implicit-0.3.0.1: Graphics/Implicit/Export/Render.hs
-- Implicit CAD. Copyright (C) 2011, Christopher Olah (chris@colah.ca)
-- Copyright 2016, Julia Longtin (julial@turinglace.com)
-- Released under the GNU AGPLV3+, see LICENSE
-- Allow us to use the tearser parallel list comprehension syntax, to avoid having to call zip in the complicated comprehensions below.
{-# LANGUAGE ParallelListComp #-}
-- export getContour and getMesh, which returns the edge of a 2D object, or the surface of a 3D object, respectively.
module Graphics.Implicit.Export.Render (getMesh, getContour) where
import Prelude(ceiling, ($), (+), (*), max, div, tail, fmap, reverse, (.), foldMap, min, Int, (<>), (<$>))
import Graphics.Implicit.Definitions (ℝ, ℕ, Fastℕ, ℝ2, ℝ3, TriangleMesh, Obj2, Obj3, Polyline(Polyline), (⋯/), both, allthree, fromℕtoℝ, fromℕ)
import Data.VectorSpace ((^-^))
import Data.Foldable(fold)
-- Here's the plan for rendering a cube (the 2D case is trivial):
-- (1) We calculate midpoints using interpolate.
-- This guarentees that our mesh will line up everywhere.
-- (Contrast with calculating them in getSegs)
import Graphics.Implicit.Export.Render.Interpolate (interpolate)
-- (2) We calculate the segments separating the inside and outside of our
-- object on the sides of the cube.
-- getSegs internally uses refine from RefineSegs to subdivide the segs
-- to better match the boundary.
import Graphics.Implicit.Export.Render.GetSegs (getSegs)
-- (3) We put the segments from all sides of the cube together
-- and extract closed loops.
import Graphics.Implicit.Export.Render.GetLoops (getLoops)
-- (4) We tesselate the loops, using a mixture of triangles and squares
import Graphics.Implicit.Export.Render.TesselateLoops (tesselateLoop)
-- (5) We try to merge squares, then turn everything into triangles.
import Graphics.Implicit.Export.Render.HandleSquares (mergedSquareTris)
-- Success: This is our mesh.
-- Each step on the Z axis is done in parallel using Control.Parallel.Strategies
import Control.Parallel.Strategies (using, rdeepseq, parBuffer)
-- The actual code is just a bunch of ugly argument passing.
-- Utility functions can be found at the end.
-- For efficiency, we need to avoid looking things up in other lists
-- (since they're 3D, it's an O(n³) operation...). So we need to make
-- our algorithms "flow" along the data structure instead of accessing
-- within it. To do this we use the ParallelListComp GHC extention.
-- We also compute lots of things in advance and pass them in as arguments,
-- to reduce redundant computations.
-- All in all, this is kind of ugly. But it is necessary.
-- Note: As far as the actual results of the rendering algorithm, nothing in
-- this file really matters. All the actual decisions about how to build
-- the mesh are abstracted into the imported files.
-- For the 2D case, we need one last thing, cleanLoopsFromSegs:
import Graphics.Implicit.Export.Render.HandlePolylines (cleanLoopsFromSegs)
-- Set the default types for the numbers in this file.
default (ℕ, Fastℕ, ℝ)
getMesh :: ℝ3 -> ℝ3 -> ℝ3 -> Obj3 -> TriangleMesh
getMesh p1@(x1,y1,z1) p2 res@(xres,yres,zres) obj =
let
-- How much space are we rendering?
d = p2 ^-^ p1
-- How many steps will we take on each axis?
nx :: ℕ
ny :: ℕ
nz :: ℕ
(nx,ny,nz) = ceiling `allthree` ( d ⋯/ res)
-- How big are the steps?
(rx,ry,rz) = d ⋯/ (fromℕtoℝ `allthree` (nx,ny,nz))
-- The positions we're rendering.
pXs = [ x1 + rx*fromℕtoℝ n | n <- [0.. nx] ]
pYs = [ y1 + ry*fromℕtoℝ n | n <- [0.. ny] ]
pZs = [ z1 + rz*fromℕtoℝ n | n <- [0.. nz] ]
-- | performance tuning.
