Rectangle.js

/*global define*/
define([
        './Cartographic',
        './Check',
        './defaultValue',
        './defined',
        './defineProperties',
        './DeveloperError',
        './Ellipsoid',
        './freezeObject',
        './Math'
    ], function(
        Cartographic,
        Check,
        defaultValue,
        defined,
        defineProperties,
        DeveloperError,
        Ellipsoid,
        freezeObject,
        CesiumMath) {
    'use strict';

    /**
     * A two dimensional region specified as longitude and latitude coordinates.
     *
     * @alias Rectangle
     * @constructor
     *
     * @param {Number} [west=0.0] The westernmost longitude, in radians, in the range [-Pi, Pi].
     * @param {Number} [south=0.0] The southernmost latitude, in radians, in the range [-Pi/2, Pi/2].
     * @param {Number} [east=0.0] The easternmost longitude, in radians, in the range [-Pi, Pi].
     * @param {Number} [north=0.0] The northernmost latitude, in radians, in the range [-Pi/2, Pi/2].
     *
     * @see Packable
     */
    function Rectangle(west, south, east, north) {
        /**
         * The westernmost longitude in radians in the range [-Pi, Pi].
         *
         * @type {Number}
         * @default 0.0
         */
        this.west = defaultValue(west, 0.0);

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

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

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

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

        /**
         * Gets the height of the rectangle in radians.
         * @memberof Rectangle.prototype
         * @type {Number}
         */
        height : {
            get : function() {
                return Rectangle.computeHeight(this);
            }
        }
    });

    /**
     * The number of elements used to pack the object into an array.
     * @type {Number}
     */
    Rectangle.packedLength = 4;

    /**
     * Stores the provided instance into the provided array.
     *
     * @param {Rectangle} value The value to pack.
     * @param {Number[]} array The array to pack into.
     * @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
     *
     * @returns {Number[]} The array that was packed into
     */
    Rectangle.pack = function(value, array, startingIndex) {
        //>>includeStart('debug', pragmas.debug);
        Check.typeOf.object('value', value);
        Check.defined('array', array);
        //>>includeEnd('debug');

        startingIndex = defaultValue(startingIndex, 0);

        array[startingIndex++] = value.west;
        array[startingIndex++] = value.south;
        array[startingIndex++] = value.east;
        array[startingIndex] = value.north;

        return array;
    };

    /**
     * Retrieves an instance from a packed array.
     *
     * @param {Number[]} array The packed array.
     * @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
     * @param {Rectangle} [result] The object into which to store the result.
     * @returns {Rectangle} The modified result parameter or a new Rectangle instance if one was not provided.
     */
    Rectangle.unpack = function(array, startingIndex, result) {
        //>>includeStart('debug', pragmas.debug);
        Check.defined('array', array);
        //>>includeEnd('debug');

        startingIndex = defaultValue(startingIndex, 0);

        if (!defined(result)) {
            result = new Rectangle();
        }

        result.west = array[startingIndex++];
        result.south = array[startingIndex++];
        result.east = array[startingIndex++];
        result.north = array[startingIndex];
        return result;
    };

    /**
     * Computes the width of a rectangle in radians.
     * @param {Rectangle} rectangle The rectangle to compute the width of.
     * @returns {Number} The width.
     */
    Rectangle.computeWidth = function(rectangle) {
        //>>includeStart('debug', pragmas.debug);
        Check.typeOf.object('rectangle', rectangle);
        //>>includeEnd('debug');
        var east = rectangle.east;
        var west = rectangle.west;
        if (east < west) {
            east += CesiumMath.TWO_PI;
        }
        return east - west;
    };

    /**
     * Computes the height of a rectangle in radians.
     * @param {Rectangle} rectangle The rectangle to compute the height of.
     * @returns {Number} The height.
     */
    Rectangle.computeHeight = function(rectangle) {
        //>>includeStart('debug', pragmas.debug);
        Check.typeOf.object('rectangle', rectangle);
        //>>includeEnd('debug');
        return rectangle.north - rectangle.south;
    };

