text: /**
   * Cesium - https://github.com/AnalyticalGraphicsInc/cesium
   *
   * Copyright 2011-2017 Cesium Contributors
   *
   * 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.
   *
   * Columbus View (Pat. Pend.)
   *
   * Portions licensed separately.
   * See https://github.com/AnalyticalGraphicsInc/cesium/blob/master/LICENSE.md for full licensing details.
   */
  (function () {
  define('Core/defined',[],function() {
      'use strict';
  
      /**
       * @exports defined
       *
       * @param {Object} value The object.
       * @returns {Boolean} Returns true if the object is defined, returns false otherwise.
       *
       * @example
       * if (Cesium.defined(positions)) {
       *      doSomething();
       * } else {
       *      doSomethingElse();
       * }
       */
      function defined(value) {
          return value !== undefined && value !== null;
      }
  
      return defined;
  });
  
  define('Core/DeveloperError',[
          './defined'
      ], function(
          defined) {
      'use strict';
  
      /**
       * Constructs an exception object that is thrown due to a developer error, e.g., invalid argument,
       * argument out of range, etc.  This exception should only be thrown during development;
       * it usually indicates a bug in the calling code.  This exception should never be
       * caught; instead the calling code should strive not to generate it.
       * <br /><br />
       * On the other hand, a {@link RuntimeError} indicates an exception that may
       * be thrown at runtime, e.g., out of memory, that the calling code should be prepared
       * to catch.
       *
       * @alias DeveloperError
       * @constructor
       * @extends Error
       *
       * @param {String} [message] The error message for this exception.
       *
       * @see RuntimeError
       */
      function DeveloperError(message) {
          /**
           * 'DeveloperError' indicating that this exception was thrown due to a developer error.
           * @type {String}
           * @readonly
           */
          this.name = 'DeveloperError';
  
          /**
           * The explanation for why this exception was thrown.
           * @type {String}
           * @readonly
           */
          this.message = message;
  
          //Browsers such as IE don't have a stack property until you actually throw the error.
          var stack;
          try {
              throw new Error();
          } catch (e) {
              stack = e.stack;
          }
  
          /**
           * The stack trace of this exception, if available.
           * @type {String}
           * @readonly
           */
          this.stack = stack;
      }
  
      if (defined(Object.create)) {
          DeveloperError.prototype = Object.create(Error.prototype);
          DeveloperError.prototype.constructor = DeveloperError;
      }
  
      DeveloperError.prototype.toString = function() {
          var str = this.name + ': ' + this.message;
  
          if (defined(this.stack)) {
              str += '\n' + this.stack.toString();
          }
  
          return str;
      };
  
      /**
       * @private
       */
      DeveloperError.throwInstantiationError = function() {
          throw new DeveloperError('This function defines an interface and should not be called directly.');
      };
  
      return DeveloperError;
  });
  
  define('Core/Check',[
          './defined',
          './DeveloperError'
      ], function(
          defined,
          DeveloperError) {
      'use strict';
  
      /**
       * Contains functions for checking that supplied arguments are of a specified type
       * or meet specified conditions
       * @private
       */
      var Check = {};
  
      /**
       * Contains type checking functions, all using the typeof operator
       */
      Check.typeOf = {};
  
      function getUndefinedErrorMessage(name) {
          return name + ' is required, actual value was undefined';
      }
  
      function getFailedTypeErrorMessage(actual, expected, name) {
          return 'Expected ' + name + ' to be typeof ' + expected + ', actual typeof was ' + actual;
      }
  
      /**
       * Throws if test is not defined
       *
       * @param {String} name The name of the variable being tested
       * @param {*} test The value that is to be checked
       * @exception {DeveloperError} test must be defined
       */
      Check.defined = function (name, test) {
          if (!defined(test)) {
              throw new DeveloperError(getUndefinedErrorMessage(name));
          }
      };
  
      /**
       * Throws if test is not typeof 'function'
       *
       * @param {String} name The name of the variable being tested
       * @param {*} test The value to test
       * @exception {DeveloperError} test must be typeof 'function'
       */
      Check.typeOf.func = function (name, test) {
          if (typeof test !== 'function') {
              throw new DeveloperError(getFailedTypeErrorMessage(typeof test, 'function', name));
          }
      };
  
      /**
       * Throws if test is not typeof 'string'
       *
       * @param {String} name The name of the variable being tested
       * @param {*} test The value to test
       * @exception {DeveloperError} test must be typeof 'string'
       */
      Check.typeOf.string = function (name, test) {
          if (typeof test !== 'string') {
              throw new DeveloperError(getFailedTypeErrorMessage(typeof test, 'string', name));
          }
      };
  
      /**
       * Throws if test is not typeof 'number'
       *
       * @param {String} name The name of the variable being tested
       * @param {*} test The value to test
       * @exception {DeveloperError} test must be typeof 'number'
       */
      Check.typeOf.number = function (name, test) {
          if (typeof test !== 'number') {
              throw new DeveloperError(getFailedTypeErrorMessage(typeof test, 'number', name));
          }
      };
  
      /**
       * Throws if test is not typeof 'number' and less than limit
       *
       * @param {String} name The name of the variable being tested
       * @param {*} test The value to test
       * @param {Number} limit The limit value to compare against
       * @exception {DeveloperError} test must be typeof 'number' and less than limit
       */
      Check.typeOf.number.lessThan = function (name, test, limit) {
          Check.typeOf.number(name, test);
          if (test >= limit) {
              throw new DeveloperError('Expected ' + name + ' to be less than ' + limit + ', actual value was ' + test);
          }
      };
  
      /**
       * Throws if test is not typeof 'number' and less than or equal to limit
       *
       * @param {String} name The name of the variable being tested
       * @param {*} test The value to test
       * @param {Number} limit The limit value to compare against
       * @exception {DeveloperError} test must be typeof 'number' and less than or equal to limit
       */
      Check.typeOf.number.lessThanOrEquals = function (name, test, limit) {
          Check.typeOf.number(name, test);
          if (test > limit) {
              throw new DeveloperError('Expected ' + name + ' to be less than or equal to ' + limit + ', actual value was ' + test);
          }
      };
  
      /**
       * Throws if test is not typeof 'number' and greater than limit
       *
       * @param {String} name The name of the variable being tested
       * @param {*} test The value to test
       * @param {Number} limit The limit value to compare against
       * @exception {DeveloperError} test must be typeof 'number' and greater than limit
       */
      Check.typeOf.number.greaterThan = function (name, test, limit) {
          Check.typeOf.number(name, test);
          if (test <= limit) {
              throw new DeveloperError('Expected ' + name + ' to be greater than ' + limit + ', actual value was ' + test);
          }
      };
  
      /**
       * Throws if test is not typeof 'number' and greater than or equal to limit
       *
       * @param {String} name The name of the variable being tested
       * @param {*} test The value to test
       * @param {Number} limit The limit value to compare against
       * @exception {DeveloperError} test must be typeof 'number' and greater than or equal to limit
       */
      Check.typeOf.number.greaterThanOrEquals = function (name, test, limit) {
          Check.typeOf.number(name, test);
          if (test < limit) {
              throw new DeveloperError('Expected ' + name + ' to be greater than or equal to' + limit + ', actual value was ' + test);
          }
      };
  
      /**
       * Throws if test is not typeof 'object'
       *
       * @param {String} name The name of the variable being tested
       * @param {*} test The value to test
       * @exception {DeveloperError} test must be typeof 'object'
       */
      Check.typeOf.object = function (name, test) {
          if (typeof test !== 'object') {
              throw new DeveloperError(getFailedTypeErrorMessage(typeof test, 'object', name));
          }
      };
  
      /**
       * Throws if test is not typeof 'boolean'
       *
       * @param {String} name The name of the variable being tested
       * @param {*} test The value to test
       * @exception {DeveloperError} test must be typeof 'boolean'
       */
      Check.typeOf.bool = function (name, test) {
          if (typeof test !== 'boolean') {
              throw new DeveloperError(getFailedTypeErrorMessage(typeof test, 'boolean', name));
          }
      };
  
      /**
       * Throws if test1 and test2 is not typeof 'number' and not equal in value
       *
       * @param {String} name1 The name of the first variable being tested
       * @param {String} name2 The name of the second variable being tested against
       * @param {*} test1 The value to test
       * @param {*} test2 The value to test against
       * @exception {DeveloperError} test1 and test2 should be type of 'number' and be equal in value
       */
      Check.typeOf.number.equals = function (name1, name2, test1, test2) {
          Check.typeOf.number(name1, test1);
          Check.typeOf.number(name2, test2);
          if (test1 !== test2) {
              throw new DeveloperError(name1 + ' must be equal to ' + name2 + ', the actual values are ' + test1 + ' and ' + test2);
          }
      };
  
      return Check;
  });
  
  define('Core/freezeObject',[
          './defined'
      ], function(
          defined) {
      'use strict';
  
      /**
       * Freezes an object, using Object.freeze if available, otherwise returns
       * the object unchanged.  This function should be used in setup code to prevent
       * errors from completely halting JavaScript execution in legacy browsers.
       *
       * @private
       *
       * @exports freezeObject
       */
      var freezeObject = Object.freeze;
      if (!defined(freezeObject)) {
          freezeObject = function(o) {
              return o;
          };
      }
  
      return freezeObject;
  });
  
  define('Core/defaultValue',[
          './freezeObject'
      ], function(
          freezeObject) {
      'use strict';
  
      /**
       * Returns the first parameter if not undefined, otherwise the second parameter.
       * Useful for setting a default value for a parameter.
       *
       * @exports defaultValue
       *
       * @param {*} a
       * @param {*} b
       * @returns {*} Returns the first parameter if not undefined, otherwise the second parameter.
       *
       * @example
       * param = Cesium.defaultValue(param, 'default');
       */
      function defaultValue(a, b) {
          if (a !== undefined && a !== null) {
              return a;
          }
          return b;
      }
  
      /**
       * A frozen empty object that can be used as the default value for options passed as
       * an object literal.
       */
      defaultValue.EMPTY_OBJECT = freezeObject({});
  
      return defaultValue;
  });
  
  /*
    I've wrapped Makoto Matsumoto and Takuji Nishimura's code in a namespace
    so it's better encapsulated. Now you can have multiple random number generators
    and they won't stomp all over eachother's state.
  
    If you want to use this as a substitute for Math.random(), use the random()
    method like so:
  
    var m = new MersenneTwister();
    var randomNumber = m.random();
  
    You can also call the other genrand_{foo}() methods on the instance.
  
    If you want to use a specific seed in order to get a repeatable random
    sequence, pass an integer into the constructor:
  
    var m = new MersenneTwister(123);
  
    and that will always produce the same random sequence.
  
    Sean McCullough (banksean@gmail.com)
  */
  
  /*
     A C-program for MT19937, with initialization improved 2002/1/26.
     Coded by Takuji Nishimura and Makoto Matsumoto.
  
     Before using, initialize the state by using init_genrand(seed)
     or init_by_array(init_key, key_length).
  */
  /**
  @license
  mersenne-twister.js - https://gist.github.com/banksean/300494
  
     Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
     All rights reserved.
  
     Redistribution and use in source and binary forms, with or without
     modification, are permitted provided that the following conditions
     are met:
  
       1. Redistributions of source code must retain the above copyright
          notice, this list of conditions and the following disclaimer.
  
       2. Redistributions in binary form must reproduce the above copyright
          notice, this list of conditions and the following disclaimer in the
          documentation and/or other materials provided with the distribution.
  
       3. The names of its contributors may not be used to endorse or promote
          products derived from this software without specific prior written
          permission.
  
     THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
     "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
     LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
     A PARTICULAR PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE COPYRIGHT OWNER OR
     CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
     EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
     PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
     PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
     LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
     NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
     SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  */
  /*
     Any feedback is very welcome.
     http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html
     email: m-mat @ math.sci.hiroshima-u.ac.jp (remove space)
  */
  define('ThirdParty/mersenne-twister',[],function() {
  var MersenneTwister = function(seed) {
    if (seed == undefined) {
      seed = new Date().getTime();
    }
    /* Period parameters */
    this.N = 624;
    this.M = 397;
    this.MATRIX_A = 0x9908b0df;   /* constant vector a */
    this.UPPER_MASK = 0x80000000; /* most significant w-r bits */
    this.LOWER_MASK = 0x7fffffff; /* least significant r bits */
  
    this.mt = new Array(this.N); /* the array for the state vector */
    this.mti=this.N+1; /* mti==N+1 means mt[N] is not initialized */
  
    this.init_genrand(seed);
  }
  
  /* initializes mt[N] with a seed */
  MersenneTwister.prototype.init_genrand = function(s) {
    this.mt[0] = s >>> 0;
    for (this.mti=1; this.mti<this.N; this.mti++) {
        var s = this.mt[this.mti-1] ^ (this.mt[this.mti-1] >>> 30);
     this.mt[this.mti] = (((((s & 0xffff0000) >>> 16) * 1812433253) << 16) + (s & 0x0000ffff) * 1812433253)
    + this.mti;
        /* See Knuth TAOCP Vol2. 3rd Ed. P.106 for multiplier. */
        /* In the previous versions, MSBs of the seed affect   */
        /* only MSBs of the array mt[].                        */
        /* 2002/01/09 modified by Makoto Matsumoto             */
        this.mt[this.mti] >>>= 0;
        /* for >32 bit machines */
    }
  }
  
  /* initialize by an array with array-length */
  /* init_key is the array for initializing keys */
  /* key_length is its length */
  /* slight change for C++, 2004/2/26 */
  //MersenneTwister.prototype.init_by_array = function(init_key, key_length) {
  //  var i, j, k;
  //  this.init_genrand(19650218);
  //  i=1; j=0;
  //  k = (this.N>key_length ? this.N : key_length);
  //  for (; k; k--) {
  //    var s = this.mt[i-1] ^ (this.mt[i-1] >>> 30)
  //    this.mt[i] = (this.mt[i] ^ (((((s & 0xffff0000) >>> 16) * 1664525) << 16) + ((s & 0x0000ffff) * 1664525)))
  //      + init_key[j] + j; /* non linear */
  //    this.mt[i] >>>= 0; /* for WORDSIZE > 32 machines */
  //    i++; j++;
  //    if (i>=this.N) { this.mt[0] = this.mt[this.N-1]; i=1; }
  //    if (j>=key_length) j=0;
  //  }
  //  for (k=this.N-1; k; k--) {
  //    var s = this.mt[i-1] ^ (this.mt[i-1] >>> 30);
  //    this.mt[i] = (this.mt[i] ^ (((((s & 0xffff0000) >>> 16) * 1566083941) << 16) + (s & 0x0000ffff) * 1566083941))
  //      - i; /* non linear */
  //    this.mt[i] >>>= 0; /* for WORDSIZE > 32 machines */
  //    i++;
  //    if (i>=this.N) { this.mt[0] = this.mt[this.N-1]; i=1; }
  //  }
  //
  //  this.mt[0] = 0x80000000; /* MSB is 1; assuring non-zero initial array */
  //}
  
  /* generates a random number on [0,0xffffffff]-interval */
  MersenneTwister.prototype.genrand_int32 = function() {
    var y;
    var mag01 = new Array(0x0, this.MATRIX_A);
    /* mag01[x] = x * MATRIX_A  for x=0,1 */
  
    if (this.mti >= this.N) { /* generate N words at one time */
      var kk;
  
      if (this.mti == this.N+1)   /* if init_genrand() has not been called, */
        this.init_genrand(5489); /* a default initial seed is used */
  
      for (kk=0;kk<this.N-this.M;kk++) {
        y = (this.mt[kk]&this.UPPER_MASK)|(this.mt[kk+1]&this.LOWER_MASK);
        this.mt[kk] = this.mt[kk+this.M] ^ (y >>> 1) ^ mag01[y & 0x1];
      }
      for (;kk<this.N-1;kk++) {
        y = (this.mt[kk]&this.UPPER_MASK)|(this.mt[kk+1]&this.LOWER_MASK);
        this.mt[kk] = this.mt[kk+(this.M-this.N)] ^ (y >>> 1) ^ mag01[y & 0x1];
      }
      y = (this.mt[this.N-1]&this.UPPER_MASK)|(this.mt[0]&this.LOWER_MASK);
      this.mt[this.N-1] = this.mt[this.M-1] ^ (y >>> 1) ^ mag01[y & 0x1];
  
      this.mti = 0;
    }
  
    y = this.mt[this.mti++];
  
    /* Tempering */
    y ^= (y >>> 11);
    y ^= (y << 7) & 0x9d2c5680;
    y ^= (y << 15) & 0xefc60000;
    y ^= (y >>> 18);
  
    return y >>> 0;
  }
  
  /* generates a random number on [0,0x7fffffff]-interval */
  //MersenneTwister.prototype.genrand_int31 = function() {
  //  return (this.genrand_int32()>>>1);
  //}
  
  /* generates a random number on [0,1]-real-interval */
  //MersenneTwister.prototype.genrand_real1 = function() {
  //  return this.genrand_int32()*(1.0/4294967295.0);
  //  /* divided by 2^32-1 */
  //}
  
  /* generates a random number on [0,1)-real-interval */
  MersenneTwister.prototype.random = function() {
    return this.genrand_int32()*(1.0/4294967296.0);
    /* divided by 2^32 */
  }
  
  /* generates a random number on (0,1)-real-interval */
  //MersenneTwister.prototype.genrand_real3 = function() {
  //  return (this.genrand_int32() + 0.5)*(1.0/4294967296.0);
  //  /* divided by 2^32 */
  //}
  
  /* generates a random number on [0,1) with 53-bit resolution*/
  //MersenneTwister.prototype.genrand_res53 = function() {
  //  var a=this.genrand_int32()>>>5, b=this.genrand_int32()>>>6;
  //  return(a*67108864.0+b)*(1.0/9007199254740992.0);
  //}
  
  /* These real versions are due to Isaku Wada, 2002/01/09 added */
  
  return MersenneTwister;
  });
  
  define('Core/Math',[
          '../ThirdParty/mersenne-twister',
          './defaultValue',
          './defined',
          './DeveloperError'
      ], function(
          MersenneTwister,
          defaultValue,
          defined,
          DeveloperError) {
      'use strict';
  
      /**
       * Math functions.
       *
       * @exports CesiumMath
       */
      var CesiumMath = {};
  
      /**
       * 0.1
       * @type {Number}
       * @constant
       */
      CesiumMath.EPSILON1 = 0.1;
  
      /**
       * 0.01
       * @type {Number}
       * @constant
       */
      CesiumMath.EPSILON2 = 0.01;
  
      /**
       * 0.001
       * @type {Number}
       * @constant
       */
      CesiumMath.EPSILON3 = 0.001;
  
      /**
       * 0.0001
       * @type {Number}
       * @constant
       */
      CesiumMath.EPSILON4 = 0.0001;
  
      /**
       * 0.00001
       * @type {Number}
       * @constant
       */
      CesiumMath.EPSILON5 = 0.00001;
  
      /**
       * 0.000001
       * @type {Number}
       * @constant
       */
      CesiumMath.EPSILON6 = 0.000001;
  
      /**
       * 0.0000001
       * @type {Number}
       * @constant
       */
      CesiumMath.EPSILON7 = 0.0000001;
  
      /**
       * 0.00000001
       * @type {Number}
       * @constant
       */
      CesiumMath.EPSILON8 = 0.00000001;
  
      /**
       * 0.000000001
       * @type {Number}
       * @constant
       */
      CesiumMath.EPSILON9 = 0.000000001;
  
      /**
       * 0.0000000001
       * @type {Number}
       * @constant
       */
      CesiumMath.EPSILON10 = 0.0000000001;
  
      /**
       * 0.00000000001
       * @type {Number}
       * @constant
       */
      CesiumMath.EPSILON11 = 0.00000000001;
  
      /**
       * 0.000000000001
       * @type {Number}
       * @constant
       */
      CesiumMath.EPSILON12 = 0.000000000001;
  
      /**
       * 0.0000000000001
       * @type {Number}
       * @constant
       */
      CesiumMath.EPSILON13 = 0.0000000000001;
  
      /**
       * 0.00000000000001
       * @type {Number}
       * @constant
       */
      CesiumMath.EPSILON14 = 0.00000000000001;
  
      /**
       * 0.000000000000001
       * @type {Number}
       * @constant
       */
      CesiumMath.EPSILON15 = 0.000000000000001;
  
      /**
       * 0.0000000000000001
       * @type {Number}
       * @constant
       */
      CesiumMath.EPSILON16 = 0.0000000000000001;
  
      /**
       * 0.00000000000000001
       * @type {Number}
       * @constant
       */
      CesiumMath.EPSILON17 = 0.00000000000000001;
  
      /**
       * 0.000000000000000001
       * @type {Number}
       * @constant
       */
      CesiumMath.EPSILON18 = 0.000000000000000001;
  
      /**
       * 0.0000000000000000001
       * @type {Number}
       * @constant
       */
      CesiumMath.EPSILON19 = 0.0000000000000000001;
  
      /**
       * 0.00000000000000000001
       * @type {Number}
       * @constant
       */
      CesiumMath.EPSILON20 = 0.00000000000000000001;
  
      /**
       * 3.986004418e14
       * @type {Number}
       * @constant
       */
      CesiumMath.GRAVITATIONALPARAMETER = 3.986004418e14;
  
      /**
       * Radius of the sun in meters: 6.955e8
       * @type {Number}
       * @constant
       */
      CesiumMath.SOLAR_RADIUS = 6.955e8;
  
      /**
       * The mean radius of the moon, according to the "Report of the IAU/IAG Working Group on
       * Cartographic Coordinates and Rotational Elements of the Planets and satellites: 2000",
       * Celestial Mechanics 82: 83-110, 2002.
       * @type {Number}
       * @constant
       */
      CesiumMath.LUNAR_RADIUS = 1737400.0;
  
      /**
       * 64 * 1024
       * @type {Number}
       * @constant
       */
      CesiumMath.SIXTY_FOUR_KILOBYTES = 64 * 1024;
  
      /**
       * Returns the sign of the value; 1 if the value is positive, -1 if the value is
       * negative, or 0 if the value is 0.
       *
       * @param {Number} value The value to return the sign of.
       * @returns {Number} The sign of value.
       */
      CesiumMath.sign = function(value) {
          if (value > 0) {
              return 1;
          }
          if (value < 0) {
              return -1;
          }
  
          return 0;
      };
  
      /**
       * Returns 1.0 if the given value is positive or zero, and -1.0 if it is negative.
       * This is similar to {@link CesiumMath#sign} except that returns 1.0 instead of
       * 0.0 when the input value is 0.0.
       * @param {Number} value The value to return the sign of.
       * @returns {Number} The sign of value.
       */
      CesiumMath.signNotZero = function(value) {
          return value < 0.0 ? -1.0 : 1.0;
      };
  
      /**
       * Converts a scalar value in the range [-1.0, 1.0] to a SNORM in the range [0, rangeMax]
       * @param {Number} value The scalar value in the range [-1.0, 1.0]
       * @param {Number} [rangeMax=255] The maximum value in the mapped range, 255 by default.
       * @returns {Number} A SNORM value, where 0 maps to -1.0 and rangeMax maps to 1.0.
       *
       * @see CesiumMath.fromSNorm
       */
      CesiumMath.toSNorm = function(value, rangeMax) {
          rangeMax = defaultValue(rangeMax, 255);
          return Math.round((CesiumMath.clamp(value, -1.0, 1.0) * 0.5 + 0.5) * rangeMax);
      };
  
      /**
       * Converts a SNORM value in the range [0, rangeMax] to a scalar in the range [-1.0, 1.0].
       * @param {Number} value SNORM value in the range [0, 255]
       * @param {Number} [rangeMax=255] The maximum value in the SNORM range, 255 by default.
       * @returns {Number} Scalar in the range [-1.0, 1.0].
       *
       * @see CesiumMath.toSNorm
       */
      CesiumMath.fromSNorm = function(value, rangeMax) {
          rangeMax = defaultValue(rangeMax, 255);
          return CesiumMath.clamp(value, 0.0, rangeMax) / rangeMax * 2.0 - 1.0;
      };
  
      /**
       * Returns the hyperbolic sine of a number.
       * The hyperbolic sine of <em>value</em> is defined to be
       * (<em>e<sup>x</sup>&nbsp;-&nbsp;e<sup>-x</sup></em>)/2.0
       * where <i>e</i> is Euler's number, approximately 2.71828183.
       *
       * <p>Special cases:
       *   <ul>
       *     <li>If the argument is NaN, then the result is NaN.</li>
       *
       *     <li>If the argument is infinite, then the result is an infinity
       *     with the same sign as the argument.</li>
       *
       *     <li>If the argument is zero, then the result is a zero with the
       *     same sign as the argument.</li>
       *   </ul>
       *</p>
       *
       * @param {Number} value The number whose hyperbolic sine is to be returned.
       * @returns {Number} The hyperbolic sine of <code>value</code>.
       */
      CesiumMath.sinh = function(value) {
          var part1 = Math.pow(Math.E, value);
          var part2 = Math.pow(Math.E, -1.0 * value);
  
          return (part1 - part2) * 0.5;
      };
  
      /**
       * Returns the hyperbolic cosine of a number.
       * The hyperbolic cosine of <strong>value</strong> is defined to be
       * (<em>e<sup>x</sup>&nbsp;+&nbsp;e<sup>-x</sup></em>)/2.0
       * where <i>e</i> is Euler's number, approximately 2.71828183.
       *
       * <p>Special cases:
       *   <ul>
       *     <li>If the argument is NaN, then the result is NaN.</li>
       *
       *     <li>If the argument is infinite, then the result is positive infinity.</li>
       *
       *     <li>If the argument is zero, then the result is 1.0.</li>
       *   </ul>
       *</p>
       *
       * @param {Number} value The number whose hyperbolic cosine is to be returned.
       * @returns {Number} The hyperbolic cosine of <code>value</code>.
       */
      CesiumMath.cosh = function(value) {
          var part1 = Math.pow(Math.E, value);
          var part2 = Math.pow(Math.E, -1.0 * value);
  
          return (part1 + part2) * 0.5;
      };
  
      /**
       * Computes the linear interpolation of two values.
       *
       * @param {Number} p The start value to interpolate.
       * @param {Number} q The end value to interpolate.
       * @param {Number} time The time of interpolation generally in the range <code>[0.0, 1.0]</code>.
       * @returns {Number} The linearly interpolated value.
       *
       * @example
       * var n = Cesium.Math.lerp(0.0, 2.0, 0.5); // returns 1.0
       */
      CesiumMath.lerp = function(p, q, time) {
          return ((1.0 - time) * p) + (time * q);
      };
  
      /**
       * pi
       *
       * @type {Number}
       * @constant
       */
      CesiumMath.PI = Math.PI;
  
      /**
       * 1/pi
       *
       * @type {Number}
       * @constant
       */
      CesiumMath.ONE_OVER_PI = 1.0 / Math.PI;
  
      /**
       * pi/2
       *
       * @type {Number}
       * @constant
       */
      CesiumMath.PI_OVER_TWO = Math.PI * 0.5;
  
      /**
       * pi/3
       *
       * @type {Number}
       * @constant
       */
      CesiumMath.PI_OVER_THREE = Math.PI / 3.0;
  
      /**
       * pi/4
       *
       * @type {Number}
       * @constant
       */
      CesiumMath.PI_OVER_FOUR = Math.PI / 4.0;
  
      /**
       * pi/6
       *
       * @type {Number}
       * @constant
       */
      CesiumMath.PI_OVER_SIX = Math.PI / 6.0;
  
      /**
       * 3pi/2
       *
       * @type {Number}
       * @constant
       */
      CesiumMath.THREE_PI_OVER_TWO = (3.0 * Math.PI) * 0.5;
  
      /**
       * 2pi
       *
       * @type {Number}
       * @constant
       */
      CesiumMath.TWO_PI = 2.0 * Math.PI;
  
      /**
       * 1/2pi
       *
       * @type {Number}
       * @constant
       */
      CesiumMath.ONE_OVER_TWO_PI = 1.0 / (2.0 * Math.PI);
  
      /**
       * The number of radians in a degree.
       *
       * @type {Number}
       * @constant
       * @default Math.PI / 180.0
       */
      CesiumMath.RADIANS_PER_DEGREE = Math.PI / 180.0;
  
      /**
       * The number of degrees in a radian.
       *
       * @type {Number}
       * @constant
       * @default 180.0 / Math.PI
       */
      CesiumMath.DEGREES_PER_RADIAN = 180.0 / Math.PI;
  
      /**
       * The number of radians in an arc second.
       *
       * @type {Number}
       * @constant
       * @default {@link CesiumMath.RADIANS_PER_DEGREE} / 3600.0
       */
      CesiumMath.RADIANS_PER_ARCSECOND = CesiumMath.RADIANS_PER_DEGREE / 3600.0;
  
      /**
       * Converts degrees to radians.
       * @param {Number} degrees The angle to convert in degrees.
       * @returns {Number} The corresponding angle in radians.
       */
      CesiumMath.toRadians = function(degrees) {
                  if (!defined(degrees)) {
              throw new DeveloperError('degrees is required.');
          }
                  return degrees * CesiumMath.RADIANS_PER_DEGREE;
      };
  
      /**
       * Converts radians to degrees.
       * @param {Number} radians The angle to convert in radians.
       * @returns {Number} The corresponding angle in degrees.
       */
      CesiumMath.toDegrees = function(radians) {
                  if (!defined(radians)) {
              throw new DeveloperError('radians is required.');
          }
                  return radians * CesiumMath.DEGREES_PER_RADIAN;
      };
  
      /**
       * Converts a longitude value, in radians, to the range [<code>-Math.PI</code>, <code>Math.PI</code>).
       *
       * @param {Number} angle The longitude value, in radians, to convert to the range [<code>-Math.PI</code>, <code>Math.PI</code>).
       * @returns {Number} The equivalent longitude value in the range [<code>-Math.PI</code>, <code>Math.PI</code>).
       *
       * @example
       * // Convert 270 degrees to -90 degrees longitude
       * var longitude = Cesium.Math.convertLongitudeRange(Cesium.Math.toRadians(270.0));
       */
      CesiumMath.convertLongitudeRange = function(angle) {
                  if (!defined(angle)) {
              throw new DeveloperError('angle is required.');
          }
                  var twoPi = CesiumMath.TWO_PI;
  
          var simplified = angle - Math.floor(angle / twoPi) * twoPi;
  
          if (simplified < -Math.PI) {
              return simplified + twoPi;
          }
          if (simplified >= Math.PI) {
              return simplified - twoPi;
          }
  
          return simplified;
      };
  
      /**
       * Convenience function that clamps a latitude value, in radians, to the range [<code>-Math.PI/2</code>, <code>Math.PI/2</code>).
       * Useful for sanitizing data before use in objects requiring correct range.
       *
       * @param {Number} angle The latitude value, in radians, to clamp to the range [<code>-Math.PI/2</code>, <code>Math.PI/2</code>).
       * @returns {Number} The latitude value clamped to the range [<code>-Math.PI/2</code>, <code>Math.PI/2</code>).
       *
       * @example
       * // Clamp 108 degrees latitude to 90 degrees latitude
       * var latitude = Cesium.Math.clampToLatitudeRange(Cesium.Math.toRadians(108.0));
       */
      CesiumMath.clampToLatitudeRange = function(angle) {
                  if (!defined(angle)) {
              throw new DeveloperError('angle is required.');
          }
          
          return CesiumMath.clamp(angle, -1*CesiumMath.PI_OVER_TWO, CesiumMath.PI_OVER_TWO);
      };
  
      /**
       * Produces an angle in the range -Pi <= angle <= Pi which is equivalent to the provided angle.
       *
       * @param {Number} angle in radians
       * @returns {Number} The angle in the range [<code>-CesiumMath.PI</code>, <code>CesiumMath.PI</code>].
       */
      CesiumMath.negativePiToPi = function(angle) {
                  if (!defined(angle)) {
              throw new DeveloperError('angle is required.');
          }
                  return CesiumMath.zeroToTwoPi(angle + CesiumMath.PI) - CesiumMath.PI;
      };
  
      /**
       * Produces an angle in the range 0 <= angle <= 2Pi which is equivalent to the provided angle.
       *
       * @param {Number} angle in radians
       * @returns {Number} The angle in the range [0, <code>CesiumMath.TWO_PI</code>].
       */
      CesiumMath.zeroToTwoPi = function(angle) {
                  if (!defined(angle)) {
              throw new DeveloperError('angle is required.');
          }
                  var mod = CesiumMath.mod(angle, CesiumMath.TWO_PI);
          if (Math.abs(mod) < CesiumMath.EPSILON14 && Math.abs(angle) > CesiumMath.EPSILON14) {
              return CesiumMath.TWO_PI;
          }
          return mod;
      };
  
      /**
       * The modulo operation that also works for negative dividends.
       *
       * @param {Number} m The dividend.
       * @param {Number} n The divisor.
       * @returns {Number} The remainder.
       */
      CesiumMath.mod = function(m, n) {
                  if (!defined(m)) {
              throw new DeveloperError('m is required.');
          }
          if (!defined(n)) {
              throw new DeveloperError('n is required.');
          }
                  return ((m % n) + n) % n;
      };
  
      /**
       * Determines if two values are equal using an absolute or relative tolerance test. This is useful
       * to avoid problems due to roundoff error when comparing floating-point values directly. The values are
       * first compared using an absolute tolerance test. If that fails, a relative tolerance test is performed.
       * Use this test if you are unsure of the magnitudes of left and right.
       *
       * @param {Number} left The first value to compare.
       * @param {Number} right The other value to compare.
       * @param {Number} relativeEpsilon The maximum inclusive delta between <code>left</code> and <code>right</code> for the relative tolerance test.
       * @param {Number} [absoluteEpsilon=relativeEpsilon] The maximum inclusive delta between <code>left</code> and <code>right</code> for the absolute tolerance test.
       * @returns {Boolean} <code>true</code> if the values are equal within the epsilon; otherwise, <code>false</code>.
       *
       * @example
       * var a = Cesium.Math.equalsEpsilon(0.0, 0.01, Cesium.Math.EPSILON2); // true
       * var b = Cesium.Math.equalsEpsilon(0.0, 0.1, Cesium.Math.EPSILON2);  // false
       * var c = Cesium.Math.equalsEpsilon(3699175.1634344, 3699175.2, Cesium.Math.EPSILON7); // true
       * var d = Cesium.Math.equalsEpsilon(3699175.1634344, 3699175.2, Cesium.Math.EPSILON9); // false
       */
      CesiumMath.equalsEpsilon = function(left, right, relativeEpsilon, absoluteEpsilon) {
                  if (!defined(left)) {
              throw new DeveloperError('left is required.');
          }
          if (!defined(right)) {
              throw new DeveloperError('right is required.');
          }
          if (!defined(relativeEpsilon)) {
              throw new DeveloperError('relativeEpsilon is required.');
          }
                  absoluteEpsilon = defaultValue(absoluteEpsilon, relativeEpsilon);
          var absDiff = Math.abs(left - right);
          return absDiff <= absoluteEpsilon || absDiff <= relativeEpsilon * Math.max(Math.abs(left), Math.abs(right));
      };
  
      var factorials = [1];
  
      /**
       * Computes the factorial of the provided number.
       *
       * @param {Number} n The number whose factorial is to be computed.
       * @returns {Number} The factorial of the provided number or undefined if the number is less than 0.
       *
       * @exception {DeveloperError} A number greater than or equal to 0 is required.
       *
       *
       * @example
       * //Compute 7!, which is equal to 5040
       * var computedFactorial = Cesium.Math.factorial(7);
       *
       * @see {@link http://en.wikipedia.org/wiki/Factorial|Factorial on Wikipedia}
       */
      CesiumMath.factorial = function(n) {
                  if (typeof n !== 'number' || n < 0) {
              throw new DeveloperError('A number greater than or equal to 0 is required.');
          }
          
          var length = factorials.length;
          if (n >= length) {
              var sum = factorials[length - 1];
              for (var i = length; i <= n; i++) {
                  factorials.push(sum * i);
              }
          }
          return factorials[n];
      };
  
      /**
       * Increments a number with a wrapping to a minimum value if the number exceeds the maximum value.
       *
       * @param {Number} [n] The number to be incremented.
       * @param {Number} [maximumValue] The maximum incremented value before rolling over to the minimum value.
       * @param {Number} [minimumValue=0.0] The number reset to after the maximum value has been exceeded.
       * @returns {Number} The incremented number.
       *
       * @exception {DeveloperError} Maximum value must be greater than minimum value.
       *
       * @example
       * var n = Cesium.Math.incrementWrap(5, 10, 0); // returns 6
       * var n = Cesium.Math.incrementWrap(10, 10, 0); // returns 0
       */
      CesiumMath.incrementWrap = function(n, maximumValue, minimumValue) {
          minimumValue = defaultValue(minimumValue, 0.0);
  
                  if (!defined(n)) {
              throw new DeveloperError('n is required.');
          }
          if (maximumValue <= minimumValue) {
              throw new DeveloperError('maximumValue must be greater than minimumValue.');
          }
          
          ++n;
          if (n > maximumValue) {
              n = minimumValue;
          }
          return n;
      };
  
      /**
       * Determines if a positive integer is a power of two.
       *
       * @param {Number} n The positive integer to test.
       * @returns {Boolean} <code>true</code> if the number if a power of two; otherwise, <code>false</code>.
       *
       * @exception {DeveloperError} A number greater than or equal to 0 is required.
       *
       * @example
       * var t = Cesium.Math.isPowerOfTwo(16); // true
       * var f = Cesium.Math.isPowerOfTwo(20); // false
       */
      CesiumMath.isPowerOfTwo = function(n) {
                  if (typeof n !== 'number' || n < 0) {
              throw new DeveloperError('A number greater than or equal to 0 is required.');
          }
          
          return (n !== 0) && ((n & (n - 1)) === 0);
      };
  
      /**
       * Computes the next power-of-two integer greater than or equal to the provided positive integer.
       *
       * @param {Number} n The positive integer to test.
       * @returns {Number} The next power-of-two integer.
       *
       * @exception {DeveloperError} A number greater than or equal to 0 is required.
       *
       * @example
       * var n = Cesium.Math.nextPowerOfTwo(29); // 32
       * var m = Cesium.Math.nextPowerOfTwo(32); // 32
       */
      CesiumMath.nextPowerOfTwo = function(n) {
                  if (typeof n !== 'number' || n < 0) {
              throw new DeveloperError('A number greater than or equal to 0 is required.');
          }
          
          // From http://graphics.stanford.edu/~seander/bithacks.html#RoundUpPowerOf2
          --n;
          n |= n >> 1;
          n |= n >> 2;
          n |= n >> 4;
          n |= n >> 8;
          n |= n >> 16;
          ++n;
  
          return n;
      };
  
      /**
       * Constraint a value to lie between two values.
       *
       * @param {Number} value The value to constrain.
       * @param {Number} min The minimum value.
       * @param {Number} max The maximum value.
       * @returns {Number} The value clamped so that min <= value <= max.
       */
      CesiumMath.clamp = function(value, min, max) {
                  if (!defined(value)) {
              throw new DeveloperError('value is required');
          }
          if (!defined(min)) {
              throw new DeveloperError('min is required.');
          }
          if (!defined(max)) {
              throw new DeveloperError('max is required.');
          }
                  return value < min ? min : value > max ? max : value;
      };
  
      var randomNumberGenerator = new MersenneTwister();
  
      /**
       * Sets the seed used by the random number generator
       * in {@link CesiumMath#nextRandomNumber}.
       *
       * @param {Number} seed An integer used as the seed.
       */
      CesiumMath.setRandomNumberSeed = function(seed) {
                  if (!defined(seed)) {
              throw new DeveloperError('seed is required.');
          }
          
          randomNumberGenerator = new MersenneTwister(seed);
      };
  
      /**
       * Generates a random floating point number in the range of [0.0, 1.0)
       * using a Mersenne twister.
       *
       * @returns {Number} A random number in the range of [0.0, 1.0).
       *
       * @see CesiumMath.setRandomNumberSeed
       * @see {@link http://en.wikipedia.org/wiki/Mersenne_twister|Mersenne twister on Wikipedia}
       */
      CesiumMath.nextRandomNumber = function() {
          return randomNumberGenerator.random();
      };
  
  
      /**
       * Generates a random number between two numbers.
       *
       * @param {Number} min The minimum value.
       * @param {Number} max The maximum value.
       * @returns {Number} A random number between the min and max.
       */
      CesiumMath.randomBetween = function(min, max) {
          return CesiumMath.nextRandomNumber() * (max - min) + min;
      };
  
      /**
       * Computes <code>Math.acos(value)</code>, but first clamps <code>value</code> to the range [-1.0, 1.0]
       * so that the function will never return NaN.
       *
       * @param {Number} value The value for which to compute acos.
       * @returns {Number} The acos of the value if the value is in the range [-1.0, 1.0], or the acos of -1.0 or 1.0,
       *          whichever is closer, if the value is outside the range.
       */
      CesiumMath.acosClamped = function(value) {
                  if (!defined(value)) {
              throw new DeveloperError('value is required.');
          }
                  return Math.acos(CesiumMath.clamp(value, -1.0, 1.0));
      };
  
      /**
       * Computes <code>Math.asin(value)</code>, but first clamps <code>value</code> to the range [-1.0, 1.0]
       * so that the function will never return NaN.
       *
       * @param {Number} value The value for which to compute asin.
       * @returns {Number} The asin of the value if the value is in the range [-1.0, 1.0], or the asin of -1.0 or 1.0,
       *          whichever is closer, if the value is outside the range.
       */
      CesiumMath.asinClamped = function(value) {
                  if (!defined(value)) {
              throw new DeveloperError('value is required.');
          }
                  return Math.asin(CesiumMath.clamp(value, -1.0, 1.0));
      };
  
      /**
       * Finds the chord length between two points given the circle's radius and the angle between the points.
       *
       * @param {Number} angle The angle between the two points.
       * @param {Number} radius The radius of the circle.
       * @returns {Number} The chord length.
       */
      CesiumMath.chordLength = function(angle, radius) {
                  if (!defined(angle)) {
              throw new DeveloperError('angle is required.');
          }
          if (!defined(radius)) {
              throw new DeveloperError('radius is required.');
          }
                  return 2.0 * radius * Math.sin(angle * 0.5);
      };
  
      /**
       * Finds the logarithm of a number to a base.
       *
       * @param {Number} number The number.
       * @param {Number} base The base.
       * @returns {Number} The result.
       */
      CesiumMath.logBase = function(number, base) {
                  if (!defined(number)) {
              throw new DeveloperError('number is required.');
          }
          if (!defined(base)) {
              throw new DeveloperError('base is required.');
          }
                  return Math.log(number) / Math.log(base);
      };
  
      /**
       * @private
       */
      CesiumMath.fog = function(distanceToCamera, density) {
          var scalar = distanceToCamera * density;
          return 1.0 - Math.exp(-(scalar * scalar));
      };
  
      return CesiumMath;
  });
  
  define('Core/Cartesian3',[
          './Check',
          './defaultValue',
          './defined',
          './DeveloperError',
          './freezeObject',
          './Math'
      ], function(
          Check,
          defaultValue,
          defined,
          DeveloperError,
          freezeObject,
          CesiumMath) {
      'use strict';
  
      /**
       * A 3D Cartesian point.
       * @alias Cartesian3
       * @constructor
       *
       * @param {Number} [x=0.0] The X component.
       * @param {Number} [y=0.0] The Y component.
       * @param {Number} [z=0.0] The Z component.
       *
       * @see Cartesian2
       * @see Cartesian4
       * @see Packable
       */
      function Cartesian3(x, y, z) {
          /**
           * The X component.
           * @type {Number}
           * @default 0.0
           */
          this.x = defaultValue(x, 0.0);
  
          /**
           * The Y component.
           * @type {Number}
           * @default 0.0
           */
          this.y = defaultValue(y, 0.0);
  
          /**
           * The Z component.
           * @type {Number}
           * @default 0.0
           */
          this.z = defaultValue(z, 0.0);
      }
  
      /**
       * Converts the provided Spherical into Cartesian3 coordinates.
       *
       * @param {Spherical} spherical The Spherical to be converted to Cartesian3.
       * @param {Cartesian3} [result] The object onto which to store the result.
       * @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if one was not provided.
       */
      Cartesian3.fromSpherical = function(spherical, result) {
                  Check.typeOf.object('spherical', spherical);
          
          if (!defined(result)) {
              result = new Cartesian3();
          }
  
          var clock = spherical.clock;
          var cone = spherical.cone;
          var magnitude = defaultValue(spherical.magnitude, 1.0);
          var radial = magnitude * Math.sin(cone);
          result.x = radial * Math.cos(clock);
          result.y = radial * Math.sin(clock);
          result.z = magnitude * Math.cos(cone);
          return result;
      };
  
      /**
       * Creates a Cartesian3 instance from x, y and z coordinates.
       *
       * @param {Number} x The x coordinate.
       * @param {Number} y The y coordinate.
       * @param {Number} z The z coordinate.
       * @param {Cartesian3} [result] The object onto which to store the result.
       * @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if one was not provided.
       */
      Cartesian3.fromElements = function(x, y, z, result) {
          if (!defined(result)) {
              return new Cartesian3(x, y, z);
          }
  
          result.x = x;
          result.y = y;
          result.z = z;
          return result;
      };
  
      /**
       * Duplicates a Cartesian3 instance.
       *
       * @param {Cartesian3} cartesian The Cartesian to duplicate.
       * @param {Cartesian3} [result] The object onto which to store the result.
       * @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if one was not provided. (Returns undefined if cartesian is undefined)
       */
      Cartesian3.clone = function(cartesian, result) {
          if (!defined(cartesian)) {
              return undefined;
          }
          if (!defined(result)) {
              return new Cartesian3(cartesian.x, cartesian.y, cartesian.z);
          }
  
          result.x = cartesian.x;
          result.y = cartesian.y;
          result.z = cartesian.z;
          return result;
      };
  
      /**
       * Creates a Cartesian3 instance from an existing Cartesian4.  This simply takes the
       * x, y, and z properties of the Cartesian4 and drops w.
       * @function
       *
       * @param {Cartesian4} cartesian The Cartesian4 instance to create a Cartesian3 instance from.
       * @param {Cartesian3} [result] The object onto which to store the result.
       * @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if one was not provided.
       */
      Cartesian3.fromCartesian4 = Cartesian3.clone;
  
      /**
       * The number of elements used to pack the object into an array.
       * @type {Number}
       */
      Cartesian3.packedLength = 3;
  
      /**
       * Stores the provided instance into the provided array.
       *
       * @param {Cartesian3} value The value to pack.
       * @param {Number[]} array The array to pack into.
       * @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
       *
       * @returns {Number[]} The array that was packed into
       */
      Cartesian3.pack = function(value, array, startingIndex) {
                  Check.typeOf.object('value', value);
          Check.defined('array', array);
          
          startingIndex = defaultValue(startingIndex, 0);
  
          array[startingIndex++] = value.x;
          array[startingIndex++] = value.y;
          array[startingIndex] = value.z;
  
          return array;
      };
  
      /**
       * Retrieves an instance from a packed array.
       *
       * @param {Number[]} array The packed array.
       * @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
       * @param {Cartesian3} [result] The object into which to store the result.
       * @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if one was not provided.
       */
      Cartesian3.unpack = function(array, startingIndex, result) {
                  Check.defined('array', array);
          
          startingIndex = defaultValue(startingIndex, 0);
  
          if (!defined(result)) {
              result = new Cartesian3();
          }
          result.x = array[startingIndex++];
          result.y = array[startingIndex++];
          result.z = array[startingIndex];
          return result;
      };
  
      /**
       * Flattens an array of Cartesian3s into an array of components.
       *
       * @param {Cartesian3[]} array The array of cartesians to pack.
       * @param {Number[]} result The array onto which to store the result.
       * @returns {Number[]} The packed array.
       */
      Cartesian3.packArray = function(array, result) {
                  Check.defined('array', array);
          
          var length = array.length;
          if (!defined(result)) {
              result = new Array(length * 3);
          } else {
              result.length = length * 3;
          }
  
          for (var i = 0; i < length; ++i) {
              Cartesian3.pack(array[i], result, i * 3);
          }
          return result;
      };
  
      /**
       * Unpacks an array of cartesian components into an array of Cartesian3s.
       *
       * @param {Number[]} array The array of components to unpack.
       * @param {Cartesian3[]} result The array onto which to store the result.
       * @returns {Cartesian3[]} The unpacked array.
       */
      Cartesian3.unpackArray = function(array, result) {
                  Check.defined('array', array);
          Check.typeOf.number.greaterThanOrEquals('array.length', array.length, 3);
          if (array.length % 3 !== 0) {
              throw new DeveloperError('array length must be a multiple of 3.');
          }
          
          var length = array.length;
          if (!defined(result)) {
              result = new Array(length / 3);
          } else {
              result.length = length / 3;
          }
  
          for (var i = 0; i < length; i += 3) {
              var index = i / 3;
              result[index] = Cartesian3.unpack(array, i, result[index]);
          }
          return result;
      };
  
      /**
       * Creates a Cartesian3 from three consecutive elements in an array.
       * @function
       *
       * @param {Number[]} array The array whose three consecutive elements correspond to the x, y, and z components, respectively.
       * @param {Number} [startingIndex=0] The offset into the array of the first element, which corresponds to the x component.
       * @param {Cartesian3} [result] The object onto which to store the result.
       * @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if one was not provided.
       *
       * @example
       * // Create a Cartesian3 with (1.0, 2.0, 3.0)
       * var v = [1.0, 2.0, 3.0];
       * var p = Cesium.Cartesian3.fromArray(v);
       *
       * // Create a Cartesian3 with (1.0, 2.0, 3.0) using an offset into an array
       * var v2 = [0.0, 0.0, 1.0, 2.0, 3.0];
       * var p2 = Cesium.Cartesian3.fromArray(v2, 2);
       */
      Cartesian3.fromArray = Cartesian3.unpack;
  
      /**
       * Computes the value of the maximum component for the supplied Cartesian.
       *
       * @param {Cartesian3} cartesian The cartesian to use.
       * @returns {Number} The value of the maximum component.
       */
      Cartesian3.maximumComponent = function(cartesian) {
                  Check.typeOf.object('cartesian', cartesian);
          
          return Math.max(cartesian.x, cartesian.y, cartesian.z);
      };
  
      /**
       * Computes the value of the minimum component for the supplied Cartesian.
       *
       * @param {Cartesian3} cartesian The cartesian to use.
       * @returns {Number} The value of the minimum component.
       */
      Cartesian3.minimumComponent = function(cartesian) {
                  Check.typeOf.object('cartesian', cartesian);
          
          return Math.min(cartesian.x, cartesian.y, cartesian.z);
      };
  
      /**
       * Compares two Cartesians and computes a Cartesian which contains the minimum components of the supplied Cartesians.
       *
       * @param {Cartesian3} first A cartesian to compare.
       * @param {Cartesian3} second A cartesian to compare.
       * @param {Cartesian3} result The object into which to store the result.
       * @returns {Cartesian3} A cartesian with the minimum components.
       */
      Cartesian3.minimumByComponent = function(first, second, result) {
                  Check.typeOf.object('first', first);
          Check.typeOf.object('second', second);
          Check.typeOf.object('result', result);
          
          result.x = Math.min(first.x, second.x);
          result.y = Math.min(first.y, second.y);
          result.z = Math.min(first.z, second.z);
  
          return result;
      };
  
      /**
       * Compares two Cartesians and computes a Cartesian which contains the maximum components of the supplied Cartesians.
       *
       * @param {Cartesian3} first A cartesian to compare.
       * @param {Cartesian3} second A cartesian to compare.
       * @param {Cartesian3} result The object into which to store the result.
       * @returns {Cartesian3} A cartesian with the maximum components.
       */
      Cartesian3.maximumByComponent = function(first, second, result) {
                  Check.typeOf.object('first', first);
          Check.typeOf.object('second', second);
          Check.typeOf.object('result', result);
          
          result.x = Math.max(first.x, second.x);
          result.y = Math.max(first.y, second.y);
          result.z = Math.max(first.z, second.z);
          return result;
      };
  
      /**
       * Computes the provided Cartesian's squared magnitude.
       *
       * @param {Cartesian3} cartesian The Cartesian instance whose squared magnitude is to be computed.
       * @returns {Number} The squared magnitude.
       */
      Cartesian3.magnitudeSquared = function(cartesian) {
                  Check.typeOf.object('cartesian', cartesian);
          
          return cartesian.x * cartesian.x + cartesian.y * cartesian.y + cartesian.z * cartesian.z;
      };
  
      /**
       * Computes the Cartesian's magnitude (length).
       *
       * @param {Cartesian3} cartesian The Cartesian instance whose magnitude is to be computed.
       * @returns {Number} The magnitude.
       */
      Cartesian3.magnitude = function(cartesian) {
          return Math.sqrt(Cartesian3.magnitudeSquared(cartesian));
      };
  
      var distanceScratch = new Cartesian3();
  
      /**
       * Computes the distance between two points.
       *
       * @param {Cartesian3} left The first point to compute the distance from.
       * @param {Cartesian3} right The second point to compute the distance to.
       * @returns {Number} The distance between two points.
       *
       * @example
       * // Returns 1.0
       * var d = Cesium.Cartesian3.distance(new Cesium.Cartesian3(1.0, 0.0, 0.0), new Cesium.Cartesian3(2.0, 0.0, 0.0));
       */
      Cartesian3.distance = function(left, right) {
                  Check.typeOf.object('left', left);
          Check.typeOf.object('right', right);
          
          Cartesian3.subtract(left, right, distanceScratch);
          return Cartesian3.magnitude(distanceScratch);
      };
  
      /**
       * Computes the squared distance between two points.  Comparing squared distances
       * using this function is more efficient than comparing distances using {@link Cartesian3#distance}.
       *
       * @param {Cartesian3} left The first point to compute the distance from.
       * @param {Cartesian3} right The second point to compute the distance to.
       * @returns {Number} The distance between two points.
       *
       * @example
       * // Returns 4.0, not 2.0
       * var d = Cesium.Cartesian3.distanceSquared(new Cesium.Cartesian3(1.0, 0.0, 0.0), new Cesium.Cartesian3(3.0, 0.0, 0.0));
       */
      Cartesian3.distanceSquared = function(left, right) {
                  Check.typeOf.object('left', left);
          Check.typeOf.object('right', right);
          
          Cartesian3.subtract(left, right, distanceScratch);
          return Cartesian3.magnitudeSquared(distanceScratch);
      };
  
      /**
       * Computes the normalized form of the supplied Cartesian.
       *
       * @param {Cartesian3} cartesian The Cartesian to be normalized.
       * @param {Cartesian3} result The object onto which to store the result.
       * @returns {Cartesian3} The modified result parameter.
       */
      Cartesian3.normalize = function(cartesian, result) {
                  Check.typeOf.object('cartesian', cartesian);
          Check.typeOf.object('result', result);
          
          var magnitude = Cartesian3.magnitude(cartesian);
  
          result.x = cartesian.x / magnitude;
          result.y = cartesian.y / magnitude;
          result.z = cartesian.z / magnitude;
  
                  if (isNaN(result.x) || isNaN(result.y) || isNaN(result.z)) {
              throw new DeveloperError('normalized result is not a number');
          }
          
          return result;
      };
  
      /**
       * Computes the dot (scalar) product of two Cartesians.
       *
       * @param {Cartesian3} left The first Cartesian.
       * @param {Cartesian3} right The second Cartesian.
       * @returns {Number} The dot product.
       */
      Cartesian3.dot = function(left, right) {
                  Check.typeOf.object('left', left);
          Check.typeOf.object('right', right);
          
          return left.x * right.x + left.y * right.y + left.z * right.z;
      };
  
      /**
       * Computes the componentwise product of two Cartesians.
       *
       * @param {Cartesian3} left The first Cartesian.
       * @param {Cartesian3} right The second Cartesian.
       * @param {Cartesian3} result The object onto which to store the result.
       * @returns {Cartesian3} The modified result parameter.
       */
      Cartesian3.multiplyComponents = function(left, right, result) {
                  Check.typeOf.object('left', left);
          Check.typeOf.object('right', right);
          Check.typeOf.object('result', result);
          
          result.x = left.x * right.x;
          result.y = left.y * right.y;
          result.z = left.z * right.z;
          return result;
      };
  
      /**
       * Computes the componentwise quotient of two Cartesians.
       *
       * @param {Cartesian3} left The first Cartesian.
       * @param {Cartesian3} right The second Cartesian.
       * @param {Cartesian3} result The object onto which to store the result.
       * @returns {Cartesian3} The modified result parameter.
       */
      Cartesian3.divideComponents = function(left, right, result) {
                  Check.typeOf.object('left', left);
          Check.typeOf.object('right', right);
          Check.typeOf.object('result', result);
          
          result.x = left.x / right.x;
          result.y = left.y / right.y;
          result.z = left.z / right.z;
          return result;
      };
  
      /**
       * Computes the componentwise sum of two Cartesians.
       *
       * @param {Cartesian3} left The first Cartesian.
       * @param {Cartesian3} right The second Cartesian.
       * @param {Cartesian3} result The object onto which to store the result.
       * @returns {Cartesian3} The modified result parameter.
       */
      Cartesian3.add = function(left, right, result) {
                  Check.typeOf.object('left', left);
          Check.typeOf.object('right', right);
          Check.typeOf.object('result', result);
          
          result.x = left.x + right.x;
          result.y = left.y + right.y;
          result.z = left.z + right.z;
          return result;
      };
  
      /**
       * Computes the componentwise difference of two Cartesians.
       *
       * @param {Cartesian3} left The first Cartesian.
       * @param {Cartesian3} right The second Cartesian.
       * @param {Cartesian3} result The object onto which to store the result.
       * @returns {Cartesian3} The modified result parameter.
       */
      Cartesian3.subtract = function(left, right, result) {
                  Check.typeOf.object('left', left);
          Check.typeOf.object('right', right);
          Check.typeOf.object('result', result);
          
          result.x = left.x - right.x;
          result.y = left.y - right.y;
          result.z = left.z - right.z;
          return result;
      };
  
      /**
       * Multiplies the provided Cartesian componentwise by the provided scalar.
       *
       * @param {Cartesian3} cartesian The Cartesian to be scaled.
       * @param {Number} scalar The scalar to multiply with.
       * @param {Cartesian3} result The object onto which to store the result.
       * @returns {Cartesian3} The modified result parameter.
       */
      Cartesian3.multiplyByScalar = function(cartesian, scalar, result) {
                  Check.typeOf.object('cartesian', cartesian);
          Check.typeOf.number('scalar', scalar);
          Check.typeOf.object('result', result);
          
          result.x = cartesian.x * scalar;
          result.y = cartesian.y * scalar;
          result.z = cartesian.z * scalar;
          return result;
      };
  
      /**
       * Divides the provided Cartesian componentwise by the provided scalar.
       *
       * @param {Cartesian3} cartesian The Cartesian to be divided.
       * @param {Number} scalar The scalar to divide by.
       * @param {Cartesian3} result The object onto which to store the result.
       * @returns {Cartesian3} The modified result parameter.
       */
      Cartesian3.divideByScalar = function(cartesian, scalar, result) {
                  Check.typeOf.object('cartesian', cartesian);
          Check.typeOf.number('scalar', scalar);
          Check.typeOf.object('result', result);
          
          result.x = cartesian.x / scalar;
          result.y = cartesian.y / scalar;
          result.z = cartesian.z / scalar;
          return result;
      };
  
      /**
       * Negates the provided Cartesian.
       *
       * @param {Cartesian3} cartesian The Cartesian to be negated.
       * @param {Cartesian3} result The object onto which to store the result.
       * @returns {Cartesian3} The modified result parameter.
       */
      Cartesian3.negate = function(cartesian, result) {
                  Check.typeOf.object('cartesian', cartesian);
          Check.typeOf.object('result', result);
          
          result.x = -cartesian.x;
          result.y = -cartesian.y;
          result.z = -cartesian.z;
          return result;
      };
  
      /**
       * Computes the absolute value of the provided Cartesian.
       *
       * @param {Cartesian3} cartesian The Cartesian whose absolute value is to be computed.
       * @param {Cartesian3} result The object onto which to store the result.
       * @returns {Cartesian3} The modified result parameter.
       */
      Cartesian3.abs = function(cartesian, result) {
                  Check.typeOf.object('cartesian', cartesian);
          Check.typeOf.object('result', result);
          
          result.x = Math.abs(cartesian.x);
          result.y = Math.abs(cartesian.y);
          result.z = Math.abs(cartesian.z);
          return result;
      };
  
      var lerpScratch = new Cartesian3();
      /**
       * Computes the linear interpolation or extrapolation at t using the provided cartesians.
       *
       * @param {Cartesian3} start The value corresponding to t at 0.0.
       * @param {Cartesian3} end The value corresponding to t at 1.0.
       * @param {Number} t The point along t at which to interpolate.
       * @param {Cartesian3} result The object onto which to store the result.
       * @returns {Cartesian3} The modified result parameter.
       */
      Cartesian3.lerp = function(start, end, t, result) {
                  Check.typeOf.object('start', start);
          Check.typeOf.object('end', end);
          Check.typeOf.number('t', t);
          Check.typeOf.object('result', result);
          
          Cartesian3.multiplyByScalar(end, t, lerpScratch);
          result = Cartesian3.multiplyByScalar(start, 1.0 - t, result);
          return Cartesian3.add(lerpScratch, result, result);
      };
  
      var angleBetweenScratch = new Cartesian3();
      var angleBetweenScratch2 = new Cartesian3();
      /**
       * Returns the angle, in radians, between the provided Cartesians.
       *
       * @param {Cartesian3} left The first Cartesian.
       * @param {Cartesian3} right The second Cartesian.
       * @returns {Number} The angle between the Cartesians.
       */
      Cartesian3.angleBetween = function(left, right) {
                  Check.typeOf.object('left', left);
          Check.typeOf.object('right', right);
          
          Cartesian3.normalize(left, angleBetweenScratch);
          Cartesian3.normalize(right, angleBetweenScratch2);
          var cosine = Cartesian3.dot(angleBetweenScratch, angleBetweenScratch2);
          var sine = Cartesian3.magnitude(Cartesian3.cross(angleBetweenScratch, angleBetweenScratch2, angleBetweenScratch));
          return Math.atan2(sine, cosine);
      };
  
      var mostOrthogonalAxisScratch = new Cartesian3();
      /**
       * Returns the axis that is most orthogonal to the provided Cartesian.
       *
       * @param {Cartesian3} cartesian The Cartesian on which to find the most orthogonal axis.
       * @param {Cartesian3} result The object onto which to store the result.
       * @returns {Cartesian3} The most orthogonal axis.
       */
      Cartesian3.mostOrthogonalAxis = function(cartesian, result) {
                  Check.typeOf.object('cartesian', cartesian);
          Check.typeOf.object('result', result);
          
          var f = Cartesian3.normalize(cartesian, mostOrthogonalAxisScratch);
          Cartesian3.abs(f, f);
  
          if (f.x <= f.y) {
              if (f.x <= f.z) {
                  result = Cartesian3.clone(Cartesian3.UNIT_X, result);
              } else {
                  result = Cartesian3.clone(Cartesian3.UNIT_Z, result);
              }
          } else if (f.y <= f.z) {
              result = Cartesian3.clone(Cartesian3.UNIT_Y, result);
          } else {
              result = Cartesian3.clone(Cartesian3.UNIT_Z, result);
          }
  
          return result;
      };
  
      /**
       * Compares the provided Cartesians componentwise and returns
       * <code>true</code> if they are equal, <code>false</code> otherwise.
       *
       * @param {Cartesian3} [left] The first Cartesian.
       * @param {Cartesian3} [right] The second Cartesian.
       * @returns {Boolean} <code>true</code> if left and right are equal, <code>false</code> otherwise.
       */
      Cartesian3.equals = function(left, right) {
              return (left === right) ||
                ((defined(left)) &&
                 (defined(right)) &&
                 (left.x === right.x) &&
                 (left.y === right.y) &&
                 (left.z === right.z));
      };
  
      /**
       * @private
       */
      Cartesian3.equalsArray = function(cartesian, array, offset) {
          return cartesian.x === array[offset] &&
                 cartesian.y === array[offset + 1] &&
                 cartesian.z === array[offset + 2];
      };
  
      /**
       * Compares the provided Cartesians componentwise and returns
       * <code>true</code> if they pass an absolute or relative tolerance test,
       * <code>false</code> otherwise.
       *
       * @param {Cartesian3} [left] The first Cartesian.
       * @param {Cartesian3} [right] The second Cartesian.
       * @param {Number} relativeEpsilon The relative epsilon tolerance to use for equality testing.
       * @param {Number} [absoluteEpsilon=relativeEpsilon] The absolute epsilon tolerance to use for equality testing.
       * @returns {Boolean} <code>true</code> if left and right are within the provided epsilon, <code>false</code> otherwise.
       */
      Cartesian3.equalsEpsilon = function(left, right, relativeEpsilon, absoluteEpsilon) {
          return (left === right) ||
                 (defined(left) &&
                  defined(right) &&
                  CesiumMath.equalsEpsilon(left.x, right.x, relativeEpsilon, absoluteEpsilon) &&
                  CesiumMath.equalsEpsilon(left.y, right.y, relativeEpsilon, absoluteEpsilon) &&
                  CesiumMath.equalsEpsilon(left.z, right.z, relativeEpsilon, absoluteEpsilon));
      };
  
      /**
       * Computes the cross (outer) product of two Cartesians.
       *
       * @param {Cartesian3} left The first Cartesian.
       * @param {Cartesian3} right The second Cartesian.
       * @param {Cartesian3} result The object onto which to store the result.
       * @returns {Cartesian3} The cross product.
       */
      Cartesian3.cross = function(left, right, result) {
                  Check.typeOf.object('left', left);
          Check.typeOf.object('right', right);
          Check.typeOf.object('result', result);
          
          var leftX = left.x;
          var leftY = left.y;
          var leftZ = left.z;
          var rightX = right.x;
          var rightY = right.y;
          var rightZ = right.z;
  
          var x = leftY * rightZ - leftZ * rightY;
          var y = leftZ * rightX - leftX * rightZ;
          var z = leftX * rightY - leftY * rightX;
  
          result.x = x;
          result.y = y;
          result.z = z;
          return result;
      };
  
      /**
       * Returns a Cartesian3 position from longitude and latitude values given in degrees.
       *
       * @param {Number} longitude The longitude, in degrees
       * @param {Number} latitude The latitude, in degrees
       * @param {Number} [height=0.0] The height, in meters, above the ellipsoid.
       * @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the position lies.
       * @param {Cartesian3} [result] The object onto which to store the result.
       * @returns {Cartesian3} The position
       *
       * @example
       * var position = Cesium.Cartesian3.fromDegrees(-115.0, 37.0);
       */
      Cartesian3.fromDegrees = function(longitude, latitude, height, ellipsoid, result) {
                  Check.typeOf.number('longitude', longitude);
          Check.typeOf.number('latitude', latitude);
          
          longitude = CesiumMath.toRadians(longitude);
          latitude = CesiumMath.toRadians(latitude);
          return Cartesian3.fromRadians(longitude, latitude, height, ellipsoid, result);
      };
  
      var scratchN = new Cartesian3();
      var scratchK = new Cartesian3();
      var wgs84RadiiSquared = new Cartesian3(6378137.0 * 6378137.0, 6378137.0 * 6378137.0, 6356752.3142451793 * 6356752.3142451793);
  
      /**
       * Returns a Cartesian3 position from longitude and latitude values given in radians.
       *
       * @param {Number} longitude The longitude, in radians
       * @param {Number} latitude The latitude, in radians
       * @param {Number} [height=0.0] The height, in meters, above the ellipsoid.
       * @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the position lies.
       * @param {Cartesian3} [result] The object onto which to store the result.
       * @returns {Cartesian3} The position
       *
       * @example
       * var position = Cesium.Cartesian3.fromRadians(-2.007, 0.645);
       */
      Cartesian3.fromRadians = function(longitude, latitude, height, ellipsoid, result) {
                  Check.typeOf.number('longitude', longitude);
          Check.typeOf.number('latitude', latitude);
          
          height = defaultValue(height, 0.0);
          var radiiSquared = defined(ellipsoid) ? ellipsoid.radiiSquared : wgs84RadiiSquared;
  
          var cosLatitude = Math.cos(latitude);
          scratchN.x = cosLatitude * Math.cos(longitude);
          scratchN.y = cosLatitude * Math.sin(longitude);
          scratchN.z = Math.sin(latitude);
          scratchN = Cartesian3.normalize(scratchN, scratchN);
  
          Cartesian3.multiplyComponents(radiiSquared, scratchN, scratchK);
          var gamma = Math.sqrt(Cartesian3.dot(scratchN, scratchK));
          scratchK = Cartesian3.divideByScalar(scratchK, gamma, scratchK);
          scratchN = Cartesian3.multiplyByScalar(scratchN, height, scratchN);
  
          if (!defined(result)) {
              result = new Cartesian3();
          }
          return Cartesian3.add(scratchK, scratchN, result);
      };
  
      /**
       * Returns an array of Cartesian3 positions given an array of longitude and latitude values given in degrees.
       *
       * @param {Number[]} coordinates A list of longitude and latitude values. Values alternate [longitude, latitude, longitude, latitude...].
       * @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the coordinates lie.
       * @param {Cartesian3[]} [result] An array of Cartesian3 objects to store the result.
       * @returns {Cartesian3[]} The array of positions.
       *
       * @example
       * var positions = Cesium.Cartesian3.fromDegreesArray([-115.0, 37.0, -107.0, 33.0]);
       */
      Cartesian3.fromDegreesArray = function(coordinates, ellipsoid, result) {
                  Check.defined('coordinates', coordinates);
          if (coordinates.length < 2 || coordinates.length % 2 !== 0) {
              throw new DeveloperError('the number of coordinates must be a multiple of 2 and at least 2');
          }
          
          var length = coordinates.length;
          if (!defined(result)) {
              result = new Array(length / 2);
          } else {
              result.length = length / 2;
          }
  
          for (var i = 0; i < length; i += 2) {
              var longitude = coordinates[i];
              var latitude = coordinates[i + 1];
              var index = i / 2;
              result[index] = Cartesian3.fromDegrees(longitude, latitude, 0, ellipsoid, result[index]);
          }
  
          return result;
      };
  
      /**
       * Returns an array of Cartesian3 positions given an array of longitude and latitude values given in radians.
       *
       * @param {Number[]} coordinates A list of longitude and latitude values. Values alternate [longitude, latitude, longitude, latitude...].
       * @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the coordinates lie.
       * @param {Cartesian3[]} [result] An array of Cartesian3 objects to store the result.
       * @returns {Cartesian3[]} The array of positions.
       *
       * @example
       * var positions = Cesium.Cartesian3.fromRadiansArray([-2.007, 0.645, -1.867, .575]);
       */
      Cartesian3.fromRadiansArray = function(coordinates, ellipsoid, result) {
                  Check.defined('coordinates', coordinates);
          if (coordinates.length < 2 || coordinates.length % 2 !== 0) {
              throw new DeveloperError('the number of coordinates must be a multiple of 2 and at least 2');
          }
          
          var length = coordinates.length;
          if (!defined(result)) {
              result = new Array(length / 2);
          } else {
              result.length = length / 2;
          }
  
          for (var i = 0; i < length; i += 2) {
              var longitude = coordinates[i];
              var latitude = coordinates[i + 1];
              var index = i / 2;
              result[index] = Cartesian3.fromRadians(longitude, latitude, 0, ellipsoid, result[index]);
          }
  
          return result;
      };
  
      /**
       * Returns an array of Cartesian3 positions given an array of longitude, latitude and height values where longitude and latitude are given in degrees.
       *
       * @param {Number[]} coordinates A list of longitude, latitude and height values. Values alternate [longitude, latitude, height, longitude, latitude, height...].
       * @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the position lies.
       * @param {Cartesian3[]} [result] An array of Cartesian3 objects to store the result.
       * @returns {Cartesian3[]} The array of positions.
       *
       * @example
       * var positions = Cesium.Cartesian3.fromDegreesArrayHeights([-115.0, 37.0, 100000.0, -107.0, 33.0, 150000.0]);
       */
      Cartesian3.fromDegreesArrayHeights = function(coordinates, ellipsoid, result) {
                  Check.defined('coordinates', coordinates);
          if (coordinates.length < 3 || coordinates.length % 3 !== 0) {
              throw new DeveloperError('the number of coordinates must be a multiple of 3 and at least 3');
          }
          
          var length = coordinates.length;
          if (!defined(result)) {
              result = new Array(length / 3);
          } else {
              result.length = length / 3;
          }
  
          for (var i = 0; i < length; i += 3) {
              var longitude = coordinates[i];
              var latitude = coordinates[i + 1];
              var height = coordinates[i + 2];
              var index = i / 3;
              result[index] = Cartesian3.fromDegrees(longitude, latitude, height, ellipsoid, result[index]);
          }
  
          return result;
      };
  
