/** * Cesium - https://github.com/CesiumGS/cesium * * Copyright 2011-2020 Cesium Contributors * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. * * Columbus View (Pat. Pend.) * * Portions licensed separately. * See https://github.com/CesiumGS/cesium/blob/master/LICENSE.md for full licensing details. */ define(['exports', './when-54c2dc71', './Check-6c0211bc', './Math-1124a290'], function (exports, when, Check, _Math) { 'use strict'; /** * A 3D Cartesian point. * @alias Cartesian3 * @constructor * * @param {Number} [x=0.0] The X component. * @param {Number} [y=0.0] The Y component. * @param {Number} [z=0.0] The Z component. * * @see Cartesian2 * @see Cartesian4 * @see Packable */ function Cartesian3(x, y, z) { /** * The X component. * @type {Number} * @default 0.0 */ this.x = when.defaultValue(x, 0.0); /** * The Y component. * @type {Number} * @default 0.0 */ this.y = when.defaultValue(y, 0.0); /** * The Z component. * @type {Number} * @default 0.0 */ this.z = when.defaultValue(z, 0.0); } /** * Converts the provided Spherical into Cartesian3 coordinates. * * @param {Spherical} spherical The Spherical to be converted to Cartesian3. * @param {Cartesian3} [result] The object onto which to store the result. * @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if one was not provided. */ Cartesian3.fromSpherical = function (spherical, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("spherical", spherical); //>>includeEnd('debug'); if (!when.defined(result)) { result = new Cartesian3(); } var clock = spherical.clock; var cone = spherical.cone; var magnitude = when.defaultValue(spherical.magnitude, 1.0); var radial = magnitude * Math.sin(cone); result.x = radial * Math.cos(clock); result.y = radial * Math.sin(clock); result.z = magnitude * Math.cos(cone); return result; }; /** * Creates a Cartesian3 instance from x, y and z coordinates. * * @param {Number} x The x coordinate. * @param {Number} y The y coordinate. * @param {Number} z The z coordinate. * @param {Cartesian3} [result] The object onto which to store the result. * @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if one was not provided. */ Cartesian3.fromElements = function (x, y, z, result) { if (!when.defined(result)) { return new Cartesian3(x, y, z); } result.x = x; result.y = y; result.z = z; return result; }; /** * Duplicates a Cartesian3 instance. * * @param {Cartesian3} cartesian The Cartesian to duplicate. * @param {Cartesian3} [result] The object onto which to store the result. * @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if one was not provided. (Returns undefined if cartesian is undefined) */ Cartesian3.clone = function (cartesian, result) { if (!when.defined(cartesian)) { return undefined; } if (!when.defined(result)) { return new Cartesian3(cartesian.x, cartesian.y, cartesian.z); } result.x = cartesian.x; result.y = cartesian.y; result.z = cartesian.z; return result; }; /** * Creates a Cartesian3 instance from an existing Cartesian4. This simply takes the * x, y, and z properties of the Cartesian4 and drops w. * @function * * @param {Cartesian4} cartesian The Cartesian4 instance to create a Cartesian3 instance from. * @param {Cartesian3} [result] The object onto which to store the result. * @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if one was not provided. */ Cartesian3.fromCartesian4 = Cartesian3.clone; /** * The number of elements used to pack the object into an array. * @type {Number} */ Cartesian3.packedLength = 3; /** * Stores the provided instance into the provided array. * * @param {Cartesian3} value The value to pack. * @param {Number[]} array The array to pack into. * @param {Number} [startingIndex=0] The index into the array at which to start packing the elements. * * @returns {Number[]} The array that was packed into */ Cartesian3.pack = function (value, array, startingIndex) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("value", value); Check.Check.defined("array", array); //>>includeEnd('debug'); startingIndex = when.defaultValue(startingIndex, 0); array[startingIndex++] = value.x; array[startingIndex++] = value.y; array[startingIndex] = value.z; return array; }; /** * Retrieves an instance from a packed array. * * @param {Number[]} array The packed array. * @param {Number} [startingIndex=0] The starting index of the element to be unpacked. * @param {Cartesian3} [result] The object into which to store the result. * @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if one was not provided. */ Cartesian3.unpack = function (array, startingIndex, result) { //>>includeStart('debug', pragmas.debug); Check.Check.defined("array", array); //>>includeEnd('debug'); startingIndex = when.defaultValue(startingIndex, 0); if (!when.defined(result)) { result = new Cartesian3(); } result.x = array[startingIndex++]; result.y = array[startingIndex++]; result.z = array[startingIndex]; return result; }; /** * Flattens an array of Cartesian3s into an array of components. * * @param {Cartesian3[]} array The array of cartesians to pack. * @param {Number[]} [result] The array onto which to store the result. If this is a typed array, it must have array.length * 3 components, else a {@link DeveloperError} will be thrown. If it is a regular array, it will be resized to have (array.length * 3) elements. * @returns {Number[]} The packed array. */ Cartesian3.packArray = function (array, result) { //>>includeStart('debug', pragmas.debug); Check.Check.defined("array", array); //>>includeEnd('debug'); var length = array.length; var resultLength = length * 3; if (!when.defined(result)) { result = new Array(resultLength); } else if (!Array.isArray(result) && result.length !== resultLength) { throw new Check.DeveloperError( "If result is a typed array, it must have exactly array.length * 3 elements" ); } else if (result.length !== resultLength) { result.length = resultLength; } for (var i = 0; i < length; ++i) { Cartesian3.pack(array[i], result, i * 3); } return result; }; /** * Unpacks an array of cartesian components into an array of Cartesian3s. * * @param {Number[]} array The array of components to unpack. * @param {Cartesian3[]} [result] The array onto which to store the result. * @returns {Cartesian3[]} The unpacked array. */ Cartesian3.unpackArray = function (array, result) { //>>includeStart('debug', pragmas.debug); Check.Check.defined("array", array); Check.Check.typeOf.number.greaterThanOrEquals("array.length", array.length, 3); if (array.length % 3 !== 0) { throw new Check.DeveloperError("array length must be a multiple of 3."); } //>>includeEnd('debug'); var length = array.length; if (!when.defined(result)) { result = new Array(length / 3); } else { result.length = length / 3; } for (var i = 0; i < length; i += 3) { var index = i / 3; result[index] = Cartesian3.unpack(array, i, result[index]); } return result; }; /** * Creates a Cartesian3 from three consecutive elements in an array. * @function * * @param {Number[]} array The array whose three consecutive elements correspond to the x, y, and z components, respectively. * @param {Number} [startingIndex=0] The offset into the array of the first element, which corresponds to the x component. * @param {Cartesian3} [result] The object onto which to store the result. * @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if one was not provided. * * @example * // Create a Cartesian3 with (1.0, 2.0, 3.0) * var v = [1.0, 2.0, 3.0]; * var p = Cesium.Cartesian3.fromArray(v); * * // Create a Cartesian3 with (1.0, 2.0, 3.0) using an offset into an array * var v2 = [0.0, 0.0, 1.0, 2.0, 3.0]; * var p2 = Cesium.Cartesian3.fromArray(v2, 2); */ Cartesian3.fromArray = Cartesian3.unpack; /** * Computes the value of the maximum component for the supplied Cartesian. * * @param {Cartesian3} cartesian The cartesian to use. * @returns {Number} The value of the maximum component. */ Cartesian3.maximumComponent = function (cartesian) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("cartesian", cartesian); //>>includeEnd('debug'); return Math.max(cartesian.x, cartesian.y, cartesian.z); }; /** * Computes the value of the minimum component for the supplied Cartesian. * * @param {Cartesian3} cartesian The cartesian to use. * @returns {Number} The value of the minimum component. */ Cartesian3.minimumComponent = function (cartesian) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("cartesian", cartesian); //>>includeEnd('debug'); return Math.min(cartesian.x, cartesian.y, cartesian.z); }; /** * Compares two Cartesians and computes a Cartesian which contains the minimum components of the supplied Cartesians. * * @param {Cartesian3} first A cartesian to compare. * @param {Cartesian3} second A cartesian to compare. * @param {Cartesian3} result The object into which to store the result. * @returns {Cartesian3} A cartesian with the minimum components. */ Cartesian3.minimumByComponent = function (first, second, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("first", first); Check.Check.typeOf.object("second", second); Check.Check.typeOf.object("result", result); //>>includeEnd('debug'); result.x = Math.min(first.x, second.x); result.y = Math.min(first.y, second.y); result.z = Math.min(first.z, second.z); return result; }; /** * Compares two Cartesians and computes a Cartesian which contains the maximum components of the supplied Cartesians. * * @param {Cartesian3} first A cartesian to compare. * @param {Cartesian3} second A cartesian to compare. * @param {Cartesian3} result The object into which to store the result. * @returns {Cartesian3} A cartesian with the maximum components. */ Cartesian3.maximumByComponent = function (first, second, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("first", first); Check.Check.typeOf.object("second", second); Check.Check.typeOf.object("result", result); //>>includeEnd('debug'); result.x = Math.max(first.x, second.x); result.y = Math.max(first.y, second.y); result.z = Math.max(first.z, second.z); return result; }; /** * Computes the provided Cartesian's squared magnitude. * * @param {Cartesian3} cartesian The Cartesian instance whose squared magnitude is to be computed. * @returns {Number} The squared magnitude. */ Cartesian3.magnitudeSquared = function (cartesian) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("cartesian", cartesian); //>>includeEnd('debug'); return ( cartesian.x * cartesian.x + cartesian.y * cartesian.y + cartesian.z * cartesian.z ); }; /** * Computes the Cartesian's magnitude (length). * * @param {Cartesian3} cartesian The Cartesian instance whose magnitude is to be computed. * @returns {Number} The magnitude. */ Cartesian3.magnitude = function (cartesian) { return Math.sqrt(Cartesian3.magnitudeSquared(cartesian)); }; var distanceScratch = new Cartesian3(); /** * Computes the distance between two points. * * @param {Cartesian3} left The first point to compute the distance from. * @param {Cartesian3} right The second point to compute the distance to. * @returns {Number} The distance between two points. * * @example * // Returns 1.0 * var d = Cesium.Cartesian3.distance(new Cesium.Cartesian3(1.0, 0.0, 0.0), new Cesium.Cartesian3(2.0, 0.0, 0.0)); */ Cartesian3.distance = function (left, right) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("left", left); Check.Check.typeOf.object("right", right); //>>includeEnd('debug'); Cartesian3.subtract(left, right, distanceScratch); return Cartesian3.magnitude(distanceScratch); }; /** * Computes the squared distance between two points. Comparing squared distances * using this function is more efficient than comparing distances using {@link Cartesian3#distance}. * * @param {Cartesian3} left The first point to compute the distance from. * @param {Cartesian3} right The second point to compute the distance to. * @returns {Number} The distance between two points. * * @example * // Returns 4.0, not 2.0 * var d = Cesium.Cartesian3.distanceSquared(new Cesium.Cartesian3(1.0, 0.0, 0.0), new Cesium.Cartesian3(3.0, 0.0, 0.0)); */ Cartesian3.distanceSquared = function (left, right) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("left", left); Check.Check.typeOf.object("right", right); //>>includeEnd('debug'); Cartesian3.subtract(left, right, distanceScratch); return Cartesian3.magnitudeSquared(distanceScratch); }; /** * Computes the normalized form of the supplied Cartesian. * * @param {Cartesian3} cartesian The Cartesian to be normalized. * @param {Cartesian3} result The object onto which to store the result. * @returns {Cartesian3} The modified result parameter. */ Cartesian3.normalize = function (cartesian, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("cartesian", cartesian); Check.Check.typeOf.object("result", result); //>>includeEnd('debug'); var magnitude = Cartesian3.magnitude(cartesian); result.x = cartesian.x / magnitude; result.y = cartesian.y / magnitude; result.z = cartesian.z / magnitude; //>>includeStart('debug', pragmas.debug); if (isNaN(result.x) || isNaN(result.y) || isNaN(result.z)) { throw new Check.DeveloperError("normalized result is not a number"); } //>>includeEnd('debug'); return result; }; /** * Computes the dot (scalar) product of two Cartesians. * * @param {Cartesian3} left The first Cartesian. * @param {Cartesian3} right The second Cartesian. * @returns {Number} The dot product. */ Cartesian3.dot = function (left, right) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("left", left); Check.Check.typeOf.object("right", right); //>>includeEnd('debug'); return left.x * right.x + left.y * right.y + left.z * right.z; }; /** * Computes the componentwise product of two Cartesians. * * @param {Cartesian3} left The first Cartesian. * @param {Cartesian3} right The second Cartesian. * @param {Cartesian3} result The object onto which to store the result. * @returns {Cartesian3} The modified result parameter. */ Cartesian3.multiplyComponents = function (left, right, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("left", left); Check.Check.typeOf.object("right", right); Check.Check.typeOf.object("result", result); //>>includeEnd('debug'); result.x = left.x * right.x; result.y = left.y * right.y; result.z = left.z * right.z; return result; }; /** * Computes the componentwise quotient of two Cartesians. * * @param {Cartesian3} left The first Cartesian. * @param {Cartesian3} right The second Cartesian. * @param {Cartesian3} result The object onto which to store the result. * @returns {Cartesian3} The modified result parameter. */ Cartesian3.divideComponents = function (left, right, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("left", left); Check.Check.typeOf.object("right", right); Check.Check.typeOf.object("result", result); //>>includeEnd('debug'); result.x = left.x / right.x; result.y = left.y / right.y; result.z = left.z / right.z; return result; }; /** * Computes the componentwise sum of two Cartesians. * * @param {Cartesian3} left The first Cartesian. * @param {Cartesian3} right The second Cartesian. * @param {Cartesian3} result The object onto which to store the result. * @returns {Cartesian3} The modified result parameter. */ Cartesian3.add = function (left, right, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("left", left); Check.Check.typeOf.object("right", right); Check.Check.typeOf.object("result", result); //>>includeEnd('debug'); result.x = left.x + right.x; result.y = left.y + right.y; result.z = left.z + right.z; return result; }; /** * Computes the componentwise difference of two Cartesians. * * @param {Cartesian3} left The first Cartesian. * @param {Cartesian3} right The second Cartesian. * @param {Cartesian3} result The object onto which to store the result. * @returns {Cartesian3} The modified result parameter. */ Cartesian3.subtract = function (left, right, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("left", left); Check.Check.typeOf.object("right", right); Check.Check.typeOf.object("result", result); //>>includeEnd('debug'); result.x = left.x - right.x; result.y = left.y - right.y; result.z = left.z - right.z; return result; }; /** * Multiplies the provided Cartesian componentwise by the provided scalar. * * @param {Cartesian3} cartesian The Cartesian to be scaled. * @param {Number} scalar The scalar to multiply with. * @param {Cartesian3} result The object onto which to store the result. * @returns {Cartesian3} The modified result parameter. */ Cartesian3.multiplyByScalar = function (cartesian, scalar, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("cartesian", cartesian); Check.Check.typeOf.number("scalar", scalar); Check.Check.typeOf.object("result", result); //>>includeEnd('debug'); result.x = cartesian.x * scalar; result.y = cartesian.y * scalar; result.z = cartesian.z * scalar; return result; }; /** * Divides the provided Cartesian componentwise by the provided scalar. * * @param {Cartesian3} cartesian The Cartesian to be divided. * @param {Number} scalar The scalar to divide by. * @param {Cartesian3} result The object onto which to store the result. * @returns {Cartesian3} The modified result parameter. */ Cartesian3.divideByScalar = function (cartesian, scalar, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("cartesian", cartesian); Check.Check.typeOf.number("scalar", scalar); Check.Check.typeOf.object("result", result); //>>includeEnd('debug'); result.x = cartesian.x / scalar; result.y = cartesian.y / scalar; result.z = cartesian.z / scalar; return result; }; /** * Negates the provided Cartesian. * * @param {Cartesian3} cartesian The Cartesian to be negated. * @param {Cartesian3} result The object onto which to store the result. * @returns {Cartesian3} The modified result parameter. */ Cartesian3.negate = function (cartesian, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("cartesian", cartesian); Check.Check.typeOf.object("result", result); //>>includeEnd('debug'); result.x = -cartesian.x; result.y = -cartesian.y; result.z = -cartesian.z; return result; }; /** * Computes the absolute value of the provided Cartesian. * * @param {Cartesian3} cartesian The Cartesian whose absolute value is to be computed. * @param {Cartesian3} result The object onto which to store the result. * @returns {Cartesian3} The modified result parameter. */ Cartesian3.abs = function (cartesian, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("cartesian", cartesian); Check.Check.typeOf.object("result", result); //>>includeEnd('debug'); result.x = Math.abs(cartesian.x); result.y = Math.abs(cartesian.y); result.z = Math.abs(cartesian.z); return result; }; var lerpScratch = new Cartesian3(); /** * Computes the linear interpolation or extrapolation at t using the provided cartesians. * * @param {Cartesian3} start The value corresponding to t at 0.0. * @param {Cartesian3} end The value corresponding to t at 1.0. * @param {Number} t The point along t at which to interpolate. * @param {Cartesian3} result The object onto which to store the result. * @returns {Cartesian3} The modified result parameter. */ Cartesian3.lerp = function (start, end, t, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("start", start); Check.Check.typeOf.object("end", end); Check.Check.typeOf.number("t", t); Check.Check.typeOf.object("result", result); //>>includeEnd('debug'); Cartesian3.multiplyByScalar(end, t, lerpScratch); result = Cartesian3.multiplyByScalar(start, 1.0 - t, result); return Cartesian3.add(lerpScratch, result, result); }; var angleBetweenScratch = new Cartesian3(); var angleBetweenScratch2 = new Cartesian3(); /** * Returns the angle, in radians, between the provided Cartesians. * * @param {Cartesian3} left The first Cartesian. * @param {Cartesian3} right The second Cartesian. * @returns {Number} The angle between the Cartesians. */ Cartesian3.angleBetween = function (left, right) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("left", left); Check.Check.typeOf.object("right", right); //>>includeEnd('debug'); Cartesian3.normalize(left, angleBetweenScratch); Cartesian3.normalize(right, angleBetweenScratch2); var cosine = Cartesian3.dot(angleBetweenScratch, angleBetweenScratch2); var sine = Cartesian3.magnitude( Cartesian3.cross( angleBetweenScratch, angleBetweenScratch2, angleBetweenScratch ) ); return Math.atan2(sine, cosine); }; var mostOrthogonalAxisScratch = new Cartesian3(); /** * Returns the axis that is most orthogonal to the provided Cartesian. * * @param {Cartesian3} cartesian The Cartesian on which to find the most orthogonal axis. * @param {Cartesian3} result The object onto which to store the result. * @returns {Cartesian3} The most orthogonal axis. */ Cartesian3.mostOrthogonalAxis = function (cartesian, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("cartesian", cartesian); Check.Check.typeOf.object("result", result); //>>includeEnd('debug'); var f = Cartesian3.normalize(cartesian, mostOrthogonalAxisScratch); Cartesian3.abs(f, f); if (f.x <= f.y) { if (f.x <= f.z) { result = Cartesian3.clone(Cartesian3.UNIT_X, result); } else { result = Cartesian3.clone(Cartesian3.UNIT_Z, result); } } else if (f.y <= f.z) { result = Cartesian3.clone(Cartesian3.UNIT_Y, result); } else { result = Cartesian3.clone(Cartesian3.UNIT_Z, result); } return result; }; /** * Projects vector a onto vector b * @param {Cartesian3} a The vector that needs projecting * @param {Cartesian3} b The vector to project onto * @param {Cartesian3} result The result cartesian * @returns {Cartesian3} The modified result parameter */ Cartesian3.projectVector = function (a, b, result) { //>>includeStart('debug', pragmas.debug); Check.Check.defined("a", a); Check.Check.defined("b", b); Check.Check.defined("result", result); //>>includeEnd('debug'); var scalar = Cartesian3.dot(a, b) / Cartesian3.dot(b, b); return Cartesian3.multiplyByScalar(b, scalar, result); }; /** * Compares the provided Cartesians componentwise and returns * true if they are equal, false otherwise. * * @param {Cartesian3} [left] The first Cartesian. * @param {Cartesian3} [right] The second Cartesian. * @returns {Boolean} true if left and right are equal, false 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 * true if they pass an absolute or relative tolerance test, * false otherwise. * * @param {Cartesian3} [left] The first Cartesian. * @param {Cartesian3} [right] The second Cartesian. * @param {Number} [relativeEpsilon=0] The relative epsilon tolerance to use for equality testing. * @param {Number} [absoluteEpsilon=relativeEpsilon] The absolute epsilon tolerance to use for equality testing. * @returns {Boolean} true if left and right are within the provided epsilon, false otherwise. */ Cartesian3.equalsEpsilon = function ( left, right, relativeEpsilon, absoluteEpsilon ) { return ( left === right || (when.defined(left) && when.defined(right) && _Math.CesiumMath.equalsEpsilon( left.x, right.x, relativeEpsilon, absoluteEpsilon ) && _Math.CesiumMath.equalsEpsilon( left.y, right.y, relativeEpsilon, absoluteEpsilon ) && _Math.CesiumMath.equalsEpsilon( left.z, right.z, relativeEpsilon, absoluteEpsilon )) ); }; /** * Computes the cross (outer) product of two Cartesians. * * @param {Cartesian3} left The first Cartesian. * @param {Cartesian3} right The second Cartesian. * @param {Cartesian3} result The object onto which to store the result. * @returns {Cartesian3} The cross product. */ Cartesian3.cross = function (left, right, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("left", left); Check.Check.typeOf.object("right", right); Check.Check.typeOf.object("result", result); //>>includeEnd('debug'); var leftX = left.x; var leftY = left.y; var leftZ = left.z; var rightX = right.x; var rightY = right.y; var rightZ = right.z; var x = leftY * rightZ - leftZ * rightY; var y = leftZ * rightX - leftX * rightZ; var z = leftX * rightY - leftY * rightX; result.x = x; result.y = y; result.z = z; return result; }; /** * Computes the midpoint between the right and left Cartesian. * @param {Cartesian3} left The first Cartesian. * @param {Cartesian3} right The second Cartesian. * @param {Cartesian3} result The object onto which to store the result. * @returns {Cartesian3} The midpoint. */ Cartesian3.midpoint = function (left, right, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("left", left); Check.Check.typeOf.object("right", right); Check.Check.typeOf.object("result", result); //>>includeEnd('debug'); result.x = (left.x + right.x) * 0.5; result.y = (left.y + right.y) * 0.5; result.z = (left.z + right.z) * 0.5; return result; }; /** * Returns a Cartesian3 position from longitude and latitude values given in degrees. * * @param {Number} longitude The longitude, in degrees * @param {Number} latitude The latitude, in degrees * @param {Number} [height=0.0] The height, in meters, above the ellipsoid. * @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the position lies. * @param {Cartesian3} [result] The object onto which to store the result. * @returns {Cartesian3} The position * * @example * var position = Cesium.Cartesian3.fromDegrees(-115.0, 37.0); */ Cartesian3.fromDegrees = function ( longitude, latitude, height, ellipsoid, result ) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.number("longitude", longitude); Check.Check.typeOf.number("latitude", latitude); //>>includeEnd('debug'); longitude = _Math.CesiumMath.toRadians(longitude); latitude = _Math.CesiumMath.toRadians(latitude); return Cartesian3.fromRadians(longitude, latitude, height, ellipsoid, result); }; var scratchN = new Cartesian3(); var scratchK = new Cartesian3(); var wgs84RadiiSquared = new Cartesian3( 6378137.0 * 6378137.0, 6378137.0 * 6378137.0, 6356752.3142451793 * 6356752.3142451793 ); /** * Returns a Cartesian3 position from longitude and latitude values given in radians. * * @param {Number} longitude The longitude, in radians * @param {Number} latitude The latitude, in radians * @param {Number} [height=0.0] The height, in meters, above the ellipsoid. * @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the position lies. * @param {Cartesian3} [result] The object onto which to store the result. * @returns {Cartesian3} The position * * @example * var position = Cesium.Cartesian3.fromRadians(-2.007, 0.645); */ Cartesian3.fromRadians = function ( longitude, latitude, height, ellipsoid, result ) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.number("longitude", longitude); Check.Check.typeOf.number("latitude", latitude); //>>includeEnd('debug'); height = when.defaultValue(height, 0.0); var radiiSquared = when.defined(ellipsoid) ? ellipsoid.radiiSquared : wgs84RadiiSquared; var cosLatitude = Math.cos(latitude); scratchN.x = cosLatitude * Math.cos(longitude); scratchN.y = cosLatitude * Math.sin(longitude); scratchN.z = Math.sin(latitude); scratchN = Cartesian3.normalize(scratchN, scratchN); Cartesian3.multiplyComponents(radiiSquared, scratchN, scratchK); var gamma = Math.sqrt(Cartesian3.dot(scratchN, scratchK)); scratchK = Cartesian3.divideByScalar(scratchK, gamma, scratchK); scratchN = Cartesian3.multiplyByScalar(scratchN, height, scratchN); if (!when.defined(result)) { result = new Cartesian3(); } return Cartesian3.add(scratchK, scratchN, result); }; /** * Returns an array of Cartesian3 positions given an array of longitude and latitude values given in degrees. * * @param {Number[]} coordinates A list of longitude and latitude values. Values alternate [longitude, latitude, longitude, latitude...]. * @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the coordinates lie. * @param {Cartesian3[]} [result] An array of Cartesian3 objects to store the result. * @returns {Cartesian3[]} The array of positions. * * @example * var positions = Cesium.Cartesian3.fromDegreesArray([-115.0, 37.0, -107.0, 33.0]); */ Cartesian3.fromDegreesArray = function (coordinates, ellipsoid, result) { //>>includeStart('debug', pragmas.debug); Check.Check.defined("coordinates", coordinates); if (coordinates.length < 2 || coordinates.length % 2 !== 0) { throw new Check.DeveloperError( "the number of coordinates must be a multiple of 2 and at least 2" ); } //>>includeEnd('debug'); var length = coordinates.length; if (!when.defined(result)) { result = new Array(length / 2); } else { result.length = length / 2; } for (var i = 0; i < length; i += 2) { var longitude = coordinates[i]; var latitude = coordinates[i + 1]; var index = i / 2; result[index] = Cartesian3.fromDegrees( longitude, latitude, 0, ellipsoid, result[index] ); } return result; }; /** * Returns an array of Cartesian3 positions given an array of longitude and latitude values given in radians. * * @param {Number[]} coordinates A list of longitude and latitude values. Values alternate [longitude, latitude, longitude, latitude...]. * @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the coordinates lie. * @param {Cartesian3[]} [result] An array of Cartesian3 objects to store the result. * @returns {Cartesian3[]} The array of positions. * * @example * var positions = Cesium.Cartesian3.fromRadiansArray([-2.007, 0.645, -1.867, .575]); */ Cartesian3.fromRadiansArray = function (coordinates, ellipsoid, result) { //>>includeStart('debug', pragmas.debug); Check.Check.defined("coordinates", coordinates); if (coordinates.length < 2 || coordinates.length % 2 !== 0) { throw new Check.DeveloperError( "the number of coordinates must be a multiple of 2 and at least 2" ); } //>>includeEnd('debug'); var length = coordinates.length; if (!when.defined(result)) { result = new Array(length / 2); } else { result.length = length / 2; } for (var i = 0; i < length; i += 2) { var longitude = coordinates[i]; var latitude = coordinates[i + 1]; var index = i / 2; result[index] = Cartesian3.fromRadians( longitude, latitude, 0, ellipsoid, result[index] ); } return result; }; /** * Returns an array of Cartesian3 positions given an array of longitude, latitude and height values where longitude and latitude are given in degrees. * * @param {Number[]} coordinates A list of longitude, latitude and height values. Values alternate [longitude, latitude, height, longitude, latitude, height...]. * @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the position lies. * @param {Cartesian3[]} [result] An array of Cartesian3 objects to store the result. * @returns {Cartesian3[]} The array of positions. * * @example * var positions = Cesium.Cartesian3.fromDegreesArrayHeights([-115.0, 37.0, 100000.0, -107.0, 33.0, 150000.0]); */ Cartesian3.fromDegreesArrayHeights = function (coordinates, ellipsoid, result) { //>>includeStart('debug', pragmas.debug); Check.Check.defined("coordinates", coordinates); if (coordinates.length < 3 || coordinates.length % 3 !