Cartesian2.js

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

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

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

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

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

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

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

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

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

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

    /**
     * Stores the provided instance into the provided array.
     *
     * @param {Cartesian2} value The value to pack.
     * @param {Number[]} array The array to pack into.
     * @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
     *
     * @returns {Number[]} The array that was packed into
     */
    Cartesian2.pack = function(value, array, startingIndex) {
        //>>includeStart('debug', pragmas.debug);
        if (!defined(value)) {
            throw new DeveloperError('value is required');
        }
        if (!defined(array)) {
            throw new DeveloperError('array is required');
        }
        //>>includeEnd('debug');

        startingIndex = defaultValue(startingIndex, 0);

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

        return array;
    };

    /**
     * Retrieves an instance from a packed array.
     *
     * @param {Number[]} array The packed array.
     * @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
     * @param {Cartesian2} [result] The object into which to store the result.
     * @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided.
     */
    Cartesian2.unpack = function(array, startingIndex, result) {
        //>>includeStart('debug', pragmas.debug);
        if (!defined(array)) {
            throw new DeveloperError('array is required');
        }
        //>>includeEnd('debug');

        startingIndex = defaultValue(startingIndex, 0);

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

    /**
     * Flattens an array of Cartesian2s into and array of components.
     *
     * @param {Cartesian2[]} array The array of cartesians to pack.
     * @param {Number[]} result The array onto which to store the result.
     * @returns {Number[]} The packed array.
     */
    Cartesian2.packArray = function(array, result) {
        //>>includeStart('debug', pragmas.debug);
        if (!defined(array)) {
            throw new DeveloperError('array is required');
        }
        //>>includeEnd('debug');

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

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

    /**
     * Unpacks an array of cartesian components into and array of Cartesian2s.
     *
     * @param {Number[]} array The array of components to unpack.
     * @param {Cartesian2[]} result The array onto which to store the result.
     * @returns {Cartesian2[]} The unpacked array.
     */
    Cartesian2.unpackArray = function(array, result) {
        //>>includeStart('debug', pragmas.debug);
        if (!defined(array)) {
            throw new DeveloperError('array is required');
        }
        //>>includeEnd('debug');

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

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

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

    /**
     * Computes the value of the maximum component for the supplied Cartesian.
     *
     * @param {Cartesian2} cartesian The cartesian to use.
     * @returns {Number} The value of the maximum component.
     */
    Cartesian2.maximumComponent = function(cartesian) {
        //>>includeStart('debug', pragmas.debug);
        if (!defined(cartesian)) {
            throw new DeveloperError('cartesian is required');
        }
        //>>includeEnd('debug');

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

    /**
     * Computes the value of the minimum component for the supplied Cartesian.
     *
     * @param {Cartesian2} cartesian The cartesian to use.
     * @returns {Number} The value of the minimum component.
     */
    Cartesian2.minimumComponent = function(cartesian) {
        //>>includeStart('debug', pragmas.debug);
        if (!defined(cartesian)) {
            throw new DeveloperError('cartesian is required');
        }
        //>>includeEnd('debug');

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

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


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

        return result;
    };

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

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

    /**
     * Computes the provided Cartesian's squared magnitude.
     *
     * @param {Cartesian2} cartesian The Cartesian instance whose squared magnitude is to be computed.
     * @returns {Number} The squared magnitude.
     */
    Cartesian2.magnitudeSquared = function(cartesian) {
        //>>includeStart('debug', pragmas.debug);
        if (!defined(cartesian)) {
            throw new DeveloperError('cartesian is required');
        }
        //>>includeEnd('debug');

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

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

    var distanceScratch = new Cartesian2();

    /**
     * Computes the distance between two points.
     *
     * @param {Cartesian2} left The first point to compute the distance from.
     * @param {Cartesian2} right The second point to compute the distance to.
     * @returns {Number} The distance between two points.
     *
     * @example
     * // Returns 1.0
     * var d = Cesium.Cartesian2.distance(new Cesium.Cartesian2(1.0, 0.0), new Cesium.Cartesian2(2.0, 0.0));
     */
    Cartesian2.distance = function(left, right) {
        //>>includeStart('debug', pragmas.debug);
        if (!defined(left) || !defined(right)) {
            throw new DeveloperError('left and right are required.');
        }
        //>>includeEnd('debug');

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

    /**
     * Computes the squared distance between two points.  Comparing squared distances
     * using this function is more efficient than comparing distances using {@link Cartesian2#distance}.
     *
     * @param {Cartesian2} left The first point to compute the distance from.
     * @param {Cartesian2} right The second point to compute the distance to.
     * @returns {Number} The distance between two points.
     *
     * @example
     * // Returns 4.0, not 2.0
     * var d = Cesium.Cartesian2.distance(new Cesium.Cartesian2(1.0, 0.0), new Cesium.Cartesian2(3.0, 0.0));
     */
    Cartesian2.distanceSquared = function(left, right) {
        //>>includeStart('debug', pragmas.debug);
        if (!defined(left) || !defined(right)) {
            throw new DeveloperError('left and right are required.');
        }
        //>>includeEnd('debug');

