Added distance function that can handle different types of spaces.

git-svn-id: svn+ssh://src.earth.threerings.net/nenya/trunk@371 ed5b42cb-e716-0410-a449-f6a68f950b19

src/as/com/threerings/flash/MathUtil.as

@@ -19,8 +19,7 @@
 // License along with this library; if not, write to the Free Software
 // Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
 
-package com.threerings.flash {
-    
+package com.threerings.flash {    
 
 /**
  * Collection of math utility functions.
@@ -34,6 +33,55 @@ public class MathUtil
     {
         return Math.min(Math.max(n, min), max);
     }
+
+    /**
+     * Returns distance from point (x1, y1) to (x2, y2) in 2D.
+     *
+     * <p>Supports various distance metrics: the common Euclidean distance, taxicab distance,
+     * arbitrary Minkowski distances, and Chebyshev distance.
+     *
+     * <p>See the <a href="http://www.nist.gov/dads/HTML/lmdistance.html">NIST web page on 
+     * distance definitions</a>.<p>
+     *
+     * @param x1 x value of the first point
+     * @param y1 y value of the first point
+     * @param x2 x value of the second point
+     * @param y2 y value of the second point    
+     * @param p Optional: p value of the norm function. Common cases:
+     *          <ul><li>p = 2 (default): standard Euclidean distance on a plane
+     *              <li>p = 1: taxicab distance (aka Manhattan distance)
+     *              <li>p = Infinity: Chebyshev distance
+     *          </ul>
+     *          <b>Note</b>: p < 1 or p = NaN are treated as equivalent to p = Infinity
+     */
+    public static function distance (
+        x1 :Number, y1 :Number, x2 :Number, y2 :Number, p :int = 2) :Number
+    {
+        if (! isFinite(p) || p < 1) {
+            p = Infinity;
+        }
+
+        var dx :Number = x2 - x1;
+        var dy :Number = y2 - y1;
+        
+        switch (p) {
+        case 1:
+            // optimized version for taxicab distance
+            return dx + dy;
+        case 2:
+            // optimized version for Euclidean
+            return Math.sqrt(dx * dx + dy * dy);
+        case Infinity:
+            // optimized version for Chebyshev
+            return Math.max(dx, dy);
+        default:
+            // generic version
+            var xx :Number = Math.pow(dx, p);
+            var yy :Number = Math.pow(dy, p);
+            return Math.pow(xx + yy, 1 / p);
+        }
+    }
+            
 }
 
 }