      /**
       * Returns an array of Cartesian3 positions given an array of longitude, latitude and height values where longitude and latitude are given in radians.
       *
       * @param {Number[]} coordinates A list of longitude, latitude and height values. Values alternate [longitude, latitude, height, longitude, latitude, height...].
       * @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the position lies.
       * @param {Cartesian3[]} [result] An array of Cartesian3 objects to store the result.
       * @returns {Cartesian3[]} The array of positions.
       *
       * @example
       * var positions = Cesium.Cartesian3.fromRadiansArrayHeights([-2.007, 0.645, 100000.0, -1.867, .575, 150000.0]);
       */
      Cartesian3.fromRadiansArrayHeights = function(coordinates, ellipsoid, result) {
                  Check.defined('coordinates', coordinates);
          if (coordinates.length < 3 || coordinates.length % 3 !== 0) {
              throw new DeveloperError('the number of coordinates must be a multiple of 3 and at least 3');
          }
          
          var length = coordinates.length;
          if (!defined(result)) {
              result = new Array(length / 3);
          } else {
              result.length = length / 3;
          }
  
          for (var i = 0; i < length; i += 3) {
              var longitude = coordinates[i];
              var latitude = coordinates[i + 1];
              var height = coordinates[i + 2];
              var index = i / 3;
              result[index] = Cartesian3.fromRadians(longitude, latitude, height, ellipsoid, result[index]);
          }
  
          return result;
      };
  
      /**
       * An immutable Cartesian3 instance initialized to (0.0, 0.0, 0.0).
       *
       * @type {Cartesian3}
       * @constant
       */
      Cartesian3.ZERO = freezeObject(new Cartesian3(0.0, 0.0, 0.0));
  
      /**
       * An immutable Cartesian3 instance initialized to (1.0, 0.0, 0.0).
       *
       * @type {Cartesian3}
       * @constant
       */
      Cartesian3.UNIT_X = freezeObject(new Cartesian3(1.0, 0.0, 0.0));
  
      /**
       * An immutable Cartesian3 instance initialized to (0.0, 1.0, 0.0).
       *
       * @type {Cartesian3}
       * @constant
       */
      Cartesian3.UNIT_Y = freezeObject(new Cartesian3(0.0, 1.0, 0.0));
  
      /**
       * An immutable Cartesian3 instance initialized to (0.0, 0.0, 1.0).
       *
       * @type {Cartesian3}
       * @constant
       */
      Cartesian3.UNIT_Z = freezeObject(new Cartesian3(0.0, 0.0, 1.0));
  
      /**
       * Duplicates this Cartesian3 instance.
       *
       * @param {Cartesian3} [result] The object onto which to store the result.
       * @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if one was not provided.
       */
      Cartesian3.prototype.clone = function(result) {
          return Cartesian3.clone(this, result);
      };
  
      /**
       * Compares this Cartesian against the provided Cartesian componentwise and returns
       * <code>true</code> if they are equal, <code>false</code> otherwise.
       *
       * @param {Cartesian3} [right] The right hand side Cartesian.
       * @returns {Boolean} <code>true</code> if they are equal, <code>false</code> otherwise.
       */
      Cartesian3.prototype.equals = function(right) {
          return Cartesian3.equals(this, right);
      };
  
      /**
       * Compares this Cartesian against the provided Cartesian componentwise and returns
       * <code>true</code> if they pass an absolute or relative tolerance test,
       * <code>false</code> otherwise.
       *
       * @param {Cartesian3} [right] The right hand side Cartesian.
       * @param {Number} relativeEpsilon The relative epsilon tolerance to use for equality testing.
       * @param {Number} [absoluteEpsilon=relativeEpsilon] The absolute epsilon tolerance to use for equality testing.
       * @returns {Boolean} <code>true</code> if they are within the provided epsilon, <code>false</code> otherwise.
       */
      Cartesian3.prototype.equalsEpsilon = function(right, relativeEpsilon, absoluteEpsilon) {
          return Cartesian3.equalsEpsilon(this, right, relativeEpsilon, absoluteEpsilon);
      };
  
      /**
       * Creates a string representing this Cartesian in the format '(x, y, z)'.
       *
       * @returns {String} A string representing this Cartesian in the format '(x, y, z)'.
       */
      Cartesian3.prototype.toString = function() {
          return '(' + this.x + ', ' + this.y + ', ' + this.z + ')';
      };
  
      return Cartesian3;
  });
  
  define('Core/scaleToGeodeticSurface',[
          './Cartesian3',
          './defined',
          './DeveloperError',
          './Math'
      ], function(
          Cartesian3,
          defined,
          DeveloperError,
          CesiumMath) {
      'use strict';
  
      var scaleToGeodeticSurfaceIntersection = new Cartesian3();
      var scaleToGeodeticSurfaceGradient = new Cartesian3();
  
      /**
       * Scales the provided Cartesian position along the geodetic surface normal
       * so that it is on the surface of this ellipsoid.  If the position is
       * at the center of the ellipsoid, this function returns undefined.
       *
       * @param {Cartesian3} cartesian The Cartesian position to scale.
       * @param {Cartesian3} oneOverRadii One over radii of the ellipsoid.
       * @param {Cartesian3} oneOverRadiiSquared One over radii squared of the ellipsoid.
       * @param {Number} centerToleranceSquared Tolerance for closeness to the center.
       * @param {Cartesian3} [result] The object onto which to store the result.
       * @returns {Cartesian3} The modified result parameter, a new Cartesian3 instance if none was provided, or undefined if the position is at the center.
       *
       * @exports scaleToGeodeticSurface
       *
       * @private
       */
      function scaleToGeodeticSurface(cartesian, oneOverRadii, oneOverRadiiSquared, centerToleranceSquared, result) {
                  if (!defined(cartesian)) {
              throw new DeveloperError('cartesian is required.');
          }
          if (!defined(oneOverRadii)) {
              throw new DeveloperError('oneOverRadii is required.');
          }
          if (!defined(oneOverRadiiSquared)) {
              throw new DeveloperError('oneOverRadiiSquared is required.');
          }
          if (!defined(centerToleranceSquared)) {
              throw new DeveloperError('centerToleranceSquared is required.');
          }
          
          var positionX = cartesian.x;
          var positionY = cartesian.y;
          var positionZ = cartesian.z;
  
          var oneOverRadiiX = oneOverRadii.x;
          var oneOverRadiiY = oneOverRadii.y;
          var oneOverRadiiZ = oneOverRadii.z;
  
          var x2 = positionX * positionX * oneOverRadiiX * oneOverRadiiX;
          var y2 = positionY * positionY * oneOverRadiiY * oneOverRadiiY;
          var z2 = positionZ * positionZ * oneOverRadiiZ * oneOverRadiiZ;
  
          // Compute the squared ellipsoid norm.
          var squaredNorm = x2 + y2 + z2;
          var ratio = Math.sqrt(1.0 / squaredNorm);
  
          // As an initial approximation, assume that the radial intersection is the projection point.
          var intersection = Cartesian3.multiplyByScalar(cartesian, ratio, scaleToGeodeticSurfaceIntersection);
  
          // If the position is near the center, the iteration will not converge.
          if (squaredNorm < centerToleranceSquared) {
              return !isFinite(ratio) ? undefined : Cartesian3.clone(intersection, result);
          }
  
          var oneOverRadiiSquaredX = oneOverRadiiSquared.x;
          var oneOverRadiiSquaredY = oneOverRadiiSquared.y;
          var oneOverRadiiSquaredZ = oneOverRadiiSquared.z;
  
          // Use the gradient at the intersection point in place of the true unit normal.
          // The difference in magnitude will be absorbed in the multiplier.
          var gradient = scaleToGeodeticSurfaceGradient;
          gradient.x = intersection.x * oneOverRadiiSquaredX * 2.0;
          gradient.y = intersection.y * oneOverRadiiSquaredY * 2.0;
          gradient.z = intersection.z * oneOverRadiiSquaredZ * 2.0;
  
          // Compute the initial guess at the normal vector multiplier, lambda.
          var lambda = (1.0 - ratio) * Cartesian3.magnitude(cartesian) / (0.5 * Cartesian3.magnitude(gradient));
          var correction = 0.0;
  
          var func;
          var denominator;
          var xMultiplier;
          var yMultiplier;
          var zMultiplier;
          var xMultiplier2;
          var yMultiplier2;
          var zMultiplier2;
          var xMultiplier3;
          var yMultiplier3;
          var zMultiplier3;
  
          do {
              lambda -= correction;
  
              xMultiplier = 1.0 / (1.0 + lambda * oneOverRadiiSquaredX);
              yMultiplier = 1.0 / (1.0 + lambda * oneOverRadiiSquaredY);
              zMultiplier = 1.0 / (1.0 + lambda * oneOverRadiiSquaredZ);
  
              xMultiplier2 = xMultiplier * xMultiplier;
              yMultiplier2 = yMultiplier * yMultiplier;
              zMultiplier2 = zMultiplier * zMultiplier;
  
              xMultiplier3 = xMultiplier2 * xMultiplier;
              yMultiplier3 = yMultiplier2 * yMultiplier;
              zMultiplier3 = zMultiplier2 * zMultiplier;
  
              func = x2 * xMultiplier2 + y2 * yMultiplier2 + z2 * zMultiplier2 - 1.0;
  
              // "denominator" here refers to the use of this expression in the velocity and acceleration
              // computations in the sections to follow.
              denominator = x2 * xMultiplier3 * oneOverRadiiSquaredX + y2 * yMultiplier3 * oneOverRadiiSquaredY + z2 * zMultiplier3 * oneOverRadiiSquaredZ;
  
              var derivative = -2.0 * denominator;
  
              correction = func / derivative;
          } while (Math.abs(func) > CesiumMath.EPSILON12);
  
          if (!defined(result)) {
              return new Cartesian3(positionX * xMultiplier, positionY * yMultiplier, positionZ * zMultiplier);
          }
          result.x = positionX * xMultiplier;
          result.y = positionY * yMultiplier;
          result.z = positionZ * zMultiplier;
          return result;
      }
  
      return scaleToGeodeticSurface;
  });
  
  define('Core/Cartographic',[
          './Cartesian3',
          './Check',
          './defaultValue',
          './defined',
          './freezeObject',
          './Math',
          './scaleToGeodeticSurface'
      ], function(
          Cartesian3,
          Check,
          defaultValue,
          defined,
          freezeObject,
          CesiumMath,
          scaleToGeodeticSurface) {
      'use strict';
  
      /**
       * A position defined by longitude, latitude, and height.
       * @alias Cartographic
       * @constructor
       *
       * @param {Number} [longitude=0.0] The longitude, in radians.
       * @param {Number} [latitude=0.0] The latitude, in radians.
       * @param {Number} [height=0.0] The height, in meters, above the ellipsoid.
       *
       * @see Ellipsoid
       */
      function Cartographic(longitude, latitude, height) {
          /**
           * The longitude, in radians.
           * @type {Number}
           * @default 0.0
           */
          this.longitude = defaultValue(longitude, 0.0);
  
          /**
           * The latitude, in radians.
           * @type {Number}
           * @default 0.0
           */
          this.latitude = defaultValue(latitude, 0.0);
  
          /**
           * The height, in meters, above the ellipsoid.
           * @type {Number}
           * @default 0.0
           */
          this.height = defaultValue(height, 0.0);
      }
  
      /**
       * Creates a new Cartographic instance from longitude and latitude
       * specified in radians.
       *
       * @param {Number} longitude The longitude, in radians.
       * @param {Number} latitude The latitude, in radians.
       * @param {Number} [height=0.0] The height, in meters, above the ellipsoid.
       * @param {Cartographic} [result] The object onto which to store the result.
       * @returns {Cartographic} The modified result parameter or a new Cartographic instance if one was not provided.
       */
      Cartographic.fromRadians = function(longitude, latitude, height, result) {
                  Check.typeOf.number('longitude', longitude);
          Check.typeOf.number('latitude', latitude);
          
          height = defaultValue(height, 0.0);
  
          if (!defined(result)) {
              return new Cartographic(longitude, latitude, height);
          }
  
          result.longitude = longitude;
          result.latitude = latitude;
          result.height = height;
          return result;
      };
  
      /**
       * Creates a new Cartographic instance from longitude and latitude
       * specified in degrees.  The values in the resulting object will
       * be in radians.
       *
       * @param {Number} longitude The longitude, in degrees.
       * @param {Number} latitude The latitude, in degrees.
       * @param {Number} [height=0.0] The height, in meters, above the ellipsoid.
       * @param {Cartographic} [result] The object onto which to store the result.
       * @returns {Cartographic} The modified result parameter or a new Cartographic instance if one was not provided.
       */
      Cartographic.fromDegrees = function(longitude, latitude, height, result) {
                  Check.typeOf.number('longitude', longitude);
          Check.typeOf.number('latitude', latitude);
                  longitude = CesiumMath.toRadians(longitude);
          latitude = CesiumMath.toRadians(latitude);
  
          return Cartographic.fromRadians(longitude, latitude, height, result);
      };
  
      var cartesianToCartographicN = new Cartesian3();
      var cartesianToCartographicP = new Cartesian3();
      var cartesianToCartographicH = new Cartesian3();
      var wgs84OneOverRadii = new Cartesian3(1.0 / 6378137.0, 1.0 / 6378137.0, 1.0 / 6356752.3142451793);
      var wgs84OneOverRadiiSquared = new Cartesian3(1.0 / (6378137.0 * 6378137.0), 1.0 / (6378137.0 * 6378137.0), 1.0 / (6356752.3142451793 * 6356752.3142451793));
      var wgs84CenterToleranceSquared = CesiumMath.EPSILON1;
  
      /**
       * Creates a new Cartographic instance from a Cartesian position. The values in the
       * resulting object will be in radians.
       *
       * @param {Cartesian3} cartesian The Cartesian position to convert to cartographic representation.
       * @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the position lies.
       * @param {Cartographic} [result] The object onto which to store the result.
       * @returns {Cartographic} The modified result parameter, new Cartographic instance if none was provided, or undefined if the cartesian is at the center of the ellipsoid.
       */
      Cartographic.fromCartesian = function(cartesian, ellipsoid, result) {
          var oneOverRadii = defined(ellipsoid) ? ellipsoid.oneOverRadii : wgs84OneOverRadii;
          var oneOverRadiiSquared = defined(ellipsoid) ? ellipsoid.oneOverRadiiSquared : wgs84OneOverRadiiSquared;
          var centerToleranceSquared = defined(ellipsoid) ? ellipsoid._centerToleranceSquared : wgs84CenterToleranceSquared;
  
          //`cartesian is required.` is thrown from scaleToGeodeticSurface
          var p = scaleToGeodeticSurface(cartesian, oneOverRadii, oneOverRadiiSquared, centerToleranceSquared, cartesianToCartographicP);
  
          if (!defined(p)) {
              return undefined;
          }
  
          var n = Cartesian3.multiplyComponents(p, oneOverRadiiSquared, cartesianToCartographicN);
          n = Cartesian3.normalize(n, n);
  
          var h = Cartesian3.subtract(cartesian, p, cartesianToCartographicH);
  
          var longitude = Math.atan2(n.y, n.x);
          var latitude = Math.asin(n.z);
          var height = CesiumMath.sign(Cartesian3.dot(h, cartesian)) * Cartesian3.magnitude(h);
  
          if (!defined(result)) {
              return new Cartographic(longitude, latitude, height);
          }
          result.longitude = longitude;
          result.latitude = latitude;
          result.height = height;
          return result;
      };
  
      /**
       * Duplicates a Cartographic instance.
       *
       * @param {Cartographic} cartographic The cartographic to duplicate.
       * @param {Cartographic} [result] The object onto which to store the result.
       * @returns {Cartographic} The modified result parameter or a new Cartographic instance if one was not provided. (Returns undefined if cartographic is undefined)
       */
      Cartographic.clone = function(cartographic, result) {
          if (!defined(cartographic)) {
              return undefined;
          }
          if (!defined(result)) {
              return new Cartographic(cartographic.longitude, cartographic.latitude, cartographic.height);
          }
          result.longitude = cartographic.longitude;
          result.latitude = cartographic.latitude;
          result.height = cartographic.height;
          return result;
      };
  
      /**
       * Compares the provided cartographics componentwise and returns
       * <code>true</code> if they are equal, <code>false</code> otherwise.
       *
       * @param {Cartographic} [left] The first cartographic.
       * @param {Cartographic} [right] The second cartographic.
       * @returns {Boolean} <code>true</code> if left and right are equal, <code>false</code> otherwise.
       */
      Cartographic.equals = function(left, right) {
          return (left === right) ||
                  ((defined(left)) &&
                   (defined(right)) &&
                   (left.longitude === right.longitude) &&
                   (left.latitude === right.latitude) &&
                   (left.height === right.height));
      };
  
      /**
       * Compares the provided cartographics componentwise and returns
       * <code>true</code> if they are within the provided epsilon,
       * <code>false</code> otherwise.
       *
       * @param {Cartographic} [left] The first cartographic.
       * @param {Cartographic} [right] The second cartographic.
       * @param {Number} epsilon The epsilon to use for equality testing.
       * @returns {Boolean} <code>true</code> if left and right are within the provided epsilon, <code>false</code> otherwise.
       */
      Cartographic.equalsEpsilon = function(left, right, epsilon) {
                  Check.typeOf.number('epsilon', epsilon);
          
          return (left === right) ||
                 ((defined(left)) &&
                  (defined(right)) &&
                  (Math.abs(left.longitude - right.longitude) <= epsilon) &&
                  (Math.abs(left.latitude - right.latitude) <= epsilon) &&
                  (Math.abs(left.height - right.height) <= epsilon));
      };
  
      /**
       * An immutable Cartographic instance initialized to (0.0, 0.0, 0.0).
       *
       * @type {Cartographic}
       * @constant
       */
      Cartographic.ZERO = freezeObject(new Cartographic(0.0, 0.0, 0.0));
  
      /**
       * Duplicates this instance.
       *
       * @param {Cartographic} [result] The object onto which to store the result.
       * @returns {Cartographic} The modified result parameter or a new Cartographic instance if one was not provided.
       */
      Cartographic.prototype.clone = function(result) {
          return Cartographic.clone(this, result);
      };
  
      /**
       * Compares the provided against this cartographic componentwise and returns
       * <code>true</code> if they are equal, <code>false</code> otherwise.
       *
       * @param {Cartographic} [right] The second cartographic.
       * @returns {Boolean} <code>true</code> if left and right are equal, <code>false</code> otherwise.
       */
      Cartographic.prototype.equals = function(right) {
          return Cartographic.equals(this, right);
      };
  
      /**
       * Compares the provided against this cartographic componentwise and returns
       * <code>true</code> if they are within the provided epsilon,
       * <code>false</code> otherwise.
       *
       * @param {Cartographic} [right] The second cartographic.
       * @param {Number} epsilon The epsilon to use for equality testing.
       * @returns {Boolean} <code>true</code> if left and right are within the provided epsilon, <code>false</code> otherwise.
       */
      Cartographic.prototype.equalsEpsilon = function(right, epsilon) {
          return Cartographic.equalsEpsilon(this, right, epsilon);
      };
  
      /**
       * Creates a string representing this cartographic in the format '(longitude, latitude, height)'.
       *
       * @returns {String} A string representing the provided cartographic in the format '(longitude, latitude, height)'.
       */
      Cartographic.prototype.toString = function() {
          return '(' + this.longitude + ', ' + this.latitude + ', ' + this.height + ')';
      };
  
      return Cartographic;
  });
  
  define('Core/defineProperties',[
          './defined'
      ], function(
          defined) {
      'use strict';
  
      var definePropertyWorks = (function() {
          try {
              return 'x' in Object.defineProperty({}, 'x', {});
          } catch (e) {
              return false;
          }
      })();
  
      /**
       * Defines properties on an object, using Object.defineProperties if available,
       * otherwise returns the object unchanged.  This function should be used in
       * setup code to prevent errors from completely halting JavaScript execution
       * in legacy browsers.
       *
       * @private
       *
       * @exports defineProperties
       */
      var defineProperties = Object.defineProperties;
      if (!definePropertyWorks || !defined(defineProperties)) {
          defineProperties = function(o) {
              return o;
          };
      }
  
      return defineProperties;
  });
  
  define('Core/Ellipsoid',[
          './Cartesian3',
          './Cartographic',
          './Check',
          './defaultValue',
          './defined',
          './defineProperties',
          './DeveloperError',
          './freezeObject',
          './Math',
          './scaleToGeodeticSurface'
      ], function(
          Cartesian3,
          Cartographic,
          Check,
          defaultValue,
          defined,
          defineProperties,
          DeveloperError,
          freezeObject,
          CesiumMath,
          scaleToGeodeticSurface) {
      'use strict';
  
      function initialize(ellipsoid, x, y, z) {
          x = defaultValue(x, 0.0);
          y = defaultValue(y, 0.0);
          z = defaultValue(z, 0.0);
  
                  Check.typeOf.number.greaterThanOrEquals('x', x, 0.0);
          Check.typeOf.number.greaterThanOrEquals('y', y, 0.0);
          Check.typeOf.number.greaterThanOrEquals('z', z, 0.0);
          
          ellipsoid._radii = new Cartesian3(x, y, z);
  
          ellipsoid._radiiSquared = new Cartesian3(x * x,
                                              y * y,
                                              z * z);
  
          ellipsoid._radiiToTheFourth = new Cartesian3(x * x * x * x,
                                                  y * y * y * y,
                                                  z * z * z * z);
  
          ellipsoid._oneOverRadii = new Cartesian3(x === 0.0 ? 0.0 : 1.0 / x,
                                              y === 0.0 ? 0.0 : 1.0 / y,
                                              z === 0.0 ? 0.0 : 1.0 / z);
  
          ellipsoid._oneOverRadiiSquared = new Cartesian3(x === 0.0 ? 0.0 : 1.0 / (x * x),
                                                     y === 0.0 ? 0.0 : 1.0 / (y * y),
                                                     z === 0.0 ? 0.0 : 1.0 / (z * z));
  
          ellipsoid._minimumRadius = Math.min(x, y, z);
  
          ellipsoid._maximumRadius = Math.max(x, y, z);
  
          ellipsoid._centerToleranceSquared = CesiumMath.EPSILON1;
  
          if (ellipsoid._radiiSquared.z !== 0) {
              ellipsoid._squaredXOverSquaredZ = ellipsoid._radiiSquared.x / ellipsoid._radiiSquared.z;
          }
      }
  
      /**
       * A quadratic surface defined in Cartesian coordinates by the equation
       * <code>(x / a)^2 + (y / b)^2 + (z / c)^2 = 1</code>.  Primarily used
       * by Cesium to represent the shape of planetary bodies.
       *
       * Rather than constructing this object directly, one of the provided
       * constants is normally used.
       * @alias Ellipsoid
       * @constructor
       *
       * @param {Number} [x=0] The radius in the x direction.
       * @param {Number} [y=0] The radius in the y direction.
       * @param {Number} [z=0] The radius in the z direction.
       *
       * @exception {DeveloperError} All radii components must be greater than or equal to zero.
       *
       * @see Ellipsoid.fromCartesian3
       * @see Ellipsoid.WGS84
       * @see Ellipsoid.UNIT_SPHERE
       */
      function Ellipsoid(x, y, z) {
          this._radii = undefined;
          this._radiiSquared = undefined;
          this._radiiToTheFourth = undefined;
          this._oneOverRadii = undefined;
          this._oneOverRadiiSquared = undefined;
          this._minimumRadius = undefined;
          this._maximumRadius = undefined;
          this._centerToleranceSquared = undefined;
          this._squaredXOverSquaredZ = undefined;
  
          initialize(this, x, y, z);
      }
  
      defineProperties(Ellipsoid.prototype, {
          /**
           * Gets the radii of the ellipsoid.
           * @memberof Ellipsoid.prototype
           * @type {Cartesian3}
           * @readonly
           */
          radii : {
              get: function() {
                  return this._radii;
              }
          },
          /**
           * Gets the squared radii of the ellipsoid.
           * @memberof Ellipsoid.prototype
           * @type {Cartesian3}
           * @readonly
           */
          radiiSquared : {
              get : function() {
                  return this._radiiSquared;
              }
          },
          /**
           * Gets the radii of the ellipsoid raise to the fourth power.
           * @memberof Ellipsoid.prototype
           * @type {Cartesian3}
           * @readonly
           */
          radiiToTheFourth : {
              get : function() {
                  return this._radiiToTheFourth;
              }
          },
          /**
           * Gets one over the radii of the ellipsoid.
           * @memberof Ellipsoid.prototype
           * @type {Cartesian3}
           * @readonly
           */
          oneOverRadii : {
              get : function() {
                  return this._oneOverRadii;
              }
          },
          /**
           * Gets one over the squared radii of the ellipsoid.
           * @memberof Ellipsoid.prototype
           * @type {Cartesian3}
           * @readonly
           */
          oneOverRadiiSquared : {
              get : function() {
                  return this._oneOverRadiiSquared;
              }
          },
          /**
           * Gets the minimum radius of the ellipsoid.
           * @memberof Ellipsoid.prototype
           * @type {Number}
           * @readonly
           */
          minimumRadius : {
              get : function() {
                  return this._minimumRadius;
              }
          },
          /**
           * Gets the maximum radius of the ellipsoid.
           * @memberof Ellipsoid.prototype
           * @type {Number}
           * @readonly
           */
          maximumRadius : {
              get : function() {
                  return this._maximumRadius;
              }
          }
      });
  
      /**
       * Duplicates an Ellipsoid instance.
       *
       * @param {Ellipsoid} ellipsoid The ellipsoid to duplicate.
       * @param {Ellipsoid} [result] The object onto which to store the result, or undefined if a new
       *                    instance should be created.
       * @returns {Ellipsoid} The cloned Ellipsoid. (Returns undefined if ellipsoid is undefined)
       */
      Ellipsoid.clone = function(ellipsoid, result) {
          if (!defined(ellipsoid)) {
              return undefined;
          }
          var radii = ellipsoid._radii;
  
          if (!defined(result)) {
              return new Ellipsoid(radii.x, radii.y, radii.z);
          }
  
          Cartesian3.clone(radii, result._radii);
          Cartesian3.clone(ellipsoid._radiiSquared, result._radiiSquared);
          Cartesian3.clone(ellipsoid._radiiToTheFourth, result._radiiToTheFourth);
          Cartesian3.clone(ellipsoid._oneOverRadii, result._oneOverRadii);
          Cartesian3.clone(ellipsoid._oneOverRadiiSquared, result._oneOverRadiiSquared);
          result._minimumRadius = ellipsoid._minimumRadius;
          result._maximumRadius = ellipsoid._maximumRadius;
          result._centerToleranceSquared = ellipsoid._centerToleranceSquared;
  
          return result;
      };
  
      /**
       * Computes an Ellipsoid from a Cartesian specifying the radii in x, y, and z directions.
       *
       * @param {Cartesian3} [cartesian=Cartesian3.ZERO] The ellipsoid's radius in the x, y, and z directions.
       * @param {Ellipsoid} [result] The object onto which to store the result, or undefined if a new
       *                    instance should be created.
       * @returns {Ellipsoid} A new Ellipsoid instance.
       *
       * @exception {DeveloperError} All radii components must be greater than or equal to zero.
       *
       * @see Ellipsoid.WGS84
       * @see Ellipsoid.UNIT_SPHERE
       */
      Ellipsoid.fromCartesian3 = function(cartesian, result) {
          if (!defined(result)) {
              result = new Ellipsoid();
          }
  
          if (!defined(cartesian)) {
              return result;
          }
  
          initialize(result, cartesian.x, cartesian.y, cartesian.z);
          return result;
      };
  
      /**
       * An Ellipsoid instance initialized to the WGS84 standard.
       *
       * @type {Ellipsoid}
       * @constant
       */
      Ellipsoid.WGS84 = freezeObject(new Ellipsoid(6378137.0, 6378137.0, 6356752.3142451793));
  
      /**
       * An Ellipsoid instance initialized to radii of (1.0, 1.0, 1.0).
       *
       * @type {Ellipsoid}
       * @constant
       */
      Ellipsoid.UNIT_SPHERE = freezeObject(new Ellipsoid(1.0, 1.0, 1.0));
  
      /**
       * An Ellipsoid instance initialized to a sphere with the lunar radius.
       *
       * @type {Ellipsoid}
       * @constant
       */
      Ellipsoid.MOON = freezeObject(new Ellipsoid(CesiumMath.LUNAR_RADIUS, CesiumMath.LUNAR_RADIUS, CesiumMath.LUNAR_RADIUS));
  
      /**
       * Duplicates an Ellipsoid instance.
       *
       * @param {Ellipsoid} [result] The object onto which to store the result, or undefined if a new
       *                    instance should be created.
       * @returns {Ellipsoid} The cloned Ellipsoid.
       */
      Ellipsoid.prototype.clone = function(result) {
          return Ellipsoid.clone(this, result);
      };
  
      /**
       * The number of elements used to pack the object into an array.
       * @type {Number}
       */
      Ellipsoid.packedLength = Cartesian3.packedLength;
  
      /**
       * Stores the provided instance into the provided array.
       *
       * @param {Ellipsoid} value The value to pack.
       * @param {Number[]} array The array to pack into.
       * @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
       *
       * @returns {Number[]} The array that was packed into
       */
      Ellipsoid.pack = function(value, array, startingIndex) {
                  Check.typeOf.object('value', value);
          Check.defined('array', array);
          
          startingIndex = defaultValue(startingIndex, 0);
  
          Cartesian3.pack(value._radii, array, startingIndex);
  
          return array;
      };
  
      /**
       * Retrieves an instance from a packed array.
       *
       * @param {Number[]} array The packed array.
       * @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
       * @param {Ellipsoid} [result] The object into which to store the result.
       * @returns {Ellipsoid} The modified result parameter or a new Ellipsoid instance if one was not provided.
       */
      Ellipsoid.unpack = function(array, startingIndex, result) {
                  Check.defined('array', array);
          
          startingIndex = defaultValue(startingIndex, 0);
  
          var radii = Cartesian3.unpack(array, startingIndex);
          return Ellipsoid.fromCartesian3(radii, result);
      };
  
      /**
       * Computes the unit vector directed from the center of this ellipsoid toward the provided Cartesian position.
       * @function
       *
       * @param {Cartesian3} cartesian The Cartesian for which to to determine the geocentric normal.
       * @param {Cartesian3} [result] The object onto which to store the result.
       * @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if none was provided.
       */
      Ellipsoid.prototype.geocentricSurfaceNormal = Cartesian3.normalize;
  
      /**
       * Computes the normal of the plane tangent to the surface of the ellipsoid at the provided position.
       *
       * @param {Cartographic} cartographic The cartographic position for which to to determine the geodetic normal.
       * @param {Cartesian3} [result] The object onto which to store the result.
       * @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if none was provided.
       */
      Ellipsoid.prototype.geodeticSurfaceNormalCartographic = function(cartographic, result) {
                  Check.typeOf.object('cartographic', cartographic);
          
          var longitude = cartographic.longitude;
          var latitude = cartographic.latitude;
          var cosLatitude = Math.cos(latitude);
  
          var x = cosLatitude * Math.cos(longitude);
          var y = cosLatitude * Math.sin(longitude);
          var z = Math.sin(latitude);
  
          if (!defined(result)) {
              result = new Cartesian3();
          }
          result.x = x;
          result.y = y;
          result.z = z;
          return Cartesian3.normalize(result, result);
      };
  
      /**
       * Computes the normal of the plane tangent to the surface of the ellipsoid at the provided position.
       *
       * @param {Cartesian3} cartesian The Cartesian position for which to to determine the surface normal.
       * @param {Cartesian3} [result] The object onto which to store the result.
       * @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if none was provided.
       */
      Ellipsoid.prototype.geodeticSurfaceNormal = function(cartesian, result) {
          if (!defined(result)) {
              result = new Cartesian3();
          }
          result = Cartesian3.multiplyComponents(cartesian, this._oneOverRadiiSquared, result);
          return Cartesian3.normalize(result, result);
      };
  
      var cartographicToCartesianNormal = new Cartesian3();
      var cartographicToCartesianK = new Cartesian3();
  
      /**
       * Converts the provided cartographic to Cartesian representation.
       *
       * @param {Cartographic} cartographic The cartographic position.
       * @param {Cartesian3} [result] The object onto which to store the result.
       * @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if none was provided.
       *
       * @example
       * //Create a Cartographic and determine it's Cartesian representation on a WGS84 ellipsoid.
       * var position = new Cesium.Cartographic(Cesium.Math.toRadians(21), Cesium.Math.toRadians(78), 5000);
       * var cartesianPosition = Cesium.Ellipsoid.WGS84.cartographicToCartesian(position);
       */
      Ellipsoid.prototype.cartographicToCartesian = function(cartographic, result) {
          //`cartographic is required` is thrown from geodeticSurfaceNormalCartographic.
          var n = cartographicToCartesianNormal;
          var k = cartographicToCartesianK;
          this.geodeticSurfaceNormalCartographic(cartographic, n);
          Cartesian3.multiplyComponents(this._radiiSquared, n, k);
          var gamma = Math.sqrt(Cartesian3.dot(n, k));
          Cartesian3.divideByScalar(k, gamma, k);
          Cartesian3.multiplyByScalar(n, cartographic.height, n);
  
          if (!defined(result)) {
              result = new Cartesian3();
          }
          return Cartesian3.add(k, n, result);
      };
  
      /**
       * Converts the provided array of cartographics to an array of Cartesians.
       *
       * @param {Cartographic[]} cartographics An array of cartographic positions.
       * @param {Cartesian3[]} [result] The object onto which to store the result.
       * @returns {Cartesian3[]} The modified result parameter or a new Array instance if none was provided.
       *
       * @example
       * //Convert an array of Cartographics and determine their Cartesian representation on a WGS84 ellipsoid.
       * var positions = [new Cesium.Cartographic(Cesium.Math.toRadians(21), Cesium.Math.toRadians(78), 0),
       *                  new Cesium.Cartographic(Cesium.Math.toRadians(21.321), Cesium.Math.toRadians(78.123), 100),
       *                  new Cesium.Cartographic(Cesium.Math.toRadians(21.645), Cesium.Math.toRadians(78.456), 250)];
       * var cartesianPositions = Cesium.Ellipsoid.WGS84.cartographicArrayToCartesianArray(positions);
       */
      Ellipsoid.prototype.cartographicArrayToCartesianArray = function(cartographics, result) {
                  Check.defined('cartographics', cartographics);
          
          var length = cartographics.length;
          if (!defined(result)) {
              result = new Array(length);
          } else {
              result.length = length;
          }
          for ( var i = 0; i < length; i++) {
              result[i] = this.cartographicToCartesian(cartographics[i], result[i]);
          }
          return result;
      };
  
      var cartesianToCartographicN = new Cartesian3();
      var cartesianToCartographicP = new Cartesian3();
      var cartesianToCartographicH = new Cartesian3();
  
      /**
       * Converts the provided cartesian to cartographic representation.
       * The cartesian is undefined at the center of the ellipsoid.
       *
       * @param {Cartesian3} cartesian The Cartesian position to convert to cartographic representation.
       * @param {Cartographic} [result] The object onto which to store the result.
       * @returns {Cartographic} The modified result parameter, new Cartographic instance if none was provided, or undefined if the cartesian is at the center of the ellipsoid.
       *
       * @example
       * //Create a Cartesian and determine it's Cartographic representation on a WGS84 ellipsoid.
       * var position = new Cesium.Cartesian3(17832.12, 83234.52, 952313.73);
       * var cartographicPosition = Cesium.Ellipsoid.WGS84.cartesianToCartographic(position);
       */
      Ellipsoid.prototype.cartesianToCartographic = function(cartesian, result) {
          //`cartesian is required.` is thrown from scaleToGeodeticSurface
          var p = this.scaleToGeodeticSurface(cartesian, cartesianToCartographicP);
  
          if (!defined(p)) {
              return undefined;
          }
  
          var n = this.geodeticSurfaceNormal(p, cartesianToCartographicN);
          var h = Cartesian3.subtract(cartesian, p, cartesianToCartographicH);
  
          var longitude = Math.atan2(n.y, n.x);
          var latitude = Math.asin(n.z);
          var height = CesiumMath.sign(Cartesian3.dot(h, cartesian)) * Cartesian3.magnitude(h);
  
          if (!defined(result)) {
              return new Cartographic(longitude, latitude, height);
          }
          result.longitude = longitude;
          result.latitude = latitude;
          result.height = height;
          return result;
      };
  
      /**
       * Converts the provided array of cartesians to an array of cartographics.
       *
       * @param {Cartesian3[]} cartesians An array of Cartesian positions.
       * @param {Cartographic[]} [result] The object onto which to store the result.
       * @returns {Cartographic[]} The modified result parameter or a new Array instance if none was provided.
       *
       * @example
       * //Create an array of Cartesians and determine their Cartographic representation on a WGS84 ellipsoid.
       * var positions = [new Cesium.Cartesian3(17832.12, 83234.52, 952313.73),
       *                  new Cesium.Cartesian3(17832.13, 83234.53, 952313.73),
       *                  new Cesium.Cartesian3(17832.14, 83234.54, 952313.73)]
       * var cartographicPositions = Cesium.Ellipsoid.WGS84.cartesianArrayToCartographicArray(positions);
       */
      Ellipsoid.prototype.cartesianArrayToCartographicArray = function(cartesians, result) {
                  Check.defined('cartesians', cartesians);
          
          var length = cartesians.length;
          if (!defined(result)) {
              result = new Array(length);
          } else {
              result.length = length;
          }
          for ( var i = 0; i < length; ++i) {
              result[i] = this.cartesianToCartographic(cartesians[i], result[i]);
          }
          return result;
      };
  
      /**
       * Scales the provided Cartesian position along the geodetic surface normal
       * so that it is on the surface of this ellipsoid.  If the position is
       * at the center of the ellipsoid, this function returns undefined.
       *
       * @param {Cartesian3} cartesian The Cartesian position to scale.
       * @param {Cartesian3} [result] The object onto which to store the result.
       * @returns {Cartesian3} The modified result parameter, a new Cartesian3 instance if none was provided, or undefined if the position is at the center.
       */
      Ellipsoid.prototype.scaleToGeodeticSurface = function(cartesian, result) {
          return scaleToGeodeticSurface(cartesian, this._oneOverRadii, this._oneOverRadiiSquared, this._centerToleranceSquared, result);
      };
  
      /**
       * Scales the provided Cartesian position along the geocentric surface normal
       * so that it is on the surface of this ellipsoid.
       *
       * @param {Cartesian3} cartesian The Cartesian position to scale.
       * @param {Cartesian3} [result] The object onto which to store the result.
       * @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if none was provided.
       */
      Ellipsoid.prototype.scaleToGeocentricSurface = function(cartesian, result) {
                  Check.typeOf.object('cartesian', cartesian);
          
          if (!defined(result)) {
              result = new Cartesian3();
          }
  
          var positionX = cartesian.x;
          var positionY = cartesian.y;
          var positionZ = cartesian.z;
          var oneOverRadiiSquared = this._oneOverRadiiSquared;
  
          var beta = 1.0 / Math.sqrt((positionX * positionX) * oneOverRadiiSquared.x +
                                     (positionY * positionY) * oneOverRadiiSquared.y +
                                     (positionZ * positionZ) * oneOverRadiiSquared.z);
  
          return Cartesian3.multiplyByScalar(cartesian, beta, result);
      };
  
      /**
       * Transforms a Cartesian X, Y, Z position to the ellipsoid-scaled space by multiplying
       * its components by the result of {@link Ellipsoid#oneOverRadii}.
       *
       * @param {Cartesian3} position The position to transform.
       * @param {Cartesian3} [result] The position to which to copy the result, or undefined to create and
       *        return a new instance.
       * @returns {Cartesian3} The position expressed in the scaled space.  The returned instance is the
       *          one passed as the result parameter if it is not undefined, or a new instance of it is.
       */
      Ellipsoid.prototype.transformPositionToScaledSpace = function(position, result) {
          if (!defined(result)) {
              result = new Cartesian3();
          }
  
          return Cartesian3.multiplyComponents(position, this._oneOverRadii, result);
      };
  
      /**
       * Transforms a Cartesian X, Y, Z position from the ellipsoid-scaled space by multiplying
       * its components by the result of {@link Ellipsoid#radii}.
       *
       * @param {Cartesian3} position The position to transform.
       * @param {Cartesian3} [result] The position to which to copy the result, or undefined to create and
       *        return a new instance.
       * @returns {Cartesian3} The position expressed in the unscaled space.  The returned instance is the
       *          one passed as the result parameter if it is not undefined, or a new instance of it is.
       */
      Ellipsoid.prototype.transformPositionFromScaledSpace = function(position, result) {
          if (!defined(result)) {
              result = new Cartesian3();
          }
  
          return Cartesian3.multiplyComponents(position, this._radii, result);
      };
  
      /**
       * Compares this Ellipsoid against the provided Ellipsoid componentwise and returns
       * <code>true</code> if they are equal, <code>false</code> otherwise.
       *
       * @param {Ellipsoid} [right] The other Ellipsoid.
       * @returns {Boolean} <code>true</code> if they are equal, <code>false</code> otherwise.
       */
      Ellipsoid.prototype.equals = function(right) {
          return (this === right) ||
                 (defined(right) &&
                  Cartesian3.equals(this._radii, right._radii));
      };
  
      /**
       * Creates a string representing this Ellipsoid in the format '(radii.x, radii.y, radii.z)'.
       *
       * @returns {String} A string representing this ellipsoid in the format '(radii.x, radii.y, radii.z)'.
       */
      Ellipsoid.prototype.toString = function() {
          return this._radii.toString();
      };
  
      /**
       * Computes a point which is the intersection of the surface normal with the z-axis.
       *
       * @param {Cartesian3} position the position. must be on the surface of the ellipsoid.
       * @param {Number} [buffer = 0.0] A buffer to subtract from the ellipsoid size when checking if the point is inside the ellipsoid.
       *                                In earth case, with common earth datums, there is no need for this buffer since the intersection point is always (relatively) very close to the center.
       *                                In WGS84 datum, intersection point is at max z = +-42841.31151331382 (0.673% of z-axis).
       *                                Intersection point could be outside the ellipsoid if the ratio of MajorAxis / AxisOfRotation is bigger than the square root of 2
       * @param {Cartesian3} [result] The cartesian to which to copy the result, or undefined to create and
       *        return a new instance.
       * @returns {Cartesian3 | undefined} the intersection point if it's inside the ellipsoid, undefined otherwise
       *
       * @exception {DeveloperError} position is required.
       * @exception {DeveloperError} Ellipsoid must be an ellipsoid of revolution (radii.x == radii.y).
       * @exception {DeveloperError} Ellipsoid.radii.z must be greater than 0.
       */
      Ellipsoid.prototype.getSurfaceNormalIntersectionWithZAxis = function(position, buffer, result) {
                  Check.typeOf.object('position', position);
  
          if (!CesiumMath.equalsEpsilon(this._radii.x, this._radii.y, CesiumMath.EPSILON15)) {
              throw new DeveloperError('Ellipsoid must be an ellipsoid of revolution (radii.x == radii.y)');
          }
  
          Check.typeOf.number.greaterThan('Ellipsoid.radii.z', this._radii.z, 0);
          
          buffer = defaultValue(buffer, 0.0);
  
          var squaredXOverSquaredZ = this._squaredXOverSquaredZ;
  
          if (!defined(result)) {
              result = new Cartesian3();
          }
  
          result.x = 0.0;
          result.y = 0.0;
          result.z = position.z * (1 - squaredXOverSquaredZ);
  
          if (Math.abs(result.z) >= this._radii.z - buffer) {
              return undefined;
          }
  
          return result;
      };
  
      return Ellipsoid;
  });
  
  define('Core/GeographicProjection',[
          './Cartesian3',
          './Cartographic',
          './defaultValue',
          './defined',
          './defineProperties',
          './DeveloperError',
          './Ellipsoid'
      ], function(
          Cartesian3,
          Cartographic,
          defaultValue,
          defined,
          defineProperties,
          DeveloperError,
          Ellipsoid) {
      'use strict';
  
      /**
       * A simple map projection where longitude and latitude are linearly mapped to X and Y by multiplying
       * them by the {@link Ellipsoid#maximumRadius}.  This projection
       * is commonly known as geographic, equirectangular, equidistant cylindrical, or plate carrée.  It
       * is also known as EPSG:4326.
       *
       * @alias GeographicProjection
       * @constructor
       *
       * @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid.
       *
       * @see WebMercatorProjection
       */
      function GeographicProjection(ellipsoid) {
          this._ellipsoid = defaultValue(ellipsoid, Ellipsoid.WGS84);
          this._semimajorAxis = this._ellipsoid.maximumRadius;
          this._oneOverSemimajorAxis = 1.0 / this._semimajorAxis;
      }
  
      defineProperties(GeographicProjection.prototype, {
          /**
           * Gets the {@link Ellipsoid}.
           *
           * @memberof GeographicProjection.prototype
           *
           * @type {Ellipsoid}
           * @readonly
           */
          ellipsoid : {
              get : function() {
                  return this._ellipsoid;
              }
          }
      });
  
      /**
       * Projects a set of {@link Cartographic} coordinates, in radians, to map coordinates, in meters.
       * X and Y are the longitude and latitude, respectively, multiplied by the maximum radius of the
       * ellipsoid.  Z is the unmodified height.
       *
       * @param {Cartographic} cartographic The coordinates to project.
       * @param {Cartesian3} [result] An instance into which to copy the result.  If this parameter is
       *        undefined, a new instance is created and returned.
       * @returns {Cartesian3} The projected coordinates.  If the result parameter is not undefined, the
       *          coordinates are copied there and that instance is returned.  Otherwise, a new instance is
       *          created and returned.
       */
      GeographicProjection.prototype.project = function(cartographic, result) {
          // Actually this is the special case of equidistant cylindrical called the plate carree
          var semimajorAxis = this._semimajorAxis;
          var x = cartographic.longitude * semimajorAxis;
          var y = cartographic.latitude * semimajorAxis;
          var z = cartographic.height;
  
          if (!defined(result)) {
              return new Cartesian3(x, y, z);
          }
  
          result.x = x;
          result.y = y;
          result.z = z;
          return result;
      };
  
      /**
       * Unprojects a set of projected {@link Cartesian3} coordinates, in meters, to {@link Cartographic}
       * coordinates, in radians.  Longitude and Latitude are the X and Y coordinates, respectively,
       * divided by the maximum radius of the ellipsoid.  Height is the unmodified Z coordinate.
       *
       * @param {Cartesian3} cartesian The Cartesian position to unproject with height (z) in meters.
       * @param {Cartographic} [result] An instance into which to copy the result.  If this parameter is
       *        undefined, a new instance is created and returned.
       * @returns {Cartographic} The unprojected coordinates.  If the result parameter is not undefined, the
       *          coordinates are copied there and that instance is returned.  Otherwise, a new instance is
       *          created and returned.
       */
      GeographicProjection.prototype.unproject = function(cartesian, result) {
                  if (!defined(cartesian)) {
              throw new DeveloperError('cartesian is required');
          }
          
          var oneOverEarthSemimajorAxis = this._oneOverSemimajorAxis;
          var longitude = cartesian.x * oneOverEarthSemimajorAxis;
          var latitude = cartesian.y * oneOverEarthSemimajorAxis;
          var height = cartesian.z;
  
          if (!defined(result)) {
              return new Cartographic(longitude, latitude, height);
          }
  
          result.longitude = longitude;
          result.latitude = latitude;
          result.height = height;
          return result;
      };
  
      return GeographicProjection;
  });
  
  define('Core/Intersect',[
          './freezeObject'
      ], function(
          freezeObject) {
      'use strict';
  
      /**
       * This enumerated type is used in determining where, relative to the frustum, an
       * object is located. The object can either be fully contained within the frustum (INSIDE),
       * partially inside the frustum and partially outside (INTERSECTING), or somwhere entirely
       * outside of the frustum's 6 planes (OUTSIDE).
       *
       * @exports Intersect
       */
      var Intersect = {
          /**
           * Represents that an object is not contained within the frustum.
           *
           * @type {Number}
           * @constant
           */
          OUTSIDE : -1,
  
          /**
           * Represents that an object intersects one of the frustum's planes.
           *
           * @type {Number}
           * @constant
           */
          INTERSECTING : 0,
  
          /**
           * Represents that an object is fully within the frustum.
           *
           * @type {Number}
           * @constant
           */
          INSIDE : 1
      };
  
      return freezeObject(Intersect);
  });
  
  define('Core/Interval',[
          './defaultValue'
      ], function(
          defaultValue) {
      'use strict';
  
      /**
       * Represents the closed interval [start, stop].
       * @alias Interval
       * @constructor
       *
       * @param {Number} [start=0.0] The beginning of the interval.
       * @param {Number} [stop=0.0] The end of the interval.
       */
      function Interval(start, stop) {
          /**
           * The beginning of the interval.
           * @type {Number}
           * @default 0.0
           */
          this.start = defaultValue(start, 0.0);
          /**
           * The end of the interval.
           * @type {Number}
           * @default 0.0
           */
          this.stop = defaultValue(stop, 0.0);
      }
  
      return Interval;
  });
  
  define('Core/Matrix3',[
          './Cartesian3',
          './Check',
          './defaultValue',
          './defined',
          './defineProperties',
          './DeveloperError',
          './freezeObject',
          './Math'
      ], function(
          Cartesian3,
          Check,
          defaultValue,
          defined,
          defineProperties,
          DeveloperError,
          freezeObject,
          CesiumMath) {
      'use strict';
  
      /**
       * A 3x3 matrix, indexable as a column-major order array.
       * Constructor parameters are in row-major order for code readability.
       * @alias Matrix3
       * @constructor
       *
       * @param {Number} [column0Row0=0.0] The value for column 0, row 0.
       * @param {Number} [column1Row0=0.0] The value for column 1, row 0.
       * @param {Number} [column2Row0=0.0] The value for column 2, row 0.
       * @param {Number} [column0Row1=0.0] The value for column 0, row 1.
       * @param {Number} [column1Row1=0.0] The value for column 1, row 1.
       * @param {Number} [column2Row1=0.0] The value for column 2, row 1.
       * @param {Number} [column0Row2=0.0] The value for column 0, row 2.
       * @param {Number} [column1Row2=0.0] The value for column 1, row 2.
       * @param {Number} [column2Row2=0.0] The value for column 2, row 2.
       *
       * @see Matrix3.fromColumnMajorArray
       * @see Matrix3.fromRowMajorArray
       * @see Matrix3.fromQuaternion
       * @see Matrix3.fromScale
       * @see Matrix3.fromUniformScale
       * @see Matrix2
       * @see Matrix4
       */
      function Matrix3(column0Row0, column1Row0, column2Row0,
                             column0Row1, column1Row1, column2Row1,
                             column0Row2, column1Row2, column2Row2) {
          this[0] = defaultValue(column0Row0, 0.0);
          this[1] = defaultValue(column0Row1, 0.0);
          this[2] = defaultValue(column0Row2, 0.0);
          this[3] = defaultValue(column1Row0, 0.0);
          this[4] = defaultValue(column1Row1, 0.0);
          this[5] = defaultValue(column1Row2, 0.0);
          this[6] = defaultValue(column2Row0, 0.0);
          this[7] = defaultValue(column2Row1, 0.0);
          this[8] = defaultValue(column2Row2, 0.0);
      }
  
      /**
       * The number of elements used to pack the object into an array.
       * @type {Number}
       */
      Matrix3.packedLength = 9;
  
      /**
       * Stores the provided instance into the provided array.
       *
       * @param {Matrix3} value The value to pack.
       * @param {Number[]} array The array to pack into.
       * @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
       *
       * @returns {Number[]} The array that was packed into
       */
      Matrix3.pack = function(value, array, startingIndex) {
                  Check.typeOf.object('value', value);
          Check.defined('array', array);
          
          startingIndex = defaultValue(startingIndex, 0);
  
          array[startingIndex++] = value[0];
          array[startingIndex++] = value[1];
          array[startingIndex++] = value[2];
          array[startingIndex++] = value[3];
          array[startingIndex++] = value[4];
          array[startingIndex++] = value[5];
          array[startingIndex++] = value[6];
          array[startingIndex++] = value[7];
          array[startingIndex++] = value[8];
  
          return array;
      };
  
      /**
       * Retrieves an instance from a packed array.
       *
       * @param {Number[]} array The packed array.
       * @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
       * @param {Matrix3} [result] The object into which to store the result.
       * @returns {Matrix3} The modified result parameter or a new Matrix3 instance if one was not provided.
       */
      Matrix3.unpack = function(array, startingIndex, result) {
                  Check.defined('array', array);
          
          startingIndex = defaultValue(startingIndex, 0);
  
          if (!defined(result)) {
              result = new Matrix3();
          }
  
          result[0] = array[startingIndex++];
          result[1] = array[startingIndex++];
          result[2] = array[startingIndex++];
          result[3] = array[startingIndex++];
          result[4] = array[startingIndex++];
          result[5] = array[startingIndex++];
          result[6] = array[startingIndex++];
          result[7] = array[startingIndex++];
          result[8] = array[startingIndex++];
          return result;
      };
  
      /**
       * Duplicates a Matrix3 instance.
       *
       * @param {Matrix3} matrix The matrix to duplicate.
       * @param {Matrix3} [result] The object onto which to store the result.
       * @returns {Matrix3} The modified result parameter or a new Matrix3 instance if one was not provided. (Returns undefined if matrix is undefined)
       */
      Matrix3.clone = function(matrix, result) {
          if (!defined(matrix)) {
              return undefined;
          }
          if (!defined(result)) {
              return new Matrix3(matrix[0], matrix[3], matrix[6],
                                 matrix[1], matrix[4], matrix[7],
                                 matrix[2], matrix[5], matrix[8]);
          }
          result[0] = matrix[0];
          result[1] = matrix[1];
          result[2] = matrix[2];
          result[3] = matrix[3];
          result[4] = matrix[4];
          result[5] = matrix[5];
          result[6] = matrix[6];
          result[7] = matrix[7];
          result[8] = matrix[8];
          return result;
      };
  
      /**
       * Creates a Matrix3 from 9 consecutive elements in an array.
       *
       * @param {Number[]} array The array whose 9 consecutive elements correspond to the positions of the matrix.  Assumes column-major order.
       * @param {Number} [startingIndex=0] The offset into the array of the first element, which corresponds to first column first row position in the matrix.
       * @param {Matrix3} [result] The object onto which to store the result.
       * @returns {Matrix3} The modified result parameter or a new Matrix3 instance if one was not provided.
       *
       * @example
       * // Create the Matrix3:
       * // [1.0, 2.0, 3.0]
       * // [1.0, 2.0, 3.0]
       * // [1.0, 2.0, 3.0]
       *
       * var v = [1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 3.0, 3.0, 3.0];
       * var m = Cesium.Matrix3.fromArray(v);
       *
       * // Create same Matrix3 with using an offset into an array
       * var v2 = [0.0, 0.0, 1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 3.0, 3.0, 3.0];
       * var m2 = Cesium.Matrix3.fromArray(v2, 2);
       */
      Matrix3.fromArray = function(array, startingIndex, result) {
                  Check.defined('array', array);
          
          startingIndex = defaultValue(startingIndex, 0);
  
          if (!defined(result)) {
              result = new Matrix3();
          }
  
          result[0] = array[startingIndex];
          result[1] = array[startingIndex + 1];
          result[2] = array[startingIndex + 2];
          result[3] = array[startingIndex + 3];
          result[4] = array[startingIndex + 4];
          result[5] = array[startingIndex + 5];
          result[6] = array[startingIndex + 6];
          result[7] = array[startingIndex + 7];
          result[8] = array[startingIndex + 8];
          return result;
      };
  
      /**
       * Creates a Matrix3 instance from a column-major order array.
       *
       * @param {Number[]} values The column-major order array.
       * @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
       * @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
       */
      Matrix3.fromColumnMajorArray = function(values, result) {
                  Check.defined('values', values);
          
          return Matrix3.clone(values, result);
      };
  
      /**
       * Creates a Matrix3 instance from a row-major order array.
       * The resulting matrix will be in column-major order.
       *
       * @param {Number[]} values The row-major order array.
       * @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
       * @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
       */
      Matrix3.fromRowMajorArray = function(values, result) {
                  Check.defined('values', values);
          
          if (!defined(result)) {
              return new Matrix3(values[0], values[1], values[2],
                                 values[3], values[4], values[5],
                                 values[6], values[7], values[8]);
          }
          result[0] = values[0];
          result[1] = values[3];
          result[2] = values[6];
          result[3] = values[1];
          result[4] = values[4];
          result[5] = values[7];
          result[6] = values[2];
          result[7] = values[5];
          result[8] = values[8];
          return result;
      };
  
      /**
       * Computes a 3x3 rotation matrix from the provided quaternion.
       *
       * @param {Quaternion} quaternion the quaternion to use.
       * @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
       * @returns {Matrix3} The 3x3 rotation matrix from this quaternion.
       */
      Matrix3.fromQuaternion = function(quaternion, result) {
                  Check.typeOf.object('quaternion', quaternion);
          
          var x2 = quaternion.x * quaternion.x;
          var xy = quaternion.x * quaternion.y;
          var xz = quaternion.x * quaternion.z;
          var xw = quaternion.x * quaternion.w;
          var y2 = quaternion.y * quaternion.y;
          var yz = quaternion.y * quaternion.z;
          var yw = quaternion.y * quaternion.w;
          var z2 = quaternion.z * quaternion.z;
          var zw = quaternion.z * quaternion.w;
          var w2 = quaternion.w * quaternion.w;
  
          var m00 = x2 - y2 - z2 + w2;
          var m01 = 2.0 * (xy - zw);
          var m02 = 2.0 * (xz + yw);
  
          var m10 = 2.0 * (xy + zw);
          var m11 = -x2 + y2 - z2 + w2;
          var m12 = 2.0 * (yz - xw);
  
          var m20 = 2.0 * (xz - yw);
          var m21 = 2.0 * (yz + xw);
          var m22 = -x2 - y2 + z2 + w2;
  
          if (!defined(result)) {
              return new Matrix3(m00, m01, m02,
                                 m10, m11, m12,
                                 m20, m21, m22);
          }
          result[0] = m00;
          result[1] = m10;
          result[2] = m20;
          result[3] = m01;
          result[4] = m11;
          result[5] = m21;
          result[6] = m02;
          result[7] = m12;
          result[8] = m22;
          return result;
      };
  
      /**
       * Computes a 3x3 rotation matrix from the provided headingPitchRoll. (see http://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles )
       *
       * @param {HeadingPitchRoll} headingPitchRoll the headingPitchRoll to use.
       * @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
       * @returns {Matrix3} The 3x3 rotation matrix from this headingPitchRoll.
       */
      Matrix3.fromHeadingPitchRoll = function(headingPitchRoll, result) {
                  Check.typeOf.object('headingPitchRoll', headingPitchRoll);
          
          var cosTheta = Math.cos(-headingPitchRoll.pitch);
          var cosPsi = Math.cos(-headingPitchRoll.heading);
          var cosPhi = Math.cos(headingPitchRoll.roll);
          var sinTheta = Math.sin(-headingPitchRoll.pitch);
          var sinPsi = Math.sin(-headingPitchRoll.heading);
          var sinPhi = Math.sin(headingPitchRoll.roll);
  
          var m00 = cosTheta * cosPsi;
          var m01 = -cosPhi * sinPsi + sinPhi * sinTheta * cosPsi;
          var m02 = sinPhi * sinPsi + cosPhi * sinTheta * cosPsi;
  
          var m10 = cosTheta * sinPsi;
          var m11 = cosPhi * cosPsi + sinPhi * sinTheta * sinPsi;
          var m12 = -sinPhi * cosPsi + cosPhi * sinTheta * sinPsi;
  
          var m20 = -sinTheta;
          var m21 = sinPhi * cosTheta;
          var m22 = cosPhi * cosTheta;
  
          if (!defined(result)) {
              return new Matrix3(m00, m01, m02,
                  m10, m11, m12,
                  m20, m21, m22);
          }
          result[0] = m00;
          result[1] = m10;
          result[2] = m20;
          result[3] = m01;
          result[4] = m11;
          result[5] = m21;
          result[6] = m02;
          result[7] = m12;
          result[8] = m22;
          return result;
      };
  
      /**
       * Computes a Matrix3 instance representing a non-uniform scale.
       *
       * @param {Cartesian3} scale The x, y, and z scale factors.
       * @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
       * @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
       *
       * @example
       * // Creates
       * //   [7.0, 0.0, 0.0]
       * //   [0.0, 8.0, 0.0]
       * //   [0.0, 0.0, 9.0]
       * var m = Cesium.Matrix3.fromScale(new Cesium.Cartesian3(7.0, 8.0, 9.0));
       */
      Matrix3.fromScale = function(scale, result) {
                  Check.typeOf.object('scale', scale);
          
          if (!defined(result)) {
              return new Matrix3(
                  scale.x, 0.0,     0.0,
                  0.0,     scale.y, 0.0,
                  0.0,     0.0,     scale.z);
          }
  
          result[0] = scale.x;
          result[1] = 0.0;
          result[2] = 0.0;
          result[3] = 0.0;
          result[4] = scale.y;
          result[5] = 0.0;
          result[6] = 0.0;
          result[7] = 0.0;
          result[8] = scale.z;
          return result;
      };
  
      /**
       * Computes a Matrix3 instance representing a uniform scale.
       *
       * @param {Number} scale The uniform scale factor.
       * @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
       * @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
       *
       * @example
       * // Creates
       * //   [2.0, 0.0, 0.0]
       * //   [0.0, 2.0, 0.0]
       * //   [0.0, 0.0, 2.0]
       * var m = Cesium.Matrix3.fromUniformScale(2.0);
       */
      Matrix3.fromUniformScale = function(scale, result) {
                  Check.typeOf.number('scale', scale);
          
          if (!defined(result)) {
              return new Matrix3(
                  scale, 0.0,   0.0,
                  0.0,   scale, 0.0,
                  0.0,   0.0,   scale);
          }
  
          result[0] = scale;
          result[1] = 0.0;
          result[2] = 0.0;
          result[3] = 0.0;
          result[4] = scale;
          result[5] = 0.0;
          result[6] = 0.0;
          result[7] = 0.0;
          result[8] = scale;
          return result;
      };
  
      /**
       * Computes a Matrix3 instance representing the cross product equivalent matrix of a Cartesian3 vector.
       *
       * @param {Cartesian3} vector the vector on the left hand side of the cross product operation.
       * @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
       * @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
       *
       * @example
       * // Creates
       * //   [0.0, -9.0,  8.0]
       * //   [9.0,  0.0, -7.0]
       * //   [-8.0, 7.0,  0.0]
       * var m = Cesium.Matrix3.fromCrossProduct(new Cesium.Cartesian3(7.0, 8.0, 9.0));
       */
      Matrix3.fromCrossProduct = function(vector, result) {
                  Check.typeOf.object('vector', vector);
          
          if (!defined(result)) {
              return new Matrix3(
                        0.0, -vector.z,  vector.y,
                   vector.z,       0.0, -vector.x,
                  -vector.y,  vector.x,       0.0);
          }
  
          result[0] = 0.0;
          result[1] = vector.z;
          result[2] = -vector.y;
          result[3] = -vector.z;
          result[4] = 0.0;
          result[5] = vector.x;
          result[6] = vector.y;
          result[7] = -vector.x;
          result[8] = 0.0;
          return result;
      };
  
      /**
       * Creates a rotation matrix around the x-axis.
       *
       * @param {Number} angle The angle, in radians, of the rotation.  Positive angles are counterclockwise.
       * @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
       * @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
       *
       * @example
       * // Rotate a point 45 degrees counterclockwise around the x-axis.
       * var p = new Cesium.Cartesian3(5, 6, 7);
       * var m = Cesium.Matrix3.fromRotationX(Cesium.Math.toRadians(45.0));
       * var rotated = Cesium.Matrix3.multiplyByVector(m, p, new Cesium.Cartesian3());
       */
      Matrix3.fromRotationX = function(angle, result) {
                  Check.typeOf.number('angle', angle);
          
          var cosAngle = Math.cos(angle);
          var sinAngle = Math.sin(angle);
  
          if (!defined(result)) {
              return new Matrix3(
                  1.0, 0.0, 0.0,
                  0.0, cosAngle, -sinAngle,
                  0.0, sinAngle, cosAngle);
          }
  
          result[0] = 1.0;
          result[1] = 0.0;
          result[2] = 0.0;
          result[3] = 0.0;
          result[4] = cosAngle;
          result[5] = sinAngle;
          result[6] = 0.0;
          result[7] = -sinAngle;
          result[8] = cosAngle;
  
          return result;
      };
  
      /**
       * Creates a rotation matrix around the y-axis.
       *
       * @param {Number} angle The angle, in radians, of the rotation.  Positive angles are counterclockwise.
       * @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
       * @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
       *
       * @example
       * // Rotate a point 45 degrees counterclockwise around the y-axis.
       * var p = new Cesium.Cartesian3(5, 6, 7);
       * var m = Cesium.Matrix3.fromRotationY(Cesium.Math.toRadians(45.0));
       * var rotated = Cesium.Matrix3.multiplyByVector(m, p, new Cesium.Cartesian3());
       */
      Matrix3.fromRotationY = function(angle, result) {
                  Check.typeOf.number('angle', angle);
          
          var cosAngle = Math.cos(angle);
          var sinAngle = Math.sin(angle);
  
          if (!defined(result)) {
              return new Matrix3(
                  cosAngle, 0.0, sinAngle,
                  0.0, 1.0, 0.0,
                  -sinAngle, 0.0, cosAngle);
          }
  
          result[0] = cosAngle;
          result[1] = 0.0;
          result[2] = -sinAngle;
          result[3] = 0.0;
          result[4] = 1.0;
          result[5] = 0.0;
          result[6] = sinAngle;
          result[7] = 0.0;
          result[8] = cosAngle;
  
          return result;
      };
  
      /**
       * Creates a rotation matrix around the z-axis.
       *
       * @param {Number} angle The angle, in radians, of the rotation.  Positive angles are counterclockwise.
       * @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
       * @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
       *
       * @example
       * // Rotate a point 45 degrees counterclockwise around the z-axis.
       * var p = new Cesium.Cartesian3(5, 6, 7);
       * var m = Cesium.Matrix3.fromRotationZ(Cesium.Math.toRadians(45.0));
       * var rotated = Cesium.Matrix3.multiplyByVector(m, p, new Cesium.Cartesian3());
       */
      Matrix3.fromRotationZ = function(angle, result) {
                  Check.typeOf.number('angle', angle);
          
          var cosAngle = Math.cos(angle);
          var sinAngle = Math.sin(angle);
  
          if (!defined(result)) {
              return new Matrix3(
                  cosAngle, -sinAngle, 0.0,
                  sinAngle, cosAngle, 0.0,
                  0.0, 0.0, 1.0);
          }
  
          result[0] = cosAngle;
          result[1] = sinAngle;
          result[2] = 0.0;
          result[3] = -sinAngle;
          result[4] = cosAngle;
          result[5] = 0.0;
          result[6] = 0.0;
          result[7] = 0.0;
          result[8] = 1.0;
  
          return result;
      };
  
      /**
       * Creates an Array from the provided Matrix3 instance.
       * The array will be in column-major order.
       *
       * @param {Matrix3} matrix The matrix to use..
       * @param {Number[]} [result] The Array onto which to store the result.
       * @returns {Number[]} The modified Array parameter or a new Array instance if one was not provided.
       */
      Matrix3.toArray = function(matrix, result) {
                  Check.typeOf.object('matrix', matrix);
          
          if (!defined(result)) {
              return [matrix[0], matrix[1], matrix[2], matrix[3], matrix[4], matrix[5], matrix[6], matrix[7], matrix[8]];
          }
          result[0] = matrix[0];
          result[1] = matrix[1];
          result[2] = matrix[2];
          result[3] = matrix[3];
          result[4] = matrix[4];
          result[5] = matrix[5];
          result[6] = matrix[6];
          result[7] = matrix[7];
          result[8] = matrix[8];
          return result;
      };
  
      /**
       * Computes the array index of the element at the provided row and column.
       *
       * @param {Number} row The zero-based index of the row.
       * @param {Number} column The zero-based index of the column.
       * @returns {Number} The index of the element at the provided row and column.
       *
       * @exception {DeveloperError} row must be 0, 1, or 2.
       * @exception {DeveloperError} column must be 0, 1, or 2.
       *
       * @example
       * var myMatrix = new Cesium.Matrix3();
       * var column1Row0Index = Cesium.Matrix3.getElementIndex(1, 0);
       * var column1Row0 = myMatrix[column1Row0Index]
       * myMatrix[column1Row0Index] = 10.0;
       */
      Matrix3.getElementIndex = function(column, row) {
                  Check.typeOf.number.greaterThanOrEquals('row', row, 0);
          Check.typeOf.number.lessThanOrEquals('row', row, 2);
          Check.typeOf.number.greaterThanOrEquals('column', column, 0);
          Check.typeOf.number.lessThanOrEquals('column', column, 2);
          
          return column * 3 + row;
      };
  
      /**
       * Retrieves a copy of the matrix column at the provided index as a Cartesian3 instance.
       *
       * @param {Matrix3} matrix The matrix to use.
       * @param {Number} index The zero-based index of the column to retrieve.
       * @param {Cartesian3} result The object onto which to store the result.
       * @returns {Cartesian3} The modified result parameter.
       *
       * @exception {DeveloperError} index must be 0, 1, or 2.
       */
      Matrix3.getColumn = function(matrix, index, result) {
                  Check.typeOf.object('matrix', matrix);
          Check.typeOf.number.greaterThanOrEquals('index', index, 0);
          Check.typeOf.number.lessThanOrEquals('index', index, 2);
          Check.typeOf.object('result', result);
          
          var startIndex = index * 3;
          var x = matrix[startIndex];
          var y = matrix[startIndex + 1];
          var z = matrix[startIndex + 2];
  
          result.x = x;
          result.y = y;
          result.z = z;
          return result;
      };
  
      /**
       * Computes a new matrix that replaces the specified column in the provided matrix with the provided Cartesian3 instance.
       *
       * @param {Matrix3} matrix The matrix to use.
       * @param {Number} index The zero-based index of the column to set.
       * @param {Cartesian3} cartesian The Cartesian whose values will be assigned to the specified column.
       * @param {Matrix3} result The object onto which to store the result.
       * @returns {Matrix3} The modified result parameter.
       *
       * @exception {DeveloperError} index must be 0, 1, or 2.
       */
      Matrix3.setColumn = function(matrix, index, cartesian, result) {
                  Check.typeOf.object('matrix', matrix);
          Check.typeOf.number.greaterThanOrEquals('index', index, 0);
          Check.typeOf.number.lessThanOrEquals('index', index, 2);
          Check.typeOf.object('cartesian', cartesian);
          Check.typeOf.object('result', result);
          
          result = Matrix3.clone(matrix, result);
          var startIndex = index * 3;
          result[startIndex] = cartesian.x;
          result[startIndex + 1] = cartesian.y;
          result[startIndex + 2] = cartesian.z;
          return result;
      };
  
      /**
       * Retrieves a copy of the matrix row at the provided index as a Cartesian3 instance.
       *
       * @param {Matrix3} matrix The matrix to use.
       * @param {Number} index The zero-based index of the row to retrieve.
       * @param {Cartesian3} result The object onto which to store the result.
       * @returns {Cartesian3} The modified result parameter.
       *
       * @exception {DeveloperError} index must be 0, 1, or 2.
       */
      Matrix3.getRow = function(matrix, index, result) {
                  Check.typeOf.object('matrix', matrix);
          Check.typeOf.number.greaterThanOrEquals('index', index, 0);
          Check.typeOf.number.lessThanOrEquals('index', index, 2);
          Check.typeOf.object('result', result);
          
          var x = matrix[index];
          var y = matrix[index + 3];
          var z = matrix[index + 6];
  
          result.x = x;
          result.y = y;
          result.z = z;
          return result;
      };
  
      /**
       * Computes a new matrix that replaces the specified row in the provided matrix with the provided Cartesian3 instance.
       *
       * @param {Matrix3} matrix The matrix to use.
       * @param {Number} index The zero-based index of the row to set.
       * @param {Cartesian3} cartesian The Cartesian whose values will be assigned to the specified row.
       * @param {Matrix3} result The object onto which to store the result.
       * @returns {Matrix3} The modified result parameter.
       *
       * @exception {DeveloperError} index must be 0, 1, or 2.
       */
      Matrix3.setRow = function(matrix, index, cartesian, result) {
                  Check.typeOf.object('matrix', matrix);
          Check.typeOf.number.greaterThanOrEquals('index', index, 0);
          Check.typeOf.number.lessThanOrEquals('index', index, 2);
          Check.typeOf.object('cartesian', cartesian);
          Check.typeOf.object('result', result);
          
          result = Matrix3.clone(matrix, result);
          result[index] = cartesian.x;
          result[index + 3] = cartesian.y;
          result[index + 6] = cartesian.z;
          return result;
      };
  
      var scratchColumn = new Cartesian3();
  
      /**
       * Extracts the non-uniform scale assuming the matrix is an affine transformation.
       *
       * @param {Matrix3} matrix The matrix.
       * @param {Cartesian3} result The object onto which to store the result.
       * @returns {Cartesian3} The modified result parameter.
       */
      Matrix3.getScale = function(matrix, result) {
                  Check.typeOf.object('matrix', matrix);
          Check.typeOf.object('result', result);
          
          result.x = Cartesian3.magnitude(Cartesian3.fromElements(matrix[0], matrix[1], matrix[2], scratchColumn));
          result.y = Cartesian3.magnitude(Cartesian3.fromElements(matrix[3], matrix[4], matrix[5], scratchColumn));
          result.z = Cartesian3.magnitude(Cartesian3.fromElements(matrix[6], matrix[7], matrix[8], scratchColumn));
          return result;
      };
  
      var scratchScale = new Cartesian3();
  
      /**
       * Computes the maximum scale assuming the matrix is an affine transformation.
       * The maximum scale is the maximum length of the column vectors.
       *
       * @param {Matrix3} matrix The matrix.
       * @returns {Number} The maximum scale.
       */
      Matrix3.getMaximumScale = function(matrix) {
          Matrix3.getScale(matrix, scratchScale);
          return Cartesian3.maximumComponent(scratchScale);
      };
  
