src/Point.hs

   1 {-# LANGUAGE FlexibleInstances #-}
   2
   3 module Point (
   4   Point,
   5   dot,
   6   scale
   7   )
   8 where
   9
  10 import Comparisons ((~=))
  11
  12
  13 type Point = (Double, Double, Double)
  14
  15 instance Num Point where
  16     (x1,y1,z1) + (x2,y2,z2) = (x1+x2, y1+y2, z1+z2)
  17     (x1,y1,z1) - (x2,y2,z2) = (x1-x2, y1-y2, z1-z2)
  18     (x1,y1,z1) * (x2,y2,z2) = (x1*x2, y1*y2, z1*z2)
  19     abs (x, y, z) = (abs x, abs y, abs z)
  20     signum (x, y, z) = (signum x, signum y, signum z)
  21     fromInteger n = (fromInteger n, fromInteger n, fromInteger n)
  22
  23
  24 -- | Scale a point by a constant.
  25 scale :: Point -> Double -> Point
  26 scale (x, y, z) d = (x*d, y*d, z*d)
  27
  28
  29 -- | Returns the dot product of two points (taken as three-vectors).
  30 {-# INLINE dot #-}
  31 dot :: Point -> Point -> Double
  32 dot (x1, y1, z1) (x2, y2, z2) =
  33     (x2 - x1)^(2::Int) + (y2 - y1)^(2::Int) + (z2 - z1)^(2::Int)