-{-# LANGUAGE TypeSynonymInstances #-}
+{-# LANGUAGE FlexibleInstances #-}
-module Point
+module Point (
+ Point,
+ dot,
+ scale
+ )
where
-import Comparisons
+import Comparisons ((~=))
type Point = (Double, Double, Double)
-x_coord :: Point -> Double
-x_coord (x, _, _) = x
-
-y_coord :: Point -> Double
-y_coord (_, y, _) = y
-
-z_coord :: Point -> Double
-z_coord (_, _, z) = z
-
instance Num Point where
(x1,y1,z1) + (x2,y2,z2) = (x1+x2, y1+y2, z1+z2)
(x1,y1,z1) - (x2,y2,z2) = (x1-x2, y1-y2, z1-z2)
scale (x, y, z) d = (x*d, y*d, z*d)
--- | Returns the distance between p1 and p2.
-distance :: Point -> Point -> Double
-distance p1 p2 =
- sqrt $ (x2 - x1)^(2::Int) + (y2 - y1)^(2::Int) + (z2 - z1)^(2::Int)
- where
- x1 = x_coord p1
- x2 = x_coord p2
- y1 = y_coord p1
- y2 = y_coord p2
- z1 = z_coord p1
- z2 = z_coord p2
-
-
--- | Returns 'True' if p1 is close to (within 'epsilon' of) p2,
--- 'False' otherwise.
-is_close :: Point -> Point -> Bool
-is_close p1 p2 = (distance p1 p2) ~= 0
+-- | 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)