      /**
       * Computes the product of two matrices.
       *
       * @param {Matrix3} left The first matrix.
       * @param {Matrix3} right The second matrix.
       * @param {Matrix3} result The object onto which to store the result.
       * @returns {Matrix3} The modified result parameter.
       */
      Matrix3.multiply = function(left, right, result) {
                  Check.typeOf.object('left', left);
          Check.typeOf.object('right', right);
          Check.typeOf.object('result', result);
          
          var column0Row0 = left[0] * right[0] + left[3] * right[1] + left[6] * right[2];
          var column0Row1 = left[1] * right[0] + left[4] * right[1] + left[7] * right[2];
          var column0Row2 = left[2] * right[0] + left[5] * right[1] + left[8] * right[2];
  
          var column1Row0 = left[0] * right[3] + left[3] * right[4] + left[6] * right[5];
          var column1Row1 = left[1] * right[3] + left[4] * right[4] + left[7] * right[5];
          var column1Row2 = left[2] * right[3] + left[5] * right[4] + left[8] * right[5];
  
          var column2Row0 = left[0] * right[6] + left[3] * right[7] + left[6] * right[8];
          var column2Row1 = left[1] * right[6] + left[4] * right[7] + left[7] * right[8];
          var column2Row2 = left[2] * right[6] + left[5] * right[7] + left[8] * right[8];
  
          result[0] = column0Row0;
          result[1] = column0Row1;
          result[2] = column0Row2;
          result[3] = column1Row0;
          result[4] = column1Row1;
          result[5] = column1Row2;
          result[6] = column2Row0;
          result[7] = column2Row1;
          result[8] = column2Row2;
          return result;
      };
  
      /**
       * Computes the sum of two matrices.
       *
       * @param {Matrix3} left The first matrix.
       * @param {Matrix3} right The second matrix.
       * @param {Matrix3} result The object onto which to store the result.
       * @returns {Matrix3} The modified result parameter.
       */
      Matrix3.add = function(left, right, result) {
                  Check.typeOf.object('left', left);
          Check.typeOf.object('right', right);
          Check.typeOf.object('result', result);
          
          result[0] = left[0] + right[0];
          result[1] = left[1] + right[1];
          result[2] = left[2] + right[2];
          result[3] = left[3] + right[3];
          result[4] = left[4] + right[4];
          result[5] = left[5] + right[5];
          result[6] = left[6] + right[6];
          result[7] = left[7] + right[7];
          result[8] = left[8] + right[8];
          return result;
      };
  
      /**
       * Computes the difference of two matrices.
       *
       * @param {Matrix3} left The first matrix.
       * @param {Matrix3} right The second matrix.
       * @param {Matrix3} result The object onto which to store the result.
       * @returns {Matrix3} The modified result parameter.
       */
      Matrix3.subtract = function(left, right, result) {
                  Check.typeOf.object('left', left);
          Check.typeOf.object('right', right);
          Check.typeOf.object('result', result);
          
          result[0] = left[0] - right[0];
          result[1] = left[1] - right[1];
          result[2] = left[2] - right[2];
          result[3] = left[3] - right[3];
          result[4] = left[4] - right[4];
          result[5] = left[5] - right[5];
          result[6] = left[6] - right[6];
          result[7] = left[7] - right[7];
          result[8] = left[8] - right[8];
          return result;
      };
  
      /**
       * Computes the product of a matrix and a column vector.
       *
       * @param {Matrix3} matrix The matrix.
       * @param {Cartesian3} cartesian The column.
       * @param {Cartesian3} result The object onto which to store the result.
       * @returns {Cartesian3} The modified result parameter.
       */
      Matrix3.multiplyByVector = function(matrix, cartesian, result) {
                  Check.typeOf.object('matrix', matrix);
          Check.typeOf.object('cartesian', cartesian);
          Check.typeOf.object('result', result);
          
          var vX = cartesian.x;
          var vY = cartesian.y;
          var vZ = cartesian.z;
  
          var x = matrix[0] * vX + matrix[3] * vY + matrix[6] * vZ;
          var y = matrix[1] * vX + matrix[4] * vY + matrix[7] * vZ;
          var z = matrix[2] * vX + matrix[5] * vY + matrix[8] * vZ;
  
          result.x = x;
          result.y = y;
          result.z = z;
          return result;
      };
  
      /**
       * Computes the product of a matrix and a scalar.
       *
       * @param {Matrix3} matrix The matrix.
       * @param {Number} scalar The number to multiply by.
       * @param {Matrix3} result The object onto which to store the result.
       * @returns {Matrix3} The modified result parameter.
       */
      Matrix3.multiplyByScalar = function(matrix, scalar, result) {
                  Check.typeOf.object('matrix', matrix);
          Check.typeOf.number('scalar', scalar);
          Check.typeOf.object('result', result);
          
          result[0] = matrix[0] * scalar;
          result[1] = matrix[1] * scalar;
          result[2] = matrix[2] * scalar;
          result[3] = matrix[3] * scalar;
          result[4] = matrix[4] * scalar;
          result[5] = matrix[5] * scalar;
          result[6] = matrix[6] * scalar;
          result[7] = matrix[7] * scalar;
          result[8] = matrix[8] * scalar;
          return result;
      };
  
      /**
       * Computes the product of a matrix times a (non-uniform) scale, as if the scale were a scale matrix.
       *
       * @param {Matrix3} matrix The matrix on the left-hand side.
       * @param {Cartesian3} scale The non-uniform scale on the right-hand side.
       * @param {Matrix3} result The object onto which to store the result.
       * @returns {Matrix3} The modified result parameter.
       *
       *
       * @example
       * // Instead of Cesium.Matrix3.multiply(m, Cesium.Matrix3.fromScale(scale), m);
       * Cesium.Matrix3.multiplyByScale(m, scale, m);
       *
       * @see Matrix3.fromScale
       * @see Matrix3.multiplyByUniformScale
       */
      Matrix3.multiplyByScale = function(matrix, scale, result) {
                  Check.typeOf.object('matrix', matrix);
          Check.typeOf.object('scale', scale);
          Check.typeOf.object('result', result);
          
          result[0] = matrix[0] * scale.x;
          result[1] = matrix[1] * scale.x;
          result[2] = matrix[2] * scale.x;
          result[3] = matrix[3] * scale.y;
          result[4] = matrix[4] * scale.y;
          result[5] = matrix[5] * scale.y;
          result[6] = matrix[6] * scale.z;
          result[7] = matrix[7] * scale.z;
          result[8] = matrix[8] * scale.z;
          return result;
      };
  
      /**
       * Creates a negated copy of the provided matrix.
       *
       * @param {Matrix3} matrix The matrix to negate.
       * @param {Matrix3} result The object onto which to store the result.
       * @returns {Matrix3} The modified result parameter.
       */
      Matrix3.negate = function(matrix, result) {
                  Check.typeOf.object('matrix', matrix);
          Check.typeOf.object('result', result);
          
          result[0] = -matrix[0];
          result[1] = -matrix[1];
          result[2] = -matrix[2];
          result[3] = -matrix[3];
          result[4] = -matrix[4];
          result[5] = -matrix[5];
          result[6] = -matrix[6];
          result[7] = -matrix[7];
          result[8] = -matrix[8];
          return result;
      };
  
      /**
       * Computes the transpose of the provided matrix.
       *
       * @param {Matrix3} matrix The matrix to transpose.
       * @param {Matrix3} result The object onto which to store the result.
       * @returns {Matrix3} The modified result parameter.
       */
      Matrix3.transpose = function(matrix, result) {
                  Check.typeOf.object('matrix', matrix);
          Check.typeOf.object('result', result);
          
          var column0Row0 = matrix[0];
          var column0Row1 = matrix[3];
          var column0Row2 = matrix[6];
          var column1Row0 = matrix[1];
          var column1Row1 = matrix[4];
          var column1Row2 = matrix[7];
          var column2Row0 = matrix[2];
          var column2Row1 = matrix[5];
          var column2Row2 = matrix[8];
  
          result[0] = column0Row0;
          result[1] = column0Row1;
          result[2] = column0Row2;
          result[3] = column1Row0;
          result[4] = column1Row1;
          result[5] = column1Row2;
          result[6] = column2Row0;
          result[7] = column2Row1;
          result[8] = column2Row2;
          return result;
      };
  
      function computeFrobeniusNorm(matrix) {
          var norm = 0.0;
          for (var i = 0; i < 9; ++i) {
              var temp = matrix[i];
              norm += temp * temp;
          }
  
          return Math.sqrt(norm);
      }
  
      var rowVal = [1, 0, 0];
      var colVal = [2, 2, 1];
  
      function offDiagonalFrobeniusNorm(matrix) {
          // Computes the "off-diagonal" Frobenius norm.
          // Assumes matrix is symmetric.
  
          var norm = 0.0;
          for (var i = 0; i < 3; ++i) {
              var temp = matrix[Matrix3.getElementIndex(colVal[i], rowVal[i])];
              norm += 2.0 * temp * temp;
          }
  
          return Math.sqrt(norm);
      }
  
      function shurDecomposition(matrix, result) {
          // This routine was created based upon Matrix Computations, 3rd ed., by Golub and Van Loan,
          // section 8.4.2 The 2by2 Symmetric Schur Decomposition.
          //
          // The routine takes a matrix, which is assumed to be symmetric, and
          // finds the largest off-diagonal term, and then creates
          // a matrix (result) which can be used to help reduce it
  
          var tolerance = CesiumMath.EPSILON15;
  
          var maxDiagonal = 0.0;
          var rotAxis = 1;
  
          // find pivot (rotAxis) based on max diagonal of matrix
          for (var i = 0; i < 3; ++i) {
              var temp = Math.abs(matrix[Matrix3.getElementIndex(colVal[i], rowVal[i])]);
              if (temp > maxDiagonal) {
                  rotAxis = i;
                  maxDiagonal = temp;
              }
          }
  
          var c = 1.0;
          var s = 0.0;
  
          var p = rowVal[rotAxis];
          var q = colVal[rotAxis];
  
          if (Math.abs(matrix[Matrix3.getElementIndex(q, p)]) > tolerance) {
              var qq = matrix[Matrix3.getElementIndex(q, q)];
              var pp = matrix[Matrix3.getElementIndex(p, p)];
              var qp = matrix[Matrix3.getElementIndex(q, p)];
  
              var tau = (qq - pp) / 2.0 / qp;
              var t;
  
              if (tau < 0.0) {
                  t = -1.0 / (-tau + Math.sqrt(1.0 + tau * tau));
              } else {
                  t = 1.0 / (tau + Math.sqrt(1.0 + tau * tau));
              }
  
              c = 1.0 / Math.sqrt(1.0 + t * t);
              s = t * c;
          }
  
          result = Matrix3.clone(Matrix3.IDENTITY, result);
  
          result[Matrix3.getElementIndex(p, p)] = result[Matrix3.getElementIndex(q, q)] = c;
          result[Matrix3.getElementIndex(q, p)] = s;
          result[Matrix3.getElementIndex(p, q)] = -s;
  
          return result;
      }
  
      var jMatrix = new Matrix3();
      var jMatrixTranspose = new Matrix3();
  
      /**
       * Computes the eigenvectors and eigenvalues of a symmetric matrix.
       * <p>
       * Returns a diagonal matrix and unitary matrix such that:
       * <code>matrix = unitary matrix * diagonal matrix * transpose(unitary matrix)</code>
       * </p>
       * <p>
       * The values along the diagonal of the diagonal matrix are the eigenvalues. The columns
       * of the unitary matrix are the corresponding eigenvectors.
       * </p>
       *
       * @param {Matrix3} matrix The matrix to decompose into diagonal and unitary matrix. Expected to be symmetric.
       * @param {Object} [result] An object with unitary and diagonal properties which are matrices onto which to store the result.
       * @returns {Object} An object with unitary and diagonal properties which are the unitary and diagonal matrices, respectively.
       *
       * @example
       * var a = //... symetric matrix
       * var result = {
       *     unitary : new Cesium.Matrix3(),
       *     diagonal : new Cesium.Matrix3()
       * };
       * Cesium.Matrix3.computeEigenDecomposition(a, result);
       *
       * var unitaryTranspose = Cesium.Matrix3.transpose(result.unitary, new Cesium.Matrix3());
       * var b = Cesium.Matrix3.multiply(result.unitary, result.diagonal, new Cesium.Matrix3());
       * Cesium.Matrix3.multiply(b, unitaryTranspose, b); // b is now equal to a
       *
       * var lambda = Cesium.Matrix3.getColumn(result.diagonal, 0, new Cesium.Cartesian3()).x;  // first eigenvalue
       * var v = Cesium.Matrix3.getColumn(result.unitary, 0, new Cesium.Cartesian3());          // first eigenvector
       * var c = Cesium.Cartesian3.multiplyByScalar(v, lambda, new Cesium.Cartesian3());        // equal to Cesium.Matrix3.multiplyByVector(a, v)
       */
      Matrix3.computeEigenDecomposition = function(matrix, result) {
                  Check.typeOf.object('matrix', matrix);
          
          // This routine was created based upon Matrix Computations, 3rd ed., by Golub and Van Loan,
          // section 8.4.3 The Classical Jacobi Algorithm
  
          var tolerance = CesiumMath.EPSILON20;
          var maxSweeps = 10;
  
          var count = 0;
          var sweep = 0;
  
          if (!defined(result)) {
              result = {};
          }
  
          var unitaryMatrix = result.unitary = Matrix3.clone(Matrix3.IDENTITY, result.unitary);
          var diagMatrix = result.diagonal = Matrix3.clone(matrix, result.diagonal);
  
          var epsilon = tolerance * computeFrobeniusNorm(diagMatrix);
  
          while (sweep < maxSweeps && offDiagonalFrobeniusNorm(diagMatrix) > epsilon) {
              shurDecomposition(diagMatrix, jMatrix);
              Matrix3.transpose(jMatrix, jMatrixTranspose);
              Matrix3.multiply(diagMatrix, jMatrix, diagMatrix);
              Matrix3.multiply(jMatrixTranspose, diagMatrix, diagMatrix);
              Matrix3.multiply(unitaryMatrix, jMatrix, unitaryMatrix);
  
              if (++count > 2) {
                  ++sweep;
                  count = 0;
              }
          }
  
          return result;
      };
  
      /**
       * Computes a matrix, which contains the absolute (unsigned) values of the provided matrix's elements.
       *
       * @param {Matrix3} matrix The matrix with signed elements.
       * @param {Matrix3} result The object onto which to store the result.
       * @returns {Matrix3} The modified result parameter.
       */
      Matrix3.abs = function(matrix, result) {
                  Check.typeOf.object('matrix', matrix);
          Check.typeOf.object('result', result);
          
          result[0] = Math.abs(matrix[0]);
          result[1] = Math.abs(matrix[1]);
          result[2] = Math.abs(matrix[2]);
          result[3] = Math.abs(matrix[3]);
          result[4] = Math.abs(matrix[4]);
          result[5] = Math.abs(matrix[5]);
          result[6] = Math.abs(matrix[6]);
          result[7] = Math.abs(matrix[7]);
          result[8] = Math.abs(matrix[8]);
  
          return result;
      };
  
      /**
       * Computes the determinant of the provided matrix.
       *
       * @param {Matrix3} matrix The matrix to use.
       * @returns {Number} The value of the determinant of the matrix.
       */
      Matrix3.determinant = function(matrix) {
                  Check.typeOf.object('matrix', matrix);
          
          var m11 = matrix[0];
          var m21 = matrix[3];
          var m31 = matrix[6];
          var m12 = matrix[1];
          var m22 = matrix[4];
          var m32 = matrix[7];
          var m13 = matrix[2];
          var m23 = matrix[5];
          var m33 = matrix[8];
  
          return m11 * (m22 * m33 - m23 * m32) + m12 * (m23 * m31 - m21 * m33) + m13 * (m21 * m32 - m22 * m31);
      };
  
      /**
       * Computes the inverse of the provided matrix.
       *
       * @param {Matrix3} matrix The matrix to invert.
       * @param {Matrix3} result The object onto which to store the result.
       * @returns {Matrix3} The modified result parameter.
       *
       * @exception {DeveloperError} matrix is not invertible.
       */
      Matrix3.inverse = function(matrix, result) {
                  Check.typeOf.object('matrix', matrix);
          Check.typeOf.object('result', result);
          
          var m11 = matrix[0];
          var m21 = matrix[1];
          var m31 = matrix[2];
          var m12 = matrix[3];
          var m22 = matrix[4];
          var m32 = matrix[5];
          var m13 = matrix[6];
          var m23 = matrix[7];
          var m33 = matrix[8];
  
          var determinant = Matrix3.determinant(matrix);
  
                  if (Math.abs(determinant) <= CesiumMath.EPSILON15) {
              throw new DeveloperError('matrix is not invertible');
          }
          
          result[0] = m22 * m33 - m23 * m32;
          result[1] = m23 * m31 - m21 * m33;
          result[2] = m21 * m32 - m22 * m31;
          result[3] = m13 * m32 - m12 * m33;
          result[4] = m11 * m33 - m13 * m31;
          result[5] = m12 * m31 - m11 * m32;
          result[6] = m12 * m23 - m13 * m22;
          result[7] = m13 * m21 - m11 * m23;
          result[8] = m11 * m22 - m12 * m21;
  
         var scale = 1.0 / determinant;
         return Matrix3.multiplyByScalar(result, scale, result);
      };
  
      /**
       * Compares the provided matrices componentwise and returns
       * <code>true</code> if they are equal, <code>false</code> otherwise.
       *
       * @param {Matrix3} [left] The first matrix.
       * @param {Matrix3} [right] The second matrix.
       * @returns {Boolean} <code>true</code> if left and right are equal, <code>false</code> otherwise.
       */
      Matrix3.equals = function(left, right) {
          return (left === right) ||
                 (defined(left) &&
                  defined(right) &&
                  left[0] === right[0] &&
                  left[1] === right[1] &&
                  left[2] === right[2] &&
                  left[3] === right[3] &&
                  left[4] === right[4] &&
                  left[5] === right[5] &&
                  left[6] === right[6] &&
                  left[7] === right[7] &&
                  left[8] === right[8]);
      };
  
      /**
       * Compares the provided matrices componentwise and returns
       * <code>true</code> if they are within the provided epsilon,
       * <code>false</code> otherwise.
       *
       * @param {Matrix3} [left] The first matrix.
       * @param {Matrix3} [right] The second matrix.
       * @param {Number} epsilon The epsilon to use for equality testing.
       * @returns {Boolean} <code>true</code> if left and right are within the provided epsilon, <code>false</code> otherwise.
       */
      Matrix3.equalsEpsilon = function(left, right, epsilon) {
                  Check.typeOf.number('epsilon', epsilon);
          
          return (left === right) ||
                  (defined(left) &&
                  defined(right) &&
                  Math.abs(left[0] - right[0]) <= epsilon &&
                  Math.abs(left[1] - right[1]) <= epsilon &&
                  Math.abs(left[2] - right[2]) <= epsilon &&
                  Math.abs(left[3] - right[3]) <= epsilon &&
                  Math.abs(left[4] - right[4]) <= epsilon &&
                  Math.abs(left[5] - right[5]) <= epsilon &&
                  Math.abs(left[6] - right[6]) <= epsilon &&
                  Math.abs(left[7] - right[7]) <= epsilon &&
                  Math.abs(left[8] - right[8]) <= epsilon);
      };
  
      /**
       * An immutable Matrix3 instance initialized to the identity matrix.
       *
       * @type {Matrix3}
       * @constant
       */
      Matrix3.IDENTITY = freezeObject(new Matrix3(1.0, 0.0, 0.0,
                                                  0.0, 1.0, 0.0,
                                                  0.0, 0.0, 1.0));
  
      /**
       * An immutable Matrix3 instance initialized to the zero matrix.
       *
       * @type {Matrix3}
       * @constant
       */
      Matrix3.ZERO = freezeObject(new Matrix3(0.0, 0.0, 0.0,
                                              0.0, 0.0, 0.0,
                                              0.0, 0.0, 0.0));
  
      /**
       * The index into Matrix3 for column 0, row 0.
       *
       * @type {Number}
       * @constant
       */
      Matrix3.COLUMN0ROW0 = 0;
  
      /**
       * The index into Matrix3 for column 0, row 1.
       *
       * @type {Number}
       * @constant
       */
      Matrix3.COLUMN0ROW1 = 1;
  
      /**
       * The index into Matrix3 for column 0, row 2.
       *
       * @type {Number}
       * @constant
       */
      Matrix3.COLUMN0ROW2 = 2;
  
      /**
       * The index into Matrix3 for column 1, row 0.
       *
       * @type {Number}
       * @constant
       */
      Matrix3.COLUMN1ROW0 = 3;
  
      /**
       * The index into Matrix3 for column 1, row 1.
       *
       * @type {Number}
       * @constant
       */
      Matrix3.COLUMN1ROW1 = 4;
  
      /**
       * The index into Matrix3 for column 1, row 2.
       *
       * @type {Number}
       * @constant
       */
      Matrix3.COLUMN1ROW2 = 5;
  
      /**
       * The index into Matrix3 for column 2, row 0.
       *
       * @type {Number}
       * @constant
       */
      Matrix3.COLUMN2ROW0 = 6;
  
      /**
       * The index into Matrix3 for column 2, row 1.
       *
       * @type {Number}
       * @constant
       */
      Matrix3.COLUMN2ROW1 = 7;
  
      /**
       * The index into Matrix3 for column 2, row 2.
       *
       * @type {Number}
       * @constant
       */
      Matrix3.COLUMN2ROW2 = 8;
  
      defineProperties(Matrix3.prototype, {
          /**
           * Gets the number of items in the collection.
           * @memberof Matrix3.prototype
           *
           * @type {Number}
           */
          length : {
              get : function() {
                  return Matrix3.packedLength;
              }
          }
      });
  
      /**
       * Duplicates the provided Matrix3 instance.
       *
       * @param {Matrix3} [result] The object onto which to store the result.
       * @returns {Matrix3} The modified result parameter or a new Matrix3 instance if one was not provided.
       */
      Matrix3.prototype.clone = function(result) {
          return Matrix3.clone(this, result);
      };
  
      /**
       * Compares this matrix to the provided matrix componentwise and returns
       * <code>true</code> if they are equal, <code>false</code> otherwise.
       *
       * @param {Matrix3} [right] The right hand side matrix.
       * @returns {Boolean} <code>true</code> if they are equal, <code>false</code> otherwise.
       */
      Matrix3.prototype.equals = function(right) {
          return Matrix3.equals(this, right);
      };
  
      /**
       * @private
       */
      Matrix3.equalsArray = function(matrix, array, offset) {
          return matrix[0] === array[offset] &&
                 matrix[1] === array[offset + 1] &&
                 matrix[2] === array[offset + 2] &&
                 matrix[3] === array[offset + 3] &&
                 matrix[4] === array[offset + 4] &&
                 matrix[5] === array[offset + 5] &&
                 matrix[6] === array[offset + 6] &&
                 matrix[7] === array[offset + 7] &&
                 matrix[8] === array[offset + 8];
      };
  
      /**
       * Compares this matrix to the provided matrix componentwise and returns
       * <code>true</code> if they are within the provided epsilon,
       * <code>false</code> otherwise.
       *
       * @param {Matrix3} [right] The right hand side matrix.
       * @param {Number} epsilon The epsilon to use for equality testing.
       * @returns {Boolean} <code>true</code> if they are within the provided epsilon, <code>false</code> otherwise.
       */
      Matrix3.prototype.equalsEpsilon = function(right, epsilon) {
          return Matrix3.equalsEpsilon(this, right, epsilon);
      };
  
      /**
       * Creates a string representing this Matrix with each row being
       * on a separate line and in the format '(column0, column1, column2)'.
       *
       * @returns {String} A string representing the provided Matrix with each row being on a separate line and in the format '(column0, column1, column2)'.
       */
      Matrix3.prototype.toString = function() {
          return '(' + this[0] + ', ' + this[3] + ', ' + this[6] + ')\n' +
                 '(' + this[1] + ', ' + this[4] + ', ' + this[7] + ')\n' +
                 '(' + this[2] + ', ' + this[5] + ', ' + this[8] + ')';
      };
  
      return Matrix3;
  });
  
  define('Core/Cartesian4',[
          './Check',
          './defaultValue',
          './defined',
          './DeveloperError',
          './freezeObject',
          './Math'
      ], function(
          Check,
          defaultValue,
          defined,
          DeveloperError,
          freezeObject,
          CesiumMath) {
      'use strict';
  
      /**
       * A 4D Cartesian point.
       * @alias Cartesian4
       * @constructor
       *
       * @param {Number} [x=0.0] The X component.
       * @param {Number} [y=0.0] The Y component.
       * @param {Number} [z=0.0] The Z component.
       * @param {Number} [w=0.0] The W component.
       *
       * @see Cartesian2
       * @see Cartesian3
       * @see Packable
       */
      function Cartesian4(x, y, z, w) {
          /**
           * The X component.
           * @type {Number}
           * @default 0.0
           */
          this.x = defaultValue(x, 0.0);
  
          /**
           * The Y component.
           * @type {Number}
           * @default 0.0
           */
          this.y = defaultValue(y, 0.0);
  
          /**
           * The Z component.
           * @type {Number}
           * @default 0.0
           */
          this.z = defaultValue(z, 0.0);
  
          /**
           * The W component.
           * @type {Number}
           * @default 0.0
           */
          this.w = defaultValue(w, 0.0);
      }
  
      /**
       * Creates a Cartesian4 instance from x, y, z and w coordinates.
       *
       * @param {Number} x The x coordinate.
       * @param {Number} y The y coordinate.
       * @param {Number} z The z coordinate.
       * @param {Number} w The w coordinate.
       * @param {Cartesian4} [result] The object onto which to store the result.
       * @returns {Cartesian4} The modified result parameter or a new Cartesian4 instance if one was not provided.
       */
      Cartesian4.fromElements = function(x, y, z, w, result) {
          if (!defined(result)) {
              return new Cartesian4(x, y, z, w);
          }
  
          result.x = x;
          result.y = y;
          result.z = z;
          result.w = w;
          return result;
      };
  
      /**
       * Creates a Cartesian4 instance from a {@link Color}. <code>red</code>, <code>green</code>, <code>blue</code>,
       * and <code>alpha</code> map to <code>x</code>, <code>y</code>, <code>z</code>, and <code>w</code>, respectively.
       *
       * @param {Color} color The source color.
       * @param {Cartesian4} [result] The object onto which to store the result.
       * @returns {Cartesian4} The modified result parameter or a new Cartesian4 instance if one was not provided.
       */
      Cartesian4.fromColor = function(color, result) {
                  Check.typeOf.object('color', color);
                  if (!defined(result)) {
              return new Cartesian4(color.red, color.green, color.blue, color.alpha);
          }
  
          result.x = color.red;
          result.y = color.green;
          result.z = color.blue;
          result.w = color.alpha;
          return result;
      };
  
      /**
       * Duplicates a Cartesian4 instance.
       *
       * @param {Cartesian4} cartesian The Cartesian to duplicate.
       * @param {Cartesian4} [result] The object onto which to store the result.
       * @returns {Cartesian4} The modified result parameter or a new Cartesian4 instance if one was not provided. (Returns undefined if cartesian is undefined)
       */
      Cartesian4.clone = function(cartesian, result) {
          if (!defined(cartesian)) {
              return undefined;
          }
  
          if (!defined(result)) {
              return new Cartesian4(cartesian.x, cartesian.y, cartesian.z, cartesian.w);
          }
  
          result.x = cartesian.x;
          result.y = cartesian.y;
          result.z = cartesian.z;
          result.w = cartesian.w;
          return result;
      };
  
  
      /**
       * The number of elements used to pack the object into an array.
       * @type {Number}
       */
      Cartesian4.packedLength = 4;
  
      /**
       * Stores the provided instance into the provided array.
       *
       * @param {Cartesian4} value The value to pack.
       * @param {Number[]} array The array to pack into.
       * @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
       *
       * @returns {Number[]} The array that was packed into
       */
      Cartesian4.pack = function(value, array, startingIndex) {
                  Check.typeOf.object('value', value);
          Check.defined('array', array);
          
          startingIndex = defaultValue(startingIndex, 0);
  
          array[startingIndex++] = value.x;
          array[startingIndex++] = value.y;
          array[startingIndex++] = value.z;
          array[startingIndex] = value.w;
  
          return array;
      };
  
      /**
       * Retrieves an instance from a packed array.
       *
       * @param {Number[]} array The packed array.
       * @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
       * @param {Cartesian4} [result] The object into which to store the result.
       * @returns {Cartesian4}  The modified result parameter or a new Cartesian4 instance if one was not provided.
       */
      Cartesian4.unpack = function(array, startingIndex, result) {
                  Check.defined('array', array);
          
          startingIndex = defaultValue(startingIndex, 0);
  
          if (!defined(result)) {
              result = new Cartesian4();
          }
          result.x = array[startingIndex++];
          result.y = array[startingIndex++];
          result.z = array[startingIndex++];
          result.w = array[startingIndex];
          return result;
      };
  
      /**
       * Flattens an array of Cartesian4s into and array of components.
       *
       * @param {Cartesian4[]} array The array of cartesians to pack.
       * @param {Number[]} result The array onto which to store the result.
       * @returns {Number[]} The packed array.
       */
      Cartesian4.packArray = function(array, result) {
                  Check.defined('array', array);
          
          var length = array.length;
          if (!defined(result)) {
              result = new Array(length * 4);
          } else {
              result.length = length * 4;
          }
  
          for (var i = 0; i < length; ++i) {
              Cartesian4.pack(array[i], result, i * 4);
          }
          return result;
      };
  
      /**
       * Unpacks an array of cartesian components into and array of Cartesian4s.
       *
       * @param {Number[]} array The array of components to unpack.
       * @param {Cartesian4[]} result The array onto which to store the result.
       * @returns {Cartesian4[]} The unpacked array.
       */
      Cartesian4.unpackArray = function(array, result) {
                  Check.defined('array', array);
          
          var length = array.length;
          if (!defined(result)) {
              result = new Array(length / 4);
          } else {
              result.length = length / 4;
          }
  
          for (var i = 0; i < length; i += 4) {
              var index = i / 4;
              result[index] = Cartesian4.unpack(array, i, result[index]);
          }
          return result;
      };
  
      /**
       * Creates a Cartesian4 from four consecutive elements in an array.
       * @function
       *
       * @param {Number[]} array The array whose four consecutive elements correspond to the x, y, z, and w components, respectively.
       * @param {Number} [startingIndex=0] The offset into the array of the first element, which corresponds to the x component.
       * @param {Cartesian4} [result] The object onto which to store the result.
       * @returns {Cartesian4}  The modified result parameter or a new Cartesian4 instance if one was not provided.
       *
       * @example
       * // Create a Cartesian4 with (1.0, 2.0, 3.0, 4.0)
       * var v = [1.0, 2.0, 3.0, 4.0];
       * var p = Cesium.Cartesian4.fromArray(v);
       *
       * // Create a Cartesian4 with (1.0, 2.0, 3.0, 4.0) using an offset into an array
       * var v2 = [0.0, 0.0, 1.0, 2.0, 3.0, 4.0];
       * var p2 = Cesium.Cartesian4.fromArray(v2, 2);
       */
      Cartesian4.fromArray = Cartesian4.unpack;
  
      /**
       * Computes the value of the maximum component for the supplied Cartesian.
       *
       * @param {Cartesian4} cartesian The cartesian to use.
       * @returns {Number} The value of the maximum component.
       */
      Cartesian4.maximumComponent = function(cartesian) {
                  Check.typeOf.object('cartesian', cartesian);
          
          return Math.max(cartesian.x, cartesian.y, cartesian.z, cartesian.w);
      };
  
      /**
       * Computes the value of the minimum component for the supplied Cartesian.
       *
       * @param {Cartesian4} cartesian The cartesian to use.
       * @returns {Number} The value of the minimum component.
       */
      Cartesian4.minimumComponent = function(cartesian) {
                  Check.typeOf.object('cartesian', cartesian);
          
          return Math.min(cartesian.x, cartesian.y, cartesian.z, cartesian.w);
      };
  
      /**
       * Compares two Cartesians and computes a Cartesian which contains the minimum components of the supplied Cartesians.
       *
       * @param {Cartesian4} first A cartesian to compare.
       * @param {Cartesian4} second A cartesian to compare.
       * @param {Cartesian4} result The object into which to store the result.
       * @returns {Cartesian4} A cartesian with the minimum components.
       */
      Cartesian4.minimumByComponent = function(first, second, result) {
                  Check.typeOf.object('first', first);
          Check.typeOf.object('second', second);
          Check.typeOf.object('result', result);
          
          result.x = Math.min(first.x, second.x);
          result.y = Math.min(first.y, second.y);
          result.z = Math.min(first.z, second.z);
          result.w = Math.min(first.w, second.w);
  
          return result;
      };
  
      /**
       * Compares two Cartesians and computes a Cartesian which contains the maximum components of the supplied Cartesians.
       *
       * @param {Cartesian4} first A cartesian to compare.
       * @param {Cartesian4} second A cartesian to compare.
       * @param {Cartesian4} result The object into which to store the result.
       * @returns {Cartesian4} A cartesian with the maximum components.
       */
      Cartesian4.maximumByComponent = function(first, second, result) {
                  Check.typeOf.object('first', first);
          Check.typeOf.object('second', second);
          Check.typeOf.object('result', result);
          
          result.x = Math.max(first.x, second.x);
          result.y = Math.max(first.y, second.y);
          result.z = Math.max(first.z, second.z);
          result.w = Math.max(first.w, second.w);
  
          return result;
      };
  
      /**
       * Computes the provided Cartesian's squared magnitude.
       *
       * @param {Cartesian4} cartesian The Cartesian instance whose squared magnitude is to be computed.
       * @returns {Number} The squared magnitude.
       */
      Cartesian4.magnitudeSquared = function(cartesian) {
                  Check.typeOf.object('cartesian', cartesian);
          
          return cartesian.x * cartesian.x + cartesian.y * cartesian.y + cartesian.z * cartesian.z + cartesian.w * cartesian.w;
      };
  
      /**
       * Computes the Cartesian's magnitude (length).
       *
       * @param {Cartesian4} cartesian The Cartesian instance whose magnitude is to be computed.
       * @returns {Number} The magnitude.
       */
      Cartesian4.magnitude = function(cartesian) {
          return Math.sqrt(Cartesian4.magnitudeSquared(cartesian));
      };
  
      var distanceScratch = new Cartesian4();
  
      /**
       * Computes the 4-space distance between two points.
       *
       * @param {Cartesian4} left The first point to compute the distance from.
       * @param {Cartesian4} right The second point to compute the distance to.
       * @returns {Number} The distance between two points.
       *
       * @example
       * // Returns 1.0
       * var d = Cesium.Cartesian4.distance(
       *   new Cesium.Cartesian4(1.0, 0.0, 0.0, 0.0),
       *   new Cesium.Cartesian4(2.0, 0.0, 0.0, 0.0));
       */
      Cartesian4.distance = function(left, right) {
                  Check.typeOf.object('left', left);
          Check.typeOf.object('right', right);
          
          Cartesian4.subtract(left, right, distanceScratch);
          return Cartesian4.magnitude(distanceScratch);
      };
  
      /**
       * Computes the squared distance between two points.  Comparing squared distances
       * using this function is more efficient than comparing distances using {@link Cartesian4#distance}.
       *
       * @param {Cartesian4} left The first point to compute the distance from.
       * @param {Cartesian4} right The second point to compute the distance to.
       * @returns {Number} The distance between two points.
       *
       * @example
       * // Returns 4.0, not 2.0
       * var d = Cesium.Cartesian4.distance(
       *   new Cesium.Cartesian4(1.0, 0.0, 0.0, 0.0),
       *   new Cesium.Cartesian4(3.0, 0.0, 0.0, 0.0));
       */
      Cartesian4.distanceSquared = function(left, right) {
                  Check.typeOf.object('left', left);
          Check.typeOf.object('right', right);
          
          Cartesian4.subtract(left, right, distanceScratch);
          return Cartesian4.magnitudeSquared(distanceScratch);
      };
  
      /**
       * Computes the normalized form of the supplied Cartesian.
       *
       * @param {Cartesian4} cartesian The Cartesian to be normalized.
       * @param {Cartesian4} result The object onto which to store the result.
       * @returns {Cartesian4} The modified result parameter.
       */
      Cartesian4.normalize = function(cartesian, result) {
                  Check.typeOf.object('cartesian', cartesian);
          Check.typeOf.object('result', result);
          
          var magnitude = Cartesian4.magnitude(cartesian);
  
          result.x = cartesian.x / magnitude;
          result.y = cartesian.y / magnitude;
          result.z = cartesian.z / magnitude;
          result.w = cartesian.w / magnitude;
  
                  if (isNaN(result.x) || isNaN(result.y) || isNaN(result.z) || isNaN(result.w)) {
              throw new DeveloperError('normalized result is not a number');
          }
          
          return result;
      };
  
      /**
       * Computes the dot (scalar) product of two Cartesians.
       *
       * @param {Cartesian4} left The first Cartesian.
       * @param {Cartesian4} right The second Cartesian.
       * @returns {Number} The dot product.
       */
      Cartesian4.dot = function(left, right) {
                  Check.typeOf.object('left', left);
          Check.typeOf.object('right', right);
          
          return left.x * right.x + left.y * right.y + left.z * right.z + left.w * right.w;
      };
  
      /**
       * Computes the componentwise product of two Cartesians.
       *
       * @param {Cartesian4} left The first Cartesian.
       * @param {Cartesian4} right The second Cartesian.
       * @param {Cartesian4} result The object onto which to store the result.
       * @returns {Cartesian4} The modified result parameter.
       */
      Cartesian4.multiplyComponents = function(left, right, result) {
                  Check.typeOf.object('left', left);
          Check.typeOf.object('right', right);
          Check.typeOf.object('result', result);
          
          result.x = left.x * right.x;
          result.y = left.y * right.y;
          result.z = left.z * right.z;
          result.w = left.w * right.w;
          return result;
      };
  
      /**
       * Computes the componentwise quotient of two Cartesians.
       *
       * @param {Cartesian4} left The first Cartesian.
       * @param {Cartesian4} right The second Cartesian.
       * @param {Cartesian4} result The object onto which to store the result.
       * @returns {Cartesian4} The modified result parameter.
       */
      Cartesian4.divideComponents = function(left, right, result) {
                  Check.typeOf.object('left', left);
          Check.typeOf.object('right', right);
          Check.typeOf.object('result', result);
          
          result.x = left.x / right.x;
          result.y = left.y / right.y;
          result.z = left.z / right.z;
          result.w = left.w / right.w;
          return result;
      };
  
      /**
       * Computes the componentwise sum of two Cartesians.
       *
       * @param {Cartesian4} left The first Cartesian.
       * @param {Cartesian4} right The second Cartesian.
       * @param {Cartesian4} result The object onto which to store the result.
       * @returns {Cartesian4} The modified result parameter.
       */
      Cartesian4.add = function(left, right, result) {
                  Check.typeOf.object('left', left);
          Check.typeOf.object('right', right);
          Check.typeOf.object('result', result);
          
          result.x = left.x + right.x;
          result.y = left.y + right.y;
          result.z = left.z + right.z;
          result.w = left.w + right.w;
          return result;
      };
  
      /**
       * Computes the componentwise difference of two Cartesians.
       *
       * @param {Cartesian4} left The first Cartesian.
       * @param {Cartesian4} right The second Cartesian.
       * @param {Cartesian4} result The object onto which to store the result.
       * @returns {Cartesian4} The modified result parameter.
       */
      Cartesian4.subtract = function(left, right, result) {
                  Check.typeOf.object('left', left);
          Check.typeOf.object('right', right);
          Check.typeOf.object('result', result);
          
          result.x = left.x - right.x;
          result.y = left.y - right.y;
          result.z = left.z - right.z;
          result.w = left.w - right.w;
          return result;
      };
  
      /**
       * Multiplies the provided Cartesian componentwise by the provided scalar.
       *
       * @param {Cartesian4} cartesian The Cartesian to be scaled.
       * @param {Number} scalar The scalar to multiply with.
       * @param {Cartesian4} result The object onto which to store the result.
       * @returns {Cartesian4} The modified result parameter.
       */
      Cartesian4.multiplyByScalar = function(cartesian, scalar, result) {
                  Check.typeOf.object('cartesian', cartesian);
          Check.typeOf.number('scalar', scalar);
          Check.typeOf.object('result', result);
          
          result.x = cartesian.x * scalar;
          result.y = cartesian.y * scalar;
          result.z = cartesian.z * scalar;
          result.w = cartesian.w * scalar;
          return result;
      };
  
      /**
       * Divides the provided Cartesian componentwise by the provided scalar.
       *
       * @param {Cartesian4} cartesian The Cartesian to be divided.
       * @param {Number} scalar The scalar to divide by.
       * @param {Cartesian4} result The object onto which to store the result.
       * @returns {Cartesian4} The modified result parameter.
       */
      Cartesian4.divideByScalar = function(cartesian, scalar, result) {
                  Check.typeOf.object('cartesian', cartesian);
          Check.typeOf.number('scalar', scalar);
          Check.typeOf.object('result', result);
          
          result.x = cartesian.x / scalar;
          result.y = cartesian.y / scalar;
          result.z = cartesian.z / scalar;
          result.w = cartesian.w / scalar;
          return result;
      };
  
      /**
       * Negates the provided Cartesian.
       *
       * @param {Cartesian4} cartesian The Cartesian to be negated.
       * @param {Cartesian4} result The object onto which to store the result.
       * @returns {Cartesian4} The modified result parameter.
       */
      Cartesian4.negate = function(cartesian, result) {
                  Check.typeOf.object('cartesian', cartesian);
          Check.typeOf.object('result', result);
          
          result.x = -cartesian.x;
          result.y = -cartesian.y;
          result.z = -cartesian.z;
          result.w = -cartesian.w;
          return result;
      };
  
      /**
       * Computes the absolute value of the provided Cartesian.
       *
       * @param {Cartesian4} cartesian The Cartesian whose absolute value is to be computed.
       * @param {Cartesian4} result The object onto which to store the result.
       * @returns {Cartesian4} The modified result parameter.
       */
      Cartesian4.abs = function(cartesian, result) {
                  Check.typeOf.object('cartesian', cartesian);
          Check.typeOf.object('result', result);
          
          result.x = Math.abs(cartesian.x);
          result.y = Math.abs(cartesian.y);
          result.z = Math.abs(cartesian.z);
          result.w = Math.abs(cartesian.w);
          return result;
      };
  
      var lerpScratch = new Cartesian4();
      /**
       * Computes the linear interpolation or extrapolation at t using the provided cartesians.
       *
       * @param {Cartesian4} start The value corresponding to t at 0.0.
       * @param {Cartesian4}end The value corresponding to t at 1.0.
       * @param {Number} t The point along t at which to interpolate.
       * @param {Cartesian4} result The object onto which to store the result.
       * @returns {Cartesian4} The modified result parameter.
       */
      Cartesian4.lerp = function(start, end, t, result) {
                  Check.typeOf.object('start', start);
          Check.typeOf.object('end', end);
          Check.typeOf.number('t', t);
          Check.typeOf.object('result', result);
          
          Cartesian4.multiplyByScalar(end, t, lerpScratch);
          result = Cartesian4.multiplyByScalar(start, 1.0 - t, result);
          return Cartesian4.add(lerpScratch, result, result);
      };
  
      var mostOrthogonalAxisScratch = new Cartesian4();
      /**
       * Returns the axis that is most orthogonal to the provided Cartesian.
       *
       * @param {Cartesian4} cartesian The Cartesian on which to find the most orthogonal axis.
       * @param {Cartesian4} result The object onto which to store the result.
       * @returns {Cartesian4} The most orthogonal axis.
       */
      Cartesian4.mostOrthogonalAxis = function(cartesian, result) {
                  Check.typeOf.object('cartesian', cartesian);
          Check.typeOf.object('result', result);
          
          var f = Cartesian4.normalize(cartesian, mostOrthogonalAxisScratch);
          Cartesian4.abs(f, f);
  
          if (f.x <= f.y) {
              if (f.x <= f.z) {
                  if (f.x <= f.w) {
                      result = Cartesian4.clone(Cartesian4.UNIT_X, result);
                  } else {
                      result = Cartesian4.clone(Cartesian4.UNIT_W, result);
                  }
              } else if (f.z <= f.w) {
                  result = Cartesian4.clone(Cartesian4.UNIT_Z, result);
              } else {
                  result = Cartesian4.clone(Cartesian4.UNIT_W, result);
              }
          } else if (f.y <= f.z) {
              if (f.y <= f.w) {
                  result = Cartesian4.clone(Cartesian4.UNIT_Y, result);
              } else {
                  result = Cartesian4.clone(Cartesian4.UNIT_W, result);
              }
          } else if (f.z <= f.w) {
              result = Cartesian4.clone(Cartesian4.UNIT_Z, result);
          } else {
              result = Cartesian4.clone(Cartesian4.UNIT_W, result);
          }
  
          return result;
      };
  
      /**
       * Compares the provided Cartesians componentwise and returns
       * <code>true</code> if they are equal, <code>false</code> otherwise.
       *
       * @param {Cartesian4} [left] The first Cartesian.
       * @param {Cartesian4} [right] The second Cartesian.
       * @returns {Boolean} <code>true</code> if left and right are equal, <code>false</code> otherwise.
       */
      Cartesian4.equals = function(left, right) {
          return (left === right) ||
                 ((defined(left)) &&
                  (defined(right)) &&
                  (left.x === right.x) &&
                  (left.y === right.y) &&
                  (left.z === right.z) &&
                  (left.w === right.w));
      };
  
      /**
       * @private
       */
      Cartesian4.equalsArray = function(cartesian, array, offset) {
          return cartesian.x === array[offset] &&
                 cartesian.y === array[offset + 1] &&
                 cartesian.z === array[offset + 2] &&
                 cartesian.w === array[offset + 3];
      };
  
      /**
       * Compares the provided Cartesians componentwise and returns
       * <code>true</code> if they pass an absolute or relative tolerance test,
       * <code>false</code> otherwise.
       *
       * @param {Cartesian4} [left] The first Cartesian.
       * @param {Cartesian4} [right] The second Cartesian.
       * @param {Number} relativeEpsilon The relative epsilon tolerance to use for equality testing.
       * @param {Number} [absoluteEpsilon=relativeEpsilon] The absolute epsilon tolerance to use for equality testing.
       * @returns {Boolean} <code>true</code> if left and right are within the provided epsilon, <code>false</code> otherwise.
       */
      Cartesian4.equalsEpsilon = function(left, right, relativeEpsilon, absoluteEpsilon) {
          return (left === right) ||
                 (defined(left) &&
                  defined(right) &&
                  CesiumMath.equalsEpsilon(left.x, right.x, relativeEpsilon, absoluteEpsilon) &&
                  CesiumMath.equalsEpsilon(left.y, right.y, relativeEpsilon, absoluteEpsilon) &&
                  CesiumMath.equalsEpsilon(left.z, right.z, relativeEpsilon, absoluteEpsilon) &&
                  CesiumMath.equalsEpsilon(left.w, right.w, relativeEpsilon, absoluteEpsilon));
      };
  
      /**
       * An immutable Cartesian4 instance initialized to (0.0, 0.0, 0.0, 0.0).
       *
       * @type {Cartesian4}
       * @constant
       */
      Cartesian4.ZERO = freezeObject(new Cartesian4(0.0, 0.0, 0.0, 0.0));
  
      /**
       * An immutable Cartesian4 instance initialized to (1.0, 0.0, 0.0, 0.0).
       *
       * @type {Cartesian4}
       * @constant
       */
      Cartesian4.UNIT_X = freezeObject(new Cartesian4(1.0, 0.0, 0.0, 0.0));
  
      /**
       * An immutable Cartesian4 instance initialized to (0.0, 1.0, 0.0, 0.0).
       *
       * @type {Cartesian4}
       * @constant
       */
      Cartesian4.UNIT_Y = freezeObject(new Cartesian4(0.0, 1.0, 0.0, 0.0));
  
      /**
       * An immutable Cartesian4 instance initialized to (0.0, 0.0, 1.0, 0.0).
       *
       * @type {Cartesian4}
       * @constant
       */
      Cartesian4.UNIT_Z = freezeObject(new Cartesian4(0.0, 0.0, 1.0, 0.0));
  
      /**
       * An immutable Cartesian4 instance initialized to (0.0, 0.0, 0.0, 1.0).
       *
       * @type {Cartesian4}
       * @constant
       */
      Cartesian4.UNIT_W = freezeObject(new Cartesian4(0.0, 0.0, 0.0, 1.0));
  
      /**
       * Duplicates this Cartesian4 instance.
       *
       * @param {Cartesian4} [result] The object onto which to store the result.
       * @returns {Cartesian4} The modified result parameter or a new Cartesian4 instance if one was not provided.
       */
      Cartesian4.prototype.clone = function(result) {
          return Cartesian4.clone(this, result);
      };
  
      /**
       * Compares this Cartesian against the provided Cartesian componentwise and returns
       * <code>true</code> if they are equal, <code>false</code> otherwise.
       *
       * @param {Cartesian4} [right] The right hand side Cartesian.
       * @returns {Boolean} <code>true</code> if they are equal, <code>false</code> otherwise.
       */
      Cartesian4.prototype.equals = function(right) {
          return Cartesian4.equals(this, right);
      };
  
      /**
       * Compares this Cartesian against the provided Cartesian componentwise and returns
       * <code>true</code> if they pass an absolute or relative tolerance test,
       * <code>false</code> otherwise.
       *
       * @param {Cartesian4} [right] The right hand side Cartesian.
       * @param {Number} relativeEpsilon The relative epsilon tolerance to use for equality testing.
       * @param {Number} [absoluteEpsilon=relativeEpsilon] The absolute epsilon tolerance to use for equality testing.
       * @returns {Boolean} <code>true</code> if they are within the provided epsilon, <code>false</code> otherwise.
       */
      Cartesian4.prototype.equalsEpsilon = function(right, relativeEpsilon, absoluteEpsilon) {
          return Cartesian4.equalsEpsilon(this, right, relativeEpsilon, absoluteEpsilon);
      };
  
      /**
       * Creates a string representing this Cartesian in the format '(x, y)'.
       *
       * @returns {String} A string representing the provided Cartesian in the format '(x, y)'.
       */
      Cartesian4.prototype.toString = function() {
          return '(' + this.x + ', ' + this.y + ', ' + this.z + ', ' + this.w + ')';
      };
  
      return Cartesian4;
  });
  
  define('Core/RuntimeError',[
          './defined'
      ], function(
          defined) {
      'use strict';
  
      /**
       * Constructs an exception object that is thrown due to an error that can occur at runtime, e.g.,
       * out of memory, could not compile shader, etc.  If a function may throw this
       * exception, the calling code should be prepared to catch it.
       * <br /><br />
       * On the other hand, a {@link DeveloperError} indicates an exception due
       * to a developer error, e.g., invalid argument, that usually indicates a bug in the
       * calling code.
       *
       * @alias RuntimeError
       * @constructor
       * @extends Error
       *
       * @param {String} [message] The error message for this exception.
       *
       * @see DeveloperError
       */
      function RuntimeError(message) {
          /**
           * 'RuntimeError' indicating that this exception was thrown due to a runtime error.
           * @type {String}
           * @readonly
           */
          this.name = 'RuntimeError';
  
          /**
           * The explanation for why this exception was thrown.
           * @type {String}
           * @readonly
           */
          this.message = message;
  
          //Browsers such as IE don't have a stack property until you actually throw the error.
          var stack;
          try {
              throw new Error();
          } catch (e) {
              stack = e.stack;
          }
  
          /**
           * The stack trace of this exception, if available.
           * @type {String}
           * @readonly
           */
          this.stack = stack;
      }
  
      if (defined(Object.create)) {
          RuntimeError.prototype = Object.create(Error.prototype);
          RuntimeError.prototype.constructor = RuntimeError;
      }
  
      RuntimeError.prototype.toString = function() {
          var str = this.name + ': ' + this.message;
  
          if (defined(this.stack)) {
              str += '\n' + this.stack.toString();
          }
  
          return str;
      };
  
      return RuntimeError;
  });
  
  define('Core/Matrix4',[
          './Cartesian3',
          './Cartesian4',
          './Check',
          './defaultValue',
          './defined',
          './defineProperties',
          './freezeObject',
          './Math',
          './Matrix3',
          './RuntimeError'
      ], function(
          Cartesian3,
          Cartesian4,
          Check,
          defaultValue,
          defined,
          defineProperties,
          freezeObject,
          CesiumMath,
          Matrix3,
          RuntimeError) {
      'use strict';
  
      /**
       * A 4x4 matrix, indexable as a column-major order array.
       * Constructor parameters are in row-major order for code readability.
       * @alias Matrix4
       * @constructor
       *
       * @param {Number} [column0Row0=0.0] The value for column 0, row 0.
       * @param {Number} [column1Row0=0.0] The value for column 1, row 0.
       * @param {Number} [column2Row0=0.0] The value for column 2, row 0.
       * @param {Number} [column3Row0=0.0] The value for column 3, row 0.
       * @param {Number} [column0Row1=0.0] The value for column 0, row 1.
       * @param {Number} [column1Row1=0.0] The value for column 1, row 1.
       * @param {Number} [column2Row1=0.0] The value for column 2, row 1.
       * @param {Number} [column3Row1=0.0] The value for column 3, row 1.
       * @param {Number} [column0Row2=0.0] The value for column 0, row 2.
       * @param {Number} [column1Row2=0.0] The value for column 1, row 2.
       * @param {Number} [column2Row2=0.0] The value for column 2, row 2.
       * @param {Number} [column3Row2=0.0] The value for column 3, row 2.
       * @param {Number} [column0Row3=0.0] The value for column 0, row 3.
       * @param {Number} [column1Row3=0.0] The value for column 1, row 3.
       * @param {Number} [column2Row3=0.0] The value for column 2, row 3.
       * @param {Number} [column3Row3=0.0] The value for column 3, row 3.
       *
       * @see Matrix4.fromColumnMajorArray
       * @see Matrix4.fromRowMajorArray
       * @see Matrix4.fromRotationTranslation
       * @see Matrix4.fromTranslationRotationScale
       * @see Matrix4.fromTranslationQuaternionRotationScale
       * @see Matrix4.fromTranslation
       * @see Matrix4.fromScale
       * @see Matrix4.fromUniformScale
       * @see Matrix4.fromCamera
       * @see Matrix4.computePerspectiveFieldOfView
       * @see Matrix4.computeOrthographicOffCenter
       * @see Matrix4.computePerspectiveOffCenter
       * @see Matrix4.computeInfinitePerspectiveOffCenter
       * @see Matrix4.computeViewportTransformation
       * @see Matrix4.computeView
       * @see Matrix2
       * @see Matrix3
       * @see Packable
       */
      function Matrix4(column0Row0, column1Row0, column2Row0, column3Row0,
                             column0Row1, column1Row1, column2Row1, column3Row1,
                             column0Row2, column1Row2, column2Row2, column3Row2,
                             column0Row3, column1Row3, column2Row3, column3Row3) {
          this[0] = defaultValue(column0Row0, 0.0);
          this[1] = defaultValue(column0Row1, 0.0);
          this[2] = defaultValue(column0Row2, 0.0);
          this[3] = defaultValue(column0Row3, 0.0);
          this[4] = defaultValue(column1Row0, 0.0);
          this[5] = defaultValue(column1Row1, 0.0);
          this[6] = defaultValue(column1Row2, 0.0);
          this[7] = defaultValue(column1Row3, 0.0);
          this[8] = defaultValue(column2Row0, 0.0);
          this[9] = defaultValue(column2Row1, 0.0);
          this[10] = defaultValue(column2Row2, 0.0);
          this[11] = defaultValue(column2Row3, 0.0);
          this[12] = defaultValue(column3Row0, 0.0);
          this[13] = defaultValue(column3Row1, 0.0);
          this[14] = defaultValue(column3Row2, 0.0);
          this[15] = defaultValue(column3Row3, 0.0);
      }
  
      /**
       * The number of elements used to pack the object into an array.
       * @type {Number}
       */
      Matrix4.packedLength = 16;
  
      /**
       * Stores the provided instance into the provided array.
       *
       * @param {Matrix4} value The value to pack.
       * @param {Number[]} array The array to pack into.
       * @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
       *
       * @returns {Number[]} The array that was packed into
       */
      Matrix4.pack = function(value, array, startingIndex) {
                  Check.typeOf.object('value', value);
          Check.defined('array', array);
          
          startingIndex = defaultValue(startingIndex, 0);
  
          array[startingIndex++] = value[0];
          array[startingIndex++] = value[1];
          array[startingIndex++] = value[2];
          array[startingIndex++] = value[3];
          array[startingIndex++] = value[4];
          array[startingIndex++] = value[5];
          array[startingIndex++] = value[6];
          array[startingIndex++] = value[7];
          array[startingIndex++] = value[8];
          array[startingIndex++] = value[9];
          array[startingIndex++] = value[10];
          array[startingIndex++] = value[11];
          array[startingIndex++] = value[12];
          array[startingIndex++] = value[13];
          array[startingIndex++] = value[14];
          array[startingIndex] = value[15];
  
          return array;
      };
  
      /**
       * Retrieves an instance from a packed array.
       *
       * @param {Number[]} array The packed array.
       * @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
       * @param {Matrix4} [result] The object into which to store the result.
       * @returns {Matrix4} The modified result parameter or a new Matrix4 instance if one was not provided.
       */
      Matrix4.unpack = function(array, startingIndex, result) {
                  Check.defined('array', array);
          
          startingIndex = defaultValue(startingIndex, 0);
  
          if (!defined(result)) {
              result = new Matrix4();
          }
  
          result[0] = array[startingIndex++];
          result[1] = array[startingIndex++];
          result[2] = array[startingIndex++];
          result[3] = array[startingIndex++];
          result[4] = array[startingIndex++];
          result[5] = array[startingIndex++];
          result[6] = array[startingIndex++];
          result[7] = array[startingIndex++];
          result[8] = array[startingIndex++];
          result[9] = array[startingIndex++];
          result[10] = array[startingIndex++];
          result[11] = array[startingIndex++];
          result[12] = array[startingIndex++];
          result[13] = array[startingIndex++];
          result[14] = array[startingIndex++];
          result[15] = array[startingIndex];
          return result;
      };
  
      /**
       * Duplicates a Matrix4 instance.
       *
       * @param {Matrix4} matrix The matrix to duplicate.
       * @param {Matrix4} [result] The object onto which to store the result.
       * @returns {Matrix4} The modified result parameter or a new Matrix4 instance if one was not provided. (Returns undefined if matrix is undefined)
       */
      Matrix4.clone = function(matrix, result) {
          if (!defined(matrix)) {
              return undefined;
          }
          if (!defined(result)) {
              return new Matrix4(matrix[0], matrix[4], matrix[8], matrix[12],
                                 matrix[1], matrix[5], matrix[9], matrix[13],
                                 matrix[2], matrix[6], matrix[10], matrix[14],
                                 matrix[3], matrix[7], matrix[11], matrix[15]);
          }
          result[0] = matrix[0];
          result[1] = matrix[1];
          result[2] = matrix[2];
          result[3] = matrix[3];
          result[4] = matrix[4];
          result[5] = matrix[5];
          result[6] = matrix[6];
          result[7] = matrix[7];
          result[8] = matrix[8];
          result[9] = matrix[9];
          result[10] = matrix[10];
          result[11] = matrix[11];
          result[12] = matrix[12];
          result[13] = matrix[13];
          result[14] = matrix[14];
          result[15] = matrix[15];
          return result;
      };
  
      /**
       * Creates a Matrix4 from 16 consecutive elements in an array.
       * @function
       *
       * @param {Number[]} array The array whose 16 consecutive elements correspond to the positions of the matrix.  Assumes column-major order.
       * @param {Number} [startingIndex=0] The offset into the array of the first element, which corresponds to first column first row position in the matrix.
       * @param {Matrix4} [result] The object onto which to store the result.
       * @returns {Matrix4} The modified result parameter or a new Matrix4 instance if one was not provided.
       *
       * @example
       * // Create the Matrix4:
       * // [1.0, 2.0, 3.0, 4.0]
       * // [1.0, 2.0, 3.0, 4.0]
       * // [1.0, 2.0, 3.0, 4.0]
       * // [1.0, 2.0, 3.0, 4.0]
       *
       * var v = [1.0, 1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 2.0, 3.0, 3.0, 3.0, 3.0, 4.0, 4.0, 4.0, 4.0];
       * var m = Cesium.Matrix4.fromArray(v);
       *
       * // Create same Matrix4 with using an offset into an array
       * var v2 = [0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 2.0, 3.0, 3.0, 3.0, 3.0, 4.0, 4.0, 4.0, 4.0];
       * var m2 = Cesium.Matrix4.fromArray(v2, 2);
       */
      Matrix4.fromArray = Matrix4.unpack;
  
      /**
       * Computes a Matrix4 instance from a column-major order array.
       *
       * @param {Number[]} values The column-major order array.
       * @param {Matrix4} [result] The object in which the result will be stored, if undefined a new instance will be created.
       * @returns {Matrix4} The modified result parameter, or a new Matrix4 instance if one was not provided.
       */
      Matrix4.fromColumnMajorArray = function(values, result) {
                  Check.defined('values', values);
          
          return Matrix4.clone(values, result);
      };
  
      /**
       * Computes a Matrix4 instance from a row-major order array.
       * The resulting matrix will be in column-major order.
       *
       * @param {Number[]} values The row-major order array.
       * @param {Matrix4} [result] The object in which the result will be stored, if undefined a new instance will be created.
       * @returns {Matrix4} The modified result parameter, or a new Matrix4 instance if one was not provided.
       */
      Matrix4.fromRowMajorArray = function(values, result) {
                  Check.defined('values', values);
          
          if (!defined(result)) {
              return new Matrix4(values[0], values[1], values[2], values[3],
                                 values[4], values[5], values[6], values[7],
                                 values[8], values[9], values[10], values[11],
                                 values[12], values[13], values[14], values[15]);
          }
          result[0] = values[0];
          result[1] = values[4];
          result[2] = values[8];
          result[3] = values[12];
          result[4] = values[1];
          result[5] = values[5];
          result[6] = values[9];
          result[7] = values[13];
          result[8] = values[2];
          result[9] = values[6];
          result[10] = values[10];
          result[11] = values[14];
          result[12] = values[3];
          result[13] = values[7];
          result[14] = values[11];
          result[15] = values[15];
          return result;
      };
  
      /**
       * Computes a Matrix4 instance from a Matrix3 representing the rotation
       * and a Cartesian3 representing the translation.
       *
       * @param {Matrix3} rotation The upper left portion of the matrix representing the rotation.
       * @param {Cartesian3} [translation=Cartesian3.ZERO] The upper right portion of the matrix representing the translation.
       * @param {Matrix4} [result] The object in which the result will be stored, if undefined a new instance will be created.
       * @returns {Matrix4} The modified result parameter, or a new Matrix4 instance if one was not provided.
       */
      Matrix4.fromRotationTranslation = function(rotation, translation, result) {
                  Check.typeOf.object('rotation', rotation);
          
          translation = defaultValue(translation, Cartesian3.ZERO);
  
          if (!defined(result)) {
              return new Matrix4(rotation[0], rotation[3], rotation[6], translation.x,
                                 rotation[1], rotation[4], rotation[7], translation.y,
                                 rotation[2], rotation[5], rotation[8], translation.z,
                                         0.0,         0.0,         0.0,           1.0);
          }
  
          result[0] = rotation[0];
          result[1] = rotation[1];
          result[2] = rotation[2];
          result[3] = 0.0;
          result[4] = rotation[3];
          result[5] = rotation[4];
          result[6] = rotation[5];
          result[7] = 0.0;
          result[8] = rotation[6];
          result[9] = rotation[7];
          result[10] = rotation[8];
          result[11] = 0.0;
          result[12] = translation.x;
          result[13] = translation.y;
          result[14] = translation.z;
          result[15] = 1.0;
          return result;
      };
  
      /**
       * Computes a Matrix4 instance from a translation, rotation, and scale (TRS)
       * representation with the rotation represented as a quaternion.
       *
       * @param {Cartesian3} translation The translation transformation.
       * @param {Quaternion} rotation The rotation transformation.
       * @param {Cartesian3} scale The non-uniform scale transformation.
       * @param {Matrix4} [result] The object in which the result will be stored, if undefined a new instance will be created.
       * @returns {Matrix4} The modified result parameter, or a new Matrix4 instance if one was not provided.
       *
       * @example
       * var result = Cesium.Matrix4.fromTranslationQuaternionRotationScale(
       *   new Cesium.Cartesian3(1.0, 2.0, 3.0), // translation
       *   Cesium.Quaternion.IDENTITY,           // rotation
       *   new Cesium.Cartesian3(7.0, 8.0, 9.0), // scale
       *   result);
       */
      Matrix4.fromTranslationQuaternionRotationScale = function(translation, rotation, scale, result) {
                  Check.typeOf.object('translation', translation);
          Check.typeOf.object('rotation', rotation);
          Check.typeOf.object('scale', scale);
          
          if (!defined(result)) {
              result = new Matrix4();
          }
  
          var scaleX = scale.x;
          var scaleY = scale.y;
          var scaleZ = scale.z;
  
          var x2 = rotation.x * rotation.x;
          var xy = rotation.x * rotation.y;
          var xz = rotation.x * rotation.z;
          var xw = rotation.x * rotation.w;
          var y2 = rotation.y * rotation.y;
          var yz = rotation.y * rotation.z;
          var yw = rotation.y * rotation.w;
          var z2 = rotation.z * rotation.z;
          var zw = rotation.z * rotation.w;
          var w2 = rotation.w * rotation.w;
  
          var m00 = x2 - y2 - z2 + w2;
          var m01 = 2.0 * (xy - zw);
          var m02 = 2.0 * (xz + yw);
  
          var m10 = 2.0 * (xy + zw);
          var m11 = -x2 + y2 - z2 + w2;
          var m12 = 2.0 * (yz - xw);
  
          var m20 = 2.0 * (xz - yw);
          var m21 = 2.0 * (yz + xw);
          var m22 = -x2 - y2 + z2 + w2;
  
          result[0]  = m00 * scaleX;
          result[1]  = m10 * scaleX;
          result[2]  = m20 * scaleX;
          result[3]  = 0.0;
          result[4]  = m01 * scaleY;
          result[5]  = m11 * scaleY;
          result[6]  = m21 * scaleY;
          result[7]  = 0.0;
          result[8]  = m02 * scaleZ;
          result[9]  = m12 * scaleZ;
          result[10] = m22 * scaleZ;
          result[11] = 0.0;
          result[12] = translation.x;
          result[13] = translation.y;
          result[14] = translation.z;
          result[15] = 1.0;
  
          return result;
      };
  
      /**
       * Creates a Matrix4 instance from a {@link TranslationRotationScale} instance.
       *
       * @param {TranslationRotationScale} translationRotationScale The instance.
       * @param {Matrix4} [result] The object in which the result will be stored, if undefined a new instance will be created.
       * @returns {Matrix4} The modified result parameter, or a new Matrix4 instance if one was not provided.
       */
      Matrix4.fromTranslationRotationScale = function(translationRotationScale, result) {
                  Check.typeOf.object('translationRotationScale', translationRotationScale);
          
          return Matrix4.fromTranslationQuaternionRotationScale(translationRotationScale.translation, translationRotationScale.rotation, translationRotationScale.scale, result);
      };
  
      /**
       * Creates a Matrix4 instance from a Cartesian3 representing the translation.
       *
       * @param {Cartesian3} translation The upper right portion of the matrix representing the translation.
       * @param {Matrix4} [result] The object in which the result will be stored, if undefined a new instance will be created.
       * @returns {Matrix4} The modified result parameter, or a new Matrix4 instance if one was not provided.
       *
       * @see Matrix4.multiplyByTranslation
       */
      Matrix4.fromTranslation = function(translation, result) {
                  Check.typeOf.object('translation', translation);
          
          return Matrix4.fromRotationTranslation(Matrix3.IDENTITY, translation, result);
      };
  
      /**
       * Computes a Matrix4 instance representing a non-uniform scale.
       *
       * @param {Cartesian3} scale The x, y, and z scale factors.
       * @param {Matrix4} [result] The object in which the result will be stored, if undefined a new instance will be created.
       * @returns {Matrix4} The modified result parameter, or a new Matrix4 instance if one was not provided.
       *
       * @example
       * // Creates
       * //   [7.0, 0.0, 0.0, 0.0]
       * //   [0.0, 8.0, 0.0, 0.0]
       * //   [0.0, 0.0, 9.0, 0.0]
       * //   [0.0, 0.0, 0.0, 1.0]
       * var m = Cesium.Matrix4.fromScale(new Cesium.Cartesian3(7.0, 8.0, 9.0));
       */
      Matrix4.fromScale = function(scale, result) {
                  Check.typeOf.object('scale', scale);
          
          if (!defined(result)) {
              return new Matrix4(
                  scale.x, 0.0,     0.0,     0.0,
                  0.0,     scale.y, 0.0,     0.0,
                  0.0,     0.0,     scale.z, 0.0,
                  0.0,     0.0,     0.0,     1.0);
          }
  
          result[0] = scale.x;
          result[1] = 0.0;
          result[2] = 0.0;
          result[3] = 0.0;
          result[4] = 0.0;
          result[5] = scale.y;
          result[6] = 0.0;
          result[7] = 0.0;
          result[8] = 0.0;
          result[9] = 0.0;
          result[10] = scale.z;
          result[11] = 0.0;
          result[12] = 0.0;
          result[13] = 0.0;
          result[14] = 0.0;
          result[15] = 1.0;
          return result;
      };
  
      /**
       * Computes a Matrix4 instance representing a uniform scale.
       *
       * @param {Number} scale The uniform scale factor.
       * @param {Matrix4} [result] The object in which the result will be stored, if undefined a new instance will be created.
       * @returns {Matrix4} The modified result parameter, or a new Matrix4 instance if one was not provided.
       *
       * @example
       * // Creates
       * //   [2.0, 0.0, 0.0, 0.0]
       * //   [0.0, 2.0, 0.0, 0.0]
       * //   [0.0, 0.0, 2.0, 0.0]
       * //   [0.0, 0.0, 0.0, 1.0]
       * var m = Cesium.Matrix4.fromUniformScale(2.0);
       */
      Matrix4.fromUniformScale = function(scale, result) {
                  Check.typeOf.number('scale', scale);
          
          if (!defined(result)) {
              return new Matrix4(scale, 0.0,   0.0,   0.0,
                                 0.0,   scale, 0.0,   0.0,
                                 0.0,   0.0,   scale, 0.0,
                                 0.0,   0.0,   0.0,   1.0);
          }
  
          result[0] = scale;
          result[1] = 0.0;
          result[2] = 0.0;
          result[3] = 0.0;
          result[4] = 0.0;
          result[5] = scale;
          result[6] = 0.0;
          result[7] = 0.0;
          result[8] = 0.0;
          result[9] = 0.0;
          result[10] = scale;
          result[11] = 0.0;
          result[12] = 0.0;
          result[13] = 0.0;
          result[14] = 0.0;
          result[15] = 1.0;
          return result;
      };
  
      var fromCameraF = new Cartesian3();
      var fromCameraR = new Cartesian3();
      var fromCameraU = new Cartesian3();
  
      /**
       * Computes a Matrix4 instance from a Camera.
       *
       * @param {Camera} camera The camera to use.
       * @param {Matrix4} [result] The object in which the result will be stored, if undefined a new instance will be created.
       * @returns {Matrix4} The modified result parameter, or a new Matrix4 instance if one was not provided.
       */
      Matrix4.fromCamera = function(camera, result) {
                  Check.typeOf.object('camera', camera);
          
          var position = camera.position;
          var direction = camera.direction;
          var up = camera.up;
  
                  Check.typeOf.object('camera.position', position);
          Check.typeOf.object('camera.direction', direction);
          Check.typeOf.object('camera.up', up);
          
          Cartesian3.normalize(direction, fromCameraF);
          Cartesian3.normalize(Cartesian3.cross(fromCameraF, up, fromCameraR), fromCameraR);
          Cartesian3.normalize(Cartesian3.cross(fromCameraR, fromCameraF, fromCameraU), fromCameraU);
  
          var sX = fromCameraR.x;
          var sY = fromCameraR.y;
          var sZ = fromCameraR.z;
          var fX = fromCameraF.x;
          var fY = fromCameraF.y;
          var fZ = fromCameraF.z;
          var uX = fromCameraU.x;
          var uY = fromCameraU.y;
          var uZ = fromCameraU.z;
          var positionX = position.x;
          var positionY = position.y;
          var positionZ = position.z;
          var t0 = sX * -positionX + sY * -positionY+ sZ * -positionZ;
          var t1 = uX * -positionX + uY * -positionY+ uZ * -positionZ;
          var t2 = fX * positionX + fY * positionY + fZ * positionZ;
  
