-{-# LANGUAGE TypeSynonymInstances #-}
+{-# LANGUAGE FlexibleInstances #-}
module Point
where
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
- p1 + p2 = (x1+x2, y1+y2, z1+z2)
- 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
-
- p1 - p2 = (x1-x2, y1-y2, z1-z2)
- 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
-
- p1 * p2 = (x1*x2, y1*y2, z1*z2)
- 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
-
+ (x1,y1,z1) + (x2,y2,z2) = (x1+x2, y1+y2, z1+z2)
+ (x1,y1,z1) - (x2,y2,z2) = (x1-x2, y1-y2, z1-z2)
+ (x1,y1,z1) * (x2,y2,z2) = (x1*x2, y1*y2, z1*z2)
abs (x, y, z) = (abs x, abs y, abs z)
signum (x, y, z) = (signum x, signum y, signum z)
fromInteger n = (fromInteger n, fromInteger n, fromInteger n)
+-- | Scale a point by a constant.
scale :: Point -> Double -> Point
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 =
+distance (x1, y1, z1) (x2, y2, z2) =
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