-- FIXME: magic number.
forcesteps :: Int
forcesteps=32
-- | Perform a given function on every point in a 3D grid.
par3DList :: ℕ -> ℕ -> ℕ -> ((ℕ -> ℝ) -> ℕ -> (ℕ -> ℝ) -> ℕ -> (ℕ -> ℝ) -> ℕ -> ℝ) -> [[[ℝ]]]
par3DList lenx leny lenz f =
[[[f
(\n -> x1 + rx*fromℕtoℝ (mx+n)) mx
(\n -> y1 + ry*fromℕtoℝ (my+n)) my
(\n -> z1 + rz*fromℕtoℝ (mz+n)) mz
| mx <- [0..lenx] ] | my <- [0..leny] ] | mz <- [0..lenz] ]
`using` parBuffer (max 1 $ div (fromℕ $ lenx+leny+lenz) forcesteps) rdeepseq
-- | Evaluate obj to avoid waste in mids, segs, later.
objV = par3DList (nx+2) (ny+2) (nz+2) $ \x _ y _ z _ -> obj (x 0, y 0, z 0)
-- (1) Calculate mid points on X, Y, and Z axis in 3D space.
midsZ = [[[
interpolate (z0, objX0Y0Z0) (z1', objX0Y0Z1) (appABC obj x0 y0) zres
| x0 <- pXs | objX0Y0Z0 <- objY0Z0 | objX0Y0Z1 <- objY0Z1
]| y0 <- pYs | objY0Z0 <- objZ0 | objY0Z1 <- objZ1
]| z0 <- pZs | z1' <- tail pZs | objZ0 <- objV | objZ1 <- tail objV
] `using` parBuffer (max 1 $ div (fromℕ nz) forcesteps) rdeepseq
midsY = [[[
interpolate (y0, objX0Y0Z0) (y1', objX0Y1Z0) (appACB obj x0 z0) yres
| x0 <- pXs | objX0Y0Z0 <- objY0Z0 | objX0Y1Z0 <- objY1Z0
]| y0 <- pYs | y1' <- tail pYs | objY0Z0 <- objZ0 | objY1Z0 <- tail objZ0
]| z0 <- pZs | objZ0 <- objV
] `using` parBuffer (max 1 $ div (fromℕ ny) forcesteps) rdeepseq
midsX = [[[
interpolate (x0, objX0Y0Z0) (x1', objX1Y0Z0) (appBCA obj y0 z0) xres
| x0 <- pXs | x1' <- tail pXs | objX0Y0Z0 <- objY0Z0 | objX1Y0Z0 <- tail objY0Z0
]| y0 <- pYs | objY0Z0 <- objZ0
]| z0 <- pZs | objZ0 <- objV
] `using` parBuffer (max 1 $ div (fromℕ nx) forcesteps) rdeepseq
-- (2) Calculate segments for each side
segsZ = [[[
injZ z0 <$> getSegs (x0,y0) (x1',y1') (obj **$ z0) (objX0Y0Z0, objX1Y0Z0, objX0Y1Z0, objX1Y1Z0) (midA0, midA1, midB0, midB1)
| x0<-pXs | x1'<-tail pXs |midB0<-mX'' | midB1<-mX'T | midA0<-mY'' | midA1<-tail mY'' | objX0Y0Z0<-objY0Z0 | objX1Y0Z0<- tail objY0Z0 | objX0Y1Z0<-objY1Z0 | objX1Y1Z0<-tail objY1Z0
]| y0<-pYs | y1'<-tail pYs |mX'' <-mX' | mX'T <-tail mX' | mY'' <-mY' | objY0Z0 <-objZ0 | objY1Z0 <-tail objZ0
]| z0<-pZs |mX' <-midsX | mY' <-midsY | objZ0 <-objV
] `using` parBuffer (max 1 $ div (fromℕ nz) forcesteps) rdeepseq
segsY = [[[
injY y0 <$> getSegs (x0,z0) (x1',z1') (obj *$* y0) (objX0Y0Z0, objX1Y0Z0, objX0Y0Z1, objX1Y0Z1) (midA0, midA1, midB0, midB1)
