Cache centroid

js/id/core/entity.js

@@ -108,6 +108,14 @@ iD.Entity.prototype = {
         });
     },
 
+    // Returns the centroid of the area, in unprojected coordinates.
+    centroid: function(resolver) {
+        return resolver.transient(this, 'centroid', function() {
+            return iD.Entity.areaPath.projection().invert(
+                iD.Entity.areaPath.centroid(this.asGeoJSON(resolver, true)));
+        });
+    },
+
     hasInterestingTags: function() {
         return _.keys(this.tags).some(function(key) {
             return key != 'attribution' &&

js/id/svg/labels.js

@@ -362,8 +362,7 @@ iD.svg.Labels = function(projection, context) {
         }
 
         function getAreaLabel(entity, width, height) {
-            var path = d3.geo.path().projection(projection),
-                centroid = path.centroid(entity.asGeoJSON(graph, true)),
+            var centroid = projection(entity.centroid(graph)),
                 extent = entity.extent(graph),
                 entitywidth = projection(extent[1])[0] - projection(extent[0])[0],
                 rect;