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raytracer.hs
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raytracer.hs
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{-# LANGUAGE BangPatterns #-}
import Graphics.Rendering.OpenGL.GL.Tensor
import Data.Array.Accelerate as A
import qualified Data.Array.Accelerate.CUDA as I
import Data.List hiding (intersect)
import Foreign.C.Types
import Foreign.Ptr
import Data.Int
import Prelude as P
import Data.Word
import qualified Graphics.UI.GLUT as G
import Graphics.Rendering.OpenGL.GL.CoordTrans
width :: Int
width = 640
height :: Int
height = 480
fov :: Float
fov = 45.0
maxdepth :: Int
maxdepth = 6
type VectorF = Vertex3 Float
type VectorI = Vertex3 Int
type Vec a = (a, a, a)
type VecF = Vec Float
type SphereIntersect = (Bool, Sphere, Float)
type Index = (Int, Int)
type ArrayPlane a = Array DIM2 a
nullVector :: Exp (VecF)
nullVector = constant (0.0, 0.0, 0.0)
infixl 6 -.
infixl 6 +.
infixl 7 *.
(-.), (+.), (*.) :: (Elt a, IsNum a) => Exp (Vec a) -> Exp (Vec a) -> Exp (Vec a)
(-.) = vzipWith (-)
(+.) = vzipWith (+)
(*.) = vzipWith (*)
infixl 6 --.
infixl 6 ++.
infix 7 //.
infixl 7 **.
(--.), (++.), (**.) :: (Elt a, IsNum a) => Exp (Vec a) -> Exp a -> Exp (Vec a)
(--.) v f = vmap (flip (-) f) v
(++.) v f = vmap (f+) v
(**.) v f = vmap (f*) v
(//.) :: (Elt a, IsNum a, IsFloating a) => Exp (Vec a) -> Exp a -> Exp (Vec a)
(//.) v f = vmap (flip (/) f) v
cfalse :: Exp Bool
cfalse = constant False
ctrue :: Exp Bool
ctrue = constant True
vmap :: (Elt a, Elt b) => (Exp a -> Exp b) -> Exp (Vec a) -> Exp (Vec b)
vmap f v = let (x1,y1,z1) = unlift v
in
lift (f x1, f y1, f z1)
vzipWith :: (Elt a, Elt b, Elt c) => (Exp a -> Exp b -> Exp c) -> Exp (Vec a) -> Exp (Vec b) -> Exp (Vec c)
vzipWith f v1 v2
= let (x1,y1,z1) = unlift v1
(x2,y2,z2) = unlift v2
in
lift (f x1 x2, f y1 y2, f z1 z2)
dot :: (Elt a, IsNum a) => Exp (Vec a) -> Exp (Vec a) -> Exp a
dot a b = let
(x1, y1, z1) = unlift a
(x2, y2, z2) = unlift b
in
x1 * x2 + y1 * y2 + z1 * z2
mag :: (Elt a, IsNum a, A.IsFloating a) => A.Exp (Vec a) -> A.Exp a
mag l = sqrt $ dot l l
normalized :: (Elt a, A.IsNum a, IsFloating a) => A.Exp (Vec a) -> (A.Exp (Vec a))
normalized l = l //. (mag l)
type Ray = (VecF, --start
VecF) --dir
start :: Exp Ray -> Exp VecF
start r = A.fst r
dir :: Exp Ray -> Exp VecF
dir r = A.snd r
nullRay :: Exp Ray
nullRay = lift (nullVector, nullVector)
type Sphere = (VecF, --center
Float, --radius
VecF, --scolor
Float, --reflection
Float) --transparency
center :: Exp Sphere -> Exp VecF
center s = let (c, _, _, _, _) = unlift s :: (Exp VecF, Exp Float, Exp VecF, Exp Float, Exp Float)
in c
radius :: Exp Sphere -> Exp Float
radius s = let (_, r, _, _, _) = unlift s :: (Exp VecF, Exp Float, Exp VecF, Exp Float, Exp Float)
in lift r
scolor :: Exp Sphere -> Exp VecF
scolor s = let (_, _, c, _, _) = unlift s :: (Exp VecF, Exp Float, Exp VecF, Exp Float, Exp Float)
in lift c
reflection :: Exp Sphere -> Exp Float
reflection s = let (_, _, _, r, _) = unlift s :: (Exp VecF, Exp Float, Exp VecF, Exp Float, Exp Float)
in lift r
transparency :: Exp Sphere -> Exp Float
transparency s = let (_, _, _, _, t) = unlift s :: (Exp VecF, Exp Float, Exp VecF, Exp Float, Exp Float)
in lift t
type Light = (VecF, --position
VecF) --color
position :: Exp Light -> Exp VecF
position l = A.fst l
color :: Exp Light -> Exp VecF
color l = A.snd l
