{-# LANGUAGE TypeSynonymInstances #-}

module Point
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 distance between p1 and p2.
distance :: Point -> Point -> Double
distance (x1, y1, z1) (x2, y2, z2) =
    sqrt $ (x2 - x1)^(2::Int) + (y2 - y1)^(2::Int) + (z2 - z1)^(2::Int)


-- | Returns 'True' if p1 is close to (within 'epsilon' of) p2,
--   'False' otherwise.
is_close :: Point -> Point -> Bool
is_close p1 p2 = (distance p1 p2) ~= 0