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

    /**
     * Computes the normalized form of the supplied Cartesian.
     *
     * @param {Cartesian2} cartesian The Cartesian to be normalized.
     * @param {Cartesian2} result The object onto which to store the result.
     * @returns {Cartesian2} The modified result parameter.
     */
    Cartesian2.normalize = function(cartesian, result) {
        //>>includeStart('debug', pragmas.debug);
        if (!defined(cartesian)) {
            throw new DeveloperError('cartesian is required');
        }
        if (!defined(result)) {
            throw new DeveloperError('result is required');
        }
        //>>includeEnd('debug');

        var magnitude = Cartesian2.magnitude(cartesian);

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

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

        return result;
    };

    /**
     * Computes the dot (scalar) product of two Cartesians.
     *
     * @param {Cartesian2} left The first Cartesian.
     * @param {Cartesian2} right The second Cartesian.
     * @returns {Number} The dot product.
     */
    Cartesian2.dot = function(left, right) {
        //>>includeStart('debug', pragmas.debug);
        if (!defined(left)) {
            throw new DeveloperError('left is required');
        }
        if (!defined(right)) {
            throw new DeveloperError('right is required');
        }
        //>>includeEnd('debug');

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

    /**
     * Computes the componentwise product of two Cartesians.
     *
     * @param {Cartesian2} left The first Cartesian.
     * @param {Cartesian2} right The second Cartesian.
     * @param {Cartesian2} result The object onto which to store the result.
     * @returns {Cartesian2} The modified result parameter.
     */
    Cartesian2.multiplyComponents = function(left, right, result) {
        //>>includeStart('debug', pragmas.debug);
        if (!defined(left)) {
            throw new DeveloperError('left is required');
        }
        if (!defined(right)) {
            throw new DeveloperError('right is required');
        }
        if (!defined(result)) {
            throw new DeveloperError('result is required');
        }
        //>>includeEnd('debug');

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

    /**
     * Computes the componentwise quotient of two Cartesians.
     *
     * @param {Cartesian2} left The first Cartesian.
     * @param {Cartesian2} right The second Cartesian.
     * @param {Cartesian2} result The object onto which to store the result.
     * @returns {Cartesian2} The modified result parameter.
     */
    Cartesian2.divideComponents = function(left, right, result) {
        //>>includeStart('debug', pragmas.debug);
        if (!defined(left)) {
            throw new DeveloperError('left is required');
        }
        if (!defined(right)) {
            throw new DeveloperError('right is required');
        }
        if (!defined(result)) {
            throw new DeveloperError('result is required');
        }
        //>>includeEnd('debug');

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

    /**
     * Computes the componentwise sum of two Cartesians.
     *
     * @param {Cartesian2} left The first Cartesian.
     * @param {Cartesian2} right The second Cartesian.
     * @param {Cartesian2} result The object onto which to store the result.
     * @returns {Cartesian2} The modified result parameter.
     */
    Cartesian2.add = function(left, right, result) {
        //>>includeStart('debug', pragmas.debug);
        if (!defined(left)) {
            throw new DeveloperError('left is required');
        }
        if (!defined(right)) {
            throw new DeveloperError('right is required');
        }
        if (!defined(result)) {
            throw new DeveloperError('result is required');
        }
        //>>includeEnd('debug');

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

    /**
     * Computes the componentwise difference of two Cartesians.
     *
     * @param {Cartesian2} left The first Cartesian.
     * @param {Cartesian2} right The second Cartesian.
     * @param {Cartesian2} result The object onto which to store the result.
     * @returns {Cartesian2} The modified result parameter.
     */
    Cartesian2.subtract = function(left, right, result) {
        //>>includeStart('debug', pragmas.debug);
        if (!defined(left)) {
            throw new DeveloperError('left is required');
        }
        if (!defined(right)) {
            throw new DeveloperError('right is required');
        }
        if (!defined(result)) {
            throw new DeveloperError('result is required');
        }
        //>>includeEnd('debug');

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

    /**
     * Multiplies the provided Cartesian componentwise by the provided scalar.
     *
     * @param {Cartesian2} cartesian The Cartesian to be scaled.
     * @param {Number} scalar The scalar to multiply with.
     * @param {Cartesian2} result The object onto which to store the result.
     * @returns {Cartesian2} The modified result parameter.
     */
    Cartesian2.multiplyByScalar = function(cartesian, scalar, result) {
        //>>includeStart('debug', pragmas.debug);
        if (!defined(cartesian)) {
            throw new DeveloperError('cartesian is required');
        }
        if (typeof scalar !== 'number') {
            throw new DeveloperError('scalar is required and must be a number.');
        }
        if (!defined(result)) {
            throw new DeveloperError('result is required');
        }
        //>>includeEnd('debug');

