cesium_nxmap/_cesium@1.72.0@cesium/Build/CesiumUnminified/Workers/Cartesian2-33d2657c.js

/**
 * Cesium - https://github.com/CesiumGS/cesium
 *
 * Copyright 2011-2020 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/CesiumGS/cesium/blob/master/LICENSE.md for full licensing details.
 */

define(['exports', './when-54c2dc71', './Check-6c0211bc', './Math-1124a290'], function (exports, when, Check, _Math) { '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 = when.defaultValue(x, 0.0);

    /**
     * The Y component.
     * @type {Number}
     * @default 0.0
     */
    this.y = when.defaultValue(y, 0.0);

    /**
     * The Z component.
     * @type {Number}
     * @default 0.0
     */
    this.z = when.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.Check.typeOf.object("spherical", spherical);
    //>>includeEnd('debug');

    if (!when.defined(result)) {
      result = new Cartesian3();
    }

    var clock = spherical.clock;
    var cone = spherical.cone;
    var magnitude = when.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 (!when.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 (!when.defined(cartesian)) {
      return undefined;
    }
    if (!when.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.Check.typeOf.object("value", value);
    Check.Check.defined("array", array);
    //>>includeEnd('debug');

    startingIndex = when.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.Check.defined("array", array);
    //>>includeEnd('debug');

    startingIndex = when.defaultValue(startingIndex, 0);

    if (!when.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. If this is a typed array, it must have array.length * 3 components, else a {@link DeveloperError} will be thrown. If it is a regular array, it will be resized to have (array.length * 3) elements.
   * @returns {Number[]} The packed array.
   */
  Cartesian3.packArray = function (array, result) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.defined("array", array);
    //>>includeEnd('debug');

    var length = array.length;
    var resultLength = length * 3;
    if (!when.defined(result)) {
      result = new Array(resultLength);
    } else if (!Array.isArray(result) && result.length !== resultLength) {
      throw new Check.DeveloperError(
        "If result is a typed array, it must have exactly array.length * 3 elements"
      );
    } else if (result.length !== resultLength) {
      result.length = resultLength;
    }

    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.Check.defined("array", array);
    Check.Check.typeOf.number.greaterThanOrEquals("array.length", array.length, 3);
    if (array.length % 3 !== 0) {
      throw new Check.DeveloperError("array length must be a multiple of 3.");
    }
    //>>includeEnd('debug');

    var length = array.length;
    if (!when.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.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.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.Check.typeOf.object("first", first);
    Check.Check.typeOf.object("second", second);
    Check.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.Check.typeOf.object("first", first);
    Check.Check.typeOf.object("second", second);
    Check.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.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.Check.typeOf.object("left", left);
    Check.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.Check.typeOf.object("left", left);
    Check.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.Check.typeOf.object("cartesian", cartesian);
    Check.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 Check.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.Check.typeOf.object("left", left);
    Check.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.Check.typeOf.object("left", left);
    Check.Check.typeOf.object("right", right);
    Check.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);
    Check.Check.typeOf.object("left", left);
    Check.Check.typeOf.object("right", right);
    Check.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 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.Check.typeOf.object("left", left);
    Check.Check.typeOf.object("right", right);
    Check.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.Check.typeOf.object("left", left);
    Check.Check.typeOf.object("right", right);
    Check.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.Check.typeOf.object("cartesian", cartesian);
    Check.Check.typeOf.number("scalar", scalar);
    Check.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.Check.typeOf.object("cartesian", cartesian);
    Check.Check.typeOf.number("scalar", scalar);
    Check.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.Check.typeOf.object("cartesian", cartesian);
    Check.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.Check.typeOf.object("cartesian", cartesian);
    Check.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.Check.typeOf.object("start", start);
    Check.Check.typeOf.object("end", end);
    Check.Check.typeOf.number("t", t);
    Check.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.Check.typeOf.object("left", left);
    Check.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.Check.typeOf.object("cartesian", cartesian);
    Check.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;
  };

  /**
   * Projects vector a onto vector b
   * @param {Cartesian3} a The vector that needs projecting
   * @param {Cartesian3} b The vector to project onto
   * @param {Cartesian3} result The result cartesian
   * @returns {Cartesian3} The modified result parameter
   */
  Cartesian3.projectVector = function (a, b, result) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.defined("a", a);
    Check.Check.defined("b", b);
    Check.Check.defined("result", result);
    //>>includeEnd('debug');

    var scalar = Cartesian3.dot(a, b) / Cartesian3.dot(b, b);
    return Cartesian3.multiplyByScalar(b, scalar, 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 ||
      (when.defined(left) &&
        when.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=0] 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 ||
      (when.defined(left) &&
        when.defined(right) &&
        _Math.CesiumMath.equalsEpsilon(
          left.x,
          right.x,
          relativeEpsilon,
          absoluteEpsilon
        ) &&
        _Math.CesiumMath.equalsEpsilon(
          left.y,
          right.y,
          relativeEpsilon,
          absoluteEpsilon
        ) &&
        _Math.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.Check.typeOf.object("left", left);
    Check.Check.typeOf.object("right", right);
    Check.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;
  };

  /**
   * Computes the midpoint between the right and left Cartesian.
   * @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 midpoint.
   */
  Cartesian3.midpoint = function (left, right, result) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.object("left", left);
    Check.Check.typeOf.object("right", right);
    Check.Check.typeOf.object("result", result);
    //>>includeEnd('debug');

    result.x = (left.x + right.x) * 0.5;
    result.y = (left.y + right.y) * 0.5;
    result.z = (left.z + right.z) * 0.5;