type Scene = (Vector Sphere, Vector Light)
type MultiBounceFactor = (Float, -- reflection
Float) -- refraction
nullMultiBounceFactor :: Exp MultiBounceFactor
nullMultiBounceFactor = constant $ (0.0, 0.0)
type MultiRay = (Ray, Ray, MultiBounceFactor)
nullMultiRay :: Exp MultiRay
nullMultiRay = lift (nullRay, nullRay, nullMultiBounceFactor) :: Exp MultiRay
objects :: Scene -> Vector Sphere
objects (spheres, lights) = spheres
lights :: Scene -> Vector Light
lights (spheres, lights) = lights
intersect :: Exp Sphere -> Exp Ray -> Exp Bool
intersect se re =
let
rs = start re
cs = center se
sr = radius se
dr = dir re
v = cs -. rs
a = dot v dr
b2 = dot v v - a * a
r2 = sr * sr
in
(a <* 0 ||* b2 >* r2) ? (constant False, constant True)
normalizeSphereSurface :: Exp Sphere -> Exp VecF -> Exp VecF
normalizeSphereSurface s v = normalized (v -. (center s))
intersectDist :: Exp Ray -> Exp Sphere -> Exp SphereIntersect
intersectDist r s =
let
v = (center s) -. (start r)
a = dot v (dir r)
b2 = dot v v - a * a
r2 = (radius s) * (radius s)
c = sqrt(r2 - b2)
near = a - c
far = a + c
distance = (near <* 0) ? (far, near)
in
(a <* 0 ||* b2 >* r2) ? (
lift $ (constant False, s, constant (-1.0)),
lift $ (constant True, s, distance)
)
predComp :: Exp SphereIntersect -> Exp SphereIntersect -> Exp SphereIntersect
predComp a b = (b1 ==* cfalse &&* b2 ==* cfalse) ? (a,
(b1 ==* cfalse &&* b2 ==* ctrue) ? (b,
(b1 ==* ctrue &&* b2 ==* cfalse) ? (a,
(b1 ==* ctrue &&* b2 ==* ctrue &&* d1 A.<* d2) ? (a, b))))
where
(b1, s1, d1) = A.unlift a :: (Exp Bool, Exp Sphere, Exp Float)
(b2, s2, d2) = A.unlift b :: (Exp Bool, Exp Sphere, Exp Float)
minInterSects :: Scene -> Acc (Array DIM2 Ray) -> Acc (Array DIM2 SphereIntersect)
minInterSects s rays = let
objs = objects s
usedObjs = use objs
dummySphere = ((0.0, 0, 0),
0.0,
(0.0, 0.0, 0.0),
0.0,
0.0)
dummyTuple = constant (False, dummySphere, -1.0)
k = size usedObjs
cols = A.replicate (lift $ Z :. All :. All :. k) rays
rows = A.replicate (lift $ Z :. width :. height :. All) usedObjs
intersects = A.fold predComp dummyTuple $ A.zipWith intersectDist cols rows
in
intersects
colorforlight :: Scene -> Exp Sphere -> Exp VecF -> Exp VecF -> Exp Light -> Exp VecF
colorforlight s sph pip norm l =
let
lightpos = position l
lightdirection = normalized (lightpos -. pip)
blocked = Main.intersect sph $ lift (pip, lightdirection)
clr = ((color l) **. (P.max 0.0 (dot norm lightdirection)))
*. (scolor sph) **. (1.0 - reflection sph)
in
(blocked) ? (constant (0.0, 0.0, 0.0), clr)
traceStep :: Scene -> Acc (ArrayPlane Int) -> Acc (ArrayPlane Ray) -> Acc (ArrayPlane MultiBounceFactor) -> Acc (ArrayPlane (MultiRay, Int, VecF))
traceStep scene depths rays factors = let
minintersects = minInterSects scene rays
intersectsWithRays = A.zip minintersects rays
usedLights = use $ lights scene
l = size usedLights
bounceCols = A.replicate (lift $ Z :. All :. All :. l) factors
depthCols = A.replicate (lift $ Z :. All :. All :. l) depths
cols = A.replicate (lift $ Z :. All :. All :. l) intersectsWithRays
rows = A.replicate (lift $ Z :. width :. height :. All) usedLights
in
A.fold1
(
\a b ->
let
(multiray1, depth1, color1) = unlift a :: (Exp MultiRay, Exp Int, Exp VecF)
(multiray2, depth2, color2) = unlift b :: (Exp MultiRay, Exp Int, Exp VecF)
in
lift (multiray2, depth1 + depth2, color1 +. color2)
)
$
A.zipWith4 (trace scene) depthCols cols rows bounceCols
infixl 6 $+.
