Fix polygon.centroid for open polygons.

The implementation assumed closed polygons, but it should work on either. This
is a partial fix for #443.

d3.geom.js

@@ -192,16 +192,16 @@ d3.geom.polygon = function(coordinates) {
 
   coordinates.centroid = function(k) {
     var i = -1,
-        n = coordinates.length - 1,
+        n = coordinates.length,
         x = 0,
         y = 0,
         a,
-        b,
+        b = coordinates[n - 1],
         c;
     if (!arguments.length) k = -1 / (6 * coordinates.area());
     while (++i < n) {
-      a = coordinates[i];
+      a = b;
-      b = coordinates[i + 1];
+      b = coordinates[i];
       c = a[0] * b[1] - b[0] * a[1];
       x += (a[0] + b[0]) * c;
       y += (a[1] + b[1]) * c;

src/geom/polygon.js

@@ -15,16 +15,16 @@ d3.geom.polygon = function(coordinates) {
 
   coordinates.centroid = function(k) {
     var i = -1,
-        n = coordinates.length - 1,
+        n = coordinates.length,
         x = 0,
         y = 0,
         a,
-        b,
+        b = coordinates[n - 1],
         c;
     if (!arguments.length) k = -1 / (6 * coordinates.area());
     while (++i < n) {
-      a = coordinates[i];
+      a = b;
-      b = coordinates[i + 1];
+      b = coordinates[i];
       c = a[0] * b[1] - b[0] * a[1];
       x += (a[0] + b[0]) * c;
       y += (a[1] + b[1]) * c;

test/geom/polygon-test.js

@@ -8,49 +8,75 @@ var vows = require("vows"),
 var suite = vows.describe("d3.geom.polygon");
 
 suite.addBatch({
-  "counterclockwise polygon (last point equal to start point)": {
+  "closed counterclockwise unit square": {
     topic: function() {
       return d3.geom.polygon([[0, 0], [0, 1], [1, 1], [1, 0], [0, 0]]);
     },
-    "area": function(polygon) {
+    "has area 1": function(polygon) {
       assert.equal(polygon.area(), 1);
     },
-    "centroid": function(polygon) {
+    "has centroid ⟨.5,.5⟩": function(polygon) {
       assert.deepEqual(polygon.centroid(), [.5, .5]);
     }
   },
-  "counterclockwise polygon (implicitly ending at start point)": {
+  "closed clockwise unit square": {
-    topic: function() {
-      return d3.geom.polygon([[0, 0], [0, 1], [1, 1], [1, 0]]);
-    },
-    "area": function(polygon) {
-      assert.equal(polygon.area(), 1);
-    },
-    "centroid": function(polygon) {
-      assert.deepEqual(polygon.centroid(), [.5, .5]);
-    }
-  },
-  "clockwise polygon (last point equal to start point)": {
     topic: function() {
       return d3.geom.polygon([[0, 0], [1, 0], [1, 1], [0, 1], [0, 0]]);
     },
-    "area": function(polygon) {
+    "has area 1": function(polygon) {
       assert.equal(polygon.area(), -1);
     },
-    "centroid": function(polygon) {
+    "has centroid ⟨.5,.5⟩": function(polygon) {
       assert.deepEqual(polygon.centroid(), [.5, .5]);
     }
   },
-  "clockwise polygon (implicitly ending at start point)": {
+  "closed clockwise triangle": {
+    topic: function() {
+      return d3.geom.polygon([[1, 1], [3, 2], [2, 3], [1, 1]]);
+    },
+    "has area 1.5": function(polygon) {
+      assert.equal(polygon.area(), -1.5);
+    },
+    "has centroid ⟨2,2⟩": function(polygon) {
+      var centroid = polygon.centroid();
+      assert.inDelta(centroid[0], 2, 1e-6);
+      assert.inDelta(centroid[1], 2, 1e-6);
+    }
+  },
+  "open counterclockwise unit square": {
+    topic: function() {
+      return d3.geom.polygon([[0, 0], [0, 1], [1, 1], [1, 0]]);
+    },
+    "has area 1": function(polygon) {
+      assert.equal(polygon.area(), 1);
+    },
+    "has centroid ⟨.5,.5⟩": function(polygon) {
+      assert.deepEqual(polygon.centroid(), [.5, .5]);
+    }
+  },
+  "open clockwise unit square": {
     topic: function() {
       return d3.geom.polygon([[0, 0], [1, 0], [1, 1], [0, 1]]);
     },
-    "area": function(polygon) {
+    "has area 1": function(polygon) {
       assert.equal(polygon.area(), -1);
     },
-    "centroid": function(polygon) {
+    "has centroid ⟨.5,.5⟩": function(polygon) {
       assert.deepEqual(polygon.centroid(), [.5, .5]);
     }
+  },
+  "open clockwise triangle": {
+    topic: function() {
+      return d3.geom.polygon([[1, 1], [3, 2], [2, 3]]);
+    },
+    "has area 1.5": function(polygon) {
+      assert.equal(polygon.area(), -1.5);
+    },
+    "has centroid ⟨2,2⟩": function(polygon) {
+      var centroid = polygon.centroid();
+      assert.inDelta(centroid[0], 2, 1e-6);
+      assert.inDelta(centroid[1], 2, 1e-6);
+    }
   }
 });