Add tests for d3.geom.polygon and fix centroid bug.

d3.geom.polygon(…).area() assumes screen pixel coordinates with (0, 0)
at the top left, and y increasing going downwards.  This results in a
positive area for counterclockwise coordinates.  Howver, the default
centroid calculation was assuming "usual" Cartesian coordinates with y
increasing going upwards, hence the centroid coordinates were
incorrectly multiplied by -1.

This fix won't affect d3.geo.path(…).centroid() as it passes a constant
to d3.geom.centroid.

d3.geom.js

@@ -198,7 +198,7 @@ d3.geom.polygon = function(coordinates) {
         a,
         b,
         c;
-    if (!arguments.length) k = 1 / (6 * coordinates.area());
+    if (!arguments.length) k = -1 / (6 * coordinates.area());
     while (++i < n) {
       a = coordinates[i];
       b = coordinates[i + 1];

src/geom/polygon.js

@@ -21,7 +21,7 @@ d3.geom.polygon = function(coordinates) {
         a,
         b,
         c;
-    if (!arguments.length) k = 1 / (6 * coordinates.area());
+    if (!arguments.length) k = -1 / (6 * coordinates.area());
     while (++i < n) {
       a = coordinates[i];
       b = coordinates[i + 1];

test/geom/polygon-test.js

@@ -0,0 +1,34 @@
+require("../env");
+require("../../d3");
+require("../../d3.geom");
+
+var vows = require("vows"),
+    assert = require("assert");
+
+var suite = vows.describe("d3.geom.polygon");
+
+suite.addBatch({
+  "polygon": {
+    topic: function() {
+      return d3.geom.polygon;
+    },
+    "area": {
+      "last point equal to start point": function(polygon) {
+        assert.equal(polygon([[0, 0], [0, 1], [1, 1], [1, 0], [0, 0]]).area(), 1);
+      },
+      "implicitly ending at start point": function(polygon) {
+        assert.equal(polygon([[0, 0], [0, 1], [1, 1], [1, 0]]).area(), 1);
+      }
+    },
+    "centroid": {
+      "last point equal to start point": function(polygon) {
+        assert.deepEqual(polygon([[0, 0], [0, 1], [1, 1], [1, 0], [0, 0]]).centroid(), [.5, .5]);
+      },
+      "implicitly ending at start point": function(polygon) {
+        assert.deepEqual(polygon([[0, 0], [0, 1], [1, 1], [1, 0]]).centroid(), [.5, .5]);
+      }
+    }
+  }
+});
+
+suite.export(module);