($+.) :: Acc (ArrayPlane VecF) -> Acc (ArrayPlane VecF) -> Acc (ArrayPlane VecF)
($+.) a b = A.zipWith (+.) a b
infixl 6 $-.
($-.) :: Acc (ArrayPlane VecF) -> Acc (ArrayPlane VecF) -> Acc (ArrayPlane VecF)
($-.) a b = A.zipWith (-.) a b
infixl 7 $*.
($*.) :: Acc (ArrayPlane VecF) -> Acc (ArrayPlane Float) -> Acc (ArrayPlane VecF)
($*.) a b = A.zipWith (**.) a b
traceAll :: Acc (ArrayPlane Ray) -> Scene -> Acc (ArrayPlane VecF)
traceAll rays scene = let
d0 = generate (index2 (lift width) (lift height)) (\a -> (constant 0))
factor0 = generate (index2 (lift width) (lift height)) (\a -> (constant (1.0, 0.0)))
ray0 = generate (index2 (lift width) (lift height)) (\a -> nullRay)
multiray0 = A.zip3 rays ray0 factor0
traceMapStep :: Acc (ArrayPlane MultiRay) ->
(Acc (ArrayPlane VecF), [Acc (ArrayPlane MultiRay)])
traceMapStep r = let
(reflectionRays, refractionRays, bounceFactors) = A.unzip3 r
(reflectionFactors, refractionFactors) = A.unzip bounceFactors
reflectionContribution = traceStep scene d0 reflectionRays bounceFactors
(reflMultiRays, reflDepths, reflImage) = A.unzip3 reflectionContribution
refractionContribution = traceStep scene d0 refractionRays bounceFactors
(refrMultiRays, refrDepths, refrImage) = A.unzip3 refractionContribution
(refrReflRays, refrRefrRays, refrBounceFactors) = A.unzip3 refrMultiRays
reflDeltaImage = reflImage $+. refrImage
newList = [reflMultiRays]
--P.++ [refrMultiRays]
in
(reflDeltaImage, newList)
traceIter :: (Acc (ArrayPlane VecF), [Acc (ArrayPlane MultiRay)]) ->
(Acc (ArrayPlane VecF), [Acc (ArrayPlane MultiRay)])
traceIter (c0, rayList) = let
(newDeltaImages, newRays) = P.unzip $
P.map traceMapStep rayList
accImage = P.foldl ($+.) c0 newDeltaImages
newRayList = P.concat newRays
in
(accImage, newRayList)
trace0 = traceMapStep multiray0
(accImage, _) = foldr ($) trace0 (Data.List.take maxdepth (repeat traceIter))
in
accImage
-- Ray -> Sphere -> Normal -> dotNormal -> PointOfHit -> FresnelEffect -> (FresnelEffect, Ray)
reflectionFactorAndRay :: Exp Ray -> Exp Sphere -> Exp VecF -> Exp Float -> Exp VecF -> Exp Float -> Exp (Float, Ray)
reflectionFactorAndRay r s n dn pip f = lift (f, lift (pip, reflectiondirection) :: Exp Ray)
where
reflectionRatio = reflection (lift s)
facing = P.max 0.0 (-dn)
reflectiondirection = (dir r) -. (n **. (2.0 * dn))
-- Ray -> Sphere -> Normal -> PointOfImpact -> Inside -> Fresnel -> Depth -> (RefractionEffect, Ray)
refractionFactorAndRay :: Exp Ray -> Exp Sphere -> Exp VecF -> Exp VecF -> Exp Bool -> Exp Float -> Exp Int -> Exp (Float, Ray)
refractionFactorAndRay r s n pip ins f d = let
nullRay = ((constant (0.0, 0.0, 0.0)), (constant (0.0, 0.0, 0.0)))
nullElement = lift (constant 0, nullRay)
in
(transparency s >* 0.0) ?