          // The code below this comment is an optimized
          // version of the commented lines.
          // Rather that create two matrices and then multiply,
          // we just bake in the multiplcation as part of creation.
          // var rotation = new Matrix4(
          //                 sX,  sY,  sZ, 0.0,
          //                 uX,  uY,  uZ, 0.0,
          //                -fX, -fY, -fZ, 0.0,
          //                 0.0,  0.0,  0.0, 1.0);
          // var translation = new Matrix4(
          //                 1.0, 0.0, 0.0, -position.x,
          //                 0.0, 1.0, 0.0, -position.y,
          //                 0.0, 0.0, 1.0, -position.z,
          //                 0.0, 0.0, 0.0, 1.0);
          // return rotation.multiply(translation);
          if (!defined(result)) {
              return new Matrix4(
                      sX,   sY,  sZ, t0,
                      uX,   uY,  uZ, t1,
                     -fX,  -fY, -fZ, t2,
                      0.0, 0.0, 0.0, 1.0);
          }
          result[0] = sX;
          result[1] = uX;
          result[2] = -fX;
          result[3] = 0.0;
          result[4] = sY;
          result[5] = uY;
          result[6] = -fY;
          result[7] = 0.0;
          result[8] = sZ;
          result[9] = uZ;
          result[10] = -fZ;
          result[11] = 0.0;
          result[12] = t0;
          result[13] = t1;
          result[14] = t2;
          result[15] = 1.0;
          return result;
      };
  
       /**
        * Computes a Matrix4 instance representing a perspective transformation matrix.
        *
        * @param {Number} fovY The field of view along the Y axis in radians.
        * @param {Number} aspectRatio The aspect ratio.
        * @param {Number} near The distance to the near plane in meters.
        * @param {Number} far The distance to the far plane in meters.
        * @param {Matrix4} result The object in which the result will be stored.
        * @returns {Matrix4} The modified result parameter.
        *
        * @exception {DeveloperError} fovY must be in (0, PI].
        * @exception {DeveloperError} aspectRatio must be greater than zero.
        * @exception {DeveloperError} near must be greater than zero.
        * @exception {DeveloperError} far must be greater than zero.
        */
      Matrix4.computePerspectiveFieldOfView = function(fovY, aspectRatio, near, far, result) {
                  Check.typeOf.number.greaterThan('fovY', fovY, 0.0);
          Check.typeOf.number.lessThan('fovY', fovY, Math.PI);
          Check.typeOf.number.greaterThan('near', near, 0.0);
          Check.typeOf.number.greaterThan('far', far, 0.0);
          Check.typeOf.object('result', result);
          
          var bottom = Math.tan(fovY * 0.5);
  
          var column1Row1 = 1.0 / bottom;
          var column0Row0 = column1Row1 / aspectRatio;
          var column2Row2 = (far + near) / (near - far);
          var column3Row2 = (2.0 * far * near) / (near - far);
  
          result[0] = column0Row0;
          result[1] = 0.0;
          result[2] = 0.0;
          result[3] = 0.0;
          result[4] = 0.0;
          result[5] = column1Row1;
          result[6] = 0.0;
          result[7] = 0.0;
          result[8] = 0.0;
          result[9] = 0.0;
          result[10] = column2Row2;
          result[11] = -1.0;
          result[12] = 0.0;
          result[13] = 0.0;
          result[14] = column3Row2;
          result[15] = 0.0;
          return result;
      };
  
      /**
      * Computes a Matrix4 instance representing an orthographic transformation matrix.
      *
      * @param {Number} left The number of meters to the left of the camera that will be in view.
      * @param {Number} right The number of meters to the right of the camera that will be in view.
      * @param {Number} bottom The number of meters below of the camera that will be in view.
      * @param {Number} top The number of meters above of the camera that will be in view.
      * @param {Number} near The distance to the near plane in meters.
      * @param {Number} far The distance to the far plane in meters.
      * @param {Matrix4} result The object in which the result will be stored.
      * @returns {Matrix4} The modified result parameter.
      */
      Matrix4.computeOrthographicOffCenter = function(left, right, bottom, top, near, far, result) {
                  Check.typeOf.number('left', left);
          Check.typeOf.number('right', right);
          Check.typeOf.number('bottom', bottom);
          Check.typeOf.number('top', top);
          Check.typeOf.number('near', near);
          Check.typeOf.number('far', far);
          Check.typeOf.object('result', result);
          
          var a = 1.0 / (right - left);
          var b = 1.0 / (top - bottom);
          var c = 1.0 / (far - near);
  
          var tx = -(right + left) * a;
          var ty = -(top + bottom) * b;
          var tz = -(far + near) * c;
          a *= 2.0;
          b *= 2.0;
          c *= -2.0;
  
          result[0] = a;
          result[1] = 0.0;
          result[2] = 0.0;
          result[3] = 0.0;
          result[4] = 0.0;
          result[5] = b;
          result[6] = 0.0;
          result[7] = 0.0;
          result[8] = 0.0;
          result[9] = 0.0;
          result[10] = c;
          result[11] = 0.0;
          result[12] = tx;
          result[13] = ty;
          result[14] = tz;
          result[15] = 1.0;
          return result;
      };
  
      /**
       * Computes a Matrix4 instance representing an off center perspective transformation.
       *
       * @param {Number} left The number of meters to the left of the camera that will be in view.
       * @param {Number} right The number of meters to the right of the camera that will be in view.
       * @param {Number} bottom The number of meters below of the camera that will be in view.
       * @param {Number} top The number of meters above of the camera that will be in view.
       * @param {Number} near The distance to the near plane in meters.
       * @param {Number} far The distance to the far plane in meters.
       * @param {Matrix4} result The object in which the result will be stored.
       * @returns {Matrix4} The modified result parameter.
       */
      Matrix4.computePerspectiveOffCenter = function(left, right, bottom, top, near, far, result) {
                  Check.typeOf.number('left', left);
          Check.typeOf.number('right', right);
          Check.typeOf.number('bottom', bottom);
          Check.typeOf.number('top', top);
          Check.typeOf.number('near', near);
          Check.typeOf.number('far', far);
          Check.typeOf.object('result', result);
          
          var column0Row0 = 2.0 * near / (right - left);
          var column1Row1 = 2.0 * near / (top - bottom);
          var column2Row0 = (right + left) / (right - left);
          var column2Row1 = (top + bottom) / (top - bottom);
          var column2Row2 = -(far + near) / (far - near);
          var column2Row3 = -1.0;
          var column3Row2 = -2.0 * far * near / (far - near);
  
          result[0] = column0Row0;
          result[1] = 0.0;
          result[2] = 0.0;
          result[3] = 0.0;
          result[4] = 0.0;
          result[5] = column1Row1;
          result[6] = 0.0;
          result[7] = 0.0;
          result[8] = column2Row0;
          result[9] = column2Row1;
          result[10] = column2Row2;
          result[11] = column2Row3;
          result[12] = 0.0;
          result[13] = 0.0;
          result[14] = column3Row2;
          result[15] = 0.0;
          return result;
      };
  
      /**
       * Computes a Matrix4 instance representing an infinite off center perspective transformation.
       *
       * @param {Number} left The number of meters to the left of the camera that will be in view.
       * @param {Number} right The number of meters to the right of the camera that will be in view.
       * @param {Number} bottom The number of meters below of the camera that will be in view.
       * @param {Number} top The number of meters above of the camera that will be in view.
       * @param {Number} near The distance to the near plane in meters.
       * @param {Matrix4} result The object in which the result will be stored.
       * @returns {Matrix4} The modified result parameter.
       */
      Matrix4.computeInfinitePerspectiveOffCenter = function(left, right, bottom, top, near, result) {
                  Check.typeOf.number('left', left);
          Check.typeOf.number('right', right);
          Check.typeOf.number('bottom', bottom);
          Check.typeOf.number('top', top);
          Check.typeOf.number('near', near);
          Check.typeOf.object('result', result);
          
          var column0Row0 = 2.0 * near / (right - left);
          var column1Row1 = 2.0 * near / (top - bottom);
          var column2Row0 = (right + left) / (right - left);
          var column2Row1 = (top + bottom) / (top - bottom);
          var column2Row2 = -1.0;
          var column2Row3 = -1.0;
          var column3Row2 = -2.0 * near;
  
          result[0] = column0Row0;
          result[1] = 0.0;
          result[2] = 0.0;
          result[3] = 0.0;
          result[4] = 0.0;
          result[5] = column1Row1;
          result[6] = 0.0;
          result[7] = 0.0;
          result[8] = column2Row0;
          result[9] = column2Row1;
          result[10] = column2Row2;
          result[11] = column2Row3;
          result[12] = 0.0;
          result[13] = 0.0;
          result[14] = column3Row2;
          result[15] = 0.0;
          return result;
      };
  
      /**
       * Computes a Matrix4 instance that transforms from normalized device coordinates to window coordinates.
       *
       * @param {Object}[viewport = { x : 0.0, y : 0.0, width : 0.0, height : 0.0 }] The viewport's corners as shown in Example 1.
       * @param {Number}[nearDepthRange=0.0] The near plane distance in window coordinates.
       * @param {Number}[farDepthRange=1.0] The far plane distance in window coordinates.
       * @param {Matrix4} result The object in which the result will be stored.
       * @returns {Matrix4} The modified result parameter.
       *
       * @example
       * // Create viewport transformation using an explicit viewport and depth range.
       * var m = Cesium.Matrix4.computeViewportTransformation({
       *     x : 0.0,
       *     y : 0.0,
       *     width : 1024.0,
       *     height : 768.0
       * }, 0.0, 1.0, new Cesium.Matrix4());
       */
      Matrix4.computeViewportTransformation = function(viewport, nearDepthRange, farDepthRange, result) {
                  Check.typeOf.object('result', result);
          
          viewport = defaultValue(viewport, defaultValue.EMPTY_OBJECT);
          var x = defaultValue(viewport.x, 0.0);
          var y = defaultValue(viewport.y, 0.0);
          var width = defaultValue(viewport.width, 0.0);
          var height = defaultValue(viewport.height, 0.0);
          nearDepthRange = defaultValue(nearDepthRange, 0.0);
          farDepthRange = defaultValue(farDepthRange, 1.0);
  
          var halfWidth = width * 0.5;
          var halfHeight = height * 0.5;
          var halfDepth = (farDepthRange - nearDepthRange) * 0.5;
  
          var column0Row0 = halfWidth;
          var column1Row1 = halfHeight;
          var column2Row2 = halfDepth;
          var column3Row0 = x + halfWidth;
          var column3Row1 = y + halfHeight;
          var column3Row2 = nearDepthRange + halfDepth;
          var column3Row3 = 1.0;
  
          result[0] = column0Row0;
          result[1] = 0.0;
          result[2] = 0.0;
          result[3] = 0.0;
          result[4] = 0.0;
          result[5] = column1Row1;
          result[6] = 0.0;
          result[7] = 0.0;
          result[8] = 0.0;
          result[9] = 0.0;
          result[10] = column2Row2;
          result[11] = 0.0;
          result[12] = column3Row0;
          result[13] = column3Row1;
          result[14] = column3Row2;
          result[15] = column3Row3;
          return result;
      };
  
      /**
       * Computes a Matrix4 instance that transforms from world space to view space.
       *
       * @param {Cartesian3} position The position of the camera.
       * @param {Cartesian3} direction The forward direction.
       * @param {Cartesian3} up The up direction.
       * @param {Cartesian3} right The right direction.
       * @param {Matrix4} result The object in which the result will be stored.
       * @returns {Matrix4} The modified result parameter.
       */
      Matrix4.computeView = function(position, direction, up, right, result) {
                  Check.typeOf.object('position', position);
          Check.typeOf.object('direction', direction);
          Check.typeOf.object('up', up);
          Check.typeOf.object('right', right);
          Check.typeOf.object('result', result);
          
          result[0] = right.x;
          result[1] = up.x;
          result[2] = -direction.x;
          result[3] = 0.0;
          result[4] = right.y;
          result[5] = up.y;
          result[6] = -direction.y;
          result[7] = 0.0;
          result[8] = right.z;
          result[9] = up.z;
          result[10] = -direction.z;
          result[11] = 0.0;
          result[12] = -Cartesian3.dot(right, position);
          result[13] = -Cartesian3.dot(up, position);
          result[14] = Cartesian3.dot(direction, position);
          result[15] = 1.0;
          return result;
      };
  
      /**
       * Computes an Array from the provided Matrix4 instance.
       * The array will be in column-major order.
       *
       * @param {Matrix4} matrix The matrix to use..
       * @param {Number[]} [result] The Array onto which to store the result.
       * @returns {Number[]} The modified Array parameter or a new Array instance if one was not provided.
       *
       * @example
       * //create an array from an instance of Matrix4
       * // m = [10.0, 14.0, 18.0, 22.0]
       * //     [11.0, 15.0, 19.0, 23.0]
       * //     [12.0, 16.0, 20.0, 24.0]
       * //     [13.0, 17.0, 21.0, 25.0]
       * var a = Cesium.Matrix4.toArray(m);
       *
       * // m remains the same
       * //creates a = [10.0, 11.0, 12.0, 13.0, 14.0, 15.0, 16.0, 17.0, 18.0, 19.0, 20.0, 21.0, 22.0, 23.0, 24.0, 25.0]
       */
      Matrix4.toArray = function(matrix, result) {
                  Check.typeOf.object('matrix', matrix);
          
          if (!defined(result)) {
              return [matrix[0], matrix[1], matrix[2], matrix[3],
                      matrix[4], matrix[5], matrix[6], matrix[7],
                      matrix[8], matrix[9], matrix[10], matrix[11],
                      matrix[12], matrix[13], matrix[14], matrix[15]];
          }
          result[0] = matrix[0];
          result[1] = matrix[1];
          result[2] = matrix[2];
          result[3] = matrix[3];
          result[4] = matrix[4];
          result[5] = matrix[5];
          result[6] = matrix[6];
          result[7] = matrix[7];
          result[8] = matrix[8];
          result[9] = matrix[9];
          result[10] = matrix[10];
          result[11] = matrix[11];
          result[12] = matrix[12];
          result[13] = matrix[13];
          result[14] = matrix[14];
          result[15] = matrix[15];
          return result;
      };
  
      /**
       * Computes the array index of the element at the provided row and column.
       *
       * @param {Number} row The zero-based index of the row.
       * @param {Number} column The zero-based index of the column.
       * @returns {Number} The index of the element at the provided row and column.
       *
       * @exception {DeveloperError} row must be 0, 1, 2, or 3.
       * @exception {DeveloperError} column must be 0, 1, 2, or 3.
       *
       * @example
       * var myMatrix = new Cesium.Matrix4();
       * var column1Row0Index = Cesium.Matrix4.getElementIndex(1, 0);
       * var column1Row0 = myMatrix[column1Row0Index];
       * myMatrix[column1Row0Index] = 10.0;
       */
      Matrix4.getElementIndex = function(column, row) {
                  Check.typeOf.number.greaterThanOrEquals('row', row, 0);
          Check.typeOf.number.lessThanOrEquals('row', row, 3);
  
          Check.typeOf.number.greaterThanOrEquals('column', column, 0);
          Check.typeOf.number.lessThanOrEquals('column', column, 3);
          
          return column * 4 + row;
      };
  
      /**
       * Retrieves a copy of the matrix column at the provided index as a Cartesian4 instance.
       *
       * @param {Matrix4} matrix The matrix to use.
       * @param {Number} index The zero-based index of the column to retrieve.
       * @param {Cartesian4} result The object onto which to store the result.
       * @returns {Cartesian4} The modified result parameter.
       *
       * @exception {DeveloperError} index must be 0, 1, 2, or 3.
       *
       * @example
       * //returns a Cartesian4 instance with values from the specified column
       * // m = [10.0, 11.0, 12.0, 13.0]
       * //     [14.0, 15.0, 16.0, 17.0]
       * //     [18.0, 19.0, 20.0, 21.0]
       * //     [22.0, 23.0, 24.0, 25.0]
       *
       * //Example 1: Creates an instance of Cartesian
       * var a = Cesium.Matrix4.getColumn(m, 2, new Cesium.Cartesian4());
       *
       * @example
       * //Example 2: Sets values for Cartesian instance
       * var a = new Cesium.Cartesian4();
       * Cesium.Matrix4.getColumn(m, 2, a);
       *
       * // a.x = 12.0; a.y = 16.0; a.z = 20.0; a.w = 24.0;
       */
      Matrix4.getColumn = function(matrix, index, result) {
                  Check.typeOf.object('matrix', matrix);
  
          Check.typeOf.number.greaterThanOrEquals('index', index, 0);
          Check.typeOf.number.lessThanOrEquals('index', index, 3);
  
          Check.typeOf.object('result', result);
          
          var startIndex = index * 4;
          var x = matrix[startIndex];
          var y = matrix[startIndex + 1];
          var z = matrix[startIndex + 2];
          var w = matrix[startIndex + 3];
  
          result.x = x;
          result.y = y;
          result.z = z;
          result.w = w;
          return result;
      };
  
      /**
       * Computes a new matrix that replaces the specified column in the provided matrix with the provided Cartesian4 instance.
       *
       * @param {Matrix4} matrix The matrix to use.
       * @param {Number} index The zero-based index of the column to set.
       * @param {Cartesian4} cartesian The Cartesian whose values will be assigned to the specified column.
       * @param {Matrix4} result The object onto which to store the result.
       * @returns {Matrix4} The modified result parameter.
       *
       * @exception {DeveloperError} index must be 0, 1, 2, or 3.
       *
       * @example
       * //creates a new Matrix4 instance with new column values from the Cartesian4 instance
       * // m = [10.0, 11.0, 12.0, 13.0]
       * //     [14.0, 15.0, 16.0, 17.0]
       * //     [18.0, 19.0, 20.0, 21.0]
       * //     [22.0, 23.0, 24.0, 25.0]
       *
       * var a = Cesium.Matrix4.setColumn(m, 2, new Cesium.Cartesian4(99.0, 98.0, 97.0, 96.0), new Cesium.Matrix4());
       *
       * // m remains the same
       * // a = [10.0, 11.0, 99.0, 13.0]
       * //     [14.0, 15.0, 98.0, 17.0]
       * //     [18.0, 19.0, 97.0, 21.0]
       * //     [22.0, 23.0, 96.0, 25.0]
       */
      Matrix4.setColumn = function(matrix, index, cartesian, result) {
                  Check.typeOf.object('matrix', matrix);
  
          Check.typeOf.number.greaterThanOrEquals('index', index, 0);
          Check.typeOf.number.lessThanOrEquals('index', index, 3);
  
          Check.typeOf.object('cartesian', cartesian);
          Check.typeOf.object('result', result);
          
          result = Matrix4.clone(matrix, result);
          var startIndex = index * 4;
          result[startIndex] = cartesian.x;
          result[startIndex + 1] = cartesian.y;
          result[startIndex + 2] = cartesian.z;
          result[startIndex + 3] = cartesian.w;
          return result;
      };
  
      /**
       * Computes a new matrix that replaces the translation in the rightmost column of the provided
       * matrix with the provided translation.  This assumes the matrix is an affine transformation
       *
       * @param {Matrix4} matrix The matrix to use.
       * @param {Cartesian3} translation The translation that replaces the translation of the provided matrix.
       * @param {Cartesian4} result The object onto which to store the result.
       * @returns {Matrix4} The modified result parameter.
       */
      Matrix4.setTranslation = function(matrix, translation, result) {
                  Check.typeOf.object('matrix', matrix);
          Check.typeOf.object('translation', translation);
          Check.typeOf.object('result', result);
          
          result[0] = matrix[0];
          result[1] = matrix[1];
          result[2] = matrix[2];
          result[3] = matrix[3];
  
          result[4] = matrix[4];
          result[5] = matrix[5];
          result[6] = matrix[6];
          result[7] = matrix[7];
  
          result[8] = matrix[8];
          result[9] = matrix[9];
          result[10] = matrix[10];
          result[11] = matrix[11];
  
          result[12] = translation.x;
          result[13] = translation.y;
          result[14] = translation.z;
          result[15] = matrix[15];
  
          return result;
      };
  
      /**
       * Retrieves a copy of the matrix row at the provided index as a Cartesian4 instance.
       *
       * @param {Matrix4} matrix The matrix to use.
       * @param {Number} index The zero-based index of the row to retrieve.
       * @param {Cartesian4} result The object onto which to store the result.
       * @returns {Cartesian4} The modified result parameter.
       *
       * @exception {DeveloperError} index must be 0, 1, 2, or 3.
       *
       * @example
       * //returns a Cartesian4 instance with values from the specified column
       * // m = [10.0, 11.0, 12.0, 13.0]
       * //     [14.0, 15.0, 16.0, 17.0]
       * //     [18.0, 19.0, 20.0, 21.0]
       * //     [22.0, 23.0, 24.0, 25.0]
       *
       * //Example 1: Returns an instance of Cartesian
       * var a = Cesium.Matrix4.getRow(m, 2, new Cesium.Cartesian4());
       *
       * @example
       * //Example 2: Sets values for a Cartesian instance
       * var a = new Cesium.Cartesian4();
       * Cesium.Matrix4.getRow(m, 2, a);
       *
       * // a.x = 18.0; a.y = 19.0; a.z = 20.0; a.w = 21.0;
       */
      Matrix4.getRow = function(matrix, index, result) {
                  Check.typeOf.object('matrix', matrix);
  
          Check.typeOf.number.greaterThanOrEquals('index', index, 0);
          Check.typeOf.number.lessThanOrEquals('index', index, 3);
  
          Check.typeOf.object('result', result);
          
          var x = matrix[index];
          var y = matrix[index + 4];
          var z = matrix[index + 8];
          var w = matrix[index + 12];
  
          result.x = x;
          result.y = y;
          result.z = z;
          result.w = w;
          return result;
      };
  
      /**
       * Computes a new matrix that replaces the specified row in the provided matrix with the provided Cartesian4 instance.
       *
       * @param {Matrix4} matrix The matrix to use.
       * @param {Number} index The zero-based index of the row to set.
       * @param {Cartesian4} cartesian The Cartesian whose values will be assigned to the specified row.
       * @param {Matrix4} result The object onto which to store the result.
       * @returns {Matrix4} The modified result parameter.
       *
       * @exception {DeveloperError} index must be 0, 1, 2, or 3.
       *
       * @example
       * //create a new Matrix4 instance with new row values from the Cartesian4 instance
       * // m = [10.0, 11.0, 12.0, 13.0]
       * //     [14.0, 15.0, 16.0, 17.0]
       * //     [18.0, 19.0, 20.0, 21.0]
       * //     [22.0, 23.0, 24.0, 25.0]
       *
       * var a = Cesium.Matrix4.setRow(m, 2, new Cesium.Cartesian4(99.0, 98.0, 97.0, 96.0), new Cesium.Matrix4());
       *
       * // m remains the same
       * // a = [10.0, 11.0, 12.0, 13.0]
       * //     [14.0, 15.0, 16.0, 17.0]
       * //     [99.0, 98.0, 97.0, 96.0]
       * //     [22.0, 23.0, 24.0, 25.0]
       */
      Matrix4.setRow = function(matrix, index, cartesian, result) {
                  Check.typeOf.object('matrix', matrix);
  
          Check.typeOf.number.greaterThanOrEquals('index', index, 0);
          Check.typeOf.number.lessThanOrEquals('index', index, 3);
  
          Check.typeOf.object('cartesian', cartesian);
          Check.typeOf.object('result', result);
          
          result = Matrix4.clone(matrix, result);
          result[index] = cartesian.x;
          result[index + 4] = cartesian.y;
          result[index + 8] = cartesian.z;
          result[index + 12] = cartesian.w;
          return result;
      };
  
      var scratchColumn = new Cartesian3();
  
      /**
       * Extracts the non-uniform scale assuming the matrix is an affine transformation.
       *
       * @param {Matrix4} matrix The matrix.
       * @param {Cartesian3} result The object onto which to store the result.
       * @returns {Cartesian3} The modified result parameter
       */
      Matrix4.getScale = function(matrix, result) {
                  Check.typeOf.object('matrix', matrix);
          Check.typeOf.object('result', result);
          
          result.x = Cartesian3.magnitude(Cartesian3.fromElements(matrix[0], matrix[1], matrix[2], scratchColumn));
          result.y = Cartesian3.magnitude(Cartesian3.fromElements(matrix[4], matrix[5], matrix[6], scratchColumn));
          result.z = Cartesian3.magnitude(Cartesian3.fromElements(matrix[8], matrix[9], matrix[10], scratchColumn));
          return result;
      };
  
      var scratchScale = new Cartesian3();
  
      /**
       * Computes the maximum scale assuming the matrix is an affine transformation.
       * The maximum scale is the maximum length of the column vectors in the upper-left
       * 3x3 matrix.
       *
       * @param {Matrix4} matrix The matrix.
       * @returns {Number} The maximum scale.
       */
      Matrix4.getMaximumScale = function(matrix) {
          Matrix4.getScale(matrix, scratchScale);
          return Cartesian3.maximumComponent(scratchScale);
      };
  
      /**
       * Computes the product of two matrices.
       *
       * @param {Matrix4} left The first matrix.
       * @param {Matrix4} right The second matrix.
       * @param {Matrix4} result The object onto which to store the result.
       * @returns {Matrix4} The modified result parameter.
       */
      Matrix4.multiply = function(left, right, result) {
                  Check.typeOf.object('left', left);
          Check.typeOf.object('right', right);
          Check.typeOf.object('result', result);
          
          var left0 = left[0];
          var left1 = left[1];
          var left2 = left[2];
          var left3 = left[3];
          var left4 = left[4];
          var left5 = left[5];
          var left6 = left[6];
          var left7 = left[7];
          var left8 = left[8];
          var left9 = left[9];
          var left10 = left[10];
          var left11 = left[11];
          var left12 = left[12];
          var left13 = left[13];
          var left14 = left[14];
          var left15 = left[15];
  
          var right0 = right[0];
          var right1 = right[1];
          var right2 = right[2];
          var right3 = right[3];
          var right4 = right[4];
          var right5 = right[5];
          var right6 = right[6];
          var right7 = right[7];
          var right8 = right[8];
          var right9 = right[9];
          var right10 = right[10];
          var right11 = right[11];
          var right12 = right[12];
          var right13 = right[13];
          var right14 = right[14];
          var right15 = right[15];
  
          var column0Row0 = left0 * right0 + left4 * right1 + left8 * right2 + left12 * right3;
          var column0Row1 = left1 * right0 + left5 * right1 + left9 * right2 + left13 * right3;
          var column0Row2 = left2 * right0 + left6 * right1 + left10 * right2 + left14 * right3;
          var column0Row3 = left3 * right0 + left7 * right1 + left11 * right2 + left15 * right3;
  
          var column1Row0 = left0 * right4 + left4 * right5 + left8 * right6 + left12 * right7;
          var column1Row1 = left1 * right4 + left5 * right5 + left9 * right6 + left13 * right7;
          var column1Row2 = left2 * right4 + left6 * right5 + left10 * right6 + left14 * right7;
          var column1Row3 = left3 * right4 + left7 * right5 + left11 * right6 + left15 * right7;
  
          var column2Row0 = left0 * right8 + left4 * right9 + left8 * right10 + left12 * right11;
          var column2Row1 = left1 * right8 + left5 * right9 + left9 * right10 + left13 * right11;
          var column2Row2 = left2 * right8 + left6 * right9 + left10 * right10 + left14 * right11;
          var column2Row3 = left3 * right8 + left7 * right9 + left11 * right10 + left15 * right11;
  
          var column3Row0 = left0 * right12 + left4 * right13 + left8 * right14 + left12 * right15;
          var column3Row1 = left1 * right12 + left5 * right13 + left9 * right14 + left13 * right15;
          var column3Row2 = left2 * right12 + left6 * right13 + left10 * right14 + left14 * right15;
          var column3Row3 = left3 * right12 + left7 * right13 + left11 * right14 + left15 * right15;
  
          result[0] = column0Row0;
          result[1] = column0Row1;
          result[2] = column0Row2;
          result[3] = column0Row3;
          result[4] = column1Row0;
          result[5] = column1Row1;
          result[6] = column1Row2;
          result[7] = column1Row3;
          result[8] = column2Row0;
          result[9] = column2Row1;
          result[10] = column2Row2;
          result[11] = column2Row3;
          result[12] = column3Row0;
          result[13] = column3Row1;
          result[14] = column3Row2;
          result[15] = column3Row3;
          return result;
      };
  
      /**
       * Computes the sum of two matrices.
       *
       * @param {Matrix4} left The first matrix.
       * @param {Matrix4} right The second matrix.
       * @param {Matrix4} result The object onto which to store the result.
       * @returns {Matrix4} The modified result parameter.
       */
      Matrix4.add = function(left, right, result) {
                  Check.typeOf.object('left', left);
          Check.typeOf.object('right', right);
          Check.typeOf.object('result', result);
          
          result[0] = left[0] + right[0];
          result[1] = left[1] + right[1];
          result[2] = left[2] + right[2];
          result[3] = left[3] + right[3];
          result[4] = left[4] + right[4];
          result[5] = left[5] + right[5];
          result[6] = left[6] + right[6];
          result[7] = left[7] + right[7];
          result[8] = left[8] + right[8];
          result[9] = left[9] + right[9];
          result[10] = left[10] + right[10];
          result[11] = left[11] + right[11];
          result[12] = left[12] + right[12];
          result[13] = left[13] + right[13];
          result[14] = left[14] + right[14];
          result[15] = left[15] + right[15];
          return result;
      };
  
      /**
       * Computes the difference of two matrices.
       *
       * @param {Matrix4} left The first matrix.
       * @param {Matrix4} right The second matrix.
       * @param {Matrix4} result The object onto which to store the result.
       * @returns {Matrix4} The modified result parameter.
       */
      Matrix4.subtract = function(left, right, result) {
                  Check.typeOf.object('left', left);
          Check.typeOf.object('right', right);
          Check.typeOf.object('result', result);
          
          result[0] = left[0] - right[0];
          result[1] = left[1] - right[1];
          result[2] = left[2] - right[2];
          result[3] = left[3] - right[3];
          result[4] = left[4] - right[4];
          result[5] = left[5] - right[5];
          result[6] = left[6] - right[6];
          result[7] = left[7] - right[7];
          result[8] = left[8] - right[8];
          result[9] = left[9] - right[9];
          result[10] = left[10] - right[10];
          result[11] = left[11] - right[11];
          result[12] = left[12] - right[12];
          result[13] = left[13] - right[13];
          result[14] = left[14] - right[14];
          result[15] = left[15] - right[15];
          return result;
      };
  
      /**
       * Computes the product of two matrices assuming the matrices are
       * affine transformation matrices, where the upper left 3x3 elements
       * are a rotation matrix, and the upper three elements in the fourth
       * column are the translation.  The bottom row is assumed to be [0, 0, 0, 1].
       * The matrix is not verified to be in the proper form.
       * This method is faster than computing the product for general 4x4
       * matrices using {@link Matrix4.multiply}.
       *
       * @param {Matrix4} left The first matrix.
       * @param {Matrix4} right The second matrix.
       * @param {Matrix4} result The object onto which to store the result.
       * @returns {Matrix4} The modified result parameter.
       *
       * @example
       * var m1 = new Cesium.Matrix4(1.0, 6.0, 7.0, 0.0, 2.0, 5.0, 8.0, 0.0, 3.0, 4.0, 9.0, 0.0, 0.0, 0.0, 0.0, 1.0);
       * var m2 = Cesium.Transforms.eastNorthUpToFixedFrame(new Cesium.Cartesian3(1.0, 1.0, 1.0));
       * var m3 = Cesium.Matrix4.multiplyTransformation(m1, m2, new Cesium.Matrix4());
       */
      Matrix4.multiplyTransformation = function(left, right, result) {
                  Check.typeOf.object('left', left);
          Check.typeOf.object('right', right);
          Check.typeOf.object('result', result);
          
          var left0 = left[0];
          var left1 = left[1];
          var left2 = left[2];
          var left4 = left[4];
          var left5 = left[5];
          var left6 = left[6];
          var left8 = left[8];
          var left9 = left[9];
          var left10 = left[10];
          var left12 = left[12];
          var left13 = left[13];
          var left14 = left[14];
  
          var right0 = right[0];
          var right1 = right[1];
          var right2 = right[2];
          var right4 = right[4];
          var right5 = right[5];
          var right6 = right[6];
          var right8 = right[8];
          var right9 = right[9];
          var right10 = right[10];
          var right12 = right[12];
          var right13 = right[13];
          var right14 = right[14];
  
          var column0Row0 = left0 * right0 + left4 * right1 + left8 * right2;
          var column0Row1 = left1 * right0 + left5 * right1 + left9 * right2;
          var column0Row2 = left2 * right0 + left6 * right1 + left10 * right2;
  
          var column1Row0 = left0 * right4 + left4 * right5 + left8 * right6;
          var column1Row1 = left1 * right4 + left5 * right5 + left9 * right6;
          var column1Row2 = left2 * right4 + left6 * right5 + left10 * right6;
  
          var column2Row0 = left0 * right8 + left4 * right9 + left8 * right10;
          var column2Row1 = left1 * right8 + left5 * right9 + left9 * right10;
          var column2Row2 = left2 * right8 + left6 * right9 + left10 * right10;
  
          var column3Row0 = left0 * right12 + left4 * right13 + left8 * right14 + left12;
          var column3Row1 = left1 * right12 + left5 * right13 + left9 * right14 + left13;
          var column3Row2 = left2 * right12 + left6 * right13 + left10 * right14 + left14;
  
          result[0] = column0Row0;
          result[1] = column0Row1;
          result[2] = column0Row2;
          result[3] = 0.0;
          result[4] = column1Row0;
          result[5] = column1Row1;
          result[6] = column1Row2;
          result[7] = 0.0;
          result[8] = column2Row0;
          result[9] = column2Row1;
          result[10] = column2Row2;
          result[11] = 0.0;
          result[12] = column3Row0;
          result[13] = column3Row1;
          result[14] = column3Row2;
          result[15] = 1.0;
          return result;
      };
  
      /**
       * Multiplies a transformation matrix (with a bottom row of <code>[0.0, 0.0, 0.0, 1.0]</code>)
       * by a 3x3 rotation matrix.  This is an optimization
       * for <code>Matrix4.multiply(m, Matrix4.fromRotationTranslation(rotation), m);</code> with less allocations and arithmetic operations.
       *
       * @param {Matrix4} matrix The matrix on the left-hand side.
       * @param {Matrix3} rotation The 3x3 rotation matrix on the right-hand side.
       * @param {Matrix4} result The object onto which to store the result.
       * @returns {Matrix4} The modified result parameter.
       *
       * @example
       * // Instead of Cesium.Matrix4.multiply(m, Cesium.Matrix4.fromRotationTranslation(rotation), m);
       * Cesium.Matrix4.multiplyByMatrix3(m, rotation, m);
       */
      Matrix4.multiplyByMatrix3 = function(matrix, rotation, result) {
                  Check.typeOf.object('matrix', matrix);
          Check.typeOf.object('rotation', rotation);
          Check.typeOf.object('result', result);
          
          var left0 = matrix[0];
          var left1 = matrix[1];
          var left2 = matrix[2];
          var left4 = matrix[4];
          var left5 = matrix[5];
          var left6 = matrix[6];
          var left8 = matrix[8];
          var left9 = matrix[9];
          var left10 = matrix[10];
  
          var right0 = rotation[0];
          var right1 = rotation[1];
          var right2 = rotation[2];
          var right4 = rotation[3];
          var right5 = rotation[4];
          var right6 = rotation[5];
          var right8 = rotation[6];
          var right9 = rotation[7];
          var right10 = rotation[8];
  
          var column0Row0 = left0 * right0 + left4 * right1 + left8 * right2;
          var column0Row1 = left1 * right0 + left5 * right1 + left9 * right2;
          var column0Row2 = left2 * right0 + left6 * right1 + left10 * right2;
  
          var column1Row0 = left0 * right4 + left4 * right5 + left8 * right6;
          var column1Row1 = left1 * right4 + left5 * right5 + left9 * right6;
          var column1Row2 = left2 * right4 + left6 * right5 + left10 * right6;
  
          var column2Row0 = left0 * right8 + left4 * right9 + left8 * right10;
          var column2Row1 = left1 * right8 + left5 * right9 + left9 * right10;
          var column2Row2 = left2 * right8 + left6 * right9 + left10 * right10;
  
          result[0] = column0Row0;
          result[1] = column0Row1;
          result[2] = column0Row2;
          result[3] = 0.0;
          result[4] = column1Row0;
          result[5] = column1Row1;
          result[6] = column1Row2;
          result[7] = 0.0;
          result[8] = column2Row0;
          result[9] = column2Row1;
          result[10] = column2Row2;
          result[11] = 0.0;
          result[12] = matrix[12];
          result[13] = matrix[13];
          result[14] = matrix[14];
          result[15] = matrix[15];
          return result;
      };
  
      /**
       * Multiplies a transformation matrix (with a bottom row of <code>[0.0, 0.0, 0.0, 1.0]</code>)
       * by an implicit translation matrix defined by a {@link Cartesian3}.  This is an optimization
       * for <code>Matrix4.multiply(m, Matrix4.fromTranslation(position), m);</code> with less allocations and arithmetic operations.
       *
       * @param {Matrix4} matrix The matrix on the left-hand side.
       * @param {Cartesian3} translation The translation on the right-hand side.
       * @param {Matrix4} result The object onto which to store the result.
       * @returns {Matrix4} The modified result parameter.
       *
       * @example
       * // Instead of Cesium.Matrix4.multiply(m, Cesium.Matrix4.fromTranslation(position), m);
       * Cesium.Matrix4.multiplyByTranslation(m, position, m);
       */
      Matrix4.multiplyByTranslation = function(matrix, translation, result) {
                  Check.typeOf.object('matrix', matrix);
          Check.typeOf.object('translation', translation);
          Check.typeOf.object('result', result);
          
          var x = translation.x;
          var y = translation.y;
          var z = translation.z;
  
          var tx = (x * matrix[0]) + (y * matrix[4]) + (z * matrix[8]) + matrix[12];
          var ty = (x * matrix[1]) + (y * matrix[5]) + (z * matrix[9]) + matrix[13];
          var tz = (x * matrix[2]) + (y * matrix[6]) + (z * matrix[10]) + matrix[14];
  
          result[0] = matrix[0];
          result[1] = matrix[1];
          result[2] = matrix[2];
          result[3] = matrix[3];
          result[4] = matrix[4];
          result[5] = matrix[5];
          result[6] = matrix[6];
          result[7] = matrix[7];
          result[8] = matrix[8];
          result[9] = matrix[9];
          result[10] = matrix[10];
          result[11] = matrix[11];
          result[12] = tx;
          result[13] = ty;
          result[14] = tz;
          result[15] = matrix[15];
          return result;
      };
  
      var uniformScaleScratch = new Cartesian3();
  
      /**
       * Multiplies an affine transformation matrix (with a bottom row of <code>[0.0, 0.0, 0.0, 1.0]</code>)
       * by an implicit uniform scale matrix.  This is an optimization
       * for <code>Matrix4.multiply(m, Matrix4.fromUniformScale(scale), m);</code>, where
       * <code>m</code> must be an affine matrix.
       * This function performs fewer allocations and arithmetic operations.
       *
       * @param {Matrix4} matrix The affine matrix on the left-hand side.
       * @param {Number} scale The uniform scale on the right-hand side.
       * @param {Matrix4} result The object onto which to store the result.
       * @returns {Matrix4} The modified result parameter.
       *
       *
       * @example
       * // Instead of Cesium.Matrix4.multiply(m, Cesium.Matrix4.fromUniformScale(scale), m);
       * Cesium.Matrix4.multiplyByUniformScale(m, scale, m);
       *
       * @see Matrix4.fromUniformScale
       * @see Matrix4.multiplyByScale
       */
      Matrix4.multiplyByUniformScale = function(matrix, scale, result) {
                  Check.typeOf.object('matrix', matrix);
          Check.typeOf.number('scale', scale);
          Check.typeOf.object('result', result);
          
          uniformScaleScratch.x = scale;
          uniformScaleScratch.y = scale;
          uniformScaleScratch.z = scale;
          return Matrix4.multiplyByScale(matrix, uniformScaleScratch, result);
      };
  
      /**
       * Multiplies an affine transformation matrix (with a bottom row of <code>[0.0, 0.0, 0.0, 1.0]</code>)
       * by an implicit non-uniform scale matrix.  This is an optimization
       * for <code>Matrix4.multiply(m, Matrix4.fromUniformScale(scale), m);</code>, where
       * <code>m</code> must be an affine matrix.
       * This function performs fewer allocations and arithmetic operations.
       *
       * @param {Matrix4} matrix The affine matrix on the left-hand side.
       * @param {Cartesian3} scale The non-uniform scale on the right-hand side.
       * @param {Matrix4} result The object onto which to store the result.
       * @returns {Matrix4} The modified result parameter.
       *
       *
       * @example
       * // Instead of Cesium.Matrix4.multiply(m, Cesium.Matrix4.fromScale(scale), m);
       * Cesium.Matrix4.multiplyByScale(m, scale, m);
       *
       * @see Matrix4.fromScale
       * @see Matrix4.multiplyByUniformScale
       */
      Matrix4.multiplyByScale = function(matrix, scale, result) {
                  Check.typeOf.object('matrix', matrix);
          Check.typeOf.object('scale', scale);
          Check.typeOf.object('result', result);
          
          var scaleX = scale.x;
          var scaleY = scale.y;
          var scaleZ = scale.z;
  
          // Faster than Cartesian3.equals
          if ((scaleX === 1.0) && (scaleY === 1.0) && (scaleZ === 1.0)) {
              return Matrix4.clone(matrix, result);
          }
  
          result[0] = scaleX * matrix[0];
          result[1] = scaleX * matrix[1];
          result[2] = scaleX * matrix[2];
          result[3] = 0.0;
          result[4] = scaleY * matrix[4];
          result[5] = scaleY * matrix[5];
          result[6] = scaleY * matrix[6];
          result[7] = 0.0;
          result[8] = scaleZ * matrix[8];
          result[9] = scaleZ * matrix[9];
          result[10] = scaleZ * matrix[10];
          result[11] = 0.0;
          result[12] = matrix[12];
          result[13] = matrix[13];
          result[14] = matrix[14];
          result[15] = 1.0;
          return result;
      };
  
      /**
       * Computes the product of a matrix and a column vector.
       *
       * @param {Matrix4} matrix The matrix.
       * @param {Cartesian4} cartesian The vector.
       * @param {Cartesian4} result The object onto which to store the result.
       * @returns {Cartesian4} The modified result parameter.
       */
      Matrix4.multiplyByVector = function(matrix, cartesian, result) {
                  Check.typeOf.object('matrix', matrix);
          Check.typeOf.object('cartesian', cartesian);
          Check.typeOf.object('result', result);
          
          var vX = cartesian.x;
          var vY = cartesian.y;
          var vZ = cartesian.z;
          var vW = cartesian.w;
  
          var x = matrix[0] * vX + matrix[4] * vY + matrix[8] * vZ + matrix[12] * vW;
          var y = matrix[1] * vX + matrix[5] * vY + matrix[9] * vZ + matrix[13] * vW;
          var z = matrix[2] * vX + matrix[6] * vY + matrix[10] * vZ + matrix[14] * vW;
          var w = matrix[3] * vX + matrix[7] * vY + matrix[11] * vZ + matrix[15] * vW;
  
          result.x = x;
          result.y = y;
          result.z = z;
          result.w = w;
          return result;
      };
  
      /**
       * Computes the product of a matrix and a {@link Cartesian3}.  This is equivalent to calling {@link Matrix4.multiplyByVector}
       * with a {@link Cartesian4} with a <code>w</code> component of zero.
       *
       * @param {Matrix4} matrix The matrix.
       * @param {Cartesian3} cartesian The point.
       * @param {Cartesian3} result The object onto which to store the result.
       * @returns {Cartesian3} The modified result parameter.
       *
       * @example
       * var p = new Cesium.Cartesian3(1.0, 2.0, 3.0);
       * var result = Cesium.Matrix4.multiplyByPointAsVector(matrix, p, new Cesium.Cartesian3());
       * // A shortcut for
       * //   Cartesian3 p = ...
       * //   Cesium.Matrix4.multiplyByVector(matrix, new Cesium.Cartesian4(p.x, p.y, p.z, 0.0), result);
       */
      Matrix4.multiplyByPointAsVector = function(matrix, cartesian, result) {
                  Check.typeOf.object('matrix', matrix);
          Check.typeOf.object('cartesian', cartesian);
          Check.typeOf.object('result', result);
          
          var vX = cartesian.x;
          var vY = cartesian.y;
          var vZ = cartesian.z;
  
          var x = matrix[0] * vX + matrix[4] * vY + matrix[8] * vZ;
          var y = matrix[1] * vX + matrix[5] * vY + matrix[9] * vZ;
          var z = matrix[2] * vX + matrix[6] * vY + matrix[10] * vZ;
  
          result.x = x;
          result.y = y;
          result.z = z;
          return result;
      };
  
      /**
       * Computes the product of a matrix and a {@link Cartesian3}. This is equivalent to calling {@link Matrix4.multiplyByVector}
       * with a {@link Cartesian4} with a <code>w</code> component of 1, but returns a {@link Cartesian3} instead of a {@link Cartesian4}.
       *
       * @param {Matrix4} matrix The matrix.
       * @param {Cartesian3} cartesian The point.
       * @param {Cartesian3} result The object onto which to store the result.
       * @returns {Cartesian3} The modified result parameter.
       *
       * @example
       * var p = new Cesium.Cartesian3(1.0, 2.0, 3.0);
       * var result = Cesium.Matrix4.multiplyByPoint(matrix, p, new Cesium.Cartesian3());
       */
      Matrix4.multiplyByPoint = function(matrix, cartesian, result) {
                  Check.typeOf.object('matrix', matrix);
          Check.typeOf.object('cartesian', cartesian);
          Check.typeOf.object('result', result);
          
          var vX = cartesian.x;
          var vY = cartesian.y;
          var vZ = cartesian.z;
  
          var x = matrix[0] * vX + matrix[4] * vY + matrix[8] * vZ + matrix[12];
          var y = matrix[1] * vX + matrix[5] * vY + matrix[9] * vZ + matrix[13];
          var z = matrix[2] * vX + matrix[6] * vY + matrix[10] * vZ + matrix[14];
  
          result.x = x;
          result.y = y;
          result.z = z;
          return result;
      };
  
      /**
       * Computes the product of a matrix and a scalar.
       *
       * @param {Matrix4} matrix The matrix.
       * @param {Number} scalar The number to multiply by.
       * @param {Matrix4} result The object onto which to store the result.
       * @returns {Matrix4} The modified result parameter.
       *
       * @example
       * //create a Matrix4 instance which is a scaled version of the supplied Matrix4
       * // m = [10.0, 11.0, 12.0, 13.0]
       * //     [14.0, 15.0, 16.0, 17.0]
       * //     [18.0, 19.0, 20.0, 21.0]
       * //     [22.0, 23.0, 24.0, 25.0]
       *
       * var a = Cesium.Matrix4.multiplyByScalar(m, -2, new Cesium.Matrix4());
       *
       * // m remains the same
       * // a = [-20.0, -22.0, -24.0, -26.0]
       * //     [-28.0, -30.0, -32.0, -34.0]
       * //     [-36.0, -38.0, -40.0, -42.0]
       * //     [-44.0, -46.0, -48.0, -50.0]
       */
      Matrix4.multiplyByScalar = function(matrix, scalar, result) {
                  Check.typeOf.object('matrix', matrix);
          Check.typeOf.number('scalar', scalar);
          Check.typeOf.object('result', result);
          
          result[0] = matrix[0] * scalar;
          result[1] = matrix[1] * scalar;
          result[2] = matrix[2] * scalar;
          result[3] = matrix[3] * scalar;
          result[4] = matrix[4] * scalar;
          result[5] = matrix[5] * scalar;
          result[6] = matrix[6] * scalar;
          result[7] = matrix[7] * scalar;
          result[8] = matrix[8] * scalar;
          result[9] = matrix[9] * scalar;
          result[10] = matrix[10] * scalar;
          result[11] = matrix[11] * scalar;
          result[12] = matrix[12] * scalar;
          result[13] = matrix[13] * scalar;
          result[14] = matrix[14] * scalar;
          result[15] = matrix[15] * scalar;
          return result;
      };
  
      /**
       * Computes a negated copy of the provided matrix.
       *
       * @param {Matrix4} matrix The matrix to negate.
       * @param {Matrix4} result The object onto which to store the result.
       * @returns {Matrix4} The modified result parameter.
       *
       * @example
       * //create a new Matrix4 instance which is a negation of a Matrix4
       * // m = [10.0, 11.0, 12.0, 13.0]
       * //     [14.0, 15.0, 16.0, 17.0]
       * //     [18.0, 19.0, 20.0, 21.0]
       * //     [22.0, 23.0, 24.0, 25.0]
       *
       * var a = Cesium.Matrix4.negate(m, new Cesium.Matrix4());
       *
       * // m remains the same
       * // a = [-10.0, -11.0, -12.0, -13.0]
       * //     [-14.0, -15.0, -16.0, -17.0]
       * //     [-18.0, -19.0, -20.0, -21.0]
       * //     [-22.0, -23.0, -24.0, -25.0]
       */
      Matrix4.negate = function(matrix, result) {
                  Check.typeOf.object('matrix', matrix);
          Check.typeOf.object('result', result);
          
          result[0] = -matrix[0];
          result[1] = -matrix[1];
          result[2] = -matrix[2];
          result[3] = -matrix[3];
          result[4] = -matrix[4];
          result[5] = -matrix[5];
          result[6] = -matrix[6];
          result[7] = -matrix[7];
          result[8] = -matrix[8];
          result[9] = -matrix[9];
          result[10] = -matrix[10];
          result[11] = -matrix[11];
          result[12] = -matrix[12];
          result[13] = -matrix[13];
          result[14] = -matrix[14];
          result[15] = -matrix[15];
          return result;
      };
  
      /**
       * Computes the transpose of the provided matrix.
       *
       * @param {Matrix4} matrix The matrix to transpose.
       * @param {Matrix4} result The object onto which to store the result.
       * @returns {Matrix4} The modified result parameter.
       *
       * @example
       * //returns transpose of a Matrix4
       * // m = [10.0, 11.0, 12.0, 13.0]
       * //     [14.0, 15.0, 16.0, 17.0]
       * //     [18.0, 19.0, 20.0, 21.0]
       * //     [22.0, 23.0, 24.0, 25.0]
       *
       * var a = Cesium.Matrix4.transpose(m, new Cesium.Matrix4());
       *
       * // m remains the same
       * // a = [10.0, 14.0, 18.0, 22.0]
       * //     [11.0, 15.0, 19.0, 23.0]
       * //     [12.0, 16.0, 20.0, 24.0]
       * //     [13.0, 17.0, 21.0, 25.0]
       */
      Matrix4.transpose = function(matrix, result) {
                  Check.typeOf.object('matrix', matrix);
          Check.typeOf.object('result', result);
          
          var matrix1 = matrix[1];
          var matrix2 = matrix[2];
          var matrix3 = matrix[3];
          var matrix6 = matrix[6];
          var matrix7 = matrix[7];
          var matrix11 = matrix[11];
  
          result[0] = matrix[0];
          result[1] = matrix[4];
          result[2] = matrix[8];
          result[3] = matrix[12];
          result[4] = matrix1;
          result[5] = matrix[5];
          result[6] = matrix[9];
          result[7] = matrix[13];
          result[8] = matrix2;
          result[9] = matrix6;
          result[10] = matrix[10];
          result[11] = matrix[14];
          result[12] = matrix3;
          result[13] = matrix7;
          result[14] = matrix11;
          result[15] = matrix[15];
          return result;
      };
  
      /**
       * Computes a matrix, which contains the absolute (unsigned) values of the provided matrix's elements.
       *
       * @param {Matrix4} matrix The matrix with signed elements.
       * @param {Matrix4} result The object onto which to store the result.
       * @returns {Matrix4} The modified result parameter.
       */
      Matrix4.abs = function(matrix, result) {
                  Check.typeOf.object('matrix', matrix);
          Check.typeOf.object('result', result);
          
          result[0] = Math.abs(matrix[0]);
          result[1] = Math.abs(matrix[1]);
          result[2] = Math.abs(matrix[2]);
          result[3] = Math.abs(matrix[3]);
          result[4] = Math.abs(matrix[4]);
          result[5] = Math.abs(matrix[5]);
          result[6] = Math.abs(matrix[6]);
          result[7] = Math.abs(matrix[7]);
          result[8] = Math.abs(matrix[8]);
          result[9] = Math.abs(matrix[9]);
          result[10] = Math.abs(matrix[10]);
          result[11] = Math.abs(matrix[11]);
          result[12] = Math.abs(matrix[12]);
          result[13] = Math.abs(matrix[13]);
          result[14] = Math.abs(matrix[14]);
          result[15] = Math.abs(matrix[15]);
  
          return result;
      };
  
      /**
       * Compares the provided matrices componentwise and returns
       * <code>true</code> if they are equal, <code>false</code> otherwise.
       *
       * @param {Matrix4} [left] The first matrix.
       * @param {Matrix4} [right] The second matrix.
       * @returns {Boolean} <code>true</code> if left and right are equal, <code>false</code> otherwise.
       *
       * @example
       * //compares two Matrix4 instances
       *
       * // a = [10.0, 14.0, 18.0, 22.0]
       * //     [11.0, 15.0, 19.0, 23.0]
       * //     [12.0, 16.0, 20.0, 24.0]
       * //     [13.0, 17.0, 21.0, 25.0]
       *
       * // b = [10.0, 14.0, 18.0, 22.0]
       * //     [11.0, 15.0, 19.0, 23.0]
       * //     [12.0, 16.0, 20.0, 24.0]
       * //     [13.0, 17.0, 21.0, 25.0]
       *
       * if(Cesium.Matrix4.equals(a,b)) {
       *      console.log("Both matrices are equal");
       * } else {
       *      console.log("They are not equal");
       * }
       *
       * //Prints "Both matrices are equal" on the console
       */
      Matrix4.equals = function(left, right) {
          // Given that most matrices will be transformation matrices, the elements
          // are tested in order such that the test is likely to fail as early
          // as possible.  I _think_ this is just as friendly to the L1 cache
          // as testing in index order.  It is certainty faster in practice.
          return (left === right) ||
                 (defined(left) &&
                  defined(right) &&
                  // Translation
                  left[12] === right[12] &&
                  left[13] === right[13] &&
                  left[14] === right[14] &&
  
                  // Rotation/scale
                  left[0] === right[0] &&
                  left[1] === right[1] &&
                  left[2] === right[2] &&
                  left[4] === right[4] &&
                  left[5] === right[5] &&
                  left[6] === right[6] &&
                  left[8] === right[8] &&
                  left[9] === right[9] &&
                  left[10] === right[10] &&
  
                  // Bottom row
                  left[3] === right[3] &&
                  left[7] === right[7] &&
                  left[11] === right[11] &&
                  left[15] === right[15]);
      };
  
      /**
       * Compares the provided matrices componentwise and returns
       * <code>true</code> if they are within the provided epsilon,
       * <code>false</code> otherwise.
       *
       * @param {Matrix4} [left] The first matrix.
       * @param {Matrix4} [right] The second matrix.
       * @param {Number} epsilon The epsilon to use for equality testing.
       * @returns {Boolean} <code>true</code> if left and right are within the provided epsilon, <code>false</code> otherwise.
       *
       * @example
       * //compares two Matrix4 instances
       *
       * // a = [10.5, 14.5, 18.5, 22.5]
       * //     [11.5, 15.5, 19.5, 23.5]
       * //     [12.5, 16.5, 20.5, 24.5]
       * //     [13.5, 17.5, 21.5, 25.5]
       *
       * // b = [10.0, 14.0, 18.0, 22.0]
       * //     [11.0, 15.0, 19.0, 23.0]
       * //     [12.0, 16.0, 20.0, 24.0]
       * //     [13.0, 17.0, 21.0, 25.0]
       *
       * if(Cesium.Matrix4.equalsEpsilon(a,b,0.1)){
       *      console.log("Difference between both the matrices is less than 0.1");
       * } else {
       *      console.log("Difference between both the matrices is not less than 0.1");
       * }
       *
       * //Prints "Difference between both the matrices is not less than 0.1" on the console
       */
      Matrix4.equalsEpsilon = function(left, right, epsilon) {
                  Check.typeOf.number('epsilon', epsilon);
          
          return (left === right) ||
                  (defined(left) &&
                  defined(right) &&
                  Math.abs(left[0] - right[0]) <= epsilon &&
                  Math.abs(left[1] - right[1]) <= epsilon &&
                  Math.abs(left[2] - right[2]) <= epsilon &&
                  Math.abs(left[3] - right[3]) <= epsilon &&
                  Math.abs(left[4] - right[4]) <= epsilon &&
                  Math.abs(left[5] - right[5]) <= epsilon &&
                  Math.abs(left[6] - right[6]) <= epsilon &&
                  Math.abs(left[7] - right[7]) <= epsilon &&
                  Math.abs(left[8] - right[8]) <= epsilon &&
                  Math.abs(left[9] - right[9]) <= epsilon &&
                  Math.abs(left[10] - right[10]) <= epsilon &&
                  Math.abs(left[11] - right[11]) <= epsilon &&
                  Math.abs(left[12] - right[12]) <= epsilon &&
                  Math.abs(left[13] - right[13]) <= epsilon &&
                  Math.abs(left[14] - right[14]) <= epsilon &&
                  Math.abs(left[15] - right[15]) <= epsilon);
      };
  
      /**
       * Gets the translation portion of the provided matrix, assuming the matrix is a affine transformation matrix.
       *
       * @param {Matrix4} matrix The matrix to use.
       * @param {Cartesian3} result The object onto which to store the result.
       * @returns {Cartesian3} The modified result parameter.
       */
      Matrix4.getTranslation = function(matrix, result) {
                  Check.typeOf.object('matrix', matrix);
          Check.typeOf.object('result', result);
          
          result.x = matrix[12];
          result.y = matrix[13];
          result.z = matrix[14];
          return result;
      };
  
      /**
       * Gets the upper left 3x3 rotation matrix of the provided matrix, assuming the matrix is a affine transformation matrix.
       *
       * @param {Matrix4} matrix The matrix to use.
       * @param {Matrix3} result The object onto which to store the result.
       * @returns {Matrix3} The modified result parameter.
       *
       * @example
       * // returns a Matrix3 instance from a Matrix4 instance
       *
       * // m = [10.0, 14.0, 18.0, 22.0]
       * //     [11.0, 15.0, 19.0, 23.0]
       * //     [12.0, 16.0, 20.0, 24.0]
       * //     [13.0, 17.0, 21.0, 25.0]
       *
       * var b = new Cesium.Matrix3();
       * Cesium.Matrix4.getRotation(m,b);
       *
       * // b = [10.0, 14.0, 18.0]
       * //     [11.0, 15.0, 19.0]
       * //     [12.0, 16.0, 20.0]
       */
      Matrix4.getRotation = function(matrix, result) {
                  Check.typeOf.object('matrix', matrix);
          Check.typeOf.object('result', result);
          
          result[0] = matrix[0];
          result[1] = matrix[1];
          result[2] = matrix[2];
          result[3] = matrix[4];
          result[4] = matrix[5];
          result[5] = matrix[6];
          result[6] = matrix[8];
          result[7] = matrix[9];
          result[8] = matrix[10];
          return result;
      };
  
      var scratchInverseRotation = new Matrix3();
      var scratchMatrix3Zero = new Matrix3();
      var scratchBottomRow = new Cartesian4();
      var scratchExpectedBottomRow = new Cartesian4(0.0, 0.0, 0.0, 1.0);
  
       /**
        * Computes the inverse of the provided matrix using Cramers Rule.
        * If the determinant is zero, the matrix can not be inverted, and an exception is thrown.
        * If the matrix is an affine transformation matrix, it is more efficient
        * to invert it with {@link Matrix4.inverseTransformation}.
        *
        * @param {Matrix4} matrix The matrix to invert.
        * @param {Matrix4} result The object onto which to store the result.
        * @returns {Matrix4} The modified result parameter.
        *
        * @exception {RuntimeError} matrix is not invertible because its determinate is zero.
        */
      Matrix4.inverse = function(matrix, result) {
                  Check.typeOf.object('matrix', matrix);
          Check.typeOf.object('result', result);
          
          // Special case for a zero scale matrix that can occur, for example,
          // when a model's node has a [0, 0, 0] scale.
          if (Matrix3.equalsEpsilon(Matrix4.getRotation(matrix, scratchInverseRotation), scratchMatrix3Zero, CesiumMath.EPSILON7) &&
              Cartesian4.equals(Matrix4.getRow(matrix, 3, scratchBottomRow), scratchExpectedBottomRow)) {
  
              result[0] = 0.0;
              result[1] = 0.0;
              result[2] = 0.0;
              result[3] = 0.0;
              result[4] = 0.0;
              result[5] = 0.0;
              result[6] = 0.0;
              result[7] = 0.0;
              result[8] = 0.0;
              result[9] = 0.0;
              result[10] = 0.0;
              result[11] = 0.0;
              result[12] = -matrix[12];
              result[13] = -matrix[13];
              result[14] = -matrix[14];
              result[15] = 1.0;
              return result;
          }
  
          //
          // Ported from:
          //   ftp://download.intel.com/design/PentiumIII/sml/24504301.pdf
          //
          var src0 = matrix[0];
          var src1 = matrix[4];
          var src2 = matrix[8];
          var src3 = matrix[12];
          var src4 = matrix[1];
          var src5 = matrix[5];
          var src6 = matrix[9];
          var src7 = matrix[13];
          var src8 = matrix[2];
          var src9 = matrix[6];
          var src10 = matrix[10];
          var src11 = matrix[14];
          var src12 = matrix[3];
          var src13 = matrix[7];
          var src14 = matrix[11];
          var src15 = matrix[15];
  
          // calculate pairs for first 8 elements (cofactors)
          var tmp0 = src10 * src15;
          var tmp1 = src11 * src14;
          var tmp2 = src9 * src15;
          var tmp3 = src11 * src13;
          var tmp4 = src9 * src14;
          var tmp5 = src10 * src13;
          var tmp6 = src8 * src15;
          var tmp7 = src11 * src12;
          var tmp8 = src8 * src14;
          var tmp9 = src10 * src12;
          var tmp10 = src8 * src13;
          var tmp11 = src9 * src12;
  
          // calculate first 8 elements (cofactors)
          var dst0 = (tmp0 * src5 + tmp3 * src6 + tmp4 * src7) - (tmp1 * src5 + tmp2 * src6 + tmp5 * src7);
          var dst1 = (tmp1 * src4 + tmp6 * src6 + tmp9 * src7) - (tmp0 * src4 + tmp7 * src6 + tmp8 * src7);
          var dst2 = (tmp2 * src4 + tmp7 * src5 + tmp10 * src7) - (tmp3 * src4 + tmp6 * src5 + tmp11 * src7);
          var dst3 = (tmp5 * src4 + tmp8 * src5 + tmp11 * src6) - (tmp4 * src4 + tmp9 * src5 + tmp10 * src6);
          var dst4 = (tmp1 * src1 + tmp2 * src2 + tmp5 * src3) - (tmp0 * src1 + tmp3 * src2 + tmp4 * src3);
          var dst5 = (tmp0 * src0 + tmp7 * src2 + tmp8 * src3) - (tmp1 * src0 + tmp6 * src2 + tmp9 * src3);
          var dst6 = (tmp3 * src0 + tmp6 * src1 + tmp11 * src3) - (tmp2 * src0 + tmp7 * src1 + tmp10 * src3);
          var dst7 = (tmp4 * src0 + tmp9 * src1 + tmp10 * src2) - (tmp5 * src0 + tmp8 * src1 + tmp11 * src2);
  
          // calculate pairs for second 8 elements (cofactors)
          tmp0 = src2 * src7;
          tmp1 = src3 * src6;
          tmp2 = src1 * src7;
          tmp3 = src3 * src5;
          tmp4 = src1 * src6;
          tmp5 = src2 * src5;
          tmp6 = src0 * src7;
          tmp7 = src3 * src4;
          tmp8 = src0 * src6;
          tmp9 = src2 * src4;
          tmp10 = src0 * src5;
          tmp11 = src1 * src4;
  
          // calculate second 8 elements (cofactors)
          var dst8 = (tmp0 * src13 + tmp3 * src14 + tmp4 * src15) - (tmp1 * src13 + tmp2 * src14 + tmp5 * src15);
          var dst9 = (tmp1 * src12 + tmp6 * src14 + tmp9 * src15) - (tmp0 * src12 + tmp7 * src14 + tmp8 * src15);
          var dst10 = (tmp2 * src12 + tmp7 * src13 + tmp10 * src15) - (tmp3 * src12 + tmp6 * src13 + tmp11 * src15);
          var dst11 = (tmp5 * src12 + tmp8 * src13 + tmp11 * src14) - (tmp4 * src12 + tmp9 * src13 + tmp10 * src14);
          var dst12 = (tmp2 * src10 + tmp5 * src11 + tmp1 * src9) - (tmp4 * src11 + tmp0 * src9 + tmp3 * src10);
          var dst13 = (tmp8 * src11 + tmp0 * src8 + tmp7 * src10) - (tmp6 * src10 + tmp9 * src11 + tmp1 * src8);
          var dst14 = (tmp6 * src9 + tmp11 * src11 + tmp3 * src8) - (tmp10 * src11 + tmp2 * src8 + tmp7 * src9);
          var dst15 = (tmp10 * src10 + tmp4 * src8 + tmp9 * src9) - (tmp8 * src9 + tmp11 * src10 + tmp5 * src8);
  
          // calculate determinant
          var det = src0 * dst0 + src1 * dst1 + src2 * dst2 + src3 * dst3;
  
          if (Math.abs(det) < CesiumMath.EPSILON20) {
              throw new RuntimeError('matrix is not invertible because its determinate is zero.');
          }
  
          // calculate matrix inverse
          det = 1.0 / det;
  
          result[0] = dst0 * det;
          result[1] = dst1 * det;
          result[2] = dst2 * det;
          result[3] = dst3 * det;
          result[4] = dst4 * det;
          result[5] = dst5 * det;
          result[6] = dst6 * det;
          result[7] = dst7 * det;
          result[8] = dst8 * det;
          result[9] = dst9 * det;
          result[10] = dst10 * det;
          result[11] = dst11 * det;
          result[12] = dst12 * det;
          result[13] = dst13 * det;
          result[14] = dst14 * det;
          result[15] = dst15 * det;
          return result;
      };
  
      /**
       * Computes the inverse of the provided matrix assuming it is
       * an affine transformation matrix, where the upper left 3x3 elements
       * are a rotation matrix, and the upper three elements in the fourth
       * column are the translation.  The bottom row is assumed to be [0, 0, 0, 1].
       * The matrix is not verified to be in the proper form.
       * This method is faster than computing the inverse for a general 4x4
       * matrix using {@link Matrix4.inverse}.
       *
       * @param {Matrix4} matrix The matrix to invert.
       * @param {Matrix4} result The object onto which to store the result.
       * @returns {Matrix4} The modified result parameter.
       */
      Matrix4.inverseTransformation = function(matrix, result) {
                  Check.typeOf.object('matrix', matrix);
          Check.typeOf.object('result', result);
          
          //This function is an optimized version of the below 4 lines.
          //var rT = Matrix3.transpose(Matrix4.getRotation(matrix));
          //var rTN = Matrix3.negate(rT);
          //var rTT = Matrix3.multiplyByVector(rTN, Matrix4.getTranslation(matrix));
          //return Matrix4.fromRotationTranslation(rT, rTT, result);
  
          var matrix0 = matrix[0];
          var matrix1 = matrix[1];
          var matrix2 = matrix[2];
          var matrix4 = matrix[4];
          var matrix5 = matrix[5];
          var matrix6 = matrix[6];
          var matrix8 = matrix[8];
          var matrix9 = matrix[9];
          var matrix10 = matrix[10];
  
          var vX = matrix[12];
          var vY = matrix[13];
          var vZ = matrix[14];
  
          var x = -matrix0 * vX - matrix1 * vY - matrix2 * vZ;
          var y = -matrix4 * vX - matrix5 * vY - matrix6 * vZ;
          var z = -matrix8 * vX - matrix9 * vY - matrix10 * vZ;
  
          result[0] = matrix0;
          result[1] = matrix4;
          result[2] = matrix8;
          result[3] = 0.0;
          result[4] = matrix1;
          result[5] = matrix5;
          result[6] = matrix9;
          result[7] = 0.0;
          result[8] = matrix2;
          result[9] = matrix6;
          result[10] = matrix10;
          result[11] = 0.0;
          result[12] = x;
          result[13] = y;
          result[14] = z;
          result[15] = 1.0;
          return result;
      };
  
      /**
       * An immutable Matrix4 instance initialized to the identity matrix.
       *
       * @type {Matrix4}
       * @constant
       */
      Matrix4.IDENTITY = freezeObject(new Matrix4(1.0, 0.0, 0.0, 0.0,
                                                  0.0, 1.0, 0.0, 0.0,
                                                  0.0, 0.0, 1.0, 0.0,
                                                  0.0, 0.0, 0.0, 1.0));
  
      /**
       * An immutable Matrix4 instance initialized to the zero matrix.
       *
       * @type {Matrix4}
       * @constant
       */
      Matrix4.ZERO = freezeObject(new Matrix4(0.0, 0.0, 0.0, 0.0,
                                              0.0, 0.0, 0.0, 0.0,
                                              0.0, 0.0, 0.0, 0.0,
                                              0.0, 0.0, 0.0, 0.0));
  
      /**
       * The index into Matrix4 for column 0, row 0.
       *
       * @type {Number}
       * @constant
       */
      Matrix4.COLUMN0ROW0 = 0;
  
      /**
       * The index into Matrix4 for column 0, row 1.
       *
       * @type {Number}
       * @constant
       */
      Matrix4.COLUMN0ROW1 = 1;
  
      /**
       * The index into Matrix4 for column 0, row 2.
       *
       * @type {Number}
       * @constant
       */
      Matrix4.COLUMN0ROW2 = 2;
  
      /**
       * The index into Matrix4 for column 0, row 3.
       *
       * @type {Number}
       * @constant
       */
      Matrix4.COLUMN0ROW3 = 3;
  
      /**
       * The index into Matrix4 for column 1, row 0.
       *
       * @type {Number}
       * @constant
       */
      Matrix4.COLUMN1ROW0 = 4;
  
      /**
       * The index into Matrix4 for column 1, row 1.
       *
       * @type {Number}
       * @constant
       */
      Matrix4.COLUMN1ROW1 = 5;
  
      /**
       * The index into Matrix4 for column 1, row 2.
       *
       * @type {Number}
       * @constant
       */
      Matrix4.COLUMN1ROW2 = 6;
  
      /**
       * The index into Matrix4 for column 1, row 3.
       *
       * @type {Number}
       * @constant
       */
      Matrix4.COLUMN1ROW3 = 7;
  
      /**
       * The index into Matrix4 for column 2, row 0.
       *
       * @type {Number}
       * @constant
       */
      Matrix4.COLUMN2ROW0 = 8;
  
      /**
       * The index into Matrix4 for column 2, row 1.
       *
       * @type {Number}
       * @constant
       */
      Matrix4.COLUMN2ROW1 = 9;
  
      /**
       * The index into Matrix4 for column 2, row 2.
       *
       * @type {Number}
       * @constant
       */
      Matrix4.COLUMN2ROW2 = 10;
  
      /**
       * The index into Matrix4 for column 2, row 3.
       *
       * @type {Number}
       * @constant
       */
      Matrix4.COLUMN2ROW3 = 11;
  
      /**
       * The index into Matrix4 for column 3, row 0.
       *
       * @type {Number}
       * @constant
       */
      Matrix4.COLUMN3ROW0 = 12;
  
      /**
       * The index into Matrix4 for column 3, row 1.
       *
       * @type {Number}
       * @constant
       */
      Matrix4.COLUMN3ROW1 = 13;
  
      /**
       * The index into Matrix4 for column 3, row 2.
       *
       * @type {Number}
       * @constant
       */
      Matrix4.COLUMN3ROW2 = 14;
  
      /**
       * The index into Matrix4 for column 3, row 3.
       *
       * @type {Number}
       * @constant
       */
      Matrix4.COLUMN3ROW3 = 15;
  
      defineProperties(Matrix4.prototype, {
          /**
           * Gets the number of items in the collection.
           * @memberof Matrix4.prototype
           *
           * @type {Number}
           */
          length : {
              get : function() {
                  return Matrix4.packedLength;
              }
          }
      });
  
      /**
       * Duplicates the provided Matrix4 instance.
       *
       * @param {Matrix4} [result] The object onto which to store the result.
       * @returns {Matrix4} The modified result parameter or a new Matrix4 instance if one was not provided.
       */
      Matrix4.prototype.clone = function(result) {
          return Matrix4.clone(this, result);
      };
  
      /**
       * Compares this matrix to the provided matrix componentwise and returns
       * <code>true</code> if they are equal, <code>false</code> otherwise.
       *
       * @param {Matrix4} [right] The right hand side matrix.
       * @returns {Boolean} <code>true</code> if they are equal, <code>false</code> otherwise.
       */
      Matrix4.prototype.equals = function(right) {
          return Matrix4.equals(this, right);
      };
  
      /**
       * @private
       */
      Matrix4.equalsArray = function(matrix, array, offset) {
          return matrix[0] === array[offset] &&
                 matrix[1] === array[offset + 1] &&
                 matrix[2] === array[offset + 2] &&
                 matrix[3] === array[offset + 3] &&
                 matrix[4] === array[offset + 4] &&
                 matrix[5] === array[offset + 5] &&
                 matrix[6] === array[offset + 6] &&
                 matrix[7] === array[offset + 7] &&
                 matrix[8] === array[offset + 8] &&
                 matrix[9] === array[offset + 9] &&
                 matrix[10] === array[offset + 10] &&
                 matrix[11] === array[offset + 11] &&
                 matrix[12] === array[offset + 12] &&
                 matrix[13] === array[offset + 13] &&
                 matrix[14] === array[offset + 14] &&
                 matrix[15] === array[offset + 15];
      };
  
