{-# LANGUAGE FlexibleInstances #-}

module Point (
  Point(..),
  dot,
  scale )
where

import Test.Tasty.QuickCheck ( Arbitrary(..) )


-- | Represents a point in three dimensions. We use a custom type (as
--   opposed to a 3-tuple) so that we can make the coordinates strict.
--
data Point =
  Point !Double !Double !Double
  deriving (Eq, Show)


instance Arbitrary Point where
  arbitrary = do
    (x,y,z) <- arbitrary
    return $ Point x y z


instance Num Point where
  (Point x1 y1 z1) + (Point x2 y2 z2) = Point (x1+x2) (y1+y2) (z1+z2)
  (Point x1 y1 z1) - (Point x2 y2 z2) = Point (x1-x2) (y1-y2) (z1-z2)
  (Point x1 y1 z1) * (Point x2 y2 z2) = Point (x1*x2) (y1*y2) (z1*z2)
  abs (Point x y z) = Point (abs x) (abs y) (abs z)
  signum (Point x y z) = Point (signum x) (signum y) (signum z)
  fromInteger n =
    Point coord coord coord
    where
      coord = fromInteger n


-- | Scale a point by a constant.
scale :: Point -> Double -> Point
scale (Point x y z) d = Point (x*d) (y*d) (z*d)


-- | Returns the dot product of two points (taken as three-vectors).
{-# INLINE dot #-}
dot :: Point -> Point -> Double
dot (Point x1 y1 z1) (Point x2 y2 z2) =
    (x2 - x1)^(2::Int) + (y2 - y1)^(2::Int) + (z2 - z1)^(2::Int)