+
+
+-- | Returns the distance between p1 and p2.
+distance :: Point -> Point -> Double
+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,
+-- 'False' otherwise.
+is_close :: Point -> Point -> Bool
+is_close p1 p2 = (distance p1 p2) ~= 0