{-# LANGUAGE TypeSynonymInstances #-}

module Point
where

type Point = (Double, Double, Double)

x_coord :: Point -> Double
x_coord (x, _, _) = x

y_coord :: Point -> Double
y_coord (_, y, _) = y

z_coord :: Point -> Double
z_coord (_, _, z) = z

instance Num Point where
    p1 + p2 = (x1+x2, y1+y2, z1+z2)
        where
          x1 = x_coord p1
          x2 = x_coord p2
          y1 = y_coord p1
          y2 = y_coord p2
          z1 = z_coord p1
          z2 = z_coord p2

    p1 - p2 = (x1-x2, y1-y2, z1-z2)
        where
          x1 = x_coord p1
          x2 = x_coord p2
          y1 = y_coord p1
          y2 = y_coord p2
          z1 = z_coord p1
          z2 = z_coord p2

    p1 * p2 = (x1*x2, y1*y2, z1*z2)
        where
          x1 = x_coord p1
          x2 = x_coord p2
          y1 = y_coord p1
          y2 = y_coord p2
          z1 = z_coord p1
          z2 = z_coord p2

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