{-# LANGUAGE FlexibleInstances #-}

module Point (
  Point,
  dot,
  scale
  )
where

import Comparisons ((~=))


type Point = (Double, Double, Double)

instance Num Point where
    (x1,y1,z1) + (x2,y2,z2) = (x1+x2, y1+y2, z1+z2)
    (x1,y1,z1) - (x2,y2,z2) = (x1-x2, y1-y2, z1-z2)
    (x1,y1,z1) * (x2,y2,z2) = (x1*x2, y1*y2, z1*z2)
    abs (x, y, z) = (abs x, abs y, abs z)
    signum (x, y, z) = (signum x, signum y, signum z)
    fromInteger n = (fromInteger n, fromInteger n, fromInteger n)


-- | Scale a point by a constant.
scale :: Point -> Double -> Point
scale (x, y, z) d = (x*d, y*d, z*d)


-- | Returns the dot product of two points (taken as three-vectors).
dot :: Point -> Point -> Double
dot (x1, y1, z1) (x2, y2, z2) =
    (x2 - x1)^(2::Int) + (y2 - y1)^(2::Int) + (z2 - z1)^(2::Int)