src/Point.hs

   1 {-# LANGUAGE TypeSynonymInstances #-}
   2
   3 module Point
   4 where
   5
   6 import Comparisons
   7
   8
   9 type Point = (Double, Double, Double)
  10
  11 x_coord :: Point -> Double
  12 x_coord (x, _, _) = x
  13
  14 y_coord :: Point -> Double
  15 y_coord (_, y, _) = y
  16
  17 z_coord :: Point -> Double
  18 z_coord (_, _, z) = z
  19
  20 instance Num Point where
  21     (x1,y1,z1) + (x2,y2,z2) = (x1+x2, y1+y2, z1+z2)
  22     (x1,y1,z1) - (x2,y2,z2) = (x1-x2, y1-y2, z1-z2)
  23     (x1,y1,z1) * (x2,y2,z2) = (x1*x2, y1*y2, z1*z2)
  24     abs (x, y, z) = (abs x, abs y, abs z)
  25     signum (x, y, z) = (signum x, signum y, signum z)
  26     fromInteger n = (fromInteger n, fromInteger n, fromInteger n)
  27
  28
  29 -- | Scale a point by a constant.
  30 scale :: Point -> Double -> Point
  31 scale (x, y, z) d = (x*d, y*d, z*d)
  32
  33
  34 -- | Returns the distance between p1 and p2.
  35 distance :: Point -> Point -> Double
  36 distance p1 p2 =
  37     sqrt $ (x2 - x1)^(2::Int) + (y2 - y1)^(2::Int) + (z2 - z1)^(2::Int)
  38     where
  39       x1 = x_coord p1
  40       x2 = x_coord p2
  41       y1 = y_coord p1
  42       y2 = y_coord p2
  43       z1 = z_coord p1
  44       z2 = z_coord p2
  45
  46
  47 -- | Returns 'True' if p1 is close to (within 'epsilon' of) p2,
  48 --   'False' otherwise.
  49 is_close :: Point -> Point -> Bool
  50 is_close p1 p2 = (distance p1 p2) ~= 0