      /**
       * Compares this matrix to the provided matrix componentwise and returns
       * <code>true</code> if they are within the provided epsilon,
       * <code>false</code> otherwise.
       *
       * @param {Matrix4} [right] The right hand side matrix.
       * @param {Number} epsilon The epsilon to use for equality testing.
       * @returns {Boolean} <code>true</code> if they are within the provided epsilon, <code>false</code> otherwise.
       */
      Matrix4.prototype.equalsEpsilon = function(right, epsilon) {
          return Matrix4.equalsEpsilon(this, right, epsilon);
      };
  
      /**
       * Computes a string representing this Matrix with each row being
       * on a separate line and in the format '(column0, column1, column2, column3)'.
       *
       * @returns {String} A string representing the provided Matrix with each row being on a separate line and in the format '(column0, column1, column2, column3)'.
       */
      Matrix4.prototype.toString = function() {
          return '(' + this[0] + ', ' + this[4] + ', ' + this[8] + ', ' + this[12] +')\n' +
                 '(' + this[1] + ', ' + this[5] + ', ' + this[9] + ', ' + this[13] +')\n' +
                 '(' + this[2] + ', ' + this[6] + ', ' + this[10] + ', ' + this[14] +')\n' +
                 '(' + this[3] + ', ' + this[7] + ', ' + this[11] + ', ' + this[15] +')';
      };
  
      return Matrix4;
  });
  
  define('Core/Rectangle',[
          './Cartographic',
          './Check',
          './defaultValue',
          './defined',
          './defineProperties',
          './Ellipsoid',
          './freezeObject',
          './Math'
      ], function(
          Cartographic,
          Check,
          defaultValue,
          defined,
          defineProperties,
          Ellipsoid,
          freezeObject,
          CesiumMath) {
      'use strict';
  
      /**
       * A two dimensional region specified as longitude and latitude coordinates.
       *
       * @alias Rectangle
       * @constructor
       *
       * @param {Number} [west=0.0] The westernmost longitude, in radians, in the range [-Pi, Pi].
       * @param {Number} [south=0.0] The southernmost latitude, in radians, in the range [-Pi/2, Pi/2].
       * @param {Number} [east=0.0] The easternmost longitude, in radians, in the range [-Pi, Pi].
       * @param {Number} [north=0.0] The northernmost latitude, in radians, in the range [-Pi/2, Pi/2].
       *
       * @see Packable
       */
      function Rectangle(west, south, east, north) {
          /**
           * The westernmost longitude in radians in the range [-Pi, Pi].
           *
           * @type {Number}
           * @default 0.0
           */
          this.west = defaultValue(west, 0.0);
  
          /**
           * The southernmost latitude in radians in the range [-Pi/2, Pi/2].
           *
           * @type {Number}
           * @default 0.0
           */
          this.south = defaultValue(south, 0.0);
  
          /**
           * The easternmost longitude in radians in the range [-Pi, Pi].
           *
           * @type {Number}
           * @default 0.0
           */
          this.east = defaultValue(east, 0.0);
  
          /**
           * The northernmost latitude in radians in the range [-Pi/2, Pi/2].
           *
           * @type {Number}
           * @default 0.0
           */
          this.north = defaultValue(north, 0.0);
      }
  
      defineProperties(Rectangle.prototype, {
          /**
           * Gets the width of the rectangle in radians.
           * @memberof Rectangle.prototype
           * @type {Number}
           */
          width : {
              get : function() {
                  return Rectangle.computeWidth(this);
              }
          },
  
          /**
           * Gets the height of the rectangle in radians.
           * @memberof Rectangle.prototype
           * @type {Number}
           */
          height : {
              get : function() {
                  return Rectangle.computeHeight(this);
              }
          }
      });
  
      /**
       * The number of elements used to pack the object into an array.
       * @type {Number}
       */
      Rectangle.packedLength = 4;
  
      /**
       * Stores the provided instance into the provided array.
       *
       * @param {Rectangle} value The value to pack.
       * @param {Number[]} array The array to pack into.
       * @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
       *
       * @returns {Number[]} The array that was packed into
       */
      Rectangle.pack = function(value, array, startingIndex) {
                  Check.typeOf.object('value', value);
          Check.defined('array', array);
          
          startingIndex = defaultValue(startingIndex, 0);
  
          array[startingIndex++] = value.west;
          array[startingIndex++] = value.south;
          array[startingIndex++] = value.east;
          array[startingIndex] = value.north;
  
          return array;
      };
  
      /**
       * Retrieves an instance from a packed array.
       *
       * @param {Number[]} array The packed array.
       * @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
       * @param {Rectangle} [result] The object into which to store the result.
       * @returns {Rectangle} The modified result parameter or a new Rectangle instance if one was not provided.
       */
      Rectangle.unpack = function(array, startingIndex, result) {
                  Check.defined('array', array);
          
          startingIndex = defaultValue(startingIndex, 0);
  
          if (!defined(result)) {
              result = new Rectangle();
          }
  
          result.west = array[startingIndex++];
          result.south = array[startingIndex++];
          result.east = array[startingIndex++];
          result.north = array[startingIndex];
          return result;
      };
  
      /**
       * Computes the width of a rectangle in radians.
       * @param {Rectangle} rectangle The rectangle to compute the width of.
       * @returns {Number} The width.
       */
      Rectangle.computeWidth = function(rectangle) {
                  Check.typeOf.object('rectangle', rectangle);
                  var east = rectangle.east;
          var west = rectangle.west;
          if (east < west) {
              east += CesiumMath.TWO_PI;
          }
          return east - west;
      };
  
      /**
       * Computes the height of a rectangle in radians.
       * @param {Rectangle} rectangle The rectangle to compute the height of.
       * @returns {Number} The height.
       */
      Rectangle.computeHeight = function(rectangle) {
                  Check.typeOf.object('rectangle', rectangle);
                  return rectangle.north - rectangle.south;
      };
  
      /**
       * Creates a rectangle given the boundary longitude and latitude in degrees.
       *
       * @param {Number} [west=0.0] The westernmost longitude in degrees in the range [-180.0, 180.0].
       * @param {Number} [south=0.0] The southernmost latitude in degrees in the range [-90.0, 90.0].
       * @param {Number} [east=0.0] The easternmost longitude in degrees in the range [-180.0, 180.0].
       * @param {Number} [north=0.0] The northernmost latitude in degrees in the range [-90.0, 90.0].
       * @param {Rectangle} [result] The object onto which to store the result, or undefined if a new instance should be created.
       * @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided.
       *
       * @example
       * var rectangle = Cesium.Rectangle.fromDegrees(0.0, 20.0, 10.0, 30.0);
       */
      Rectangle.fromDegrees = function(west, south, east, north, result) {
          west = CesiumMath.toRadians(defaultValue(west, 0.0));
          south = CesiumMath.toRadians(defaultValue(south, 0.0));
          east = CesiumMath.toRadians(defaultValue(east, 0.0));
          north = CesiumMath.toRadians(defaultValue(north, 0.0));
  
          if (!defined(result)) {
              return new Rectangle(west, south, east, north);
          }
  
          result.west = west;
          result.south = south;
          result.east = east;
          result.north = north;
  
          return result;
      };
  
      /**
       * Creates a rectangle given the boundary longitude and latitude in radians.
       *
       * @param {Number} [west=0.0] The westernmost longitude in radians in the range [-Math.PI, Math.PI].
       * @param {Number} [south=0.0] The southernmost latitude in radians in the range [-Math.PI/2, Math.PI/2].
       * @param {Number} [east=0.0] The easternmost longitude in radians in the range [-Math.PI, Math.PI].
       * @param {Number} [north=0.0] The northernmost latitude in radians in the range [-Math.PI/2, Math.PI/2].
       * @param {Rectangle} [result] The object onto which to store the result, or undefined if a new instance should be created.
       * @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided.
       *
       * @example
       * var rectangle = Cesium.Rectangle.fromRadians(0.0, Math.PI/4, Math.PI/8, 3*Math.PI/4);
       */
      Rectangle.fromRadians = function(west, south, east, north, result) {
          if (!defined(result)) {
              return new Rectangle(west, south, east, north);
          }
  
          result.west = defaultValue(west, 0.0);
          result.south = defaultValue(south, 0.0);
          result.east = defaultValue(east, 0.0);
          result.north = defaultValue(north, 0.0);
  
          return result;
      };
  
      /**
       * Creates the smallest possible Rectangle that encloses all positions in the provided array.
       *
       * @param {Cartographic[]} cartographics The list of Cartographic instances.
       * @param {Rectangle} [result] The object onto which to store the result, or undefined if a new instance should be created.
       * @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided.
       */
      Rectangle.fromCartographicArray = function(cartographics, result) {
                  Check.defined('cartographics', cartographics);
          
          var west = Number.MAX_VALUE;
          var east = -Number.MAX_VALUE;
          var westOverIDL = Number.MAX_VALUE;
          var eastOverIDL = -Number.MAX_VALUE;
          var south = Number.MAX_VALUE;
          var north = -Number.MAX_VALUE;
  
          for ( var i = 0, len = cartographics.length; i < len; i++) {
              var position = cartographics[i];
              west = Math.min(west, position.longitude);
              east = Math.max(east, position.longitude);
              south = Math.min(south, position.latitude);
              north = Math.max(north, position.latitude);
  
              var lonAdjusted = position.longitude >= 0 ?  position.longitude : position.longitude +  CesiumMath.TWO_PI;
              westOverIDL = Math.min(westOverIDL, lonAdjusted);
              eastOverIDL = Math.max(eastOverIDL, lonAdjusted);
          }
  
          if(east - west > eastOverIDL - westOverIDL) {
              west = westOverIDL;
              east = eastOverIDL;
  
              if (east > CesiumMath.PI) {
                  east = east - CesiumMath.TWO_PI;
              }
              if (west > CesiumMath.PI) {
                  west = west - CesiumMath.TWO_PI;
              }
          }
  
          if (!defined(result)) {
              return new Rectangle(west, south, east, north);
          }
  
          result.west = west;
          result.south = south;
          result.east = east;
          result.north = north;
          return result;
      };
  
      /**
       * Creates the smallest possible Rectangle that encloses all positions in the provided array.
       *
       * @param {Cartesian3[]} cartesians The list of Cartesian instances.
       * @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid the cartesians are on.
       * @param {Rectangle} [result] The object onto which to store the result, or undefined if a new instance should be created.
       * @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided.
       */
      Rectangle.fromCartesianArray = function(cartesians, ellipsoid, result) {
                  Check.defined('cartesians', cartesians);
                  ellipsoid = defaultValue(ellipsoid, Ellipsoid.WGS84);
  
          var west = Number.MAX_VALUE;
          var east = -Number.MAX_VALUE;
          var westOverIDL = Number.MAX_VALUE;
          var eastOverIDL = -Number.MAX_VALUE;
          var south = Number.MAX_VALUE;
          var north = -Number.MAX_VALUE;
  
          for ( var i = 0, len = cartesians.length; i < len; i++) {
              var position = ellipsoid.cartesianToCartographic(cartesians[i]);
              west = Math.min(west, position.longitude);
              east = Math.max(east, position.longitude);
              south = Math.min(south, position.latitude);
              north = Math.max(north, position.latitude);
  
              var lonAdjusted = position.longitude >= 0 ?  position.longitude : position.longitude +  CesiumMath.TWO_PI;
              westOverIDL = Math.min(westOverIDL, lonAdjusted);
              eastOverIDL = Math.max(eastOverIDL, lonAdjusted);
          }
  
          if(east - west > eastOverIDL - westOverIDL) {
              west = westOverIDL;
              east = eastOverIDL;
  
              if (east > CesiumMath.PI) {
                  east = east - CesiumMath.TWO_PI;
              }
              if (west > CesiumMath.PI) {
                  west = west - CesiumMath.TWO_PI;
              }
          }
  
          if (!defined(result)) {
              return new Rectangle(west, south, east, north);
          }
  
          result.west = west;
          result.south = south;
          result.east = east;
          result.north = north;
          return result;
      };
  
      /**
       * Duplicates a Rectangle.
       *
       * @param {Rectangle} rectangle The rectangle to clone.
       * @param {Rectangle} [result] The object onto which to store the result, or undefined if a new instance should be created.
       * @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided. (Returns undefined if rectangle is undefined)
       */
      Rectangle.clone = function(rectangle, result) {
          if (!defined(rectangle)) {
              return undefined;
          }
  
          if (!defined(result)) {
              return new Rectangle(rectangle.west, rectangle.south, rectangle.east, rectangle.north);
          }
  
          result.west = rectangle.west;
          result.south = rectangle.south;
          result.east = rectangle.east;
          result.north = rectangle.north;
          return result;
      };
  
      /**
       * Duplicates this Rectangle.
       *
       * @param {Rectangle} [result] The object onto which to store the result.
       * @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided.
       */
      Rectangle.prototype.clone = function(result) {
          return Rectangle.clone(this, result);
      };
  
      /**
       * Compares the provided Rectangle with this Rectangle componentwise and returns
       * <code>true</code> if they are equal, <code>false</code> otherwise.
       *
       * @param {Rectangle} [other] The Rectangle to compare.
       * @returns {Boolean} <code>true</code> if the Rectangles are equal, <code>false</code> otherwise.
       */
      Rectangle.prototype.equals = function(other) {
          return Rectangle.equals(this, other);
      };
  
      /**
       * Compares the provided rectangles and returns <code>true</code> if they are equal,
       * <code>false</code> otherwise.
       *
       * @param {Rectangle} [left] The first Rectangle.
       * @param {Rectangle} [right] The second Rectangle.
       * @returns {Boolean} <code>true</code> if left and right are equal; otherwise <code>false</code>.
       */
      Rectangle.equals = function(left, right) {
          return (left === right) ||
                 ((defined(left)) &&
                  (defined(right)) &&
                  (left.west === right.west) &&
                  (left.south === right.south) &&
                  (left.east === right.east) &&
                  (left.north === right.north));
      };
  
      /**
       * Compares the provided Rectangle with this Rectangle componentwise and returns
       * <code>true</code> if they are within the provided epsilon,
       * <code>false</code> otherwise.
       *
       * @param {Rectangle} [other] The Rectangle to compare.
       * @param {Number} epsilon The epsilon to use for equality testing.
       * @returns {Boolean} <code>true</code> if the Rectangles are within the provided epsilon, <code>false</code> otherwise.
       */
      Rectangle.prototype.equalsEpsilon = function(other, epsilon) {
                  Check.typeOf.number('epsilon', epsilon);
          
          return defined(other) &&
                 (Math.abs(this.west - other.west) <= epsilon) &&
                 (Math.abs(this.south - other.south) <= epsilon) &&
                 (Math.abs(this.east - other.east) <= epsilon) &&
                 (Math.abs(this.north - other.north) <= epsilon);
      };
  
      /**
       * Checks a Rectangle's properties and throws if they are not in valid ranges.
       *
       * @param {Rectangle} rectangle The rectangle to validate
       *
       * @exception {DeveloperError} <code>north</code> must be in the interval [<code>-Pi/2</code>, <code>Pi/2</code>].
       * @exception {DeveloperError} <code>south</code> must be in the interval [<code>-Pi/2</code>, <code>Pi/2</code>].
       * @exception {DeveloperError} <code>east</code> must be in the interval [<code>-Pi</code>, <code>Pi</code>].
       * @exception {DeveloperError} <code>west</code> must be in the interval [<code>-Pi</code>, <code>Pi</code>].
       */
      Rectangle.validate = function(rectangle) {
                  Check.typeOf.object('rectangle', rectangle);
  
          var north = rectangle.north;
          Check.typeOf.number.greaterThanOrEquals('north', north, -CesiumMath.PI_OVER_TWO);
          Check.typeOf.number.lessThanOrEquals('north', north, CesiumMath.PI_OVER_TWO);
  
          var south = rectangle.south;
          Check.typeOf.number.greaterThanOrEquals('south', south, -CesiumMath.PI_OVER_TWO);
          Check.typeOf.number.lessThanOrEquals('south', south, CesiumMath.PI_OVER_TWO);
  
          var west = rectangle.west;
          Check.typeOf.number.greaterThanOrEquals('west', west, -Math.PI);
          Check.typeOf.number.lessThanOrEquals('west', west, Math.PI);
  
          var east = rectangle.east;
          Check.typeOf.number.greaterThanOrEquals('east', east, -Math.PI);
          Check.typeOf.number.lessThanOrEquals('east', east, Math.PI);
              };
  
      /**
       * Computes the southwest corner of a rectangle.
       *
       * @param {Rectangle} rectangle The rectangle for which to find the corner
       * @param {Cartographic} [result] The object onto which to store the result.
       * @returns {Cartographic} The modified result parameter or a new Cartographic instance if none was provided.
       */
      Rectangle.southwest = function(rectangle, result) {
                  Check.typeOf.object('rectangle', rectangle);
          
          if (!defined(result)) {
              return new Cartographic(rectangle.west, rectangle.south);
          }
          result.longitude = rectangle.west;
          result.latitude = rectangle.south;
          result.height = 0.0;
          return result;
      };
  
      /**
       * Computes the northwest corner of a rectangle.
       *
       * @param {Rectangle} rectangle The rectangle for which to find the corner
       * @param {Cartographic} [result] The object onto which to store the result.
       * @returns {Cartographic} The modified result parameter or a new Cartographic instance if none was provided.
       */
      Rectangle.northwest = function(rectangle, result) {
                  Check.typeOf.object('rectangle', rectangle);
          
          if (!defined(result)) {
              return new Cartographic(rectangle.west, rectangle.north);
          }
          result.longitude = rectangle.west;
          result.latitude = rectangle.north;
          result.height = 0.0;
          return result;
      };
  
      /**
       * Computes the northeast corner of a rectangle.
       *
       * @param {Rectangle} rectangle The rectangle for which to find the corner
       * @param {Cartographic} [result] The object onto which to store the result.
       * @returns {Cartographic} The modified result parameter or a new Cartographic instance if none was provided.
       */
      Rectangle.northeast = function(rectangle, result) {
                  Check.typeOf.object('rectangle', rectangle);
          
          if (!defined(result)) {
              return new Cartographic(rectangle.east, rectangle.north);
          }
          result.longitude = rectangle.east;
          result.latitude = rectangle.north;
          result.height = 0.0;
          return result;
      };
  
      /**
       * Computes the southeast corner of a rectangle.
       *
       * @param {Rectangle} rectangle The rectangle for which to find the corner
       * @param {Cartographic} [result] The object onto which to store the result.
       * @returns {Cartographic} The modified result parameter or a new Cartographic instance if none was provided.
       */
      Rectangle.southeast = function(rectangle, result) {
                  Check.typeOf.object('rectangle', rectangle);
          
          if (!defined(result)) {
              return new Cartographic(rectangle.east, rectangle.south);
          }
          result.longitude = rectangle.east;
          result.latitude = rectangle.south;
          result.height = 0.0;
          return result;
      };
  
      /**
       * Computes the center of a rectangle.
       *
       * @param {Rectangle} rectangle The rectangle for which to find the center
       * @param {Cartographic} [result] The object onto which to store the result.
       * @returns {Cartographic} The modified result parameter or a new Cartographic instance if none was provided.
       */
      Rectangle.center = function(rectangle, result) {
                  Check.typeOf.object('rectangle', rectangle);
          
          var east = rectangle.east;
          var west = rectangle.west;
  
          if (east < west) {
              east += CesiumMath.TWO_PI;
          }
  
          var longitude = CesiumMath.negativePiToPi((west + east) * 0.5);
          var latitude = (rectangle.south + rectangle.north) * 0.5;
  
          if (!defined(result)) {
              return new Cartographic(longitude, latitude);
          }
  
          result.longitude = longitude;
          result.latitude = latitude;
          result.height = 0.0;
          return result;
      };
  
      /**
       * Computes the intersection of two rectangles.  This function assumes that the rectangle's coordinates are
       * latitude and longitude in radians and produces a correct intersection, taking into account the fact that
       * the same angle can be represented with multiple values as well as the wrapping of longitude at the
       * anti-meridian.  For a simple intersection that ignores these factors and can be used with projected
       * coordinates, see {@link Rectangle.simpleIntersection}.
       *
       * @param {Rectangle} rectangle On rectangle to find an intersection
       * @param {Rectangle} otherRectangle Another rectangle to find an intersection
       * @param {Rectangle} [result] The object onto which to store the result.
       * @returns {Rectangle|undefined} The modified result parameter, a new Rectangle instance if none was provided or undefined if there is no intersection.
       */
      Rectangle.intersection = function(rectangle, otherRectangle, result) {
                  Check.typeOf.object('rectangle', rectangle);
          Check.typeOf.object('otherRectangle', otherRectangle);
          
          var rectangleEast = rectangle.east;
          var rectangleWest = rectangle.west;
  
          var otherRectangleEast = otherRectangle.east;
          var otherRectangleWest = otherRectangle.west;
  
          if (rectangleEast < rectangleWest && otherRectangleEast > 0.0) {
              rectangleEast += CesiumMath.TWO_PI;
          } else if (otherRectangleEast < otherRectangleWest && rectangleEast > 0.0) {
              otherRectangleEast += CesiumMath.TWO_PI;
          }
  
          if (rectangleEast < rectangleWest && otherRectangleWest < 0.0) {
              otherRectangleWest += CesiumMath.TWO_PI;
          } else if (otherRectangleEast < otherRectangleWest && rectangleWest < 0.0) {
              rectangleWest += CesiumMath.TWO_PI;
          }
  
          var west = CesiumMath.negativePiToPi(Math.max(rectangleWest, otherRectangleWest));
          var east = CesiumMath.negativePiToPi(Math.min(rectangleEast, otherRectangleEast));
  
          if ((rectangle.west < rectangle.east || otherRectangle.west < otherRectangle.east) && east <= west) {
              return undefined;
          }
  
          var south = Math.max(rectangle.south, otherRectangle.south);
          var north = Math.min(rectangle.north, otherRectangle.north);
  
          if (south >= north) {
              return undefined;
          }
  
          if (!defined(result)) {
              return new Rectangle(west, south, east, north);
          }
          result.west = west;
          result.south = south;
          result.east = east;
          result.north = north;
          return result;
      };
  
      /**
       * Computes a simple intersection of two rectangles.  Unlike {@link Rectangle.intersection}, this function
       * does not attempt to put the angular coordinates into a consistent range or to account for crossing the
       * anti-meridian.  As such, it can be used for rectangles where the coordinates are not simply latitude
       * and longitude (i.e. projected coordinates).
       *
       * @param {Rectangle} rectangle On rectangle to find an intersection
       * @param {Rectangle} otherRectangle Another rectangle to find an intersection
       * @param {Rectangle} [result] The object onto which to store the result.
       * @returns {Rectangle|undefined} The modified result parameter, a new Rectangle instance if none was provided or undefined if there is no intersection.
       */
      Rectangle.simpleIntersection = function(rectangle, otherRectangle, result) {
                  Check.typeOf.object('rectangle', rectangle);
          Check.typeOf.object('otherRectangle', otherRectangle);
          
          var west = Math.max(rectangle.west, otherRectangle.west);
          var south = Math.max(rectangle.south, otherRectangle.south);
          var east = Math.min(rectangle.east, otherRectangle.east);
          var north = Math.min(rectangle.north, otherRectangle.north);
  
          if (south >= north || west >= east) {
              return undefined;
          }
  
          if (!defined(result)) {
              return new Rectangle(west, south, east, north);
          }
  
          result.west = west;
          result.south = south;
          result.east = east;
          result.north = north;
          return result;
      };
  
      /**
       * Computes a rectangle that is the union of two rectangles.
       *
       * @param {Rectangle} rectangle A rectangle to enclose in rectangle.
       * @param {Rectangle} otherRectangle A rectangle to enclose in a rectangle.
       * @param {Rectangle} [result] The object onto which to store the result.
       * @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided.
       */
      Rectangle.union = function(rectangle, otherRectangle, result) {
                  Check.typeOf.object('rectangle', rectangle);
          Check.typeOf.object('otherRectangle', otherRectangle);
          
          if (!defined(result)) {
              result = new Rectangle();
          }
  
          var rectangleEast = rectangle.east;
          var rectangleWest = rectangle.west;
  
          var otherRectangleEast = otherRectangle.east;
          var otherRectangleWest = otherRectangle.west;
  
          if (rectangleEast < rectangleWest && otherRectangleEast > 0.0) {
              rectangleEast += CesiumMath.TWO_PI;
          } else if (otherRectangleEast < otherRectangleWest && rectangleEast > 0.0) {
              otherRectangleEast += CesiumMath.TWO_PI;
          }
  
          if (rectangleEast < rectangleWest && otherRectangleWest < 0.0) {
              otherRectangleWest += CesiumMath.TWO_PI;
          } else if (otherRectangleEast < otherRectangleWest && rectangleWest < 0.0) {
              rectangleWest += CesiumMath.TWO_PI;
          }
  
          var west = CesiumMath.convertLongitudeRange(Math.min(rectangleWest, otherRectangleWest));
          var east = CesiumMath.convertLongitudeRange(Math.max(rectangleEast, otherRectangleEast));
  
          result.west = west;
          result.south = Math.min(rectangle.south, otherRectangle.south);
          result.east = east;
          result.north = Math.max(rectangle.north, otherRectangle.north);
  
          return result;
      };
  
      /**
       * Computes a rectangle by enlarging the provided rectangle until it contains the provided cartographic.
       *
       * @param {Rectangle} rectangle A rectangle to expand.
       * @param {Cartographic} cartographic A cartographic to enclose in a rectangle.
       * @param {Rectangle} [result] The object onto which to store the result.
       * @returns {Rectangle} The modified result parameter or a new Rectangle instance if one was not provided.
       */
      Rectangle.expand = function(rectangle, cartographic, result) {
                  Check.typeOf.object('rectangle', rectangle);
          Check.typeOf.object('cartographic', cartographic);
          
          if (!defined(result)) {
              result = new Rectangle();
          }
  
          result.west = Math.min(rectangle.west, cartographic.longitude);
          result.south = Math.min(rectangle.south, cartographic.latitude);
          result.east = Math.max(rectangle.east, cartographic.longitude);
          result.north = Math.max(rectangle.north, cartographic.latitude);
  
          return result;
      };
  
      /**
       * Returns true if the cartographic is on or inside the rectangle, false otherwise.
       *
       * @param {Rectangle} rectangle The rectangle
       * @param {Cartographic} cartographic The cartographic to test.
       * @returns {Boolean} true if the provided cartographic is inside the rectangle, false otherwise.
       */
      Rectangle.contains = function(rectangle, cartographic) {
                  Check.typeOf.object('rectangle', rectangle);
          Check.typeOf.object('cartographic', cartographic);
          
          var longitude = cartographic.longitude;
          var latitude = cartographic.latitude;
  
          var west = rectangle.west;
          var east = rectangle.east;
  
          if (east < west) {
              east += CesiumMath.TWO_PI;
              if (longitude < 0.0) {
                  longitude += CesiumMath.TWO_PI;
              }
          }
          return (longitude > west || CesiumMath.equalsEpsilon(longitude, west, CesiumMath.EPSILON14)) &&
                 (longitude < east || CesiumMath.equalsEpsilon(longitude, east, CesiumMath.EPSILON14)) &&
                 latitude >= rectangle.south &&
                 latitude <= rectangle.north;
      };
  
      var subsampleLlaScratch = new Cartographic();
      /**
       * Samples a rectangle so that it includes a list of Cartesian points suitable for passing to
       * {@link BoundingSphere#fromPoints}.  Sampling is necessary to account
       * for rectangles that cover the poles or cross the equator.
       *
       * @param {Rectangle} rectangle The rectangle to subsample.
       * @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid to use.
       * @param {Number} [surfaceHeight=0.0] The height of the rectangle above the ellipsoid.
       * @param {Cartesian3[]} [result] The array of Cartesians onto which to store the result.
       * @returns {Cartesian3[]} The modified result parameter or a new Array of Cartesians instances if none was provided.
       */
      Rectangle.subsample = function(rectangle, ellipsoid, surfaceHeight, result) {
                  Check.typeOf.object('rectangle', rectangle);
          
          ellipsoid = defaultValue(ellipsoid, Ellipsoid.WGS84);
          surfaceHeight = defaultValue(surfaceHeight, 0.0);
  
          if (!defined(result)) {
              result = [];
          }
          var length = 0;
  
          var north = rectangle.north;
          var south = rectangle.south;
          var east = rectangle.east;
          var west = rectangle.west;
  
          var lla = subsampleLlaScratch;
          lla.height = surfaceHeight;
  
          lla.longitude = west;
          lla.latitude = north;
          result[length] = ellipsoid.cartographicToCartesian(lla, result[length]);
          length++;
  
          lla.longitude = east;
          result[length] = ellipsoid.cartographicToCartesian(lla, result[length]);
          length++;
  
          lla.latitude = south;
          result[length] = ellipsoid.cartographicToCartesian(lla, result[length]);
          length++;
  
          lla.longitude = west;
          result[length] = ellipsoid.cartographicToCartesian(lla, result[length]);
          length++;
  
          if (north < 0.0) {
              lla.latitude = north;
          } else if (south > 0.0) {
              lla.latitude = south;
          } else {
              lla.latitude = 0.0;
          }
  
          for ( var i = 1; i < 8; ++i) {
              lla.longitude = -Math.PI + i * CesiumMath.PI_OVER_TWO;
              if (Rectangle.contains(rectangle, lla)) {
                  result[length] = ellipsoid.cartographicToCartesian(lla, result[length]);
                  length++;
              }
          }
  
          if (lla.latitude === 0.0) {
              lla.longitude = west;
              result[length] = ellipsoid.cartographicToCartesian(lla, result[length]);
              length++;
              lla.longitude = east;
              result[length] = ellipsoid.cartographicToCartesian(lla, result[length]);
              length++;
          }
          result.length = length;
          return result;
      };
  
      /**
       * The largest possible rectangle.
       *
       * @type {Rectangle}
       * @constant
      */
      Rectangle.MAX_VALUE = freezeObject(new Rectangle(-Math.PI, -CesiumMath.PI_OVER_TWO, Math.PI, CesiumMath.PI_OVER_TWO));
  
      return Rectangle;
  });
  
  define('Core/BoundingSphere',[
          './Cartesian3',
          './Cartographic',
          './Check',
          './defaultValue',
          './defined',
          './Ellipsoid',
          './GeographicProjection',
          './Intersect',
          './Interval',
          './Matrix3',
          './Matrix4',
          './Rectangle'
      ], function(
          Cartesian3,
          Cartographic,
          Check,
          defaultValue,
          defined,
          Ellipsoid,
          GeographicProjection,
          Intersect,
          Interval,
          Matrix3,
          Matrix4,
          Rectangle) {
      'use strict';
  
      /**
       * A bounding sphere with a center and a radius.
       * @alias BoundingSphere
       * @constructor
       *
       * @param {Cartesian3} [center=Cartesian3.ZERO] The center of the bounding sphere.
       * @param {Number} [radius=0.0] The radius of the bounding sphere.
       *
       * @see AxisAlignedBoundingBox
       * @see BoundingRectangle
       * @see Packable
       */
      function BoundingSphere(center, radius) {
          /**
           * The center point of the sphere.
           * @type {Cartesian3}
           * @default {@link Cartesian3.ZERO}
           */
          this.center = Cartesian3.clone(defaultValue(center, Cartesian3.ZERO));
  
          /**
           * The radius of the sphere.
           * @type {Number}
           * @default 0.0
           */
          this.radius = defaultValue(radius, 0.0);
      }
  
      var fromPointsXMin = new Cartesian3();
      var fromPointsYMin = new Cartesian3();
      var fromPointsZMin = new Cartesian3();
      var fromPointsXMax = new Cartesian3();
      var fromPointsYMax = new Cartesian3();
      var fromPointsZMax = new Cartesian3();
      var fromPointsCurrentPos = new Cartesian3();
      var fromPointsScratch = new Cartesian3();
      var fromPointsRitterCenter = new Cartesian3();
      var fromPointsMinBoxPt = new Cartesian3();
      var fromPointsMaxBoxPt = new Cartesian3();
      var fromPointsNaiveCenterScratch = new Cartesian3();
  
      /**
       * Computes a tight-fitting bounding sphere enclosing a list of 3D Cartesian points.
       * The bounding sphere is computed by running two algorithms, a naive algorithm and
       * Ritter's algorithm. The smaller of the two spheres is used to ensure a tight fit.
       *
       * @param {Cartesian3[]} [positions] An array of points that the bounding sphere will enclose.  Each point must have <code>x</code>, <code>y</code>, and <code>z</code> properties.
       * @param {BoundingSphere} [result] The object onto which to store the result.
       * @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if one was not provided.
       *
       * @see {@link http://blogs.agi.com/insight3d/index.php/2008/02/04/a-bounding/|Bounding Sphere computation article}
       */
      BoundingSphere.fromPoints = function(positions, result) {
          if (!defined(result)) {
              result = new BoundingSphere();
          }
  
          if (!defined(positions) || positions.length === 0) {
              result.center = Cartesian3.clone(Cartesian3.ZERO, result.center);
              result.radius = 0.0;
              return result;
          }
  
          var currentPos = Cartesian3.clone(positions[0], fromPointsCurrentPos);
  
          var xMin = Cartesian3.clone(currentPos, fromPointsXMin);
          var yMin = Cartesian3.clone(currentPos, fromPointsYMin);
          var zMin = Cartesian3.clone(currentPos, fromPointsZMin);
  
          var xMax = Cartesian3.clone(currentPos, fromPointsXMax);
          var yMax = Cartesian3.clone(currentPos, fromPointsYMax);
          var zMax = Cartesian3.clone(currentPos, fromPointsZMax);
  
          var numPositions = positions.length;
          var i;
          for (i = 1; i < numPositions; i++) {
              Cartesian3.clone(positions[i], currentPos);
  
              var x = currentPos.x;
              var y = currentPos.y;
              var z = currentPos.z;
  
              // Store points containing the the smallest and largest components
              if (x < xMin.x) {
                  Cartesian3.clone(currentPos, xMin);
              }
  
              if (x > xMax.x) {
                  Cartesian3.clone(currentPos, xMax);
              }
  
              if (y < yMin.y) {
                  Cartesian3.clone(currentPos, yMin);
              }
  
              if (y > yMax.y) {
                  Cartesian3.clone(currentPos, yMax);
              }
  
              if (z < zMin.z) {
                  Cartesian3.clone(currentPos, zMin);
              }
  
              if (z > zMax.z) {
                  Cartesian3.clone(currentPos, zMax);
              }
          }
  
          // Compute x-, y-, and z-spans (Squared distances b/n each component's min. and max.).
          var xSpan = Cartesian3.magnitudeSquared(Cartesian3.subtract(xMax, xMin, fromPointsScratch));
          var ySpan = Cartesian3.magnitudeSquared(Cartesian3.subtract(yMax, yMin, fromPointsScratch));
          var zSpan = Cartesian3.magnitudeSquared(Cartesian3.subtract(zMax, zMin, fromPointsScratch));
  
          // Set the diameter endpoints to the largest span.
          var diameter1 = xMin;
          var diameter2 = xMax;
          var maxSpan = xSpan;
          if (ySpan > maxSpan) {
              maxSpan = ySpan;
              diameter1 = yMin;
              diameter2 = yMax;
          }
          if (zSpan > maxSpan) {
              maxSpan = zSpan;
              diameter1 = zMin;
              diameter2 = zMax;
          }
  
          // Calculate the center of the initial sphere found by Ritter's algorithm
          var ritterCenter = fromPointsRitterCenter;
          ritterCenter.x = (diameter1.x + diameter2.x) * 0.5;
          ritterCenter.y = (diameter1.y + diameter2.y) * 0.5;
          ritterCenter.z = (diameter1.z + diameter2.z) * 0.5;
  
          // Calculate the radius of the initial sphere found by Ritter's algorithm
          var radiusSquared = Cartesian3.magnitudeSquared(Cartesian3.subtract(diameter2, ritterCenter, fromPointsScratch));
          var ritterRadius = Math.sqrt(radiusSquared);
  
          // Find the center of the sphere found using the Naive method.
          var minBoxPt = fromPointsMinBoxPt;
          minBoxPt.x = xMin.x;
          minBoxPt.y = yMin.y;
          minBoxPt.z = zMin.z;
  
          var maxBoxPt = fromPointsMaxBoxPt;
          maxBoxPt.x = xMax.x;
          maxBoxPt.y = yMax.y;
          maxBoxPt.z = zMax.z;
  
          var naiveCenter = Cartesian3.multiplyByScalar(Cartesian3.add(minBoxPt, maxBoxPt, fromPointsScratch), 0.5, fromPointsNaiveCenterScratch);
  
          // Begin 2nd pass to find naive radius and modify the ritter sphere.
          var naiveRadius = 0;
          for (i = 0; i < numPositions; i++) {
              Cartesian3.clone(positions[i], currentPos);
  
              // Find the furthest point from the naive center to calculate the naive radius.
              var r = Cartesian3.magnitude(Cartesian3.subtract(currentPos, naiveCenter, fromPointsScratch));
              if (r > naiveRadius) {
                  naiveRadius = r;
              }
  
              // Make adjustments to the Ritter Sphere to include all points.
              var oldCenterToPointSquared = Cartesian3.magnitudeSquared(Cartesian3.subtract(currentPos, ritterCenter, fromPointsScratch));
              if (oldCenterToPointSquared > radiusSquared) {
                  var oldCenterToPoint = Math.sqrt(oldCenterToPointSquared);
                  // Calculate new radius to include the point that lies outside
                  ritterRadius = (ritterRadius + oldCenterToPoint) * 0.5;
                  radiusSquared = ritterRadius * ritterRadius;
                  // Calculate center of new Ritter sphere
                  var oldToNew = oldCenterToPoint - ritterRadius;
                  ritterCenter.x = (ritterRadius * ritterCenter.x + oldToNew * currentPos.x) / oldCenterToPoint;
                  ritterCenter.y = (ritterRadius * ritterCenter.y + oldToNew * currentPos.y) / oldCenterToPoint;
                  ritterCenter.z = (ritterRadius * ritterCenter.z + oldToNew * currentPos.z) / oldCenterToPoint;
              }
          }
  
          if (ritterRadius < naiveRadius) {
              Cartesian3.clone(ritterCenter, result.center);
              result.radius = ritterRadius;
          } else {
              Cartesian3.clone(naiveCenter, result.center);
              result.radius = naiveRadius;
          }
  
          return result;
      };
  
      var defaultProjection = new GeographicProjection();
      var fromRectangle2DLowerLeft = new Cartesian3();
      var fromRectangle2DUpperRight = new Cartesian3();
      var fromRectangle2DSouthwest = new Cartographic();
      var fromRectangle2DNortheast = new Cartographic();
  
      /**
       * Computes a bounding sphere from a rectangle projected in 2D.
       *
       * @param {Rectangle} [rectangle] The rectangle around which to create a bounding sphere.
       * @param {Object} [projection=GeographicProjection] The projection used to project the rectangle into 2D.
       * @param {BoundingSphere} [result] The object onto which to store the result.
       * @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if none was provided.
       */
      BoundingSphere.fromRectangle2D = function(rectangle, projection, result) {
          return BoundingSphere.fromRectangleWithHeights2D(rectangle, projection, 0.0, 0.0, result);
      };
  
      /**
       * Computes a bounding sphere from a rectangle projected in 2D.  The bounding sphere accounts for the
       * object's minimum and maximum heights over the rectangle.
       *
       * @param {Rectangle} [rectangle] The rectangle around which to create a bounding sphere.
       * @param {Object} [projection=GeographicProjection] The projection used to project the rectangle into 2D.
       * @param {Number} [minimumHeight=0.0] The minimum height over the rectangle.
       * @param {Number} [maximumHeight=0.0] The maximum height over the rectangle.
       * @param {BoundingSphere} [result] The object onto which to store the result.
       * @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if none was provided.
       */
      BoundingSphere.fromRectangleWithHeights2D = function(rectangle, projection, minimumHeight, maximumHeight, result) {
          if (!defined(result)) {
              result = new BoundingSphere();
          }
  
          if (!defined(rectangle)) {
              result.center = Cartesian3.clone(Cartesian3.ZERO, result.center);
              result.radius = 0.0;
              return result;
          }
  
          projection = defaultValue(projection, defaultProjection);
  
          Rectangle.southwest(rectangle, fromRectangle2DSouthwest);
          fromRectangle2DSouthwest.height = minimumHeight;
          Rectangle.northeast(rectangle, fromRectangle2DNortheast);
          fromRectangle2DNortheast.height = maximumHeight;
  
          var lowerLeft = projection.project(fromRectangle2DSouthwest, fromRectangle2DLowerLeft);
          var upperRight = projection.project(fromRectangle2DNortheast, fromRectangle2DUpperRight);
  
          var width = upperRight.x - lowerLeft.x;
          var height = upperRight.y - lowerLeft.y;
          var elevation = upperRight.z - lowerLeft.z;
  
          result.radius = Math.sqrt(width * width + height * height + elevation * elevation) * 0.5;
          var center = result.center;
          center.x = lowerLeft.x + width * 0.5;
          center.y = lowerLeft.y + height * 0.5;
          center.z = lowerLeft.z + elevation * 0.5;
          return result;
      };
  
      var fromRectangle3DScratch = [];
  
      /**
       * Computes a bounding sphere from a rectangle in 3D. The bounding sphere is created using a subsample of points
       * on the ellipsoid and contained in the rectangle. It may not be accurate for all rectangles on all types of ellipsoids.
       *
       * @param {Rectangle} [rectangle] The valid rectangle used to create a bounding sphere.
       * @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid used to determine positions of the rectangle.
       * @param {Number} [surfaceHeight=0.0] The height above the surface of the ellipsoid.
       * @param {BoundingSphere} [result] The object onto which to store the result.
       * @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if none was provided.
       */
      BoundingSphere.fromRectangle3D = function(rectangle, ellipsoid, surfaceHeight, result) {
          ellipsoid = defaultValue(ellipsoid, Ellipsoid.WGS84);
          surfaceHeight = defaultValue(surfaceHeight, 0.0);
  
          if (!defined(result)) {
              result = new BoundingSphere();
          }
  
          if (!defined(rectangle)) {
              result.center = Cartesian3.clone(Cartesian3.ZERO, result.center);
              result.radius = 0.0;
              return result;
          }
  
          var positions = Rectangle.subsample(rectangle, ellipsoid, surfaceHeight, fromRectangle3DScratch);
          return BoundingSphere.fromPoints(positions, result);
      };
  
      /**
       * Computes a tight-fitting bounding sphere enclosing a list of 3D points, where the points are
       * stored in a flat array in X, Y, Z, order.  The bounding sphere is computed by running two
       * algorithms, a naive algorithm and Ritter's algorithm. The smaller of the two spheres is used to
       * ensure a tight fit.
       *
       * @param {Number[]} [positions] An array of points that the bounding sphere will enclose.  Each point
       *        is formed from three elements in the array in the order X, Y, Z.
       * @param {Cartesian3} [center=Cartesian3.ZERO] The position to which the positions are relative, which need not be the
       *        origin of the coordinate system.  This is useful when the positions are to be used for
       *        relative-to-center (RTC) rendering.
       * @param {Number} [stride=3] The number of array elements per vertex.  It must be at least 3, but it may
       *        be higher.  Regardless of the value of this parameter, the X coordinate of the first position
       *        is at array index 0, the Y coordinate is at array index 1, and the Z coordinate is at array index
       *        2.  When stride is 3, the X coordinate of the next position then begins at array index 3.  If
       *        the stride is 5, however, two array elements are skipped and the next position begins at array
       *        index 5.
       * @param {BoundingSphere} [result] The object onto which to store the result.
       * @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if one was not provided.
       *
       * @example
       * // Compute the bounding sphere from 3 positions, each specified relative to a center.
       * // In addition to the X, Y, and Z coordinates, the points array contains two additional
       * // elements per point which are ignored for the purpose of computing the bounding sphere.
       * var center = new Cesium.Cartesian3(1.0, 2.0, 3.0);
       * var points = [1.0, 2.0, 3.0, 0.1, 0.2,
       *               4.0, 5.0, 6.0, 0.1, 0.2,
       *               7.0, 8.0, 9.0, 0.1, 0.2];
       * var sphere = Cesium.BoundingSphere.fromVertices(points, center, 5);
       *
       * @see {@link http://blogs.agi.com/insight3d/index.php/2008/02/04/a-bounding/|Bounding Sphere computation article}
       */
      BoundingSphere.fromVertices = function(positions, center, stride, result) {
          if (!defined(result)) {
              result = new BoundingSphere();
          }
  
          if (!defined(positions) || positions.length === 0) {
              result.center = Cartesian3.clone(Cartesian3.ZERO, result.center);
              result.radius = 0.0;
              return result;
          }
  
          center = defaultValue(center, Cartesian3.ZERO);
  
          stride = defaultValue(stride, 3);
  
                  Check.typeOf.number.greaterThanOrEquals('stride', stride, 3);
          
          var currentPos = fromPointsCurrentPos;
          currentPos.x = positions[0] + center.x;
          currentPos.y = positions[1] + center.y;
          currentPos.z = positions[2] + center.z;
  
          var xMin = Cartesian3.clone(currentPos, fromPointsXMin);
          var yMin = Cartesian3.clone(currentPos, fromPointsYMin);
          var zMin = Cartesian3.clone(currentPos, fromPointsZMin);
  
          var xMax = Cartesian3.clone(currentPos, fromPointsXMax);
          var yMax = Cartesian3.clone(currentPos, fromPointsYMax);
          var zMax = Cartesian3.clone(currentPos, fromPointsZMax);
  
          var numElements = positions.length;
          var i;
          for (i = 0; i < numElements; i += stride) {
              var x = positions[i] + center.x;
              var y = positions[i + 1] + center.y;
              var z = positions[i + 2] + center.z;
  
              currentPos.x = x;
              currentPos.y = y;
              currentPos.z = z;
  
              // Store points containing the the smallest and largest components
              if (x < xMin.x) {
                  Cartesian3.clone(currentPos, xMin);
              }
  
              if (x > xMax.x) {
                  Cartesian3.clone(currentPos, xMax);
              }
  
              if (y < yMin.y) {
                  Cartesian3.clone(currentPos, yMin);
              }
  
              if (y > yMax.y) {
                  Cartesian3.clone(currentPos, yMax);
              }
  
              if (z < zMin.z) {
                  Cartesian3.clone(currentPos, zMin);
              }
  
              if (z > zMax.z) {
                  Cartesian3.clone(currentPos, zMax);
              }
          }
  
          // Compute x-, y-, and z-spans (Squared distances b/n each component's min. and max.).
          var xSpan = Cartesian3.magnitudeSquared(Cartesian3.subtract(xMax, xMin, fromPointsScratch));
          var ySpan = Cartesian3.magnitudeSquared(Cartesian3.subtract(yMax, yMin, fromPointsScratch));
          var zSpan = Cartesian3.magnitudeSquared(Cartesian3.subtract(zMax, zMin, fromPointsScratch));
  
          // Set the diameter endpoints to the largest span.
          var diameter1 = xMin;
          var diameter2 = xMax;
          var maxSpan = xSpan;
          if (ySpan > maxSpan) {
              maxSpan = ySpan;
              diameter1 = yMin;
              diameter2 = yMax;
          }
          if (zSpan > maxSpan) {
              maxSpan = zSpan;
              diameter1 = zMin;
              diameter2 = zMax;
          }
  
          // Calculate the center of the initial sphere found by Ritter's algorithm
          var ritterCenter = fromPointsRitterCenter;
          ritterCenter.x = (diameter1.x + diameter2.x) * 0.5;
          ritterCenter.y = (diameter1.y + diameter2.y) * 0.5;
          ritterCenter.z = (diameter1.z + diameter2.z) * 0.5;
  
          // Calculate the radius of the initial sphere found by Ritter's algorithm
          var radiusSquared = Cartesian3.magnitudeSquared(Cartesian3.subtract(diameter2, ritterCenter, fromPointsScratch));
          var ritterRadius = Math.sqrt(radiusSquared);
  
          // Find the center of the sphere found using the Naive method.
          var minBoxPt = fromPointsMinBoxPt;
          minBoxPt.x = xMin.x;
          minBoxPt.y = yMin.y;
          minBoxPt.z = zMin.z;
  
          var maxBoxPt = fromPointsMaxBoxPt;
          maxBoxPt.x = xMax.x;
          maxBoxPt.y = yMax.y;
          maxBoxPt.z = zMax.z;
  
          var naiveCenter = Cartesian3.multiplyByScalar(Cartesian3.add(minBoxPt, maxBoxPt, fromPointsScratch), 0.5, fromPointsNaiveCenterScratch);
  
          // Begin 2nd pass to find naive radius and modify the ritter sphere.
          var naiveRadius = 0;
          for (i = 0; i < numElements; i += stride) {
              currentPos.x = positions[i] + center.x;
              currentPos.y = positions[i + 1] + center.y;
              currentPos.z = positions[i + 2] + center.z;
  
              // Find the furthest point from the naive center to calculate the naive radius.
              var r = Cartesian3.magnitude(Cartesian3.subtract(currentPos, naiveCenter, fromPointsScratch));
              if (r > naiveRadius) {
                  naiveRadius = r;
              }
  
              // Make adjustments to the Ritter Sphere to include all points.
              var oldCenterToPointSquared = Cartesian3.magnitudeSquared(Cartesian3.subtract(currentPos, ritterCenter, fromPointsScratch));
              if (oldCenterToPointSquared > radiusSquared) {
                  var oldCenterToPoint = Math.sqrt(oldCenterToPointSquared);
                  // Calculate new radius to include the point that lies outside
                  ritterRadius = (ritterRadius + oldCenterToPoint) * 0.5;
                  radiusSquared = ritterRadius * ritterRadius;
                  // Calculate center of new Ritter sphere
                  var oldToNew = oldCenterToPoint - ritterRadius;
                  ritterCenter.x = (ritterRadius * ritterCenter.x + oldToNew * currentPos.x) / oldCenterToPoint;
                  ritterCenter.y = (ritterRadius * ritterCenter.y + oldToNew * currentPos.y) / oldCenterToPoint;
                  ritterCenter.z = (ritterRadius * ritterCenter.z + oldToNew * currentPos.z) / oldCenterToPoint;
              }
          }
  
          if (ritterRadius < naiveRadius) {
              Cartesian3.clone(ritterCenter, result.center);
              result.radius = ritterRadius;
          } else {
              Cartesian3.clone(naiveCenter, result.center);
              result.radius = naiveRadius;
          }
  
          return result;
      };
  
      /**
       * Computes a tight-fitting bounding sphere enclosing a list of {@link EncodedCartesian3}s, where the points are
       * stored in parallel flat arrays in X, Y, Z, order.  The bounding sphere is computed by running two
       * algorithms, a naive algorithm and Ritter's algorithm. The smaller of the two spheres is used to
       * ensure a tight fit.
       *
       * @param {Number[]} [positionsHigh] An array of high bits of the encoded cartesians that the bounding sphere will enclose.  Each point
       *        is formed from three elements in the array in the order X, Y, Z.
       * @param {Number[]} [positionsLow] An array of low bits of the encoded cartesians that the bounding sphere will enclose.  Each point
       *        is formed from three elements in the array in the order X, Y, Z.
       * @param {BoundingSphere} [result] The object onto which to store the result.
       * @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if one was not provided.
       *
       * @see {@link http://blogs.agi.com/insight3d/index.php/2008/02/04/a-bounding/|Bounding Sphere computation article}
       */
      BoundingSphere.fromEncodedCartesianVertices = function(positionsHigh, positionsLow, result) {
          if (!defined(result)) {
              result = new BoundingSphere();
          }
  
          if (!defined(positionsHigh) || !defined(positionsLow) || positionsHigh.length !== positionsLow.length || positionsHigh.length === 0) {
              result.center = Cartesian3.clone(Cartesian3.ZERO, result.center);
              result.radius = 0.0;
              return result;
          }
  
          var currentPos = fromPointsCurrentPos;
          currentPos.x = positionsHigh[0] + positionsLow[0];
          currentPos.y = positionsHigh[1] + positionsLow[1];
          currentPos.z = positionsHigh[2] + positionsLow[2];
  
          var xMin = Cartesian3.clone(currentPos, fromPointsXMin);
          var yMin = Cartesian3.clone(currentPos, fromPointsYMin);
          var zMin = Cartesian3.clone(currentPos, fromPointsZMin);
  
          var xMax = Cartesian3.clone(currentPos, fromPointsXMax);
          var yMax = Cartesian3.clone(currentPos, fromPointsYMax);
          var zMax = Cartesian3.clone(currentPos, fromPointsZMax);
  
          var numElements = positionsHigh.length;
          var i;
          for (i = 0; i < numElements; i += 3) {
              var x = positionsHigh[i] + positionsLow[i];
              var y = positionsHigh[i + 1] + positionsLow[i + 1];
              var z = positionsHigh[i + 2] + positionsLow[i + 2];
  
              currentPos.x = x;
              currentPos.y = y;
              currentPos.z = z;
  
              // Store points containing the the smallest and largest components
              if (x < xMin.x) {
                  Cartesian3.clone(currentPos, xMin);
              }
  
              if (x > xMax.x) {
                  Cartesian3.clone(currentPos, xMax);
              }
  
              if (y < yMin.y) {
                  Cartesian3.clone(currentPos, yMin);
              }
  
              if (y > yMax.y) {
                  Cartesian3.clone(currentPos, yMax);
              }
  
              if (z < zMin.z) {
                  Cartesian3.clone(currentPos, zMin);
              }
  
              if (z > zMax.z) {
                  Cartesian3.clone(currentPos, zMax);
              }
          }
  
          // Compute x-, y-, and z-spans (Squared distances b/n each component's min. and max.).
          var xSpan = Cartesian3.magnitudeSquared(Cartesian3.subtract(xMax, xMin, fromPointsScratch));
          var ySpan = Cartesian3.magnitudeSquared(Cartesian3.subtract(yMax, yMin, fromPointsScratch));
          var zSpan = Cartesian3.magnitudeSquared(Cartesian3.subtract(zMax, zMin, fromPointsScratch));
  
          // Set the diameter endpoints to the largest span.
          var diameter1 = xMin;
          var diameter2 = xMax;
          var maxSpan = xSpan;
          if (ySpan > maxSpan) {
              maxSpan = ySpan;
              diameter1 = yMin;
              diameter2 = yMax;
          }
          if (zSpan > maxSpan) {
              maxSpan = zSpan;
              diameter1 = zMin;
              diameter2 = zMax;
          }
  
          // Calculate the center of the initial sphere found by Ritter's algorithm
          var ritterCenter = fromPointsRitterCenter;
          ritterCenter.x = (diameter1.x + diameter2.x) * 0.5;
          ritterCenter.y = (diameter1.y + diameter2.y) * 0.5;
          ritterCenter.z = (diameter1.z + diameter2.z) * 0.5;
  
          // Calculate the radius of the initial sphere found by Ritter's algorithm
          var radiusSquared = Cartesian3.magnitudeSquared(Cartesian3.subtract(diameter2, ritterCenter, fromPointsScratch));
          var ritterRadius = Math.sqrt(radiusSquared);
  
          // Find the center of the sphere found using the Naive method.
          var minBoxPt = fromPointsMinBoxPt;
          minBoxPt.x = xMin.x;
          minBoxPt.y = yMin.y;
          minBoxPt.z = zMin.z;
  
          var maxBoxPt = fromPointsMaxBoxPt;
          maxBoxPt.x = xMax.x;
          maxBoxPt.y = yMax.y;
          maxBoxPt.z = zMax.z;
  
          var naiveCenter = Cartesian3.multiplyByScalar(Cartesian3.add(minBoxPt, maxBoxPt, fromPointsScratch), 0.5, fromPointsNaiveCenterScratch);
  
          // Begin 2nd pass to find naive radius and modify the ritter sphere.
          var naiveRadius = 0;
          for (i = 0; i < numElements; i += 3) {
              currentPos.x = positionsHigh[i] + positionsLow[i];
              currentPos.y = positionsHigh[i + 1] + positionsLow[i + 1];
              currentPos.z = positionsHigh[i + 2] + positionsLow[i + 2];
  
              // Find the furthest point from the naive center to calculate the naive radius.
              var r = Cartesian3.magnitude(Cartesian3.subtract(currentPos, naiveCenter, fromPointsScratch));
              if (r > naiveRadius) {
                  naiveRadius = r;
              }
  
              // Make adjustments to the Ritter Sphere to include all points.
              var oldCenterToPointSquared = Cartesian3.magnitudeSquared(Cartesian3.subtract(currentPos, ritterCenter, fromPointsScratch));
              if (oldCenterToPointSquared > radiusSquared) {
                  var oldCenterToPoint = Math.sqrt(oldCenterToPointSquared);
                  // Calculate new radius to include the point that lies outside
                  ritterRadius = (ritterRadius + oldCenterToPoint) * 0.5;
                  radiusSquared = ritterRadius * ritterRadius;
                  // Calculate center of new Ritter sphere
                  var oldToNew = oldCenterToPoint - ritterRadius;
                  ritterCenter.x = (ritterRadius * ritterCenter.x + oldToNew * currentPos.x) / oldCenterToPoint;
                  ritterCenter.y = (ritterRadius * ritterCenter.y + oldToNew * currentPos.y) / oldCenterToPoint;
                  ritterCenter.z = (ritterRadius * ritterCenter.z + oldToNew * currentPos.z) / oldCenterToPoint;
              }
          }
  
          if (ritterRadius < naiveRadius) {
              Cartesian3.clone(ritterCenter, result.center);
              result.radius = ritterRadius;
          } else {
              Cartesian3.clone(naiveCenter, result.center);
              result.radius = naiveRadius;
          }
  
          return result;
      };
  
      /**
       * Computes a bounding sphere from the corner points of an axis-aligned bounding box.  The sphere
       * tighly and fully encompases the box.
       *
       * @param {Cartesian3} [corner] The minimum height over the rectangle.
       * @param {Cartesian3} [oppositeCorner] The maximum height over the rectangle.
       * @param {BoundingSphere} [result] The object onto which to store the result.
       * @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if none was provided.
       *
       * @example
       * // Create a bounding sphere around the unit cube
       * var sphere = Cesium.BoundingSphere.fromCornerPoints(new Cesium.Cartesian3(-0.5, -0.5, -0.5), new Cesium.Cartesian3(0.5, 0.5, 0.5));
       */
      BoundingSphere.fromCornerPoints = function(corner, oppositeCorner, result) {
                  Check.typeOf.object('corner', corner);
          Check.typeOf.object('oppositeCorner', oppositeCorner);
          
          if (!defined(result)) {
              result = new BoundingSphere();
          }
  
          var center = result.center;
          Cartesian3.add(corner, oppositeCorner, center);
          Cartesian3.multiplyByScalar(center, 0.5, center);
          result.radius = Cartesian3.distance(center, oppositeCorner);
          return result;
      };
  
      /**
       * Creates a bounding sphere encompassing an ellipsoid.
       *
       * @param {Ellipsoid} ellipsoid The ellipsoid around which to create a bounding sphere.
       * @param {BoundingSphere} [result] The object onto which to store the result.
       * @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if none was provided.
       *
       * @example
       * var boundingSphere = Cesium.BoundingSphere.fromEllipsoid(ellipsoid);
       */
      BoundingSphere.fromEllipsoid = function(ellipsoid, result) {
                  Check.typeOf.object('ellipsoid', ellipsoid);
          
          if (!defined(result)) {
              result = new BoundingSphere();
          }
  
          Cartesian3.clone(Cartesian3.ZERO, result.center);
          result.radius = ellipsoid.maximumRadius;
          return result;
      };
  
      var fromBoundingSpheresScratch = new Cartesian3();
  
      /**
       * Computes a tight-fitting bounding sphere enclosing the provided array of bounding spheres.
       *
       * @param {BoundingSphere[]} [boundingSpheres] The array of bounding spheres.
       * @param {BoundingSphere} [result] The object onto which to store the result.
       * @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if none was provided.
       */
      BoundingSphere.fromBoundingSpheres = function(boundingSpheres, result) {
          if (!defined(result)) {
              result = new BoundingSphere();
          }
  
          if (!defined(boundingSpheres) || boundingSpheres.length === 0) {
              result.center = Cartesian3.clone(Cartesian3.ZERO, result.center);
              result.radius = 0.0;
              return result;
          }
  
          var length = boundingSpheres.length;
          if (length === 1) {
              return BoundingSphere.clone(boundingSpheres[0], result);
          }
  
          if (length === 2) {
              return BoundingSphere.union(boundingSpheres[0], boundingSpheres[1], result);
          }
  
          var positions = [];
          var i;
          for (i = 0; i < length; i++) {
              positions.push(boundingSpheres[i].center);
          }
  
          result = BoundingSphere.fromPoints(positions, result);
  
          var center = result.center;
          var radius = result.radius;
          for (i = 0; i < length; i++) {
              var tmp = boundingSpheres[i];
              radius = Math.max(radius, Cartesian3.distance(center, tmp.center, fromBoundingSpheresScratch) + tmp.radius);
          }
          result.radius = radius;
  
          return result;
      };
  
      var fromOrientedBoundingBoxScratchU = new Cartesian3();
      var fromOrientedBoundingBoxScratchV = new Cartesian3();
      var fromOrientedBoundingBoxScratchW = new Cartesian3();
  
      /**
       * Computes a tight-fitting bounding sphere enclosing the provided oriented bounding box.
       *
       * @param {OrientedBoundingBox} orientedBoundingBox The oriented bounding box.
       * @param {BoundingSphere} [result] The object onto which to store the result.
       * @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if none was provided.
       */
      BoundingSphere.fromOrientedBoundingBox = function(orientedBoundingBox, result) {
                  Check.defined('orientedBoundingBox', orientedBoundingBox);
          
          if (!defined(result)) {
              result = new BoundingSphere();
          }
  
          var halfAxes = orientedBoundingBox.halfAxes;
          var u = Matrix3.getColumn(halfAxes, 0, fromOrientedBoundingBoxScratchU);
          var v = Matrix3.getColumn(halfAxes, 1, fromOrientedBoundingBoxScratchV);
          var w = Matrix3.getColumn(halfAxes, 2, fromOrientedBoundingBoxScratchW);
  
          Cartesian3.add(u, v, u);
          Cartesian3.add(u, w, u);
  
          result.center = Cartesian3.clone(orientedBoundingBox.center, result.center);
          result.radius = Cartesian3.magnitude(u);
  
          return result;
      };
  
      /**
       * Duplicates a BoundingSphere instance.
       *
       * @param {BoundingSphere} sphere The bounding sphere to duplicate.
       * @param {BoundingSphere} [result] The object onto which to store the result.
       * @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if none was provided. (Returns undefined if sphere is undefined)
       */
      BoundingSphere.clone = function(sphere, result) {
          if (!defined(sphere)) {
              return undefined;
          }
  
          if (!defined(result)) {
              return new BoundingSphere(sphere.center, sphere.radius);
          }
  
          result.center = Cartesian3.clone(sphere.center, result.center);
          result.radius = sphere.radius;
          return result;
      };
  
      /**
       * The number of elements used to pack the object into an array.
       * @type {Number}
       */
      BoundingSphere.packedLength = 4;
  
      /**
       * Stores the provided instance into the provided array.
       *
       * @param {BoundingSphere} value The value to pack.
       * @param {Number[]} array The array to pack into.
       * @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
       *
       * @returns {Number[]} The array that was packed into
       */
      BoundingSphere.pack = function(value, array, startingIndex) {
                  Check.typeOf.object('value', value);
          Check.defined('array', array);
          
          startingIndex = defaultValue(startingIndex, 0);
  
          var center = value.center;
          array[startingIndex++] = center.x;
          array[startingIndex++] = center.y;
          array[startingIndex++] = center.z;
          array[startingIndex] = value.radius;
  
          return array;
      };
  
      /**
       * Retrieves an instance from a packed array.
       *
       * @param {Number[]} array The packed array.
       * @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
       * @param {BoundingSphere} [result] The object into which to store the result.
       * @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if one was not provided.
       */
      BoundingSphere.unpack = function(array, startingIndex, result) {
                  Check.defined('array', array);
          
          startingIndex = defaultValue(startingIndex, 0);
  
          if (!defined(result)) {
              result = new BoundingSphere();
          }
  
          var center = result.center;
          center.x = array[startingIndex++];
          center.y = array[startingIndex++];
          center.z = array[startingIndex++];
          result.radius = array[startingIndex];
          return result;
      };
  
      var unionScratch = new Cartesian3();
      var unionScratchCenter = new Cartesian3();
      /**
       * Computes a bounding sphere that contains both the left and right bounding spheres.
       *
       * @param {BoundingSphere} left A sphere to enclose in a bounding sphere.
       * @param {BoundingSphere} right A sphere to enclose in a bounding sphere.
       * @param {BoundingSphere} [result] The object onto which to store the result.
       * @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if none was provided.
       */
      BoundingSphere.union = function(left, right, result) {
                  Check.typeOf.object('left', left);
          Check.typeOf.object('right', right);
          
          if (!defined(result)) {
              result = new BoundingSphere();
          }
  
          var leftCenter = left.center;
          var leftRadius = left.radius;
          var rightCenter = right.center;
          var rightRadius = right.radius;
  
          var toRightCenter = Cartesian3.subtract(rightCenter, leftCenter, unionScratch);
          var centerSeparation = Cartesian3.magnitude(toRightCenter);
  
          if (leftRadius >= (centerSeparation + rightRadius)) {
              // Left sphere wins.
              left.clone(result);
              return result;
          }
  
          if (rightRadius >= (centerSeparation + leftRadius)) {
              // Right sphere wins.
              right.clone(result);
              return result;
          }
  
          // There are two tangent points, one on far side of each sphere.
          var halfDistanceBetweenTangentPoints = (leftRadius + centerSeparation + rightRadius) * 0.5;
  
          // Compute the center point halfway between the two tangent points.
          var center = Cartesian3.multiplyByScalar(toRightCenter,
                  (-leftRadius + halfDistanceBetweenTangentPoints) / centerSeparation, unionScratchCenter);
          Cartesian3.add(center, leftCenter, center);
          Cartesian3.clone(center, result.center);
          result.radius = halfDistanceBetweenTangentPoints;
  
          return result;
      };
  
      var expandScratch = new Cartesian3();
      /**
       * Computes a bounding sphere by enlarging the provided sphere to contain the provided point.
       *
       * @param {BoundingSphere} sphere A sphere to expand.
       * @param {Cartesian3} point A point to enclose in a bounding sphere.
       * @param {BoundingSphere} [result] The object onto which to store the result.
       * @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if none was provided.
       */
      BoundingSphere.expand = function(sphere, point, result) {
                  Check.typeOf.object('sphere', sphere);
          Check.typeOf.object('point', point);
          
          result = BoundingSphere.clone(sphere, result);
  
          var radius = Cartesian3.magnitude(Cartesian3.subtract(point, result.center, expandScratch));
          if (radius > result.radius) {
              result.radius = radius;
          }
  
          return result;
      };
  
      /**
       * Determines which side of a plane a sphere is located.
       *
       * @param {BoundingSphere} sphere The bounding sphere to test.
       * @param {Plane} plane The plane to test against.
       * @returns {Intersect} {@link Intersect.INSIDE} if the entire sphere is on the side of the plane
       *                      the normal is pointing, {@link Intersect.OUTSIDE} if the entire sphere is
       *                      on the opposite side, and {@link Intersect.INTERSECTING} if the sphere
       *                      intersects the plane.
       */
      BoundingSphere.intersectPlane = function(sphere, plane) {
                  Check.typeOf.object('sphere', sphere);
          Check.typeOf.object('plane', plane);
          
          var center = sphere.center;
          var radius = sphere.radius;
          var normal = plane.normal;
          var distanceToPlane = Cartesian3.dot(normal, center) + plane.distance;
  
          if (distanceToPlane < -radius) {
              // The center point is negative side of the plane normal
              return Intersect.OUTSIDE;
          } else if (distanceToPlane < radius) {
              // The center point is positive side of the plane, but radius extends beyond it; partial overlap
              return Intersect.INTERSECTING;
          }
          return Intersect.INSIDE;
      };
  
      /**
       * Applies a 4x4 affine transformation matrix to a bounding sphere.
       *
       * @param {BoundingSphere} sphere The bounding sphere to apply the transformation to.
       * @param {Matrix4} transform The transformation matrix to apply to the bounding sphere.
       * @param {BoundingSphere} [result] The object onto which to store the result.
       * @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if none was provided.
       */
      BoundingSphere.transform = function(sphere, transform, result) {
                  Check.typeOf.object('sphere', sphere);
          Check.typeOf.object('transform', transform);
          
          if (!defined(result)) {
              result = new BoundingSphere();
          }
  
          result.center = Matrix4.multiplyByPoint(transform, sphere.center, result.center);
          result.radius = Matrix4.getMaximumScale(transform) * sphere.radius;
  
          return result;
      };
  
      var distanceSquaredToScratch = new Cartesian3();
  
      /**
       * Computes the estimated distance squared from the closest point on a bounding sphere to a point.
       *
       * @param {BoundingSphere} sphere The sphere.
       * @param {Cartesian3} cartesian The point
       * @returns {Number} The estimated distance squared from the bounding sphere to the point.
       *
       * @example
       * // Sort bounding spheres from back to front
       * spheres.sort(function(a, b) {
       *     return Cesium.BoundingSphere.distanceSquaredTo(b, camera.positionWC) - Cesium.BoundingSphere.distanceSquaredTo(a, camera.positionWC);
       * });
       */
      BoundingSphere.distanceSquaredTo = function(sphere, cartesian) {
                  Check.typeOf.object('sphere', sphere);
          Check.typeOf.object('cartesian', cartesian);
          
          var diff = Cartesian3.subtract(sphere.center, cartesian, distanceSquaredToScratch);
          return Cartesian3.magnitudeSquared(diff) - sphere.radius * sphere.radius;
      };
  
      /**
       * Applies a 4x4 affine transformation matrix to a bounding sphere where there is no scale
       * The transformation matrix is not verified to have a uniform scale of 1.
       * This method is faster than computing the general bounding sphere transform using {@link BoundingSphere.transform}.
       *
       * @param {BoundingSphere} sphere The bounding sphere to apply the transformation to.
       * @param {Matrix4} transform The transformation matrix to apply to the bounding sphere.
       * @param {BoundingSphere} [result] The object onto which to store the result.
       * @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if none was provided.
       *
       * @example
       * var modelMatrix = Cesium.Transforms.eastNorthUpToFixedFrame(positionOnEllipsoid);
       * var boundingSphere = new Cesium.BoundingSphere();
       * var newBoundingSphere = Cesium.BoundingSphere.transformWithoutScale(boundingSphere, modelMatrix);
       */
      BoundingSphere.transformWithoutScale = function(sphere, transform, result) {
                  Check.typeOf.object('sphere', sphere);
          Check.typeOf.object('transform', transform);
          
          if (!defined(result)) {
              result = new BoundingSphere();
          }
  
          result.center = Matrix4.multiplyByPoint(transform, sphere.center, result.center);
          result.radius = sphere.radius;
  
          return result;
      };
  
      var scratchCartesian3 = new Cartesian3();
      /**
       * The distances calculated by the vector from the center of the bounding sphere to position projected onto direction
       * plus/minus the radius of the bounding sphere.
       * <br>
       * If you imagine the infinite number of planes with normal direction, this computes the smallest distance to the
       * closest and farthest planes from position that intersect the bounding sphere.
       *
       * @param {BoundingSphere} sphere The bounding sphere to calculate the distance to.
       * @param {Cartesian3} position The position to calculate the distance from.
       * @param {Cartesian3} direction The direction from position.
       * @param {Interval} [result] A Interval to store the nearest and farthest distances.
       * @returns {Interval} The nearest and farthest distances on the bounding sphere from position in direction.
       */
      BoundingSphere.computePlaneDistances = function(sphere, position, direction, result) {
                  Check.typeOf.object('sphere', sphere);
          Check.typeOf.object('position', position);
          Check.typeOf.object('direction', direction);
          
          if (!defined(result)) {
              result = new Interval();
          }
  
          var toCenter = Cartesian3.subtract(sphere.center, position, scratchCartesian3);
          var mag = Cartesian3.dot(direction, toCenter);
  
          result.start = mag - sphere.radius;
          result.stop = mag + sphere.radius;
          return result;
      };
  
      var projectTo2DNormalScratch = new Cartesian3();
      var projectTo2DEastScratch = new Cartesian3();
      var projectTo2DNorthScratch = new Cartesian3();
      var projectTo2DWestScratch = new Cartesian3();
      var projectTo2DSouthScratch = new Cartesian3();
      var projectTo2DCartographicScratch = new Cartographic();
      var projectTo2DPositionsScratch = new Array(8);
      for (var n = 0; n < 8; ++n) {
          projectTo2DPositionsScratch[n] = new Cartesian3();
      }
  
      var projectTo2DProjection = new GeographicProjection();
      /**
       * Creates a bounding sphere in 2D from a bounding sphere in 3D world coordinates.
       *
       * @param {BoundingSphere} sphere The bounding sphere to transform to 2D.
       * @param {Object} [projection=GeographicProjection] The projection to 2D.
       * @param {BoundingSphere} [result] The object onto which to store the result.
       * @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if none was provided.
       */
      BoundingSphere.projectTo2D = function(sphere, projection, result) {
                  Check.typeOf.object('sphere', sphere);
          
          projection = defaultValue(projection, projectTo2DProjection);
  
          var ellipsoid = projection.ellipsoid;
          var center = sphere.center;
          var radius = sphere.radius;
  
          var normal = ellipsoid.geodeticSurfaceNormal(center, projectTo2DNormalScratch);
          var east = Cartesian3.cross(Cartesian3.UNIT_Z, normal, projectTo2DEastScratch);
          Cartesian3.normalize(east, east);
          var north = Cartesian3.cross(normal, east, projectTo2DNorthScratch);
          Cartesian3.normalize(north, north);
  
