Use a slightly more stable (I think?) formula for the {x,y,z}{min,max}.

[spline3.git] / src / Point.hs

diff --git a/src/Point.hs b/src/Point.hs
index 5d7954c810634f64fa65599afd352502fce40eca..95b33640f4e81406f71a685c617a3c273a2a6284 100644 (file)
--- a/src/Point.hs
+++ b/src/Point.hs
@@ -1,4 +1,4 @@
-{-# LANGUAGE TypeSynonymInstances #-}
+{-# LANGUAGE FlexibleInstances #-}
 
 module Point
 where
@@ -8,63 +8,33 @@ 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
-    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
+    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