    /**
     * Creates an rectangle given the boundary longitude and latitude in degrees.
     *
     * @param {Number} [west=0.0] The westernmost longitude in degrees in the range [-180.0, 180.0].
     * @param {Number} [south=0.0] The southernmost latitude in degrees in the range [-90.0, 90.0].
     * @param {Number} [east=0.0] The easternmost longitude in degrees in the range [-180.0, 180.0].
     * @param {Number} [north=0.0] The northernmost latitude in degrees in the range [-90.0, 90.0].
     * @param {Rectangle} [result] The object onto which to store the result, or undefined if a new instance should be created.
     * @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided.
     *
     * @example
     * var rectangle = Cesium.Rectangle.fromDegrees(0.0, 20.0, 10.0, 30.0);
     */
    Rectangle.fromDegrees = function(west, south, east, north, result) {
        west = CesiumMath.toRadians(defaultValue(west, 0.0));
        south = CesiumMath.toRadians(defaultValue(south, 0.0));
        east = CesiumMath.toRadians(defaultValue(east, 0.0));
        north = CesiumMath.toRadians(defaultValue(north, 0.0));

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

        result.west = west;
        result.south = south;
        result.east = east;
        result.north = north;

        return result;
    };

    /**
     * Creates an rectangle given the boundary longitude and latitude in radians.
     *
     * @param {Number} [west=0.0] The westernmost longitude in radians in the range [-Math.PI, Math.PI].
     * @param {Number} [south=0.0] The southernmost latitude in radians in the range [-Math.PI/2, Math.PI/2].
     * @param {Number} [east=0.0] The easternmost longitude in radians in the range [-Math.PI, Math.PI].
     * @param {Number} [north=0.0] The northernmost latitude in radians in the range [-Math.PI/2, Math.PI/2].
     * @param {Rectangle} [result] The object onto which to store the result, or undefined if a new instance should be created.
     * @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided.
     *
     * @example
     * var rectangle = Cesium.Rectangle.fromRadians(0.0, Math.PI/4, Math.PI/8, 3*Math.PI/4);
     */
    Rectangle.fromRadians = function(west, south, east, north, result) {
        if (!defined(result)) {
            return new Rectangle(west, south, east, north);
        }

        result.west = defaultValue(west, 0.0);
        result.south = defaultValue(south, 0.0);
        result.east = defaultValue(east, 0.0);
        result.north = defaultValue(north, 0.0);

        return result;
    };

    /**
     * Creates the smallest possible Rectangle that encloses all positions in the provided array.
     *
     * @param {Cartographic[]} cartographics The list of Cartographic instances.
     * @param {Rectangle} [result] The object onto which to store the result, or undefined if a new instance should be created.
     * @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided.
     */
    Rectangle.fromCartographicArray = function(cartographics, result) {
        //>>includeStart('debug', pragmas.debug);
        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 +  CesiumMath.TWO_PI;
            westOverIDL = Math.min(westOverIDL, lonAdjusted);
            eastOverIDL = Math.max(eastOverIDL, lonAdjusted);
        }

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

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

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

        result.west = west;
        result.south = south;
        result.east = east;
        result.north = north;
        return result;
    };

    /**
     * Creates the smallest possible Rectangle that encloses all positions in the provided array.
     *
     * @param {Cartesian[]} 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.defined('cartesians', cartesians);
        //>>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 = cartesians.length; i < len; i++) {
            var position = ellipsoid.cartesianToCartographic(cartesians[i]);
            west = Math.min(west, position.longitude);
            east = Math.max(east, position.longitude);
            south = Math.min(south, position.latitude);
            north = Math.max(north, position.latitude);

            var lonAdjusted = position.longitude >= 0 ?  position.longitude : position.longitude +  CesiumMath.TWO_PI;
            westOverIDL = Math.min(westOverIDL, lonAdjusted);
            eastOverIDL = Math.max(eastOverIDL, lonAdjusted);
        }