| x0<-pXs | x1'<-tail pXs | midB0<-mB'' | midB1<-mBT' | midA0<-mA'' | midA1<-tail mA'' | objX0Y0Z0<-objY0Z0 | objX1Y0Z0<-tail objY0Z0 | objX0Y0Z1<-objY0Z1 | objX1Y0Z1<-tail objY0Z1
]| y0<-pYs | mB'' <-mB' | mBT' <-mBT | mA'' <-mA' | objY0Z0 <-objZ0 | objY0Z1 <-objZ1
]| z0<-pZs | z1'<-tail pZs | mB' <-midsX | mBT <-tail midsX | mA' <-midsZ | objZ0 <-objV | objZ1 <-tail objV
] `using` parBuffer (max 1 $ div (fromℕ ny) forcesteps) rdeepseq
segsX = [[[
injX x0 <$> getSegs (y0,z0) (y1',z1') (obj $** x0) (objX0Y0Z0, objX0Y1Z0, objX0Y0Z1, objX0Y1Z1) (midA0, midA1, midB0, midB1)
| x0<-pXs | midB0<-mB'' | midB1<-mBT' | midA0<-mA'' | midA1<-mA'T | objX0Y0Z0<-objY0Z0 | objX0Y1Z0<-objY1Z0 | objX0Y0Z1<-objY0Z1 | objX0Y1Z1<- objY1Z1
]| y0<-pYs | y1'<-tail pYs | mB'' <-mB' | mBT' <-mBT | mA'' <-mA' | mA'T <-tail mA' | objY0Z0 <-objZ0 | objY1Z0 <-tail objZ0 | objY0Z1 <-objZ1 | objY1Z1 <-tail objZ1
]| z0<-pZs | z1'<-tail pZs | mB' <-midsY | mBT <-tail midsY | mA' <-midsZ | objZ0 <- objV | objZ1 <- tail objV
] `using` parBuffer (max 1 $ div (fromℕ nx) forcesteps) rdeepseq
-- (3) & (4) : get and tesselate loops
-- FIXME: hack.
minres = xres `min` yres `min` zres
sqTris = [[[
foldMap (tesselateLoop minres obj) $ getLoops $
segX''' <>
mapR segX''T <>
mapR segY''' <>
segY'T' <>
segZ''' <>
mapR segZT''
| segZ'''<- segZ''| segZT''<- segZT'
| segY'''<- segY''| segY'T'<- segY'T
| segX'''<- segX''| segX''T<- tail segX''
]| segZ'' <- segZ' | segZT' <- segZT
| segY'' <- segY' | segY'T <- tail segY'
| segX'' <- segX'
]| segZ' <- segsZ | segZT <- tail segsZ
| segY' <- segsY
| segX' <- segsX
] `using` parBuffer (max 1 $ div (fromℕ $ nx+ny+nz) forcesteps) rdeepseq
in
-- (5) merge squares, etc
mergedSquareTris . fold . fold $ fold sqTris
-- | getContour gets a polyline describing the edge of a 2D object.
getContour :: ℝ2 -> ℝ2 -> ℝ2 -> Obj2 -> [Polyline]
getContour p1@(x1, y1) p2 res@(xres,yres) obj =
let
-- | The size of the region we're being asked to search.
d = p2 ^-^ p1
-- | How many steps will we take on each axis?
nx :: ℕ
ny :: ℕ
(nx,ny) = ceiling `both` (d ⋯/ res)
-- | How big are the steps?
(rx,ry) = d ⋯/ (fromℕtoℝ `both` (nx,ny))
-- The points inside of the region.
pYs = [ y1 + ry*fromℕtoℝ p | p <- [0.. ny] ]
pXs = [ x1 + rx*fromℕtoℝ p | p <- [0.. nx] ]
-- | Performance tuning.
