module Point
where
+import Comparisons
+
+
type Point = (Double, Double, Double)
x_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 =
+ 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