(
let
ce = (dot (dir r) n) * (-1.0)
iorconst = constant 1.5
ior = ins ? (1.0 / iorconst, iorconst) :: Exp Float
eta = 1.0 / ior
gf = (dir r) +. (n **. (ce * eta))
sin_t1_2 = 1.0 - ce * ce
sin_t2_2 = sin_t1_2 * (eta * eta)
in
(sin_t2_2 <* 1.0) ? (
let
gc = n **. (sqrt 1 - sin_t2_2)
refraction_direction = gf -. gc
refraction = (1.0 - f) * (transparency s)
in
lift (refraction, (pip, refraction_direction)),
nullElement
),
nullElement)
trace :: Scene -> Exp Int -> Exp (SphereIntersect, Ray) -> Exp Light -> Exp (Float, Float)-> Exp (MultiRay, Int, VecF)
trace s d i l f = let
(reflectionFactor, refractionFactor) = unlift f :: (Exp Float, Exp Float)
(intersectingSphere, ray) = unlift i :: (Exp SphereIntersect, Exp Ray)
(hasIntersect, sp, di) = unlift intersectingSphere :: (Exp Bool, Exp Sphere, Exp Float)
(rstart, rdir) = unlift ray :: (Exp VecF, Exp VecF)
in
--((ray /=* nullRay) &&* hasIntersect) ? (
(hasIntersect) ? (
let
pointofhit = (dir ray) **. (lift di) +. start ray
normal_unrefl = normalizeSphereSurface (lift sp) pointofhit
dotnormalray_unrefl = dot normal_unrefl (dir ray)
isinside = (dotnormalray_unrefl >* 0) ? (ctrue, cfalse)
dotnormalray = (dotnormalray_unrefl >* 0) ? (-dotnormalray_unrefl, dotnormalray_unrefl)
normal = (dotnormalray_unrefl >* 0) ? (normal_unrefl **. (-1.0), normal_unrefl)
refl = reflection (lift sp)
transparencyratio = transparency (lift sp)
facing = P.max 0.0 (-dotnormalray)
fresneleffect = refl + (1.0 - refl) * ((1.0 -facing) ^^ 5)
traceclr = colorforlight s (lift sp) pointofhit (normal **. 1.0) l
clr = traceclr **. (reflectionFactor + refractionFactor)
nullFloatRay = lift ((constant 0.0), nullRay) :: Exp (Float, Ray)
(newReflectionFactor, reflectionRay) = unlift (
(d <* constant maxdepth) ? (
--reflection
(refl ==* 0.0) ? (
nullFloatRay,
--calculate next ray direction and color factor for next trace
reflectionFactorAndRay ray
sp
normal
dotnormalray
pointofhit
fresneleffect),
nullFloatRay)) :: (Exp Float, Exp Ray)
(newRefractionFactor, refractionRay) = unlift (
(d <* constant maxdepth) ? (
--reflection
(refractionFactor ==* 0.0) ? (
nullFloatRay,
--calculate next ray direction and color factor for next trace
refractionFactorAndRay ray
sp
normal
pointofhit
isinside
fresneleffect
d),
nullFloatRay)) :: (Exp Float, Exp Ray)
in
lift (
lift (
reflectionRay, refractionRay,
lift (newReflectionFactor, newRefractionFactor) :: Exp MultiBounceFactor
) :: Exp MultiRay,
d + 1, clr),
lift (nullMultiRay, d, nullVector)
)
updatePixel :: Index -> VecF -> IO ()
updatePixel p@(x, y) c@(r, g, b) = do
G.renderPrimitive G.Points $ do
G.color $ G.Color3 (CFloat r) (CFloat g) (CFloat b)
G.vertex $ Vertex3 (CFloat (P.fromIntegral x)) (CFloat (P.fromIntegral (height - y))) 0
constructRay :: Scene -> Exp VecF -> Exp Index -> Exp Ray
