-{-# LANGUAGE TypeSynonymInstances #-}
-
-module Point
+{-# LANGUAGE FlexibleInstances #-}
+
+module Point (
+ Point,
+ distance,
+ dot,
+ is_close,
+ scale
+ )
where
-import Comparisons
+import Comparisons ((~=))
type Point = (Double, Double, Double)
-- | Returns the distance between p1 and p2.
distance :: Point -> Point -> Double
-distance (x1, y1, z1) (x2, y2, z2) =
- sqrt $ (x2 - x1)^(2::Int) + (y2 - y1)^(2::Int) + (z2 - z1)^(2::Int)
+distance p1 p2 =
+ sqrt $ p1 `dot` p2
+
+
+-- | Returns the dot product of two points (taken as three-vectors).
+dot :: Point -> Point -> Double
+dot (x1, y1, z1) (x2, y2, z2) =
+ (x2 - x1)^(2::Int) + (y2 - y1)^(2::Int) + (z2 - z1)^(2::Int)
-- | Returns 'True' if p1 is close to (within 'epsilon' of) p2,