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import System.IO
import Data.Char
import Debug.Trace
-- ppm image file
-- P3 width height maxcolorval r g b r g b r g b ...
-- max line length: 70
type Angle = Double
type ScreenCoord = (Angle, Angle)
type Color = (Int, Int, Int)
type Coord = (Double, Double, Double)
data Sphere = Sphere Coord Double Color deriving (Show, Eq)
degrees = pi / 180
eye :: Coord
eye = (0, -20, 20)
x_of (x, _, _) = x
y_of (_, y, _) = y
z_of (_, _, z) = z
sphere1 = Sphere (0, 80, 5) 10 (55,255,0)
sphere2 = Sphere (80, 0, 5) 20 (255,60,0)
--sphere3 = Sphere (0, -80, 5) 20 (5,60,200)
--sphere4 = Sphere (-80, 0, 5) 20 (0,255,255)
--spheres = [sphere1, sphere2, sphere3, sphere4]
filename num = "foo/foo" ++ show num ++ ".ppm"
--spherepos = take 1 [0,20..]
spherepos = take 10 [0,36..]
spheres num = [ trace ("Sphere at " ++
show (round (80 * sin(num * degrees))) ++ "," ++
show (round (80 * cos(num * degrees))) ++ ",5" )
Sphere (80 * sin(num * degrees), 80 * cos(num * degrees), 5) 10 (255,60,0),
sphere1, sphere2]
writenum :: Double -> IO ()
writenum num = trace ("Rendering " ++ show (filename $ round num))
writeFile (filename num) (image $ spheres num)
main = mapM writenum spherepos
alpha1 = 0 * degrees
alpha2 = 360 * degrees
beta1 = 70 * degrees
beta2 = 180 * degrees
floorscale = 4
w = 500
h = 200
oversampling = 1 -- each pixel is 2x2 rays
black :: Color
black = (0,0,0)
ov_alphaoffset = ((alpha2 - alpha1) / (w-1)) / oversampling
ov_betaoffset = ((beta2 - beta1) / (h-1)) / oversampling
ov_alphaoffsets = take (round oversampling) [0,ov_alphaoffset..]
ov_betaoffsets = take (round oversampling) [0,ov_betaoffset..]
imgheader = "P3 " ++ (show $ round w) ++ " " ++ (show $ round h) ++ " 255\n"
alphas = take (round w) [alpha1,(alpha1 + ((alpha2 - alpha1) / (w-1)))..]
betas = take (round h) [beta1,(beta1 + ((beta2 - beta1) / (h-1)))..]
-- spherical projection,
-- return coordinates from a given coordinate, extended by given
-- angles to some distance
spherical_proj :: Coord -> Angle -> Angle -> Double -> Coord
spherical_proj (x,y,z) alpha beta dist = (x + dist*(sin beta * cos alpha),
y + dist*(sin beta * sin alpha),
z + dist*cos beta)
-- intersect sphere
-- discr = 4(( A u + B v + C w )^2 - (A^2 + B^2 + C^2)(u^2 + v^2 + w^2))
discr :: Coord -> ScreenCoord -> Sphere -> Double
discr source (alpha, beta) (Sphere centre radius _) = 4*(( aa * u + bb * v + cc * w )^2 -
(aa*aa + bb*bb + cc*cc)*(u*u + v*v + w*w - radius^2))
where u = (x_of source) - (x_of centre)
v = (y_of source) - (y_of centre)
w = (z_of source) - (z_of centre)
aa = sin beta * cos alpha
bb = sin beta * sin alpha
cc = cos beta
-- the intersect functions return (Coord, Distance, Color)
-- distance = 0 means no intersection
intersect_sphere :: Coord -> ScreenCoord -> Sphere -> (Coord, Double, Color)
intersect_sphere source (alpha, beta) (Sphere centre radius color)
| delta > 0 = (spherical_proj source alpha beta t, t, color)
| otherwise = ((0,0,0), 0, black)
where t = min ((-b - sqrt(delta)) / (2*a)) ((-b + sqrt(delta)) / (2*a))
delta = discr source (alpha, beta) (Sphere centre radius color)
a = aa^2 + bb^2 + cc^2
b = 2 * (aa*u + bb*v + cc*w)
u = (x_of source) - (x_of centre)
v = (y_of source) - (y_of centre)
w = (z_of source) - (z_of centre)
aa = sin beta * cos alpha
bb = sin beta * sin alpha
cc = cos beta
intersect_point_floor :: Coord -> ScreenCoord -> (Coord, Double)
intersect_point_floor (x, y, z) (alpha, beta) =
( (x - z * sin beta * cos alpha / cos beta,
y - z * sin beta * sin alpha / cos beta,
0),
-z / (cos beta) )
direction_color :: Double -> Double -> Int -> Color
direction_color x y attn
| x > 0 && y > 0 = (attn, 0, 0) -- red