    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.Check.typeOf.number("longitude", longitude);
    Check.Check.typeOf.number("latitude", latitude);
    //>>includeEnd('debug');

    longitude = _Math.CesiumMath.toRadians(longitude);
    latitude = _Math.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.Check.typeOf.number("longitude", longitude);
    Check.Check.typeOf.number("latitude", latitude);
    //>>includeEnd('debug');

    height = when.defaultValue(height, 0.0);
    var radiiSquared = when.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 (!when.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.Check.defined("coordinates", coordinates);
    if (coordinates.length < 2 || coordinates.length % 2 !== 0) {
      throw new Check.DeveloperError(
        "the number of coordinates must be a multiple of 2 and at least 2"
      );
    }
    //>>includeEnd('debug');

    var length = coordinates.length;
    if (!when.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.Check.defined("coordinates", coordinates);
    if (coordinates.length < 2 || coordinates.length % 2 !== 0) {
      throw new Check.DeveloperError(
        "the number of coordinates must be a multiple of 2 and at least 2"
      );
    }
    //>>includeEnd('debug');

    var length = coordinates.length;
    if (!when.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.Check.defined("coordinates", coordinates);
    if (coordinates.length < 3 || coordinates.length % 3 !== 0) {
      throw new Check.DeveloperError(
        "the number of coordinates must be a multiple of 3 and at least 3"
      );
    }
    //>>includeEnd('debug');

    var length = coordinates.length;
    if (!when.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.Check.defined("coordinates", coordinates);
    if (coordinates.length < 3 || coordinates.length % 3 !== 0) {
      throw new Check.DeveloperError(
        "the number of coordinates must be a multiple of 3 and at least 3"
      );
    }
    //>>includeEnd('debug');

    var length = coordinates.length;
    if (!when.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 = Object.freeze(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 = Object.freeze(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 = Object.freeze(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 = Object.freeze(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=0] 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 + ")";
  };

  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.
   *
   * @function scaleToGeodeticSurface
   *
   * @private
   */
  function scaleToGeodeticSurface(
    cartesian,
    oneOverRadii,
    oneOverRadiiSquared,
    centerToleranceSquared,
    result
  ) {
    //>>includeStart('debug', pragmas.debug);
    if (!when.defined(cartesian)) {
      throw new Check.DeveloperError("cartesian is required.");
    }
    if (!when.defined(oneOverRadii)) {
      throw new Check.DeveloperError("oneOverRadii is required.");
    }
    if (!when.defined(oneOverRadiiSquared)) {
      throw new Check.DeveloperError("oneOverRadiiSquared is required.");
    }
    if (!when.defined(centerToleranceSquared)) {
      throw new Check.DeveloperError("centerToleranceSquared is required.");
    }
    //>>includeEnd('debug');

    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) > _Math.CesiumMath.EPSILON12);

    if (!when.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;
  }

  /**
   * 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 = when.defaultValue(longitude, 0.0);

    /**
     * The latitude, in radians.
     * @type {Number}
     * @default 0.0
     */
    this.latitude = when.defaultValue(latitude, 0.0);

    /**
     * The height, in meters, above the ellipsoid.
     * @type {Number}
     * @default 0.0
     */
    this.height = when.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) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.number("longitude", longitude);
    Check.Check.typeOf.number("latitude", latitude);
    //>>includeEnd('debug');

    height = when.defaultValue(height, 0.0);

    if (!when.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) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.number("longitude", longitude);
    Check.Check.typeOf.number("latitude", latitude);
    //>>includeEnd('debug');
    longitude = _Math.CesiumMath.toRadians(longitude);
    latitude = _Math.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 = _Math.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 = when.defined(ellipsoid)
      ? ellipsoid.oneOverRadii
      : wgs84OneOverRadii;
    var oneOverRadiiSquared = when.defined(ellipsoid)
      ? ellipsoid.oneOverRadiiSquared
      : wgs84OneOverRadiiSquared;
    var centerToleranceSquared = when.defined(ellipsoid)
      ? ellipsoid._centerToleranceSquared
      : wgs84CenterToleranceSquared;

    //`cartesian is required.` is thrown from scaleToGeodeticSurface
    var p = scaleToGeodeticSurface(
      cartesian,
      oneOverRadii,
      oneOverRadiiSquared,
      centerToleranceSquared,
      cartesianToCartographicP
    );

    if (!when.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 =
      _Math.CesiumMath.sign(Cartesian3.dot(h, cartesian)) * Cartesian3.magnitude(h);

    if (!when.defined(result)) {
      return new Cartographic(longitude, latitude, height);
    }
    result.longitude = longitude;
    result.latitude = latitude;
    result.height = height;
    return result;
  };

  /**
   * Creates a new Cartesian3 instance from a Cartographic input. The values in the inputted
   * object should be in radians.
   *
   * @param {Cartographic} cartographic Input to be converted into a Cartesian3 output.
   * @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
   */
  Cartographic.toCartesian = function (cartographic, ellipsoid, result) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.defined("cartographic", cartographic);
    //>>includeEnd('debug');

    return Cartesian3.fromRadians(
      cartographic.longitude,
      cartographic.latitude,
      cartographic.height,
      ellipsoid,
      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 (!when.defined(cartographic)) {
      return undefined;
    }
    if (!when.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 ||
      (when.defined(left) &&
        when.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=0] 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) {
    epsilon = when.defaultValue(epsilon, 0);

    return (
      left === right ||
      (when.defined(left) &&
        when.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 = Object.freeze(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=0] 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 + ")";
  };

  function initialize(ellipsoid, x, y, z) {
    x = when.defaultValue(x, 0.0);
    y = when.defaultValue(y, 0.0);
    z = when.defaultValue(z, 0.0);

    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.number.greaterThanOrEquals("x", x, 0.0);
    Check.Check.typeOf.number.greaterThanOrEquals("y", y, 0.0);
    Check.Check.typeOf.number.greaterThanOrEquals("z", z, 0.0);
    //>>includeEnd('debug');

    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 = _Math.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);
  }

  Object.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 (!when.defined(ellipsoid)) {
      return undefined;
    }
    var radii = ellipsoid._radii;

    if (!when.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 (!when.defined(result)) {
      result = new Ellipsoid();
    }

    if (!when.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 = Object.freeze(
    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 = Object.freeze(new Ellipsoid(1.0, 1.0, 1.0));

  /**
   * An Ellipsoid instance initialized to a sphere with the lunar radius.
   *
   * @type {Ellipsoid}
   * @constant
   */
  Ellipsoid.MOON = Object.freeze(
    new Ellipsoid(
      _Math.CesiumMath.LUNAR_RADIUS,
      _Math.CesiumMath.LUNAR_RADIUS,
      _Math.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) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.object("value", value);
    Check.Check.defined("array", array);
    //>>includeEnd('debug');

    startingIndex = when.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) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.defined("array", array);
    //>>includeEnd('debug');

    startingIndex = when.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
  ) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.object("cartographic", cartographic);
    //>>includeEnd('debug');

