data Point = Point Double Double Double
	deriving (Eq, Show)

mkPoint :: Double -> Double -> Double -> Point
mkPoint = Point

instance Num Point where
	(Point x y z) + (Point x' y' z') = Point (x+x') (y+y') (z+z')
	(Point x y z) - (Point x' y' z') = Point (x-x') (y-y') (z-z')

times :: Point -> Double -> Point
times (Point x y z) d = Point (x*d) (y*d) (z*d)

mapPointToNormalized2D :: Double -> Double -> Double -> Point -> (Double,Double)
mapPointToNormalized2D xO yO zO (Point x y z)
	= ((zO * x / (z + zO)) + xO,(zO * y / (z + zO)) + yO)