OL APIMethod: getCentroid

getCentroid: function() {
    if (this.components) {
        var len = this.components.length;
        if (len > 0 && len <= 2) {
            return this.components[0].clone();
        } else if (len > 2) {
            var sumX = 0.0;
            var sumY = 0.0;
            var averX = this.components[0].x;
            var averY = this.components[0].y;
            for (var i = 0; i < len - 1; i++) {
                var b = this.components[i];
                var c = this.components[i+1];
                sumX += (b.x + c.x - 2 * averX) * ((b.x - averX) * (c.y - averY) - (c.x - averX) * (b.y - averY));
                sumY += (b.y + c.y - 2 * averY) * ((b.x - averX) * (c.y - averY) - (c.x - averX) * (b.y - averY));
            }
            var area = -1 * this.getArea();
            var x = averX + sumX / (6 * area);
            var y = averY + sumY / (6 * area);
            return new OpenLayers.Geometry.Point(x, y);
        } else {
            return null;
        }
    }
},