    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 (!when.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 (
      Cartesian3.equalsEpsilon(cartesian, Cartesian3.ZERO, _Math.CesiumMath.EPSILON14)
    ) {
      return undefined;
    }
    if (!when.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 (!when.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
  ) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.defined("cartographics", cartographics);
    //>>includeEnd('debug')

    var length = cartographics.length;
    if (!when.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$1 = new Cartesian3();
  var cartesianToCartographicP$1 = new Cartesian3();
  var cartesianToCartographicH$1 = 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$1);

    if (!when.defined(p)) {
      return undefined;
    }

    var n = this.geodeticSurfaceNormal(p, cartesianToCartographicN$1);
    var h = Cartesian3.subtract(cartesian, p, cartesianToCartographicH$1);

    var longitude = Math.atan2(n.y, n.x);
    var latitude = Math.asin(n.z);
    var height =
      _Math.CesiumMath.sign(Cartesian3.dot(h, cartesian)) * Cartesian3.magnitude(h);

    if (!when.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
  ) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.defined("cartesians", cartesians);
    //>>includeEnd('debug');

    var length = cartesians.length;
    if (!when.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) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.object("cartesian", cartesian);
    //>>includeEnd('debug');

    if (!when.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 (!when.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 (!when.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 ||
      (when.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
  ) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.object("position", position);

    if (
      !_Math.CesiumMath.equalsEpsilon(
        this._radii.x,
        this._radii.y,
        _Math.CesiumMath.EPSILON15
      )
    ) {
      throw new Check.DeveloperError(
        "Ellipsoid must be an ellipsoid of revolution (radii.x == radii.y)"
      );
    }

    Check.Check.typeOf.number.greaterThan("Ellipsoid.radii.z", this._radii.z, 0);
    //>>includeEnd('debug');

    buffer = when.defaultValue(buffer, 0.0);

    var squaredXOverSquaredZ = this._squaredXOverSquaredZ;

    if (!when.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;
  };

  var abscissas = [
    0.14887433898163,
    0.43339539412925,
    0.67940956829902,
    0.86506336668898,
    0.97390652851717,
    0.0,
  ];
  var weights = [
    0.29552422471475,
    0.26926671930999,
    0.21908636251598,
    0.14945134915058,
    0.066671344308684,
    0.0,
  ];

  /**
   * Compute the 10th order Gauss-Legendre Quadrature of the given definite integral.
   *
   * @param {Number} a The lower bound for the integration.
   * @param {Number} b The upper bound for the integration.
   * @param {Ellipsoid~RealValuedScalarFunction} func The function to integrate.
   * @returns {Number} The value of the integral of the given function over the given domain.
   *
   * @private
   */
  function gaussLegendreQuadrature(a, b, func) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.number("a", a);
    Check.Check.typeOf.number("b", b);
    Check.Check.typeOf.func("func", func);
    //>>includeEnd('debug');

    // The range is half of the normal range since the five weights add to one (ten weights add to two).
    // The values of the abscissas are multiplied by two to account for this.
    var xMean = 0.5 * (b + a);
    var xRange = 0.5 * (b - a);

    var sum = 0.0;
    for (var i = 0; i < 5; i++) {
      var dx = xRange * abscissas[i];
      sum += weights[i] * (func(xMean + dx) + func(xMean - dx));
    }

    // Scale the sum to the range of x.
    sum *= xRange;
    return sum;
  }

  /**
   * A real valued scalar function.
   * @callback Ellipsoid~RealValuedScalarFunction
   *
   * @param {Number} x The value used to evaluate the function.
   * @returns {Number} The value of the function at x.
   *
   * @private
   */

  /**
   * Computes an approximation of the surface area of a rectangle on the surface of an ellipsoid using
   * Gauss-Legendre 10th order quadrature.
   *
   * @param {Rectangle} rectangle The rectangle used for computing the surface area.
   * @returns {Number} The approximate area of the rectangle on the surface of this ellipsoid.
   */
  Ellipsoid.prototype.surfaceArea = function (rectangle) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.object("rectangle", rectangle);
    //>>includeEnd('debug');
    var minLongitude = rectangle.west;
    var maxLongitude = rectangle.east;
    var minLatitude = rectangle.south;
    var maxLatitude = rectangle.north;

    while (maxLongitude < minLongitude) {
      maxLongitude += _Math.CesiumMath.TWO_PI;
    }

    var radiiSquared = this._radiiSquared;
    var a2 = radiiSquared.x;
    var b2 = radiiSquared.y;
    var c2 = radiiSquared.z;
    var a2b2 = a2 * b2;
    return gaussLegendreQuadrature(minLatitude, maxLatitude, function (lat) {
      // phi represents the angle measured from the north pole
      // sin(phi) = sin(pi / 2 - lat) = cos(lat), cos(phi) is similar
      var sinPhi = Math.cos(lat);
      var cosPhi = Math.sin(lat);
      return (
        Math.cos(lat) *
        gaussLegendreQuadrature(minLongitude, maxLongitude, function (lon) {
          var cosTheta = Math.cos(lon);
          var sinTheta = Math.sin(lon);
          return Math.sqrt(
            a2b2 * cosPhi * cosPhi +
              c2 *
                (b2 * cosTheta * cosTheta + a2 * sinTheta * sinTheta) *
                sinPhi *
                sinPhi
          );
        })
      );
    });
  };

  /**
   * 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 = when.defaultValue(west, 0.0);

    /**
     * The southernmost latitude in radians in the range [-Pi/2, Pi/2].
     *
     * @type {Number}
     * @default 0.0
     */
    this.south = when.defaultValue(south, 0.0);

    /**
     * The easternmost longitude in radians in the range [-Pi, Pi].
     *
     * @type {Number}
     * @default 0.0
     */
    this.east = when.defaultValue(east, 0.0);

    /**
     * The northernmost latitude in radians in the range [-Pi/2, Pi/2].
     *
     * @type {Number}
     * @default 0.0
     */
    this.north = when.defaultValue(north, 0.0);
  }

  Object.defineProperties(Rectangle.prototype, {
    /**
     * Gets the width of the rectangle in radians.
     * @memberof Rectangle.prototype
     * @type {Number}
     * @readonly
     */
    width: {
      get: function () {
        return Rectangle.computeWidth(this);
      },
    },