          Cartesian3.multiplyByScalar(normal, radius, normal);
          Cartesian3.multiplyByScalar(north, radius, north);
          Cartesian3.multiplyByScalar(east, radius, east);
  
          var south = Cartesian3.negate(north, projectTo2DSouthScratch);
          var west = Cartesian3.negate(east, projectTo2DWestScratch);
  
          var positions = projectTo2DPositionsScratch;
  
          // top NE corner
          var corner = positions[0];
          Cartesian3.add(normal, north, corner);
          Cartesian3.add(corner, east, corner);
  
          // top NW corner
          corner = positions[1];
          Cartesian3.add(normal, north, corner);
          Cartesian3.add(corner, west, corner);
  
          // top SW corner
          corner = positions[2];
          Cartesian3.add(normal, south, corner);
          Cartesian3.add(corner, west, corner);
  
          // top SE corner
          corner = positions[3];
          Cartesian3.add(normal, south, corner);
          Cartesian3.add(corner, east, corner);
  
          Cartesian3.negate(normal, normal);
  
          // bottom NE corner
          corner = positions[4];
          Cartesian3.add(normal, north, corner);
          Cartesian3.add(corner, east, corner);
  
          // bottom NW corner
          corner = positions[5];
          Cartesian3.add(normal, north, corner);
          Cartesian3.add(corner, west, corner);
  
          // bottom SW corner
          corner = positions[6];
          Cartesian3.add(normal, south, corner);
          Cartesian3.add(corner, west, corner);
  
          // bottom SE corner
          corner = positions[7];
          Cartesian3.add(normal, south, corner);
          Cartesian3.add(corner, east, corner);
  
          var length = positions.length;
          for (var i = 0; i < length; ++i) {
              var position = positions[i];
              Cartesian3.add(center, position, position);
              var cartographic = ellipsoid.cartesianToCartographic(position, projectTo2DCartographicScratch);
              projection.project(cartographic, position);
          }
  
          result = BoundingSphere.fromPoints(positions, result);
  
          // swizzle center components
          center = result.center;
          var x = center.x;
          var y = center.y;
          var z = center.z;
          center.x = z;
          center.y = x;
          center.z = y;
  
          return result;
      };
  
      /**
       * Determines whether or not a sphere is hidden from view by the occluder.
       *
       * @param {BoundingSphere} sphere The bounding sphere surrounding the occludee object.
       * @param {Occluder} occluder The occluder.
       * @returns {Boolean} <code>true</code> if the sphere is not visible; otherwise <code>false</code>.
       */
      BoundingSphere.isOccluded = function(sphere, occluder) {
                  Check.typeOf.object('sphere', sphere);
          Check.typeOf.object('occluder', occluder);
                  return !occluder.isBoundingSphereVisible(sphere);
      };
  
      /**
       * Compares the provided BoundingSphere componentwise and returns
       * <code>true</code> if they are equal, <code>false</code> otherwise.
       *
       * @param {BoundingSphere} [left] The first BoundingSphere.
       * @param {BoundingSphere} [right] The second BoundingSphere.
       * @returns {Boolean} <code>true</code> if left and right are equal, <code>false</code> otherwise.
       */
      BoundingSphere.equals = function(left, right) {
          return (left === right) ||
                 ((defined(left)) &&
                  (defined(right)) &&
                  Cartesian3.equals(left.center, right.center) &&
                  left.radius === right.radius);
      };
  
      /**
       * Determines which side of a plane the sphere is located.
       *
       * @param {Plane} plane The plane to test against.
       * @returns {Intersect} {@link Intersect.INSIDE} if the entire sphere is on the side of the plane
       *                      the normal is pointing, {@link Intersect.OUTSIDE} if the entire sphere is
       *                      on the opposite side, and {@link Intersect.INTERSECTING} if the sphere
       *                      intersects the plane.
       */
      BoundingSphere.prototype.intersectPlane = function(plane) {
          return BoundingSphere.intersectPlane(this, plane);
      };
  
      /**
       * Computes the estimated distance squared from the closest point on a bounding sphere to a point.
       *
       * @param {Cartesian3} cartesian The point
       * @returns {Number} The estimated distance squared from the bounding sphere to the point.
       *
       * @example
       * // Sort bounding spheres from back to front
       * spheres.sort(function(a, b) {
       *     return b.distanceSquaredTo(camera.positionWC) - a.distanceSquaredTo(camera.positionWC);
       * });
       */
      BoundingSphere.prototype.distanceSquaredTo = function(cartesian) {
          return BoundingSphere.distanceSquaredTo(this, cartesian);
      };
  
      /**
       * The distances calculated by the vector from the center of the bounding sphere to position projected onto direction
       * plus/minus the radius of the bounding sphere.
       * <br>
       * If you imagine the infinite number of planes with normal direction, this computes the smallest distance to the
       * closest and farthest planes from position that intersect the bounding sphere.
       *
       * @param {Cartesian3} position The position to calculate the distance from.
       * @param {Cartesian3} direction The direction from position.
       * @param {Interval} [result] A Interval to store the nearest and farthest distances.
       * @returns {Interval} The nearest and farthest distances on the bounding sphere from position in direction.
       */
      BoundingSphere.prototype.computePlaneDistances = function(position, direction, result) {
          return BoundingSphere.computePlaneDistances(this, position, direction, result);
      };
  
      /**
       * Determines whether or not a sphere is hidden from view by the occluder.
       *
       * @param {Occluder} occluder The occluder.
       * @returns {Boolean} <code>true</code> if the sphere is not visible; otherwise <code>false</code>.
       */
      BoundingSphere.prototype.isOccluded = function(occluder) {
          return BoundingSphere.isOccluded(this, occluder);
      };
  
      /**
       * Compares this BoundingSphere against the provided BoundingSphere componentwise and returns
       * <code>true</code> if they are equal, <code>false</code> otherwise.
       *
       * @param {BoundingSphere} [right] The right hand side BoundingSphere.
       * @returns {Boolean} <code>true</code> if they are equal, <code>false</code> otherwise.
       */
      BoundingSphere.prototype.equals = function(right) {
          return BoundingSphere.equals(this, right);
      };
  
      /**
       * Duplicates this BoundingSphere instance.
       *
       * @param {BoundingSphere} [result] The object onto which to store the result.
       * @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if none was provided.
       */
      BoundingSphere.prototype.clone = function(result) {
          return BoundingSphere.clone(this, result);
      };
  
      return BoundingSphere;
  });
  
  define('Core/Fullscreen',[
          './defined',
          './defineProperties'
      ], function(
          defined,
          defineProperties) {
      'use strict';
  
      var _supportsFullscreen;
      var _names = {
          requestFullscreen : undefined,
          exitFullscreen : undefined,
          fullscreenEnabled : undefined,
          fullscreenElement : undefined,
          fullscreenchange : undefined,
          fullscreenerror : undefined
      };
  
      /**
       * Browser-independent functions for working with the standard fullscreen API.
       *
       * @exports Fullscreen
       *
       * @see {@link http://dvcs.w3.org/hg/fullscreen/raw-file/tip/Overview.html|W3C Fullscreen Living Specification}
       */
      var Fullscreen = {};
  
      defineProperties(Fullscreen, {
          /**
           * The element that is currently fullscreen, if any.  To simply check if the
           * browser is in fullscreen mode or not, use {@link Fullscreen#fullscreen}.
           * @memberof Fullscreen
           * @type {Object}
           * @readonly
           */
          element : {
              get : function() {
                  if (!Fullscreen.supportsFullscreen()) {
                      return undefined;
                  }
  
                  return document[_names.fullscreenElement];
              }
          },
  
          /**
           * The name of the event on the document that is fired when fullscreen is
           * entered or exited.  This event name is intended for use with addEventListener.
           * In your event handler, to determine if the browser is in fullscreen mode or not,
           * use {@link Fullscreen#fullscreen}.
           * @memberof Fullscreen
           * @type {String}
           * @readonly
           */
          changeEventName : {
              get : function() {
                  if (!Fullscreen.supportsFullscreen()) {
                      return undefined;
                  }
  
                  return _names.fullscreenchange;
              }
          },
  
          /**
           * The name of the event that is fired when a fullscreen error
           * occurs.  This event name is intended for use with addEventListener.
           * @memberof Fullscreen
           * @type {String}
           * @readonly
           */
          errorEventName : {
              get : function() {
                  if (!Fullscreen.supportsFullscreen()) {
                      return undefined;
                  }
  
                  return _names.fullscreenerror;
              }
          },
  
          /**
           * Determine whether the browser will allow an element to be made fullscreen, or not.
           * For example, by default, iframes cannot go fullscreen unless the containing page
           * adds an "allowfullscreen" attribute (or prefixed equivalent).
           * @memberof Fullscreen
           * @type {Boolean}
           * @readonly
           */
          enabled : {
              get : function() {
                  if (!Fullscreen.supportsFullscreen()) {
                      return undefined;
                  }
  
                  return document[_names.fullscreenEnabled];
              }
          },
  
          /**
           * Determines if the browser is currently in fullscreen mode.
           * @memberof Fullscreen
           * @type {Boolean}
           * @readonly
           */
          fullscreen : {
              get : function() {
                  if (!Fullscreen.supportsFullscreen()) {
                      return undefined;
                  }
  
                  return Fullscreen.element !== null;
              }
          }
      });
  
      /**
       * Detects whether the browser supports the standard fullscreen API.
       *
       * @returns {Boolean} <code>true</code> if the browser supports the standard fullscreen API,
       * <code>false</code> otherwise.
       */
      Fullscreen.supportsFullscreen = function() {
          if (defined(_supportsFullscreen)) {
              return _supportsFullscreen;
          }
  
          _supportsFullscreen = false;
  
          var body = document.body;
          if (typeof body.requestFullscreen === 'function') {
              // go with the unprefixed, standard set of names
              _names.requestFullscreen = 'requestFullscreen';
              _names.exitFullscreen = 'exitFullscreen';
              _names.fullscreenEnabled = 'fullscreenEnabled';
              _names.fullscreenElement = 'fullscreenElement';
              _names.fullscreenchange = 'fullscreenchange';
              _names.fullscreenerror = 'fullscreenerror';
              _supportsFullscreen = true;
              return _supportsFullscreen;
          }
  
          //check for the correct combination of prefix plus the various names that browsers use
          var prefixes = ['webkit', 'moz', 'o', 'ms', 'khtml'];
          var name;
          for (var i = 0, len = prefixes.length; i < len; ++i) {
              var prefix = prefixes[i];
  
              // casing of Fullscreen differs across browsers
              name = prefix + 'RequestFullscreen';
              if (typeof body[name] === 'function') {
                  _names.requestFullscreen = name;
                  _supportsFullscreen = true;
              } else {
                  name = prefix + 'RequestFullScreen';
                  if (typeof body[name] === 'function') {
                      _names.requestFullscreen = name;
                      _supportsFullscreen = true;
                  }
              }
  
              // disagreement about whether it's "exit" as per spec, or "cancel"
              name = prefix + 'ExitFullscreen';
              if (typeof document[name] === 'function') {
                  _names.exitFullscreen = name;
              } else {
                  name = prefix + 'CancelFullScreen';
                  if (typeof document[name] === 'function') {
                      _names.exitFullscreen = name;
                  }
              }
  
              // casing of Fullscreen differs across browsers
              name = prefix + 'FullscreenEnabled';
              if (document[name] !== undefined) {
                  _names.fullscreenEnabled = name;
              } else {
                  name = prefix + 'FullScreenEnabled';
                  if (document[name] !== undefined) {
                      _names.fullscreenEnabled = name;
                  }
              }
  
              // casing of Fullscreen differs across browsers
              name = prefix + 'FullscreenElement';
              if (document[name] !== undefined) {
                  _names.fullscreenElement = name;
              } else {
                  name = prefix + 'FullScreenElement';
                  if (document[name] !== undefined) {
                      _names.fullscreenElement = name;
                  }
              }
  
              // thankfully, event names are all lowercase per spec
              name = prefix + 'fullscreenchange';
              // event names do not have 'on' in the front, but the property on the document does
              if (document['on' + name] !== undefined) {
                  //except on IE
                  if (prefix === 'ms') {
                      name = 'MSFullscreenChange';
                  }
                  _names.fullscreenchange = name;
              }
  
              name = prefix + 'fullscreenerror';
              if (document['on' + name] !== undefined) {
                  //except on IE
                  if (prefix === 'ms') {
                      name = 'MSFullscreenError';
                  }
                  _names.fullscreenerror = name;
              }
          }
  
          return _supportsFullscreen;
      };
  
      /**
       * Asynchronously requests the browser to enter fullscreen mode on the given element.
       * If fullscreen mode is not supported by the browser, does nothing.
       *
       * @param {Object} element The HTML element which will be placed into fullscreen mode.
       * @param {HMDVRDevice} [vrDevice] The VR device.
       *
       * @example
       * // Put the entire page into fullscreen.
       * Cesium.Fullscreen.requestFullscreen(document.body)
       *
       * // Place only the Cesium canvas into fullscreen.
       * Cesium.Fullscreen.requestFullscreen(scene.canvas)
       */
      Fullscreen.requestFullscreen = function(element, vrDevice) {
          if (!Fullscreen.supportsFullscreen()) {
              return;
          }
  
          element[_names.requestFullscreen]({ vrDisplay: vrDevice });
      };
  
      /**
       * Asynchronously exits fullscreen mode.  If the browser is not currently
       * in fullscreen, or if fullscreen mode is not supported by the browser, does nothing.
       */
      Fullscreen.exitFullscreen = function() {
          if (!Fullscreen.supportsFullscreen()) {
              return;
          }
  
          document[_names.exitFullscreen]();
      };
  
      return Fullscreen;
  });
  
  define('Core/FeatureDetection',[
          './defaultValue',
          './defined',
          './Fullscreen'
      ], function(
          defaultValue,
          defined,
          Fullscreen) {
      'use strict';
  
      var theNavigator;
      if (typeof navigator !== 'undefined') {
          theNavigator = navigator;
      } else {
          theNavigator = {};
      }
  
      function extractVersion(versionString) {
          var parts = versionString.split('.');
          for (var i = 0, len = parts.length; i < len; ++i) {
              parts[i] = parseInt(parts[i], 10);
          }
          return parts;
      }
  
      var isChromeResult;
      var chromeVersionResult;
      function isChrome() {
          if (!defined(isChromeResult)) {
              isChromeResult = false;
              // Edge contains Chrome in the user agent too
              if (!isEdge()) {
                  var fields = (/ Chrome\/([\.0-9]+)/).exec(theNavigator.userAgent);
                  if (fields !== null) {
                      isChromeResult = true;
                      chromeVersionResult = extractVersion(fields[1]);
                  }
              }
          }
  
          return isChromeResult;
      }
  
      function chromeVersion() {
          return isChrome() && chromeVersionResult;
      }
  
      var isSafariResult;
      var safariVersionResult;
      function isSafari() {
          if (!defined(isSafariResult)) {
              isSafariResult = false;
  
              // Chrome and Edge contain Safari in the user agent too
              if (!isChrome() && !isEdge() && (/ Safari\/[\.0-9]+/).test(theNavigator.userAgent)) {
                  var fields = (/ Version\/([\.0-9]+)/).exec(theNavigator.userAgent);
                  if (fields !== null) {
                      isSafariResult = true;
                      safariVersionResult = extractVersion(fields[1]);
                  }
              }
          }
  
          return isSafariResult;
      }
  
      function safariVersion() {
          return isSafari() && safariVersionResult;
      }
  
      var isWebkitResult;
      var webkitVersionResult;
      function isWebkit() {
          if (!defined(isWebkitResult)) {
              isWebkitResult = false;
  
              var fields = (/ AppleWebKit\/([\.0-9]+)(\+?)/).exec(theNavigator.userAgent);
              if (fields !== null) {
                  isWebkitResult = true;
                  webkitVersionResult = extractVersion(fields[1]);
                  webkitVersionResult.isNightly = !!fields[2];
              }
          }
  
          return isWebkitResult;
      }
  
      function webkitVersion() {
          return isWebkit() && webkitVersionResult;
      }
  
      var isInternetExplorerResult;
      var internetExplorerVersionResult;
      function isInternetExplorer() {
          if (!defined(isInternetExplorerResult)) {
              isInternetExplorerResult = false;
  
              var fields;
              if (theNavigator.appName === 'Microsoft Internet Explorer') {
                  fields = /MSIE ([0-9]{1,}[\.0-9]{0,})/.exec(theNavigator.userAgent);
                  if (fields !== null) {
                      isInternetExplorerResult = true;
                      internetExplorerVersionResult = extractVersion(fields[1]);
                  }
              } else if (theNavigator.appName === 'Netscape') {
                  fields = /Trident\/.*rv:([0-9]{1,}[\.0-9]{0,})/.exec(theNavigator.userAgent);
                  if (fields !== null) {
                      isInternetExplorerResult = true;
                      internetExplorerVersionResult = extractVersion(fields[1]);
                  }
              }
          }
          return isInternetExplorerResult;
      }
  
      function internetExplorerVersion() {
          return isInternetExplorer() && internetExplorerVersionResult;
      }
  
      var isEdgeResult;
      var edgeVersionResult;
      function isEdge() {
          if (!defined(isEdgeResult)) {
              isEdgeResult = false;
              var fields = (/ Edge\/([\.0-9]+)/).exec(theNavigator.userAgent);
              if (fields !== null) {
                  isEdgeResult = true;
                  edgeVersionResult = extractVersion(fields[1]);
              }
          }
          return isEdgeResult;
      }
  
      function edgeVersion() {
          return isEdge() && edgeVersionResult;
      }
  
      var isFirefoxResult;
      var firefoxVersionResult;
      function isFirefox() {
          if (!defined(isFirefoxResult)) {
              isFirefoxResult = false;
  
              var fields = /Firefox\/([\.0-9]+)/.exec(theNavigator.userAgent);
              if (fields !== null) {
                  isFirefoxResult = true;
                  firefoxVersionResult = extractVersion(fields[1]);
              }
          }
          return isFirefoxResult;
      }
  
      var isWindowsResult;
      function isWindows() {
          if (!defined(isWindowsResult)) {
              isWindowsResult = /Windows/i.test(theNavigator.appVersion);
          }
          return isWindowsResult;
      }
  
  
      function firefoxVersion() {
          return isFirefox() && firefoxVersionResult;
      }
  
      var hasPointerEvents;
      function supportsPointerEvents() {
          if (!defined(hasPointerEvents)) {
              //While navigator.pointerEnabled is deprecated in the W3C specification
              //we still need to use it if it exists in order to support browsers
              //that rely on it, such as the Windows WebBrowser control which defines
              //PointerEvent but sets navigator.pointerEnabled to false.
              hasPointerEvents = typeof PointerEvent !== 'undefined' && (!defined(theNavigator.pointerEnabled) || theNavigator.pointerEnabled);
          }
          return hasPointerEvents;
      }
  
      var imageRenderingValueResult;
      var supportsImageRenderingPixelatedResult;
      function supportsImageRenderingPixelated() {
          if (!defined(supportsImageRenderingPixelatedResult)) {
              var canvas = document.createElement('canvas');
              canvas.setAttribute('style',
                                  'image-rendering: -moz-crisp-edges;' +
                                  'image-rendering: pixelated;');
              //canvas.style.imageRendering will be undefined, null or an empty string on unsupported browsers.
              var tmp = canvas.style.imageRendering;
              supportsImageRenderingPixelatedResult = defined(tmp) && tmp !== '';
              if (supportsImageRenderingPixelatedResult) {
                  imageRenderingValueResult = tmp;
              }
          }
          return supportsImageRenderingPixelatedResult;
      }
  
      function imageRenderingValue() {
          return supportsImageRenderingPixelated() ? imageRenderingValueResult : undefined;
      }
  
      /**
       * A set of functions to detect whether the current browser supports
       * various features.
       *
       * @exports FeatureDetection
       */
      var FeatureDetection = {
          isChrome : isChrome,
          chromeVersion : chromeVersion,
          isSafari : isSafari,
          safariVersion : safariVersion,
          isWebkit : isWebkit,
          webkitVersion : webkitVersion,
          isInternetExplorer : isInternetExplorer,
          internetExplorerVersion : internetExplorerVersion,
          isEdge : isEdge,
          edgeVersion : edgeVersion,
          isFirefox : isFirefox,
          firefoxVersion : firefoxVersion,
          isWindows : isWindows,
          hardwareConcurrency : defaultValue(theNavigator.hardwareConcurrency, 3),
          supportsPointerEvents : supportsPointerEvents,
          supportsImageRenderingPixelated: supportsImageRenderingPixelated,
          imageRenderingValue: imageRenderingValue
      };
  
      /**
       * Detects whether the current browser supports the full screen standard.
       *
       * @returns {Boolean} true if the browser supports the full screen standard, false if not.
       *
       * @see Fullscreen
       * @see {@link http://dvcs.w3.org/hg/fullscreen/raw-file/tip/Overview.html|W3C Fullscreen Living Specification}
       */
      FeatureDetection.supportsFullscreen = function() {
          return Fullscreen.supportsFullscreen();
      };
  
      /**
       * Detects whether the current browser supports typed arrays.
       *
       * @returns {Boolean} true if the browser supports typed arrays, false if not.
       *
       * @see {@link http://www.khronos.org/registry/typedarray/specs/latest/|Typed Array Specification}
       */
      FeatureDetection.supportsTypedArrays = function() {
          return typeof ArrayBuffer !== 'undefined';
      };
  
      /**
       * Detects whether the current browser supports Web Workers.
       *
       * @returns {Boolean} true if the browsers supports Web Workers, false if not.
       *
       * @see {@link http://www.w3.org/TR/workers/}
       */
      FeatureDetection.supportsWebWorkers = function() {
          return typeof Worker !== 'undefined';
      };
  
      return FeatureDetection;
  });
  
  define('Core/WebGLConstants',[
          './freezeObject'
      ], function(
          freezeObject) {
      'use strict';
  
      /**
       * Enum containing WebGL Constant values by name.
       * for use without an active WebGL context, or in cases where certain constants are unavailable using the WebGL context
       * (For example, in [Safari 9]{@link https://github.com/AnalyticalGraphicsInc/cesium/issues/2989}).
       *
       * These match the constants from the [WebGL 1.0]{@link https://www.khronos.org/registry/webgl/specs/latest/1.0/}
       * and [WebGL 2.0]{@link https://www.khronos.org/registry/webgl/specs/latest/2.0/}
       * specifications.
       *
       * @exports WebGLConstants
       */
      var WebGLConstants = {
          DEPTH_BUFFER_BIT : 0x00000100,
          STENCIL_BUFFER_BIT : 0x00000400,
          COLOR_BUFFER_BIT : 0x00004000,
          POINTS : 0x0000,
          LINES : 0x0001,
          LINE_LOOP : 0x0002,
          LINE_STRIP : 0x0003,
          TRIANGLES : 0x0004,
          TRIANGLE_STRIP : 0x0005,
          TRIANGLE_FAN : 0x0006,
          ZERO : 0,
          ONE : 1,
          SRC_COLOR : 0x0300,
          ONE_MINUS_SRC_COLOR : 0x0301,
          SRC_ALPHA : 0x0302,
          ONE_MINUS_SRC_ALPHA : 0x0303,
          DST_ALPHA : 0x0304,
          ONE_MINUS_DST_ALPHA : 0x0305,
          DST_COLOR : 0x0306,
          ONE_MINUS_DST_COLOR : 0x0307,
          SRC_ALPHA_SATURATE : 0x0308,
          FUNC_ADD : 0x8006,
          BLEND_EQUATION : 0x8009,
          BLEND_EQUATION_RGB : 0x8009, // same as BLEND_EQUATION
          BLEND_EQUATION_ALPHA : 0x883D,
          FUNC_SUBTRACT : 0x800A,
          FUNC_REVERSE_SUBTRACT : 0x800B,
          BLEND_DST_RGB : 0x80C8,
          BLEND_SRC_RGB : 0x80C9,
          BLEND_DST_ALPHA : 0x80CA,
          BLEND_SRC_ALPHA : 0x80CB,
          CONSTANT_COLOR : 0x8001,
          ONE_MINUS_CONSTANT_COLOR : 0x8002,
          CONSTANT_ALPHA : 0x8003,
          ONE_MINUS_CONSTANT_ALPHA : 0x8004,
          BLEND_COLOR : 0x8005,
          ARRAY_BUFFER : 0x8892,
          ELEMENT_ARRAY_BUFFER : 0x8893,
          ARRAY_BUFFER_BINDING : 0x8894,
          ELEMENT_ARRAY_BUFFER_BINDING : 0x8895,
          STREAM_DRAW : 0x88E0,
          STATIC_DRAW : 0x88E4,
          DYNAMIC_DRAW : 0x88E8,
          BUFFER_SIZE : 0x8764,
          BUFFER_USAGE : 0x8765,
          CURRENT_VERTEX_ATTRIB : 0x8626,
          FRONT : 0x0404,
          BACK : 0x0405,
          FRONT_AND_BACK : 0x0408,
          CULL_FACE : 0x0B44,
          BLEND : 0x0BE2,
          DITHER : 0x0BD0,
          STENCIL_TEST : 0x0B90,
          DEPTH_TEST : 0x0B71,
          SCISSOR_TEST : 0x0C11,
          POLYGON_OFFSET_FILL : 0x8037,
          SAMPLE_ALPHA_TO_COVERAGE : 0x809E,
          SAMPLE_COVERAGE : 0x80A0,
          NO_ERROR : 0,
          INVALID_ENUM : 0x0500,
          INVALID_VALUE : 0x0501,
          INVALID_OPERATION : 0x0502,
          OUT_OF_MEMORY : 0x0505,
          CW : 0x0900,
          CCW : 0x0901,
          LINE_WIDTH : 0x0B21,
          ALIASED_POINT_SIZE_RANGE : 0x846D,
          ALIASED_LINE_WIDTH_RANGE : 0x846E,
          CULL_FACE_MODE : 0x0B45,
          FRONT_FACE : 0x0B46,
          DEPTH_RANGE : 0x0B70,
          DEPTH_WRITEMASK : 0x0B72,
          DEPTH_CLEAR_VALUE : 0x0B73,
          DEPTH_FUNC : 0x0B74,
          STENCIL_CLEAR_VALUE : 0x0B91,
          STENCIL_FUNC : 0x0B92,
          STENCIL_FAIL : 0x0B94,
          STENCIL_PASS_DEPTH_FAIL : 0x0B95,
          STENCIL_PASS_DEPTH_PASS : 0x0B96,
          STENCIL_REF : 0x0B97,
          STENCIL_VALUE_MASK : 0x0B93,
          STENCIL_WRITEMASK : 0x0B98,
          STENCIL_BACK_FUNC : 0x8800,
          STENCIL_BACK_FAIL : 0x8801,
          STENCIL_BACK_PASS_DEPTH_FAIL : 0x8802,
          STENCIL_BACK_PASS_DEPTH_PASS : 0x8803,
          STENCIL_BACK_REF : 0x8CA3,
          STENCIL_BACK_VALUE_MASK : 0x8CA4,
          STENCIL_BACK_WRITEMASK : 0x8CA5,
          VIEWPORT : 0x0BA2,
          SCISSOR_BOX : 0x0C10,
          COLOR_CLEAR_VALUE : 0x0C22,
          COLOR_WRITEMASK : 0x0C23,
          UNPACK_ALIGNMENT : 0x0CF5,
          PACK_ALIGNMENT : 0x0D05,
          MAX_TEXTURE_SIZE : 0x0D33,
          MAX_VIEWPORT_DIMS : 0x0D3A,
          SUBPIXEL_BITS : 0x0D50,
          RED_BITS : 0x0D52,
          GREEN_BITS : 0x0D53,
          BLUE_BITS : 0x0D54,
          ALPHA_BITS : 0x0D55,
          DEPTH_BITS : 0x0D56,
          STENCIL_BITS : 0x0D57,
          POLYGON_OFFSET_UNITS : 0x2A00,
          POLYGON_OFFSET_FACTOR : 0x8038,
          TEXTURE_BINDING_2D : 0x8069,
          SAMPLE_BUFFERS : 0x80A8,
          SAMPLES : 0x80A9,
          SAMPLE_COVERAGE_VALUE : 0x80AA,
          SAMPLE_COVERAGE_INVERT : 0x80AB,
          COMPRESSED_TEXTURE_FORMATS : 0x86A3,
          DONT_CARE : 0x1100,
          FASTEST : 0x1101,
          NICEST : 0x1102,
          GENERATE_MIPMAP_HINT : 0x8192,
          BYTE : 0x1400,
          UNSIGNED_BYTE : 0x1401,
          SHORT : 0x1402,
          UNSIGNED_SHORT : 0x1403,
          INT : 0x1404,
          UNSIGNED_INT : 0x1405,
          FLOAT : 0x1406,
          DEPTH_COMPONENT : 0x1902,
          ALPHA : 0x1906,
          RGB : 0x1907,
          RGBA : 0x1908,
          LUMINANCE : 0x1909,
          LUMINANCE_ALPHA : 0x190A,
          UNSIGNED_SHORT_4_4_4_4 : 0x8033,
          UNSIGNED_SHORT_5_5_5_1 : 0x8034,
          UNSIGNED_SHORT_5_6_5 : 0x8363,
          FRAGMENT_SHADER : 0x8B30,
          VERTEX_SHADER : 0x8B31,
          MAX_VERTEX_ATTRIBS : 0x8869,
          MAX_VERTEX_UNIFORM_VECTORS : 0x8DFB,
          MAX_VARYING_VECTORS : 0x8DFC,
          MAX_COMBINED_TEXTURE_IMAGE_UNITS : 0x8B4D,
          MAX_VERTEX_TEXTURE_IMAGE_UNITS : 0x8B4C,
          MAX_TEXTURE_IMAGE_UNITS : 0x8872,
          MAX_FRAGMENT_UNIFORM_VECTORS : 0x8DFD,
          SHADER_TYPE : 0x8B4F,
          DELETE_STATUS : 0x8B80,
          LINK_STATUS : 0x8B82,
          VALIDATE_STATUS : 0x8B83,
          ATTACHED_SHADERS : 0x8B85,
          ACTIVE_UNIFORMS : 0x8B86,
          ACTIVE_ATTRIBUTES : 0x8B89,
          SHADING_LANGUAGE_VERSION : 0x8B8C,
          CURRENT_PROGRAM : 0x8B8D,
          NEVER : 0x0200,
          LESS : 0x0201,
          EQUAL : 0x0202,
          LEQUAL : 0x0203,
          GREATER : 0x0204,
          NOTEQUAL : 0x0205,
          GEQUAL : 0x0206,
          ALWAYS : 0x0207,
          KEEP : 0x1E00,
          REPLACE : 0x1E01,
          INCR : 0x1E02,
          DECR : 0x1E03,
          INVERT : 0x150A,
          INCR_WRAP : 0x8507,
          DECR_WRAP : 0x8508,
          VENDOR : 0x1F00,
          RENDERER : 0x1F01,
          VERSION : 0x1F02,
          NEAREST : 0x2600,
          LINEAR : 0x2601,
          NEAREST_MIPMAP_NEAREST : 0x2700,
          LINEAR_MIPMAP_NEAREST : 0x2701,
          NEAREST_MIPMAP_LINEAR : 0x2702,
          LINEAR_MIPMAP_LINEAR : 0x2703,
          TEXTURE_MAG_FILTER : 0x2800,
          TEXTURE_MIN_FILTER : 0x2801,
          TEXTURE_WRAP_S : 0x2802,
          TEXTURE_WRAP_T : 0x2803,
          TEXTURE_2D : 0x0DE1,
          TEXTURE : 0x1702,
          TEXTURE_CUBE_MAP : 0x8513,
          TEXTURE_BINDING_CUBE_MAP : 0x8514,
          TEXTURE_CUBE_MAP_POSITIVE_X : 0x8515,
          TEXTURE_CUBE_MAP_NEGATIVE_X : 0x8516,
          TEXTURE_CUBE_MAP_POSITIVE_Y : 0x8517,
          TEXTURE_CUBE_MAP_NEGATIVE_Y : 0x8518,
          TEXTURE_CUBE_MAP_POSITIVE_Z : 0x8519,
          TEXTURE_CUBE_MAP_NEGATIVE_Z : 0x851A,
          MAX_CUBE_MAP_TEXTURE_SIZE : 0x851C,
          TEXTURE0 : 0x84C0,
          TEXTURE1 : 0x84C1,
          TEXTURE2 : 0x84C2,
          TEXTURE3 : 0x84C3,
          TEXTURE4 : 0x84C4,
          TEXTURE5 : 0x84C5,
          TEXTURE6 : 0x84C6,
          TEXTURE7 : 0x84C7,
          TEXTURE8 : 0x84C8,
          TEXTURE9 : 0x84C9,
          TEXTURE10 : 0x84CA,
          TEXTURE11 : 0x84CB,
          TEXTURE12 : 0x84CC,
          TEXTURE13 : 0x84CD,
          TEXTURE14 : 0x84CE,
          TEXTURE15 : 0x84CF,
          TEXTURE16 : 0x84D0,
          TEXTURE17 : 0x84D1,
          TEXTURE18 : 0x84D2,
          TEXTURE19 : 0x84D3,
          TEXTURE20 : 0x84D4,
          TEXTURE21 : 0x84D5,
          TEXTURE22 : 0x84D6,
          TEXTURE23 : 0x84D7,
          TEXTURE24 : 0x84D8,
          TEXTURE25 : 0x84D9,
          TEXTURE26 : 0x84DA,
          TEXTURE27 : 0x84DB,
          TEXTURE28 : 0x84DC,
          TEXTURE29 : 0x84DD,
          TEXTURE30 : 0x84DE,
          TEXTURE31 : 0x84DF,
          ACTIVE_TEXTURE : 0x84E0,
          REPEAT : 0x2901,
          CLAMP_TO_EDGE : 0x812F,
          MIRRORED_REPEAT : 0x8370,
          FLOAT_VEC2 : 0x8B50,
          FLOAT_VEC3 : 0x8B51,
          FLOAT_VEC4 : 0x8B52,
          INT_VEC2 : 0x8B53,
          INT_VEC3 : 0x8B54,
          INT_VEC4 : 0x8B55,
          BOOL : 0x8B56,
          BOOL_VEC2 : 0x8B57,
          BOOL_VEC3 : 0x8B58,
          BOOL_VEC4 : 0x8B59,
          FLOAT_MAT2 : 0x8B5A,
          FLOAT_MAT3 : 0x8B5B,
          FLOAT_MAT4 : 0x8B5C,
          SAMPLER_2D : 0x8B5E,
          SAMPLER_CUBE : 0x8B60,
          VERTEX_ATTRIB_ARRAY_ENABLED : 0x8622,
          VERTEX_ATTRIB_ARRAY_SIZE : 0x8623,
          VERTEX_ATTRIB_ARRAY_STRIDE : 0x8624,
          VERTEX_ATTRIB_ARRAY_TYPE : 0x8625,
          VERTEX_ATTRIB_ARRAY_NORMALIZED : 0x886A,
          VERTEX_ATTRIB_ARRAY_POINTER : 0x8645,
          VERTEX_ATTRIB_ARRAY_BUFFER_BINDING : 0x889F,
          IMPLEMENTATION_COLOR_READ_TYPE : 0x8B9A,
          IMPLEMENTATION_COLOR_READ_FORMAT : 0x8B9B,
          COMPILE_STATUS : 0x8B81,
          LOW_FLOAT : 0x8DF0,
          MEDIUM_FLOAT : 0x8DF1,
          HIGH_FLOAT : 0x8DF2,
          LOW_INT : 0x8DF3,
          MEDIUM_INT : 0x8DF4,
          HIGH_INT : 0x8DF5,
          FRAMEBUFFER : 0x8D40,
          RENDERBUFFER : 0x8D41,
          RGBA4 : 0x8056,
          RGB5_A1 : 0x8057,
          RGB565 : 0x8D62,
          DEPTH_COMPONENT16 : 0x81A5,
          STENCIL_INDEX : 0x1901,
          STENCIL_INDEX8 : 0x8D48,
          DEPTH_STENCIL : 0x84F9,
          RENDERBUFFER_WIDTH : 0x8D42,
          RENDERBUFFER_HEIGHT : 0x8D43,
          RENDERBUFFER_INTERNAL_FORMAT : 0x8D44,
          RENDERBUFFER_RED_SIZE : 0x8D50,
          RENDERBUFFER_GREEN_SIZE : 0x8D51,
          RENDERBUFFER_BLUE_SIZE : 0x8D52,
          RENDERBUFFER_ALPHA_SIZE : 0x8D53,
          RENDERBUFFER_DEPTH_SIZE : 0x8D54,
          RENDERBUFFER_STENCIL_SIZE : 0x8D55,
          FRAMEBUFFER_ATTACHMENT_OBJECT_TYPE : 0x8CD0,
          FRAMEBUFFER_ATTACHMENT_OBJECT_NAME : 0x8CD1,
          FRAMEBUFFER_ATTACHMENT_TEXTURE_LEVEL : 0x8CD2,
          FRAMEBUFFER_ATTACHMENT_TEXTURE_CUBE_MAP_FACE : 0x8CD3,
          COLOR_ATTACHMENT0 : 0x8CE0,
          DEPTH_ATTACHMENT : 0x8D00,
          STENCIL_ATTACHMENT : 0x8D20,
          DEPTH_STENCIL_ATTACHMENT : 0x821A,
          NONE : 0,
          FRAMEBUFFER_COMPLETE : 0x8CD5,
          FRAMEBUFFER_INCOMPLETE_ATTACHMENT : 0x8CD6,
          FRAMEBUFFER_INCOMPLETE_MISSING_ATTACHMENT : 0x8CD7,
          FRAMEBUFFER_INCOMPLETE_DIMENSIONS : 0x8CD9,
          FRAMEBUFFER_UNSUPPORTED : 0x8CDD,
          FRAMEBUFFER_BINDING : 0x8CA6,
          RENDERBUFFER_BINDING : 0x8CA7,
          MAX_RENDERBUFFER_SIZE : 0x84E8,
          INVALID_FRAMEBUFFER_OPERATION : 0x0506,
          UNPACK_FLIP_Y_WEBGL : 0x9240,
          UNPACK_PREMULTIPLY_ALPHA_WEBGL : 0x9241,
          CONTEXT_LOST_WEBGL : 0x9242,
          UNPACK_COLORSPACE_CONVERSION_WEBGL : 0x9243,
          BROWSER_DEFAULT_WEBGL : 0x9244,
  
          // WEBGL_compressed_texture_s3tc
          COMPRESSED_RGB_S3TC_DXT1_EXT : 0x83F0,
          COMPRESSED_RGBA_S3TC_DXT1_EXT : 0x83F1,
          COMPRESSED_RGBA_S3TC_DXT3_EXT : 0x83F2,
          COMPRESSED_RGBA_S3TC_DXT5_EXT : 0x83F3,
  
          // WEBGL_compressed_texture_pvrtc
          COMPRESSED_RGB_PVRTC_4BPPV1_IMG : 0x8C00,
          COMPRESSED_RGB_PVRTC_2BPPV1_IMG : 0x8C01,
          COMPRESSED_RGBA_PVRTC_4BPPV1_IMG : 0x8C02,
          COMPRESSED_RGBA_PVRTC_2BPPV1_IMG : 0x8C03,
  
          // WEBGL_compressed_texture_etc1
          COMPRESSED_RGB_ETC1_WEBGL : 0x8D64,
  
          // Desktop OpenGL
          DOUBLE : 0x140A,
  
          // WebGL 2
          READ_BUFFER : 0x0C02,
          UNPACK_ROW_LENGTH : 0x0CF2,
          UNPACK_SKIP_ROWS : 0x0CF3,
          UNPACK_SKIP_PIXELS : 0x0CF4,
          PACK_ROW_LENGTH : 0x0D02,
          PACK_SKIP_ROWS : 0x0D03,
          PACK_SKIP_PIXELS : 0x0D04,
          COLOR : 0x1800,
          DEPTH : 0x1801,
          STENCIL : 0x1802,
          RED : 0x1903,
          RGB8 : 0x8051,
          RGBA8 : 0x8058,
          RGB10_A2 : 0x8059,
          TEXTURE_BINDING_3D : 0x806A,
          UNPACK_SKIP_IMAGES : 0x806D,
          UNPACK_IMAGE_HEIGHT : 0x806E,
          TEXTURE_3D : 0x806F,
          TEXTURE_WRAP_R : 0x8072,
          MAX_3D_TEXTURE_SIZE : 0x8073,
          UNSIGNED_INT_2_10_10_10_REV : 0x8368,
          MAX_ELEMENTS_VERTICES : 0x80E8,
          MAX_ELEMENTS_INDICES : 0x80E9,
          TEXTURE_MIN_LOD : 0x813A,
          TEXTURE_MAX_LOD : 0x813B,
          TEXTURE_BASE_LEVEL : 0x813C,
          TEXTURE_MAX_LEVEL : 0x813D,
          MIN : 0x8007,
          MAX : 0x8008,
          DEPTH_COMPONENT24 : 0x81A6,
          MAX_TEXTURE_LOD_BIAS : 0x84FD,
          TEXTURE_COMPARE_MODE : 0x884C,
          TEXTURE_COMPARE_FUNC : 0x884D,
          CURRENT_QUERY : 0x8865,
          QUERY_RESULT : 0x8866,
          QUERY_RESULT_AVAILABLE : 0x8867,
          STREAM_READ : 0x88E1,
          STREAM_COPY : 0x88E2,
          STATIC_READ : 0x88E5,
          STATIC_COPY : 0x88E6,
          DYNAMIC_READ : 0x88E9,
          DYNAMIC_COPY : 0x88EA,
          MAX_DRAW_BUFFERS : 0x8824,
          DRAW_BUFFER0 : 0x8825,
          DRAW_BUFFER1 : 0x8826,
          DRAW_BUFFER2 : 0x8827,
          DRAW_BUFFER3 : 0x8828,
          DRAW_BUFFER4 : 0x8829,
          DRAW_BUFFER5 : 0x882A,
          DRAW_BUFFER6 : 0x882B,
          DRAW_BUFFER7 : 0x882C,
          DRAW_BUFFER8 : 0x882D,
          DRAW_BUFFER9 : 0x882E,
          DRAW_BUFFER10 : 0x882F,
          DRAW_BUFFER11 : 0x8830,
          DRAW_BUFFER12 : 0x8831,
          DRAW_BUFFER13 : 0x8832,
          DRAW_BUFFER14 : 0x8833,
          DRAW_BUFFER15 : 0x8834,
          MAX_FRAGMENT_UNIFORM_COMPONENTS : 0x8B49,
          MAX_VERTEX_UNIFORM_COMPONENTS : 0x8B4A,
          SAMPLER_3D : 0x8B5F,
          SAMPLER_2D_SHADOW : 0x8B62,
          FRAGMENT_SHADER_DERIVATIVE_HINT : 0x8B8B,
          PIXEL_PACK_BUFFER : 0x88EB,
          PIXEL_UNPACK_BUFFER : 0x88EC,
          PIXEL_PACK_BUFFER_BINDING : 0x88ED,
          PIXEL_UNPACK_BUFFER_BINDING : 0x88EF,
          FLOAT_MAT2x3 : 0x8B65,
          FLOAT_MAT2x4 : 0x8B66,
          FLOAT_MAT3x2 : 0x8B67,
          FLOAT_MAT3x4 : 0x8B68,
          FLOAT_MAT4x2 : 0x8B69,
          FLOAT_MAT4x3 : 0x8B6A,
          SRGB : 0x8C40,
          SRGB8 : 0x8C41,
          SRGB8_ALPHA8 : 0x8C43,
          COMPARE_REF_TO_TEXTURE : 0x884E,
          RGBA32F : 0x8814,
          RGB32F : 0x8815,
          RGBA16F : 0x881A,
          RGB16F : 0x881B,
          VERTEX_ATTRIB_ARRAY_INTEGER : 0x88FD,
          MAX_ARRAY_TEXTURE_LAYERS : 0x88FF,
          MIN_PROGRAM_TEXEL_OFFSET : 0x8904,
          MAX_PROGRAM_TEXEL_OFFSET : 0x8905,
          MAX_VARYING_COMPONENTS : 0x8B4B,
          TEXTURE_2D_ARRAY : 0x8C1A,
          TEXTURE_BINDING_2D_ARRAY : 0x8C1D,
          R11F_G11F_B10F : 0x8C3A,
          UNSIGNED_INT_10F_11F_11F_REV : 0x8C3B,
          RGB9_E5 : 0x8C3D,
          UNSIGNED_INT_5_9_9_9_REV : 0x8C3E,
          TRANSFORM_FEEDBACK_BUFFER_MODE : 0x8C7F,
          MAX_TRANSFORM_FEEDBACK_SEPARATE_COMPONENTS : 0x8C80,
          TRANSFORM_FEEDBACK_VARYINGS : 0x8C83,
          TRANSFORM_FEEDBACK_BUFFER_START : 0x8C84,
          TRANSFORM_FEEDBACK_BUFFER_SIZE : 0x8C85,
          TRANSFORM_FEEDBACK_PRIMITIVES_WRITTEN : 0x8C88,
          RASTERIZER_DISCARD : 0x8C89,
          MAX_TRANSFORM_FEEDBACK_INTERLEAVED_COMPONENTS : 0x8C8A,
          MAX_TRANSFORM_FEEDBACK_SEPARATE_ATTRIBS : 0x8C8B,
          INTERLEAVED_ATTRIBS : 0x8C8C,
          SEPARATE_ATTRIBS : 0x8C8D,
          TRANSFORM_FEEDBACK_BUFFER : 0x8C8E,
          TRANSFORM_FEEDBACK_BUFFER_BINDING : 0x8C8F,
          RGBA32UI : 0x8D70,
          RGB32UI : 0x8D71,
          RGBA16UI : 0x8D76,
          RGB16UI : 0x8D77,
          RGBA8UI : 0x8D7C,
          RGB8UI : 0x8D7D,
          RGBA32I : 0x8D82,
          RGB32I : 0x8D83,
          RGBA16I : 0x8D88,
          RGB16I : 0x8D89,
          RGBA8I : 0x8D8E,
          RGB8I : 0x8D8F,
          RED_INTEGER : 0x8D94,
          RGB_INTEGER : 0x8D98,
          RGBA_INTEGER : 0x8D99,
          SAMPLER_2D_ARRAY : 0x8DC1,
          SAMPLER_2D_ARRAY_SHADOW : 0x8DC4,
          SAMPLER_CUBE_SHADOW : 0x8DC5,
          UNSIGNED_INT_VEC2 : 0x8DC6,
          UNSIGNED_INT_VEC3 : 0x8DC7,
          UNSIGNED_INT_VEC4 : 0x8DC8,
          INT_SAMPLER_2D : 0x8DCA,
          INT_SAMPLER_3D : 0x8DCB,
          INT_SAMPLER_CUBE : 0x8DCC,
          INT_SAMPLER_2D_ARRAY : 0x8DCF,
          UNSIGNED_INT_SAMPLER_2D : 0x8DD2,
          UNSIGNED_INT_SAMPLER_3D : 0x8DD3,
          UNSIGNED_INT_SAMPLER_CUBE : 0x8DD4,
          UNSIGNED_INT_SAMPLER_2D_ARRAY : 0x8DD7,
          DEPTH_COMPONENT32F : 0x8CAC,
          DEPTH32F_STENCIL8 : 0x8CAD,
          FLOAT_32_UNSIGNED_INT_24_8_REV : 0x8DAD,
          FRAMEBUFFER_ATTACHMENT_COLOR_ENCODING : 0x8210,
          FRAMEBUFFER_ATTACHMENT_COMPONENT_TYPE : 0x8211,
          FRAMEBUFFER_ATTACHMENT_RED_SIZE : 0x8212,
          FRAMEBUFFER_ATTACHMENT_GREEN_SIZE : 0x8213,
          FRAMEBUFFER_ATTACHMENT_BLUE_SIZE : 0x8214,
          FRAMEBUFFER_ATTACHMENT_ALPHA_SIZE : 0x8215,
          FRAMEBUFFER_ATTACHMENT_DEPTH_SIZE : 0x8216,
          FRAMEBUFFER_ATTACHMENT_STENCIL_SIZE : 0x8217,
          FRAMEBUFFER_DEFAULT : 0x8218,
          UNSIGNED_INT_24_8 : 0x84FA,
          DEPTH24_STENCIL8 : 0x88F0,
          UNSIGNED_NORMALIZED : 0x8C17,
          DRAW_FRAMEBUFFER_BINDING : 0x8CA6, // Same as FRAMEBUFFER_BINDING
          READ_FRAMEBUFFER : 0x8CA8,
          DRAW_FRAMEBUFFER : 0x8CA9,
          READ_FRAMEBUFFER_BINDING : 0x8CAA,
          RENDERBUFFER_SAMPLES : 0x8CAB,
          FRAMEBUFFER_ATTACHMENT_TEXTURE_LAYER : 0x8CD4,
          MAX_COLOR_ATTACHMENTS : 0x8CDF,
          COLOR_ATTACHMENT1 : 0x8CE1,
          COLOR_ATTACHMENT2 : 0x8CE2,
          COLOR_ATTACHMENT3 : 0x8CE3,
          COLOR_ATTACHMENT4 : 0x8CE4,
          COLOR_ATTACHMENT5 : 0x8CE5,
          COLOR_ATTACHMENT6 : 0x8CE6,
          COLOR_ATTACHMENT7 : 0x8CE7,
          COLOR_ATTACHMENT8 : 0x8CE8,
          COLOR_ATTACHMENT9 : 0x8CE9,
          COLOR_ATTACHMENT10 : 0x8CEA,
          COLOR_ATTACHMENT11 : 0x8CEB,
          COLOR_ATTACHMENT12 : 0x8CEC,
          COLOR_ATTACHMENT13 : 0x8CED,
          COLOR_ATTACHMENT14 : 0x8CEE,
          COLOR_ATTACHMENT15 : 0x8CEF,
          FRAMEBUFFER_INCOMPLETE_MULTISAMPLE : 0x8D56,
          MAX_SAMPLES : 0x8D57,
          HALF_FLOAT : 0x140B,
          RG : 0x8227,
          RG_INTEGER : 0x8228,
          R8 : 0x8229,
          RG8 : 0x822B,
          R16F : 0x822D,
          R32F : 0x822E,
          RG16F : 0x822F,
          RG32F : 0x8230,
          R8I : 0x8231,
          R8UI : 0x8232,
          R16I : 0x8233,
          R16UI : 0x8234,
          R32I : 0x8235,
          R32UI : 0x8236,
          RG8I : 0x8237,
          RG8UI : 0x8238,
          RG16I : 0x8239,
          RG16UI : 0x823A,
          RG32I : 0x823B,
          RG32UI : 0x823C,
          VERTEX_ARRAY_BINDING : 0x85B5,
          R8_SNORM : 0x8F94,
          RG8_SNORM : 0x8F95,
          RGB8_SNORM : 0x8F96,
          RGBA8_SNORM : 0x8F97,
          SIGNED_NORMALIZED : 0x8F9C,
          COPY_READ_BUFFER : 0x8F36,
          COPY_WRITE_BUFFER : 0x8F37,
          COPY_READ_BUFFER_BINDING : 0x8F36, // Same as COPY_READ_BUFFER
          COPY_WRITE_BUFFER_BINDING : 0x8F37, // Same as COPY_WRITE_BUFFER
          UNIFORM_BUFFER : 0x8A11,
          UNIFORM_BUFFER_BINDING : 0x8A28,
          UNIFORM_BUFFER_START : 0x8A29,
          UNIFORM_BUFFER_SIZE : 0x8A2A,
          MAX_VERTEX_UNIFORM_BLOCKS : 0x8A2B,
          MAX_FRAGMENT_UNIFORM_BLOCKS : 0x8A2D,
          MAX_COMBINED_UNIFORM_BLOCKS : 0x8A2E,
          MAX_UNIFORM_BUFFER_BINDINGS : 0x8A2F,
          MAX_UNIFORM_BLOCK_SIZE : 0x8A30,
          MAX_COMBINED_VERTEX_UNIFORM_COMPONENTS : 0x8A31,
          MAX_COMBINED_FRAGMENT_UNIFORM_COMPONENTS : 0x8A33,
          UNIFORM_BUFFER_OFFSET_ALIGNMENT : 0x8A34,
          ACTIVE_UNIFORM_BLOCKS : 0x8A36,
          UNIFORM_TYPE : 0x8A37,
          UNIFORM_SIZE : 0x8A38,
          UNIFORM_BLOCK_INDEX : 0x8A3A,
          UNIFORM_OFFSET : 0x8A3B,
          UNIFORM_ARRAY_STRIDE : 0x8A3C,
          UNIFORM_MATRIX_STRIDE : 0x8A3D,
          UNIFORM_IS_ROW_MAJOR : 0x8A3E,
          UNIFORM_BLOCK_BINDING : 0x8A3F,
          UNIFORM_BLOCK_DATA_SIZE : 0x8A40,
          UNIFORM_BLOCK_ACTIVE_UNIFORMS : 0x8A42,
          UNIFORM_BLOCK_ACTIVE_UNIFORM_INDICES : 0x8A43,
          UNIFORM_BLOCK_REFERENCED_BY_VERTEX_SHADER : 0x8A44,
          UNIFORM_BLOCK_REFERENCED_BY_FRAGMENT_SHADER : 0x8A46,
          INVALID_INDEX : 0xFFFFFFFF,
          MAX_VERTEX_OUTPUT_COMPONENTS : 0x9122,
          MAX_FRAGMENT_INPUT_COMPONENTS : 0x9125,
          MAX_SERVER_WAIT_TIMEOUT : 0x9111,
          OBJECT_TYPE : 0x9112,
          SYNC_CONDITION : 0x9113,
          SYNC_STATUS : 0x9114,
          SYNC_FLAGS : 0x9115,
          SYNC_FENCE : 0x9116,
          SYNC_GPU_COMMANDS_COMPLETE : 0x9117,
          UNSIGNALED : 0x9118,
          SIGNALED : 0x9119,
          ALREADY_SIGNALED : 0x911A,
          TIMEOUT_EXPIRED : 0x911B,
          CONDITION_SATISFIED : 0x911C,
          WAIT_FAILED : 0x911D,
          SYNC_FLUSH_COMMANDS_BIT : 0x00000001,
          VERTEX_ATTRIB_ARRAY_DIVISOR : 0x88FE,
          ANY_SAMPLES_PASSED : 0x8C2F,
          ANY_SAMPLES_PASSED_CONSERVATIVE : 0x8D6A,
          SAMPLER_BINDING : 0x8919,
          RGB10_A2UI : 0x906F,
          INT_2_10_10_10_REV : 0x8D9F,
          TRANSFORM_FEEDBACK : 0x8E22,
          TRANSFORM_FEEDBACK_PAUSED : 0x8E23,
          TRANSFORM_FEEDBACK_ACTIVE : 0x8E24,
          TRANSFORM_FEEDBACK_BINDING : 0x8E25,
          COMPRESSED_R11_EAC : 0x9270,
          COMPRESSED_SIGNED_R11_EAC : 0x9271,
          COMPRESSED_RG11_EAC : 0x9272,
          COMPRESSED_SIGNED_RG11_EAC : 0x9273,
          COMPRESSED_RGB8_ETC2 : 0x9274,
          COMPRESSED_SRGB8_ETC2 : 0x9275,
          COMPRESSED_RGB8_PUNCHTHROUGH_ALPHA1_ETC2 : 0x9276,
          COMPRESSED_SRGB8_PUNCHTHROUGH_ALPHA1_ETC2 : 0x9277,
          COMPRESSED_RGBA8_ETC2_EAC : 0x9278,
          COMPRESSED_SRGB8_ALPHA8_ETC2_EAC : 0x9279,
          TEXTURE_IMMUTABLE_FORMAT : 0x912F,
          MAX_ELEMENT_INDEX : 0x8D6B,
          TEXTURE_IMMUTABLE_LEVELS : 0x82DF,
  
          // Extensions
          MAX_TEXTURE_MAX_ANISOTROPY_EXT : 0x84FF
      };
  
      return freezeObject(WebGLConstants);
  });
  
  define('Core/ComponentDatatype',[
          './defaultValue',
          './defined',
          './DeveloperError',
          './FeatureDetection',
          './freezeObject',
          './WebGLConstants'
      ], function(
          defaultValue,
          defined,
          DeveloperError,
          FeatureDetection,
          freezeObject,
          WebGLConstants) {
      'use strict';
  
      // Bail out if the browser doesn't support typed arrays, to prevent the setup function
      // from failing, since we won't be able to create a WebGL context anyway.
      if (!FeatureDetection.supportsTypedArrays()) {
          return {};
      }
  
      /**
       * WebGL component datatypes.  Components are intrinsics,
       * which form attributes, which form vertices.
       *
       * @exports ComponentDatatype
       */
      var ComponentDatatype = {
          /**
           * 8-bit signed byte corresponding to <code>gl.BYTE</code> and the type
           * of an element in <code>Int8Array</code>.
           *
           * @type {Number}
           * @constant
           */
          BYTE : WebGLConstants.BYTE,
  
          /**
           * 8-bit unsigned byte corresponding to <code>UNSIGNED_BYTE</code> and the type
           * of an element in <code>Uint8Array</code>.
           *
           * @type {Number}
           * @constant
           */
          UNSIGNED_BYTE : WebGLConstants.UNSIGNED_BYTE,
  
          /**
           * 16-bit signed short corresponding to <code>SHORT</code> and the type
           * of an element in <code>Int16Array</code>.
           *
           * @type {Number}
           * @constant
           */
          SHORT : WebGLConstants.SHORT,
  
          /**
           * 16-bit unsigned short corresponding to <code>UNSIGNED_SHORT</code> and the type
           * of an element in <code>Uint16Array</code>.
           *
           * @type {Number}
           * @constant
           */
          UNSIGNED_SHORT : WebGLConstants.UNSIGNED_SHORT,
  
          /**
           * 32-bit signed int corresponding to <code>INT</code> and the type
           * of an element in <code>Int32Array</code>.
           *
           * @memberOf ComponentDatatype
           *
           * @type {Number}
           * @constant
           */
          INT : WebGLConstants.INT,
  
          /**
           * 32-bit unsigned int corresponding to <code>UNSIGNED_INT</code> and the type
           * of an element in <code>Uint32Array</code>.
           *
           * @memberOf ComponentDatatype
           *
           * @type {Number}
           * @constant
           */
          UNSIGNED_INT : WebGLConstants.UNSIGNED_INT,
  
          /**
           * 32-bit floating-point corresponding to <code>FLOAT</code> and the type
           * of an element in <code>Float32Array</code>.
           *
           * @type {Number}
           * @constant
           */
          FLOAT : WebGLConstants.FLOAT,
  
          /**
           * 64-bit floating-point corresponding to <code>gl.DOUBLE</code> (in Desktop OpenGL;
           * this is not supported in WebGL, and is emulated in Cesium via {@link GeometryPipeline.encodeAttribute})
           * and the type of an element in <code>Float64Array</code>.
           *
           * @memberOf ComponentDatatype
           *
           * @type {Number}
           * @constant
           * @default 0x140A
           */
          DOUBLE : WebGLConstants.DOUBLE
      };
  
      /**
       * Returns the size, in bytes, of the corresponding datatype.
       *
       * @param {ComponentDatatype} componentDatatype The component datatype to get the size of.
       * @returns {Number} The size in bytes.
       *
       * @exception {DeveloperError} componentDatatype is not a valid value.
       *
       * @example
       * // Returns Int8Array.BYTES_PER_ELEMENT
       * var size = Cesium.ComponentDatatype.getSizeInBytes(Cesium.ComponentDatatype.BYTE);
       */
      ComponentDatatype.getSizeInBytes = function(componentDatatype){
                  if (!defined(componentDatatype)) {
              throw new DeveloperError('value is required.');
          }
          
          switch (componentDatatype) {
          case ComponentDatatype.BYTE:
              return Int8Array.BYTES_PER_ELEMENT;
          case ComponentDatatype.UNSIGNED_BYTE:
              return Uint8Array.BYTES_PER_ELEMENT;
          case ComponentDatatype.SHORT:
              return Int16Array.BYTES_PER_ELEMENT;
          case ComponentDatatype.UNSIGNED_SHORT:
              return Uint16Array.BYTES_PER_ELEMENT;
          case ComponentDatatype.INT:
              return Int32Array.BYTES_PER_ELEMENT;
          case ComponentDatatype.UNSIGNED_INT:
              return Uint32Array.BYTES_PER_ELEMENT;
          case ComponentDatatype.FLOAT:
              return Float32Array.BYTES_PER_ELEMENT;
          case ComponentDatatype.DOUBLE:
              return Float64Array.BYTES_PER_ELEMENT;
                  default:
              throw new DeveloperError('componentDatatype is not a valid value.');
                  }
      };
  
      /**
       * Gets the {@link ComponentDatatype} for the provided TypedArray instance.
       *
       * @param {TypedArray} array The typed array.
       * @returns {ComponentDatatype} The ComponentDatatype for the provided array, or undefined if the array is not a TypedArray.
       */
      ComponentDatatype.fromTypedArray = function(array) {
          if (array instanceof Int8Array) {
              return ComponentDatatype.BYTE;
          }
          if (array instanceof Uint8Array) {
              return ComponentDatatype.UNSIGNED_BYTE;
          }
          if (array instanceof Int16Array) {
              return ComponentDatatype.SHORT;
          }
          if (array instanceof Uint16Array) {
              return ComponentDatatype.UNSIGNED_SHORT;
          }
          if (array instanceof Int32Array) {
              return ComponentDatatype.INT;
          }
          if (array instanceof Uint32Array) {
              return ComponentDatatype.UNSIGNED_INT;
          }
          if (array instanceof Float32Array) {
              return ComponentDatatype.FLOAT;
          }
          if (array instanceof Float64Array) {
              return ComponentDatatype.DOUBLE;
          }
      };
  
      /**
       * Validates that the provided component datatype is a valid {@link ComponentDatatype}
       *
       * @param {ComponentDatatype} componentDatatype The component datatype to validate.
       * @returns {Boolean} <code>true</code> if the provided component datatype is a valid value; otherwise, <code>false</code>.
       *
       * @example
       * if (!Cesium.ComponentDatatype.validate(componentDatatype)) {
       *   throw new Cesium.DeveloperError('componentDatatype must be a valid value.');
       * }
       */
      ComponentDatatype.validate = function(componentDatatype) {
          return defined(componentDatatype) &&
                 (componentDatatype === ComponentDatatype.BYTE ||
                  componentDatatype === ComponentDatatype.UNSIGNED_BYTE ||
                  componentDatatype === ComponentDatatype.SHORT ||
                  componentDatatype === ComponentDatatype.UNSIGNED_SHORT ||
                  componentDatatype === ComponentDatatype.INT ||
                  componentDatatype === ComponentDatatype.UNSIGNED_INT ||
                  componentDatatype === ComponentDatatype.FLOAT ||
                  componentDatatype === ComponentDatatype.DOUBLE);
      };
  
      /**
       * Creates a typed array corresponding to component data type.
       *
       * @param {ComponentDatatype} componentDatatype The component data type.
       * @param {Number|Array} valuesOrLength The length of the array to create or an array.
       * @returns {Int8Array|Uint8Array|Int16Array|Uint16Array|Int32Array|Uint32Array|Float32Array|Float64Array} A typed array.
       *
       * @exception {DeveloperError} componentDatatype is not a valid value.
       *
       * @example
       * // creates a Float32Array with length of 100
       * var typedArray = Cesium.ComponentDatatype.createTypedArray(Cesium.ComponentDatatype.FLOAT, 100);
       */
      ComponentDatatype.createTypedArray = function(componentDatatype, valuesOrLength) {
                  if (!defined(componentDatatype)) {
              throw new DeveloperError('componentDatatype is required.');
          }
          if (!defined(valuesOrLength)) {
              throw new DeveloperError('valuesOrLength is required.');
          }
          
          switch (componentDatatype) {
          case ComponentDatatype.BYTE:
              return new Int8Array(valuesOrLength);
          case ComponentDatatype.UNSIGNED_BYTE:
              return new Uint8Array(valuesOrLength);
          case ComponentDatatype.SHORT:
              return new Int16Array(valuesOrLength);
          case ComponentDatatype.UNSIGNED_SHORT:
              return new Uint16Array(valuesOrLength);
          case ComponentDatatype.INT:
              return new Int32Array(valuesOrLength);
          case ComponentDatatype.UNSIGNED_INT:
              return new Uint32Array(valuesOrLength);
          case ComponentDatatype.FLOAT:
              return new Float32Array(valuesOrLength);
          case ComponentDatatype.DOUBLE:
              return new Float64Array(valuesOrLength);
                  default:
              throw new DeveloperError('componentDatatype is not a valid value.');
                  }
      };
  
      /**
       * Creates a typed view of an array of bytes.
       *
       * @param {ComponentDatatype} componentDatatype The type of the view to create.
       * @param {ArrayBuffer} buffer The buffer storage to use for the view.
       * @param {Number} [byteOffset] The offset, in bytes, to the first element in the view.
       * @param {Number} [length] The number of elements in the view.
       * @returns {Int8Array|Uint8Array|Int16Array|Uint16Array|Int32Array|Uint32Array|Float32Array|Float64Array} A typed array view of the buffer.
       *
       * @exception {DeveloperError} componentDatatype is not a valid value.
       */
      ComponentDatatype.createArrayBufferView = function(componentDatatype, buffer, byteOffset, length) {
                  if (!defined(componentDatatype)) {
              throw new DeveloperError('componentDatatype is required.');
          }
          if (!defined(buffer)) {
              throw new DeveloperError('buffer is required.');
          }
          
          byteOffset = defaultValue(byteOffset, 0);
          length = defaultValue(length, (buffer.byteLength - byteOffset) / ComponentDatatype.getSizeInBytes(componentDatatype));
  
          switch (componentDatatype) {
          case ComponentDatatype.BYTE:
              return new Int8Array(buffer, byteOffset, length);
          case ComponentDatatype.UNSIGNED_BYTE:
              return new Uint8Array(buffer, byteOffset, length);
          case ComponentDatatype.SHORT:
              return new Int16Array(buffer, byteOffset, length);
          case ComponentDatatype.UNSIGNED_SHORT:
              return new Uint16Array(buffer, byteOffset, length);
          case ComponentDatatype.INT:
              return new Int32Array(buffer, byteOffset, length);
          case ComponentDatatype.UNSIGNED_INT:
              return new Uint32Array(buffer, byteOffset, length);
          case ComponentDatatype.FLOAT:
              return new Float32Array(buffer, byteOffset, length);
          case ComponentDatatype.DOUBLE:
              return new Float64Array(buffer, byteOffset, length);
                  default:
              throw new DeveloperError('componentDatatype is not a valid value.');
                  }
      };
  
      /**
       * Get the ComponentDatatype from its name.
       *
       * @param {String} name The name of the ComponentDatatype.
       * @returns {ComponentDatatype} The ComponentDatatype.
       *
       * @exception {DeveloperError} name is not a valid value.
       */
      ComponentDatatype.fromName = function(name) {
          switch (name) {
              case 'BYTE':
                  return ComponentDatatype.BYTE;
              case 'UNSIGNED_BYTE':
                  return ComponentDatatype.UNSIGNED_BYTE;
              case 'SHORT':
                  return ComponentDatatype.SHORT;
              case 'UNSIGNED_SHORT':
                  return ComponentDatatype.UNSIGNED_SHORT;
              case 'INT':
                  return ComponentDatatype.INT;
              case 'UNSIGNED_INT':
                  return ComponentDatatype.UNSIGNED_INT;
              case 'FLOAT':
                  return ComponentDatatype.FLOAT;
              case 'DOUBLE':
                  return ComponentDatatype.DOUBLE;
                          default:
                  throw new DeveloperError('name is not a valid value.');
                      }
      };
  
      return freezeObject(ComponentDatatype);
  });
  
  define('Core/GeometryType',[
          './freezeObject'
      ], function(
          freezeObject) {
      'use strict';
  
      /**
       * @private
       */
      var GeometryType = {
          NONE : 0,
          TRIANGLES : 1,
          LINES : 2,
          POLYLINES : 3
      };
  
      return freezeObject(GeometryType);
  });
  
  define('Core/PrimitiveType',[
          './freezeObject',
          './WebGLConstants'
      ], function(
          freezeObject,
          WebGLConstants) {
      'use strict';
  
      /**
       * The type of a geometric primitive, i.e., points, lines, and triangles.
       *
       * @exports PrimitiveType
       */
      var PrimitiveType = {
          /**
           * Points primitive where each vertex (or index) is a separate point.
           *
           * @type {Number}
           * @constant
           */
          POINTS : WebGLConstants.POINTS,
  
          /**
           * Lines primitive where each two vertices (or indices) is a line segment.  Line segments are not necessarily connected.
           *
           * @type {Number}
           * @constant
           */
          LINES : WebGLConstants.LINES,
  
          /**
           * Line loop primitive where each vertex (or index) after the first connects a line to
           * the previous vertex, and the last vertex implicitly connects to the first.
           *
           * @type {Number}
           * @constant
           */
          LINE_LOOP : WebGLConstants.LINE_LOOP,
  
          /**
           * Line strip primitive where each vertex (or index) after the first connects a line to the previous vertex.
           *
           * @type {Number}
           * @constant
           */
          LINE_STRIP : WebGLConstants.LINE_STRIP,
  
          /**
           * Triangles primitive where each three vertices (or indices) is a triangle.  Triangles do not necessarily share edges.
           *
           * @type {Number}
           * @constant
           */
          TRIANGLES : WebGLConstants.TRIANGLES,
  
          /**
           * Triangle strip primitive where each vertex (or index) after the first two connect to
           * the previous two vertices forming a triangle.  For example, this can be used to model a wall.
           *
           * @type {Number}
           * @constant
           */
          TRIANGLE_STRIP : WebGLConstants.TRIANGLE_STRIP,
  
          /**
           * Triangle fan primitive where each vertex (or index) after the first two connect to
           * the previous vertex and the first vertex forming a triangle.  For example, this can be used
           * to model a cone or circle.
           *
           * @type {Number}
           * @constant
           */
          TRIANGLE_FAN : WebGLConstants.TRIANGLE_FAN,
  
          /**
           * @private
           */
          validate : function(primitiveType) {
              return primitiveType === PrimitiveType.POINTS ||
                     primitiveType === PrimitiveType.LINES ||
                     primitiveType === PrimitiveType.LINE_LOOP ||
                     primitiveType === PrimitiveType.LINE_STRIP ||
                     primitiveType === PrimitiveType.TRIANGLES ||
                     primitiveType === PrimitiveType.TRIANGLE_STRIP ||
                     primitiveType === PrimitiveType.TRIANGLE_FAN;
          }
      };
  
      return freezeObject(PrimitiveType);
  });
  
  define('Core/Geometry',[
          './Check',
          './defaultValue',
          './defined',
          './DeveloperError',
          './GeometryType',
          './PrimitiveType'
      ], function(
          Check,
          defaultValue,
          defined,
          DeveloperError,
          GeometryType,
          PrimitiveType) {
      'use strict';
  
      /**
       * A geometry representation with attributes forming vertices and optional index data
       * defining primitives.  Geometries and an {@link Appearance}, which describes the shading,
       * can be assigned to a {@link Primitive} for visualization.  A <code>Primitive</code> can
       * be created from many heterogeneous - in many cases - geometries for performance.
       * <p>
       * Geometries can be transformed and optimized using functions in {@link GeometryPipeline}.
       * </p>
       *
       * @alias Geometry
       * @constructor
       *
       * @param {Object} options Object with the following properties:
       * @param {GeometryAttributes} options.attributes Attributes, which make up the geometry's vertices.
       * @param {PrimitiveType} [options.primitiveType=PrimitiveType.TRIANGLES] The type of primitives in the geometry.
       * @param {Uint16Array|Uint32Array} [options.indices] Optional index data that determines the primitives in the geometry.
       * @param {BoundingSphere} [options.boundingSphere] An optional bounding sphere that fully enclosed the geometry.
       *
       * @see PolygonGeometry
       * @see RectangleGeometry
       * @see EllipseGeometry
       * @see CircleGeometry
       * @see WallGeometry
       * @see SimplePolylineGeometry
       * @see BoxGeometry
       * @see EllipsoidGeometry
       *
       * @demo {@link http://cesiumjs.org/Cesium/Apps/Sandcastle/index.html?src=Geometry%20and%20Appearances.html|Geometry and Appearances Demo}
       *
       * @example
       * // Create geometry with a position attribute and indexed lines.
       * var positions = new Float64Array([
       *   0.0, 0.0, 0.0,
       *   7500000.0, 0.0, 0.0,
       *   0.0, 7500000.0, 0.0
       * ]);
       *
       * var geometry = new Cesium.Geometry({
       *   attributes : {
       *     position : new Cesium.GeometryAttribute({
       *       componentDatatype : Cesium.ComponentDatatype.DOUBLE,
       *       componentsPerAttribute : 3,
       *       values : positions
       *     })
       *   },
       *   indices : new Uint16Array([0, 1, 1, 2, 2, 0]),
       *   primitiveType : Cesium.PrimitiveType.LINES,
       *   boundingSphere : Cesium.BoundingSphere.fromVertices(positions)
       * });
       */
      function Geometry(options) {
          options = defaultValue(options, defaultValue.EMPTY_OBJECT);
  