-- FIXME: magic number.
forcesteps :: Int
forcesteps=32
par2DList :: ℕ -> ℕ -> ((ℕ -> ℝ) -> ℕ -> (ℕ -> ℝ) -> ℕ -> ℝ) -> [[ℝ]]
par2DList lenx leny f =
[[ f
(\n -> x1 + rx*fromℕtoℝ (mx+n)) mx
(\n -> y1 + ry*fromℕtoℝ (my+n)) my
| mx <- [0..lenx]
] | my <- [0..leny]
] `using` parBuffer (max 1 $ div (fromℕ $ lenx+leny) forcesteps) rdeepseq
-- | Fully evaluate obj to avoid waste in mids, segs, later.
objV = par2DList (nx+2) (ny+2) $ \x _ y _ -> obj (x 0, y 0)
-- | Calculate mid points on X, and Y axis in 2D space.
midsY = [[
interpolate (y0, objX0Y0) (y1', objX0Y1) (obj $* x0) yres
| x0 <- pXs | objX0Y0 <- objY0 | objX0Y1 <- objY1
]| y0 <- pYs | y1' <- tail pYs | objY0 <- objV | objY1 <- tail objV
] `using` parBuffer (max 1 $ div (fromℕ ny) forcesteps) rdeepseq
midsX = [[
interpolate (x0, objX0Y0) (x1', objX1Y0) (obj *$ y0) xres
| x0 <- pXs | x1' <- tail pXs | objX0Y0 <- objY0 | objX1Y0 <- tail objY0
]| y0 <- pYs | objY0 <- objV
] `using` parBuffer (max 1 $ div (fromℕ nx) forcesteps) rdeepseq
-- | Calculate segments for each side
segs = [[
getSegs (x0,y0) (x1',y1') obj (objX0Y0, objX1Y0, objX0Y1, objX1Y1) (midA0, midA1, midB0, midB1)
| x0<-pXs | x1'<-tail pXs |midB0<-mX'' | midB1<-mX'T | midA0<-mY'' | midA1<-tail mY'' | objX0Y0<-objY0 | objX1Y0<-tail objY0 | objX0Y1<-objY1 | objX1Y1<-tail objY1
]| y0<-pYs | y1'<-tail pYs |mX'' <-midsX | mX'T <-tail midsX | mY'' <-midsY | objY0 <- objV | objY1 <- tail objV
] `using` parBuffer (max 1 $ div (fromℕ $ nx+ny) forcesteps) rdeepseq
in
-- Merge squares
cleanLoopsFromSegs . fold $ fold segs
-- utility functions
injX :: ℝ -> Polyline -> [ℝ3]
injX a (Polyline xs) = fmap (prepend a) xs
prepend :: ℝ -> ℝ2 -> ℝ3
prepend a (b,c) = (a,b,c)
injY :: ℝ -> Polyline -> [ℝ3]
injY a (Polyline xs) = fmap (insert a) xs
insert :: ℝ -> ℝ2 -> ℝ3
insert b (a,c) = (a,b,c)
injZ :: ℝ -> Polyline -> [ℝ3]
injZ a (Polyline xs) = fmap (postfix a) xs
postfix :: ℝ -> ℝ2 -> ℝ3
postfix c (a,b) = (a,b,c)
($**) :: Obj3 -> ℝ -> ℝ2 -> ℝ
f $** a = \(b,c) -> f (a,b,c)
infixr 0 $**
(*$*) :: Obj3 -> ℝ -> ℝ2 -> ℝ
f *$* b = \(a,c) -> f (a,b,c)
infixr 0 *$*
(**$) :: Obj3 -> ℝ -> ℝ2 -> ℝ
f **$ c = \(a,b) -> f (a,b,c)
infixr 0 **$
($*) :: Obj2 -> ℝ -> ℝ -> ℝ
f $* a = \b -> f (a,b)
infixr 0 $*
(*$) :: Obj2 -> ℝ -> ℝ -> ℝ
f *$ b = \a -> f (a,b)
infixr 0 *$
appABC :: Obj3 -> ℝ -> ℝ -> ℝ -> ℝ
appABC f a b c = f (a,b,c)
appBCA :: Obj3 -> ℝ -> ℝ -> ℝ -> ℝ
appBCA f b c a = f (a,b,c)
appACB :: Obj3 -> ℝ -> ℝ -> ℝ -> ℝ
appACB f a c b = f (a,b,c)
mapR :: [[ℝ3]] -> [[ℝ3]]
mapR = fmap reverse