    /**
     * Gets the height of the rectangle in radians.
     * @memberof Rectangle.prototype
     * @type {Number}
     * @readonly
     */
    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) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.object("value", value);
    Check.Check.defined("array", array);
    //>>includeEnd('debug');

    startingIndex = when.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) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.defined("array", array);
    //>>includeEnd('debug');

    startingIndex = when.defaultValue(startingIndex, 0);

    if (!when.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) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.object("rectangle", rectangle);
    //>>includeEnd('debug');
    var east = rectangle.east;
    var west = rectangle.west;
    if (east < west) {
      east += _Math.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) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.object("rectangle", rectangle);
    //>>includeEnd('debug');
    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 = _Math.CesiumMath.toRadians(when.defaultValue(west, 0.0));
    south = _Math.CesiumMath.toRadians(when.defaultValue(south, 0.0));
    east = _Math.CesiumMath.toRadians(when.defaultValue(east, 0.0));
    north = _Math.CesiumMath.toRadians(when.defaultValue(north, 0.0));

    if (!when.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 (!when.defined(result)) {
      return new Rectangle(west, south, east, north);
    }

    result.west = when.defaultValue(west, 0.0);
    result.south = when.defaultValue(south, 0.0);
    result.east = when.defaultValue(east, 0.0);
    result.north = when.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) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.defined("cartographics", cartographics);
    //>>includeEnd('debug');

    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 + _Math.CesiumMath.TWO_PI;
      westOverIDL = Math.min(westOverIDL, lonAdjusted);
      eastOverIDL = Math.max(eastOverIDL, lonAdjusted);
    }

    if (east - west > eastOverIDL - westOverIDL) {
      west = westOverIDL;
      east = eastOverIDL;

      if (east > _Math.CesiumMath.PI) {
        east = east - _Math.CesiumMath.TWO_PI;
      }
      if (west > _Math.CesiumMath.PI) {
        west = west - _Math.CesiumMath.TWO_PI;
      }
    }

    if (!when.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) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.defined("cartesians", cartesians);
    //>>includeEnd('debug');
    ellipsoid = when.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 + _Math.CesiumMath.TWO_PI;
      westOverIDL = Math.min(westOverIDL, lonAdjusted);
      eastOverIDL = Math.max(eastOverIDL, lonAdjusted);
    }

    if (east - west > eastOverIDL - westOverIDL) {
      west = westOverIDL;
      east = eastOverIDL;

      if (east > _Math.CesiumMath.PI) {
        east = east - _Math.CesiumMath.TWO_PI;
      }
      if (west > _Math.CesiumMath.PI) {
        west = west - _Math.CesiumMath.TWO_PI;
      }
    }

    if (!when.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 (!when.defined(rectangle)) {
      return undefined;
    }

    if (!when.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;
  };

  /**
   * Compares the provided Rectangles componentwise and returns
   * <code>true</code> if they pass an absolute or relative tolerance test,
   * <code>false</code> otherwise.
   *
   * @param {Rectangle} [left] The first Rectangle.
   * @param {Rectangle} [right] The second Rectangle.
   * @param {Number} [absoluteEpsilon=0] 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.
   */
  Rectangle.equalsEpsilon = function (left, right, absoluteEpsilon) {
    absoluteEpsilon = when.defaultValue(absoluteEpsilon, 0);

    return (
      left === right ||
      (when.defined(left) &&
        when.defined(right) &&
        Math.abs(left.west - right.west) <= absoluteEpsilon &&
        Math.abs(left.south - right.south) <= absoluteEpsilon &&
        Math.abs(left.east - right.east) <= absoluteEpsilon &&
        Math.abs(left.north - right.north) <= absoluteEpsilon)
    );
  };

  /**
   * 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 ||
      (when.defined(left) &&
        when.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=0] 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) {
    return Rectangle.equalsEpsilon(this, other, 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) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.object("rectangle", rectangle);

    var north = rectangle.north;
    Check.Check.typeOf.number.greaterThanOrEquals(
      "north",
      north,
      -_Math.CesiumMath.PI_OVER_TWO
    );
    Check.Check.typeOf.number.lessThanOrEquals("north", north, _Math.CesiumMath.PI_OVER_TWO);

    var south = rectangle.south;
    Check.Check.typeOf.number.greaterThanOrEquals(
      "south",
      south,
      -_Math.CesiumMath.PI_OVER_TWO
    );
    Check.Check.typeOf.number.lessThanOrEquals("south", south, _Math.CesiumMath.PI_OVER_TWO);

    var west = rectangle.west;
    Check.Check.typeOf.number.greaterThanOrEquals("west", west, -Math.PI);
    Check.Check.typeOf.number.lessThanOrEquals("west", west, Math.PI);

    var east = rectangle.east;
    Check.Check.typeOf.number.greaterThanOrEquals("east", east, -Math.PI);
    Check.Check.typeOf.number.lessThanOrEquals("east", east, Math.PI);
    //>>includeEnd('debug');
  };

  /**
   * 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) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.object("rectangle", rectangle);
    //>>includeEnd('debug');

    if (!when.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) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.object("rectangle", rectangle);
    //>>includeEnd('debug');

    if (!when.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) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.object("rectangle", rectangle);
    //>>includeEnd('debug');

    if (!when.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) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.object("rectangle", rectangle);
    //>>includeEnd('debug');

    if (!when.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) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.object("rectangle", rectangle);
    //>>includeEnd('debug');

    var east = rectangle.east;
    var west = rectangle.west;

    if (east < west) {
      east += _Math.CesiumMath.TWO_PI;
    }

    var longitude = _Math.CesiumMath.negativePiToPi((west + east) * 0.5);
    var latitude = (rectangle.south + rectangle.north) * 0.5;

    if (!when.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) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.object("rectangle", rectangle);
    Check.Check.typeOf.object("otherRectangle", otherRectangle);
    //>>includeEnd('debug');

    var rectangleEast = rectangle.east;
    var rectangleWest = rectangle.west;

    var otherRectangleEast = otherRectangle.east;
    var otherRectangleWest = otherRectangle.west;

    if (rectangleEast < rectangleWest && otherRectangleEast > 0.0) {
      rectangleEast += _Math.CesiumMath.TWO_PI;
    } else if (otherRectangleEast < otherRectangleWest && rectangleEast > 0.0) {
      otherRectangleEast += _Math.CesiumMath.TWO_PI;
    }

    if (rectangleEast < rectangleWest && otherRectangleWest < 0.0) {
      otherRectangleWest += _Math.CesiumMath.TWO_PI;
    } else if (otherRectangleEast < otherRectangleWest && rectangleWest < 0.0) {
      rectangleWest += _Math.CesiumMath.TWO_PI;
    }

    var west = _Math.CesiumMath.negativePiToPi(
      Math.max(rectangleWest, otherRectangleWest)
    );
    var east = _Math.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 (!when.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) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.object("rectangle", rectangle);
    Check.Check.typeOf.object("otherRectangle", otherRectangle);
    //>>includeEnd('debug');

