sphere intersection detection

1 files changed, 45 insertions, 6 deletions

diff --git a/raytracer.hs b/raytracer.hs
index 8b78ae8..80fa348 100644
--- a/raytracer.hs
+++ b/raytracer.hs
@@ -9,23 +9,29 @@ type Angle = Double
 type ScreenCoord = (Angle, Angle)
 type Color = (Int, Int, Int)
 type Coord = (Double, Double, Double)
+type Sphere = (Coord, Double)
 
 degrees = pi / 180
 
-eye = (0, 0, 2)
+eye = (100, 100, 2)
 
 x_of (x, _, _) = x
 y_of (_, y, _) = y
 z_of (_, _, z) = z
 
+sphere1 = ((10, 85, 0), 4)
+sphere2 = ((-10, 45, 0), 4)
+
 alpha1 = 80 * degrees
 alpha2 = -40 * degrees
 
-beta1 = 15 * degrees
-beta2 = -30 * degrees
+beta1 = 25 * degrees
+beta2 = -20 * degrees
+
+floorscale = 1
 
-w = 1000
-h = 500
+w = 800
+h = 400
 
 oversampling = 1 -- each pixel is 2x2 rays
 ov_alphaoffset = ((alpha2 - alpha1) / (w-1)) / oversampling
@@ -39,6 +45,35 @@ 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 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) (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
+
+intersect_sphere :: Coord -> ScreenCoord -> Sphere -> Bool
+intersect_sphere source (alpha, beta) (centre, radius)
+        | discr source (alpha, beta) (centre, radius) > 0 = True
+        | otherwise = False
+
+
+
+
 --                     intersect at  (x     , y     , depth )
 intersect_floor :: Coord -> ScreenCoord -> (Double, Double, Double)
 intersect_floor source (alpha, beta)
@@ -49,7 +84,9 @@ intersect_floor source (alpha, beta)
 
 floorcolor :: Coord -> ScreenCoord -> Color
 floorcolor source (alpha, beta)
-        | (round (x/8) `mod` 2) == (round (y/8) `mod` 2) = (attn, 0, 0)
+        | x > 0.5 && x < 0.5 = (0, attn, attn)
+        | y > (-0.5) && y < 0.5 = (attn, attn, 0)
+        | (round (x/floorscale) `mod` 2) == (round (y/floorscale) `mod` 2) = (attn, 0, 0)
         | otherwise              = (attn, attn, attn)
         where attn = max 0 (round (255 - 8*(sqrt t)))
               (x, y, t) = intersect_floor source (alpha, beta)
@@ -62,6 +99,8 @@ skycolor source (alpha, beta) = (60,
 
 pixel_color :: Coord -> ScreenCoord -> Color
 pixel_color source (alpha, beta)
+        | intersect_sphere source (alpha, beta) sphere1 = (200, 0, 0)
+        | intersect_sphere source (alpha, beta) sphere2 = (0, 200, 0)
         | beta > 0  = skycolor source (alpha, beta)
         | beta == 0 = (0, 255, 0)
         | otherwise = floorcolor source (alpha, beta)