== 0) { throw new Check.DeveloperError( "the number of coordinates must be a multiple of 3 and at least 3" ); } //>>includeEnd('debug'); var length = coordinates.length; if (!when.defined(result)) { result = new Array(length / 3); } else { result.length = length / 3; } for (var i = 0; i < length; i += 3) { var longitude = coordinates[i]; var latitude = coordinates[i + 1]; var height = coordinates[i + 2]; var index = i / 3; result[index] = Cartesian3.fromDegrees( longitude, latitude, height, ellipsoid, result[index] ); } return result; }; /** * Returns an array of Cartesian3 positions given an array of longitude, latitude and height values where longitude and latitude are given in radians. * * @param {Number[]} coordinates A list of longitude, latitude and height values. Values alternate [longitude, latitude, height, longitude, latitude, height...]. * @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the position lies. * @param {Cartesian3[]} [result] An array of Cartesian3 objects to store the result. * @returns {Cartesian3[]} The array of positions. * * @example * var positions = Cesium.Cartesian3.fromRadiansArrayHeights([-2.007, 0.645, 100000.0, -1.867, .575, 150000.0]); */ Cartesian3.fromRadiansArrayHeights = function (coordinates, ellipsoid, result) { //>>includeStart('debug', pragmas.debug); Check.Check.defined("coordinates", coordinates); if (coordinates.length < 3 || coordinates.length % 3 !== 0) { throw new Check.DeveloperError( "the number of coordinates must be a multiple of 3 and at least 3" ); } //>>includeEnd('debug'); var length = coordinates.length; if (!when.defined(result)) { result = new Array(length / 3); } else { result.length = length / 3; } for (var i = 0; i < length; i += 3) { var longitude = coordinates[i]; var latitude = coordinates[i + 1]; var height = coordinates[i + 2]; var index = i / 3; result[index] = Cartesian3.fromRadians( longitude, latitude, height, ellipsoid, result[index] ); } return result; }; /** * An immutable Cartesian3 instance initialized to (0.0, 0.0, 0.0). * * @type {Cartesian3} * @constant */ Cartesian3.ZERO = Object.freeze(new Cartesian3(0.0, 0.0, 0.0)); /** * An immutable Cartesian3 instance initialized to (1.0, 0.0, 0.0). * * @type {Cartesian3} * @constant */ Cartesian3.UNIT_X = Object.freeze(new Cartesian3(1.0, 0.0, 0.0)); /** * An immutable Cartesian3 instance initialized to (0.0, 1.0, 0.0). * * @type {Cartesian3} * @constant */ Cartesian3.UNIT_Y = Object.freeze(new Cartesian3(0.0, 1.0, 0.0)); /** * An immutable Cartesian3 instance initialized to (0.0, 0.0, 1.0). * * @type {Cartesian3} * @constant */ Cartesian3.UNIT_Z = Object.freeze(new Cartesian3(0.0, 0.0, 1.0)); /** * Duplicates this Cartesian3 instance. * * @param {Cartesian3} [result] The object onto which to store the result. * @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if one was not provided. */ Cartesian3.prototype.clone = function (result) { return Cartesian3.clone(this, result); }; /** * Compares this Cartesian against the provided Cartesian componentwise and returns * true if they are equal, false otherwise. * * @param {Cartesian3} [right] The right hand side Cartesian. * @returns {Boolean} true if they are equal, false otherwise. */ Cartesian3.prototype.equals = function (right) { return Cartesian3.equals(this, right); }; /** * Compares this Cartesian against the provided Cartesian componentwise and returns * true if they pass an absolute or relative tolerance test, * false otherwise. * * @param {Cartesian3} [right] The right hand side Cartesian. * @param {Number} [relativeEpsilon=0] The relative epsilon tolerance to use for equality testing. * @param {Number} [absoluteEpsilon=relativeEpsilon] The absolute epsilon tolerance to use for equality testing. * @returns {Boolean} true if they are within the provided epsilon, false otherwise. */ Cartesian3.prototype.equalsEpsilon = function ( right, relativeEpsilon, absoluteEpsilon ) { return Cartesian3.equalsEpsilon( this, right, relativeEpsilon, absoluteEpsilon ); }; /** * Creates a string representing this Cartesian in the format '(x, y, z)'. * * @returns {String} A string representing this Cartesian in the format '(x, y, z)'. */ Cartesian3.prototype.toString = function () { return "(" + this.x + ", " + this.y + ", " + this.z + ")"; }; var scaleToGeodeticSurfaceIntersection = new Cartesian3(); var scaleToGeodeticSurfaceGradient = new Cartesian3(); /** * Scales the provided Cartesian position along the geodetic surface normal * so that it is on the surface of this ellipsoid. If the position is * at the center of the ellipsoid, this function returns undefined. * * @param {Cartesian3} cartesian The Cartesian position to scale. * @param {Cartesian3} oneOverRadii One over radii of the ellipsoid. * @param {Cartesian3} oneOverRadiiSquared One over radii squared of the ellipsoid. * @param {Number} centerToleranceSquared Tolerance for closeness to the center. * @param {Cartesian3} [result] The object onto which to store the result. * @returns {Cartesian3} The modified result parameter, a new Cartesian3 instance if none was provided, or undefined if the position is at the center. * * @function scaleToGeodeticSurface * * @private */ function scaleToGeodeticSurface( cartesian, oneOverRadii, oneOverRadiiSquared, centerToleranceSquared, result ) { //>>includeStart('debug', pragmas.debug); if (!when.defined(cartesian)) { throw new Check.DeveloperError("cartesian is required."); } if (!when.defined(oneOverRadii)) { throw new Check.DeveloperError("oneOverRadii is required."); } if (!when.defined(oneOverRadiiSquared)) { throw new Check.DeveloperError("oneOverRadiiSquared is required."); } if (!when.defined(centerToleranceSquared)) { throw new Check.DeveloperError("centerToleranceSquared is required."); } //>>includeEnd('debug'); var positionX = cartesian.x; var positionY = cartesian.y; var positionZ = cartesian.z; var oneOverRadiiX = oneOverRadii.x; var oneOverRadiiY = oneOverRadii.y; var oneOverRadiiZ = oneOverRadii.z; var x2 = positionX * positionX * oneOverRadiiX * oneOverRadiiX; var y2 = positionY * positionY * oneOverRadiiY * oneOverRadiiY; var z2 = positionZ * positionZ * oneOverRadiiZ * oneOverRadiiZ; // Compute the squared ellipsoid norm. var squaredNorm = x2 + y2 + z2; var ratio = Math.sqrt(1.0 / squaredNorm); // As an initial approximation, assume that the radial intersection is the projection point. var intersection = Cartesian3.multiplyByScalar( cartesian, ratio, scaleToGeodeticSurfaceIntersection ); // If the position is near the center, the iteration will not converge. if (squaredNorm < centerToleranceSquared) { return !isFinite(ratio) ? undefined : Cartesian3.clone(intersection, result); } var oneOverRadiiSquaredX = oneOverRadiiSquared.x; var oneOverRadiiSquaredY = oneOverRadiiSquared.y; var oneOverRadiiSquaredZ = oneOverRadiiSquared.z; // Use the gradient at the intersection point in place of the true unit normal. // The difference in magnitude will be absorbed in the multiplier. var gradient = scaleToGeodeticSurfaceGradient; gradient.x = intersection.x * oneOverRadiiSquaredX * 2.0; gradient.y = intersection.y * oneOverRadiiSquaredY * 2.0; gradient.z = intersection.z * oneOverRadiiSquaredZ * 2.0; // Compute the initial guess at the normal vector multiplier, lambda. var lambda = ((1.0 - ratio) * Cartesian3.magnitude(cartesian)) / (0.5 * Cartesian3.magnitude(gradient)); var correction = 0.0; var func; var denominator; var xMultiplier; var yMultiplier; var zMultiplier; var xMultiplier2; var yMultiplier2; var zMultiplier2; var xMultiplier3; var yMultiplier3; var zMultiplier3; do { lambda -= correction; xMultiplier = 1.0 / (1.0 + lambda * oneOverRadiiSquaredX); yMultiplier = 1.0 / (1.0 + lambda * oneOverRadiiSquaredY); zMultiplier = 1.0 / (1.0 + lambda * oneOverRadiiSquaredZ); xMultiplier2 = xMultiplier * xMultiplier; yMultiplier2 = yMultiplier * yMultiplier; zMultiplier2 = zMultiplier * zMultiplier; xMultiplier3 = xMultiplier2 * xMultiplier; yMultiplier3 = yMultiplier2 * yMultiplier; zMultiplier3 = zMultiplier2 * zMultiplier; func = x2 * xMultiplier2 + y2 * yMultiplier2 + z2 * zMultiplier2 - 1.0; // "denominator" here refers to the use of this expression in the velocity and acceleration // computations in the sections to follow. denominator = x2 * xMultiplier3 * oneOverRadiiSquaredX + y2 * yMultiplier3 * oneOverRadiiSquaredY + z2 * zMultiplier3 * oneOverRadiiSquaredZ; var derivative = -2.0 * denominator; correction = func / derivative; } while (Math.abs(func) > _Math.CesiumMath.EPSILON12); if (!when.defined(result)) { return new Cartesian3( positionX * xMultiplier, positionY * yMultiplier, positionZ * zMultiplier ); } result.x = positionX * xMultiplier; result.y = positionY * yMultiplier; result.z = positionZ * zMultiplier; return result; } /** * A position defined by longitude, latitude, and height. * @alias Cartographic * @constructor * * @param {Number} [longitude=0.0] The longitude, in radians. * @param {Number} [latitude=0.0] The latitude, in radians. * @param {Number} [height=0.0] The height, in meters, above the ellipsoid. * * @see Ellipsoid */ function Cartographic(longitude, latitude, height) { /** * The longitude, in radians. * @type {Number} * @default 0.0 */ this.longitude = when.defaultValue(longitude, 0.0); /** * The latitude, in radians. * @type {Number} * @default 0.0 */ this.latitude = when.defaultValue(latitude, 0.0); /** * The height, in meters, above the ellipsoid. * @type {Number} * @default 0.0 */ this.height = when.defaultValue(height, 0.0); } /** * Creates a new Cartographic instance from longitude and latitude * specified in radians. * * @param {Number} longitude The longitude, in radians. * @param {Number} latitude The latitude, in radians. * @param {Number} [height=0.0] The height, in meters, above the ellipsoid. * @param {Cartographic} [result] The object onto which to store the result. * @returns {Cartographic} The modified result parameter or a new Cartographic instance if one was not provided. */ Cartographic.fromRadians = function (longitude, latitude, height, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.number("longitude", longitude); Check.Check.typeOf.number("latitude", latitude); //>>includeEnd('debug'); height = when.defaultValue(height, 0.0); if (!when.defined(result)) { return new Cartographic(longitude, latitude, height); } result.longitude = longitude; result.latitude = latitude; result.height = height; return result; }; /** * Creates a new Cartographic instance from longitude and latitude * specified in degrees. The values in the resulting object will * be in radians. * * @param {Number} longitude The longitude, in degrees. * @param {Number} latitude The latitude, in degrees. * @param {Number} [height=0.0] The height, in meters, above the ellipsoid. * @param {Cartographic} [result] The object onto which to store the result. * @returns {Cartographic} The modified result parameter or a new Cartographic instance if one was not provided. */ Cartographic.fromDegrees = function (longitude, latitude, height, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.number("longitude", longitude); Check.Check.typeOf.number("latitude", latitude); //>>includeEnd('debug'); longitude = _Math.CesiumMath.toRadians(longitude); latitude = _Math.CesiumMath.toRadians(latitude); return Cartographic.fromRadians(longitude, latitude, height, result); }; var cartesianToCartographicN = new Cartesian3(); var cartesianToCartographicP = new Cartesian3(); var cartesianToCartographicH = new Cartesian3(); var wgs84OneOverRadii = new Cartesian3( 1.0 / 6378137.0, 1.0 / 6378137.0, 1.0 / 6356752.3142451793 ); var wgs84OneOverRadiiSquared = new Cartesian3( 1.0 / (6378137.0 * 6378137.0), 1.0 / (6378137.0 * 6378137.0), 1.0 / (6356752.3142451793 * 6356752.3142451793) ); var wgs84CenterToleranceSquared = _Math.CesiumMath.EPSILON1; /** * Creates a new Cartographic instance from a Cartesian position. The values in the * resulting object will be in radians. * * @param {Cartesian3} cartesian The Cartesian position to convert to cartographic representation. * @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the position lies. * @param {Cartographic} [result] The object onto which to store the result. * @returns {Cartographic} The modified result parameter, new Cartographic instance if none was provided, or undefined if the cartesian is at the center of the ellipsoid. */ Cartographic.fromCartesian = function (cartesian, ellipsoid, result) { var oneOverRadii = when.defined(ellipsoid) ? ellipsoid.oneOverRadii : wgs84OneOverRadii; var oneOverRadiiSquared = when.defined(ellipsoid) ? ellipsoid.oneOverRadiiSquared : wgs84OneOverRadiiSquared; var centerToleranceSquared = when.defined(ellipsoid) ? ellipsoid._centerToleranceSquared : wgs84CenterToleranceSquared; //`cartesian is required.` is thrown from scaleToGeodeticSurface var p = scaleToGeodeticSurface( cartesian, oneOverRadii, oneOverRadiiSquared, centerToleranceSquared, cartesianToCartographicP ); if (!when.defined(p)) { return undefined; } var n = Cartesian3.multiplyComponents( p, oneOverRadiiSquared, cartesianToCartographicN ); n = Cartesian3.normalize(n, n); var h = Cartesian3.subtract(cartesian, p, cartesianToCartographicH); var longitude = Math.atan2(n.y, n.x); var latitude = Math.asin(n.z); var height = _Math.CesiumMath.sign(Cartesian3.dot(h, cartesian)) * Cartesian3.magnitude(h); if (!when.defined(result)) { return new Cartographic(longitude, latitude, height); } result.longitude = longitude; result.latitude = latitude; result.height = height; return result; }; /** * Creates a new Cartesian3 instance from a Cartographic input. The values in the inputted * object should be in radians. * * @param {Cartographic} cartographic Input to be converted into a Cartesian3 output. * @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the position lies. * @param {Cartesian3} [result] The object onto which to store the result. * @returns {Cartesian3} The position */ Cartographic.toCartesian = function (cartographic, ellipsoid, result) { //>>includeStart('debug', pragmas.debug); Check.Check.defined("cartographic", cartographic); //>>includeEnd('debug'); return Cartesian3.fromRadians( cartographic.longitude, cartographic.latitude, cartographic.height, ellipsoid, result ); }; /** * Duplicates a Cartographic instance. * * @param {Cartographic} cartographic The cartographic to duplicate. * @param {Cartographic} [result] The object onto which to store the result. * @returns {Cartographic} The modified result parameter or a new Cartographic instance if one was not provided. (Returns undefined if cartographic is undefined) */ Cartographic.clone = function (cartographic, result) { if (!when.defined(cartographic)) { return undefined; } if (!when.defined(result)) { return new Cartographic( cartographic.longitude, cartographic.latitude, cartographic.height ); } result.longitude = cartographic.longitude; result.latitude = cartographic.latitude; result.height = cartographic.height; return result; }; /** * Compares the provided cartographics componentwise and returns * true if they are equal, false otherwise. * * @param {Cartographic} [left] The first cartographic. * @param {Cartographic} [right] The second cartographic. * @returns {Boolean} true if left and right are equal, false 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 * true if they are within the provided epsilon, * false otherwise. * * @param {Cartographic} [left] The first cartographic. * @param {Cartographic} [right] The second cartographic. * @param {Number} [epsilon=0] The epsilon to use for equality