    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 (!when.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) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.object("rectangle", rectangle);
    Check.Check.typeOf.object("otherRectangle", otherRectangle);
    //>>includeEnd('debug');

    if (!when.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 += _Math.CesiumMath.TWO_PI;
    } else if (otherRectangleEast < otherRectangleWest && rectangleEast > 0.0) {
      otherRectangleEast += _Math.CesiumMath.TWO_PI;
    }

    if (rectangleEast < rectangleWest && otherRectangleWest < 0.0) {
      otherRectangleWest += _Math.CesiumMath.TWO_PI;
    } else if (otherRectangleEast < otherRectangleWest && rectangleWest < 0.0) {
      rectangleWest += _Math.CesiumMath.TWO_PI;
    }

    var west = _Math.CesiumMath.convertLongitudeRange(
      Math.min(rectangleWest, otherRectangleWest)
    );
    var east = _Math.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) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.object("rectangle", rectangle);
    Check.Check.typeOf.object("cartographic", cartographic);
    //>>includeEnd('debug');

    if (!when.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) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.object("rectangle", rectangle);
    Check.Check.typeOf.object("cartographic", cartographic);
    //>>includeEnd('debug');

    var longitude = cartographic.longitude;
    var latitude = cartographic.latitude;

    var west = rectangle.west;
    var east = rectangle.east;

    if (east < west) {
      east += _Math.CesiumMath.TWO_PI;
      if (longitude < 0.0) {
        longitude += _Math.CesiumMath.TWO_PI;
      }
    }
    return (
      (longitude > west ||
        _Math.CesiumMath.equalsEpsilon(longitude, west, _Math.CesiumMath.EPSILON14)) &&
      (longitude < east ||
        _Math.CesiumMath.equalsEpsilon(longitude, east, _Math.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) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.object("rectangle", rectangle);
    //>>includeEnd('debug');

    ellipsoid = when.defaultValue(ellipsoid, Ellipsoid.WGS84);
    surfaceHeight = when.defaultValue(surfaceHeight, 0.0);

    if (!when.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 * _Math.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 = Object.freeze(
    new Rectangle(
      -Math.PI,
      -_Math.CesiumMath.PI_OVER_TWO,
      Math.PI,
      _Math.CesiumMath.PI_OVER_TWO
    )
  );

  /**
   * A 2D Cartesian point.
   * @alias Cartesian2
   * @constructor
   *
   * @param {Number} [x=0.0] The X component.
   * @param {Number} [y=0.0] The Y component.
   *
   * @see Cartesian3
   * @see Cartesian4
   * @see Packable
   */
  function Cartesian2(x, y) {
    /**
     * The X component.
     * @type {Number}
     * @default 0.0
     */
    this.x = when.defaultValue(x, 0.0);

    /**
     * The Y component.
     * @type {Number}
     * @default 0.0
     */
    this.y = when.defaultValue(y, 0.0);
  }

  /**
   * Creates a Cartesian2 instance from x and y coordinates.
   *
   * @param {Number} x The x coordinate.
   * @param {Number} y The y coordinate.
   * @param {Cartesian2} [result] The object onto which to store the result.
   * @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided.
   */
  Cartesian2.fromElements = function (x, y, result) {
    if (!when.defined(result)) {
      return new Cartesian2(x, y);
    }

    result.x = x;
    result.y = y;
    return result;
  };

  /**
   * Duplicates a Cartesian2 instance.
   *
   * @param {Cartesian2} cartesian The Cartesian to duplicate.
   * @param {Cartesian2} [result] The object onto which to store the result.
   * @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided. (Returns undefined if cartesian is undefined)
   */
  Cartesian2.clone = function (cartesian, result) {
    if (!when.defined(cartesian)) {
      return undefined;
    }
    if (!when.defined(result)) {
      return new Cartesian2(cartesian.x, cartesian.y);
    }

    result.x = cartesian.x;
    result.y = cartesian.y;
    return result;
  };

  /**
   * Creates a Cartesian2 instance from an existing Cartesian3.  This simply takes the
   * x and y properties of the Cartesian3 and drops z.
   * @function
   *
   * @param {Cartesian3} cartesian The Cartesian3 instance to create a Cartesian2 instance from.
   * @param {Cartesian2} [result] The object onto which to store the result.
   * @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided.
   */
  Cartesian2.fromCartesian3 = Cartesian2.clone;

  /**
   * Creates a Cartesian2 instance from an existing Cartesian4.  This simply takes the
   * x and y properties of the Cartesian4 and drops z and w.
   * @function
   *
   * @param {Cartesian4} cartesian The Cartesian4 instance to create a Cartesian2 instance from.
   * @param {Cartesian2} [result] The object onto which to store the result.
   * @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided.
   */
  Cartesian2.fromCartesian4 = Cartesian2.clone;

  /**
   * The number of elements used to pack the object into an array.
   * @type {Number}
   */
  Cartesian2.packedLength = 2;

  /**
   * Stores the provided instance into the provided array.
   *
   * @param {Cartesian2} 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
   */
  Cartesian2.pack = function (value, array, startingIndex) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.object("value", value);
    Check.Check.defined("array", array);
    //>>includeEnd('debug');

    startingIndex = when.defaultValue(startingIndex, 0);

    array[startingIndex++] = value.x;
    array[startingIndex] = value.y;

    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 {Cartesian2} [result] The object into which to store the result.
   * @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided.
   */
  Cartesian2.unpack = function (array, startingIndex, result) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.defined("array", array);
    //>>includeEnd('debug');

    startingIndex = when.defaultValue(startingIndex, 0);

    if (!when.defined(result)) {
      result = new Cartesian2();
    }
    result.x = array[startingIndex++];
    result.y = array[startingIndex];
    return result;
  };

  /**
       * Flattens an array of Cartesian2s into and array of components.
       *
       * @param {Cartesian2[]} array The array of cartesians to pack.
       * @param {Number[]} [result] The array onto which to store the result. If this is a typed array, it must have array.length * 2 components, else a {@link DeveloperError} will be thrown. If it is a regular array, it will be resized to have (array.length * 2) elements.

