text: // Licensed under the Apache License, Version 2.0 (the "License");
  // you may not use this file except in compliance with the License.
  // You may obtain a copy of the License at
  //
  //     http://www.apache.org/licenses/LICENSE-2.0
  //
  // Unless required by applicable law or agreed to in writing, software
  // distributed under the License is distributed on an "AS IS" BASIS,
  // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  // See the License for the specific language governing permissions and
  // limitations under the License.
  
  // Copyright 2008 Google Inc. All Rights Reserved.
  
  /**
   * @fileoverview Defines a 3-element vector class that can be used for
   * coordinate math, useful for animation systems and point manipulation.
   *
   * Based heavily on code originally by:
   */
  
  
  goog.provide('goog.math.Vec3');
  
  goog.require('goog.math');
  goog.require('goog.math.Coordinate3');
  
  
  /**
   * Class for a three-dimensional vector object and assorted functions useful for
   * manipulation.
   *
   * Inherits from goog.math.Coordinate3 so that a Vec3 may be passed in to any
   * function that requires a Coordinate.
   *
   * @param {number} opt_x The x value for the vector.
   * @param {number} opt_y The y value for the vector.
   * @param {number} opt_z The z value for the vector.
   * @constructor
   * @extends {goog.math.Coordinate3}
   */
  goog.math.Vec3 = function(opt_x, opt_y, opt_z) {
    /**
     * X-value
     * @type {number}
     */
    this.x = Number(opt_x) || 0;
  
    /**
     * Y-value
     * @type {number}
     */
    this.y = Number(opt_y) || 0;
  
    /**
     * Z-value
     * @type {number}
     */
    this.z = Number(opt_z) || 0;
  };
  goog.inherits(goog.math.Vec3, goog.math.Coordinate3);
  
  
  /**
   * Generates a random unit vector.
   *
   * http://mathworld.wolfram.com/SpherePointPicking.html
   * Using (6), (7), and (8) to generate coordinates.
   * @return {goog.math.Vec3} A random unit-length vector.
   */
  goog.math.Vec3.randomUnit = function() {
    var theta = Math.random() * Math.PI * 2;
    var phi = Math.random() * Math.PI * 2;
  
    var z = Math.cos(phi);
    var x = Math.sqrt(1 - z * z) * Math.cos(theta);
    var y = Math.sqrt(1 - z * z) * Math.sin(theta);
  
    return new goog.math.Vec3(x, y, z);
  };
  
  
  /**
   * Generates a random vector inside the unit sphere.
   *
   * @return {goog.math.Vec3} A random vector.
   */
  goog.math.Vec3.random = function() {
    return new goog.math.Vec3.randomUnit().scale(Math.random());
  };
  
  
  /**
   * Returns a new Vec3 object from a given coordinate.
   *
   * @param {goog.math.Coordinate3} a The coordinate.
   * @return {goog.math.Vec3} A new vector object.
   */
  goog.math.Vec3.fromCoordinate3 = function(a) {
    return new goog.math.Vec3(a.x, a.y, a.z);
  };
  
  
  /**
   * Creates a new copy of this Vec3.
   *
   * @return {goog.math.Vec3} A new vector with the same coordinates as this one.
   */
  goog.math.Vec3.prototype.clone = function() {
    return new goog.math.Vec3(this.x, this.y, this.z);
  };
  
  
  /**
   * Returns the magnitude of the vector measured from the origin.
   *
   * @return {number} The length of the vector.
   */
  goog.math.Vec3.prototype.magnitude = function() {
    return Math.sqrt(this.x * this.x + this.y * this.y + this.z * this.z);
  };
  
  
  /**
   * Returns the squared magnitude of the vector measured from the origin.
   * NOTE: Leaving out the square root is not a significant
   * optimization in JavaScript.
   *
   * @return {number} The length of the vector, squared.
   */
  goog.math.Vec3.prototype.squaredMagnitude = function() {
    return this.x * this.x + this.y * this.y + this.z * this.z;
  };
  
  
  /**
   * Scales the current vector by a constant.
   *
   * @param {number} s The scale factor.
   * @return {goog.math.Vec3} This vector, scaled.
   */
  goog.math.Vec3.prototype.scale = function(s) {
    this.x *= s;
    this.y *= s;
    this.z *= s;
    return this;
  };
  
  
  /**
   * Reverses the sign of the vector. Equivalent to scaling the vector by -1.
   *
   * @return {goog.math.Vec3} This vector, inverted.
   */
  goog.math.Vec3.prototype.invert = function() {
    this.x = -this.x;
    this.y = -this.y;
    this.z = -this.z;
    return this;
  };
  
  
  /**
   * Normalizes the current vector to have a magnitude of 1.
   *
   * @return {goog.math.Vec3} This vector, normalized.
   */
  goog.math.Vec3.prototype.normalize = function() {
    return this.scale(1 / this.magnitude());
  };
  
