import System infinity = 1/0 delta = sqrt e where e = encodeFloat (floatRadix e) (-floatDigits e) infixl 7 .*, *| data Vector = V !Double !Double !Double deriving (Show, Eq) s *| V x y z = V (s * x) (s * y) (s * z) instance Num Vector where V x y z + V x' y' z' = V (x + x') (y + y') (z + z') V x y z - V x' y' z' = V (x - x') (y - y') (z - z') fromInteger i = V x x x where x = fromInteger i V x y z .* V x' y' z' = x * x' + y * y' + z * z' vlength r = sqrt (r .* r) unitise r = 1 / vlength r *| r data Scene = Sphere !Vector !Double | Group !Vector !Double Scene Scene Scene Scene Scene deriving (Show) ray_sphere (V dx dy dz) (V vx vy vz) r = let disc = vx * vx + vy * vy + vz * vz - r * r in if disc < 0 then infinity else let b = vx * dx + vy * dy + vz * dz b2 = b * b in if b2 < disc then infinity else let disk = sqrt(b2 - disc) t1 = b - disk in if t1 > 0 then t1 else b + disk ray_sphere' (V ox oy oz) (V dx dy dz) (V cx cy cz) r = let vx = cx - ox; vy = cy - oy; vz = cz - oz vv = vx * vx + vy * vy + vz * vz b = vx * dx + vy * dy + vz * dz disc = b * b - vv + r * r in disc >= 0 && b + sqrt disc >= 0 data Hit = H {l :: !Double, nv :: Vector } intersect dir@(V dx dy dz) hit s = case s of Sphere center@(V cx cy cz) radius -> let l' = ray_sphere dir center radius in if l' >= l hit then hit else let x = l' * dx - cx y = l' * dy - cy z = l' * dz - cz il = 1 / sqrt(x * x + y * y + z * z) in H {l = l', nv = V (il * x) (il * y) (il * z) } Group center radius a b c d e -> let l' = ray_sphere dir center radius in if l' >= l hit then hit else let f h s = intersect dir h s in f (f (f (f (f hit a) b) c) d) e intersect' orig dir s = case s of Sphere center radius -> ray_sphere' orig dir center radius Group center radius a b c d e -> let f s = intersect' orig dir s in ray_sphere' orig dir center radius && (f a || f b || f c || f d || f e) neg_light = unitise (V 1 3 (-2)) ray_trace dir scene = let hit = intersect dir (H infinity 0) scene in if l hit == infinity then 0 else let n = nv hit in let g = n .* neg_light in if g < 0 then 0 else if intersect' (l hit *| dir + delta *| n) neg_light scene then 0 else g fold5 f x a b c d e = f (f (f (f (f x a) b) c) d) e create level c r = let obj = Sphere c r in if level == 1 then obj else let a = 3 * r / sqrt 12 in let bound (c, r) s = case s of Sphere c' r' -> (c, max r (vlength (c - c') + r')) Group _ _ v w x y z -> fold5 bound (c, r) v w x y z in let aux x' z' = create (level - 1 :: Int) (c + V x' a z') (0.5 * r) in let w = aux (-a) (-a); x = aux a (-a) in let y = aux (-a) a; z = aux a a in let (c1, r1) = fold5 bound (c + V 0 r 0, 0) obj w x y z in Group c1 r1 obj w x y z ss = 4 pixel_vals n scene y x = sum [ let f a da = a - n / 2 + da / ss; d = unitise (V (f x dx) (f y dy) n) in ray_trace d scene | dx <- [0..ss-1], dy <- [0..ss-1] ] main = do [level,ni] <- fmap (map read) getArgs let n = fromIntegral ni scene = create level (V 0 (-1) 4) 1 scale x = 0.5 + 255 * x / (ss*ss) picture = [ toEnum \$ truncate \$ scale \$ pixel_vals n scene y x | y <- [n-1,n-2..0], x <- [0..n-1]] putStr \$ "P5\n" ++ show ni ++ " " ++ show ni ++ "\n255\n" ++ picture