import System.IO
import Data.Char
-- 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)

degrees = pi / 180

eye = [0, 0, 2]

alpha1 = 80 * degrees
alpha2 = -40 * degrees

beta1 = 15 * degrees
beta2 = -30 * degrees

w = 1000
h = 500

oversampling = 1 -- each pixel is 2x2 rays
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 w) ++ " " ++ (show h) ++ " 255\n"

alphas = take (round w) [alpha1,(alpha1 + ((alpha2 - alpha1) / (w-1)))..]
betas  = take (round h) [beta1,(beta1 + ((beta2 - beta1) / (h-1)))..]

--                       intersect at  (x     , y     , depth )
intersect_floor :: ScreenCoord -> (Double, Double, Double)
intersect_floor (alpha, beta)
        | beta < 0 = (-2 * (cos alpha) / (sin beta) - 2 * (cos beta) / (sin beta),
                      -2 * (sin alpha) / (sin beta),
                      -2 / (sin beta) )
        | otherwise = (0, 0, 0)

floorcolor :: ScreenCoord -> Color
floorcolor (alpha, beta)
        | (round (x/8) `mod` 2) == (round (y/8) `mod` 2) = (attn, 0, 0)
        | otherwise              = (attn, attn, attn)
        where attn = max 0 (round (255 - 8*(sqrt t)))
              (x, y, t) = intersect_floor (alpha, beta)

-- blue is beautiful, but a green tint is nice too
skycolor :: ScreenCoord -> Color
skycolor (alpha, beta) = (60,
            round ((sqrt (alpha/6)) / (sqrt (90 * degrees)) * 128),
            round ((sqrt beta) / (sqrt (90 * degrees)) * 255) )

pixel_color :: ScreenCoord -> Color
pixel_color (alpha, beta)
        | beta > 0  = skycolor (alpha, beta)
        | beta == 0 = (0, 255, 0)
        | otherwise = floorcolor (alpha, beta)

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 :: [ScreenCoord] -> Color
ov_color xs = coloraverage (map pixel_color xs)

-- list of list of (alpha, beta)-tuples
ov_pixels = map oversample (cartProdTranspose betas alphas)

allpixels = map ov_color ov_pixels

image = imgheader ++ (foldr (++) "" (map pixel_to_ppm allpixels))

main = writeFile "foo.ppm" image