Vector utility functions

add.js

/**
 * Adds two (or more) vectors. 
 *
 * @function add
 * @param {Array|Object} vector1   The first vector
 * @param {Array|Object} vector2   The second vector
 * @param {Array|Object} [vector3] The third vector, ...
 * @return {Object}                The resulting vector 
 */
function add(v1, v2) {
	var x = (v1[0] || v1.x || 0) + (v2[0] || v2.x || 0);
	var y = (v1[1] || v1.y || 0) + (v2[1] || v2.y || 0);
	var z = (v1[2] || v1.z || 0) + (v2[2] || v2.z || 0);
	var w = (v1[3] || v1.w || 0) + (v2[3] || v2.w || 0);

	// if there are more than two vectors given
	if (arguments.length > 2) {
		for (var i = 2; i < arguments.length; i++) {
			x += (arguments[i][0] || arguments[i].x || 0);
			y += (arguments[i][1] || arguments[i].y || 0);
			z += (arguments[i][2] || arguments[i].z || 0);
			w += (arguments[i][3] || arguments[i].w || 0);		
		}
	}

	return {x:x, y:y, z:z, w:w};
}

average.js

/**
 * Calculates the average angle of an array of vectors. A vector
 * could be any object, that has x, y, [z] and [w] properties or an
 * array with 2, 3 or 4 numbers. 
 *
 * @function average
 * @param {Array|Object} vector(s) The vectors or one vector
 * @param {Array|Object} [vector]  The second vector, ...
 * @return {Object}         The normalized average vector 
 * @dependency normalize(), add()
 */
function average(vectors) {
	var res = {x:0, y:0, z:0, w:0};

	if (arguments.length == 1) {
		for (var i = 0; i < vectors.length; i++) {
			var v = normalize(vectors[i]);
			res = add(res, v);
		}
	} else {
		for (var i = 0; i < arguments.length; i++) {
			var v = normalize(arguments[i]);
			res = add(res, v);
		}
	}

	return normalize(res);
}

normalize.js

/**
 * Normalizes a vector. 
 *
 * @function averageVector
 * @param {Array|Object|Number} vectors   The vector or the x coordinate
 * @param {Number} [y]                    The y coordinate
 * @param {Number} [z]                    The z coordinate
 * @param {Number} [w]                    The w coordinate
 * @return {Object}                       The normalized vector 
 */
function normalize(vector) {
	var x = vector[0] || vector.x || arguments[0] || 0;
	var y = vector[1] || vector.y || arguments[1] || 0;
	var z = vector[2] || vector.z || arguments[2] || 0;
	var w = vector[3] || vector.w || arguments[3] || 0;

	var l = Math.sqrt(x*x + y*y + z*z + w*w);
	if (l != 0) {
		x /= l;
		y /= l;
		z /= l;
		w /= l;
	}

	return {x:x, y:y, z:z, w:w};
}