src/Point.hs

   1 {-# LANGUAGE FlexibleInstances #-}
   2
   3 module Point (
   4   Point(..),
   5   dot,
   6   scale )
   7 where
   8
   9 import Test.QuickCheck ( Arbitrary(..) )
  10
  11
  12 -- | Represents a point in three dimensions. We use a custom type (as
  13 --   opposed to a 3-tuple) so that we can make the coordinates strict.
  14 --
  15 data Point =
  16   Point !Double !Double !Double
  17   deriving (Eq, Show)
  18
  19
  20 instance Arbitrary Point where
  21   arbitrary = do
  22     (x,y,z) <- arbitrary
  23     return $ Point x y z
  24
  25
  26 instance Num Point where
  27   (Point x1 y1 z1) + (Point x2 y2 z2) = Point (x1+x2) (y1+y2) (z1+z2)
  28   (Point x1 y1 z1) - (Point x2 y2 z2) = Point (x1-x2) (y1-y2) (z1-z2)
  29   (Point x1 y1 z1) * (Point x2 y2 z2) = Point (x1*x2) (y1*y2) (z1*z2)
  30   abs (Point x y z) = Point (abs x) (abs y) (abs z)
  31   signum (Point x y z) = Point (signum x) (signum y) (signum z)
  32   fromInteger n =
  33     Point coord coord coord
  34     where
  35       coord = fromInteger n
  36
  37
  38 -- | Scale a point by a constant.
  39 scale :: Point -> Double -> Point
  40 scale (Point x y z) d = Point (x*d) (y*d) (z*d)
  41
  42
  43 -- | Returns the dot product of two points (taken as three-vectors).
  44 {-# INLINE dot #-}
  45 dot :: Point -> Point -> Double
  46 dot (Point x1 y1 z1) (Point x2 y2 z2) =
  47     (x2 - x1)^(2::Int) + (y2 - y1)^(2::Int) + (z2 - z1)^(2::Int)