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

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

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

        result.west = west;
        result.south = south;
        result.east = east;
        result.north = north;
        return result;
    };

    /**
     * Duplicates an Rectangle.
     *
     * @param {Rectangle} rectangle The rectangle to clone.
     * @param {Rectangle} [result] The object onto which to store the result, or undefined if a new instance should be created.
     * @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided. (Returns undefined if rectangle is undefined)
     */
    Rectangle.clone = function(rectangle, result) {
        if (!defined(rectangle)) {
            return undefined;
        }

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

        result.west = rectangle.west;
        result.south = rectangle.south;
        result.east = rectangle.east;
        result.north = rectangle.north;
        return result;
    };

    /**
     * Duplicates this Rectangle.
     *
     * @param {Rectangle} [result] The object onto which to store the result.
     * @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided.
     */
    Rectangle.prototype.clone = function(result) {
        return Rectangle.clone(this, result);
    };

    /**
     * Compares the provided Rectangle with this Rectangle componentwise and returns
     * <code>true</code> if they are equal, <code>false</code> otherwise.
     *
     * @param {Rectangle} [other] The Rectangle to compare.
     * @returns {Boolean} <code>true</code> if the Rectangles are equal, <code>false</code> otherwise.
     */
    Rectangle.prototype.equals = function(other) {
        return Rectangle.equals(this, other);
    };

    /**
     * Compares the provided rectangles and returns <code>true</code> if they are equal,
     * <code>false</code> otherwise.
     *
     * @param {Rectangle} [left] The first Rectangle.
     * @param {Rectangle} [right] The second Rectangle.
     * @returns {Boolean} <code>true</code> if left and right are equal; otherwise <code>false</code>.
     */
    Rectangle.equals = function(left, right) {
        return (left === right) ||
               ((defined(left)) &&
                (defined(right)) &&
                (left.west === right.west) &&
                (left.south === right.south) &&
                (left.east === right.east) &&
                (left.north === right.north));
    };

    /**
     * Compares the provided Rectangle with this Rectangle componentwise and returns
     * <code>true</code> if they are within the provided epsilon,
     * <code>false</code> otherwise.
     *
     * @param {Rectangle} [other] The Rectangle to compare.
     * @param {Number} epsilon The epsilon to use for equality testing.
     * @returns {Boolean} <code>true</code> if the Rectangles are within the provided epsilon, <code>false</code> otherwise.
     */
    Rectangle.prototype.equalsEpsilon = function(other, epsilon) {
        //>>includeStart('debug', pragmas.debug);
        Check.typeOf.number('epsilon', epsilon);
        //>>includeEnd('debug');

        return defined(other) &&
               (Math.abs(this.west - other.west) <= epsilon) &&
               (Math.abs(this.south - other.south) <= epsilon) &&
               (Math.abs(this.east - other.east) <= epsilon) &&
               (Math.abs(this.north - other.north) <= epsilon);
    };

    /**
     * Checks an 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.typeOf.object('rectangle', rectangle);

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

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

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

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

    /**
     * Computes the southwest corner of an 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.typeOf.object('rectangle', rectangle);
        //>>includeEnd('debug');

        if (!defined(result)) {
            return new Cartographic(rectangle.west, rectangle.south);
        }
        result.longitude = rectangle.west;
        result.latitude = rectangle.south;
        result.height = 0.0;
        return result;
    };

    /**
     * Computes the northwest corner of an 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.typeOf.object('rectangle', rectangle);
        //>>includeEnd('debug');

        if (!defined(result)) {
            return new Cartographic(rectangle.west, rectangle.north);
        }
        result.longitude = rectangle.west;
        result.latitude = rectangle.north;
        result.height = 0.0;
        return result;
    };

    /**
     * Computes the northeast corner of an 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.typeOf.object('rectangle', rectangle);
        //>>includeEnd('debug');

        if (!defined(result)) {
            return new Cartographic(rectangle.east, rectangle.north);
        }
        result.longitude = rectangle.east;
        result.latitude = rectangle.north;
        result.height = 0.0;
        return result;
    };

