text: /*global define*/
  define([
      './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) {
          //>>includeStart('debug', pragmas.debug);
          Check.typeOf.object(spherical, 'spherical');
          //>>includeEnd('debug');
  
          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) {
          //>>includeStart('debug', pragmas.debug);
          Check.typeOf.object(value, 'value');
          Check.defined(array, 'array');
          //>>includeEnd('debug');
  
          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) {
          //>>includeStart('debug', pragmas.debug);
          Check.defined(array, 'array');
          //>>includeEnd('debug');
  
          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) {
          //>>includeStart('debug', pragmas.debug);
          Check.defined(array, 'array');
          //>>includeEnd('debug');
  
          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) {
          //>>includeStart('debug', pragmas.debug);
          Check.defined(array, 'array');
          Check.numeric.minimum(array.length, 3);
          if (array.length % 3 !== 0) {
              throw new DeveloperError('array length must be a multiple of 3.');
          }
          //>>includeEnd('debug');
  
          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) {
          //>>includeStart('debug', pragmas.debug);
          Check.typeOf.object(cartesian, 'cartesian');
          //>>includeEnd('debug');
  
          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) {
          //>>includeStart('debug', pragmas.debug);
          Check.typeOf.object(cartesian, 'cartesian');
          //>>includeEnd('debug');
  
          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) {
          //>>includeStart('debug', pragmas.debug);
          Check.typeOf.object(first, 'first');
          Check.typeOf.object(second, 'second');
          Check.typeOf.object(result, 'result');
          //>>includeEnd('debug');
  
          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) {
          //>>includeStart('debug', pragmas.debug);
          Check.typeOf.object(first, 'first');
          Check.typeOf.object(second, 'second');
          Check.typeOf.object(result, 'result');
          //>>includeEnd('debug');
  
          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) {
          //>>includeStart('debug', pragmas.debug);
          Check.typeOf.object(cartesian, 'cartesian');
          //>>includeEnd('debug');
  
          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) {
          //>>includeStart('debug', pragmas.debug);
          Check.typeOf.object(left, 'left');
          Check.typeOf.object(right, 'right');
          //>>includeEnd('debug');
  
          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) {
          //>>includeStart('debug', pragmas.debug);
          Check.typeOf.object(left, 'left');
          Check.typeOf.object(right, 'right');
          //>>includeEnd('debug');
  
          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) {
          //>>includeStart('debug', pragmas.debug);
          Check.typeOf.object(cartesian, 'cartesian');
          Check.typeOf.object(result, 'result');
          //>>includeEnd('debug');
  
          var magnitude = Cartesian3.magnitude(cartesian);
  
          result.x = cartesian.x / magnitude;
          result.y = cartesian.y / magnitude;
          result.z = cartesian.z / magnitude;
  
          //>>includeStart('debug', pragmas.debug);
          if (isNaN(result.x) || isNaN(result.y) || isNaN(result.z)) {
              throw new DeveloperError('normalized result is not a number');
          }
          //>>includeEnd('debug');
  
          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) {
          //>>includeStart('debug', pragmas.debug);
          Check.typeOf.object(left, 'left');
          Check.typeOf.object(right, 'right');
          //>>includeEnd('debug');
  
          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) {
          //>>includeStart('debug', pragmas.debug);
          Check.typeOf.object(left, 'left');
          Check.typeOf.object(right, 'right');
          Check.typeOf.object(result, 'result');
          //>>includeEnd('debug');
  
          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) {
          //>>includeStart('debug', pragmas.debug);
          if (!defined(left)) {
              throw new DeveloperError('left is required');
          }
          if (!defined(right)) {
              throw new DeveloperError('right is required');
          }
          if (!defined(result)) {
              throw new DeveloperError('result is required');
          }
          //>>includeEnd('debug');
  
          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) {
          //>>includeStart('debug', pragmas.debug);
          Check.typeOf.object(left, 'left');
          Check.typeOf.object(right, 'right');
          Check.typeOf.object(result, 'result');
          //>>includeEnd('debug');
  
          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) {
          //>>includeStart('debug', pragmas.debug);
          Check.typeOf.object(left, 'left');
          Check.typeOf.object(right, 'right');
          Check.typeOf.object(result, 'result');
          //>>includeEnd('debug');
  
          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) {
          //>>includeStart('debug', pragmas.debug);
          Check.typeOf.object(cartesian, 'cartesian');
          Check.typeOf.number(scalar, 'scalar');
          Check.typeOf.object(result, 'result');
          //>>includeEnd('debug');
  
          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) {
          //>>includeStart('debug', pragmas.debug);
          Check.typeOf.object(cartesian, 'cartesian');
          Check.typeOf.number(scalar, 'scalar');
          Check.typeOf.object(result, 'result');
          //>>includeEnd('debug');
  
          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) {
          //>>includeStart('debug', pragmas.debug);
          Check.typeOf.object(cartesian, 'cartesian');
          Check.typeOf.object(result, 'result');
          //>>includeEnd('debug');
  
          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) {
          //>>includeStart('debug', pragmas.debug);
          Check.typeOf.object(cartesian, 'cartesian');
          Check.typeOf.object(result, 'result');
          //>>includeEnd('debug');
  
          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) {
          //>>includeStart('debug', pragmas.debug);
          Check.typeOf.object(start, 'start');
          Check.typeOf.object(end, 'end');
          Check.typeOf.number(t, 't');
          Check.typeOf.object(result, 'result');
          //>>includeEnd('debug');
  
          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) {
          //>>includeStart('debug', pragmas.debug);
          Check.typeOf.object(left, 'left');
          Check.typeOf.object(right, 'right');
          //>>includeEnd('debug');
  
          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) {
          //>>includeStart('debug', pragmas.debug);
          Check.typeOf.object(cartesian, 'cartesian');
          Check.typeOf.object(result, 'result');
          //>>includeEnd('debug');
  
          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) {
          //>>includeStart('debug', pragmas.debug);
          Check.typeOf.object(left, 'left');
          Check.typeOf.object(right, 'right');
          Check.typeOf.object(result, 'result');
          //>>includeEnd('debug');
  
          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) {
          //>>includeStart('debug', pragmas.debug);
          Check.typeOf.number(longitude, 'longitude');
          Check.typeOf.number(latitude, 'latitude');
          //>>includeEnd('debug');
  
          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) {
          //>>includeStart('debug', pragmas.debug);
          Check.typeOf.number(longitude, 'longitude');
          Check.typeOf.number(latitude, 'latitude');
          //>>includeEnd('debug');
  
          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) {
          //>>includeStart('debug', pragmas.debug);
          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');
          }
          //>>includeEnd('debug');
  
          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) {
          //>>includeStart('debug', pragmas.debug);
          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');
          }
          //>>includeEnd('debug');
  
          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) {
          //>>includeStart('debug', pragmas.debug);
          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');
          }
          //>>includeEnd('debug');
  
          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) {
          //>>includeStart('debug', pragmas.debug);
          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');
          }
          //>>includeEnd('debug');
  
          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;
  });
  