testing. * @returns {Boolean} true if left and right are within the provided epsilon, false otherwise. */ Cartographic.equalsEpsilon = function (left, right, epsilon) { epsilon = when.defaultValue(epsilon, 0); return ( left === right || (when.defined(left) && when.defined(right) && Math.abs(left.longitude - right.longitude) <= epsilon && Math.abs(left.latitude - right.latitude) <= epsilon && Math.abs(left.height - right.height) <= epsilon) ); }; /** * An immutable Cartographic instance initialized to (0.0, 0.0, 0.0). * * @type {Cartographic} * @constant */ Cartographic.ZERO = Object.freeze(new Cartographic(0.0, 0.0, 0.0)); /** * Duplicates this instance. * * @param {Cartographic} [result] The object onto which to store the result. * @returns {Cartographic} The modified result parameter or a new Cartographic instance if one was not provided. */ Cartographic.prototype.clone = function (result) { return Cartographic.clone(this, result); }; /** * Compares the provided against this cartographic componentwise and returns * true if they are equal, false otherwise. * * @param {Cartographic} [right] The second cartographic. * @returns {Boolean} true if left and right are equal, false otherwise. */ Cartographic.prototype.equals = function (right) { return Cartographic.equals(this, right); }; /** * Compares the provided against this cartographic componentwise and returns * true if they are within the provided epsilon, * false otherwise. * * @param {Cartographic} [right] The second cartographic. * @param {Number} [epsilon=0] The epsilon to use for equality testing. * @returns {Boolean} true if left and right are within the provided epsilon, false otherwise. */ Cartographic.prototype.equalsEpsilon = function (right, epsilon) { return Cartographic.equalsEpsilon(this, right, epsilon); }; /** * Creates a string representing this cartographic in the format '(longitude, latitude, height)'. * * @returns {String} A string representing the provided cartographic in the format '(longitude, latitude, height)'. */ Cartographic.prototype.toString = function () { return "(" + this.longitude + ", " + this.latitude + ", " + this.height + ")"; }; function initialize(ellipsoid, x, y, z) { x = when.defaultValue(x, 0.0); y = when.defaultValue(y, 0.0); z = when.defaultValue(z, 0.0); //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.number.greaterThanOrEquals("x", x, 0.0); Check.Check.typeOf.number.greaterThanOrEquals("y", y, 0.0); Check.Check.typeOf.number.greaterThanOrEquals("z", z, 0.0); //>>includeEnd('debug'); ellipsoid._radii = new Cartesian3(x, y, z); ellipsoid._radiiSquared = new Cartesian3(x * x, y * y, z * z); ellipsoid._radiiToTheFourth = new Cartesian3( x * x * x * x, y * y * y * y, z * z * z * z ); ellipsoid._oneOverRadii = new Cartesian3( x === 0.0 ? 0.0 : 1.0 / x, y === 0.0 ? 0.0 : 1.0 / y, z === 0.0 ? 0.0 : 1.0 / z ); ellipsoid._oneOverRadiiSquared = new Cartesian3( x === 0.0 ? 0.0 : 1.0 / (x * x), y === 0.0 ? 0.0 : 1.0 / (y * y), z === 0.0 ? 0.0 : 1.0 / (z * z) ); ellipsoid._minimumRadius = Math.min(x, y, z); ellipsoid._maximumRadius = Math.max(x, y, z); ellipsoid._centerToleranceSquared = _Math.CesiumMath.EPSILON1; if (ellipsoid._radiiSquared.z !== 0) { ellipsoid._squaredXOverSquaredZ = ellipsoid._radiiSquared.x / ellipsoid._radiiSquared.z; } } /** * A quadratic surface defined in Cartesian coordinates by the equation * (x / a)^2 + (y / b)^2 + (z / c)^2 = 1. Primarily used * by Cesium to represent the shape of planetary bodies. * * Rather than constructing this object directly, one of the provided * constants is normally used. * @alias Ellipsoid * @constructor * * @param {Number} [x=0] The radius in the x direction. * @param {Number} [y=0] The radius in the y direction. * @param {Number} [z=0] The radius in the z direction. * * @exception {DeveloperError} All radii components must be greater than or equal to zero. * * @see Ellipsoid.fromCartesian3 * @see Ellipsoid.WGS84 * @see Ellipsoid.UNIT_SPHERE */ function Ellipsoid(x, y, z) { this._radii = undefined; this._radiiSquared = undefined; this._radiiToTheFourth = undefined; this._oneOverRadii = undefined; this._oneOverRadiiSquared = undefined; this._minimumRadius = undefined; this._maximumRadius = undefined; this._centerToleranceSquared = undefined; this._squaredXOverSquaredZ = undefined; initialize(this, x, y, z); } Object.defineProperties(Ellipsoid.prototype, { /** * Gets the radii of the ellipsoid. * @memberof Ellipsoid.prototype * @type {Cartesian3} * @readonly */ radii: { get: function () { return this._radii; }, }, /** * Gets the squared radii of the ellipsoid. * @memberof Ellipsoid.prototype * @type {Cartesian3} * @readonly */ radiiSquared: { get: function () { return this._radiiSquared; }, }, /** * Gets the radii of the ellipsoid raise to the fourth power. * @memberof Ellipsoid.prototype * @type {Cartesian3} * @readonly */ radiiToTheFourth: { get: function () { return this._radiiToTheFourth; }, }, /** * Gets one over the radii of the ellipsoid. * @memberof Ellipsoid.prototype * @type {Cartesian3} * @readonly */ oneOverRadii: { get: function () { return this._oneOverRadii; }, }, /** * Gets one over the squared radii of the ellipsoid. * @memberof Ellipsoid.prototype * @type {Cartesian3} * @readonly */ oneOverRadiiSquared: { get: function () { return this._oneOverRadiiSquared; }, }, /** * Gets the minimum radius of the ellipsoid. * @memberof Ellipsoid.prototype * @type {Number} * @readonly */ minimumRadius: { get: function () { return this._minimumRadius; }, }, /** * Gets the maximum radius of the ellipsoid. * @memberof Ellipsoid.prototype * @type {Number} * @readonly */ maximumRadius: { get: function () { return this._maximumRadius; }, }, }); /** * Duplicates an Ellipsoid instance. * * @param {Ellipsoid} ellipsoid The ellipsoid to duplicate. * @param {Ellipsoid} [result] The object onto which to store the result, or undefined if a new * instance should be created. * @returns {Ellipsoid} The cloned Ellipsoid. (Returns undefined if ellipsoid is undefined) */ Ellipsoid.clone = function (ellipsoid, result) { if (!when.defined(ellipsoid)) { return undefined; } var radii = ellipsoid._radii; if (!when.defined(result)) { return new Ellipsoid(radii.x, radii.y, radii.z); } Cartesian3.clone(radii, result._radii); Cartesian3.clone(ellipsoid._radiiSquared, result._radiiSquared); Cartesian3.clone(ellipsoid._radiiToTheFourth, result._radiiToTheFourth); Cartesian3.clone(ellipsoid._oneOverRadii, result._oneOverRadii); Cartesian3.clone(ellipsoid._oneOverRadiiSquared, result._oneOverRadiiSquared); result._minimumRadius = ellipsoid._minimumRadius; result._maximumRadius = ellipsoid._maximumRadius; result._centerToleranceSquared = ellipsoid._centerToleranceSquared; return result; }; /** * Computes an Ellipsoid from a Cartesian specifying the radii in x, y, and z directions. * * @param {Cartesian3} [cartesian=Cartesian3.ZERO] The ellipsoid's radius in the x, y, and z directions. * @param {Ellipsoid} [result] The object onto which to store the result, or undefined if a new * instance should be created. * @returns {Ellipsoid} A new Ellipsoid instance. * * @exception {DeveloperError} All radii components must be greater than or equal to zero. * * @see Ellipsoid.WGS84 * @see Ellipsoid.UNIT_SPHERE */ Ellipsoid.fromCartesian3 = function (cartesian, result) { if (!when.defined(result)) { result = new Ellipsoid(); } if (!when.defined(cartesian)) { return result; } initialize(result, cartesian.x, cartesian.y, cartesian.z); return result; }; /** * An Ellipsoid instance initialized to the WGS84 standard. * * @type {Ellipsoid} * @constant */ Ellipsoid.WGS84 = Object.freeze( new Ellipsoid(6378137.0, 6378137.0, 6356752.3142451793) ); /** * An Ellipsoid instance initialized to radii of (1.0, 1.0, 1.0). * * @type {Ellipsoid} * @constant */ Ellipsoid.UNIT_SPHERE = Object.freeze(new Ellipsoid(1.0, 1.0, 1.0)); /** * An Ellipsoid instance initialized to a sphere with the lunar radius. * * @type {Ellipsoid} * @constant */ Ellipsoid.MOON = Object.freeze( new Ellipsoid( _Math.CesiumMath.LUNAR_RADIUS, _Math.CesiumMath.LUNAR_RADIUS, _Math.CesiumMath.LUNAR_RADIUS ) ); /** * Duplicates an Ellipsoid instance. * * @param {Ellipsoid} [result] The object onto which to store the result, or undefined if a new * instance should be created. * @returns {Ellipsoid} The cloned Ellipsoid. */ Ellipsoid.prototype.clone = function (result) { return Ellipsoid.clone(this, result); }; /** * The number of elements used to pack the object into an array. * @type {Number} */ Ellipsoid.packedLength = Cartesian3.packedLength; /** * Stores the provided instance into the provided array. * * @param {Ellipsoid} value The value to pack. * @param {Number[]} array The array to pack into. * @param {Number} [startingIndex=0] The index into the array at which to start packing the elements. * * @returns {Number[]} The array that was packed into */ Ellipsoid.pack = function (value, array, startingIndex) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("value", value); Check.Check.defined("array", array); //>>includeEnd('debug'); startingIndex = when.defaultValue(startingIndex, 0); Cartesian3.pack(value._radii, array, startingIndex); return array; }; /** * Retrieves an instance from a packed array. * * @param {Number[]} array The packed array. * @param {Number} [startingIndex=0] The starting index of the element to be unpacked. * @param {Ellipsoid} [result] The object into which to store the result. * @returns {Ellipsoid} The modified result parameter or a new Ellipsoid instance if one was not provided. */ Ellipsoid.unpack = function (array, startingIndex, result) { //>>includeStart('debug', pragmas.debug); Check.Check.defined("array", array); //>>includeEnd('debug'); startingIndex = when.defaultValue(startingIndex, 0); var radii = Cartesian3.unpack(array, startingIndex); return Ellipsoid.fromCartesian3(radii, result); }; /** * Computes the unit vector directed from the center of this ellipsoid toward the provided Cartesian position. * @function * * @param {Cartesian3} cartesian The Cartesian for which to to determine the geocentric normal. * @param {Cartesian3} [result] The object onto which to store the result. * @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if none was provided. */ Ellipsoid.prototype.geocentricSurfaceNormal = Cartesian3.normalize; /** * Computes the normal of the plane tangent to the surface of the ellipsoid at the provided position. * * @param {Cartographic} cartographic The cartographic position for which to to determine the geodetic normal. * @param {Cartesian3} [result] The object onto which to store the result. * @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if none was provided. */ Ellipsoid.prototype.geodeticSurfaceNormalCartographic = function ( cartographic, result ) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("cartographic", cartographic); //>>includeEnd('debug'); var longitude = cartographic.longitude; var latitude = cartographic.latitude; var cosLatitude = Math.cos(latitude); var x = cosLatitude * Math.cos(longitude); var y = cosLatitude * Math.sin(longitude); var z = Math.sin(latitude); if (!when.defined(result)) { result = new Cartesian3(); } result.x = x; result.y = y; result.z = z; return Cartesian3.normalize(result, result); }; /** * Computes the normal of the plane tangent to the surface of the ellipsoid at the provided position. * * @param {Cartesian3} cartesian The Cartesian position for which to to determine the surface normal. * @param {Cartesian3} [result] The object onto which to store the result. * @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if none was provided. */ Ellipsoid.prototype.geodeticSurfaceNormal = function (cartesian, result) { if ( Cartesian3.equalsEpsilon(cartesian, Cartesian3.ZERO, _Math.CesiumMath.EPSILON14) ) { return undefined; } if (!when.defined(result)) { result = new Cartesian3(); } result = Cartesian3.multiplyComponents( cartesian, this._oneOverRadiiSquared, result ); return Cartesian3.normalize(result, result); }; var cartographicToCartesianNormal = new Cartesian3(); var cartographicToCartesianK = new Cartesian3(); /** * Converts the provided cartographic to Cartesian representation. * * @param {Cartographic} cartographic The cartographic position. * @param {Cartesian3} [result] The object onto which to store the result. * @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if none was provided. * * @example * //Create a Cartographic and determine it's Cartesian representation on a WGS84 ellipsoid. * var position = new Cesium.Cartographic(Cesium.Math.toRadians(21), Cesium.Math.toRadians(78), 5000); * var cartesianPosition = Cesium.Ellipsoid.WGS84.cartographicToCartesian(position); */ Ellipsoid.prototype.cartographicToCartesian = function (cartographic, result) { //`cartographic is required` is thrown from geodeticSurfaceNormalCartographic. var n = cartographicToCartesianNormal; var k = cartographicToCartesianK; this.geodeticSurfaceNormalCartographic(cartographic, n); Cartesian3.multiplyComponents(this._radiiSquared, n, k); var gamma = Math.sqrt(Cartesian3.dot(n, k)); Cartesian3.divideByScalar(k, gamma, k); Cartesian3.multiplyByScalar(n, cartographic.height, n); if (!when.defined(result)) { result = new Cartesian3(); } return Cartesian3.add(k, n, result); }; /** * Converts the provided array of cartographics to an array of Cartesians. * * @param {Cartographic[]} cartographics An array of cartographic positions. * @param {Cartesian3[]} [result] The object onto which to store the result. * @returns {Cartesian3[]} The modified result parameter or a new Array instance if none was provided. * * @example * //Convert an array of Cartographics and determine their Cartesian representation on a WGS84 ellipsoid. * var positions = [new Cesium.Cartographic(Cesium.Math.toRadians(21), Cesium.Math.toRadians(78), 0), * new Cesium.Cartographic(Cesium.Math.toRadians(21.321), Cesium.Math.toRadians(78.123), 100), * new Cesium.Cartographic(Cesium.Math.toRadians(21.645), Cesium.Math.toRadians(78.456), 250)]; * var cartesianPositions = Cesium.Ellipsoid.WGS84.cartographicArrayToCartesianArray(positions); */ Ellipsoid.prototype.cartographicArrayToCartesianArray = function ( cartographics, result ) { //>>includeStart('debug', pragmas.debug); Check.Check.defined("cartographics", cartographics); //>>includeEnd('debug') var length = cartographics.length; if (!when.defined(result)) { result = new Array(length); } else { result.length = length; } for (var i = 0; i < length; i++) { result[i] = this.cartographicToCartesian(cartographics[i], result[i]); } return result; }; var cartesianToCartographicN$1 = new Cartesian3(); var cartesianToCartographicP$1 = new Cartesian3(); var cartesianToCartographicH$1 = new Cartesian3(); /** * Converts the provided cartesian to cartographic representation. * The cartesian is undefined at the center of the ellipsoid. * * @param {Cartesian3} cartesian The Cartesian position to convert to cartographic representation. * @param {Cartographic} [result] The object onto which to store the result. * @returns {Cartographic} The modified result parameter, new Cartographic instance if none was provided, or undefined if the cartesian is at the center of the ellipsoid. * * @example * //Create a Cartesian and determine it's Cartographic representation on a WGS84 ellipsoid. * var position = new Cesium.Cartesian3(17832.12, 83234.52, 952313.73); * var cartographicPosition = Cesium.Ellipsoid.WGS84.cartesianToCartographic(position); */ Ellipsoid.prototype.cartesianToCartographic = function (cartesian, result) { //`cartesian is required.