    /**
     * Computes the southeast corner of an 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.typeOf.object('rectangle', rectangle);
        //>>includeEnd('debug');

        if (!defined(result)) {
            return new Cartographic(rectangle.east, rectangle.south);
        }
        result.longitude = rectangle.east;
        result.latitude = rectangle.south;
        result.height = 0.0;
        return result;
    };

    /**
     * Computes the center of an 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.typeOf.object('rectangle', rectangle);
        //>>includeEnd('debug');

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

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

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

        if (!defined(result)) {
            return new Cartographic(longitude, latitude);
        }

        result.longitude = longitude;
        result.latitude = latitude;
        result.height = 0.0;
        return result;
    };

    /**
     * Computes the intersection of two rectangles.  This function assumes that the rectangle's coordinates are
     * latitude and longitude in radians and produces a correct intersection, taking into account the fact that
     * the same angle can be represented with multiple values as well as the wrapping of longitude at the
     * anti-meridian.  For a simple intersection that ignores these factors and can be used with projected
     * coordinates, see {@link Rectangle.simpleIntersection}.
     *
     * @param {Rectangle} rectangle On rectangle to find an intersection
     * @param {Rectangle} otherRectangle Another rectangle to find an intersection
     * @param {Rectangle} [result] The object onto which to store the result.
     * @returns {Rectangle|undefined} The modified result parameter, a new Rectangle instance if none was provided or undefined if there is no intersection.
     */
    Rectangle.intersection = function(rectangle, otherRectangle, result) {
        //>>includeStart('debug', pragmas.debug);
        Check.typeOf.object('rectangle', rectangle);
        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 += CesiumMath.TWO_PI;
        } else if (otherRectangleEast < otherRectangleWest && rectangleEast > 0.0) {
            otherRectangleEast += CesiumMath.TWO_PI;
        }

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

        var west = CesiumMath.negativePiToPi(Math.max(rectangleWest, otherRectangleWest));
        var east = CesiumMath.negativePiToPi(Math.min(rectangleEast, otherRectangleEast));

        if ((rectangle.west < rectangle.east || otherRectangle.west < otherRectangle.east) && east <= west) {
            return undefined;
        }

        var south = Math.max(rectangle.south, otherRectangle.south);
        var north = Math.min(rectangle.north, otherRectangle.north);

        if (south >= north) {
            return undefined;
        }

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

    /**
     * Computes a simple intersection of two rectangles.  Unlike {@link Rectangle.intersection}, this function
     * does not attempt to put the angular coordinates into a consistent range or to account for crossing the
     * anti-meridian.  As such, it can be used for rectangles where the coordinates are not simply latitude
     * and longitude (i.e. projected coordinates).
     *
     * @param {Rectangle} rectangle On rectangle to find an intersection
     * @param {Rectangle} otherRectangle Another rectangle to find an intersection
     * @param {Rectangle} [result] The object onto which to store the result.
     * @returns {Rectangle|undefined} The modified result parameter, a new Rectangle instance if none was provided or undefined if there is no intersection.
     */
    Rectangle.simpleIntersection = function(rectangle, otherRectangle, result) {
        //>>includeStart('debug', pragmas.debug);
        Check.typeOf.object('rectangle', rectangle);
        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 (!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.typeOf.object('rectangle', rectangle);
        Check.typeOf.object('otherRectangle', otherRectangle);
        //>>includeEnd('debug');

        if (!defined(result)) {
            result = new Rectangle();
        }

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

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

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

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

        var west = CesiumMath.convertLongitudeRange(Math.min(rectangleWest, otherRectangleWest));
        var east = CesiumMath.convertLongitudeRange(Math.max(rectangleEast, otherRectangleEast));

        result.west = west;
        result.south = Math.min(rectangle.south, otherRectangle.south);
        result.east = east;
        result.north = Math.max(rectangle.north, otherRectangle.north);

        return result;
    };

