src/Point.hs

   1 {-# LANGUAGE FlexibleInstances #-}
   2
   3 module Point
   4 where
   5
   6 import Comparisons
   7
   8
   9 type Point = (Double, Double, Double)
  10
  11 instance Num Point where
  12     (x1,y1,z1) + (x2,y2,z2) = (x1+x2, y1+y2, z1+z2)
  13     (x1,y1,z1) - (x2,y2,z2) = (x1-x2, y1-y2, z1-z2)
  14     (x1,y1,z1) * (x2,y2,z2) = (x1*x2, y1*y2, z1*z2)
  15     abs (x, y, z) = (abs x, abs y, abs z)
  16     signum (x, y, z) = (signum x, signum y, signum z)
  17     fromInteger n = (fromInteger n, fromInteger n, fromInteger n)
  18
  19
  20 -- | Scale a point by a constant.
  21 scale :: Point -> Double -> Point
  22 scale (x, y, z) d = (x*d, y*d, z*d)
  23
  24
  25 -- | Returns the distance between p1 and p2.
  26 distance :: Point -> Point -> Double
  27 distance p1 p2 =
  28     sqrt $ p1 `dot` p2
  29
  30
  31 -- | Returns the dot product of two points (taken as three-vectors).
  32 dot :: Point -> Point -> Double
  33 dot (x1, y1, z1) (x2, y2, z2) =
  34     (x2 - x1)^(2::Int) + (y2 - y1)^(2::Int) + (z2 - z1)^(2::Int)
  35
  36
  37 -- | Returns 'True' if p1 is close to (within 'epsilon' of) p2,
  38 --   'False' otherwise.
  39 is_close :: Point -> Point -> Bool
  40 is_close p1 p2 = (distance p1 p2) ~= 0