| x <= 0 && y > 0 = (0, attn, 0) -- green
| x > 0 && y <= 0 = (attn, attn, 0) -- yellow
| otherwise = (0, 0, attn) -- blue
checkerboard_pattern :: Double -> Double -> Int -> Color
checkerboard_pattern x y attn
| (round (x/floorscale) `mod` 2) == (round (y/floorscale) `mod` 2) = direction_color x y attn
| otherwise = (attn, attn, attn)
intersect_floor :: Coord -> ScreenCoord -> (Coord, Double, Color)
intersect_floor source (alpha, beta)
| x > (-0.5) && x < 0.5 = ((x, y, z), t, (0, attn, attn)) -- x near 0 : cyan
| y > (-0.5) && y < 0.5 = ((x, y, z), t, (attn, attn, 0)) -- y near 0 : yellow
| beta <= 90*degrees = ((x, y, z), 0, checkerboard_pattern x y 128)
| otherwise = ((x, y, z), t, checkerboard_pattern x y attn)
where attn = max 0 (round (255 - 8*(sqrt $ abs t)))
((x, y, z), t) = intersect_point_floor source (alpha, beta)
-- blue is beautiful, but a green tint is nice too
skycolor :: Coord -> ScreenCoord -> Color
skycolor source (alpha, beta) = (60,
round ((sqrt (alpha/6)) / (sqrt (90 * degrees)) * 128),
round ((sqrt (-beta+90*degrees)) / (sqrt (90 * degrees)) * 255) )
data SphereIntersect = SphereIntersect Double Color deriving (Eq, Show) -- distance color
instance Ord SphereIntersect where
(SphereIntersect d1 _) `compare` (SphereIntersect d2 _)
| d2 <= 0 = LT
| d1 <= 0 = GT
| otherwise = d1 `compare` d2
nearest_sphere :: Coord -> ScreenCoord -> [Sphere] -> SphereIntersect
nearest_sphere source scoord spheres =
minimum [(SphereIntersect distance color) | (_, distance, color) <- intersections]
where intersections = map (intersect_sphere source scoord) spheres
-- also include floor in objects
nearest_obj :: Coord -> ScreenCoord -> [Sphere] -> (Double, Color)
nearest_obj source scoord spheres
| floordist == 0 && spheredist > 0 = (spheredist, spherecolor)
| floordist > spheredist && spheredist > 0 = (spheredist, spherecolor)
| otherwise = (floordist, floorcolor)
where (SphereIntersect spheredist spherecolor) = nearest_sphere source scoord spheres
(_, floordist, floorcolor) = intersect_floor source scoord
-- First iteration
pixel_color :: Coord -> [Sphere] -> ScreenCoord -> Color
pixel_color_only_floor source spheres scoord = floorcolor
where ((x,y,z), floordist, floorcolor) = intersect_floor source scoord
(alpha, beta) = scoord
pixel_color source spheres scoord
| nearest_object_dist > 0 = objcolor
| beta == 90 * degrees = (0, 255, 0)
| otherwise = skycolor source scoord
where (_, beta) = scoord
(nearest_object_dist, objcolor) = nearest_obj source scoord spheres
cartProdTranspose xs ys = [(y,x) | x <- xs, y <- ys]
cartProd xs ys = [(x,y) | x <- xs, y <- ys]
pixel_to_ppm (r,g,b) = show r ++ " " ++ show g ++ " " ++ show b ++ "\n"
tuple2sum x y = (a1 + b1, a2 + b2)
where (a1, a2) = x
(b1, b2) = y
-- from one pixel (alpha, beta), get a list of oversampled pixels
oversample :: ScreenCoord -> [ScreenCoord]
oversample (a,b) = map (tuple2sum (a,b)) (cartProd ov_alphaoffsets ov_betaoffsets)
tuple3sum x y = (a1 + b1, a2 + b2, a3 + b3)
where (a1, a2, a3) = x
(b1, b2, b3) = y
coloraverage :: [Color] -> Color
coloraverage xs = ( round (fromIntegral s1/l),
round (fromIntegral s2/l),
round (fromIntegral s3/l) )
where (s1, s2, s3) = foldr tuple3sum (0,0,0) xs
l = fromIntegral (length xs)
-- calculate color of oversampled pixels
ov_color :: [Sphere] -> [ScreenCoord] -> Color
ov_color spheres coords = coloraverage (map (pixel_color eye spheres) coords)
-- list of list of (alpha, beta)-tuples
ov_pixels = map oversample (cartProdTranspose betas alphas)
allpixels spheres = map (ov_color spheres) ov_pixels
image spheres = imgheader ++ (foldr (++) "" (map pixel_to_ppm (allpixels spheres)))
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