       * @returns {Number[]} The packed array.
       */
  Cartesian2.packArray = function (array, result) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.defined("array", array);
    //>>includeEnd('debug');

    var length = array.length;
    var resultLength = length * 2;
    if (!when.defined(result)) {
      result = new Array(resultLength);
    } else if (!Array.isArray(result) && result.length !== resultLength) {
      throw new Check.DeveloperError(
        "If result is a typed array, it must have exactly array.length * 2 elements"
      );
    } else if (result.length !== resultLength) {
      result.length = resultLength;
    }

    for (var i = 0; i < length; ++i) {
      Cartesian2.pack(array[i], result, i * 2);
    }
    return result;
  };

  /**
   * Unpacks an array of cartesian components into and array of Cartesian2s.
   *
   * @param {Number[]} array The array of components to unpack.
   * @param {Cartesian2[]} [result] The array onto which to store the result.
   * @returns {Cartesian2[]} The unpacked array.
   */
  Cartesian2.unpackArray = function (array, result) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.defined("array", array);
    Check.Check.typeOf.number.greaterThanOrEquals("array.length", array.length, 2);
    if (array.length % 2 !== 0) {
      throw new Check.DeveloperError("array length must be a multiple of 2.");
    }
    //>>includeEnd('debug');

    var length = array.length;
    if (!when.defined(result)) {
      result = new Array(length / 2);
    } else {
      result.length = length / 2;
    }

    for (var i = 0; i < length; i += 2) {
      var index = i / 2;
      result[index] = Cartesian2.unpack(array, i, result[index]);
    }
    return result;
  };

  /**
   * Creates a Cartesian2 from two consecutive elements in an array.
   * @function
   *
   * @param {Number[]} array The array whose two consecutive elements correspond to the x and y components, respectively.
   * @param {Number} [startingIndex=0] The offset into the array of the first element, which corresponds to the x component.
   * @param {Cartesian2} [result] The object onto which to store the result.
   * @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided.
   *
   * @example
   * // Create a Cartesian2 with (1.0, 2.0)
   * var v = [1.0, 2.0];
   * var p = Cesium.Cartesian2.fromArray(v);
   *
   * // Create a Cartesian2 with (1.0, 2.0) using an offset into an array
   * var v2 = [0.0, 0.0, 1.0, 2.0];
   * var p2 = Cesium.Cartesian2.fromArray(v2, 2);
   */
  Cartesian2.fromArray = Cartesian2.unpack;

  /**
   * Computes the value of the maximum component for the supplied Cartesian.
   *
   * @param {Cartesian2} cartesian The cartesian to use.
   * @returns {Number} The value of the maximum component.
   */
  Cartesian2.maximumComponent = function (cartesian) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.object("cartesian", cartesian);
    //>>includeEnd('debug');

    return Math.max(cartesian.x, cartesian.y);
  };

  /**
   * Computes the value of the minimum component for the supplied Cartesian.
   *
   * @param {Cartesian2} cartesian The cartesian to use.
   * @returns {Number} The value of the minimum component.
   */
  Cartesian2.minimumComponent = function (cartesian) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.object("cartesian", cartesian);
    //>>includeEnd('debug');

    return Math.min(cartesian.x, cartesian.y);
  };

  /**
   * Compares two Cartesians and computes a Cartesian which contains the minimum components of the supplied Cartesians.
   *
   * @param {Cartesian2} first A cartesian to compare.
   * @param {Cartesian2} second A cartesian to compare.
   * @param {Cartesian2} result The object into which to store the result.
   * @returns {Cartesian2} A cartesian with the minimum components.
   */
  Cartesian2.minimumByComponent = function (first, second, result) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.object("first", first);
    Check.Check.typeOf.object("second", second);
    Check.Check.typeOf.object("result", result);
    //>>includeEnd('debug');

    result.x = Math.min(first.x, second.x);
    result.y = Math.min(first.y, second.y);

    return result;
  };

  /**
   * Compares two Cartesians and computes a Cartesian which contains the maximum components of the supplied Cartesians.
   *
   * @param {Cartesian2} first A cartesian to compare.
   * @param {Cartesian2} second A cartesian to compare.
   * @param {Cartesian2} result The object into which to store the result.
   * @returns {Cartesian2} A cartesian with the maximum components.
   */
  Cartesian2.maximumByComponent = function (first, second, result) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.object("first", first);
    Check.Check.typeOf.object("second", second);
    Check.Check.typeOf.object("result", result);
    //>>includeEnd('debug');

    result.x = Math.max(first.x, second.x);
    result.y = Math.max(first.y, second.y);
    return result;
  };

  /**
   * Computes the provided Cartesian's squared magnitude.
   *
   * @param {Cartesian2} cartesian The Cartesian instance whose squared magnitude is to be computed.
   * @returns {Number} The squared magnitude.
   */
  Cartesian2.magnitudeSquared = function (cartesian) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.object("cartesian", cartesian);
    //>>includeEnd('debug');

    return cartesian.x * cartesian.x + cartesian.y * cartesian.y;
  };

  /**
   * Computes the Cartesian's magnitude (length).
   *
   * @param {Cartesian2} cartesian The Cartesian instance whose magnitude is to be computed.
   * @returns {Number} The magnitude.
   */
  Cartesian2.magnitude = function (cartesian) {
    return Math.sqrt(Cartesian2.magnitudeSquared(cartesian));
  };

  var distanceScratch$1 = new Cartesian2();

  /**
   * Computes the distance between two points.
   *
   * @param {Cartesian2} left The first point to compute the distance from.
   * @param {Cartesian2} right The second point to compute the distance to.
   * @returns {Number} The distance between two points.
   *
   * @example
   * // Returns 1.0
   * var d = Cesium.Cartesian2.distance(new Cesium.Cartesian2(1.0, 0.0), new Cesium.Cartesian2(2.0, 0.0));
   */
  Cartesian2.distance = function (left, right) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.object("left", left);
    Check.Check.typeOf.object("right", right);
    //>>includeEnd('debug');

    Cartesian2.subtract(left, right, distanceScratch$1);
    return Cartesian2.magnitude(distanceScratch$1);
  };

  /**
   * Computes the squared distance between two points.  Comparing squared distances
   * using this function is more efficient than comparing distances using {@link Cartesian2#distance}.
   *
   * @param {Cartesian2} left The first point to compute the distance from.
   * @param {Cartesian2} 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.Cartesian2.distance(new Cesium.Cartesian2(1.0, 0.0), new Cesium.Cartesian2(3.0, 0.0));
   */
  Cartesian2.distanceSquared = function (left, right) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.object("left", left);
    Check.Check.typeOf.object("right", right);
    //>>includeEnd('debug');

