yclw/public/static/Build/Cesium/Workers/Cartographic-fe4be337.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-8d13db60', './Check-70bec281', './Math-61ede240'], 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.
     * @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;
        if (!when.defined(result)) {
            result = new Array(length * 3);
        } else {
            result.length = length * 3;
        }

        for (var i = 0; i < length; ++i) {
            Cartesian3.pack(array[i], result, i * 3);
        }
        return result;
    };

    /**
     * Unpacks an array of cartesian components into an array of Cartesian3s.
     *
     * @param {Number[]} array The array of components to unpack.
     * @param {Cartesian3[]} result The array onto which to store the result.
     * @returns {Cartesian3[]} The unpacked array.
     */
    Cartesian3.unpackArray = function(array, result) {
        //>>includeStart('debug', pragmas.debug);
        Check.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 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);
    var wgs84RadiiSquaredEx = new Cartesian3(6378137.0 * 6378137.0, 6378137.0 * 6378137.0, 6378137 * 6378137);

    /**
     * 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 : wgs84RadiiSquaredEx;

        if(_Math.CesiumMath.equalsEpsilon(_Math.CesiumMath.Radius, 6356752.3142451793, _Math.CesiumMath.EPSILON10))
        {
            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 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.
         *
         * @exports 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 wgs84OneOverRadiiEx = new Cartesian3(1.0 / 6378137.0, 1.0 / 6378137.0, 1.0 / 6378137.0);
    var wgs84OneOverRadiiSquared = new Cartesian3(1.0 / (6378137.0 * 6378137.0), 1.0 / (6378137.0 * 6378137.0), 1.0 / (6356752.3142451793 * 6356752.3142451793));
    var wgs84OneOverRadiiSquaredEx = new Cartesian3(1.0 / (6378137.0 * 6378137.0), 1.0 / (6378137.0 * 6378137.0), 1.0 / (6378137.0 * 6378137.0));
    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 : wgs84OneOverRadiiEx;
        var oneOverRadiiSquared = when.defined(ellipsoid) ? ellipsoid.oneOverRadiiSquared : wgs84OneOverRadiiSquaredEx;
        var centerToleranceSquared = when.defined(ellipsoid) ? ellipsoid._centerToleranceSquared : wgs84CenterToleranceSquared;

        if(_Math.CesiumMath.equalsEpsilon(_Math.CesiumMath.Radius, 6356752.3142451793, _Math.CesiumMath.EPSILON10)) {
            oneOverRadii = when.defined(ellipsoid) ? ellipsoid.oneOverRadii : wgs84OneOverRadii;
            oneOverRadiiSquared = when.defined(ellipsoid) ? ellipsoid.oneOverRadiiSquared : wgs84OneOverRadiiSquared;
        }

        //`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);
    };

    /**
     * Computes the distance between two points by global
     *
     * @param {Number} longitudeA The longitude, in degrees.
     * @param {Number} latitudeA The latitude, in degrees.
     * @param {Number} longitudeB The longitude, in degrees.
     * @param {Number} latitudeB The latitude, in degrees.
     */
    Cartographic.sphericalDistance = function(longitudeA, latitudeA, longitudeB, latitudeB) {
        Check.Check.defined('longitudeA', longitudeA);
        Check.Check.defined('longitudeB', longitudeB);
        Check.Check.defined('latitudeA', latitudeA);
        Check.Check.defined('latitudeB', latitudeB);

        if(longitudeA === longitudeB && latitudeA === latitudeB){
            return 0.0;
        }

        var latA = _Math.CesiumMath.toRadians(latitudeA);
        var latB = _Math.CesiumMath.toRadians(latitudeB);
        var lonA = _Math.CesiumMath.toRadians(longitudeA);
        var lonB = _Math.CesiumMath.toRadians(longitudeB);

        var a2 = lonA * lonA + latA * latA;
        var b2 = lonB * lonB + latB * latB;
        var c2 = (lonA - lonB) * (lonA - lonB) + (latA - latB) * (latA - latB);

        var dacos = (a2 + b2 - c2) / (2.0 * Math.sqrt(a2) * Math.sqrt(b2));
        dacos = _Math.CesiumMath.clamp(dacos, -1.0, 1.0);
        return Math.acos(dacos) * _Math.CesiumMath.Radius;
    };

    /**
     * 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 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) {
        //>>includeStart('debug', pragmas.debug);
        Check.Check.typeOf.number('epsilon', epsilon);
        //>>includeEnd('debug');

        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 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 + ')';
    };

    exports.Cartesian3 = Cartesian3;
    exports.Cartographic = Cartographic;
    exports.scaleToGeodeticSurface = scaleToGeodeticSurface;

});