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

    /**
     * Divides the provided Cartesian componentwise by the provided scalar.
     *
     * @param {Cartesian2} cartesian The Cartesian to be divided.
     * @param {Number} scalar The scalar to divide by.
     * @param {Cartesian2} result The object onto which to store the result.
     * @returns {Cartesian2} The modified result parameter.
     */
    Cartesian2.divideByScalar = function(cartesian, scalar, result) {
        //>>includeStart('debug', pragmas.debug);
        if (!defined(cartesian)) {
            throw new DeveloperError('cartesian is required');
        }
        if (typeof scalar !== 'number') {
            throw new DeveloperError('scalar is required and must be a number.');
        }
        if (!defined(result)) {
            throw new DeveloperError('result is required');
        }
        //>>includeEnd('debug');

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

    /**
     * Negates the provided Cartesian.
     *
     * @param {Cartesian2} cartesian The Cartesian to be negated.
     * @param {Cartesian2} result The object onto which to store the result.
     * @returns {Cartesian2} The modified result parameter.
     */
    Cartesian2.negate = function(cartesian, result) {
        //>>includeStart('debug', pragmas.debug);
        if (!defined(cartesian)) {
            throw new DeveloperError('cartesian is required');
        }
        if (!defined(result)) {
            throw new DeveloperError('result is required');
        }
        //>>includeEnd('debug');

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

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

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

    var lerpScratch = new Cartesian2();
    /**
     * Computes the linear interpolation or extrapolation at t using the provided cartesians.
     *
     * @param {Cartesian2} start The value corresponding to t at 0.0.
     * @param {Cartesian2} end The value corresponding to t at 1.0.
     * @param {Number} t The point along t at which to interpolate.
     * @param {Cartesian2} result The object onto which to store the result.
     * @returns {Cartesian2} The modified result parameter.
     */
    Cartesian2.lerp = function(start, end, t, result) {
        //>>includeStart('debug', pragmas.debug);
        if (!defined(start)) {
            throw new DeveloperError('start is required.');
        }
        if (!defined(end)) {
            throw new DeveloperError('end is required.');
        }
        if (typeof t !== 'number') {
            throw new DeveloperError('t is required and must be a number.');
        }
        if (!defined(result)) {
            throw new DeveloperError('result is required.');
        }
        //>>includeEnd('debug');

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

    var angleBetweenScratch = new Cartesian2();
    var angleBetweenScratch2 = new Cartesian2();
    /**
     * Returns the angle, in radians, between the provided Cartesians.
     *
     * @param {Cartesian2} left The first Cartesian.
     * @param {Cartesian2} right The second Cartesian.
     * @returns {Number} The angle between the Cartesians.
     */
    Cartesian2.angleBetween = function(left, right) {
        //>>includeStart('debug', pragmas.debug);
        if (!defined(left)) {
            throw new DeveloperError('left is required');
        }
        if (!defined(right)) {
            throw new DeveloperError('right is required');
        }
        //>>includeEnd('debug');

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

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

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

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

        return result;
    };

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

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

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

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

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

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

    /**
     * Duplicates this Cartesian2 instance.
     *
     * @param {Cartesian2} [result] The object onto which to store the result.
     * @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided.
     */
    Cartesian2.prototype.clone = function(result) {
        return Cartesian2.clone(this, result);
    };

    /**
     * Compares this Cartesian against the provided Cartesian componentwise and returns
     * <code>true</code> if they are equal, <code>false</code> otherwise.
     *
     * @param {Cartesian2} [right] The right hand side Cartesian.
     * @returns {Boolean} <code>true</code> if they are equal, <code>false</code> otherwise.
     */
    Cartesian2.prototype.equals = function(right) {
        return Cartesian2.equals(this, right);
    };

    /**
     * Compares this Cartesian against the provided Cartesian componentwise and returns
     * <code>true</code> if they pass an absolute or relative tolerance test,
     * <code>false</code> otherwise.
     *
     * @param {Cartesian2} [right] The right hand side Cartesian.
     * @param {Number} relativeEpsilon The relative epsilon tolerance to use for equality testing.
     * @param {Number} [absoluteEpsilon=relativeEpsilon] The absolute epsilon tolerance to use for equality testing.
     * @returns {Boolean} <code>true</code> if they are within the provided epsilon, <code>false</code> otherwise.
     */
    Cartesian2.prototype.equalsEpsilon = function(right, relativeEpsilon, absoluteEpsilon) {
        return Cartesian2.equalsEpsilon(this, right, relativeEpsilon, absoluteEpsilon);
    };

    /**
     * Creates a string representing this Cartesian in the format '(x, y)'.
     *
     * @returns {String} A string representing the provided Cartesian in the format '(x, y)'.
     */
    Cartesian2.prototype.toString = function() {
        return '(' + this.x + ', ' + this.y + ')';
    };

    return Cartesian2;
});