` is thrown from scaleToGeodeticSurface var p = this.scaleToGeodeticSurface(cartesian, cartesianToCartographicP$1); if (!when.defined(p)) { return undefined; } var n = this.geodeticSurfaceNormal(p, cartesianToCartographicN$1); var h = Cartesian3.subtract(cartesian, p, cartesianToCartographicH$1); var longitude = Math.atan2(n.y, n.x); var latitude = Math.asin(n.z); var height = _Math.CesiumMath.sign(Cartesian3.dot(h, cartesian)) * Cartesian3.magnitude(h); if (!when.defined(result)) { return new Cartographic(longitude, latitude, height); } result.longitude = longitude; result.latitude = latitude; result.height = height; return result; }; /** * Converts the provided array of cartesians to an array of cartographics. * * @param {Cartesian3[]} cartesians An array of Cartesian positions. * @param {Cartographic[]} [result] The object onto which to store the result. * @returns {Cartographic[]} The modified result parameter or a new Array instance if none was provided. * * @example * //Create an array of Cartesians and determine their Cartographic representation on a WGS84 ellipsoid. * var positions = [new Cesium.Cartesian3(17832.12, 83234.52, 952313.73), * new Cesium.Cartesian3(17832.13, 83234.53, 952313.73), * new Cesium.Cartesian3(17832.14, 83234.54, 952313.73)] * var cartographicPositions = Cesium.Ellipsoid.WGS84.cartesianArrayToCartographicArray(positions); */ Ellipsoid.prototype.cartesianArrayToCartographicArray = function ( cartesians, result ) { //>>includeStart('debug', pragmas.debug); Check.Check.defined("cartesians", cartesians); //>>includeEnd('debug'); var length = cartesians.length; if (!when.defined(result)) { result = new Array(length); } else { result.length = length; } for (var i = 0; i < length; ++i) { result[i] = this.cartesianToCartographic(cartesians[i], result[i]); } return result; }; /** * Scales the provided Cartesian position along the geodetic surface normal * so that it is on the surface of this ellipsoid. If the position is * at the center of the ellipsoid, this function returns undefined. * * @param {Cartesian3} cartesian The Cartesian position to scale. * @param {Cartesian3} [result] The object onto which to store the result. * @returns {Cartesian3} The modified result parameter, a new Cartesian3 instance if none was provided, or undefined if the position is at the center. */ Ellipsoid.prototype.scaleToGeodeticSurface = function (cartesian, result) { return scaleToGeodeticSurface( cartesian, this._oneOverRadii, this._oneOverRadiiSquared, this._centerToleranceSquared, result ); }; /** * Scales the provided Cartesian position along the geocentric surface normal * so that it is on the surface of this ellipsoid. * * @param {Cartesian3} cartesian The Cartesian position to scale. * @param {Cartesian3} [result] The object onto which to store the result. * @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if none was provided. */ Ellipsoid.prototype.scaleToGeocentricSurface = function (cartesian, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("cartesian", cartesian); //>>includeEnd('debug'); if (!when.defined(result)) { result = new Cartesian3(); } var positionX = cartesian.x; var positionY = cartesian.y; var positionZ = cartesian.z; var oneOverRadiiSquared = this._oneOverRadiiSquared; var beta = 1.0 / Math.sqrt( positionX * positionX * oneOverRadiiSquared.x + positionY * positionY * oneOverRadiiSquared.y + positionZ * positionZ * oneOverRadiiSquared.z ); return Cartesian3.multiplyByScalar(cartesian, beta, result); }; /** * Transforms a Cartesian X, Y, Z position to the ellipsoid-scaled space by multiplying * its components by the result of {@link Ellipsoid#oneOverRadii}. * * @param {Cartesian3} position The position to transform. * @param {Cartesian3} [result] The position to which to copy the result, or undefined to create and * return a new instance. * @returns {Cartesian3} The position expressed in the scaled space. The returned instance is the * one passed as the result parameter if it is not undefined, or a new instance of it is. */ Ellipsoid.prototype.transformPositionToScaledSpace = function ( position, result ) { if (!when.defined(result)) { result = new Cartesian3(); } return Cartesian3.multiplyComponents(position, this._oneOverRadii, result); }; /** * Transforms a Cartesian X, Y, Z position from the ellipsoid-scaled space by multiplying * its components by the result of {@link Ellipsoid#radii}. * * @param {Cartesian3} position The position to transform. * @param {Cartesian3} [result] The position to which to copy the result, or undefined to create and * return a new instance. * @returns {Cartesian3} The position expressed in the unscaled space. The returned instance is the * one passed as the result parameter if it is not undefined, or a new instance of it is. */ Ellipsoid.prototype.transformPositionFromScaledSpace = function ( position, result ) { if (!when.defined(result)) { result = new Cartesian3(); } return Cartesian3.multiplyComponents(position, this._radii, result); }; /** * Compares this Ellipsoid against the provided Ellipsoid componentwise and returns * true if they are equal, false otherwise. * * @param {Ellipsoid} [right] The other Ellipsoid. * @returns {Boolean} true if they are equal, false otherwise. */ Ellipsoid.prototype.equals = function (right) { return ( this === right || (when.defined(right) && Cartesian3.equals(this._radii, right._radii)) ); }; /** * Creates a string representing this Ellipsoid in the format '(radii.x, radii.y, radii.z)'. * * @returns {String} A string representing this ellipsoid in the format '(radii.x, radii.y, radii.z)'. */ Ellipsoid.prototype.toString = function () { return this._radii.toString(); }; /** * Computes a point which is the intersection of the surface normal with the z-axis. * * @param {Cartesian3} position the position. must be on the surface of the ellipsoid. * @param {Number} [buffer = 0.0] A buffer to subtract from the ellipsoid size when checking if the point is inside the ellipsoid. * In earth case, with common earth datums, there is no need for this buffer since the intersection point is always (relatively) very close to the center. * In WGS84 datum, intersection point is at max z = +-42841.31151331382 (0.673% of z-axis). * Intersection point could be outside the ellipsoid if the ratio of MajorAxis / AxisOfRotation is bigger than the square root of 2 * @param {Cartesian3} [result] The cartesian to which to copy the result, or undefined to create and * return a new instance. * @returns {Cartesian3 | undefined} the intersection point if it's inside the ellipsoid, undefined otherwise * * @exception {DeveloperError} position is required. * @exception {DeveloperError} Ellipsoid must be an ellipsoid of revolution (radii.x == radii.y). * @exception {DeveloperError} Ellipsoid.radii.z must be greater than 0. */ Ellipsoid.prototype.getSurfaceNormalIntersectionWithZAxis = function ( position, buffer, result ) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("position", position); if ( !_Math.CesiumMath.equalsEpsilon( this._radii.x, this._radii.y, _Math.CesiumMath.EPSILON15 ) ) { throw new Check.DeveloperError( "Ellipsoid must be an ellipsoid of revolution (radii.x == radii.y)" ); } Check.Check.typeOf.number.greaterThan("Ellipsoid.radii.z", this._radii.z, 0); //>>includeEnd('debug'); buffer = when.defaultValue(buffer, 0.0); var squaredXOverSquaredZ = this._squaredXOverSquaredZ; if (!when.defined(result)) { result = new Cartesian3(); } result.x = 0.0; result.y = 0.0; result.z = position.z * (1 - squaredXOverSquaredZ); if (Math.abs(result.z) >= this._radii.z - buffer) { return undefined; } return result; }; var abscissas = [ 0.14887433898163, 0.43339539412925, 0.67940956829902, 0.86506336668898, 0.97390652851717, 0.0, ]; var weights = [ 0.29552422471475, 0.26926671930999, 0.21908636251598, 0.14945134915058, 0.066671344308684, 0.0, ]; /** * Compute the 10th order Gauss-Legendre Quadrature of the given definite integral. * * @param {Number} a The lower bound for the integration. * @param {Number} b The upper bound for the integration. * @param {Ellipsoid~RealValuedScalarFunction} func The function to integrate. * @returns {Number} The value of the integral of the given function over the given domain. * * @private */ function gaussLegendreQuadrature(a, b, func) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.number("a", a); Check.Check.typeOf.number("b", b); Check.Check.typeOf.func("func", func); //>>includeEnd('debug'); // The range is half of the normal range since the five weights add to one (ten weights add to two). // The values of the abscissas are multiplied by two to account for this. var xMean = 0.5 * (b + a); var xRange = 0.5 * (b - a); var sum = 0.0; for (var i = 0; i < 5; i++) { var dx = xRange * abscissas[i]; sum += weights[i] * (func(xMean + dx) + func(xMean - dx)); } // Scale the sum to the range of x. sum *= xRange; return sum; } /** * A real valued scalar function. * @callback Ellipsoid~RealValuedScalarFunction * * @param {Number} x The value used to evaluate the function. * @returns {Number} The value of the function at x. * * @private */ /** * Computes an approximation of the surface area of a rectangle on the surface of an ellipsoid using * Gauss-Legendre 10th order quadrature. * * @param {Rectangle} rectangle The rectangle used for computing the surface area. * @returns {Number} The approximate area of the rectangle on the surface of this ellipsoid. */ Ellipsoid.prototype.surfaceArea = function (rectangle) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("rectangle", rectangle); //>>includeEnd('debug'); var minLongitude = rectangle.west; var maxLongitude = rectangle.east; var minLatitude = rectangle.south; var maxLatitude = rectangle.north; while (maxLongitude < minLongitude) { maxLongitude += _Math.CesiumMath.TWO_PI; } var radiiSquared = this._radiiSquared; var a2 = radiiSquared.x; var b2 = radiiSquared.y; var c2 = radiiSquared.z; var a2b2 = a2 * b2; return gaussLegendreQuadrature(minLatitude, maxLatitude, function (lat) { // phi represents the angle measured from the north pole // sin(phi) = sin(pi / 2 - lat) = cos(lat), cos(phi) is similar var sinPhi = Math.cos(lat); var cosPhi = Math.sin(lat); return ( Math.cos(lat) * gaussLegendreQuadrature(minLongitude, maxLongitude, function (lon) { var cosTheta = Math.cos(lon); var sinTheta = Math.sin(lon); return Math.sqrt( a2b2 * cosPhi * cosPhi + c2 * (b2 * cosTheta * cosTheta + a2 * sinTheta * sinTheta) * sinPhi * sinPhi ); }) ); }); }; /** * A two dimensional region specified as longitude and latitude coordinates. * * @alias Rectangle * @constructor * * @param {Number} [west=0.0] The westernmost longitude, in radians, in the range [-Pi, Pi]. * @param {Number} [south=0.0] The southernmost latitude, in radians, in the range [-Pi/2, Pi/2]. * @param {Number} [east=0.0] The easternmost longitude, in radians, in the range [-Pi, Pi]. * @param {Number} [north=0.0] The northernmost latitude, in radians, in the range [-Pi/2, Pi/2]. * * @see Packable */ function Rectangle(west, south, east, north) { /** * The westernmost longitude in radians in the range [-Pi, Pi]. * * @type {Number} * @default 0.0 */ this.west = when.defaultValue(west, 0.0); /** * The southernmost latitude in radians in the range [-Pi/2, Pi/2]. * * @type {Number} * @default 0.0 */ this.south = when.defaultValue(south, 0.0); /** * The easternmost longitude in radians in the range [-Pi, Pi]. * * @type {Number} * @default 0.0 */ this.east = when.defaultValue(east, 0.0); /** * The northernmost latitude in radians in the range [-Pi/2, Pi/2]. * * @type {Number} * @default 0.0 */ this.north = when.defaultValue(north, 0.0); } Object.defineProperties(Rectangle.prototype, { /** * Gets the width of the rectangle in radians. * @memberof Rectangle.prototype * @type {Number} * @readonly */ width: { get: function () { return Rectangle.computeWidth(this); }, }, /** * Gets the height of the rectangle in radians. * @memberof Rectangle.prototype * @type {Number} * @readonly */ height: { get: function () { return Rectangle.computeHeight(this); }, }, }); /** * The number of elements used to pack the object into an array. * @type {Number} */ Rectangle.packedLength = 4; /** * Stores the provided instance into the provided array. * * @param {Rectangle} value The value to pack. * @param {Number[]} array The array to pack into. * @param {Number} [startingIndex=0] The index into the array at which to start packing the elements. * * @returns {Number[]} The array that was packed into */ Rectangle.pack = function (value, array, startingIndex) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("value", value); Check.Check.defined("array", array); //>>includeEnd('debug'); startingIndex = when.defaultValue(startingIndex, 0); array[startingIndex++] = value.west; array[startingIndex++] = value.south; array[startingIndex++] = value.east; array[startingIndex] = value.north; return array; }; /** * Retrieves an instance from a packed array. * * @param {Number[]} array The packed array. * @param {Number} [startingIndex=0] The starting index of the element to be unpacked. * @param {Rectangle} [result] The object into which to store the result. * @returns {Rectangle} The modified result parameter or a new Rectangle instance if one was not provided. */ Rectangle.unpack = function (array, startingIndex, result) { //>>includeStart('debug', pragmas.debug); Check.Check.defined("array", array); //>>includeEnd('debug'); startingIndex = when.defaultValue(startingIndex, 0); if (!when.defined(result)) { result = new Rectangle(); } result.west = array[startingIndex++]; result.south = array[startingIndex++]; result.east = array[startingIndex++]; result.north = array[startingIndex]; return result; }; /** * Computes the width of a rectangle in radians. * @param {Rectangle} rectangle The rectangle to compute the width of. * @returns {Number} The width. */ Rectangle.computeWidth = function (rectangle) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("rectangle", rectangle); //>>includeEnd('debug'); var east = rectangle.east; var west = rectangle.west; if (east < west) { east += _Math.CesiumMath.TWO_PI; } return east - west; }; /** * Computes the height of a rectangle in radians. * @param {Rectangle} rectangle The rectangle to compute the height of. * @returns {Number} The height. */ Rectangle.computeHeight = function (rectangle) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("rectangle", rectangle); //>>includeEnd('debug'); return rectangle.north - rectangle.south; }; /** * Creates a rectangle given the boundary longitude and latitude in degrees. * * @param {Number} [west=0.0] The westernmost longitude in degrees in the range [-180.0, 180.0]. * @param {Number} [south=0.0] The southernmost latitude in degrees in the range [-90.0, 90.0]. * @param {Number} [east=0.0] The easternmost longitude in degrees in the range [-180.0, 180.0]. * @param {Number} [north=0.0] The northernmost latitude in degrees in the range [-90.0, 90.0]. * @param {Rectangle} [result] The object onto which to store the result, or undefined if a new instance should be created. * @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided. * * @example * var rectangle = Cesium.Rectangle.fromDegrees(0.0, 20.0, 10.0, 30.0); */ Rectangle.fromDegrees = function (west, south, east, north, result) { west = _Math.CesiumMath.toRadians(when.defaultValue(west, 0.0)); south = _Math.CesiumMath.toRadians(when.defaultValue(south, 0.0)); east = _Math.CesiumMath.toRadians(when.defaultValue(east, 0.0)); north = _Math.CesiumMath.toRadians(when.defaultValue(north, 0.0)); if (!when.defined(result)) { return new Rectangle(west, south, east, north); } result.west = west; result.south = south; result.east = east; result.north = north; return result; }; /** * Creates a rectangle given the boundary longitude and latitude in radians. * * @param {Number} [west=0.0] The westernmost longitude in radians in the range [-Math.PI, Math.PI]. * @param {Number} [south=0.0] The southernmost latitude in radians in the range [-Math.PI/2, Math.PI/2]. * @param {Number} [east=0.0] The easternmost longitude in radians in the range [-Math.PI, Math.PI]. * @param {Number} [north=0.0] The northernmost latitude in radians in the range [-Math.PI/2, Math.PI/2]. * @param {Rectangle} [result] The object onto which to store the result, or undefined if a new instance should be created. * @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided. * * @example * var rectangle = Cesium.Rectangle.fromRadians(0.0, Math.PI/4, Math.PI/8, 3*Math.PI/4); */ Rectangle.fromRadians = function (west, south, east, north, result) { if (!when.defined(result)) { return new Rectangle(west, south, east, north); } result.west = when.defaultValue(west, 0.0); result.south = when.defaultValue(south, 0.0); result.east = when.defaultValue(east, 0.0); result.north = when.defaultValue(north, 0.0); return result; }; /** * Creates the smallest possible Rectangle that encloses all positions in the provided array. * * @param {Cartographic[]} cartographics The list of Cartographic instances. * @param {Rectangle} [result] The object onto which to store the result, or undefined if a new instance should be created. * @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided. */ Rectangle.fromCartographicArray = function (cartographics, result) { //>>includeStart('debug', pragmas.debug); Check.Check.defined("cartographics", cartographics); //>>includeEnd('debug'); var west = Number.MAX_VALUE; var east = -Number.MAX_VALUE; var westOverIDL = Number.MAX_VALUE; var eastOverIDL = -Number.MAX_VALUE; var south = Number.MAX_VALUE; var north = -Number.MAX_VALUE; for (var i = 0, len = cartographics.length; i < len; i++) { var position = cartographics[i]; west = Math.min(west, position.longitude); east = Math.max(east, position.longitude); south = Math.min(south, position.latitude); north = Math.max(north, position.latitude); var lonAdjusted = position.longitude >= 0 ? position.longitude : position.longitude + _Math.CesiumMath.TWO_PI; westOverIDL = Math.min(westOverIDL, lonAdjusted); eastOverIDL = Math.max(eastOverIDL, lonAdjusted); } if (east - west > eastOverIDL - westOverIDL) { west = westOverIDL; east = eastOverIDL; if (east > _Math.CesiumMath.PI) { east = east - _Math.CesiumMath.TWO_PI; } if (west > _Math.CesiumMath.PI) { west = west - _Math.CesiumMath.TWO_PI; } } if (!when.defined(result)) { return new Rectangle(west, south, east, north); } result.west = west; result.south = south; result.east = east; result.north = north; return result; }; /** * Creates the smallest possible Rectangle that encloses all positions in the provided array. * * @param {Cartesian3[]} cartesians The list of Cartesian instances. * @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid the cartesians are on. * @param {Rectangle} [result] The object onto which to store the result, or undefined if a new instance should be created. * @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided. */ Rectangle.fromCartesianArray = function (cartesians, ellipsoid, result) { //>>includeStart('debug', pragmas.debug); Check.Check.defined("cartesians", cartesians); //>>includeEnd('debug'); ellipsoid = when.defaultValue(ellipsoid, Ellipsoid.WGS84); var west = Number.MAX_VALUE; var east = -Number.MAX_VALUE; var westOverIDL = Number.MAX_VALUE; var eastOverIDL = -Number.MAX_VALUE; var south = Number.MAX_VALUE; var north = -Number.MAX_VALUE; for (var i = 0, len = cartesians.length; i < len; i++) { var position = ellipsoid.cartesianToCartographic(cartesians[i]); west = Math.min(west, position.longitude); east = Math.max(east, position.longitude); south = Math.min(south, position.latitude); north = Math.max(north, position.latitude); var lonAdjusted = position.longitude >= 0 ? position.longitude : position.longitude + _Math.CesiumMath.TWO_PI; westOverIDL = Math.min(westOverIDL, lonAdjusted); eastOverIDL = Math.max(eastOverIDL, lonAdjusted); } if (east - west > eastOverIDL - westOverIDL) { west = westOverIDL; east = eastOverIDL; if (east > _Math.CesiumMath.PI) { east = east - _Math.CesiumMath.TWO_PI; } if (west > _Math.CesiumMath.PI) { west = west - _Math.CesiumMath.TWO_PI; } } if (!when.defined(result)) { return new Rectangle(west, south, east, north); } result.west = west; result.south = south; result.east = east; result.north = north; return result; }; /** * Duplicates a Rectangle. * * @param {Rectangle} rectangle The rectangle to clone. * @param {Rectangle} [result] The object onto which to store the result, or undefined if a new instance should be created. * @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided. (Returns undefined if rectangle is undefined) */ Rectangle.clone = function (rectangle, result) { if (!when.defined(rectangle)) { return undefined; } if (!when.defined(result)) { return new Rectangle( rectangle.west, rectangle.south, rectangle.east, rectangle.north ); } result.west = rectangle.west; result.south = rectangle.south; result.east = rectangle.east; result.north = rectangle.north; return result; }; /** * Compares the provided Rectangles componentwise and returns * true if they pass an absolute or relative tolerance test, * false otherwise. * * @param {Rectangle} [left] The first Rectangle. * @param {Rectangle} [right] The second Rectangle. * @param {Number} [absoluteEpsilon=0] The absolute epsilon tolerance to use for equality testing. * @returns {Boolean} true if left and right are within the provided epsilon, false otherwise. */ Rectangle.equalsEpsilon = function (left, right, absoluteEpsilon) { absoluteEpsilon = when.defaultValue(absoluteEpsilon, 0); return ( left === right || (when.defined(left) && when.defined(right) && Math.abs(left.west - right.west) <= absoluteEpsilon && Math.abs(left.south - right.south) <= absoluteEpsilon && Math.abs(left.east - right.east) <= absoluteEpsilon && Math.abs(left.north - right.north) <= absoluteEpsilon) ); }; /** * Duplicates this Rectangle. * * @param {Rectangle} [result] The object onto which to store the result. * @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided. */ Rectangle.prototype.clone = function (result) { return Rectangle.clone(this, result); }; /** * Compares the provided Rectangle with this Rectangle componentwise and returns * true if they are equal, false otherwise. * * @param {Rectangle} [other] The Rectangle to compare. * @returns {Boolean} true if the Rectangles are equal, false otherwise. */ Rectangle.prototype.equals = function (other) { return Rectangle.equals(this, other); }; /** * Compares the provided rectangles and returns true if they are equal, * false otherwise. * * @param {Rectangle} [left] The first Rectangle. * @param {Rectangle} [right] The second Rectangle. * @returns {Boolean} true if left and right are equal; otherwise false. */ Rectangle.equals = function (left, right) { return ( left === right || (when.defined(left) && when.defined(right) && left.west === right.west && left.south === right.south && left.east === right.east && left.north === right.north) ); }; /** * Compares the provided Rectangle with this Rectangle componentwise and returns * true if they are within the provided epsilon, * false otherwise. * * @param {Rectangle} [other] The Rectangle to compare. * @param {Number} [epsilon=0] The epsilon to use for equality testing. * @returns {Boolean} true if the Rectangles are within the provided epsilon, false otherwise. */ Rectangle.prototype.equalsEpsilon = function (other, epsilon) { return Rectangle.equalsEpsilon(this, other, epsilon); }; /** * Checks a Rectangle's properties and throws if they are not in valid ranges. * * @param {Rectangle} rectangle The rectangle to validate * * @exception {DeveloperError} north must be in the interval [-Pi/2, Pi/2]. * @exception {DeveloperError} south must be in the interval [-Pi/2, Pi/2]. * @exception {DeveloperError} east must be in the interval [-Pi, Pi]. * @exception {DeveloperError} west must be in the interval [-Pi, Pi]. */ Rectangle.validate = function (rectangle) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("rectangle", rectangle); var north = rectangle.north; Check.Check.typeOf.number.greaterThanOrEquals( "north", north, -_Math.CesiumMath.PI_OVER_TWO ); Check.Check.typeOf.number.lessThanOrEquals("north", north, _Math.CesiumMath.PI_OVER_TWO); var south = rectangle.south; Check.Check.typeOf.number.greaterThanOrEquals( "south", south, -_Math.CesiumMath.PI_OVER_TWO ); Check.Check.typeOf.number.lessThanOrEquals("south", south, _Math.CesiumMath.PI_OVER_TWO); var west = rectangle.west; Check.Check.typeOf.number.greaterThanOrEquals("west", west, -Math.PI); Check.Check.typeOf.number.lessThanOrEquals("west", west, Math.PI); var east = rectangle.east; Check.Check.typeOf.number.greaterThanOrEquals("east", east, -Math.PI); Check.Check.typeOf.number.lessThanOrEquals("east", east, Math.PI); //>>includeEnd('debug'); }; /** * Computes the southwest corner of a rectangle. * * @param {Rectangle} rectangle The rectangle for which to find the corner * @param {Cartographic} [result] The object onto which to store the result. * @returns {Cartographic} The modified result parameter or a new Cartographic instance if none was provided. */ Rectangle.southwest = function (rectangle, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("rectangle", rectangle); //>>includeEnd('debug'); if (!when.defined(result)) { return new Cartographic(rectangle.west, rectangle.south); } result.longitude = rectangle.west; result.latitude = rectangle.south; result.height = 0.0; return result; }; /** * Computes the northwest corner of a rectangle. * * @param {Rectangle} rectangle The rectangle for which to find the corner * @param {Cartographic} [result] The object onto which to store the result. * @returns {Cartographic} The modified result parameter or a new Cartographic instance if none was provided. */ Rectangle.northwest = function (rectangle, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("rectangle", rectangle); //>>includeEnd('debug'); if (!when.defined(result)) { return new Cartographic(rectangle.west, rectangle.north); } result.longitude = rectangle.west; result.latitude = rectangle.north; result.height = 0.0; return result; }; /** * Computes the northeast corner of a rectangle. * * @param {Rectangle} rectangle The rectangle for which to find the corner * @param {Cartographic} [result] The object onto which to store the result. * @returns {Cartographic} The modified result parameter or a new Cartographic instance if none was provided. */ Rectangle.northeast = function (rectangle, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("rectangle", rectangle); //>>includeEnd('debug'); if (!when.defined(result)) { return new Cartographic(rectangle.east, rectangle.north); } result.longitude = rectangle.east; result.latitude = rectangle.north; result.height = 0.0; return result; }; /** * Computes the southeast corner of a rectangle. * * @param {Rectangle} rectangle The rectangle for which to find the corner * @param {Cartographic} [result] The object onto which to store the result. * @returns {Cartographic} The modified result parameter or a new Cartographic instance if none was provided. */ Rectangle.southeast = function (rectangle, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("rectangle", rectangle); //>>includeEnd('debug'); if (!when.defined(result)) { return new Cartographic(rectangle.east, rectangle.south); } result.longitude = rectangle.east; result.latitude = rectangle.south; result.height = 0.0; return result; }; /** * Computes the center of a rectangle. * * @param {Rectangle} rectangle The rectangle for which to find the center * @param {Cartographic} [result] The object onto which to store the result. * @returns {Cartographic} The modified result parameter or a new Cartographic instance if none was provided. */ Rectangle.center = function (rectangle, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("rectangle", rectangle); //>>includeEnd('debug'); var east = rectangle.east; var west = rectangle.west; if (east < west) { east += _Math.CesiumMath.TWO_PI; } var longitude = _Math.CesiumMath.negativePiToPi((west + east) * 0.5); var latitude = (rectangle.south + rectangle.north) * 0.5; if (!when.defined(result)) { return new Cartographic(longitude, latitude); } result.longitude = longitude; result.latitude = latitude; result.height = 0.0; return result; }; /** * Computes the intersection of two rectangles. This function assumes that the rectangle's coordinates are * latitude and longitude in radians and produces a correct intersection, taking into account the fact that * the same angle can be represented with multiple values as well as the wrapping of longitude at the * anti-meridian. For a simple intersection that ignores these factors and can be used with projected * coordinates, see {@link Rectangle.simpleIntersection}. * * @param {Rectangle} rectangle On rectangle to find an intersection * @param {Rectangle} otherRectangle Another rectangle to find an intersection * @param {Rectangle} [result] The object onto which to store the result. * @returns {Rectangle|undefined} The modified result parameter, a new Rectangle instance if none was provided or undefined if there is no intersection. */ Rectangle.intersection = function (rectangle, otherRectangle, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("rectangle", rectangle); Check.Check.typeOf.object("otherRectangle", otherRectangle); //>>includeEnd('debug'); var rectangleEast = rectangle.east; var rectangleWest = rectangle.west; var otherRectangleEast = otherRectangle.east; var otherRectangleWest = otherRectangle.west; if (rectangleEast < rectangleWest && otherRectangleEast > 0.0) { rectangleEast += _Math.CesiumMath.TWO_PI; } else if (otherRectangleEast < otherRectangleWest && rectangleEast > 0.0) { otherRectangleEast += _Math.CesiumMath.TWO_PI; } if (rectangleEast < rectangleWest && otherRectangleWest < 0.0) { otherRectangleWest += _Math.CesiumMath.TWO_PI; } else if (otherRectangleEast < otherRectangleWest && rectangleWest < 0.0) { rectangleWest += _Math.CesiumMath.TWO_PI; } var west = _Math.CesiumMath.negativePiToPi( Math.max(rectangleWest, otherRectangleWest) ); var east = _Math.CesiumMath.negativePiToPi( Math.min(rectangleEast, otherRectangleEast) ); if ( (rectangle.west < rectangle.east || otherRectangle.west < otherRectangle.east) && east <= west ) { return undefined; } var south = Math.max(rectangle.south, otherRectangle.south); var north = Math.min(rectangle.north, otherRectangle.north); if (south >= north) { return undefined; } if (!when.defined(result)) { return new Rectangle(west, south, east, north); } result.west = west; result.south = south; result.east = east; result.north = north; return result; }; /** * Computes a simple intersection of two rectangles. Unlike {@link Rectangle.intersection}, this function * does not attempt to put the angular coordinates into a consistent range or to account for crossing the * anti-meridian. As such, it can be used for rectangles where the coordinates are not simply latitude * and longitude (i.e. projected coordinates). * * @param {Rectangle} rectangle On rectangle to find an intersection * @param {Rectangle} otherRectangle Another rectangle to find an intersection * @param {Rectangle} [result] The object onto which to store the result. * @returns {Rectangle|undefined} The modified result parameter, a new Rectangle instance if none was provided or undefined if there is no intersection. */ Rectangle.simpleIntersection = function (rectangle, otherRectangle, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("rectangle", rectangle); Check.Check.typeOf.object("otherRectangle", otherRectangle); //>>includeEnd('debug'); var west = Math.max(rectangle.west, otherRectangle.west); var south = Math.max(rectangle.south, otherRectangle.south); var east = Math.min(rectangle.east, otherRectangle.east); var north = Math.min(rectangle.north, otherRectangle.north); if (south >= north || west >= east) { return undefined; } if (!when.defined(result)) { return new Rectangle(west, south, east, north); } result.west = west; result.south = south; result.east = east; result.north = north; return result; }; /** * Computes a rectangle that is the union of two rectangles. * * @param {Rectangle} rectangle A rectangle to enclose in rectangle. * @param {Rectangle} otherRectangle A rectangle to enclose in a rectangle. * @param {Rectangle} [result] The object onto which to store the result. * @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided. */ Rectangle.union = function (rectangle, otherRectangle, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("rectangle", rectangle); Check.Check.typeOf.object("otherRectangle", otherRectangle); //>>includeEnd('debug'); if (!when.defined(result)) { result = new Rectangle(); } var rectangleEast = rectangle.east; var rectangleWest = rectangle.west; var otherRectangleEast = otherRectangle.east; var otherRectangleWest = otherRectangle.west; if (rectangleEast < rectangleWest && otherRectangleEast > 0.0) { rectangleEast += _Math.CesiumMath.TWO_PI; } else if (otherRectangleEast < otherRectangleWest && rectangleEast > 0.0) { otherRectangleEast += _Math.CesiumMath.TWO_PI; } if (rectangleEast < rectangleWest && otherRectangleWest < 0.0) { otherRectangleWest += _Math.CesiumMath.TWO_PI; } else if (otherRectangleEast < otherRectangleWest && rectangleWest < 0.0) { rectangleWest += _Math.CesiumMath.TWO_PI; } var west = _Math.CesiumMath.convertLongitudeRange( Math.min(rectangleWest, otherRectangleWest) ); var east = _Math.CesiumMath.convertLongitudeRange( Math.max(rectangleEast, otherRectangleEast) ); result.west = west; result.south = Math.min(rectangle.south, otherRectangle.south); result.east = east; result.north = Math.max(rectangle.north, otherRectangle.north); return result; }; /** * Computes a rectangle by enlarging the provided rectangle until it contains the provided cartographic. * * @param {Rectangle} rectangle A rectangle to expand. * @param {Cartographic} cartographic A cartographic to enclose in a rectangle. * @param {Rectangle} [result] The object onto which to store the result. * @returns {Rectangle} The modified result parameter or a new Rectangle instance if one was not provided. */ Rectangle.expand = function (rectangle, cartographic, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("rectangle", rectangle); Check.Check.typeOf.object("cartographic", cartographic); //>>includeEnd('debug'); if (!when.defined(result)) { result = new Rectangle(); } result.west = Math.min(rectangle.west, cartographic.longitude); result.south = Math.min(rectangle.south, cartographic.latitude); result.east = Math.max(rectangle.east, cartographic.longitude); result.north = Math.max(rectangle.north, cartographic.latitude); return result; }; /** * Returns true if the cartographic is on or inside the rectangle, false otherwise. * * @param {Rectangle} rectangle The rectangle * @param {Cartographic} cartographic The cartographic to test. * @returns {Boolean} true if the provided cartographic is inside the rectangle, false otherwise. */ Rectangle.contains = function (rectangle, cartographic) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("rectangle", rectangle); Check.Check.typeOf.object("cartographic", cartographic); //>>includeEnd('debug'); var longitude = cartographic.longitude; var latitude = cartographic.latitude; var west = rectangle.west; var east = rectangle.east; if (east < west) { east += _Math.CesiumMath.TWO_PI; if (longitude < 0.0) { longitude += _Math.CesiumMath.TWO_PI; } } return ( (longitude > west || _Math.CesiumMath.equalsEpsilon(longitude, west, _Math.CesiumMath.EPSILON14)) && (longitude < east || _Math.CesiumMath.equalsEpsilon(longitude, east, _Math.CesiumMath.EPSILON14)) && latitude >= rectangle.south && latitude <= rectangle.north ); }; var subsampleLlaScratch = new Cartographic(); /** * Samples a rectangle so that it includes a list of Cartesian points suitable for passing to * {@link BoundingSphere#fromPoints}. Sampling is necessary to account * for rectangles that cover the poles or cross the equator. * * @param {Rectangle} rectangle The rectangle to subsample. * @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid to use. * @param {Number} [surfaceHeight=0.0] The height of the rectangle above the ellipsoid. * @param {Cartesian3[]} [result] The array of Cartesians onto which to store the result. * @returns {Cartesian3[]} The modified result parameter or a new Array of Cartesians instances if none was provided. */ Rectangle.subsample = function (rectangle, ellipsoid, surfaceHeight, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("rectangle", rectangle); //>>includeEnd('debug'); ellipsoid = when.defaultValue(ellipsoid, Ellipsoid.WGS84); surfaceHeight = when.defaultValue(surfaceHeight, 0.0); if (!when.defined(result)) { result = []; } var length = 0; var north = rectangle.north; var south = rectangle.south; var east = rectangle.east; var west = rectangle.west; var lla = subsampleLlaScratch; lla.height = surfaceHeight; lla.longitude = west; lla.latitude = north; result[length] = ellipsoid.cartographicToCartesian(lla, result[length]); length++; lla.longitude = east; result[length] = ellipsoid.cartographicToCartesian(lla, result[length]); length++; lla.latitude = south; result[length] = ellipsoid.cartographicToCartesian(lla, result[length]); length++; lla.longitude = west; result[length] = ellipsoid.cartographicToCartesian(lla, result[length]); length++; if (north < 0.0) { lla.latitude = north; } else if (south > 0.0) { lla.latitude = south; } else { lla.latitude = 0.0; } for (var i = 1; i < 8; ++i) { lla.longitude = -Math.PI + i * _Math.CesiumMath.PI_OVER_TWO; if (Rectangle.contains(rectangle, lla)) { result[length] = ellipsoid.cartographicToCartesian(lla, result[length]); length++; } } if (lla.latitude === 0.0) { lla.longitude = west; result[length] = ellipsoid.cartographicToCartesian(lla, result[length]); length++; lla.longitude = east; result[length] = ellipsoid.cartographicToCartesian(lla, result[length]); length++; } result.length = length; return result; }; /** * The largest possible rectangle. * * @type {Rectangle} * @constant */ Rectangle.MAX_VALUE = Object.freeze( new Rectangle( -Math.PI, -_Math.CesiumMath.PI_OVER_TWO, Math.PI, _Math.CesiumMath.PI_OVER_TWO ) ); /** * A 2D Cartesian point. * @alias Cartesian2 * @constructor * * @param {Number} [x=0.0] The X component. * @param {Number} [y=0.0] The Y component. * * @see Cartesian3 * @see Cartesian4 * @see Packable */ function Cartesian2(x, y) { /** * The X component. * @type {Number} * @default 0.0 */ this.x = when.defaultValue(x, 0.0); /** * The Y component. * @type {Number} * @default 0.0 */ this.y = when.defaultValue(y, 0.0); } /** * Creates a Cartesian2 instance from x and y coordinates. * * @param {Number} x The x coordinate. * @param {Number} y The y coordinate. * @param {Cartesian2} [result] The object onto which to store the result. * @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided. */ Cartesian2.fromElements = function (x, y, result) { if (!when.defined(result)) { return new Cartesian2(x, y); } result.x = x; result.y = y; return result; }; /** * Duplicates a Cartesian2 instance. * * @param {Cartesian2} cartesian The Cartesian to duplicate. * @param {Cartesian2} [result] The object onto which to store the result. * @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided. (Returns undefined if cartesian is undefined) */ Cartesian2.clone = function (cartesian, result) { if (!when.defined(cartesian)) { return undefined; } if (!when.defined(result)) { return new Cartesian2(cartesian.x, cartesian.y); } result.x = cartesian.x; result.y = cartesian.y; return result; }; /** * Creates a Cartesian2 instance from an existing Cartesian3. This simply takes the * x and y properties of the Cartesian3 and drops z. * @function * * @param {Cartesian3} cartesian The Cartesian3 instance to create a Cartesian2 instance from. * @param {Cartesian2} [result] The object onto which to store the result. * @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided. */ Cartesian2.fromCartesian3 = Cartesian2.clone; /** * Creates a Cartesian2 instance from an existing Cartesian4. This simply takes the * x and y properties of the Cartesian4 and drops z and w. * @function * * @param {Cartesian4} cartesian The Cartesian4 instance to create a Cartesian2 instance from. * @param {Cartesian2} [result] The object onto which to store the result. * @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided. */ Cartesian2.fromCartesian4 = Cartesian2.clone; /** * The number of elements used to pack the object into an array. * @type {Number} */ Cartesian2.packedLength = 2; /** * Stores the provided instance into the provided array. * * @param {Cartesian2} value The value to pack. * @param {Number[]} array The array to pack into. * @param {Number} [startingIndex=0] The index into the array at which to start packing the elements. * * @returns {Number[]} The array that was packed into */ Cartesian2.pack = function (value, array, startingIndex) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("value", value); Check.Check.defined("array", array); //>>includeEnd('debug'); startingIndex = when.defaultValue(startingIndex, 0); array[startingIndex++] = value.x; array[startingIndex] = value.y; return array; }; /** * Retrieves an instance from a packed array. * * @param {Number[]} array The packed array. * @param {Number} [startingIndex=0] The starting index of the element to be unpacked. * @param {Cartesian2} [result] The object into which to store the result. * @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided. */ Cartesian2.unpack = function (array, startingIndex, result) { //>>includeStart('debug', pragmas.debug); Check.Check.defined("array", array); //>>includeEnd('debug'); startingIndex = when.defaultValue(startingIndex, 0); if (!when.defined(result)) { result = new Cartesian2(); } result.x = array[startingIndex++]; result.y = array[startingIndex]; return result; }; /** * Flattens an array of Cartesian2s into and array of components. * * @param {Cartesian2[]} array The array of cartesians to pack. * @param {Number[]} [result] The array onto which to store the result. If this is a typed array, it must have array.length * 2 components, else a {@link DeveloperError} will be thrown. If it is a regular array, it will be resized to have (array.length * 2) elements. * @returns {Number[]} The packed array. */ Cartesian2.packArray = function (array, result) { //>>includeStart('debug', pragmas.debug); Check.Check.defined("array", array); //>>includeEnd('debug'); var length = array.length; var resultLength = length * 2; if (!when.defined(result)) { result = new Array(resultLength); } else if (!Array.isArray(result) && result.length !== resultLength) { throw new Check.DeveloperError( "If result is a typed array, it must have exactly array.length * 2 elements" ); } else if (result.length !== resultLength) { result.length = resultLength; } for (var i = 0; i < length; ++i) { Cartesian2.pack(array[i], result, i * 2); } return result; }; /** * Unpacks an array of cartesian components into and array of Cartesian2s. * * @param {Number[]} array The array of components to unpack. * @param {Cartesian2[]} [result] The array onto which to store the result. * @returns {Cartesian2[]} The unpacked array. */ Cartesian2.unpackArray = function (array, result) { //>>includeStart('debug', pragmas.debug); Check.Check.defined("array", array); Check.Check.typeOf.number.greaterThanOrEquals("array.length", array.length, 2); if (array.length % 2 !== 0) { throw new Check.DeveloperError("array length must be a multiple of 2."); } //>>includeEnd('debug'); var length = array.length; if (!when.defined(result)) { result = new Array(length / 2); } else { result.length = length / 2; } for (var i = 0; i < length; i += 2) { var index = i / 2; result[index] = Cartesian2.unpack(array, i, result[index]); } return result; }; /** * Creates a Cartesian2 from two consecutive elements in an array. * @function * * @param {Number[]} array The array whose two consecutive elements correspond to the x and y components, respectively. * @param {Number} [startingIndex=0] The offset into the array of the first element, which corresponds to the x component. * @param {Cartesian2} [result] The object onto which to store the result. * @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided. * * @example * // Create a Cartesian2 with (1.0, 2.0) * var v = [1.0, 2.0]; * var p = Cesium.Cartesian2.fromArray(v); * * // Create a Cartesian2 with (1.0, 2.0) using an offset into an array * var v2 = [0.0, 0.0, 1.0, 2.0]; * var p2 = Cesium.Cartesian2.fromArray(v2, 2); */ Cartesian2.fromArray = Cartesian2.unpack; /** * Computes the value of the maximum component for the supplied Cartesian. * * @param {Cartesian2} cartesian The cartesian to use. * @returns {Number} The value of the maximum component. */ Cartesian2.maximumComponent = function (cartesian) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("cartesian", cartesian); //>>includeEnd('debug'); return Math.max(cartesian.x, cartesian.y); }; /** * Computes the value of the minimum component for the supplied Cartesian. * * @param {Cartesian2} cartesian The cartesian to use. * @returns {Number} The value of the minimum component. */ Cartesian2.minimumComponent = function (cartesian) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("cartesian", cartesian); //>>includeEnd('debug'); return Math.min(cartesian.x, cartesian.y); }; /** * Compares two Cartesians and computes a Cartesian which contains the minimum components of the supplied Cartesians. * * @param {Cartesian2} first A cartesian to compare. * @param {Cartesian2} second A cartesian to compare. * @param {Cartesian2} result The object into which to store the result. * @returns {Cartesian2} A cartesian with the minimum components. */ Cartesian2.minimumByComponent = function (first, second, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("first", first); Check.Check.typeOf.object("second", second); Check.Check.typeOf.object("result", result); //>>includeEnd('debug'); result.x = Math.min(first.x, second.x); result.y = Math.min(first.y, second.y); return result; }; /** * Compares two Cartesians and computes a Cartesian which contains the maximum components of the supplied Cartesians. * * @param {Cartesian2} first A cartesian to compare. * @param {Cartesian2} second A cartesian to compare. * @param {Cartesian2} result The object into which to store the result. * @returns {Cartesian2} A cartesian with the maximum components. */ Cartesian2.maximumByComponent = function (first, second, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("first", first); Check.Check.typeOf.object("second", second); Check.Check.typeOf.object("result", result); //>>includeEnd('debug'); result.x = Math.max(first.x, second.x); result.y = Math.max(first.y, second.y); return result; }; /** * Computes the provided Cartesian's squared magnitude. * * @param {Cartesian2} cartesian The Cartesian instance whose squared magnitude is to be computed. * @returns {Number} The squared magnitude. */ Cartesian2.magnitudeSquared = function (cartesian) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("cartesian", cartesian); //>>includeEnd('debug'); return cartesian.x * cartesian.x + cartesian.y * cartesian.y; }; /** * Computes the Cartesian's magnitude (length). * * @param {Cartesian2} cartesian The Cartesian instance whose magnitude is to be computed. * @returns {Number} The magnitude. */ Cartesian2.magnitude = function (cartesian) { return Math.sqrt(Cartesian2.magnitudeSquared(cartesian)); }; var distanceScratch$1 = new Cartesian2(); /** * Computes the distance between two points. * * @param {Cartesian2} left The first point to compute the distance from. * @param {Cartesian2} right The second point to compute the distance to. * @returns {Number} The distance between two points. * * @example * // Returns 1.0 * var d = Cesium.Cartesian2.distance(new Cesium.Cartesian2(1.0, 0.0), new Cesium.Cartesian2(2.0, 0.0)); */ Cartesian2.distance = function (left, right) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("left", left); Check.Check.typeOf.object("right", right); //>>includeEnd('debug'); Cartesian2.subtract(left, right, distanceScratch$1); return Cartesian2.magnitude(distanceScratch$1); }; /** * Computes the squared distance between two points. Comparing squared distances * using this function is more efficient than comparing distances using {@link Cartesian2#distance}. * * @param {Cartesian2} left The first point to compute the distance from. * @param {Cartesian2} right The second point to compute the distance to. * @returns {Number} The distance between two points. * * @example * // Returns 4.0, not 2.0 * var d = Cesium.Cartesian2.distance(new Cesium.Cartesian2(1.0, 0.0), new Cesium.Cartesian2(3.0, 0.0)); */ Cartesian2.distanceSquared = function (left, right) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("left", left); Check.Check.typeOf.object("right", right); //>>includeEnd('debug'); Cartesian2.subtract(left, right, distanceScratch$1); return Cartesian2.magnitudeSquared(distanceScratch$1); }; /** * Computes the normalized form of the supplied Cartesian. * * @param {Cartesian2} cartesian The Cartesian to be normalized. * @param {Cartesian2} result The object onto which to store the result. * @returns {Cartesian2} The modified result parameter. */ Cartesian2.normalize = function (cartesian, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("cartesian", cartesian); Check.Check.typeOf.object("result", result); //>>includeEnd('debug'); var magnitude = Cartesian2.magnitude(cartesian); result.x = cartesian.x / magnitude; result.y = cartesian.y / magnitude; //>>includeStart('debug', pragmas.debug); if (isNaN(result.x) || isNaN(result.y)) { throw new Check.DeveloperError("normalized result is not a number"); } //>>includeEnd('debug'); return result; }; /** * Computes the dot (scalar) product of two Cartesians. * * @param {Cartesian2} left The first Cartesian. * @param {Cartesian2} right The second Cartesian. * @returns {Number} The dot product. */ Cartesian2.dot = function (left, right) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("left", left); Check.Check.typeOf.object("right", right); //>>includeEnd('debug'); return left.x * right.x + left.y * right.y; }; /** * Computes the componentwise product of two Cartesians. * * @param {Cartesian2} left The first Cartesian. * @param {Cartesian2} right The second Cartesian. * @param {Cartesian2} result The object onto which to store the result. * @returns {Cartesian2} The modified result parameter. */ Cartesian2.multiplyComponents = function (left, right, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("left", left); Check.Check.typeOf.object("right", right); Check.Check.typeOf.object("result", result); //>>includeEnd('debug'); result.x = left.x * right.x; result.y = left.y * right.y; return result; }; /** * Computes the componentwise quotient of two Cartesians. * * @param {Cartesian2} left The first Cartesian. * @param {Cartesian2} right The second Cartesian. * @param {Cartesian2} result The object onto which to store the result. * @returns {Cartesian2} The modified result parameter. */ Cartesian2.divideComponents = function (left, right, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("left", left); Check.Check.typeOf.object("right", right); Check.Check.typeOf.object("result", result); //>>includeEnd('debug'); result.x = left.x / right.x; result.y = left.y / right.y; return result; }; /** * Computes the componentwise sum of two Cartesians. * * @param {Cartesian2} left The first Cartesian. * @param {Cartesian2} right The second Cartesian. * @param {Cartesian2} result The object onto which to store the result. * @returns {Cartesian2} The modified result parameter. */ Cartesian2.add = function (left, right, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("left", left); Check.Check.typeOf.object("right", right); Check.Check.typeOf.object("result", result); //>>includeEnd('debug'); result.x = left.x + right.x; result.y = left.y + right.y; return result; }; /** * Computes the componentwise difference of two Cartesians. * * @param {Cartesian2} left The first Cartesian. * @param {Cartesian2} right The second Cartesian. * @param {Cartesian2} result The object onto which to store the result. * @returns {Cartesian2} The modified result parameter. */ Cartesian2.subtract = function (left, right, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("left", left); Check.Check.typeOf.object("right", right); Check.Check.typeOf.object("result", result); //>>includeEnd('debug'); result.x = left.x - right.x; result.y = left.y - right.y; return result; }; /** * Multiplies the provided Cartesian componentwise by the provided scalar. * * @param {Cartesian2} cartesian The Cartesian to be scaled. * @param {Number} scalar The scalar to multiply with. * @param {Cartesian2} result The object onto which to store the result. * @returns {Cartesian2} The modified result parameter. */ Cartesian2.multiplyByScalar = function (cartesian, scalar, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("cartesian", cartesian); Check.Check.typeOf.number("scalar", scalar); Check.Check.typeOf.object("result", result); //>>includeEnd('debug'); result.x = cartesian.x * scalar; result.y = cartesian.y * scalar; return result; }; /** * Divides the provided Cartesian componentwise by the provided scalar. * * @param {Cartesian2} cartesian The Cartesian to be divided. * @param {Number} scalar The scalar to divide by. * @param {Cartesian2} result The object onto which to store the result. * @returns {Cartesian2} The modified result parameter. */ Cartesian2.divideByScalar = function (cartesian, scalar, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("cartesian", cartesian); Check.Check.typeOf.number("scalar", scalar); Check.Check.typeOf.object("result", result); //>>includeEnd('debug'); result.x = cartesian.x / scalar; result.y = cartesian.y / scalar; return result; }; /** * Negates the provided Cartesian. * * @param {Cartesian2} cartesian The Cartesian to be negated. * @param {Cartesian2} result The object onto which to store the result. * @returns {Cartesian2} The modified result parameter. */ Cartesian2.negate = function (cartesian, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("cartesian", cartesian); Check.Check.typeOf.object("result", result); //>>includeEnd('debug'); result.x = -cartesian.x; result.y = -cartesian.y; return result; }; /** * Computes the absolute value of the provided Cartesian. * * @param {Cartesian2} cartesian The Cartesian whose absolute value is to be computed. * @param {Cartesian2} result The object onto which to store the result. * @returns {Cartesian2} The modified result parameter. */ Cartesian2.abs = function (cartesian, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("cartesian", cartesian); Check.Check.typeOf.object("result", result); //>>includeEnd('debug'); result.x = Math.abs(cartesian.x); result.y = Math.abs(cartesian.y); return result; }; var lerpScratch$1 = new Cartesian2(); /** * Computes the linear interpolation or extrapolation at t using the provided cartesians. * * @param {Cartesian2} start The value corresponding to t at 0.0. * @param {Cartesian2} end The value corresponding to t at 1.0. * @param {Number} t The point along t at which to interpolate. * @param {Cartesian2} result The object onto which to store the result. * @returns {Cartesian2} The modified result parameter. */ Cartesian2.lerp = function (start, end, t, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("start", start); Check.Check.typeOf.object("end", end); Check.Check.typeOf.number("t", t); Check.Check.typeOf.object("result", result); //>>includeEnd('debug'); Cartesian2.multiplyByScalar(end, t, lerpScratch$1); result = Cartesian2.multiplyByScalar(start, 1.0 - t, result); return Cartesian2.add(lerpScratch$1, result, result); }; var angleBetweenScratch$1 = new Cartesian2(); var angleBetweenScratch2$1 = new Cartesian2(); /** * Returns the angle, in radians, between the provided Cartesians. * * @param {Cartesian2} left The first Cartesian. * @param {Cartesian2} right The second Cartesian. * @returns {Number} The angle between the Cartesians. */ Cartesian2.angleBetween = function (left, right) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("left", left); Check.Check.typeOf.object("right", right); //>>includeEnd('debug'); Cartesian2.normalize(left, angleBetweenScratch$1); Cartesian2.normalize(right, angleBetweenScratch2$1); return _Math.CesiumMath.acosClamped( Cartesian2.dot(angleBetweenScratch$1, angleBetweenScratch2$1) ); }; var mostOrthogonalAxisScratch$1 = new Cartesian2(); /** * Returns the axis that is most orthogonal to the provided Cartesian. * * @param {Cartesian2} cartesian The Cartesian on which to find the most orthogonal axis. * @param {Cartesian2} result The object onto which to store the result. * @returns {Cartesian2} The most orthogonal axis. */ Cartesian2.mostOrthogonalAxis = function (cartesian, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("cartesian", cartesian); Check.Check.typeOf.object("result", result); //>>includeEnd('debug'); var f = Cartesian2.normalize(cartesian, mostOrthogonalAxisScratch$1); Cartesian2.abs(f, f); if (f.x <= f.y) { result = Cartesian2.clone(Cartesian2.UNIT_X, result); } else { result = Cartesian2.clone(Cartesian2.UNIT_Y, result); } return result; }; /** * Compares the provided Cartesians componentwise and returns * true if they are equal, false otherwise. * * @param {Cartesian2} [left] The first Cartesian. * @param {Cartesian2} [right] The second Cartesian. * @returns {Boolean} true if left and right are equal, false otherwise. */ Cartesian2.equals = function (left, right) { return ( left === right || (when.defined(left) && when.defined(right) && left.x === right.x && left.y === right.y) ); }; /** * @private */ Cartesian2.equalsArray = function (cartesian, array, offset) { return cartesian.x === array[offset] && cartesian.y === array[offset + 1]; }; /** * Compares the provided Cartesians componentwise and returns * true if they pass an absolute or relative tolerance test, * false otherwise. * * @param {Cartesian2} [left] The first Cartesian. * @param {Cartesian2} [right] The second Cartesian. * @param {Number} [relativeEpsilon=0] The relative epsilon tolerance to use for equality testing. * @param {Number} [absoluteEpsilon=relativeEpsilon] The absolute epsilon tolerance to use for equality testing. * @returns {Boolean} true if left and right are within the provided epsilon, false otherwise. */ Cartesian2.equalsEpsilon = function ( left, right, relativeEpsilon, absoluteEpsilon ) { return ( left === right || (when.defined(left) && when.defined(right) && _Math.CesiumMath.equalsEpsilon( left.x, right.x, relativeEpsilon, absoluteEpsilon ) && _Math.CesiumMath.equalsEpsilon( left.y, right.y, relativeEpsilon, absoluteEpsilon )) ); }; /** * An immutable Cartesian2 instance initialized to (0.0, 0.0). * * @type {Cartesian2} * @constant */ Cartesian2.ZERO = Object.freeze(new Cartesian2(0.0, 0.0)); /** * An immutable Cartesian2 instance initialized to (1.0, 0.0). * * @type {Cartesian2} * @constant */ Cartesian2.UNIT_X = Object.freeze(new Cartesian2(1.0, 0.0)); /** * An immutable Cartesian2 instance initialized to (0.0, 1.0). * * @type {Cartesian2} * @constant */ Cartesian2.UNIT_Y = Object.freeze(new Cartesian2(0.0, 1.0)); /** * Duplicates this Cartesian2 instance. * * @param {Cartesian2} [result] The object onto which to store the result. * @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided. */ Cartesian2.prototype.clone = function (result) { return Cartesian2.clone(this, result); }; /** * Compares this Cartesian against the provided Cartesian componentwise and returns * true if they are equal, false otherwise. * * @param {Cartesian2} [right] The right hand side Cartesian. * @returns {Boolean} true if they are equal, false otherwise. */ Cartesian2.prototype.equals = function (right) { return Cartesian2.equals(this, right); }; /** * Compares this Cartesian against the provided Cartesian componentwise and returns * true if they pass an absolute or relative tolerance test, * false otherwise. * * @param {Cartesian2} [right] The right hand side Cartesian. * @param {Number} [relativeEpsilon=0] The relative epsilon tolerance to use for equality testing. * @param {Number} [absoluteEpsilon=relativeEpsilon] The absolute epsilon tolerance to use for equality testing. * @returns {Boolean} true if they are within the provided epsilon, false otherwise. */ Cartesian2.prototype.equalsEpsilon = function ( right, relativeEpsilon, absoluteEpsilon ) { return Cartesian2.equalsEpsilon( this, right, relativeEpsilon, absoluteEpsilon ); }; /** * Creates a string representing this Cartesian in the format '(x, y)'. * * @returns {String} A string representing the provided Cartesian in the format '(x, y)'. */ Cartesian2.prototype.toString = function () { return "(" + this.x + ", " + this.y + ")"; }; exports.Cartesian2 = Cartesian2; exports.Cartesian3 = Cartesian3; exports.Cartographic = Cartographic; exports.Ellipsoid = Ellipsoid; exports.Rectangle = Rectangle; }); //# sourceMappingURL=Cartesian2-33d2657c.js.map