34, 12, 20, 36, 24, 40, 35, 25, 22, 44, 19, 41, 38, 28, 83, 105, 102, 92] + ] + ) + +specialPos :: V.Vector (V.Vector (UV.Vector Int)) +specialPos = V.fromList + (map + (V.fromList . map UV.fromList) + [ [[0 .. 5], [6 .. 17]] + , [[0 .. 5], [6 .. 23]] + , [[0 .. 8], [9 .. 32], [33 .. 47], [33 .. 47]] + , [ [0 .. 8] + , [0 .. 8] + , [9 .. 23] + , [9 .. 23] + , [24 .. 38] + , [24 .. 38] + , [39 .. 53] + , [39 .. 53] + , [54 .. 80] + , [54 .. 80] + , [81 .. 107] + , [81 .. 107] + , [108 .. 134] + , [108 .. 134] + , [135 .. 149] + , [150 .. 176] + ] + , [ [0 .. 11] + , [12 .. 35] + , [36 .. 59] + , [36 .. 59] + , [60 .. 83] + , [60 .. 83] + , [84 .. 95] + , [84 .. 95] + ] + , [ [0 .. 11] + , [12 .. 35] + , [36 .. 59] + , [36 .. 59] + , [60 .. 83] + , [60 .. 83] + , [84 .. 95] + , [84 .. 95] + ] + , [ [0 .. 11] + , [12 .. 29] + , [30 .. 47] + , [48 .. 65] + , [66 .. 83] + , [84 .. 101] + , [102 .. 119] + , [120 .. 149] + , [150 .. 179] + , [180 .. 209] + , [210 .. 239] + , [240 .. 269] + , [270 .. 299] + , [300 .. 329] + , [330 .. 359] + , [360 .. 389] + , [390 .. 419] + , [420 .. 449] + , [450 .. 479] + , [480 .. 515] + , [516 .. 551] + , [552 .. 587] + , [588 .. 623] + , [624 .. 641] + , [642 .. 659] + , [660 .. 677] + , [678 .. 695] + , [696 .. 725] + , [726 .. 755] + , [756 .. 785] + , [786 .. 815] + ] + ] + ) + +crf :: UV.Vector Int +crf = UV.fromList + [1, 2, 2, 3, 2, 4, 3, 6, 2, 3, 4, 6, 3, 6, 6, 9, 2, 3, 4, 6, + 5, 7, 7, 12, 4, 6, 8, 10, 7, 15, 13, 6, 2, 4, 3, 6, 4, 8, 6, + 10, 5, 7, 7, 15, 7, 13, 12, 6, 3, 6, 6, 9, 7, 13, 15, 6, 7, 12, + 13, 6, 11, 7, 7, 3, 2, 5, 4, 7, 3, 7, 6, 15, 4, 7, 8, 13, 6, + 12, 10, 6, 4, 7, 8, 13, 7, 11, 13, 7, 8, 13, 14, 8, 13, 7, 8, + 4, 3, 7, 6, 12, 6, 13, 9, 6, 7, 11, 13, 7, 15, 7, 6, 3, 6, 15, + 10, 6, 12, 7, 6, 3, 13, 7, 8, 4, 7, 5, 4, 2, 2, 4, 5, 7, 4, 8, + 7, 13, 3, 6, 7, 12, 6, 10, 15, 6, 3, 6, 7, 15, 7, 13, 11, 7, + 6, 9, 13, 6, 12, 6, 7, 3, 4, 8, 7, 13, 8, 14, 13, 8, 7, 13, 11, + 7, 13, 8, 7, 4, 6, 10, 12, 6, 13, 8, 7, 4, 15, 6, 7, 3, 7, 4, + 5, 2, 3, 7, 7, 11, 6, 13, 12, 7, 6, 15, 13, 7, 9, 6, 6, 3, 6, + 12, 13, 7, 15, 7, 7, 5, 10, 6, 8, 4, 6, 3, 4, 2, 6, 13, 15, 7, + 10, 8, 6, 4, 12, 7, 7, 5, 6, 4, 3, 2, 9, 6, 6, 3, 6, 4, 3, 2, + 6, 3, 4, 2, 3, 2, 2, 1] diff --git a/src/MarchingCubes/Utils.hs b/src/MarchingCubes/Utils.hs new file mode 100644 --- /dev/null +++ b/src/MarchingCubes/Utils.hs @@ -0,0 +1,102 @@ +{-# LANGUAGE BangPatterns #-} +{-# LANGUAGE FlexibleContexts #-} +module MarchingCubes.Utils + ( module MarchingCubes.Utils + ) where +import Data.Array.Unboxed ( (!) + , IArray(..) + , UArray + ) +import Data.List ( transpose ) +import Data.Matrix ( (<|>) + , Matrix(..) + , colVector + , getElem + , mapPos + , matrix + , toLists + ) +import qualified Data.Matrix as M +import Data.Sequence ( (><) + , Seq + , (|>) + ) +import qualified Data.Sequence as S +import qualified Data.Vector as V +import Data.Vector.Unboxed ( Vector ) +import qualified Data.Vector.Unboxed as UV + +levelMatrix :: Real a => Matrix a -> a -> Bool -> Matrix Int +levelMatrix mtrx level strict = mapPos (\_ x -> if lt x then 1 else 0) mtrx + where lt = if strict then (<) level else (<=) level + +arrayToMatrix :: IArray UArray a => UArray (Int, Int, Int) a -> Int -> Matrix a +arrayToMatrix arr k = matrix (nx + 1) + (ny + 1) + (\(i, j) -> arr ! (i - 1, j - 1, k)) + where (_, (nx, ny, _)) = bounds arr + +whichIndicesAndItems :: Matrix Int -> Seq (Int, Int) +whichIndicesAndItems mtrx = go 1 S.empty + where + m = nrows mtrx + 1 + n = ncols mtrx + 1 + go :: Int -> Seq (Int, Int) -> Seq (Int, Int) + go j !out | j == n = out + | otherwise = go (j + 1) (inner 1 j out) + inner i !j !out | i == m = out + | otherwise = inner (i + 1) j out' + where + out' = + let x = getElem i j mtrx + in if x > 0 && x < 255 + then out |> ((j - 1) * (m - 1) + i - 1, x) + else out + +kro1 :: Matrix Int -> Int -> Matrix Int +kro1 mtrx n = matrix p ny f + where + nx = nrows mtrx + ny = ncols mtrx + p = nx * n + 1 + f (i, j) = if i < p then getElem ((i - 1) `mod` nx + 1) j mtrx else 0 + +kro2 :: Matrix Int -> Int -> Matrix Int +kro2 mtrx n = matrix p ny f + where + nx = nrows mtrx + ny = ncols mtrx + p = nx * n + 1 + replicates = foldr ((><) . S.replicate n) S.empty [1 .. nx] :: Seq Int + f (i, j) = if i < p then getElem (S.index replicates (i - 1)) j mtrx else 0 + +replicateEach :: [a] -> [Int] -> Seq a +replicateEach list counts = foldr (><) S.empty sequences + where sequences = zipWith S.replicate counts list + +replicateEach' :: [a] -> Int -> Seq a +replicateEach' list n = foldr ((><) . S.replicate n) S.empty list + +vector2matrix :: [a] -> Int -> Matrix a +vector2matrix list ny = M.fromList (length list `div` ny) ny list + +cbind :: Matrix a -> [a] -> [a] -> Matrix a +cbind mtrx col1 col2 = mtrx <|> col1' <|> col2' + where + col1' = colVector (V.fromList col1) + col2' = colVector (V.fromList col2) + +subMatrix :: Matrix a -> [Int] -> Vector Int -> Matrix a +subMatrix mtrx rows cols = matrix + (length rows) + (UV.length cols) + (\(i, j) -> getElem (rows !! (i - 1) + 1) (cols UV.! (j - 1) + 1) mtrx) + +matrix2listMinusFirstColumn :: Matrix a -> [a] +matrix2listMinusFirstColumn mtrx = + concat $ transpose $ tail (toLists $ M.transpose mtrx) + +jthColumn :: Vector Int -> Int -> Int -> Vector Int +jthColumn vec ncol j = UV.map (\i -> vec UV.! (i * ncol + j)) + (UV.enumFromN 0 nrow) + where nrow = UV.length vec `div` ncol