    Cartesian2.subtract(left, right, distanceScratch$1);
    return Cartesian2.magnitudeSquared(distanceScratch$1);
  };

  /**
   * Computes the normalized form of the supplied Cartesian.
   *
   * @param {Cartesian2} cartesian The Cartesian to be normalized.
   * @param {Cartesian2} result The object onto which to store the result.
   * @returns {Cartesian2} The modified result parameter.
   */
  Cartesian2.normalize = function (cartesian, result) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.object("cartesian", cartesian);
    Check.Check.typeOf.object("result", result);
    //>>includeEnd('debug');

    var magnitude = Cartesian2.magnitude(cartesian);

    result.x = cartesian.x / magnitude;
    result.y = cartesian.y / magnitude;

    //>>includeStart('debug', pragmas.debug);
    if (isNaN(result.x) || isNaN(result.y)) {
      throw new Check.DeveloperError("normalized result is not a number");
    }
    //>>includeEnd('debug');

    return result;
  };

  /**
   * Computes the dot (scalar) product of two Cartesians.
   *
   * @param {Cartesian2} left The first Cartesian.
   * @param {Cartesian2} right The second Cartesian.
   * @returns {Number} The dot product.
   */
  Cartesian2.dot = function (left, right) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.object("left", left);
    Check.Check.typeOf.object("right", right);
    //>>includeEnd('debug');

    return left.x * right.x + left.y * right.y;
  };

  /**
   * Computes the componentwise product of two Cartesians.
   *
   * @param {Cartesian2} left The first Cartesian.
   * @param {Cartesian2} right The second Cartesian.
   * @param {Cartesian2} result The object onto which to store the result.
   * @returns {Cartesian2} The modified result parameter.
   */
  Cartesian2.multiplyComponents = function (left, right, result) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.object("left", left);
    Check.Check.typeOf.object("right", right);
    Check.Check.typeOf.object("result", result);
    //>>includeEnd('debug');

    result.x = left.x * right.x;
    result.y = left.y * right.y;
    return result;
  };

  /**
   * Computes the componentwise quotient of two Cartesians.
   *
   * @param {Cartesian2} left The first Cartesian.
   * @param {Cartesian2} right The second Cartesian.
   * @param {Cartesian2} result The object onto which to store the result.
   * @returns {Cartesian2} The modified result parameter.
   */
  Cartesian2.divideComponents = function (left, right, result) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.object("left", left);
    Check.Check.typeOf.object("right", right);
    Check.Check.typeOf.object("result", result);
    //>>includeEnd('debug');

    result.x = left.x / right.x;
    result.y = left.y / right.y;
    return result;
  };

  /**
   * Computes the componentwise sum of two Cartesians.
   *
   * @param {Cartesian2} left The first Cartesian.
   * @param {Cartesian2} right The second Cartesian.
   * @param {Cartesian2} result The object onto which to store the result.
   * @returns {Cartesian2} The modified result parameter.
   */
  Cartesian2.add = function (left, right, result) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.object("left", left);
    Check.Check.typeOf.object("right", right);
    Check.Check.typeOf.object("result", result);
    //>>includeEnd('debug');

    result.x = left.x + right.x;
    result.y = left.y + right.y;
    return result;
  };

  /**
   * Computes the componentwise difference of two Cartesians.
   *
   * @param {Cartesian2} left The first Cartesian.
   * @param {Cartesian2} right The second Cartesian.
   * @param {Cartesian2} result The object onto which to store the result.
   * @returns {Cartesian2} The modified result parameter.
   */
  Cartesian2.subtract = function (left, right, result) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.object("left", left);
    Check.Check.typeOf.object("right", right);
    Check.Check.typeOf.object("result", result);
    //>>includeEnd('debug');

    result.x = left.x - right.x;
    result.y = left.y - right.y;
    return result;
  };

  /**
   * Multiplies the provided Cartesian componentwise by the provided scalar.
   *
   * @param {Cartesian2} cartesian The Cartesian to be scaled.
   * @param {Number} scalar The scalar to multiply with.
   * @param {Cartesian2} result The object onto which to store the result.
   * @returns {Cartesian2} The modified result parameter.
   */
  Cartesian2.multiplyByScalar = function (cartesian, scalar, result) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.object("cartesian", cartesian);
    Check.Check.typeOf.number("scalar", scalar);
    Check.Check.typeOf.object("result", result);
    //>>includeEnd('debug');

    result.x = cartesian.x * scalar;
    result.y = cartesian.y * scalar;
    return result;
  };

  /**
   * Divides the provided Cartesian componentwise by the provided scalar.
   *
   * @param {Cartesian2} cartesian The Cartesian to be divided.
   * @param {Number} scalar The scalar to divide by.
   * @param {Cartesian2} result The object onto which to store the result.
   * @returns {Cartesian2} The modified result parameter.
   */
  Cartesian2.divideByScalar = function (cartesian, scalar, result) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.object("cartesian", cartesian);
    Check.Check.typeOf.number("scalar", scalar);
    Check.Check.typeOf.object("result", result);
    //>>includeEnd('debug');

    result.x = cartesian.x / scalar;
    result.y = cartesian.y / scalar;
    return result;
  };

  /**
   * Negates the provided Cartesian.
   *
   * @param {Cartesian2} cartesian The Cartesian to be negated.
   * @param {Cartesian2} result The object onto which to store the result.
   * @returns {Cartesian2} The modified result parameter.
   */
  Cartesian2.negate = function (cartesian, result) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.object("cartesian", cartesian);
    Check.Check.typeOf.object("result", result);
    //>>includeEnd('debug');

    result.x = -cartesian.x;
    result.y = -cartesian.y;
    return result;
  };