                  Check.typeOf.object('options.attributes', options.attributes);
          
          /**
           * Attributes, which make up the geometry's vertices.  Each property in this object corresponds to a
           * {@link GeometryAttribute} containing the attribute's data.
           * <p>
           * Attributes are always stored non-interleaved in a Geometry.
           * </p>
           * <p>
           * There are reserved attribute names with well-known semantics.  The following attributes
           * are created by a Geometry (depending on the provided {@link VertexFormat}.
           * <ul>
           *    <li><code>position</code> - 3D vertex position.  64-bit floating-point (for precision).  3 components per attribute.  See {@link VertexFormat#position}.</li>
           *    <li><code>normal</code> - Normal (normalized), commonly used for lighting.  32-bit floating-point.  3 components per attribute.  See {@link VertexFormat#normal}.</li>
           *    <li><code>st</code> - 2D texture coordinate.  32-bit floating-point.  2 components per attribute.  See {@link VertexFormat#st}.</li>
           *    <li><code>bitangent</code> - Bitangent (normalized), used for tangent-space effects like bump mapping.  32-bit floating-point.  3 components per attribute.  See {@link VertexFormat#bitangent}.</li>
           *    <li><code>tangent</code> - Tangent (normalized), used for tangent-space effects like bump mapping.  32-bit floating-point.  3 components per attribute.  See {@link VertexFormat#tangent}.</li>
           * </ul>
           * </p>
           * <p>
           * The following attribute names are generally not created by a Geometry, but are added
           * to a Geometry by a {@link Primitive} or {@link GeometryPipeline} functions to prepare
           * the geometry for rendering.
           * <ul>
           *    <li><code>position3DHigh</code> - High 32 bits for encoded 64-bit position computed with {@link GeometryPipeline.encodeAttribute}.  32-bit floating-point.  4 components per attribute.</li>
           *    <li><code>position3DLow</code> - Low 32 bits for encoded 64-bit position computed with {@link GeometryPipeline.encodeAttribute}.  32-bit floating-point.  4 components per attribute.</li>
           *    <li><code>position3DHigh</code> - High 32 bits for encoded 64-bit 2D (Columbus view) position computed with {@link GeometryPipeline.encodeAttribute}.  32-bit floating-point.  4 components per attribute.</li>
           *    <li><code>position2DLow</code> - Low 32 bits for encoded 64-bit 2D (Columbus view) position computed with {@link GeometryPipeline.encodeAttribute}.  32-bit floating-point.  4 components per attribute.</li>
           *    <li><code>color</code> - RGBA color (normalized) usually from {@link GeometryInstance#color}.  32-bit floating-point.  4 components per attribute.</li>
           *    <li><code>pickColor</code> - RGBA color used for picking.  32-bit floating-point.  4 components per attribute.</li>
           * </ul>
           * </p>
           *
           * @type GeometryAttributes
           *
           * @default undefined
           *
           *
           * @example
           * geometry.attributes.position = new Cesium.GeometryAttribute({
           *   componentDatatype : Cesium.ComponentDatatype.FLOAT,
           *   componentsPerAttribute : 3,
           *   values : new Float32Array(0)
           * });
           *
           * @see GeometryAttribute
           * @see VertexFormat
           */
          this.attributes = options.attributes;
  
          /**
           * Optional index data that - along with {@link Geometry#primitiveType} -
           * determines the primitives in the geometry.
           *
           * @type Array
           *
           * @default undefined
           */
          this.indices = options.indices;
  
          /**
           * The type of primitives in the geometry.  This is most often {@link PrimitiveType.TRIANGLES},
           * but can varying based on the specific geometry.
           *
           * @type PrimitiveType
           *
           * @default undefined
           */
          this.primitiveType = defaultValue(options.primitiveType, PrimitiveType.TRIANGLES);
  
          /**
           * An optional bounding sphere that fully encloses the geometry.  This is
           * commonly used for culling.
           *
           * @type BoundingSphere
           *
           * @default undefined
           */
          this.boundingSphere = options.boundingSphere;
  
          /**
           * @private
           */
          this.geometryType = defaultValue(options.geometryType, GeometryType.NONE);
  
          /**
           * @private
           */
          this.boundingSphereCV = options.boundingSphereCV;
      }
  
      /**
       * Computes the number of vertices in a geometry.  The runtime is linear with
       * respect to the number of attributes in a vertex, not the number of vertices.
       *
       * @param {Geometry} geometry The geometry.
       * @returns {Number} The number of vertices in the geometry.
       *
       * @example
       * var numVertices = Cesium.Geometry.computeNumberOfVertices(geometry);
       */
      Geometry.computeNumberOfVertices = function(geometry) {
                  Check.typeOf.object('geometry', geometry);
          
          var numberOfVertices = -1;
          for ( var property in geometry.attributes) {
              if (geometry.attributes.hasOwnProperty(property) &&
                      defined(geometry.attributes[property]) &&
                      defined(geometry.attributes[property].values)) {
  
                  var attribute = geometry.attributes[property];
                  var num = attribute.values.length / attribute.componentsPerAttribute;
                                  if ((numberOfVertices !== num) && (numberOfVertices !== -1)) {
                      throw new DeveloperError('All attribute lists must have the same number of attributes.');
                  }
                                  numberOfVertices = num;
              }
          }
  
          return numberOfVertices;
      };
  
      return Geometry;
  });
  
  define('Core/GeometryAttribute',[
          './defaultValue',
          './defined',
          './DeveloperError'
      ], function(
          defaultValue,
          defined,
          DeveloperError) {
      'use strict';
  
      /**
       * Values and type information for geometry attributes.  A {@link Geometry}
       * generally contains one or more attributes.  All attributes together form
       * the geometry's vertices.
       *
       * @alias GeometryAttribute
       * @constructor
       *
       * @param {Object} [options] Object with the following properties:
       * @param {ComponentDatatype} [options.componentDatatype] The datatype of each component in the attribute, e.g., individual elements in values.
       * @param {Number} [options.componentsPerAttribute] A number between 1 and 4 that defines the number of components in an attributes.
       * @param {Boolean} [options.normalize=false] When <code>true</code> and <code>componentDatatype</code> is an integer format, indicate that the components should be mapped to the range [0, 1] (unsigned) or [-1, 1] (signed) when they are accessed as floating-point for rendering.
       * @param {TypedArray} [options.values] The values for the attributes stored in a typed array.
       *
       * @exception {DeveloperError} options.componentsPerAttribute must be between 1 and 4.
       *
       *
       * @example
       * var geometry = new Cesium.Geometry({
       *   attributes : {
       *     position : new Cesium.GeometryAttribute({
       *       componentDatatype : Cesium.ComponentDatatype.FLOAT,
       *       componentsPerAttribute : 3,
       *       values : new Float32Array([
       *         0.0, 0.0, 0.0,
       *         7500000.0, 0.0, 0.0,
       *         0.0, 7500000.0, 0.0
       *       ])
       *     })
       *   },
       *   primitiveType : Cesium.PrimitiveType.LINE_LOOP
       * });
       *
       * @see Geometry
       */
      function GeometryAttribute(options) {
          options = defaultValue(options, defaultValue.EMPTY_OBJECT);
  
                  if (!defined(options.componentDatatype)) {
              throw new DeveloperError('options.componentDatatype is required.');
          }
          if (!defined(options.componentsPerAttribute)) {
              throw new DeveloperError('options.componentsPerAttribute is required.');
          }
          if (options.componentsPerAttribute < 1 || options.componentsPerAttribute > 4) {
              throw new DeveloperError('options.componentsPerAttribute must be between 1 and 4.');
          }
          if (!defined(options.values)) {
              throw new DeveloperError('options.values is required.');
          }
          
          /**
           * The datatype of each component in the attribute, e.g., individual elements in
           * {@link GeometryAttribute#values}.
           *
           * @type ComponentDatatype
           *
           * @default undefined
           */
          this.componentDatatype = options.componentDatatype;
  
          /**
           * A number between 1 and 4 that defines the number of components in an attributes.
           * For example, a position attribute with x, y, and z components would have 3 as
           * shown in the code example.
           *
           * @type Number
           *
           * @default undefined
           *
           * @example
           * attribute.componentDatatype = Cesium.ComponentDatatype.FLOAT;
           * attribute.componentsPerAttribute = 3;
           * attribute.values = new Float32Array([
           *   0.0, 0.0, 0.0,
           *   7500000.0, 0.0, 0.0,
           *   0.0, 7500000.0, 0.0
           * ]);
           */
          this.componentsPerAttribute = options.componentsPerAttribute;
  
          /**
           * When <code>true</code> and <code>componentDatatype</code> is an integer format,
           * indicate that the components should be mapped to the range [0, 1] (unsigned)
           * or [-1, 1] (signed) when they are accessed as floating-point for rendering.
           * <p>
           * This is commonly used when storing colors using {@link ComponentDatatype.UNSIGNED_BYTE}.
           * </p>
           *
           * @type Boolean
           *
           * @default false
           *
           * @example
           * attribute.componentDatatype = Cesium.ComponentDatatype.UNSIGNED_BYTE;
           * attribute.componentsPerAttribute = 4;
           * attribute.normalize = true;
           * attribute.values = new Uint8Array([
           *   Cesium.Color.floatToByte(color.red),
           *   Cesium.Color.floatToByte(color.green),
           *   Cesium.Color.floatToByte(color.blue),
           *   Cesium.Color.floatToByte(color.alpha)
           * ]);
           */
          this.normalize = defaultValue(options.normalize, false);
  
          /**
           * The values for the attributes stored in a typed array.  In the code example,
           * every three elements in <code>values</code> defines one attributes since
           * <code>componentsPerAttribute</code> is 3.
           *
           * @type TypedArray
           *
           * @default undefined
           *
           * @example
           * attribute.componentDatatype = Cesium.ComponentDatatype.FLOAT;
           * attribute.componentsPerAttribute = 3;
           * attribute.values = new Float32Array([
           *   0.0, 0.0, 0.0,
           *   7500000.0, 0.0, 0.0,
           *   0.0, 7500000.0, 0.0
           * ]);
           */
          this.values = options.values;
      }
  
      return GeometryAttribute;
  });
  
  define('Core/GeometryAttributes',[
          './defaultValue'
      ], function(
          defaultValue) {
      'use strict';
  
      /**
       * Attributes, which make up a geometry's vertices.  Each property in this object corresponds to a
       * {@link GeometryAttribute} containing the attribute's data.
       * <p>
       * Attributes are always stored non-interleaved in a Geometry.
       * </p>
       *
       * @alias GeometryAttributes
       * @constructor
       */
      function GeometryAttributes(options) {
          options = defaultValue(options, defaultValue.EMPTY_OBJECT);
  
          /**
           * The 3D position attribute.
           * <p>
           * 64-bit floating-point (for precision).  3 components per attribute.
           * </p>
           *
           * @type GeometryAttribute
           *
           * @default undefined
           */
          this.position = options.position;
  
          /**
           * The normal attribute (normalized), which is commonly used for lighting.
           * <p>
           * 32-bit floating-point.  3 components per attribute.
           * </p>
           *
           * @type GeometryAttribute
           *
           * @default undefined
           */
          this.normal = options.normal;
  
          /**
           * The 2D texture coordinate attribute.
           * <p>
           * 32-bit floating-point.  2 components per attribute
           * </p>
           *
           * @type GeometryAttribute
           *
           * @default undefined
           */
          this.st = options.st;
  
          /**
           * The bitangent attribute (normalized), which is used for tangent-space effects like bump mapping.
           * <p>
           * 32-bit floating-point.  3 components per attribute.
           * </p>
           *
           * @type GeometryAttribute
           *
           * @default undefined
           */
          this.bitangent = options.bitangent;
  
          /**
           * The tangent attribute (normalized), which is used for tangent-space effects like bump mapping.
           * <p>
           * 32-bit floating-point.  3 components per attribute.
           * </p>
           *
           * @type GeometryAttribute
           *
           * @default undefined
           */
          this.tangent = options.tangent;
  
          /**
           * The color attribute.
           * <p>
           * 8-bit unsigned integer. 4 components per attribute.
           * </p>
           *
           * @type GeometryAttribute
           *
           * @default undefined
           */
          this.color = options.color;
      }
  
      return GeometryAttributes;
  });
  
  define('Core/Plane',[
          './Cartesian3',
          './Check',
          './defined',
          './DeveloperError',
          './freezeObject',
          './Math',
          './Matrix4'
      ], function(
          Cartesian3,
          Check,
          defined,
          DeveloperError,
          freezeObject,
          CesiumMath,
          Matrix4) {
      'use strict';
  
      /**
       * A plane in Hessian Normal Form defined by
       * <pre>
       * ax + by + cz + d = 0
       * </pre>
       * where (a, b, c) is the plane's <code>normal</code>, d is the signed
       * <code>distance</code> to the plane, and (x, y, z) is any point on
       * the plane.
       *
       * @alias Plane
       * @constructor
       *
       * @param {Cartesian3} normal The plane's normal (normalized).
       * @param {Number} distance The shortest distance from the origin to the plane.  The sign of
       * <code>distance</code> determines which side of the plane the origin
       * is on.  If <code>distance</code> is positive, the origin is in the half-space
       * in the direction of the normal; if negative, the origin is in the half-space
       * opposite to the normal; if zero, the plane passes through the origin.
       *
       * @example
       * // The plane x=0
       * var plane = new Cesium.Plane(Cesium.Cartesian3.UNIT_X, 0.0);
       *
       * @exception {DeveloperError} Normal must be normalized
       */
      function Plane(normal, distance) {
                  Check.typeOf.object('normal', normal);
          if (!CesiumMath.equalsEpsilon(Cartesian3.magnitude(normal), 1.0, CesiumMath.EPSILON6)) {
              throw new DeveloperError('normal must be normalized.');
          }
          Check.typeOf.number('distance', distance);
          
          /**
           * The plane's normal.
           *
           * @type {Cartesian3}
           */
          this.normal = Cartesian3.clone(normal);
  
          /**
           * The shortest distance from the origin to the plane.  The sign of
           * <code>distance</code> determines which side of the plane the origin
           * is on.  If <code>distance</code> is positive, the origin is in the half-space
           * in the direction of the normal; if negative, the origin is in the half-space
           * opposite to the normal; if zero, the plane passes through the origin.
           *
           * @type {Number}
           */
          this.distance = distance;
      }
  
      /**
       * Creates a plane from a normal and a point on the plane.
       *
       * @param {Cartesian3} point The point on the plane.
       * @param {Cartesian3} normal The plane's normal (normalized).
       * @param {Plane} [result] The object onto which to store the result.
       * @returns {Plane} A new plane instance or the modified result parameter.
       *
       * @example
       * var point = Cesium.Cartesian3.fromDegrees(-72.0, 40.0);
       * var normal = ellipsoid.geodeticSurfaceNormal(point);
       * var tangentPlane = Cesium.Plane.fromPointNormal(point, normal);
       *
       * @exception {DeveloperError} Normal must be normalized
       */
      Plane.fromPointNormal = function(point, normal, result) {
                  Check.typeOf.object('point', point);
          Check.typeOf.object('normal', normal);
          if (!CesiumMath.equalsEpsilon(Cartesian3.magnitude(normal), 1.0, CesiumMath.EPSILON6)) {
              throw new DeveloperError('normal must be normalized.');
          }
          
          var distance = -Cartesian3.dot(normal, point);
  
          if (!defined(result)) {
              return new Plane(normal, distance);
          }
  
          Cartesian3.clone(normal, result.normal);
          result.distance = distance;
          return result;
      };
  
      var scratchNormal = new Cartesian3();
      /**
       * Creates a plane from the general equation
       *
       * @param {Cartesian4} coefficients The plane's normal (normalized).
       * @param {Plane} [result] The object onto which to store the result.
       * @returns {Plane} A new plane instance or the modified result parameter.
       *
       * @exception {DeveloperError} Normal must be normalized
       */
      Plane.fromCartesian4 = function(coefficients, result) {
                  Check.typeOf.object('coefficients', coefficients);
          
          var normal = Cartesian3.fromCartesian4(coefficients, scratchNormal);
          var distance = coefficients.w;
  
                  if (!CesiumMath.equalsEpsilon(Cartesian3.magnitude(normal), 1.0, CesiumMath.EPSILON6)) {
              throw new DeveloperError('normal must be normalized.');
          }
          
          if (!defined(result)) {
              return new Plane(normal, distance);
          }
          Cartesian3.clone(normal, result.normal);
          result.distance = distance;
          return result;
      };
  
      /**
       * Computes the signed shortest distance of a point to a plane.
       * The sign of the distance determines which side of the plane the point
       * is on.  If the distance is positive, the point is in the half-space
       * in the direction of the normal; if negative, the point is in the half-space
       * opposite to the normal; if zero, the plane passes through the point.
       *
       * @param {Plane} plane The plane.
       * @param {Cartesian3} point The point.
       * @returns {Number} The signed shortest distance of the point to the plane.
       */
      Plane.getPointDistance = function(plane, point) {
                  Check.typeOf.object('plane', plane);
          Check.typeOf.object('point', point);
          
          return Cartesian3.dot(plane.normal, point) + plane.distance;
      };
  
      var scratchPosition = new Cartesian3();
      /**
       * Transforms the plane by the given transformation matrix.
       *
       * @param {Plane} plane The plane.
       * @param {Matrix4} transform The transformation matrix.
       * @param {Plane} [result] The object into which to store the result.
       * @returns {Plane} The plane transformed by the given transformation matrix.
       */
      Plane.transform = function(plane, transform, result) {
                  Check.typeOf.object('plane', plane);
          Check.typeOf.object('transform', transform);
          
          Matrix4.multiplyByPointAsVector(transform, plane.normal, scratchNormal);
          Cartesian3.normalize(scratchNormal, scratchNormal);
  
          Cartesian3.multiplyByScalar(plane.normal, -plane.distance, scratchPosition);
          Matrix4.multiplyByPoint(transform, scratchPosition, scratchPosition);
  
          return Plane.fromPointNormal(scratchPosition, scratchNormal, result);
      };
  
      /**
       * Duplicates a Plane instance.
       *
       * @param {Plane} plane The plane to duplicate.
       * @param {Plane} [result] The object onto which to store the result.
       * @returns {Plane} The modified result parameter or a new Plane instance if one was not provided.
       */
      Plane.clone = function(plane, result) {
                  Check.typeOf.object('plane', plane);
          
          if (!defined(result)) {
              return new Plane(plane.normal, plane.distance);
          }
  
          Cartesian3.clone(plane.normal, result.normal);
          result.distance = plane.distance;
  
          return result;
      };
  
      /**
       * Compares the provided Planes by normal and distance and returns
       * <code>true</code> if they are equal, <code>false</code> otherwise.
       *
       * @param {Plane} left The first plane.
       * @param {Plane} right The second plane.
       * @returns {Boolean} <code>true</code> if left and right are equal, <code>false</code> otherwise.
       */
      Plane.equals = function(left, right) {
                  Check.typeOf.object('left', left);
          Check.typeOf.object('right', right);
          
          return (left.distance === right.distance) && Cartesian3.equals(left.normal, right.normal);
      };
  
      /**
       * A constant initialized to the XY plane passing through the origin, with normal in positive Z.
       *
       * @type {Plane}
       * @constant
       */
      Plane.ORIGIN_XY_PLANE = freezeObject(new Plane(Cartesian3.UNIT_Z, 0.0));
  
      /**
       * A constant initialized to the YZ plane passing through the origin, with normal in positive X.
       *
       * @type {Plane}
       * @constant
       */
      Plane.ORIGIN_YZ_PLANE = freezeObject(new Plane(Cartesian3.UNIT_X, 0.0));
  
      /**
       * A constant initialized to the ZX plane passing through the origin, with normal in positive Y.
       *
       * @type {Plane}
       * @constant
       */
      Plane.ORIGIN_ZX_PLANE = freezeObject(new Plane(Cartesian3.UNIT_Y, 0.0));
  
      return Plane;
  });
  
  define('Core/CullingVolume',[
          './Cartesian3',
          './Cartesian4',
          './defaultValue',
          './defined',
          './DeveloperError',
          './Intersect',
          './Plane'
      ], function(
          Cartesian3,
          Cartesian4,
          defaultValue,
          defined,
          DeveloperError,
          Intersect,
          Plane) {
      'use strict';
  
      /**
       * The culling volume defined by planes.
       *
       * @alias CullingVolume
       * @constructor
       *
       * @param {Cartesian4[]} [planes] An array of clipping planes.
       */
      function CullingVolume(planes) {
          /**
           * Each plane is represented by a Cartesian4 object, where the x, y, and z components
           * define the unit vector normal to the plane, and the w component is the distance of the
           * plane from the origin.
           * @type {Cartesian4[]}
           * @default []
           */
          this.planes = defaultValue(planes, []);
      }
  
      var faces = [new Cartesian3(), new Cartesian3(), new Cartesian3()];
      Cartesian3.clone(Cartesian3.UNIT_X, faces[0]);
      Cartesian3.clone(Cartesian3.UNIT_Y, faces[1]);
      Cartesian3.clone(Cartesian3.UNIT_Z, faces[2]);
  
      var scratchPlaneCenter = new Cartesian3();
      var scratchPlaneNormal = new Cartesian3();
      var scratchPlane = new Plane(new Cartesian3(1.0, 0.0, 0.0), 0.0);
  
      /**
       * Constructs a culling volume from a bounding sphere. Creates six planes that create a box containing the sphere.
       * The planes are aligned to the x, y, and z axes in world coordinates.
       *
       * @param {BoundingSphere} boundingSphere The bounding sphere used to create the culling volume.
       * @param {CullingVolume} [result] The object onto which to store the result.
       * @returns {CullingVolume} The culling volume created from the bounding sphere.
       */
      CullingVolume.fromBoundingSphere = function(boundingSphere, result) {
                  if (!defined(boundingSphere)) {
              throw new DeveloperError('boundingSphere is required.');
          }
          
          if (!defined(result)) {
              result = new CullingVolume();
          }
  
          var length = faces.length;
          var planes = result.planes;
          planes.length = 2 * length;
  
          var center = boundingSphere.center;
          var radius = boundingSphere.radius;
  
          var planeIndex = 0;
  
          for (var i = 0; i < length; ++i) {
              var faceNormal = faces[i];
  
              var plane0 = planes[planeIndex];
              var plane1 = planes[planeIndex + 1];
  
              if (!defined(plane0)) {
                  plane0 = planes[planeIndex] = new Cartesian4();
              }
              if (!defined(plane1)) {
                  plane1 = planes[planeIndex + 1] = new Cartesian4();
              }
  
              Cartesian3.multiplyByScalar(faceNormal, -radius, scratchPlaneCenter);
              Cartesian3.add(center, scratchPlaneCenter, scratchPlaneCenter);
  
              plane0.x = faceNormal.x;
              plane0.y = faceNormal.y;
              plane0.z = faceNormal.z;
              plane0.w = -Cartesian3.dot(faceNormal, scratchPlaneCenter);
  
              Cartesian3.multiplyByScalar(faceNormal, radius, scratchPlaneCenter);
              Cartesian3.add(center, scratchPlaneCenter, scratchPlaneCenter);
  
              plane1.x = -faceNormal.x;
              plane1.y = -faceNormal.y;
              plane1.z = -faceNormal.z;
              plane1.w = -Cartesian3.dot(Cartesian3.negate(faceNormal, scratchPlaneNormal), scratchPlaneCenter);
  
              planeIndex += 2;
          }
  
          return result;
      };
  
      /**
       * Determines whether a bounding volume intersects the culling volume.
       *
       * @param {Object} boundingVolume The bounding volume whose intersection with the culling volume is to be tested.
       * @returns {Intersect}  Intersect.OUTSIDE, Intersect.INTERSECTING, or Intersect.INSIDE.
       */
      CullingVolume.prototype.computeVisibility = function(boundingVolume) {
                  if (!defined(boundingVolume)) {
              throw new DeveloperError('boundingVolume is required.');
          }
          
          var planes = this.planes;
          var intersecting = false;
          for (var k = 0, len = planes.length; k < len; ++k) {
              var result = boundingVolume.intersectPlane(Plane.fromCartesian4(planes[k], scratchPlane));
              if (result === Intersect.OUTSIDE) {
                  return Intersect.OUTSIDE;
              } else if (result === Intersect.INTERSECTING) {
                  intersecting = true;
              }
          }
  
          return intersecting ? Intersect.INTERSECTING : Intersect.INSIDE;
      };
  
      /**
       * Determines whether a bounding volume intersects the culling volume.
       *
       * @param {Object} boundingVolume The bounding volume whose intersection with the culling volume is to be tested.
       * @param {Number} parentPlaneMask A bit mask from the boundingVolume's parent's check against the same culling
       *                                 volume, such that if (planeMask & (1 << planeIndex) === 0), for k < 31, then
       *                                 the parent (and therefore this) volume is completely inside plane[planeIndex]
       *                                 and that plane check can be skipped.
       * @returns {Number} A plane mask as described above (which can be applied to this boundingVolume's children).
       *
       * @private
       */
      CullingVolume.prototype.computeVisibilityWithPlaneMask = function(boundingVolume, parentPlaneMask) {
                  if (!defined(boundingVolume)) {
              throw new DeveloperError('boundingVolume is required.');
          }
          if (!defined(parentPlaneMask)) {
              throw new DeveloperError('parentPlaneMask is required.');
          }
          
          if (parentPlaneMask === CullingVolume.MASK_OUTSIDE || parentPlaneMask === CullingVolume.MASK_INSIDE) {
              // parent is completely outside or completely inside, so this child is as well.
              return parentPlaneMask;
          }
  
          // Start with MASK_INSIDE (all zeros) so that after the loop, the return value can be compared with MASK_INSIDE.
          // (Because if there are fewer than 31 planes, the upper bits wont be changed.)
          var mask = CullingVolume.MASK_INSIDE;
  
          var planes = this.planes;
          for (var k = 0, len = planes.length; k < len; ++k) {
              // For k greater than 31 (since 31 is the maximum number of INSIDE/INTERSECTING bits we can store), skip the optimization.
              var flag = (k < 31) ? (1 << k) : 0;
              if (k < 31 && (parentPlaneMask & flag) === 0) {
                  // boundingVolume is known to be INSIDE this plane.
                  continue;
              }
  
              var result = boundingVolume.intersectPlane(Plane.fromCartesian4(planes[k], scratchPlane));
              if (result === Intersect.OUTSIDE) {
                  return CullingVolume.MASK_OUTSIDE;
              } else if (result === Intersect.INTERSECTING) {
                  mask |= flag;
              }
          }
  
          return mask;
      };
  
      /**
       * For plane masks (as used in {@link CullingVolume#computeVisibilityWithPlaneMask}), this special value
       * represents the case where the object bounding volume is entirely outside the culling volume.
       *
       * @type {Number}
       * @private
       */
      CullingVolume.MASK_OUTSIDE = 0xffffffff;
  
      /**
       * For plane masks (as used in {@link CullingVolume.prototype.computeVisibilityWithPlaneMask}), this value
       * represents the case where the object bounding volume is entirely inside the culling volume.
       *
       * @type {Number}
       * @private
       */
      CullingVolume.MASK_INSIDE = 0x00000000;
  
      /**
       * For plane masks (as used in {@link CullingVolume.prototype.computeVisibilityWithPlaneMask}), this value
       * represents the case where the object bounding volume (may) intersect all planes of the culling volume.
       *
       * @type {Number}
       * @private
       */
      CullingVolume.MASK_INDETERMINATE = 0x7fffffff;
  
      return CullingVolume;
  });
  
  define('Core/OrthographicOffCenterFrustum',[
          './Cartesian3',
          './Cartesian4',
          './CullingVolume',
          './defaultValue',
          './defined',
          './defineProperties',
          './DeveloperError',
          './Matrix4'
      ], function(
          Cartesian3,
          Cartesian4,
          CullingVolume,
          defaultValue,
          defined,
          defineProperties,
          DeveloperError,
          Matrix4) {
      'use strict';
  
      /**
       * The viewing frustum is defined by 6 planes.
       * Each plane is represented by a {@link Cartesian4} object, where the x, y, and z components
       * define the unit vector normal to the plane, and the w component is the distance of the
       * plane from the origin/camera position.
       *
       * @alias OrthographicOffCenterFrustum
       * @constructor
       *
       * @param {Object} [options] An object with the following properties:
       * @param {Number} [options.left] The left clipping plane distance.
       * @param {Number} [options.right] The right clipping plane distance.
       * @param {Number} [options.top] The top clipping plane distance.
       * @param {Number} [options.bottom] The bottom clipping plane distance.
       * @param {Number} [options.near=1.0] The near clipping plane distance.
       * @param {Number} [options.far=500000000.0] The far clipping plane distance.
       *
       * @example
       * var maxRadii = ellipsoid.maximumRadius;
       *
       * var frustum = new Cesium.OrthographicOffCenterFrustum();
       * frustum.right = maxRadii * Cesium.Math.PI;
       * frustum.left = -c.frustum.right;
       * frustum.top = c.frustum.right * (canvas.clientHeight / canvas.clientWidth);
       * frustum.bottom = -c.frustum.top;
       * frustum.near = 0.01 * maxRadii;
       * frustum.far = 50.0 * maxRadii;
       */
      function OrthographicOffCenterFrustum(options) {
          options = defaultValue(options, defaultValue.EMPTY_OBJECT);
  
          /**
           * The left clipping plane.
           * @type {Number}
           * @default undefined
           */
          this.left = options.left;
          this._left = undefined;
  
          /**
           * The right clipping plane.
           * @type {Number}
           * @default undefined
           */
          this.right = options.right;
          this._right = undefined;
  
          /**
           * The top clipping plane.
           * @type {Number}
           * @default undefined
           */
          this.top = options.top;
          this._top = undefined;
  
          /**
           * The bottom clipping plane.
           * @type {Number}
           * @default undefined
           */
          this.bottom = options.bottom;
          this._bottom = undefined;
  
          /**
           * The distance of the near plane.
           * @type {Number}
           * @default 1.0
           */
          this.near = defaultValue(options.near, 1.0);
          this._near = this.near;
  
          /**
           * The distance of the far plane.
           * @type {Number}
           * @default 500000000.0;
           */
          this.far = defaultValue(options.far, 500000000.0);
          this._far = this.far;
  
          this._cullingVolume = new CullingVolume();
          this._orthographicMatrix = new Matrix4();
      }
  
      function update(frustum) {
                  if (!defined(frustum.right) || !defined(frustum.left) ||
              !defined(frustum.top) || !defined(frustum.bottom) ||
              !defined(frustum.near) || !defined(frustum.far)) {
              throw new DeveloperError('right, left, top, bottom, near, or far parameters are not set.');
          }
          
          if (frustum.top !== frustum._top || frustum.bottom !== frustum._bottom ||
              frustum.left !== frustum._left || frustum.right !== frustum._right ||
              frustum.near !== frustum._near || frustum.far !== frustum._far) {
  
                          if (frustum.left > frustum.right) {
                  throw new DeveloperError('right must be greater than left.');
              }
              if (frustum.bottom > frustum.top) {
                  throw new DeveloperError('top must be greater than bottom.');
              }
              if (frustum.near <= 0 || frustum.near > frustum.far) {
                  throw new DeveloperError('near must be greater than zero and less than far.');
              }
              
              frustum._left = frustum.left;
              frustum._right = frustum.right;
              frustum._top = frustum.top;
              frustum._bottom = frustum.bottom;
              frustum._near = frustum.near;
              frustum._far = frustum.far;
              frustum._orthographicMatrix = Matrix4.computeOrthographicOffCenter(frustum.left, frustum.right, frustum.bottom, frustum.top, frustum.near, frustum.far, frustum._orthographicMatrix);
          }
      }
  
      defineProperties(OrthographicOffCenterFrustum.prototype, {
          /**
           * Gets the orthographic projection matrix computed from the view frustum.
           * @memberof OrthographicOffCenterFrustum.prototype
           * @type {Matrix4}
           * @readonly
           */
          projectionMatrix : {
              get : function() {
                  update(this);
                  return this._orthographicMatrix;
              }
          }
      });
  
      var getPlanesRight = new Cartesian3();
      var getPlanesNearCenter = new Cartesian3();
      var getPlanesPoint = new Cartesian3();
      var negateScratch = new Cartesian3();
  
      /**
       * Creates a culling volume for this frustum.
       *
       * @param {Cartesian3} position The eye position.
       * @param {Cartesian3} direction The view direction.
       * @param {Cartesian3} up The up direction.
       * @returns {CullingVolume} A culling volume at the given position and orientation.
       *
       * @example
       * // Check if a bounding volume intersects the frustum.
       * var cullingVolume = frustum.computeCullingVolume(cameraPosition, cameraDirection, cameraUp);
       * var intersect = cullingVolume.computeVisibility(boundingVolume);
       */
      OrthographicOffCenterFrustum.prototype.computeCullingVolume = function(position, direction, up) {
                  if (!defined(position)) {
              throw new DeveloperError('position is required.');
          }
          if (!defined(direction)) {
              throw new DeveloperError('direction is required.');
          }
          if (!defined(up)) {
              throw new DeveloperError('up is required.');
          }
          
          var planes = this._cullingVolume.planes;
          var t = this.top;
          var b = this.bottom;
          var r = this.right;
          var l = this.left;
          var n = this.near;
          var f = this.far;
  
          var right = Cartesian3.cross(direction, up, getPlanesRight);
          Cartesian3.normalize(right, right);
          var nearCenter = getPlanesNearCenter;
          Cartesian3.multiplyByScalar(direction, n, nearCenter);
          Cartesian3.add(position, nearCenter, nearCenter);
  
          var point = getPlanesPoint;
  
          // Left plane
          Cartesian3.multiplyByScalar(right, l, point);
          Cartesian3.add(nearCenter, point, point);
  
          var plane = planes[0];
          if (!defined(plane)) {
              plane = planes[0] = new Cartesian4();
          }
          plane.x = right.x;
          plane.y = right.y;
          plane.z = right.z;
          plane.w = -Cartesian3.dot(right, point);
  
          // Right plane
          Cartesian3.multiplyByScalar(right, r, point);
          Cartesian3.add(nearCenter, point, point);
  
          plane = planes[1];
          if (!defined(plane)) {
              plane = planes[1] = new Cartesian4();
          }
          plane.x = -right.x;
          plane.y = -right.y;
          plane.z = -right.z;
          plane.w = -Cartesian3.dot(Cartesian3.negate(right, negateScratch), point);
  
          // Bottom plane
          Cartesian3.multiplyByScalar(up, b, point);
          Cartesian3.add(nearCenter, point, point);
  
          plane = planes[2];
          if (!defined(plane)) {
              plane = planes[2] = new Cartesian4();
          }
          plane.x = up.x;
          plane.y = up.y;
          plane.z = up.z;
          plane.w = -Cartesian3.dot(up, point);
  
          // Top plane
          Cartesian3.multiplyByScalar(up, t, point);
          Cartesian3.add(nearCenter, point, point);
  
          plane = planes[3];
          if (!defined(plane)) {
              plane = planes[3] = new Cartesian4();
          }
          plane.x = -up.x;
          plane.y = -up.y;
          plane.z = -up.z;
          plane.w = -Cartesian3.dot(Cartesian3.negate(up, negateScratch), point);
  
          // Near plane
          plane = planes[4];
          if (!defined(plane)) {
              plane = planes[4] = new Cartesian4();
          }
          plane.x = direction.x;
          plane.y = direction.y;
          plane.z = direction.z;
          plane.w = -Cartesian3.dot(direction, nearCenter);
  
          // Far plane
          Cartesian3.multiplyByScalar(direction, f, point);
          Cartesian3.add(position, point, point);
  
          plane = planes[5];
          if (!defined(plane)) {
              plane = planes[5] = new Cartesian4();
          }
          plane.x = -direction.x;
          plane.y = -direction.y;
          plane.z = -direction.z;
          plane.w = -Cartesian3.dot(Cartesian3.negate(direction, negateScratch), point);
  
          return this._cullingVolume;
      };
  
      /**
       * Returns the pixel's width and height in meters.
       *
       * @param {Number} drawingBufferWidth The width of the drawing buffer.
       * @param {Number} drawingBufferHeight The height of the drawing buffer.
       * @param {Number} distance The distance to the near plane in meters.
       * @param {Cartesian2} result The object onto which to store the result.
       * @returns {Cartesian2} The modified result parameter or a new instance of {@link Cartesian2} with the pixel's width and height in the x and y properties, respectively.
       *
       * @exception {DeveloperError} drawingBufferWidth must be greater than zero.
       * @exception {DeveloperError} drawingBufferHeight must be greater than zero.
       *
       * @example
       * // Example 1
       * // Get the width and height of a pixel.
       * var pixelSize = camera.frustum.getPixelDimensions(scene.drawingBufferWidth, scene.drawingBufferHeight, 0.0, new Cesium.Cartesian2());
       */
      OrthographicOffCenterFrustum.prototype.getPixelDimensions = function(drawingBufferWidth, drawingBufferHeight, distance, result) {
          update(this);
  
                  if (!defined(drawingBufferWidth) || !defined(drawingBufferHeight)) {
              throw new DeveloperError('Both drawingBufferWidth and drawingBufferHeight are required.');
          }
          if (drawingBufferWidth <= 0) {
              throw new DeveloperError('drawingBufferWidth must be greater than zero.');
          }
          if (drawingBufferHeight <= 0) {
              throw new DeveloperError('drawingBufferHeight must be greater than zero.');
          }
          if (!defined(distance)) {
              throw new DeveloperError('distance is required.');
          }
          if (!defined(result)) {
              throw new DeveloperError('A result object is required.');
          }
          
          var frustumWidth = this.right - this.left;
          var frustumHeight = this.top - this.bottom;
          var pixelWidth = frustumWidth / drawingBufferWidth;
          var pixelHeight = frustumHeight / drawingBufferHeight;
  
          result.x = pixelWidth;
          result.y = pixelHeight;
          return result;
      };
  
      /**
       * Returns a duplicate of a OrthographicOffCenterFrustum instance.
       *
       * @param {OrthographicOffCenterFrustum} [result] The object onto which to store the result.
       * @returns {OrthographicOffCenterFrustum} The modified result parameter or a new OrthographicOffCenterFrustum instance if one was not provided.
       */
      OrthographicOffCenterFrustum.prototype.clone = function(result) {
          if (!defined(result)) {
              result = new OrthographicOffCenterFrustum();
          }
  
          result.left = this.left;
          result.right = this.right;
          result.top = this.top;
          result.bottom = this.bottom;
          result.near = this.near;
          result.far = this.far;
  
          // force update of clone to compute matrices
          result._left = undefined;
          result._right = undefined;
          result._top = undefined;
          result._bottom = undefined;
          result._near = undefined;
          result._far = undefined;
  
          return result;
      };
  
      /**
       * Compares the provided OrthographicOffCenterFrustum componentwise and returns
       * <code>true</code> if they are equal, <code>false</code> otherwise.
       *
       * @param {OrthographicOffCenterFrustum} [other] The right hand side OrthographicOffCenterFrustum.
       * @returns {Boolean} <code>true</code> if they are equal, <code>false</code> otherwise.
       */
      OrthographicOffCenterFrustum.prototype.equals = function(other) {
          return (defined(other) &&
                  this.right === other.right &&
                  this.left === other.left &&
                  this.top === other.top &&
                  this.bottom === other.bottom &&
                  this.near === other.near &&
                  this.far === other.far);
      };
  
      return OrthographicOffCenterFrustum;
  });
  
  define('Core/OrthographicFrustum',[
          './Check',
          './defaultValue',
          './defined',
          './defineProperties',
          './DeveloperError',
          './OrthographicOffCenterFrustum'
      ], function(
          Check,
          defaultValue,
          defined,
          defineProperties,
          DeveloperError,
          OrthographicOffCenterFrustum) {
      'use strict';
  
      /**
       * The viewing frustum is defined by 6 planes.
       * Each plane is represented by a {@link Cartesian4} object, where the x, y, and z components
       * define the unit vector normal to the plane, and the w component is the distance of the
       * plane from the origin/camera position.
       *
       * @alias OrthographicFrustum
       * @constructor
       *
       * @param {Object} [options] An object with the following properties:
       * @param {Number} [options.width] The width of the frustum in meters.
       * @param {Number} [options.aspectRatio] The aspect ratio of the frustum's width to it's height.
       * @param {Number} [options.near=1.0] The distance of the near plane.
       * @param {Number} [options.far=500000000.0] The distance of the far plane.
       *
       * @example
       * var maxRadii = ellipsoid.maximumRadius;
       *
       * var frustum = new Cesium.OrthographicFrustum();
       * frustum.near = 0.01 * maxRadii;
       * frustum.far = 50.0 * maxRadii;
       */
      function OrthographicFrustum(options) {
          options = defaultValue(options, defaultValue.EMPTY_OBJECT);
  
          this._offCenterFrustum = new OrthographicOffCenterFrustum();
  
          /**
           * The horizontal width of the frustum in meters.
           * @type {Number}
           * @default undefined
           */
          this.width = options.width;
          this._width = undefined;
  
          /**
           * The aspect ratio of the frustum's width to it's height.
           * @type {Number}
           * @default undefined
           */
          this.aspectRatio = options.aspectRatio;
          this._aspectRatio = undefined;
  
          /**
           * The distance of the near plane.
           * @type {Number}
           * @default 1.0
           */
          this.near = defaultValue(options.near, 1.0);
          this._near = this.near;
  
          /**
           * The distance of the far plane.
           * @type {Number}
           * @default 500000000.0;
           */
          this.far = defaultValue(options.far, 500000000.0);
          this._far = this.far;
      }
  
      /**
       * The number of elements used to pack the object into an array.
       * @type {Number}
       */
      OrthographicFrustum.packedLength = 4;
  
      /**
       * Stores the provided instance into the provided array.
       *
       * @param {OrthographicFrustum} value The value to pack.
       * @param {Number[]} array The array to pack into.
       * @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
       *
       * @returns {Number[]} The array that was packed into
       */
      OrthographicFrustum.pack = function(value, array, startingIndex) {
                  Check.typeOf.object('value', value);
          Check.defined('array', array);
          
          startingIndex = defaultValue(startingIndex, 0);
  
          array[startingIndex++] = value.width;
          array[startingIndex++] = value.aspectRatio;
          array[startingIndex++] = value.near;
          array[startingIndex] = value.far;
  
          return array;
      };
  
      /**
       * Retrieves an instance from a packed array.
       *
       * @param {Number[]} array The packed array.
       * @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
       * @param {OrthographicFrustum} [result] The object into which to store the result.
       * @returns {OrthographicFrustum} The modified result parameter or a new OrthographicFrustum instance if one was not provided.
       */
      OrthographicFrustum.unpack = function(array, startingIndex, result) {
                  Check.defined('array', array);
          
          startingIndex = defaultValue(startingIndex, 0);
  
          if (!defined(result)) {
              result = new OrthographicFrustum();
          }
  
          result.width = array[startingIndex++];
          result.aspectRatio = array[startingIndex++];
          result.near = array[startingIndex++];
          result.far = array[startingIndex];
  
          return result;
      };
  
      function update(frustum) {
                  if (!defined(frustum.width) || !defined(frustum.aspectRatio) || !defined(frustum.near) || !defined(frustum.far)) {
              throw new DeveloperError('width, aspectRatio, near, or far parameters are not set.');
          }
          
          var f = frustum._offCenterFrustum;
  
          if (frustum.width !== frustum._width || frustum.aspectRatio !== frustum._aspectRatio ||
              frustum.near !== frustum._near || frustum.far !== frustum._far) {
                          if (frustum.aspectRatio < 0) {
                  throw new DeveloperError('aspectRatio must be positive.');
              }
              if (frustum.near < 0 || frustum.near > frustum.far) {
                  throw new DeveloperError('near must be greater than zero and less than far.');
              }
              
              frustum._aspectRatio = frustum.aspectRatio;
              frustum._width = frustum.width;
              frustum._near = frustum.near;
              frustum._far = frustum.far;
  
              var ratio = 1.0 / frustum.aspectRatio;
              f.right = frustum.width * 0.5;
              f.left = -f.right;
              f.top = ratio * f.right;
              f.bottom = -f.top;
              f.near = frustum.near;
              f.far = frustum.far;
  
          }
      }
  
      defineProperties(OrthographicFrustum.prototype, {
          /**
           * Gets the orthographic projection matrix computed from the view frustum.
           * @memberof OrthographicFrustum.prototype
           * @type {Matrix4}
           * @readonly
           */
          projectionMatrix : {
              get : function() {
                  update(this);
                  return this._offCenterFrustum.projectionMatrix;
              }
          }
  
      });
  
      /**
       * Creates a culling volume for this frustum.
       *
       * @param {Cartesian3} position The eye position.
       * @param {Cartesian3} direction The view direction.
       * @param {Cartesian3} up The up direction.
       * @returns {CullingVolume} A culling volume at the given position and orientation.
       *
       * @example
       * // Check if a bounding volume intersects the frustum.
       * var cullingVolume = frustum.computeCullingVolume(cameraPosition, cameraDirection, cameraUp);
       * var intersect = cullingVolume.computeVisibility(boundingVolume);
       */
      OrthographicFrustum.prototype.computeCullingVolume = function(position, direction, up) {
          update(this);
          return this._offCenterFrustum.computeCullingVolume(position, direction, up);
      };
  
      /**
       * Returns the pixel's width and height in meters.
       *
       * @param {Number} drawingBufferWidth The width of the drawing buffer.
       * @param {Number} drawingBufferHeight The height of the drawing buffer.
       * @param {Number} distance The distance to the near plane in meters.
       * @param {Cartesian2} result The object onto which to store the result.
       * @returns {Cartesian2} The modified result parameter or a new instance of {@link Cartesian2} with the pixel's width and height in the x and y properties, respectively.
       *
       * @exception {DeveloperError} drawingBufferWidth must be greater than zero.
       * @exception {DeveloperError} drawingBufferHeight must be greater than zero.
       *
       * @example
       * // Example 1
       * // Get the width and height of a pixel.
       * var pixelSize = camera.frustum.getPixelDimensions(scene.drawingBufferWidth, scene.drawingBufferHeight, 0.0, new Cesium.Cartesian2());
       */
      OrthographicFrustum.prototype.getPixelDimensions = function(drawingBufferWidth, drawingBufferHeight, distance, result) {
          update(this);
          return this._offCenterFrustum.getPixelDimensions(drawingBufferWidth, drawingBufferHeight, distance, result);
      };
  
      /**
       * Returns a duplicate of a OrthographicFrustum instance.
       *
       * @param {OrthographicFrustum} [result] The object onto which to store the result.
       * @returns {OrthographicFrustum} The modified result parameter or a new OrthographicFrustum instance if one was not provided.
       */
      OrthographicFrustum.prototype.clone = function(result) {
          if (!defined(result)) {
              result = new OrthographicFrustum();
          }
  
          result.aspectRatio = this.aspectRatio;
          result.width = this.width;
          result.near = this.near;
          result.far = this.far;
  
          // force update of clone to compute matrices
          result._aspectRatio = undefined;
          result._width = undefined;
          result._near = undefined;
          result._far = undefined;
  
          this._offCenterFrustum.clone(result._offCenterFrustum);
  
          return result;
      };
  
      /**
       * Compares the provided OrthographicFrustum componentwise and returns
       * <code>true</code> if they are equal, <code>false</code> otherwise.
       *
       * @param {OrthographicFrustum} [other] The right hand side OrthographicFrustum.
       * @returns {Boolean} <code>true</code> if they are equal, <code>false</code> otherwise.
       */
      OrthographicFrustum.prototype.equals = function(other) {
          if (!defined(other)) {
              return false;
          }
  
          update(this);
          update(other);
  
          return (this.width === other.width &&
                  this.aspectRatio === other.aspectRatio &&
                  this.near === other.near &&
                  this.far === other.far &&
                  this._offCenterFrustum.equals(other._offCenterFrustum));
      };
  
      return OrthographicFrustum;
  });
  
  define('Core/PerspectiveOffCenterFrustum',[
          './Cartesian3',
          './Cartesian4',
          './CullingVolume',
          './defaultValue',
          './defined',
          './defineProperties',
          './DeveloperError',
          './Matrix4'
      ], function(
          Cartesian3,
          Cartesian4,
          CullingVolume,
          defaultValue,
          defined,
          defineProperties,
          DeveloperError,
          Matrix4) {
      'use strict';
  
      /**
       * The viewing frustum is defined by 6 planes.
       * Each plane is represented by a {@link Cartesian4} object, where the x, y, and z components
       * define the unit vector normal to the plane, and the w component is the distance of the
       * plane from the origin/camera position.
       *
       * @alias PerspectiveOffCenterFrustum
       * @constructor
       *
       * @param {Object} [options] An object with the following properties:
       * @param {Number} [options.left] The left clipping plane distance.
       * @param {Number} [options.right] The right clipping plane distance.
       * @param {Number} [options.top] The top clipping plane distance.
       * @param {Number} [options.bottom] The bottom clipping plane distance.
       * @param {Number} [options.near=1.0] The near clipping plane distance.
       * @param {Number} [options.far=500000000.0] The far clipping plane distance.
       *
       * @example
       * var frustum = new Cesium.PerspectiveOffCenterFrustum({
       *     left : -1.0,
       *     right : 1.0,
       *     top : 1.0,
       *     bottom : -1.0,
       *     near : 1.0,
       *     far : 100.0
       * });
       *
       * @see PerspectiveFrustum
       */
      function PerspectiveOffCenterFrustum(options) {
          options = defaultValue(options, defaultValue.EMPTY_OBJECT);
  
          /**
           * Defines the left clipping plane.
           * @type {Number}
           * @default undefined
           */
          this.left = options.left;
          this._left = undefined;
  
          /**
           * Defines the right clipping plane.
           * @type {Number}
           * @default undefined
           */
          this.right = options.right;
          this._right = undefined;
  
          /**
           * Defines the top clipping plane.
           * @type {Number}
           * @default undefined
           */
          this.top = options.top;
          this._top = undefined;
  
          /**
           * Defines the bottom clipping plane.
           * @type {Number}
           * @default undefined
           */
          this.bottom = options.bottom;
          this._bottom = undefined;
  
          /**
           * The distance of the near plane.
           * @type {Number}
           * @default 1.0
           */
          this.near = defaultValue(options.near, 1.0);
          this._near = this.near;
  
          /**
           * The distance of the far plane.
           * @type {Number}
           * @default 500000000.0
           */
          this.far = defaultValue(options.far, 500000000.0);
          this._far = this.far;
  
          this._cullingVolume = new CullingVolume();
          this._perspectiveMatrix = new Matrix4();
          this._infinitePerspective = new Matrix4();
      }
  
      function update(frustum) {
                  if (!defined(frustum.right) || !defined(frustum.left) ||
              !defined(frustum.top) || !defined(frustum.bottom) ||
              !defined(frustum.near) || !defined(frustum.far)) {
              throw new DeveloperError('right, left, top, bottom, near, or far parameters are not set.');
          }
          
          var t = frustum.top;
          var b = frustum.bottom;
          var r = frustum.right;
          var l = frustum.left;
          var n = frustum.near;
          var f = frustum.far;
  
          if (t !== frustum._top || b !== frustum._bottom ||
              l !== frustum._left || r !== frustum._right ||
              n !== frustum._near || f !== frustum._far) {
  
                          if (frustum.near <= 0 || frustum.near > frustum.far) {
                  throw new DeveloperError('near must be greater than zero and less than far.');
              }
              
              frustum._left = l;
              frustum._right = r;
              frustum._top = t;
              frustum._bottom = b;
              frustum._near = n;
              frustum._far = f;
              frustum._perspectiveMatrix = Matrix4.computePerspectiveOffCenter(l, r, b, t, n, f, frustum._perspectiveMatrix);
              frustum._infinitePerspective = Matrix4.computeInfinitePerspectiveOffCenter(l, r, b, t, n, frustum._infinitePerspective);
          }
      }
  
      defineProperties(PerspectiveOffCenterFrustum.prototype, {
          /**
           * Gets the perspective projection matrix computed from the view frustum.
           * @memberof PerspectiveOffCenterFrustum.prototype
           * @type {Matrix4}
           * @readonly
           *
           * @see PerspectiveOffCenterFrustum#infiniteProjectionMatrix
           */
          projectionMatrix : {
              get : function() {
                  update(this);
                  return this._perspectiveMatrix;
              }
          },
  
          /**
           * Gets the perspective projection matrix computed from the view frustum with an infinite far plane.
           * @memberof PerspectiveOffCenterFrustum.prototype
           * @type {Matrix4}
           * @readonly
           *
           * @see PerspectiveOffCenterFrustum#projectionMatrix
           */
          infiniteProjectionMatrix : {
              get : function() {
                  update(this);
                  return this._infinitePerspective;
              }
          }
      });
  
      var getPlanesRight = new Cartesian3();
      var getPlanesNearCenter = new Cartesian3();
      var getPlanesFarCenter = new Cartesian3();
      var getPlanesNormal = new Cartesian3();
      /**
       * Creates a culling volume for this frustum.
       *
       * @param {Cartesian3} position The eye position.
       * @param {Cartesian3} direction The view direction.
       * @param {Cartesian3} up The up direction.
       * @returns {CullingVolume} A culling volume at the given position and orientation.
       *
       * @example
       * // Check if a bounding volume intersects the frustum.
       * var cullingVolume = frustum.computeCullingVolume(cameraPosition, cameraDirection, cameraUp);
       * var intersect = cullingVolume.computeVisibility(boundingVolume);
       */
      PerspectiveOffCenterFrustum.prototype.computeCullingVolume = function(position, direction, up) {
                  if (!defined(position)) {
              throw new DeveloperError('position is required.');
          }
  
          if (!defined(direction)) {
              throw new DeveloperError('direction is required.');
          }
  
          if (!defined(up)) {
              throw new DeveloperError('up is required.');
          }
          
          var planes = this._cullingVolume.planes;
  
          var t = this.top;
          var b = this.bottom;
          var r = this.right;
          var l = this.left;
          var n = this.near;
          var f = this.far;
  
          var right = Cartesian3.cross(direction, up, getPlanesRight);
  
          var nearCenter = getPlanesNearCenter;
          Cartesian3.multiplyByScalar(direction, n, nearCenter);
          Cartesian3.add(position, nearCenter, nearCenter);
  
          var farCenter = getPlanesFarCenter;
          Cartesian3.multiplyByScalar(direction, f, farCenter);
          Cartesian3.add(position, farCenter, farCenter);
  
          var normal = getPlanesNormal;
  
          //Left plane computation
          Cartesian3.multiplyByScalar(right, l, normal);
          Cartesian3.add(nearCenter, normal, normal);
          Cartesian3.subtract(normal, position, normal);
          Cartesian3.normalize(normal, normal);
          Cartesian3.cross(normal, up, normal);
          Cartesian3.normalize(normal, normal);
  
          var plane = planes[0];
          if (!defined(plane)) {
              plane = planes[0] = new Cartesian4();
          }
          plane.x = normal.x;
          plane.y = normal.y;
          plane.z = normal.z;
          plane.w = -Cartesian3.dot(normal, position);
  
          //Right plane computation
          Cartesian3.multiplyByScalar(right, r, normal);
          Cartesian3.add(nearCenter, normal, normal);
          Cartesian3.subtract(normal, position, normal);
          Cartesian3.cross(up, normal, normal);
          Cartesian3.normalize(normal, normal);
  
          plane = planes[1];
          if (!defined(plane)) {
              plane = planes[1] = new Cartesian4();
          }
          plane.x = normal.x;
          plane.y = normal.y;
          plane.z = normal.z;
          plane.w = -Cartesian3.dot(normal, position);
  
          //Bottom plane computation
          Cartesian3.multiplyByScalar(up, b, normal);
          Cartesian3.add(nearCenter, normal, normal);
          Cartesian3.subtract(normal, position, normal);
          Cartesian3.cross(right, normal, normal);
          Cartesian3.normalize(normal, normal);
  
          plane = planes[2];
          if (!defined(plane)) {
              plane = planes[2] = new Cartesian4();
          }
          plane.x = normal.x;
          plane.y = normal.y;
          plane.z = normal.z;
          plane.w = -Cartesian3.dot(normal, position);
  
          //Top plane computation
          Cartesian3.multiplyByScalar(up, t, normal);
          Cartesian3.add(nearCenter, normal, normal);
          Cartesian3.subtract(normal, position, normal);
          Cartesian3.cross(normal, right, normal);
          Cartesian3.normalize(normal, normal);
  
          plane = planes[3];
          if (!defined(plane)) {
              plane = planes[3] = new Cartesian4();
          }
          plane.x = normal.x;
          plane.y = normal.y;
          plane.z = normal.z;
          plane.w = -Cartesian3.dot(normal, position);
  
          //Near plane computation
          plane = planes[4];
          if (!defined(plane)) {
              plane = planes[4] = new Cartesian4();
          }
          plane.x = direction.x;
          plane.y = direction.y;
          plane.z = direction.z;
          plane.w = -Cartesian3.dot(direction, nearCenter);
  
          //Far plane computation
          Cartesian3.negate(direction, normal);
  
          plane = planes[5];
          if (!defined(plane)) {
              plane = planes[5] = new Cartesian4();
          }
          plane.x = normal.x;
          plane.y = normal.y;
          plane.z = normal.z;
          plane.w = -Cartesian3.dot(normal, farCenter);
  
          return this._cullingVolume;
      };
  
      /**
       * Returns the pixel's width and height in meters.
       *
       * @param {Number} drawingBufferWidth The width of the drawing buffer.
       * @param {Number} drawingBufferHeight The height of the drawing buffer.
       * @param {Number} distance The distance to the near plane in meters.
       * @param {Cartesian2} result The object onto which to store the result.
       * @returns {Cartesian2} The modified result parameter or a new instance of {@link Cartesian2} with the pixel's width and height in the x and y properties, respectively.
       *
       * @exception {DeveloperError} drawingBufferWidth must be greater than zero.
       * @exception {DeveloperError} drawingBufferHeight must be greater than zero.
       *
       * @example
       * // Example 1
       * // Get the width and height of a pixel.
       * var pixelSize = camera.frustum.getPixelDimensions(scene.drawingBufferWidth, scene.drawingBufferHeight, 1.0, new Cesium.Cartesian2());
       *
       * @example
       * // Example 2
       * // Get the width and height of a pixel if the near plane was set to 'distance'.
       * // For example, get the size of a pixel of an image on a billboard.
       * var position = camera.position;
       * var direction = camera.direction;
       * var toCenter = Cesium.Cartesian3.subtract(primitive.boundingVolume.center, position, new Cesium.Cartesian3());      // vector from camera to a primitive
       * var toCenterProj = Cesium.Cartesian3.multiplyByScalar(direction, Cesium.Cartesian3.dot(direction, toCenter), new Cesium.Cartesian3()); // project vector onto camera direction vector
       * var distance = Cesium.Cartesian3.magnitude(toCenterProj);
       * var pixelSize = camera.frustum.getPixelDimensions(scene.drawingBufferWidth, scene.drawingBufferHeight, distance, new Cesium.Cartesian2());
       */
      PerspectiveOffCenterFrustum.prototype.getPixelDimensions = function(drawingBufferWidth, drawingBufferHeight, distance, result) {
          update(this);
  
                  if (!defined(drawingBufferWidth) || !defined(drawingBufferHeight)) {
              throw new DeveloperError('Both drawingBufferWidth and drawingBufferHeight are required.');
          }
          if (drawingBufferWidth <= 0) {
              throw new DeveloperError('drawingBufferWidth must be greater than zero.');
          }
          if (drawingBufferHeight <= 0) {
              throw new DeveloperError('drawingBufferHeight must be greater than zero.');
          }
          if (!defined(distance)) {
              throw new DeveloperError('distance is required.');
          }
          if (!defined(result)) {
              throw new DeveloperError('A result object is required.');
          }
          
          var inverseNear = 1.0 / this.near;
          var tanTheta = this.top * inverseNear;
          var pixelHeight = 2.0 * distance * tanTheta / drawingBufferHeight;
          tanTheta = this.right * inverseNear;
          var pixelWidth = 2.0 * distance * tanTheta / drawingBufferWidth;
  
          result.x = pixelWidth;
          result.y = pixelHeight;
          return result;
      };
  
      /**
       * Returns a duplicate of a PerspectiveOffCenterFrustum instance.
       *
       * @param {PerspectiveOffCenterFrustum} [result] The object onto which to store the result.
       * @returns {PerspectiveOffCenterFrustum} The modified result parameter or a new PerspectiveFrustum instance if one was not provided.
       */
      PerspectiveOffCenterFrustum.prototype.clone = function(result) {
          if (!defined(result)) {
              result = new PerspectiveOffCenterFrustum();
          }
  
          result.right = this.right;
          result.left = this.left;
          result.top = this.top;
          result.bottom = this.bottom;
          result.near = this.near;
          result.far = this.far;
  
          // force update of clone to compute matrices
          result._left = undefined;
          result._right = undefined;
          result._top = undefined;
          result._bottom = undefined;
          result._near = undefined;
          result._far = undefined;
  
          return result;
      };
  
      /**
       * Compares the provided PerspectiveOffCenterFrustum componentwise and returns
       * <code>true</code> if they are equal, <code>false</code> otherwise.
       *
       * @param {PerspectiveOffCenterFrustum} [other] The right hand side PerspectiveOffCenterFrustum.
       * @returns {Boolean} <code>true</code> if they are equal, <code>false</code> otherwise.
       */
      PerspectiveOffCenterFrustum.prototype.equals = function(other) {
          return (defined(other) &&
                  this.right === other.right &&
                  this.left === other.left &&
                  this.top === other.top &&
                  this.bottom === other.bottom &&
                  this.near === other.near &&
                  this.far === other.far);
      };
  
      return PerspectiveOffCenterFrustum;
  });
  
  define('Core/PerspectiveFrustum',[
          './Check',
          './defaultValue',
          './defined',
          './defineProperties',
          './DeveloperError',
          './PerspectiveOffCenterFrustum'
      ], function(
          Check,
          defaultValue,
          defined,
          defineProperties,
          DeveloperError,
          PerspectiveOffCenterFrustum) {
      'use strict';
  
      /**
       * The viewing frustum is defined by 6 planes.
       * Each plane is represented by a {@link Cartesian4} object, where the x, y, and z components
       * define the unit vector normal to the plane, and the w component is the distance of the
       * plane from the origin/camera position.
       *
       * @alias PerspectiveFrustum
       * @constructor
       *
       * @param {Object} [options] An object with the following properties:
       * @param {Number} [options.fov] The angle of the field of view (FOV), in radians.
       * @param {Number} [options.aspectRatio] The aspect ratio of the frustum's width to it's height.
       * @param {Number} [options.near=1.0] The distance of the near plane.
       * @param {Number} [options.far=500000000.0] The distance of the far plane.
       * @param {Number} [options.xOffset=0.0] The offset in the x direction.
       * @param {Number} [options.yOffset=0.0] The offset in the y direction.
       *
       * @example
       * var frustum = new Cesium.PerspectiveFrustum({
       *     fov : Cesium.Math.PI_OVER_THREE,
       *     aspectRatio : canvas.clientWidth / canvas.clientHeight
       *     near : 1.0,
       *     far : 1000.0
       * });
       *
       * @see PerspectiveOffCenterFrustum
       */
      function PerspectiveFrustum(options) {
          options = defaultValue(options, defaultValue.EMPTY_OBJECT);
  
          this._offCenterFrustum = new PerspectiveOffCenterFrustum();
  
          /**
           * The angle of the field of view (FOV), in radians.  This angle will be used
           * as the horizontal FOV if the width is greater than the height, otherwise
           * it will be the vertical FOV.
           * @type {Number}
           * @default undefined
           */
          this.fov = options.fov;
          this._fov = undefined;
          this._fovy = undefined;
  
          this._sseDenominator = undefined;
  
          /**
           * The aspect ratio of the frustum's width to it's height.
           * @type {Number}
           * @default undefined
           */
          this.aspectRatio = options.aspectRatio;
          this._aspectRatio = undefined;
  
          /**
           * The distance of the near plane.
           * @type {Number}
           * @default 1.0
           */
          this.near = defaultValue(options.near, 1.0);
          this._near = this.near;
  
          /**
           * The distance of the far plane.
           * @type {Number}
           * @default 500000000.0
           */
          this.far = defaultValue(options.far, 500000000.0);
          this._far = this.far;
  
          /**
           * Offsets the frustum in the x direction.
           * @type {Number}
           * @default 0.0
           */
          this.xOffset = defaultValue(options.xOffset, 0.0);
          this._xOffset = this.xOffset;
  
          /**
           * Offsets the frustum in the y direction.
           * @type {Number}
           * @default 0.0
           */
          this.yOffset = defaultValue(options.yOffset, 0.0);
          this._yOffset = this.yOffset;
      }
  
      /**
       * The number of elements used to pack the object into an array.
       * @type {Number}
       */
      PerspectiveFrustum.packedLength = 6;
  
      /**
       * Stores the provided instance into the provided array.
       *
       * @param {PerspectiveFrustum} value The value to pack.
       * @param {Number[]} array The array to pack into.
       * @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
       *
       * @returns {Number[]} The array that was packed into
       */
      PerspectiveFrustum.pack = function(value, array, startingIndex) {
                  Check.typeOf.object('value', value);
          Check.defined('array', array);
          
          startingIndex = defaultValue(startingIndex, 0);
  
          array[startingIndex++] = value.fov;
          array[startingIndex++] = value.aspectRatio;
          array[startingIndex++] = value.near;
          array[startingIndex++] = value.far;
          array[startingIndex++] = value.xOffset;
          array[startingIndex] = value.yOffset;
  
          return array;
      };
  
      /**
       * Retrieves an instance from a packed array.
       *
       * @param {Number[]} array The packed array.
       * @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
       * @param {PerspectiveFrustum} [result] The object into which to store the result.
       * @returns {PerspectiveFrustum} The modified result parameter or a new PerspectiveFrustum instance if one was not provided.
       */
      PerspectiveFrustum.unpack = function(array, startingIndex, result) {
                  Check.defined('array', array);
          
          startingIndex = defaultValue(startingIndex, 0);
  
          if (!defined(result)) {
              result = new PerspectiveFrustum();
          }
  
          result.fov = array[startingIndex++];
          result.aspectRatio = array[startingIndex++];
          result.near = array[startingIndex++];
          result.far = array[startingIndex++];
          result.xOffset = array[startingIndex++];
          result.yOffset = array[startingIndex];
  
          return result;
      };
  
      function update(frustum) {
                  if (!defined(frustum.fov) || !defined(frustum.aspectRatio) || !defined(frustum.near) || !defined(frustum.far)) {
              throw new DeveloperError('fov, aspectRatio, near, or far parameters are not set.');
          }
          
          var f = frustum._offCenterFrustum;
  
          if (frustum.fov !== frustum._fov || frustum.aspectRatio !== frustum._aspectRatio ||
              frustum.near !== frustum._near || frustum.far !== frustum._far ||
              frustum.xOffset !== frustum._xOffset || frustum.yOffset !== frustum._yOffset) {
                          if (frustum.fov < 0 || frustum.fov >= Math.PI) {
                  throw new DeveloperError('fov must be in the range [0, PI).');
              }
  
              if (frustum.aspectRatio < 0) {
                  throw new DeveloperError('aspectRatio must be positive.');
              }
  
              if (frustum.near < 0 || frustum.near > frustum.far) {
                  throw new DeveloperError('near must be greater than zero and less than far.');
              }
              
              frustum._aspectRatio = frustum.aspectRatio;
              frustum._fov = frustum.fov;
              frustum._fovy = (frustum.aspectRatio <= 1) ? frustum.fov : Math.atan(Math.tan(frustum.fov * 0.5) / frustum.aspectRatio) * 2.0;
              frustum._near = frustum.near;
              frustum._far = frustum.far;
              frustum._sseDenominator = 2.0 * Math.tan(0.5 * frustum._fovy);
              frustum._xOffset = frustum.xOffset;
              frustum._yOffset = frustum.yOffset;
  
              f.top = frustum.near * Math.tan(0.5 * frustum._fovy);
              f.bottom = -f.top;
              f.right = frustum.aspectRatio * f.top;
              f.left = -f.right;
              f.near = frustum.near;
              f.far = frustum.far;
  
              f.right += frustum.xOffset;
              f.left += frustum.xOffset;
              f.top += frustum.yOffset;
              f.bottom += frustum.yOffset;
          }
      }
  
      defineProperties(PerspectiveFrustum.prototype, {
          /**
           * Gets the perspective projection matrix computed from the view frustum.
           * @memberof PerspectiveFrustum.prototype
           * @type {Matrix4}
           * @readonly
           *
           * @see PerspectiveFrustum#infiniteProjectionMatrix
           */
          projectionMatrix : {
              get : function() {
                  update(this);
                  return this._offCenterFrustum.projectionMatrix;
              }
          },
  
          /**
           * The perspective projection matrix computed from the view frustum with an infinite far plane.
           * @memberof PerspectiveFrustum.prototype
           * @type {Matrix4}
           * @readonly
           *
           * @see PerspectiveFrustum#projectionMatrix
           */
          infiniteProjectionMatrix : {
              get : function() {
                  update(this);
                  return this._offCenterFrustum.infiniteProjectionMatrix;
              }
          },
  
          /**
           * Gets the angle of the vertical field of view, in radians.
           * @memberof PerspectiveFrustum.prototype
           * @type {Number}
           * @readonly
           * @default undefined
           */
          fovy : {
              get : function() {
                  update(this);
                  return this._fovy;
              }
          },
  
          /**
           * @readonly
           * @private
           */
          sseDenominator : {
              get : function () {
                  update(this);
                  return this._sseDenominator;
              }
          }
      });
  
      /**
       * Creates a culling volume for this frustum.
       *
       * @param {Cartesian3} position The eye position.
       * @param {Cartesian3} direction The view direction.
       * @param {Cartesian3} up The up direction.
       * @returns {CullingVolume} A culling volume at the given position and orientation.
       *
       * @example
       * // Check if a bounding volume intersects the frustum.
       * var cullingVolume = frustum.computeCullingVolume(cameraPosition, cameraDirection, cameraUp);
       * var intersect = cullingVolume.computeVisibility(boundingVolume);
       */
      PerspectiveFrustum.prototype.computeCullingVolume = function(position, direction, up) {
          update(this);
          return this._offCenterFrustum.computeCullingVolume(position, direction, up);
      };
  
      /**
       * Returns the pixel's width and height in meters.
       *
       * @param {Number} drawingBufferWidth The width of the drawing buffer.
       * @param {Number} drawingBufferHeight The height of the drawing buffer.
       * @param {Number} distance The distance to the near plane in meters.
       * @param {Cartesian2} result The object onto which to store the result.
       * @returns {Cartesian2} The modified result parameter or a new instance of {@link Cartesian2} with the pixel's width and height in the x and y properties, respectively.
       *
       * @exception {DeveloperError} drawingBufferWidth must be greater than zero.
       * @exception {DeveloperError} drawingBufferHeight must be greater than zero.
       *
       * @example
       * // Example 1
       * // Get the width and height of a pixel.
       * var pixelSize = camera.frustum.getPixelDimensions(scene.drawingBufferWidth, scene.drawingBufferHeight, 1.0, new Cesium.Cartesian2());
       *
       * @example
       * // Example 2
       * // Get the width and height of a pixel if the near plane was set to 'distance'.
       * // For example, get the size of a pixel of an image on a billboard.
       * var position = camera.position;
       * var direction = camera.direction;
       * var toCenter = Cesium.Cartesian3.subtract(primitive.boundingVolume.center, position, new Cesium.Cartesian3());      // vector from camera to a primitive
       * var toCenterProj = Cesium.Cartesian3.multiplyByScalar(direction, Cesium.Cartesian3.dot(direction, toCenter), new Cesium.Cartesian3()); // project vector onto camera direction vector
       * var distance = Cesium.Cartesian3.magnitude(toCenterProj);
       * var pixelSize = camera.frustum.getPixelDimensions(scene.drawingBufferWidth, scene.drawingBufferHeight, distance, new Cesium.Cartesian2());
       */
      PerspectiveFrustum.prototype.getPixelDimensions = function(drawingBufferWidth, drawingBufferHeight, distance, result) {
          update(this);
          return this._offCenterFrustum.getPixelDimensions(drawingBufferWidth, drawingBufferHeight, distance, result);
      };
  
      /**
       * Returns a duplicate of a PerspectiveFrustum instance.
       *
       * @param {PerspectiveFrustum} [result] The object onto which to store the result.
       * @returns {PerspectiveFrustum} The modified result parameter or a new PerspectiveFrustum instance if one was not provided.
       */
      PerspectiveFrustum.prototype.clone = function(result) {
          if (!defined(result)) {
              result = new PerspectiveFrustum();
          }
  
          result.aspectRatio = this.aspectRatio;
          result.fov = this.fov;
          result.near = this.near;
          result.far = this.far;
  
          // force update of clone to compute matrices
          result._aspectRatio = undefined;
          result._fov = undefined;
          result._near = undefined;
          result._far = undefined;
  
          this._offCenterFrustum.clone(result._offCenterFrustum);
  
          return result;
      };
  
