Vector with '+' operator.js

(function($G)
{
  var defaultThis = (function(){ return this; })();
  
  var Vector = function(x, y, z)
  {
    // cast
    if(this === defaultThis)
    {
      return Vector.prototype._calc(x); 
    }
    
    // new operator
    this.x = x;
    this.y = y;
    this.z = z;
    this.id_ = this.instances.uuid++;
    
    this.instances[this.id_] = this;
  };

  Vector.prototype.instances = {uuid: 0};
  
  Vector.prototype.valueOf = function()
  {
    return '{' + this.id_ + '}';
  };
  
  Vector.prototype.toString = function()
  {
    return '<'.concat(this.x, ', ', this.y, ', ', this.z, '>');
  };
  
  Vector.prototype._calc = function(expr)
  {
    var ids = expr.slice(1, -1).split('}{');
    var x = 0, y = 0, z = 0;
    var instances = Vector.prototype.instances;
    
    //console.log(ids);
    var i = ids.length; while(i--)
    {
      var v = instances[ids[i]];
      
      x += v.x;
      y += v.y;
      z += v.z;
    }
    
    return new Vector(x, y, z);
  };
  
  $G.Vector = Vector;
  
})(this);