  
  /**
   * Adds another vector to this vector in-place.
   *
   * @param {goog.math.Vec3} b The vector to add.
   * @return {goog.math.Vec3} This vector with {@code b} added.
   */
  goog.math.Vec3.prototype.add = function(b) {
    this.x += b.x;
    this.y += b.y;
    this.z += b.z;
    return this;
  };
  
  
  /**
   * Subtracts another vector from this vector in-place.
   *
   * @param {goog.math.Vec3} b The vector to subtract.
   * @return {goog.math.Vec3} This vector with {@code b} subtracted.
   */
  goog.math.Vec3.prototype.subtract = function(b) {
    this.x -= b.x;
    this.y -= b.y;
    this.z -= b.z;
    return this;
  };
  
  
  /**
   * Compares this vector with another for equality.
   *
   * @param {goog.math.Vec3} b The other vector.
   * @return {boolean} True if this vector's x, y and z equal the given vector's
   *     x, y, and z, respectively.
   */
  goog.math.Vec3.prototype.equals = function(b) {
    return this == b || !!b && this.x == b.x && this.y == b.y && this.z == b.z;
  };
  
  
  /**
   * Returns the distance between two vectors.
   *
   * @param {goog.math.Vec3} a The first vector.
   * @param {goog.math.Vec3} b The second vector.
   * @return {number} The distance.
   */
  goog.math.Vec3.distance = goog.math.Coordinate3.distance;
  
  
  /**
   * Returns the squared distance between two vectors.
   *
   * @param {goog.math.Vec3} a The first vector.
   * @param {goog.math.Vec3} b The second vector.
   * @return {number} The squared distance.
   */
  goog.math.Vec3.squaredDistance = goog.math.Coordinate3.squaredDistance;
  
  
  /**
   * Returns a new 3x1 matrix object from a given coordinate.
   *
   * @param {goog.math.Coordinate3} a The coordinate.
   * @return {goog.math.Matrix} A new matrix object.
   */
  goog.math.Vec3.toMatrix3x1 = goog.math.Coordinate3.toMatrix3x1;
  
  
  /**
   * Returns a new 4x1 matrix object from a given coordinate.
   *
   * @param {goog.math.Coordinate3} a The coordinate.
   * @return {goog.math.Matrix} A new matrix object.
   */
  
  goog.math.Vec3.toMatrix4x1 = goog.math.Coordinate3.toMatrix4x1;
  
  
  /**
   * Compares vectors for equality.
   *
   * @param {goog.math.Vec3} a The first vector.
   * @param {goog.math.Vec3} b The second vector.
   * @return {boolean} True if the vectors have equal x, y, and z coordinates.
   */
  goog.math.Vec3.equals = goog.math.Coordinate3.equals;
  
  
  /**
   * Returns the sum of two vectors as a new Vec3.
   *
   * @param {goog.math.Vec3} a The first vector.
   * @param {goog.math.Vec3} b The second vector.
   * @return {goog.math.Vec3} The sum vector.
   */
  goog.math.Vec3.sum = function(a, b) {
    return new goog.math.Vec3(a.x + b.x, a.y + b.y, a.z + b.z);
  };
  
  
  /**
   * Returns the difference of two vectors as a new Vec3.
   *
   * @param {goog.math.Vec3} a The first vector.
   * @param {goog.math.Vec3} b The second vector.
   * @return {goog.math.Vec3} The difference vector.
   */
  goog.math.Vec3.difference = function(a, b) {
    return new goog.math.Vec3(a.x - b.x, a.y - b.y, a.z - b.z);
  };
  
  
  /**
   * Returns the dot-product of two vectors.
   *
   * @param {goog.math.Vec3} a The first vector.
   * @param {goog.math.Vec3} b The second vector.
   * @return {number} The dot-product of the two vectors.
   */
  goog.math.Vec3.dot = function(a, b) {
    return a.x * b.x + a.y * b.y + a.z * b.z;
  };
  
  
  /**
   * Returns the cross-product of two vectors.
   *
   * @param {goog.math.Vec3} a The first vector.
   * @param {goog.math.Vec3} b The second vector.
   * @return {goog.math.Vec3} The cross-product of the two vectors.
   */
  goog.math.Vec3.cross = function(a, b) {
    return new goog.math.Vec3(a.y * b.z - a.z * b.y,
                              a.z * b.x - a.x * b.z,
                              a.x * b.y - a.y * b.x);
  };
  
  
  /**
   * Returns a new Vec3 that is the linear interpolant between vectors a and b at
   * scale-value x.
   *
   * @param {goog.math.Vec3} a Vector a.
   * @param {goog.math.Vec3} b Vector b.
   * @param {number} x The proportion between a and b.
   * @return {goog.math.Vec3} The interpolated vector.
   */
  goog.math.Vec3.lerp = function(a, b, x) {
    return new goog.math.Vec3(goog.math.lerp(a.x, b.x, x),
                              goog.math.lerp(a.y, b.y, x),
                              goog.math.lerp(a.z, b.z, x));
  };
  
  