fix #994: Revert commit b5af47a7b1

Revert back to correct implementation of Path#getArea() and implement unit tests for it.

src/path/Curve.js

@@ -756,26 +756,17 @@ statics: /** @lends Curve */{
     },
 
     getArea: function(v) {
-        // This is a combination of the methods to decide if a path is clockwise
-        // and to calculate the area, as described here:
         // http://objectmix.com/graphics/133553-area-closed-bezier-curve.html
-        // http://stackoverflow.com/questions/1165647
-        // We treat the curve points and handles as the outline of a polygon of
-        // which we determine the orientation using the method of calculating
-        // the sum over the edges. This will work even with non-convex polygons,
-        // telling you whether it's mostly clockwise.
-        // With bezier curves, the trick appears to be to calculate edge sum
-        // with half the handles' lengths, and then:
-        // area = 6 * edge-sum / 10
         var p1x = v[0], p1y = v[1],
-            p2x = v[6], p2y = v[7],
-            h1x = (v[2] + p1x) / 2,
-            h1y = (v[3] + p1y) / 2,
-            h2x = (v[4] + v[6]) / 2,
-            h2y = (v[5] + v[7]) / 2;
-        return 6 * ((p1x - h1x) * (h1y + p1y)
-                  + (h1x - h2x) * (h2y + h1y)
-                  + (h2x - p2x) * (p2y + h2y)) / 10;
+            c1x = v[2], c1y = v[3],
+            c2x = v[4], c2y = v[5],
+            p2x = v[6], p2y = v[7];
+        return (3.0 * c1y * p1x - 1.5 * c1y * c2x
+              - 1.5 * c1y * p2x - 3.0 * p1y * c1x
+              - 1.5 * p1y * c2x - 0.5 * p1y * p2x
+              + 1.5 * c2y * p1x + 1.5 * c2y * c1x
+              - 3.0 * c2y * p2x + 0.5 * p2y * p1x
+              + 1.5 * p2y * c1x + 3.0 * p2y * c2x) / 10;
     },
 
     getBounds: function(v) {

test/tests/Path.js

@@ -14,15 +14,37 @@ QUnit.module('Path');
 
 test('path.length', function() {
     var path = new Path([
-        new Segment(new Point(121, 334), new Point(-19, 38), new Point(30.7666015625, -61.53369140625)),
-        new Segment(new Point(248, 320), new Point(-42, -74), new Point(42, 74))
+        new Segment([121, 334], [-19, 38], [30.7666015625, -61.53369140625]),
+        new Segment([248, 320], [-42, -74], [42, 74])
     ]);
 
-    var length = path.length;
-    equals(length, 172.10112809179614, 'path.length');
+    equals(function() {
+        return path.length;
+    }, 172.10112809179614);
 
-    var t = path.curves[0].getTimeAt(length / 4);
-    equals(t, 0.2255849553116685, 'path.curves[0].getTimeAt(length / 4)');
+    equals(function() {
+        return path.curves[0].getTimeAt(path.length / 4);
+    }, 0.2255849553116685);
+});
+
+test('path.area', function() {
+    var rect = new Path.Rectangle({
+        point: [0, 0],
+        size: [10, 10]
+    });
+
+    equals(function() {
+        return rect.area;
+    }, 100);
+
+    var circle = new Path.Circle({
+        center: [0, 0],
+        radius: 10
+    });
+
+    equals(function() {
+        return circle.area;
+    }, Math.PI * 100, null, { tolerance: 0.1 });
 });
 
 test('curve.getTimeAt() with straight curve', function() {