      /**
       * Compares the provided PerspectiveFrustum componentwise and returns
       * <code>true</code> if they are equal, <code>false</code> otherwise.
       *
       * @param {PerspectiveFrustum} [other] The right hand side PerspectiveFrustum.
       * @returns {Boolean} <code>true</code> if they are equal, <code>false</code> otherwise.
       */
      PerspectiveFrustum.prototype.equals = function(other) {
          if (!defined(other)) {
              return false;
          }
  
          update(this);
          update(other);
  
          return (this.fov === other.fov &&
                  this.aspectRatio === other.aspectRatio &&
                  this.near === other.near &&
                  this.far === other.far &&
                  this._offCenterFrustum.equals(other._offCenterFrustum));
      };
  
      return PerspectiveFrustum;
  });
  
  define('Core/Quaternion',[
          './Cartesian3',
          './Check',
          './defaultValue',
          './defined',
          './FeatureDetection',
          './freezeObject',
          './Math',
          './Matrix3'
      ], function(
          Cartesian3,
          Check,
          defaultValue,
          defined,
          FeatureDetection,
          freezeObject,
          CesiumMath,
          Matrix3) {
      'use strict';
  
      /**
       * A set of 4-dimensional coordinates used to represent rotation in 3-dimensional space.
       * @alias Quaternion
       * @constructor
       *
       * @param {Number} [x=0.0] The X component.
       * @param {Number} [y=0.0] The Y component.
       * @param {Number} [z=0.0] The Z component.
       * @param {Number} [w=0.0] The W component.
       *
       * @see PackableForInterpolation
       */
      function Quaternion(x, y, z, w) {
          /**
           * The X component.
           * @type {Number}
           * @default 0.0
           */
          this.x = defaultValue(x, 0.0);
  
          /**
           * The Y component.
           * @type {Number}
           * @default 0.0
           */
          this.y = defaultValue(y, 0.0);
  
          /**
           * The Z component.
           * @type {Number}
           * @default 0.0
           */
          this.z = defaultValue(z, 0.0);
  
          /**
           * The W component.
           * @type {Number}
           * @default 0.0
           */
          this.w = defaultValue(w, 0.0);
      }
  
      var fromAxisAngleScratch = new Cartesian3();
  
      /**
       * Computes a quaternion representing a rotation around an axis.
       *
       * @param {Cartesian3} axis The axis of rotation.
       * @param {Number} angle The angle in radians to rotate around the axis.
       * @param {Quaternion} [result] The object onto which to store the result.
       * @returns {Quaternion} The modified result parameter or a new Quaternion instance if one was not provided.
       */
      Quaternion.fromAxisAngle = function(axis, angle, result) {
                  Check.typeOf.object('axis', axis);
          Check.typeOf.number('angle', angle);
          
          var halfAngle = angle / 2.0;
          var s = Math.sin(halfAngle);
          fromAxisAngleScratch = Cartesian3.normalize(axis, fromAxisAngleScratch);
  
          var x = fromAxisAngleScratch.x * s;
          var y = fromAxisAngleScratch.y * s;
          var z = fromAxisAngleScratch.z * s;
          var w = Math.cos(halfAngle);
          if (!defined(result)) {
              return new Quaternion(x, y, z, w);
          }
          result.x = x;
          result.y = y;
          result.z = z;
          result.w = w;
          return result;
      };
  
      var fromRotationMatrixNext = [1, 2, 0];
      var fromRotationMatrixQuat = new Array(3);
      /**
       * Computes a Quaternion from the provided Matrix3 instance.
       *
       * @param {Matrix3} matrix The rotation matrix.
       * @param {Quaternion} [result] The object onto which to store the result.
       * @returns {Quaternion} The modified result parameter or a new Quaternion instance if one was not provided.
       *
       * @see Matrix3.fromQuaternion
       */
      Quaternion.fromRotationMatrix = function(matrix, result) {
                  Check.typeOf.object('matrix', matrix);
          
          var root;
          var x;
          var y;
          var z;
          var w;
  
          var m00 = matrix[Matrix3.COLUMN0ROW0];
          var m11 = matrix[Matrix3.COLUMN1ROW1];
          var m22 = matrix[Matrix3.COLUMN2ROW2];
          var trace = m00 + m11 + m22;
  
          if (trace > 0.0) {
              // |w| > 1/2, may as well choose w > 1/2
              root = Math.sqrt(trace + 1.0); // 2w
              w = 0.5 * root;
              root = 0.5 / root; // 1/(4w)
  
              x = (matrix[Matrix3.COLUMN1ROW2] - matrix[Matrix3.COLUMN2ROW1]) * root;
              y = (matrix[Matrix3.COLUMN2ROW0] - matrix[Matrix3.COLUMN0ROW2]) * root;
              z = (matrix[Matrix3.COLUMN0ROW1] - matrix[Matrix3.COLUMN1ROW0]) * root;
          } else {
              // |w| <= 1/2
              var next = fromRotationMatrixNext;
  
              var i = 0;
              if (m11 > m00) {
                  i = 1;
              }
              if (m22 > m00 && m22 > m11) {
                  i = 2;
              }
              var j = next[i];
              var k = next[j];
  
              root = Math.sqrt(matrix[Matrix3.getElementIndex(i, i)] - matrix[Matrix3.getElementIndex(j, j)] - matrix[Matrix3.getElementIndex(k, k)] + 1.0);
  
              var quat = fromRotationMatrixQuat;
              quat[i] = 0.5 * root;
              root = 0.5 / root;
              w = (matrix[Matrix3.getElementIndex(k, j)] - matrix[Matrix3.getElementIndex(j, k)]) * root;
              quat[j] = (matrix[Matrix3.getElementIndex(j, i)] + matrix[Matrix3.getElementIndex(i, j)]) * root;
              quat[k] = (matrix[Matrix3.getElementIndex(k, i)] + matrix[Matrix3.getElementIndex(i, k)]) * root;
  
              x = -quat[0];
              y = -quat[1];
              z = -quat[2];
          }
  
          if (!defined(result)) {
              return new Quaternion(x, y, z, w);
          }
          result.x = x;
          result.y = y;
          result.z = z;
          result.w = w;
          return result;
      };
  
      var scratchHPRQuaternion = new Quaternion();
      var scratchHeadingQuaternion = new Quaternion();
      var scratchPitchQuaternion = new Quaternion();
      var scratchRollQuaternion = new Quaternion();
  
      /**
       * Computes a rotation from the given heading, pitch and roll angles. Heading is the rotation about the
       * negative z axis. Pitch is the rotation about the negative y axis. Roll is the rotation about
       * the positive x axis.
       *
       * @param {HeadingPitchRoll} headingPitchRoll The rotation expressed as a heading, pitch and roll.
       * @param {Quaternion} [result] The object onto which to store the result.
       * @returns {Quaternion} The modified result parameter or a new Quaternion instance if none was provided.
       */
      Quaternion.fromHeadingPitchRoll = function(headingPitchRoll, result) {
                  Check.typeOf.object('headingPitchRoll', headingPitchRoll);
          
          scratchRollQuaternion = Quaternion.fromAxisAngle(Cartesian3.UNIT_X, headingPitchRoll.roll, scratchHPRQuaternion);
          scratchPitchQuaternion = Quaternion.fromAxisAngle(Cartesian3.UNIT_Y, -headingPitchRoll.pitch, result);
          result = Quaternion.multiply(scratchPitchQuaternion, scratchRollQuaternion, scratchPitchQuaternion);
          scratchHeadingQuaternion = Quaternion.fromAxisAngle(Cartesian3.UNIT_Z, -headingPitchRoll.heading, scratchHPRQuaternion);
          return Quaternion.multiply(scratchHeadingQuaternion, result, result);
      };
  
      var sampledQuaternionAxis = new Cartesian3();
      var sampledQuaternionRotation = new Cartesian3();
      var sampledQuaternionTempQuaternion = new Quaternion();
      var sampledQuaternionQuaternion0 = new Quaternion();
      var sampledQuaternionQuaternion0Conjugate = new Quaternion();
  
      /**
       * The number of elements used to pack the object into an array.
       * @type {Number}
       */
      Quaternion.packedLength = 4;
  
      /**
       * Stores the provided instance into the provided array.
       *
       * @param {Quaternion} value The value to pack.
       * @param {Number[]} array The array to pack into.
       * @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
       *
       * @returns {Number[]} The array that was packed into
       */
      Quaternion.pack = function(value, array, startingIndex) {
                  Check.typeOf.object('value', value);
          Check.defined('array', array);
          
          startingIndex = defaultValue(startingIndex, 0);
  
          array[startingIndex++] = value.x;
          array[startingIndex++] = value.y;
          array[startingIndex++] = value.z;
          array[startingIndex] = value.w;
  
          return array;
      };
  
      /**
       * Retrieves an instance from a packed array.
       *
       * @param {Number[]} array The packed array.
       * @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
       * @param {Quaternion} [result] The object into which to store the result.
       * @returns {Quaternion} The modified result parameter or a new Quaternion instance if one was not provided.
       */
      Quaternion.unpack = function(array, startingIndex, result) {
                  Check.defined('array', array);
          
          startingIndex = defaultValue(startingIndex, 0);
  
          if (!defined(result)) {
              result = new Quaternion();
          }
          result.x = array[startingIndex];
          result.y = array[startingIndex + 1];
          result.z = array[startingIndex + 2];
          result.w = array[startingIndex + 3];
          return result;
      };
  
      /**
       * The number of elements used to store the object into an array in its interpolatable form.
       * @type {Number}
       */
      Quaternion.packedInterpolationLength = 3;
  
      /**
       * Converts a packed array into a form suitable for interpolation.
       *
       * @param {Number[]} packedArray The packed array.
       * @param {Number} [startingIndex=0] The index of the first element to be converted.
       * @param {Number} [lastIndex=packedArray.length] The index of the last element to be converted.
       * @param {Number[]} result The object into which to store the result.
       */
      Quaternion.convertPackedArrayForInterpolation = function(packedArray, startingIndex, lastIndex, result) {
          Quaternion.unpack(packedArray, lastIndex * 4, sampledQuaternionQuaternion0Conjugate);
          Quaternion.conjugate(sampledQuaternionQuaternion0Conjugate, sampledQuaternionQuaternion0Conjugate);
  
          for (var i = 0, len = lastIndex - startingIndex + 1; i < len; i++) {
              var offset = i * 3;
              Quaternion.unpack(packedArray, (startingIndex + i) * 4, sampledQuaternionTempQuaternion);
  
              Quaternion.multiply(sampledQuaternionTempQuaternion, sampledQuaternionQuaternion0Conjugate, sampledQuaternionTempQuaternion);
  
              if (sampledQuaternionTempQuaternion.w < 0) {
                  Quaternion.negate(sampledQuaternionTempQuaternion, sampledQuaternionTempQuaternion);
              }
  
              Quaternion.computeAxis(sampledQuaternionTempQuaternion, sampledQuaternionAxis);
              var angle = Quaternion.computeAngle(sampledQuaternionTempQuaternion);
              result[offset] = sampledQuaternionAxis.x * angle;
              result[offset + 1] = sampledQuaternionAxis.y * angle;
              result[offset + 2] = sampledQuaternionAxis.z * angle;
          }
      };
  
      /**
       * Retrieves an instance from a packed array converted with {@link convertPackedArrayForInterpolation}.
       *
       * @param {Number[]} array The array previously packed for interpolation.
       * @param {Number[]} sourceArray The original packed array.
       * @param {Number} [firstIndex=0] The firstIndex used to convert the array.
       * @param {Number} [lastIndex=packedArray.length] The lastIndex used to convert the array.
       * @param {Quaternion} [result] The object into which to store the result.
       * @returns {Quaternion} The modified result parameter or a new Quaternion instance if one was not provided.
       */
      Quaternion.unpackInterpolationResult = function(array, sourceArray, firstIndex, lastIndex, result) {
          if (!defined(result)) {
              result = new Quaternion();
          }
          Cartesian3.fromArray(array, 0, sampledQuaternionRotation);
          var magnitude = Cartesian3.magnitude(sampledQuaternionRotation);
  
          Quaternion.unpack(sourceArray, lastIndex * 4, sampledQuaternionQuaternion0);
  
          if (magnitude === 0) {
              Quaternion.clone(Quaternion.IDENTITY, sampledQuaternionTempQuaternion);
          } else {
              Quaternion.fromAxisAngle(sampledQuaternionRotation, magnitude, sampledQuaternionTempQuaternion);
          }
  
          return Quaternion.multiply(sampledQuaternionTempQuaternion, sampledQuaternionQuaternion0, result);
      };
  
      /**
       * Duplicates a Quaternion instance.
       *
       * @param {Quaternion} quaternion The quaternion to duplicate.
       * @param {Quaternion} [result] The object onto which to store the result.
       * @returns {Quaternion} The modified result parameter or a new Quaternion instance if one was not provided. (Returns undefined if quaternion is undefined)
       */
      Quaternion.clone = function(quaternion, result) {
          if (!defined(quaternion)) {
              return undefined;
          }
  
          if (!defined(result)) {
              return new Quaternion(quaternion.x, quaternion.y, quaternion.z, quaternion.w);
          }
  
          result.x = quaternion.x;
          result.y = quaternion.y;
          result.z = quaternion.z;
          result.w = quaternion.w;
          return result;
      };
  
      /**
       * Computes the conjugate of the provided quaternion.
       *
       * @param {Quaternion} quaternion The quaternion to conjugate.
       * @param {Quaternion} result The object onto which to store the result.
       * @returns {Quaternion} The modified result parameter.
       */
      Quaternion.conjugate = function(quaternion, result) {
                  Check.typeOf.object('quaternion', quaternion);
          Check.typeOf.object('result', result);
          
          result.x = -quaternion.x;
          result.y = -quaternion.y;
          result.z = -quaternion.z;
          result.w = quaternion.w;
          return result;
      };
  
      /**
       * Computes magnitude squared for the provided quaternion.
       *
       * @param {Quaternion} quaternion The quaternion to conjugate.
       * @returns {Number} The magnitude squared.
       */
      Quaternion.magnitudeSquared = function(quaternion) {
                  Check.typeOf.object('quaternion', quaternion);
          
          return quaternion.x * quaternion.x + quaternion.y * quaternion.y + quaternion.z * quaternion.z + quaternion.w * quaternion.w;
      };
  
      /**
       * Computes magnitude for the provided quaternion.
       *
       * @param {Quaternion} quaternion The quaternion to conjugate.
       * @returns {Number} The magnitude.
       */
      Quaternion.magnitude = function(quaternion) {
          return Math.sqrt(Quaternion.magnitudeSquared(quaternion));
      };
  
      /**
       * Computes the normalized form of the provided quaternion.
       *
       * @param {Quaternion} quaternion The quaternion to normalize.
       * @param {Quaternion} result The object onto which to store the result.
       * @returns {Quaternion} The modified result parameter.
       */
      Quaternion.normalize = function(quaternion, result) {
                  Check.typeOf.object('result', result);
          
          var inverseMagnitude = 1.0 / Quaternion.magnitude(quaternion);
          var x = quaternion.x * inverseMagnitude;
          var y = quaternion.y * inverseMagnitude;
          var z = quaternion.z * inverseMagnitude;
          var w = quaternion.w * inverseMagnitude;
  
          result.x = x;
          result.y = y;
          result.z = z;
          result.w = w;
          return result;
      };
  
      /**
       * Computes the inverse of the provided quaternion.
       *
       * @param {Quaternion} quaternion The quaternion to normalize.
       * @param {Quaternion} result The object onto which to store the result.
       * @returns {Quaternion} The modified result parameter.
       */
      Quaternion.inverse = function(quaternion, result) {
                  Check.typeOf.object('result', result);
          
          var magnitudeSquared = Quaternion.magnitudeSquared(quaternion);
          result = Quaternion.conjugate(quaternion, result);
          return Quaternion.multiplyByScalar(result, 1.0 / magnitudeSquared, result);
      };
  
      /**
       * Computes the componentwise sum of two quaternions.
       *
       * @param {Quaternion} left The first quaternion.
       * @param {Quaternion} right The second quaternion.
       * @param {Quaternion} result The object onto which to store the result.
       * @returns {Quaternion} The modified result parameter.
       */
      Quaternion.add = function(left, right, result) {
                  Check.typeOf.object('left', left);
          Check.typeOf.object('right', right);
          Check.typeOf.object('result', result);
          
          result.x = left.x + right.x;
          result.y = left.y + right.y;
          result.z = left.z + right.z;
          result.w = left.w + right.w;
          return result;
      };
  
      /**
       * Computes the componentwise difference of two quaternions.
       *
       * @param {Quaternion} left The first quaternion.
       * @param {Quaternion} right The second quaternion.
       * @param {Quaternion} result The object onto which to store the result.
       * @returns {Quaternion} The modified result parameter.
       */
      Quaternion.subtract = function(left, right, result) {
                  Check.typeOf.object('left', left);
          Check.typeOf.object('right', right);
          Check.typeOf.object('result', result);
          
          result.x = left.x - right.x;
          result.y = left.y - right.y;
          result.z = left.z - right.z;
          result.w = left.w - right.w;
          return result;
      };
  
      /**
       * Negates the provided quaternion.
       *
       * @param {Quaternion} quaternion The quaternion to be negated.
       * @param {Quaternion} result The object onto which to store the result.
       * @returns {Quaternion} The modified result parameter.
       */
      Quaternion.negate = function(quaternion, result) {
                  Check.typeOf.object('quaternion', quaternion);
          Check.typeOf.object('result', result);
          
          result.x = -quaternion.x;
          result.y = -quaternion.y;
          result.z = -quaternion.z;
          result.w = -quaternion.w;
          return result;
      };
  
      /**
       * Computes the dot (scalar) product of two quaternions.
       *
       * @param {Quaternion} left The first quaternion.
       * @param {Quaternion} right The second quaternion.
       * @returns {Number} The dot product.
       */
      Quaternion.dot = function(left, right) {
                  Check.typeOf.object('left', left);
          Check.typeOf.object('right', right);
          
          return left.x * right.x + left.y * right.y + left.z * right.z + left.w * right.w;
      };
  
      /**
       * Computes the product of two quaternions.
       *
       * @param {Quaternion} left The first quaternion.
       * @param {Quaternion} right The second quaternion.
       * @param {Quaternion} result The object onto which to store the result.
       * @returns {Quaternion} The modified result parameter.
       */
      Quaternion.multiply = function(left, right, result) {
                  Check.typeOf.object('left', left);
          Check.typeOf.object('right', right);
          Check.typeOf.object('result', result);
          
          var leftX = left.x;
          var leftY = left.y;
          var leftZ = left.z;
          var leftW = left.w;
  
          var rightX = right.x;
          var rightY = right.y;
          var rightZ = right.z;
          var rightW = right.w;
  
          var x = leftW * rightX + leftX * rightW + leftY * rightZ - leftZ * rightY;
          var y = leftW * rightY - leftX * rightZ + leftY * rightW + leftZ * rightX;
          var z = leftW * rightZ + leftX * rightY - leftY * rightX + leftZ * rightW;
          var w = leftW * rightW - leftX * rightX - leftY * rightY - leftZ * rightZ;
  
          result.x = x;
          result.y = y;
          result.z = z;
          result.w = w;
          return result;
      };
  
      /**
       * Multiplies the provided quaternion componentwise by the provided scalar.
       *
       * @param {Quaternion} quaternion The quaternion to be scaled.
       * @param {Number} scalar The scalar to multiply with.
       * @param {Quaternion} result The object onto which to store the result.
       * @returns {Quaternion} The modified result parameter.
       */
      Quaternion.multiplyByScalar = function(quaternion, scalar, result) {
                  Check.typeOf.object('quaternion', quaternion);
          Check.typeOf.number('scalar', scalar);
          Check.typeOf.object('result', result);
          
          result.x = quaternion.x * scalar;
          result.y = quaternion.y * scalar;
          result.z = quaternion.z * scalar;
          result.w = quaternion.w * scalar;
          return result;
      };
  
      /**
       * Divides the provided quaternion componentwise by the provided scalar.
       *
       * @param {Quaternion} quaternion The quaternion to be divided.
       * @param {Number} scalar The scalar to divide by.
       * @param {Quaternion} result The object onto which to store the result.
       * @returns {Quaternion} The modified result parameter.
       */
      Quaternion.divideByScalar = function(quaternion, scalar, result) {
                  Check.typeOf.object('quaternion', quaternion);
          Check.typeOf.number('scalar', scalar);
          Check.typeOf.object('result', result);
          
          result.x = quaternion.x / scalar;
          result.y = quaternion.y / scalar;
          result.z = quaternion.z / scalar;
          result.w = quaternion.w / scalar;
          return result;
      };
  
      /**
       * Computes the axis of rotation of the provided quaternion.
       *
       * @param {Quaternion} quaternion The quaternion to use.
       * @param {Cartesian3} result The object onto which to store the result.
       * @returns {Cartesian3} The modified result parameter.
       */
      Quaternion.computeAxis = function(quaternion, result) {
                  Check.typeOf.object('quaternion', quaternion);
          Check.typeOf.object('result', result);
          
          var w = quaternion.w;
          if (Math.abs(w - 1.0) < CesiumMath.EPSILON6) {
              result.x = result.y = result.z = 0;
              return result;
          }
  
          var scalar = 1.0 / Math.sqrt(1.0 - (w * w));
  
          result.x = quaternion.x * scalar;
          result.y = quaternion.y * scalar;
          result.z = quaternion.z * scalar;
          return result;
      };
  
      /**
       * Computes the angle of rotation of the provided quaternion.
       *
       * @param {Quaternion} quaternion The quaternion to use.
       * @returns {Number} The angle of rotation.
       */
      Quaternion.computeAngle = function(quaternion) {
                  Check.typeOf.object('quaternion', quaternion);
          
          if (Math.abs(quaternion.w - 1.0) < CesiumMath.EPSILON6) {
              return 0.0;
          }
          return 2.0 * Math.acos(quaternion.w);
      };
  
      var lerpScratch = new Quaternion();
      /**
       * Computes the linear interpolation or extrapolation at t using the provided quaternions.
       *
       * @param {Quaternion} start The value corresponding to t at 0.0.
       * @param {Quaternion} end The value corresponding to t at 1.0.
       * @param {Number} t The point along t at which to interpolate.
       * @param {Quaternion} result The object onto which to store the result.
       * @returns {Quaternion} The modified result parameter.
       */
      Quaternion.lerp = function(start, end, t, result) {
                  Check.typeOf.object('start', start);
          Check.typeOf.object('end', end);
          Check.typeOf.number('t', t);
          Check.typeOf.object('result', result);
          
          lerpScratch = Quaternion.multiplyByScalar(end, t, lerpScratch);
          result = Quaternion.multiplyByScalar(start, 1.0 - t, result);
          return Quaternion.add(lerpScratch, result, result);
      };
  
      var slerpEndNegated = new Quaternion();
      var slerpScaledP = new Quaternion();
      var slerpScaledR = new Quaternion();
      /**
       * Computes the spherical linear interpolation or extrapolation at t using the provided quaternions.
       *
       * @param {Quaternion} start The value corresponding to t at 0.0.
       * @param {Quaternion} end The value corresponding to t at 1.0.
       * @param {Number} t The point along t at which to interpolate.
       * @param {Quaternion} result The object onto which to store the result.
       * @returns {Quaternion} The modified result parameter.
       *
       * @see Quaternion#fastSlerp
       */
      Quaternion.slerp = function(start, end, t, result) {
                  Check.typeOf.object('start', start);
          Check.typeOf.object('end', end);
          Check.typeOf.number('t', t);
          Check.typeOf.object('result', result);
          
          var dot = Quaternion.dot(start, end);
  
          // The angle between start must be acute. Since q and -q represent
          // the same rotation, negate q to get the acute angle.
          var r = end;
          if (dot < 0.0) {
              dot = -dot;
              r = slerpEndNegated = Quaternion.negate(end, slerpEndNegated);
          }
  
          // dot > 0, as the dot product approaches 1, the angle between the
          // quaternions vanishes. use linear interpolation.
          if (1.0 - dot < CesiumMath.EPSILON6) {
              return Quaternion.lerp(start, r, t, result);
          }
  
          var theta = Math.acos(dot);
          slerpScaledP = Quaternion.multiplyByScalar(start, Math.sin((1 - t) * theta), slerpScaledP);
          slerpScaledR = Quaternion.multiplyByScalar(r, Math.sin(t * theta), slerpScaledR);
          result = Quaternion.add(slerpScaledP, slerpScaledR, result);
          return Quaternion.multiplyByScalar(result, 1.0 / Math.sin(theta), result);
      };
  
      /**
       * The logarithmic quaternion function.
       *
       * @param {Quaternion} quaternion The unit quaternion.
       * @param {Cartesian3} result The object onto which to store the result.
       * @returns {Cartesian3} The modified result parameter.
       */
      Quaternion.log = function(quaternion, result) {
                  Check.typeOf.object('quaternion', quaternion);
          Check.typeOf.object('result', result);
          
          var theta = CesiumMath.acosClamped(quaternion.w);
          var thetaOverSinTheta = 0.0;
  
          if (theta !== 0.0) {
              thetaOverSinTheta = theta / Math.sin(theta);
          }
  
          return Cartesian3.multiplyByScalar(quaternion, thetaOverSinTheta, result);
      };
  
      /**
       * The exponential quaternion function.
       *
       * @param {Cartesian3} cartesian The cartesian.
       * @param {Quaternion} result The object onto which to store the result.
       * @returns {Quaternion} The modified result parameter.
       */
      Quaternion.exp = function(cartesian, result) {
                  Check.typeOf.object('cartesian', cartesian);
          Check.typeOf.object('result', result);
          
          var theta = Cartesian3.magnitude(cartesian);
          var sinThetaOverTheta = 0.0;
  
          if (theta !== 0.0) {
              sinThetaOverTheta = Math.sin(theta) / theta;
          }
  
          result.x = cartesian.x * sinThetaOverTheta;
          result.y = cartesian.y * sinThetaOverTheta;
          result.z = cartesian.z * sinThetaOverTheta;
          result.w = Math.cos(theta);
  
          return result;
      };
  
      var squadScratchCartesian0 = new Cartesian3();
      var squadScratchCartesian1 = new Cartesian3();
      var squadScratchQuaternion0 = new Quaternion();
      var squadScratchQuaternion1 = new Quaternion();
  
      /**
       * Computes an inner quadrangle point.
       * <p>This will compute quaternions that ensure a squad curve is C<sup>1</sup>.</p>
       *
       * @param {Quaternion} q0 The first quaternion.
       * @param {Quaternion} q1 The second quaternion.
       * @param {Quaternion} q2 The third quaternion.
       * @param {Quaternion} result The object onto which to store the result.
       * @returns {Quaternion} The modified result parameter.
       *
       * @see Quaternion#squad
       */
      Quaternion.computeInnerQuadrangle = function(q0, q1, q2, result) {
                  Check.typeOf.object('q0', q0);
          Check.typeOf.object('q1', q1);
          Check.typeOf.object('q2', q2);
          Check.typeOf.object('result', result);
          
          var qInv = Quaternion.conjugate(q1, squadScratchQuaternion0);
          Quaternion.multiply(qInv, q2, squadScratchQuaternion1);
          var cart0 = Quaternion.log(squadScratchQuaternion1, squadScratchCartesian0);
  
          Quaternion.multiply(qInv, q0, squadScratchQuaternion1);
          var cart1 = Quaternion.log(squadScratchQuaternion1, squadScratchCartesian1);
  
          Cartesian3.add(cart0, cart1, cart0);
          Cartesian3.multiplyByScalar(cart0, 0.25, cart0);
          Cartesian3.negate(cart0, cart0);
          Quaternion.exp(cart0, squadScratchQuaternion0);
  
          return Quaternion.multiply(q1, squadScratchQuaternion0, result);
      };
  
      /**
       * Computes the spherical quadrangle interpolation between quaternions.
       *
       * @param {Quaternion} q0 The first quaternion.
       * @param {Quaternion} q1 The second quaternion.
       * @param {Quaternion} s0 The first inner quadrangle.
       * @param {Quaternion} s1 The second inner quadrangle.
       * @param {Number} t The time in [0,1] used to interpolate.
       * @param {Quaternion} result The object onto which to store the result.
       * @returns {Quaternion} The modified result parameter.
       *
       *
       * @example
       * // 1. compute the squad interpolation between two quaternions on a curve
       * var s0 = Cesium.Quaternion.computeInnerQuadrangle(quaternions[i - 1], quaternions[i], quaternions[i + 1], new Cesium.Quaternion());
       * var s1 = Cesium.Quaternion.computeInnerQuadrangle(quaternions[i], quaternions[i + 1], quaternions[i + 2], new Cesium.Quaternion());
       * var q = Cesium.Quaternion.squad(quaternions[i], quaternions[i + 1], s0, s1, t, new Cesium.Quaternion());
       *
       * // 2. compute the squad interpolation as above but where the first quaternion is a end point.
       * var s1 = Cesium.Quaternion.computeInnerQuadrangle(quaternions[0], quaternions[1], quaternions[2], new Cesium.Quaternion());
       * var q = Cesium.Quaternion.squad(quaternions[0], quaternions[1], quaternions[0], s1, t, new Cesium.Quaternion());
       *
       * @see Quaternion#computeInnerQuadrangle
       */
      Quaternion.squad = function(q0, q1, s0, s1, t, result) {
                  Check.typeOf.object('q0', q0);
          Check.typeOf.object('q1', q1);
          Check.typeOf.object('s0', s0);
          Check.typeOf.object('s1', s1);
          Check.typeOf.number('t', t);
          Check.typeOf.object('result', result);
          
          var slerp0 = Quaternion.slerp(q0, q1, t, squadScratchQuaternion0);
          var slerp1 = Quaternion.slerp(s0, s1, t, squadScratchQuaternion1);
          return Quaternion.slerp(slerp0, slerp1, 2.0 * t * (1.0 - t), result);
      };
  
      var fastSlerpScratchQuaternion = new Quaternion();
      var opmu = 1.90110745351730037;
      var u = FeatureDetection.supportsTypedArrays() ? new Float32Array(8) : [];
      var v = FeatureDetection.supportsTypedArrays() ? new Float32Array(8) : [];
      var bT = FeatureDetection.supportsTypedArrays() ? new Float32Array(8) : [];
      var bD = FeatureDetection.supportsTypedArrays() ? new Float32Array(8) : [];
  
      for (var i = 0; i < 7; ++i) {
          var s = i + 1.0;
          var t = 2.0 * s + 1.0;
          u[i] = 1.0 / (s * t);
          v[i] = s / t;
      }
  
      u[7] = opmu / (8.0 * 17.0);
      v[7] = opmu * 8.0 / 17.0;
  
      /**
       * Computes the spherical linear interpolation or extrapolation at t using the provided quaternions.
       * This implementation is faster than {@link Quaternion#slerp}, but is only accurate up to 10<sup>-6</sup>.
       *
       * @param {Quaternion} start The value corresponding to t at 0.0.
       * @param {Quaternion} end The value corresponding to t at 1.0.
       * @param {Number} t The point along t at which to interpolate.
       * @param {Quaternion} result The object onto which to store the result.
       * @returns {Quaternion} The modified result parameter.
       *
       * @see Quaternion#slerp
       */
      Quaternion.fastSlerp = function(start, end, t, result) {
                  Check.typeOf.object('start', start);
          Check.typeOf.object('end', end);
          Check.typeOf.number('t', t);
          Check.typeOf.object('result', result);
          
          var x = Quaternion.dot(start, end);
  
          var sign;
          if (x >= 0) {
              sign = 1.0;
          } else {
              sign = -1.0;
              x = -x;
          }
  
          var xm1 = x - 1.0;
          var d = 1.0 - t;
          var sqrT = t * t;
          var sqrD = d * d;
  
          for (var i = 7; i >= 0; --i) {
              bT[i] = (u[i] * sqrT - v[i]) * xm1;
              bD[i] = (u[i] * sqrD - v[i]) * xm1;
          }
  
          var cT = sign * t * (
              1.0 + bT[0] * (1.0 + bT[1] * (1.0 + bT[2] * (1.0 + bT[3] * (
              1.0 + bT[4] * (1.0 + bT[5] * (1.0 + bT[6] * (1.0 + bT[7]))))))));
          var cD = d * (
              1.0 + bD[0] * (1.0 + bD[1] * (1.0 + bD[2] * (1.0 + bD[3] * (
              1.0 + bD[4] * (1.0 + bD[5] * (1.0 + bD[6] * (1.0 + bD[7]))))))));
  
          var temp = Quaternion.multiplyByScalar(start, cD, fastSlerpScratchQuaternion);
          Quaternion.multiplyByScalar(end, cT, result);
          return Quaternion.add(temp, result, result);
      };
  
      /**
       * Computes the spherical quadrangle interpolation between quaternions.
       * An implementation that is faster than {@link Quaternion#squad}, but less accurate.
       *
       * @param {Quaternion} q0 The first quaternion.
       * @param {Quaternion} q1 The second quaternion.
       * @param {Quaternion} s0 The first inner quadrangle.
       * @param {Quaternion} s1 The second inner quadrangle.
       * @param {Number} t The time in [0,1] used to interpolate.
       * @param {Quaternion} result The object onto which to store the result.
       * @returns {Quaternion} The modified result parameter or a new instance if none was provided.
       *
       * @see Quaternion#squad
       */
      Quaternion.fastSquad = function(q0, q1, s0, s1, t, result) {
                  Check.typeOf.object('q0', q0);
          Check.typeOf.object('q1', q1);
          Check.typeOf.object('s0', s0);
          Check.typeOf.object('s1', s1);
          Check.typeOf.number('t', t);
          Check.typeOf.object('result', result);
          
          var slerp0 = Quaternion.fastSlerp(q0, q1, t, squadScratchQuaternion0);
          var slerp1 = Quaternion.fastSlerp(s0, s1, t, squadScratchQuaternion1);
          return Quaternion.fastSlerp(slerp0, slerp1, 2.0 * t * (1.0 - t), result);
      };
  
      /**
       * Compares the provided quaternions componentwise and returns
       * <code>true</code> if they are equal, <code>false</code> otherwise.
       *
       * @param {Quaternion} [left] The first quaternion.
       * @param {Quaternion} [right] The second quaternion.
       * @returns {Boolean} <code>true</code> if left and right are equal, <code>false</code> otherwise.
       */
      Quaternion.equals = function(left, right) {
          return (left === right) ||
                 ((defined(left)) &&
                  (defined(right)) &&
                  (left.x === right.x) &&
                  (left.y === right.y) &&
                  (left.z === right.z) &&
                  (left.w === right.w));
      };
  
      /**
       * Compares the provided quaternions componentwise and returns
       * <code>true</code> if they are within the provided epsilon,
       * <code>false</code> otherwise.
       *
       * @param {Quaternion} [left] The first quaternion.
       * @param {Quaternion} [right] The second quaternion.
       * @param {Number} epsilon The epsilon to use for equality testing.
       * @returns {Boolean} <code>true</code> if left and right are within the provided epsilon, <code>false</code> otherwise.
       */
      Quaternion.equalsEpsilon = function(left, right, epsilon) {
                  Check.typeOf.number('epsilon', epsilon);
          
          return (left === right) ||
                 ((defined(left)) &&
                  (defined(right)) &&
                  (Math.abs(left.x - right.x) <= epsilon) &&
                  (Math.abs(left.y - right.y) <= epsilon) &&
                  (Math.abs(left.z - right.z) <= epsilon) &&
                  (Math.abs(left.w - right.w) <= epsilon));
      };
  
      /**
       * An immutable Quaternion instance initialized to (0.0, 0.0, 0.0, 0.0).
       *
       * @type {Quaternion}
       * @constant
       */
      Quaternion.ZERO = freezeObject(new Quaternion(0.0, 0.0, 0.0, 0.0));
  
      /**
       * An immutable Quaternion instance initialized to (0.0, 0.0, 0.0, 1.0).
       *
       * @type {Quaternion}
       * @constant
       */
      Quaternion.IDENTITY = freezeObject(new Quaternion(0.0, 0.0, 0.0, 1.0));
  
      /**
       * Duplicates this Quaternion instance.
       *
       * @param {Quaternion} [result] The object onto which to store the result.
       * @returns {Quaternion} The modified result parameter or a new Quaternion instance if one was not provided.
       */
      Quaternion.prototype.clone = function(result) {
          return Quaternion.clone(this, result);
      };
  
      /**
       * Compares this and the provided quaternion componentwise and returns
       * <code>true</code> if they are equal, <code>false</code> otherwise.
       *
       * @param {Quaternion} [right] The right hand side quaternion.
       * @returns {Boolean} <code>true</code> if left and right are equal, <code>false</code> otherwise.
       */
      Quaternion.prototype.equals = function(right) {
          return Quaternion.equals(this, right);
      };
  
      /**
       * Compares this and the provided quaternion componentwise and returns
       * <code>true</code> if they are within the provided epsilon,
       * <code>false</code> otherwise.
       *
       * @param {Quaternion} [right] The right hand side quaternion.
       * @param {Number} epsilon The epsilon to use for equality testing.
       * @returns {Boolean} <code>true</code> if left and right are within the provided epsilon, <code>false</code> otherwise.
       */
      Quaternion.prototype.equalsEpsilon = function(right, epsilon) {
          return Quaternion.equalsEpsilon(this, right, epsilon);
      };
  
      /**
       * Returns a string representing this quaternion in the format (x, y, z, w).
       *
       * @returns {String} A string representing this Quaternion.
       */
      Quaternion.prototype.toString = function() {
          return '(' + this.x + ', ' + this.y + ', ' + this.z + ', ' + this.w + ')';
      };
  
      return Quaternion;
  });
  
  define('Core/VertexFormat',[
          './defaultValue',
          './defined',
          './DeveloperError',
          './freezeObject'
      ], function(
          defaultValue,
          defined,
          DeveloperError,
          freezeObject) {
      'use strict';
  
      /**
       * A vertex format defines what attributes make up a vertex.  A VertexFormat can be provided
       * to a {@link Geometry} to request that certain properties be computed, e.g., just position,
       * position and normal, etc.
       *
       * @param {Object} [options] An object with boolean properties corresponding to VertexFormat properties as shown in the code example.
       *
       * @alias VertexFormat
       * @constructor
       *
       * @example
       * // Create a vertex format with position and 2D texture coordinate attributes.
       * var format = new Cesium.VertexFormat({
       *   position : true,
       *   st : true
       * });
       *
       * @see Geometry#attributes
       * @see Packable
       */
      function VertexFormat(options) {
          options = defaultValue(options, defaultValue.EMPTY_OBJECT);
  
          /**
           * When <code>true</code>, the vertex has a 3D position attribute.
           * <p>
           * 64-bit floating-point (for precision).  3 components per attribute.
           * </p>
           *
           * @type Boolean
           *
           * @default false
           */
          this.position = defaultValue(options.position, false);
  
          /**
           * When <code>true</code>, the vertex has a normal attribute (normalized), which is commonly used for lighting.
           * <p>
           * 32-bit floating-point.  3 components per attribute.
           * </p>
           *
           * @type Boolean
           *
           * @default false
           */
          this.normal = defaultValue(options.normal, false);
  
          /**
           * When <code>true</code>, the vertex has a 2D texture coordinate attribute.
           * <p>
           * 32-bit floating-point.  2 components per attribute
           * </p>
           *
           * @type Boolean
           *
           * @default false
           */
          this.st = defaultValue(options.st, false);
  
          /**
           * When <code>true</code>, the vertex has a bitangent attribute (normalized), which is used for tangent-space effects like bump mapping.
           * <p>
           * 32-bit floating-point.  3 components per attribute.
           * </p>
           *
           * @type Boolean
           *
           * @default false
           */
          this.bitangent = defaultValue(options.bitangent, false);
  
          /**
           * When <code>true</code>, the vertex has a tangent attribute (normalized), which is used for tangent-space effects like bump mapping.
           * <p>
           * 32-bit floating-point.  3 components per attribute.
           * </p>
           *
           * @type Boolean
           *
           * @default false
           */
          this.tangent = defaultValue(options.tangent, false);
  
          /**
           * When <code>true</code>, the vertex has an RGB color attribute.
           * <p>
           * 8-bit unsigned byte.  3 components per attribute.
           * </p>
           *
           * @type Boolean
           *
           * @default false
           */
          this.color = defaultValue(options.color, false);
      }
  
      /**
       * An immutable vertex format with only a position attribute.
       *
       * @type {VertexFormat}
       * @constant
       *
       * @see VertexFormat#position
       */
      VertexFormat.POSITION_ONLY = freezeObject(new VertexFormat({
          position : true
      }));
  
      /**
       * An immutable vertex format with position and normal attributes.
       * This is compatible with per-instance color appearances like {@link PerInstanceColorAppearance}.
       *
       * @type {VertexFormat}
       * @constant
       *
       * @see VertexFormat#position
       * @see VertexFormat#normal
       */
      VertexFormat.POSITION_AND_NORMAL = freezeObject(new VertexFormat({
          position : true,
          normal : true
      }));
  
      /**
       * An immutable vertex format with position, normal, and st attributes.
       * This is compatible with {@link MaterialAppearance} when {@link MaterialAppearance#materialSupport}
       * is <code>TEXTURED/code>.
       *
       * @type {VertexFormat}
       * @constant
       *
       * @see VertexFormat#position
       * @see VertexFormat#normal
       * @see VertexFormat#st
       */
      VertexFormat.POSITION_NORMAL_AND_ST = freezeObject(new VertexFormat({
          position : true,
          normal : true,
          st : true
      }));
  
      /**
       * An immutable vertex format with position and st attributes.
       * This is compatible with {@link EllipsoidSurfaceAppearance}.
       *
       * @type {VertexFormat}
       * @constant
       *
       * @see VertexFormat#position
       * @see VertexFormat#st
       */
      VertexFormat.POSITION_AND_ST = freezeObject(new VertexFormat({
          position : true,
          st : true
      }));
  
      /**
       * An immutable vertex format with position and color attributes.
       *
       * @type {VertexFormat}
       * @constant
       *
       * @see VertexFormat#position
       * @see VertexFormat#color
       */
      VertexFormat.POSITION_AND_COLOR = freezeObject(new VertexFormat({
          position : true,
          color : true
      }));
  
      /**
       * An immutable vertex format with well-known attributes: position, normal, st, tangent, and bitangent.
       *
       * @type {VertexFormat}
       * @constant
       *
       * @see VertexFormat#position
       * @see VertexFormat#normal
       * @see VertexFormat#st
       * @see VertexFormat#tangent
       * @see VertexFormat#bitangent
       */
      VertexFormat.ALL = freezeObject(new VertexFormat({
          position : true,
          normal : true,
          st : true,
          tangent  : true,
          bitangent : true
      }));
  
      /**
       * An immutable vertex format with position, normal, and st attributes.
       * This is compatible with most appearances and materials; however
       * normal and st attributes are not always required.  When this is
       * known in advance, another <code>VertexFormat</code> should be used.
       *
       * @type {VertexFormat}
       * @constant
       *
       * @see VertexFormat#position
       * @see VertexFormat#normal
       */
      VertexFormat.DEFAULT = VertexFormat.POSITION_NORMAL_AND_ST;
  
      /**
       * The number of elements used to pack the object into an array.
       * @type {Number}
       */
      VertexFormat.packedLength = 6;
  
      /**
       * Stores the provided instance into the provided array.
       *
       * @param {VertexFormat} value The value to pack.
       * @param {Number[]} array The array to pack into.
       * @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
       *
       * @returns {Number[]} The array that was packed into
       */
      VertexFormat.pack = function(value, array, startingIndex) {
                  if (!defined(value)) {
              throw new DeveloperError('value is required');
          }
          if (!defined(array)) {
              throw new DeveloperError('array is required');
          }
          
          startingIndex = defaultValue(startingIndex, 0);
  
          array[startingIndex++] = value.position ? 1.0 : 0.0;
          array[startingIndex++] = value.normal ? 1.0 : 0.0;
          array[startingIndex++] = value.st ? 1.0 : 0.0;
          array[startingIndex++] = value.tangent ? 1.0 : 0.0;
          array[startingIndex++] = value.bitangent ? 1.0 : 0.0;
          array[startingIndex] = value.color ? 1.0 : 0.0;
  
          return array;
      };
  
      /**
       * Retrieves an instance from a packed array.
       *
       * @param {Number[]} array The packed array.
       * @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
       * @param {VertexFormat} [result] The object into which to store the result.
       * @returns {VertexFormat} The modified result parameter or a new VertexFormat instance if one was not provided.
       */
      VertexFormat.unpack = function(array, startingIndex, result) {
                  if (!defined(array)) {
              throw new DeveloperError('array is required');
          }
          
          startingIndex = defaultValue(startingIndex, 0);
  
          if (!defined(result)) {
              result = new VertexFormat();
          }
  
          result.position  = array[startingIndex++] === 1.0;
          result.normal    = array[startingIndex++] === 1.0;
          result.st        = array[startingIndex++] === 1.0;
          result.tangent   = array[startingIndex++] === 1.0;
          result.bitangent = array[startingIndex++] === 1.0;
          result.color     = array[startingIndex] === 1.0;
          return result;
      };
  
      /**
       * Duplicates a VertexFormat instance.
       *
       * @param {VertexFormat} vertexFormat The vertex format to duplicate.
       * @param {VertexFormat} [result] The object onto which to store the result.
       * @returns {VertexFormat} The modified result parameter or a new VertexFormat instance if one was not provided. (Returns undefined if vertexFormat is undefined)
       */
      VertexFormat.clone = function(vertexFormat, result) {
          if (!defined(vertexFormat)) {
              return undefined;
          }
          if (!defined(result)) {
              result = new VertexFormat();
          }
  
          result.position = vertexFormat.position;
          result.normal = vertexFormat.normal;
          result.st = vertexFormat.st;
          result.tangent = vertexFormat.tangent;
          result.bitangent = vertexFormat.bitangent;
          result.color = vertexFormat.color;
          return result;
      };
  
      return VertexFormat;
  });
  
  define('Core/FrustumGeometry',[
          './BoundingSphere',
          './Cartesian3',
          './Cartesian4',
          './Check',
          './ComponentDatatype',
          './defaultValue',
          './defined',
          './Geometry',
          './GeometryAttribute',
          './GeometryAttributes',
          './Matrix3',
          './Matrix4',
          './OrthographicFrustum',
          './PerspectiveFrustum',
          './PrimitiveType',
          './Quaternion',
          './VertexFormat'
      ], function(
          BoundingSphere,
          Cartesian3,
          Cartesian4,
          Check,
          ComponentDatatype,
          defaultValue,
          defined,
          Geometry,
          GeometryAttribute,
          GeometryAttributes,
          Matrix3,
          Matrix4,
          OrthographicFrustum,
          PerspectiveFrustum,
          PrimitiveType,
          Quaternion,
          VertexFormat) {
      'use strict';
  
      var PERSPECTIVE = 0;
      var ORTHOGRAPHIC = 1;
  
      /**
       * Describes a frustum at the given the origin and orientation.
       *
       * @alias FrustumGeometry
       * @constructor
       *
       * @param {Object} options Object with the following properties:
       * @param {PerspectiveFrustum|OrthographicFrustum} options.frustum The frustum.
       * @param {Cartesian3} options.origin The origin of the frustum.
       * @param {Quaternion} options.orientation The orientation of the frustum.
       * @param {VertexFormat} [options.vertexFormat=VertexFormat.DEFAULT] The vertex attributes to be computed.
       */
      function FrustumGeometry(options) {
                  Check.typeOf.object('options', options);
          Check.typeOf.object('options.frustum', options.frustum);
          Check.typeOf.object('options.origin', options.origin);
          Check.typeOf.object('options.orientation', options.orientation);
          
          var frustum = options.frustum;
          var orientation = options.orientation;
          var origin = options.origin;
          var vertexFormat = defaultValue(options.vertexFormat, VertexFormat.DEFAULT);
  
          // This is private because it is used by DebugCameraPrimitive to draw a multi-frustum by
          // creating multiple FrustumGeometrys. This way the near plane of one frustum doesn't overlap
          // the far plane of another.
          var drawNearPlane = defaultValue(options._drawNearPlane, true);
  
          var frustumType;
          var frustumPackedLength;
          if (frustum instanceof PerspectiveFrustum) {
              frustumType = PERSPECTIVE;
              frustumPackedLength = PerspectiveFrustum.packedLength;
          } else if (frustum instanceof OrthographicFrustum) {
              frustumType = ORTHOGRAPHIC;
              frustumPackedLength = OrthographicFrustum.packedLength;
          }
  
          this._frustumType = frustumType;
          this._frustum = frustum.clone();
          this._origin = Cartesian3.clone(origin);
          this._orientation = Quaternion.clone(orientation);
          this._drawNearPlane = drawNearPlane;
          this._vertexFormat = vertexFormat;
          this._workerName = 'createFrustumGeometry';
  
          /**
           * The number of elements used to pack the object into an array.
           * @type {Number}
           */
          this.packedLength = 2 + frustumPackedLength + Cartesian3.packedLength + Quaternion.packedLength + VertexFormat.packedLength;
      }
  
      /**
       * Stores the provided instance into the provided array.
       *
       * @param {FrustumGeometry} value The value to pack.
       * @param {Number[]} array The array to pack into.
       * @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
       *
       * @returns {Number[]} The array that was packed into
       */
      FrustumGeometry.pack = function(value, array, startingIndex) {
                  Check.typeOf.object('value', value);
          Check.defined('array', array);
          
          startingIndex = defaultValue(startingIndex, 0);
  
          var frustumType = value._frustumType;
          var frustum = value._frustum;
  
          array[startingIndex++] = frustumType;
  
          if (frustumType === PERSPECTIVE) {
              PerspectiveFrustum.pack(frustum, array, startingIndex);
              startingIndex += PerspectiveFrustum.packedLength;
          } else {
              OrthographicFrustum.pack(frustum, array, startingIndex);
              startingIndex += OrthographicFrustum.packedLength;
          }
  
          Cartesian3.pack(value._origin, array, startingIndex);
          startingIndex += Cartesian3.packedLength;
          Quaternion.pack(value._orientation, array, startingIndex);
          startingIndex += Quaternion.packedLength;
          VertexFormat.pack(value._vertexFormat, array, startingIndex);
          startingIndex += VertexFormat.packedLength;
          array[startingIndex] = value._drawNearPlane ? 1.0 : 0.0;
  
          return array;
      };
  
      var scratchPackPerspective = new PerspectiveFrustum();
      var scratchPackOrthographic = new OrthographicFrustum();
      var scratchPackQuaternion = new Quaternion();
      var scratchPackorigin = new Cartesian3();
      var scratchVertexFormat = new VertexFormat();
  
      /**
       * Retrieves an instance from a packed array.
       *
       * @param {Number[]} array The packed array.
       * @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
       * @param {FrustumGeometry} [result] The object into which to store the result.
       */
      FrustumGeometry.unpack = function(array, startingIndex, result) {
                  Check.defined('array', array);
          
          startingIndex = defaultValue(startingIndex, 0);
  
          var frustumType = array[startingIndex++];
  
          var frustum;
          if (frustumType === PERSPECTIVE) {
              frustum = PerspectiveFrustum.unpack(array, startingIndex, scratchPackPerspective);
              startingIndex += PerspectiveFrustum.packedLength;
          } else {
              frustum = OrthographicFrustum.unpack(array, startingIndex, scratchPackOrthographic);
              startingIndex += OrthographicFrustum.packedLength;
          }
  
          var origin = Cartesian3.unpack(array, startingIndex, scratchPackorigin);
          startingIndex += Cartesian3.packedLength;
          var orientation = Quaternion.unpack(array, startingIndex, scratchPackQuaternion);
          startingIndex += Quaternion.packedLength;
          var vertexFormat = VertexFormat.unpack(array, startingIndex, scratchVertexFormat);
          startingIndex += VertexFormat.packedLength;
          var drawNearPlane = array[startingIndex] === 1.0;
  
          if (!defined(result)) {
              return new FrustumGeometry({
                  frustum : frustum,
                  origin : origin,
                  orientation : orientation,
                  vertexFormat : vertexFormat,
                  _drawNearPlane : drawNearPlane
              });
          }
  
          var frustumResult = frustumType === result._frustumType ? result._frustum : undefined;
          result._frustum = frustum.clone(frustumResult);
  
          result._frustumType = frustumType;
          result._origin = Cartesian3.clone(origin, result._origin);
          result._orientation = Quaternion.clone(orientation, result._orientation);
          result._vertexFormat = VertexFormat.clone(vertexFormat, result._vertexFormat);
          result._drawNearPlane = drawNearPlane;
  
          return result;
      };
  
      function getAttributes(offset, normals, tangents, bitangents, st, normal, tangent, bitangent) {
          var stOffset = offset / 3 * 2;
  
          for (var i = 0; i < 4; ++i) {
              if (defined(normals)) {
                  normals[offset] = normal.x;
                  normals[offset + 1] = normal.y;
                  normals[offset + 2] = normal.z;
              }
              if (defined(tangents)) {
                  tangents[offset] = tangent.x;
                  tangents[offset + 1] = tangent.y;
                  tangents[offset + 2] = tangent.z;
              }
              if (defined(bitangents)) {
                  bitangents[offset] = bitangent.x;
                  bitangents[offset + 1] = bitangent.y;
                  bitangents[offset + 2] = bitangent.z;
              }
              offset += 3;
          }
  
          st[stOffset] = 0.0;
          st[stOffset + 1] = 0.0;
          st[stOffset + 2] = 1.0;
          st[stOffset + 3] = 0.0;
          st[stOffset + 4] = 1.0;
          st[stOffset + 5] = 1.0;
          st[stOffset + 6] = 0.0;
          st[stOffset + 7] = 1.0;
      }
  
      var scratchRotationMatrix = new Matrix3();
      var scratchViewMatrix = new Matrix4();
      var scratchInverseMatrix = new Matrix4();
  
      var scratchXDirection = new Cartesian3();
      var scratchYDirection = new Cartesian3();
      var scratchZDirection = new Cartesian3();
      var scratchNegativeX = new Cartesian3();
      var scratchNegativeY = new Cartesian3();
      var scratchNegativeZ = new Cartesian3();
  
      var frustumSplits = new Array(3);
  
      var frustumCornersNDC = new Array(4);
      frustumCornersNDC[0] = new Cartesian4(-1.0, -1.0, 1.0, 1.0);
      frustumCornersNDC[1] = new Cartesian4(1.0, -1.0, 1.0, 1.0);
      frustumCornersNDC[2] = new Cartesian4(1.0, 1.0, 1.0, 1.0);
      frustumCornersNDC[3] = new Cartesian4(-1.0, 1.0, 1.0, 1.0);
  
      var scratchFrustumCorners = new Array(4);
      for (var i = 0; i < 4; ++i) {
          scratchFrustumCorners[i] = new Cartesian4();
      }
  
      FrustumGeometry._computeNearFarPlanes = function(origin, orientation, frustumType, frustum, positions, xDirection, yDirection, zDirection) {
          var rotationMatrix = Matrix3.fromQuaternion(orientation, scratchRotationMatrix);
          var x = defaultValue(xDirection, scratchXDirection);
          var y = defaultValue(yDirection, scratchYDirection);
          var z = defaultValue(zDirection, scratchZDirection);
  
          x = Matrix3.getColumn(rotationMatrix, 0, x);
          y = Matrix3.getColumn(rotationMatrix, 1, y);
          z = Matrix3.getColumn(rotationMatrix, 2, z);
  
          Cartesian3.normalize(x, x);
          Cartesian3.normalize(y, y);
          Cartesian3.normalize(z, z);
  
          Cartesian3.negate(x, x);
  
          var view = Matrix4.computeView(origin, z, y, x, scratchViewMatrix);
  
          var inverseView;
          var inverseViewProjection;
          if (frustumType === PERSPECTIVE) {
              var projection = frustum.projectionMatrix;
              var viewProjection = Matrix4.multiply(projection, view, scratchInverseMatrix);
              inverseViewProjection = Matrix4.inverse(viewProjection, scratchInverseMatrix);
          } else {
              inverseView = Matrix4.inverseTransformation(view, scratchInverseMatrix);
          }
  
          if (defined(inverseViewProjection)) {
              frustumSplits[0] = frustum.near;
              frustumSplits[1] = frustum.far;
          } else {
              frustumSplits[0] = 0.0;
              frustumSplits[1] = frustum.near;
              frustumSplits[2] = frustum.far;
          }
  
          for (var i = 0; i < 2; ++i) {
              for (var j = 0; j < 4; ++j) {
                  var corner = Cartesian4.clone(frustumCornersNDC[j], scratchFrustumCorners[j]);
  
                  if (!defined(inverseViewProjection)) {
                      if (defined(frustum._offCenterFrustum)) {
                          frustum = frustum._offCenterFrustum;
                      }
  
                      var near = frustumSplits[i];
                      var far = frustumSplits[i + 1];
  
                      corner.x = (corner.x * (frustum.right - frustum.left) + frustum.left + frustum.right) * 0.5;
                      corner.y = (corner.y * (frustum.top - frustum.bottom) + frustum.bottom + frustum.top) * 0.5;
                      corner.z = (corner.z * (near - far) - near - far) * 0.5;
                      corner.w = 1.0;
  
                      Matrix4.multiplyByVector(inverseView, corner, corner);
                  } else {
                      corner = Matrix4.multiplyByVector(inverseViewProjection, corner, corner);
  
                      // Reverse perspective divide
                      var w = 1.0 / corner.w;
                      Cartesian3.multiplyByScalar(corner, w, corner);
  
                      Cartesian3.subtract(corner, origin, corner);
                      Cartesian3.normalize(corner, corner);
  
                      var fac = Cartesian3.dot(z, corner);
                      Cartesian3.multiplyByScalar(corner, frustumSplits[i] / fac, corner);
                      Cartesian3.add(corner, origin, corner);
                  }
  
                  positions[12 * i + j * 3] = corner.x;
                  positions[12 * i + j * 3 + 1] = corner.y;
                  positions[12 * i + j * 3 + 2] = corner.z;
              }
          }
      };
  
      /**
       * Computes the geometric representation of a frustum, including its vertices, indices, and a bounding sphere.
       *
       * @param {FrustumGeometry} frustumGeometry A description of the frustum.
       * @returns {Geometry|undefined} The computed vertices and indices.
       */
      FrustumGeometry.createGeometry = function(frustumGeometry) {
          var frustumType = frustumGeometry._frustumType;
          var frustum = frustumGeometry._frustum;
          var origin = frustumGeometry._origin;
          var orientation = frustumGeometry._orientation;
          var drawNearPlane = frustumGeometry._drawNearPlane;
          var vertexFormat = frustumGeometry._vertexFormat;
  
          var numberOfPlanes = drawNearPlane ? 6 : 5;
          var positions = new Float64Array(3 * 4 * 6);
          FrustumGeometry._computeNearFarPlanes(origin, orientation, frustumType, frustum, positions);
  
          // -x plane
          var offset = 3 * 4 * 2;
          positions[offset]      = positions[3 * 4];
          positions[offset + 1]  = positions[3 * 4 + 1];
          positions[offset + 2]  = positions[3 * 4 + 2];
          positions[offset + 3]  = positions[0];
          positions[offset + 4]  = positions[1];
          positions[offset + 5]  = positions[2];
          positions[offset + 6]  = positions[3 * 3];
          positions[offset + 7]  = positions[3 * 3 + 1];
          positions[offset + 8]  = positions[3 * 3 + 2];
          positions[offset + 9]  = positions[3 * 7];
          positions[offset + 10] = positions[3 * 7 + 1];
          positions[offset + 11] = positions[3 * 7 + 2];
  
          // -y plane
          offset += 3 * 4;
          positions[offset]      = positions[3 * 5];
          positions[offset + 1]  = positions[3 * 5 + 1];
          positions[offset + 2]  = positions[3 * 5 + 2];
          positions[offset + 3]  = positions[3];
          positions[offset + 4]  = positions[3 + 1];
          positions[offset + 5]  = positions[3 + 2];
          positions[offset + 6]  = positions[0];
          positions[offset + 7]  = positions[1];
          positions[offset + 8]  = positions[2];
          positions[offset + 9]  = positions[3 * 4];
          positions[offset + 10] = positions[3 * 4 + 1];
          positions[offset + 11] = positions[3 * 4 + 2];
  
          // +x plane
          offset += 3 * 4;
          positions[offset]      = positions[3];
          positions[offset + 1]  = positions[3 + 1];
          positions[offset + 2]  = positions[3 + 2];
          positions[offset + 3]  = positions[3 * 5];
          positions[offset + 4]  = positions[3 * 5 + 1];
          positions[offset + 5]  = positions[3 * 5 + 2];
          positions[offset + 6]  = positions[3 * 6];
          positions[offset + 7]  = positions[3 * 6 + 1];
          positions[offset + 8]  = positions[3 * 6 + 2];
          positions[offset + 9]  = positions[3 * 2];
          positions[offset + 10] = positions[3 * 2 + 1];
          positions[offset + 11] = positions[3 * 2 + 2];
  
          // +y plane
          offset += 3 * 4;
          positions[offset]      = positions[3 * 2];
          positions[offset + 1]  = positions[3 * 2 + 1];
          positions[offset + 2]  = positions[3 * 2 + 2];
          positions[offset + 3]  = positions[3 * 6];
          positions[offset + 4]  = positions[3 * 6 + 1];
          positions[offset + 5]  = positions[3 * 6 + 2];
          positions[offset + 6]  = positions[3 * 7];
          positions[offset + 7]  = positions[3 * 7 + 1];
          positions[offset + 8]  = positions[3 * 7 + 2];
          positions[offset + 9]  = positions[3 * 3];
          positions[offset + 10] = positions[3 * 3 + 1];
          positions[offset + 11] = positions[3 * 3 + 2];
  
          if (!drawNearPlane) {
              positions = positions.subarray(3 * 4);
          }
  
          var attributes = new GeometryAttributes({
              position : new GeometryAttribute({
                  componentDatatype : ComponentDatatype.DOUBLE,
                  componentsPerAttribute : 3,
                  values : positions
              })
          });
  
          if (defined(vertexFormat.normal) || defined(vertexFormat.tangent) || defined(vertexFormat.bitangent) || defined(vertexFormat.st)) {
              var normals = defined(vertexFormat.normal) ? new Float32Array(3 * 4 * numberOfPlanes) : undefined;
              var tangents = defined(vertexFormat.tangent) ? new Float32Array(3 * 4 * numberOfPlanes) : undefined;
              var bitangents = defined(vertexFormat.bitangent) ? new Float32Array(3 * 4 * numberOfPlanes) : undefined;
              var st = defined(vertexFormat.st) ? new Float32Array(2 * 4 * numberOfPlanes) : undefined;
  
              var x = scratchXDirection;
              var y = scratchYDirection;
              var z = scratchZDirection;
  
              var negativeX = Cartesian3.negate(x, scratchNegativeX);
              var negativeY = Cartesian3.negate(y, scratchNegativeY);
              var negativeZ = Cartesian3.negate(z, scratchNegativeZ);
  
              offset = 0;
              if (drawNearPlane) {
                  getAttributes(offset, normals, tangents, bitangents, st, negativeZ, x, y); // near
                  offset += 3 * 4;
              }
              getAttributes(offset, normals, tangents, bitangents, st, z, negativeX, y); // far
              offset += 3 * 4;
              getAttributes(offset, normals, tangents, bitangents, st, negativeX, negativeZ, y); // -x
              offset += 3 * 4;
              getAttributes(offset, normals, tangents, bitangents, st, negativeY, negativeZ, negativeX); // -y
              offset += 3 * 4;
              getAttributes(offset, normals, tangents, bitangents, st, x, z, y); // +x
              offset += 3 * 4;
              getAttributes(offset, normals, tangents, bitangents, st, y, z, negativeX); // +y
  
              if (defined(normals)) {
                  attributes.normal = new GeometryAttribute({
                      componentDatatype : ComponentDatatype.FLOAT,
                      componentsPerAttribute : 3,
                      values : normals
                  });
              }
              if (defined(tangents)) {
                  attributes.tangent = new GeometryAttribute({
                      componentDatatype : ComponentDatatype.FLOAT,
                      componentsPerAttribute : 3,
                      values : tangents
                  });
              }
              if (defined(bitangents)) {
                  attributes.bitangent = new GeometryAttribute({
                      componentDatatype : ComponentDatatype.FLOAT,
                      componentsPerAttribute : 3,
                      values : bitangents
                  });
              }
              if (defined(st)) {
                  attributes.st = new GeometryAttribute({
                      componentDatatype : ComponentDatatype.FLOAT,
                      componentsPerAttribute : 2,
                      values : st
                  });
              }
          }
  
          var indices = new Uint16Array(6 * numberOfPlanes);
          for (var i = 0; i < numberOfPlanes; ++i) {
              var indexOffset = i * 6;
              var index = i * 4;
  
              indices[indexOffset] = index;
              indices[indexOffset + 1] = index + 1;
              indices[indexOffset + 2] = index + 2;
              indices[indexOffset + 3] = index;
              indices[indexOffset + 4] = index + 2;
              indices[indexOffset + 5] = index + 3;
          }
  
          return new Geometry({
              attributes : attributes,
              indices : indices,
              primitiveType : PrimitiveType.TRIANGLES,
              boundingSphere : BoundingSphere.fromVertices(positions)
          });
      };
  
      return FrustumGeometry;
  });
  
  define('Core/FrustumOutlineGeometry',[
          './BoundingSphere',
          './Cartesian3',
          './Check',
          './ComponentDatatype',
          './defaultValue',
          './defined',
          './FrustumGeometry',
          './Geometry',
          './GeometryAttribute',
          './GeometryAttributes',
          './OrthographicFrustum',
          './PerspectiveFrustum',
          './PrimitiveType',
          './Quaternion'
      ], function(
          BoundingSphere,
          Cartesian3,
          Check,
          ComponentDatatype,
          defaultValue,
          defined,
          FrustumGeometry,
          Geometry,
          GeometryAttribute,
          GeometryAttributes,
          OrthographicFrustum,
          PerspectiveFrustum,
          PrimitiveType,
          Quaternion) {
      'use strict';
  
      var PERSPECTIVE = 0;
      var ORTHOGRAPHIC = 1;
  
      /**
       * A description of the outline of a frustum with the given the origin and orientation.
       *
       * @alias FrustumOutlineGeometry
       * @constructor
       *
       * @param {Object} options Object with the following properties:
       * @param {PerspectiveFrustum|OrthographicFrustum} options.frustum The frustum.
       * @param {Cartesian3} options.origin The origin of the frustum.
       * @param {Quaternion} options.orientation The orientation of the frustum.
       */
      function FrustumOutlineGeometry(options) {
                  Check.typeOf.object('options', options);
          Check.typeOf.object('options.frustum', options.frustum);
          Check.typeOf.object('options.origin', options.origin);
          Check.typeOf.object('options.orientation', options.orientation);
          
          var frustum = options.frustum;
          var orientation = options.orientation;
          var origin = options.origin;
  
          // This is private because it is used by DebugCameraPrimitive to draw a multi-frustum by
          // creating multiple FrustumOutlineGeometrys. This way the near plane of one frustum doesn't overlap
          // the far plane of another.
          var drawNearPlane = defaultValue(options._drawNearPlane, true);
  
          var frustumType;
          var frustumPackedLength;
          if (frustum instanceof PerspectiveFrustum) {
              frustumType = PERSPECTIVE;
              frustumPackedLength = PerspectiveFrustum.packedLength;
          } else if (frustum instanceof OrthographicFrustum) {
              frustumType = ORTHOGRAPHIC;
              frustumPackedLength = OrthographicFrustum.packedLength;
          }
  
          this._frustumType = frustumType;
          this._frustum = frustum.clone();
          this._origin = Cartesian3.clone(origin);
          this._orientation = Quaternion.clone(orientation);
          this._drawNearPlane = drawNearPlane;
          this._workerName = 'createFrustumOutlineGeometry';
  
          /**
           * The number of elements used to pack the object into an array.
           * @type {Number}
           */
          this.packedLength = 2 + frustumPackedLength + Cartesian3.packedLength + Quaternion.packedLength;
      }
  
      /**
       * Stores the provided instance into the provided array.
       *
       * @param {FrustumOutlineGeometry} value The value to pack.
       * @param {Number[]} array The array to pack into.
       * @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
       *
       * @returns {Number[]} The array that was packed into
       */
      FrustumOutlineGeometry.pack = function(value, array, startingIndex) {
                  Check.typeOf.object('value', value);
          Check.defined('array', array);
          
          startingIndex = defaultValue(startingIndex, 0);
  
          var frustumType = value._frustumType;
          var frustum = value._frustum;
  
          array[startingIndex++] = frustumType;
  
          if (frustumType === PERSPECTIVE) {
              PerspectiveFrustum.pack(frustum, array, startingIndex);
              startingIndex += PerspectiveFrustum.packedLength;
          } else {
              OrthographicFrustum.pack(frustum, array, startingIndex);
              startingIndex += OrthographicFrustum.packedLength;
          }
  
          Cartesian3.pack(value._origin, array, startingIndex);
          startingIndex += Cartesian3.packedLength;
          Quaternion.pack(value._orientation, array, startingIndex);
          startingIndex += Quaternion.packedLength;
          array[startingIndex] = value._drawNearPlane ? 1.0 : 0.0;
  
          return array;
      };
  
      var scratchPackPerspective = new PerspectiveFrustum();
      var scratchPackOrthographic = new OrthographicFrustum();
      var scratchPackQuaternion = new Quaternion();
      var scratchPackorigin = new Cartesian3();
  
      /**
       * Retrieves an instance from a packed array.
       *
       * @param {Number[]} array The packed array.
       * @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
       * @param {FrustumOutlineGeometry} [result] The object into which to store the result.
       */
      FrustumOutlineGeometry.unpack = function(array, startingIndex, result) {
                  Check.defined('array', array);
          
          startingIndex = defaultValue(startingIndex, 0);
  
          var frustumType = array[startingIndex++];
  
          var frustum;
          if (frustumType === PERSPECTIVE) {
              frustum = PerspectiveFrustum.unpack(array, startingIndex, scratchPackPerspective);
              startingIndex += PerspectiveFrustum.packedLength;
          } else {
              frustum = OrthographicFrustum.unpack(array, startingIndex, scratchPackOrthographic);
              startingIndex += OrthographicFrustum.packedLength;
          }
  
          var origin = Cartesian3.unpack(array, startingIndex, scratchPackorigin);
          startingIndex += Cartesian3.packedLength;
          var orientation = Quaternion.unpack(array, startingIndex, scratchPackQuaternion);
          startingIndex += Quaternion.packedLength;
          var drawNearPlane = array[startingIndex] === 1.0;
  
          if (!defined(result)) {
              return new FrustumOutlineGeometry({
                  frustum : frustum,
                  origin : origin,
                  orientation : orientation,
                  _drawNearPlane : drawNearPlane
              });
          }
  
          var frustumResult = frustumType === result._frustumType ? result._frustum : undefined;
          result._frustum = frustum.clone(frustumResult);
  
          result._frustumType = frustumType;
          result._origin = Cartesian3.clone(origin, result._origin);
          result._orientation = Quaternion.clone(orientation, result._orientation);
          result._drawNearPlane = drawNearPlane;
  
          return result;
      };
  
      /**
       * Computes the geometric representation of a frustum outline, including its vertices, indices, and a bounding sphere.
       *
       * @param {FrustumOutlineGeometry} frustumGeometry A description of the frustum.
       * @returns {Geometry|undefined} The computed vertices and indices.
       */
      FrustumOutlineGeometry.createGeometry = function(frustumGeometry) {
          var frustumType = frustumGeometry._frustumType;
          var frustum = frustumGeometry._frustum;
          var origin = frustumGeometry._origin;
          var orientation = frustumGeometry._orientation;
          var drawNearPlane = frustumGeometry._drawNearPlane;
  
          var positions = new Float64Array(3 * 4 * 2);
          FrustumGeometry._computeNearFarPlanes(origin, orientation, frustumType, frustum, positions);
  
          var attributes = new GeometryAttributes({
              position : new GeometryAttribute({
                  componentDatatype : ComponentDatatype.DOUBLE,
                  componentsPerAttribute : 3,
                  values : positions
              })
          });
  
          var offset;
          var index;
  
          var numberOfPlanes = drawNearPlane ? 2 : 1;
          var indices = new Uint16Array(8 * (numberOfPlanes + 1));
  
          // Build the near/far planes
          var i = drawNearPlane ? 0 : 1;
          for (; i < 2; ++i) {
              offset = drawNearPlane ? i * 8 : 0;
              index = i * 4;
  
              indices[offset] = index;
              indices[offset + 1] = index + 1;
              indices[offset + 2] = index + 1;
              indices[offset + 3] = index + 2;
              indices[offset + 4] = index + 2;
              indices[offset + 5] = index + 3;
              indices[offset + 6] = index + 3;
              indices[offset + 7] = index;
          }
  
          // Build the sides of the frustums
          for (i = 0; i < 2; ++i) {
              offset = (numberOfPlanes + i) * 8;
              index = i * 4;
  
              indices[offset] = index;
              indices[offset + 1] = index + 4;
              indices[offset + 2] = index + 1;
              indices[offset + 3] = index + 5;
              indices[offset + 4] = index + 2;
              indices[offset + 5] = index + 6;
              indices[offset + 6] = index + 3;
              indices[offset + 7] = index + 7;
          }
  
          return new Geometry({
              attributes : attributes,
              indices : indices,
              primitiveType : PrimitiveType.LINES,
              boundingSphere : BoundingSphere.fromVertices(positions)
          });
      };
  
      return FrustumOutlineGeometry;
  });
  
  define('Workers/createFrustumOutlineGeometry',[
          '../Core/defined',
          '../Core/FrustumOutlineGeometry'
      ], function(
          defined,
          FrustumOutlineGeometry) {
      'use strict';
  
      function createFrustumOutlineGeometry(frustumGeometry, offset) {
          if (defined(offset)) {
              frustumGeometry = FrustumOutlineGeometry.unpack(frustumGeometry, offset);
          }
          return FrustumOutlineGeometry.createGeometry(frustumGeometry);
      }
  
      return createFrustumOutlineGeometry;
  });
  
  }());