  /**
   * Computes the absolute value of the provided Cartesian.
   *
   * @param {Cartesian2} cartesian The Cartesian whose absolute value is to be computed.
   * @param {Cartesian2} result The object onto which to store the result.
   * @returns {Cartesian2} The modified result parameter.
   */
  Cartesian2.abs = function (cartesian, result) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.object("cartesian", cartesian);
    Check.Check.typeOf.object("result", result);
    //>>includeEnd('debug');

    result.x = Math.abs(cartesian.x);
    result.y = Math.abs(cartesian.y);
    return result;
  };

  var lerpScratch$1 = new Cartesian2();
  /**
   * Computes the linear interpolation or extrapolation at t using the provided cartesians.
   *
   * @param {Cartesian2} start The value corresponding to t at 0.0.
   * @param {Cartesian2} end The value corresponding to t at 1.0.
   * @param {Number} t The point along t at which to interpolate.
   * @param {Cartesian2} result The object onto which to store the result.
   * @returns {Cartesian2} The modified result parameter.
   */
  Cartesian2.lerp = function (start, end, t, result) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.object("start", start);
    Check.Check.typeOf.object("end", end);
    Check.Check.typeOf.number("t", t);
    Check.Check.typeOf.object("result", result);
    //>>includeEnd('debug');

    Cartesian2.multiplyByScalar(end, t, lerpScratch$1);
    result = Cartesian2.multiplyByScalar(start, 1.0 - t, result);
    return Cartesian2.add(lerpScratch$1, result, result);
  };

  var angleBetweenScratch$1 = new Cartesian2();
  var angleBetweenScratch2$1 = new Cartesian2();
  /**
   * Returns the angle, in radians, between the provided Cartesians.
   *
   * @param {Cartesian2} left The first Cartesian.
   * @param {Cartesian2} right The second Cartesian.
   * @returns {Number} The angle between the Cartesians.
   */
  Cartesian2.angleBetween = function (left, right) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.object("left", left);
    Check.Check.typeOf.object("right", right);
    //>>includeEnd('debug');

    Cartesian2.normalize(left, angleBetweenScratch$1);
    Cartesian2.normalize(right, angleBetweenScratch2$1);
    return _Math.CesiumMath.acosClamped(
      Cartesian2.dot(angleBetweenScratch$1, angleBetweenScratch2$1)
    );
  };

  var mostOrthogonalAxisScratch$1 = new Cartesian2();
  /**
   * Returns the axis that is most orthogonal to the provided Cartesian.
   *
   * @param {Cartesian2} cartesian The Cartesian on which to find the most orthogonal axis.
   * @param {Cartesian2} result The object onto which to store the result.
   * @returns {Cartesian2} The most orthogonal axis.
   */
  Cartesian2.mostOrthogonalAxis = function (cartesian, result) {
    //>>includeStart('debug', pragmas.debug);
    Check.Check.typeOf.object("cartesian", cartesian);
    Check.Check.typeOf.object("result", result);
    //>>includeEnd('debug');

    var f = Cartesian2.normalize(cartesian, mostOrthogonalAxisScratch$1);
    Cartesian2.abs(f, f);

    if (f.x <= f.y) {
      result = Cartesian2.clone(Cartesian2.UNIT_X, result);
    } else {
      result = Cartesian2.clone(Cartesian2.UNIT_Y, result);
    }

    return result;
  };

  /**
   * Compares the provided Cartesians componentwise and returns
   * <code>true</code> if they are equal, <code>false</code> otherwise.
   *
   * @param {Cartesian2} [left] The first Cartesian.
   * @param {Cartesian2} [right] The second Cartesian.
   * @returns {Boolean} <code>true</code> if left and right are equal, <code>false</code> otherwise.
   */
  Cartesian2.equals = function (left, right) {
    return (
      left === right ||
      (when.defined(left) &&
        when.defined(right) &&
        left.x === right.x &&
        left.y === right.y)
    );
  };

  /**
   * @private
   */
  Cartesian2.equalsArray = function (cartesian, array, offset) {
    return cartesian.x === array[offset] && cartesian.y === array[offset + 1];
  };

  /**
   * Compares the provided Cartesians componentwise and returns
   * <code>true</code> if they pass an absolute or relative tolerance test,
   * <code>false</code> otherwise.
   *
   * @param {Cartesian2} [left] The first Cartesian.
   * @param {Cartesian2} [right] The second Cartesian.
   * @param {Number} [relativeEpsilon=0] 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.
   */
  Cartesian2.equalsEpsilon = function (
    left,
    right,
    relativeEpsilon,
    absoluteEpsilon
  ) {
    return (
      left === right ||
      (when.defined(left) &&
        when.defined(right) &&
        _Math.CesiumMath.equalsEpsilon(
          left.x,
          right.x,
          relativeEpsilon,
          absoluteEpsilon
        ) &&
        _Math.CesiumMath.equalsEpsilon(
          left.y,
          right.y,
          relativeEpsilon,
          absoluteEpsilon
        ))
    );
  };

  /**
   * An immutable Cartesian2 instance initialized to (0.0, 0.0).
   *
   * @type {Cartesian2}
   * @constant
   */
  Cartesian2.ZERO = Object.freeze(new Cartesian2(0.0, 0.0));

  /**
   * An immutable Cartesian2 instance initialized to (1.0, 0.0).
   *
   * @type {Cartesian2}
   * @constant
   */
  Cartesian2.UNIT_X = Object.freeze(new Cartesian2(1.0, 0.0));

  /**
   * An immutable Cartesian2 instance initialized to (0.0, 1.0).
   *
   * @type {Cartesian2}
   * @constant
   */
  Cartesian2.UNIT_Y = Object.freeze(new Cartesian2(0.0, 1.0));

  /**
   * Duplicates this Cartesian2 instance.
   *
   * @param {Cartesian2} [result] The object onto which to store the result.
   * @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided.
   */
  Cartesian2.prototype.clone = function (result) {
    return Cartesian2.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 {Cartesian2} [right] The right hand side Cartesian.
   * @returns {Boolean} <code>true</code> if they are equal, <code>false</code> otherwise.
   */
  Cartesian2.prototype.equals = function (right) {
    return Cartesian2.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 {Cartesian2} [right] The right hand side Cartesian.
   * @param {Number} [relativeEpsilon=0] 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.
   */
  Cartesian2.prototype.equalsEpsilon = function (
    right,
    relativeEpsilon,
    absoluteEpsilon
  ) {
    return Cartesian2.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)'.
   */
  Cartesian2.prototype.toString = function () {
    return "(" + this.x + ", " + this.y + ")";
  };

  exports.Cartesian2 = Cartesian2;
  exports.Cartesian3 = Cartesian3;
  exports.Cartographic = Cartographic;
  exports.Ellipsoid = Ellipsoid;
  exports.Rectangle = Rectangle;

});
//# sourceMappingURL=Cartesian2-33d2657c.js.map