Use the average perimeter as the center of a polygon or line.

src/annotation.js

@@ -137,20 +137,7 @@ var annotation = function (type, args) {
    *    or `undefined` if no such position exists.
    */
   this._labelPosition = function () {
-    var coor = this._coordinates(), position = {x: 0, y: 0}, i;
-    if (!coor || !coor.length) {
-      return undefined;
-    }
-    if (coor.length === 1) {
-      return coor[0];
-    }
-    for (i = 0; i < coor.length; i += 1) {
-      position.x += coor[i].x;
-      position.y += coor[i].y;
-    }
-    position.x /= coor.length;
-    position.y /= coor.length;
-    return position;
+    return util.centerFromPerimeter(this._coordinates());
   };
 
   /**

src/util/index.js

@@ -745,6 +745,42 @@ var util = module.exports = {
     return {map: mapParams, layer: layerParams};
   },
 
+  /**
+   * Return the coordinate associated with the center of the perimeter formed
+   * from a list of points.  This averages all of the vertices in the perimeter
+   * weighted by the line length on either side of each point.  Functionally,
+   * this is the same as the average of all the points of the lines of the
+   * perimeter.
+   *
+   * @param {geo.geoPosition[]} coor An array of coordinates.
+   * @returns {geo.geoPosition|undefined} The position for the center, or
+   *    `undefined` if no such position exists.
+   */
+  centerFromPerimeter: function (coor) {
+    var position, p0, p1, w, sumw, i;
+    if (!coor || !coor.length) {
+      return;
+    }
+    if (coor.length === 1) {
+      return {x: coor[0].x, y: coor[0].y};
+    }
+    position = {x: 0, y: 0};
+    sumw = 0;
+    p0 = coor[coor.length - 1];
+    for (i = 0; i < coor.length; i += 1) {
+      p1 = p0;
+      p0 = coor[i];
+      w = Math.sqrt(Math.pow(p1.x - p0.x, 2) + Math.pow(p1.y - p0.y, 2));
+      position.x += (p0.x + p1.x) * w;
+      position.y += (p0.y + p1.y) * w;
+      sumw += 2 * w;
+    }
+    position.x /= sumw;
+    position.y /= sumw;
+    // return a copy of p0 if all points are the same
+    return sumw ? position : {x: p0.x, y: p0.y};
+  },
+
   /**
    * Escape any character in a string that has a code point >= 127.
    *

tests/cases/annotation.js

@@ -257,7 +257,9 @@ describe('geo.annotation', function () {
       ann._coordinates = function () {
         return [{x: 1, y: 2}, {x: 3, y: 5}, {x: 8, y: 11}];
       };
-      expect(ann._labelPosition()).toEqual({x: 4, y: 6});
+      var pos = ann._labelPosition();
+      expect(pos.x).toBeCloseTo(4.447);
+      expect(pos.y).toBeCloseTo(6.539);
     });
     it('labelRecord', function () {
       var ann = geo.annotation.annotation('test', {

tests/cases/util.js

@@ -32,4 +32,17 @@ describe('geo.util', function () {
     expect(({}) instanceof iframeWindow.Object).toBe(false);
     iframe.remove();
   });
+
+  it('centerFromPerimter', function () {
+    expect(util.centerFromPerimeter()).toBe(undefined);
+    expect(util.centerFromPerimeter([])).toBe(undefined);
+    expect(util.centerFromPerimeter([{x: 1, y: 1}])).toEqual({x: 1, y: 1});
+    expect(util.centerFromPerimeter([{x: 1, y: 1}, {x: 1, y: 1}])).toEqual({x: 1, y: 1});
+    expect(util.centerFromPerimeter([
+        {x: 1, y: 1}, {x: 3, y: 1}, {x: 3, y: 3}, {x: 1, y: 3}
+    ])).toEqual({x: 2, y: 2});
+    expect(util.centerFromPerimeter([
+        {x: 1, y: 1}, {x: 3, y: 1}, {x: 5, y: 1}, {x: 5, y: 3}, {x: 1, y: 3}
+    ])).toEqual({x: 3, y: 2});
+  });
 });