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     p1 + p2 = (x1+x2, y1+y2, z1+z2)
  22         where
  23           x1 = x_coord p1
  24           x2 = x_coord p2
  25           y1 = y_coord p1
  26           y2 = y_coord p2
  27           z1 = z_coord p1
  28           z2 = z_coord p2
  29
  30     p1 - p2 = (x1-x2, y1-y2, z1-z2)
  31         where
  32           x1 = x_coord p1
  33           x2 = x_coord p2
  34           y1 = y_coord p1
  35           y2 = y_coord p2
  36           z1 = z_coord p1
  37           z2 = z_coord p2
  38
  39     p1 * p2 = (x1*x2, y1*y2, z1*z2)
  40         where
  41           x1 = x_coord p1
  42           x2 = x_coord p2
  43           y1 = y_coord p1
  44           y2 = y_coord p2
  45           z1 = z_coord p1
  46           z2 = z_coord p2
  47
  48     abs (x, y, z) = (abs x, abs y, abs z)
  49     signum (x, y, z) = (signum x, signum y, signum z)
  50     fromInteger n = (fromInteger n, fromInteger n, fromInteger n)
  51
  52
  53 -- | Scale a point by a constant.
  54 scale :: Point -> Double -> Point
  55 scale (x, y, z) d = (x*d, y*d, z*d)
  56
  57
  58 -- | Returns the distance between p1 and p2.
  59 distance :: Point -> Point -> Double
  60 distance p1 p2 =
  61     sqrt $ (x2 - x1)^(2::Int) + (y2 - y1)^(2::Int) + (z2 - z1)^(2::Int)
  62     where
  63       x1 = x_coord p1
  64       x2 = x_coord p2
  65       y1 = y_coord p1
  66       y2 = y_coord p2
  67       z1 = z_coord p1
  68       z2 = z_coord p2
  69
  70
  71 -- | Returns 'True' if p1 is close to (within 'epsilon' of) p2,
  72 --   'False' otherwise.
  73 is_close :: Point -> Point -> Bool
  74 is_close p1 p2 = (distance p1 p2) ~= 0