Sphere intersection snippet

gistfile1.hs

{-
Minimum distance for ray intersection to be considered important.
This is due to limited numerical precision with floating point numbers. A ray could be reflected and then be immediately registered as intersecting with the object it just bounced off.
-}
epsilon :: Scalar
epsilon = 0.1

{-|
Defines a mathematical sphere.
-}
data Sphere = Sphere Vec3 Scalar deriving (Show, Read, Eq, Typeable)

instance Shape Sphere where
	intersect ray@(Ray origin dir) ((Sphere center rad), material) = listToMaybe is
		where
			a = magSquared dir
			b = 2 * ( dir `dot` (origin `sub` center))
			c = (magSquared (origin `sub` center)) - rad^2
			times = filter (> epsilon) (roots a b c)
			normal_at_time t = normalize ((positionAtTime ray t) `sub` center)
			intersection_at_time t = Intersection (normal_at_time t) (positionAtTime ray t) ray material
			is = sortWith (\(t, _) -> t) $ map (\t -> (t,intersection_at_time t)) times
	center (Sphere c _) = c