learn how to do spherical coordinates again

1 files changed, 33 insertions, 37 deletions

diff --git a/raytracer.hs b/raytracer.hs
index 883331f..618c708 100644
--- a/raytracer.hs
+++ b/raytracer.hs
@@ -30,15 +30,17 @@ sphere2 = Sphere (80, 0, 5) 20 (255,60,0)
 
 filename num = "foo/foo" ++ show num ++ ".ppm"
 
-spherepos = take 1 [0,20..] -- take 80 [0,1..]
+--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))))
-            Sphere (80 * sin(num * degrees), 80 * cos(num * degrees), 5) 10 (255,60,0), sphere1]
+                    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 num))
+writenum num = trace ("Rendering " ++ show (filename $ round num))
                writeFile (filename num) (image $ spheres num)
 
 main = mapM writenum spherepos
@@ -47,8 +49,8 @@ main = mapM writenum spherepos
 alpha1 = 0 * degrees
 alpha2 = 360 * degrees
 
-beta1 = 20 * degrees
-beta2 = -100 * degrees
+beta1 = 70 * degrees
+beta2 = 180 * degrees
 
 floorscale = 4
 
@@ -76,28 +78,23 @@ betas  = take (round h) [beta1,(beta1 + ((beta2 - beta1) / (h-1)))..]
 -- 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*cos alpha + dist*cos beta,
-                                          y + dist*sin alpha,
-                                          z + dist*sin beta)
+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))
--- where u = source_x - sphere_x (v and w analogous)
--- where A = cos alpha + cos beta
---       B = sin alpha
---       C = sin beta
-
 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 = cos alpha + cos beta
-            bb = sin alpha
-            cc = sin beta
+            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
@@ -105,24 +102,24 @@ 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 = cos alpha + cos beta
-                  bb = sin alpha
-                  cc = sin beta
+            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) =
-                      (  (-z * ((cos alpha) + (cos beta)) / (sin beta) + x,
-                         -z * (sin alpha) / (sin beta) + y,
-                         0),
-                      -z / (sin 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
@@ -138,10 +135,9 @@ checkerboard_pattern x y attn
 
 intersect_floor :: Coord -> ScreenCoord -> (Coord, Double, Color)
 intersect_floor source (alpha, beta)
---        | beta >= 0              = ((0, 0, 0), 0, black)
         | 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 >= 0              = ((x, y, z), -t, checkerboard_pattern x y 128)
+        | 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)
@@ -150,7 +146,7 @@ intersect_floor source (alpha, beta)
 skycolor :: Coord -> ScreenCoord -> Color
 skycolor source (alpha, beta) = (60,
             round ((sqrt (alpha/6)) / (sqrt (90 * degrees)) * 128),
-            round ((sqrt beta) / (sqrt (90 * degrees)) * 255) )
+            round ((sqrt (-beta+90*degrees)) / (sqrt (90 * degrees)) * 255) )
 
 data SphereIntersect = SphereIntersect Double Color deriving (Eq, Show) -- distance color
 instance Ord SphereIntersect where
@@ -175,13 +171,13 @@ nearest_obj source scoord spheres
 
 -- First iteration
 pixel_color :: Coord -> [Sphere] -> ScreenCoord -> Color
-pixel_color source spheres scoord =  floorcolor
+pixel_color_only_floor source spheres scoord =  floorcolor
                     where   ((x,y,z), floordist, floorcolor) = intersect_floor source scoord
                             (alpha, beta) = scoord
 
-pixel_colorold source spheres scoord
+pixel_color source spheres scoord
             | nearest_object_dist > 0 = objcolor
-            | beta == 0               = (0, 255, 0)
+            | beta == 90 * degrees    = (0, 255, 0)
             | otherwise               = skycolor source scoord
             where   (_, beta) = scoord
                     (nearest_object_dist, objcolor) = nearest_obj source scoord spheres