    /**
     * Computes a rectangle by enlarging the provided rectangle until it contains the provided cartographic.
     *
     * @param {Rectangle} rectangle A rectangle to expand.
     * @param {Cartographic} cartographic A cartographic to enclose in a rectangle.
     * @param {Rectangle} [result] The object onto which to store the result.
     * @returns {Rectangle} The modified result parameter or a new Rectangle instance if one was not provided.
     */
    Rectangle.expand = function(rectangle, cartographic, result) {
        //>>includeStart('debug', pragmas.debug);
        Check.typeOf.object('rectangle', rectangle);
        Check.typeOf.object('cartographic', cartographic);
        //>>includeEnd('debug');

        if (!defined(result)) {
            result = new Rectangle();
        }

        result.west = Math.min(rectangle.west, cartographic.longitude);
        result.south = Math.min(rectangle.south, cartographic.latitude);
        result.east = Math.max(rectangle.east, cartographic.longitude);
        result.north = Math.max(rectangle.north, cartographic.latitude);

        return result;
    };

    /**
     * Returns true if the cartographic is on or inside the rectangle, false otherwise.
     *
     * @param {Rectangle} rectangle The rectangle
     * @param {Cartographic} cartographic The cartographic to test.
     * @returns {Boolean} true if the provided cartographic is inside the rectangle, false otherwise.
     */
    Rectangle.contains = function(rectangle, cartographic) {
        //>>includeStart('debug', pragmas.debug);
        Check.typeOf.object('rectangle', rectangle);
        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 += CesiumMath.TWO_PI;
            if (longitude < 0.0) {
                longitude += CesiumMath.TWO_PI;
            }
        }
        return (longitude > west || CesiumMath.equalsEpsilon(longitude, west, CesiumMath.EPSILON14)) &&
               (longitude < east || CesiumMath.equalsEpsilon(longitude, east, CesiumMath.EPSILON14)) &&
               latitude >= rectangle.south &&
               latitude <= rectangle.north;
    };

    var subsampleLlaScratch = new Cartographic();
    /**
     * Samples an 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.typeOf.object('rectangle', rectangle);
        //>>includeEnd('debug');

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

        if (!defined(result)) {
            result = [];
        }
        var length = 0;

        var north = rectangle.north;
        var south = rectangle.south;
        var east = rectangle.east;
        var west = rectangle.west;

        var lla = subsampleLlaScratch;
        lla.height = surfaceHeight;

        lla.longitude = west;
        lla.latitude = north;
        result[length] = ellipsoid.cartographicToCartesian(lla, result[length]);
        length++;

        lla.longitude = east;
        result[length] = ellipsoid.cartographicToCartesian(lla, result[length]);
        length++;

        lla.latitude = south;
        result[length] = ellipsoid.cartographicToCartesian(lla, result[length]);
        length++;

        lla.longitude = west;
        result[length] = ellipsoid.cartographicToCartesian(lla, result[length]);
        length++;

        if (north < 0.0) {
            lla.latitude = north;
        } else if (south > 0.0) {
            lla.latitude = south;
        } else {
            lla.latitude = 0.0;
        }

        for ( var i = 1; i < 8; ++i) {
            lla.longitude = -Math.PI + i * CesiumMath.PI_OVER_TWO;
            if (Rectangle.contains(rectangle, lla)) {
                result[length] = ellipsoid.cartographicToCartesian(lla, result[length]);
                length++;
            }
        }

        if (lla.latitude === 0.0) {
            lla.longitude = west;
            result[length] = ellipsoid.cartographicToCartesian(lla, result[length]);
            length++;
            lla.longitude = east;
            result[length] = ellipsoid.cartographicToCartesian(lla, result[length]);
            length++;
        }
        result.length = length;
        return result;
    };

    /**
     * The largest possible rectangle.
     *
     * @type {Rectangle}
     * @constant
    */
    Rectangle.MAX_VALUE = freezeObject(new Rectangle(-Math.PI, -CesiumMath.PI_OVER_TWO, Math.PI, CesiumMath.PI_OVER_TWO));

    return Rectangle;
});