constructRay s eye idx = let
(x, y) = unlift idx :: (Exp Int, Exp Int)
h = constant $ (tan (fov / 360.0 * 2.0 * pi / 2.0)) * 2.0
ww = A.fromIntegral $ constant width :: Exp Float
hh = A.fromIntegral $ constant height :: Exp Float
w = h * ww / hh
rx = ((A.fromIntegral x) - ww/2.0) /ww * w
ry = (hh / 2.0 - (A.fromIntegral y)) / hh * h
dir = normalized $ lift (rx, ry, constant (-1.0))
ray = (lift (eye, dir))
in
ray
calcPixels :: Scene -> Exp VecF -> Acc (Array DIM2 Index) -> Acc (Array DIM2 VecF)
calcPixels s eye idx = let
rays = A.map (constructRay s eye) idx
in
traceAll rays s
updateAllPixels :: Array DIM2 (Index, VecF) -> Int -> Int -> IO ()
updateAllPixels p i j
| i >= width = updateAllPixels p 0 (j+1)
| j >= height = return ()
| otherwise =
do
let (idx, color) = p `indexArray` (Z :. i :. j)
updatePixel idx color
updateAllPixels p (i+1) (j)
render :: Scene -> IO ()
render s = do
let
eye = constant (0.0, 0.0, 0.0)
indices = A.generate (lift $ Z :. width :. height) unindex2
pixels = calcPixels s eye indices
pixelsWithIndices = I.run $ A.zip indices pixels
putStrLn "calculation done"
updateAllPixels pixelsWithIndices 0 0
mainDbg :: IO ()
mainDbg = do
let scene = ( (fromList (Z :. 5) [
((0.0, -10002.0, -20.0),
10000.0,
(0.8, 0.8, 0.8),
0.0,
0.0),
((0.0, 2.0, -20.0),
4.0,
(0.8, 0.5, 0.5),
0.5,
0.0),
((5.0, 0.0, -15.0),
2.0,
(0.3, 0.8, 0.8),
0.2,
0.0),
((-5.0, 0.0, -15.0),
2.0,
(0.3, 0.5, 0.8),
0.2,
0.0),
((-2.0, -1.0, -10.0),
1.0,
(0.1, 0.1, 0.1),
0.1,
0.8)
]),
(fromList (Z :. 1) [
((-10.0, 20.0, 30.0),
(2.0, 2.0, 2.0))
])
)
eye = constant (0.0, 0.0, 0.0)
indices = A.generate (lift $ Z :. width :. height) unindex2
pixels = calcPixels scene eye indices
!pixelsWithIndices = I.run $ A.zip indices pixels
putStrLn "calculation done"
mainNormal :: IO ()
mainNormal = do
(progname, _) <- G.getArgsAndInitialize
w <- G.createWindow "Haskell raytracer"
G.windowSize G.$= (G.Size (CInt (P.fromIntegral width)) (CInt (P.fromIntegral height)))
let scene = ( (fromList (Z :. 5) [
((0.0, -10002.0, -20.0),
10000.0,
(0.8, 0.8, 0.8),
0.0,
0.0),
((0.0, 2.0, -20.0),
4.0,
(0.8, 0.5, 0.5),
0.5,
0.0),
((5.0, 0.0, -15.0),
2.0,
(0.3, 0.8, 0.8),
0.2,
0.0),
((-5.0, 0.0, -15.0),
2.0,
(0.3, 0.5, 0.8),
0.2,
0.0),
((-2.0, -1.0, -10.0),
1.0,
(0.1, 0.1, 0.1),
0.1,
0.8)
]),
(fromList (Z :. 1) [
((-10.0, 20.0, 30.0),
(2.0, 2.0, 2.0))
])
)
G.reshapeCallback G.$= Just Main.reshape
G.displayCallback G.$= display scene
G.mainLoop
main :: IO ()
main = mainNormal
reshape :: Size -> IO ()
reshape size@(Size w h) = do
G.viewport G.$= (Position 0 0, size)
G.matrixMode G.$= Projection
G.loadIdentity
ortho 0.0 (P.fromIntegral w) 0.0 (P.fromIntegral h) (-1.0) 1.0
G.matrixMode G.$= Modelview 0
display :: Scene -> IO ()
display s = do
G.clear [G.ColorBuffer]
render s
G.swapBuffers