Fix loss of significance for d3.geom.polygon.area.

d3.js

@@ -6485,12 +6485,11 @@
   }
   d3.geom.polygon = function(coordinates) {
     coordinates.area = function() {
-      var i = 0, n = coordinates.length, a = coordinates[n - 1][0] * coordinates[0][1], b = coordinates[n - 1][1] * coordinates[0][0];
+      var i = 0, n = coordinates.length, area = coordinates[n - 1][1] * coordinates[0][0] - coordinates[n - 1][0] * coordinates[0][1];
       while (++i < n) {
-        a += coordinates[i - 1][0] * coordinates[i][1];
-        b += coordinates[i - 1][1] * coordinates[i][0];
+        area += coordinates[i - 1][1] * coordinates[i][0] - coordinates[i - 1][0] * coordinates[i][1];
       }
-      return (b - a) * .5;
+      return area * .5;
     };
     coordinates.centroid = function(k) {
       var i = -1, n = coordinates.length, x = 0, y = 0, a, b = coordinates[n - 1], c;

src/geom/polygon.js

@@ -3,13 +3,11 @@ d3.geom.polygon = function(coordinates) {
   coordinates.area = function() {
     var i = 0,
         n = coordinates.length,
-        a = coordinates[n - 1][0] * coordinates[0][1],
-        b = coordinates[n - 1][1] * coordinates[0][0];
+        area = coordinates[n - 1][1] * coordinates[0][0] - coordinates[n - 1][0] * coordinates[0][1];
     while (++i < n) {
-      a += coordinates[i - 1][0] * coordinates[i][1];
-      b += coordinates[i - 1][1] * coordinates[i][0];
+      area += coordinates[i - 1][1] * coordinates[i][0] - coordinates[i - 1][0] * coordinates[i][1];
     }
-    return (b - a) * .5;
+    return area * .5;
   };
 
   coordinates.centroid = function(k) {

test/geom/polygon-test.js

@@ -75,7 +75,21 @@ suite.addBatch({
       assert.inDelta(centroid[0], 2, 1e-6);
       assert.inDelta(centroid[1], 2, 1e-6);
     }
-  }
+  },
+  "large square": {
+    topic: function() {
+      var r = 1e8,
+          d = d3.range(0, r, r / 1e4);
+      return d3.geom.polygon(
+          d.map(function(y) { return [0, y]; }).concat(
+          d.map(function(x) { return [x, r]; })).concat(
+          d.map(function(y) { return [r, y]; }).reverse()).concat(
+          d.map(function(x) { return [x, 0]; }).reverse()));
+    },
+    "has area 1e16 - 5e7": function(polygon) {
+      assert.equal(polygon.area(), 1e16 - 5e7);
+    }
+  },
 });
 
 suite.export(module);