true if they are equal, false otherwise.\n *\n * @param {Cartesian3} [left] The first Cartesian.\n * @param {Cartesian3} [right] The second Cartesian.\n * @returns {Boolean} true if left and right are equal, false otherwise.\n */\nCartesian3.equals = function (left, right) {\n return (\n left === right ||\n (defined(left) &&\n defined(right) &&\n left.x === right.x &&\n left.y === right.y &&\n left.z === right.z)\n );\n};\n\n/**\n * @private\n */\nCartesian3.equalsArray = function (cartesian, array, offset) {\n return (\n cartesian.x === array[offset] &&\n cartesian.y === array[offset + 1] &&\n cartesian.z === array[offset + 2]\n );\n};\n\n/**\n * Compares the provided Cartesians componentwise and returns\n * true if they pass an absolute or relative tolerance test,\n * false otherwise.\n *\n * @param {Cartesian3} [left] The first Cartesian.\n * @param {Cartesian3} [right] The second Cartesian.\n * @param {Number} [relativeEpsilon=0] The relative epsilon tolerance to use for equality testing.\n * @param {Number} [absoluteEpsilon=relativeEpsilon] The absolute epsilon tolerance to use for equality testing.\n * @returns {Boolean} true if left and right are within the provided epsilon, false otherwise.\n */\nCartesian3.equalsEpsilon = function (\n left,\n right,\n relativeEpsilon,\n absoluteEpsilon\n) {\n return (\n left === right ||\n (defined(left) &&\n defined(right) &&\n CesiumMath.equalsEpsilon(\n left.x,\n right.x,\n relativeEpsilon,\n absoluteEpsilon\n ) &&\n CesiumMath.equalsEpsilon(\n left.y,\n right.y,\n relativeEpsilon,\n absoluteEpsilon\n ) &&\n CesiumMath.equalsEpsilon(\n left.z,\n right.z,\n relativeEpsilon,\n absoluteEpsilon\n ))\n );\n};\n\n/**\n * Computes the cross (outer) product of two Cartesians.\n *\n * @param {Cartesian3} left The first Cartesian.\n * @param {Cartesian3} right The second Cartesian.\n * @param {Cartesian3} result The object onto which to store the result.\n * @returns {Cartesian3} The cross product.\n */\nCartesian3.cross = function (left, right, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"left\", left);\n Check.typeOf.object(\"right\", right);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n const leftX = left.x;\n const leftY = left.y;\n const leftZ = left.z;\n const rightX = right.x;\n const rightY = right.y;\n const rightZ = right.z;\n\n const x = leftY * rightZ - leftZ * rightY;\n const y = leftZ * rightX - leftX * rightZ;\n const z = leftX * rightY - leftY * rightX;\n\n result.x = x;\n result.y = y;\n result.z = z;\n return result;\n};\n\n/**\n * Computes the midpoint between the right and left Cartesian.\n * @param {Cartesian3} left The first Cartesian.\n * @param {Cartesian3} right The second Cartesian.\n * @param {Cartesian3} result The object onto which to store the result.\n * @returns {Cartesian3} The midpoint.\n */\nCartesian3.midpoint = function (left, right, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"left\", left);\n Check.typeOf.object(\"right\", right);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n result.x = (left.x + right.x) * 0.5;\n result.y = (left.y + right.y) * 0.5;\n result.z = (left.z + right.z) * 0.5;\n\n return result;\n};\n\n/**\n * Returns a Cartesian3 position from longitude and latitude values given in degrees.\n *\n * @param {Number} longitude The longitude, in degrees\n * @param {Number} latitude The latitude, in degrees\n * @param {Number} [height=0.0] The height, in meters, above the ellipsoid.\n * @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the position lies.\n * @param {Cartesian3} [result] The object onto which to store the result.\n * @returns {Cartesian3} The position\n *\n * @example\n * const position = Cesium.Cartesian3.fromDegrees(-115.0, 37.0);\n */\nCartesian3.fromDegrees = function (\n longitude,\n latitude,\n height,\n ellipsoid,\n result\n) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.number(\"longitude\", longitude);\n Check.typeOf.number(\"latitude\", latitude);\n //>>includeEnd('debug');\n\n longitude = CesiumMath.toRadians(longitude);\n latitude = CesiumMath.toRadians(latitude);\n return Cartesian3.fromRadians(longitude, latitude, height, ellipsoid, result);\n};\n\nlet scratchN = new Cartesian3();\nlet scratchK = new Cartesian3();\nconst wgs84RadiiSquared = new Cartesian3(\n 6378137.0 * 6378137.0,\n 6378137.0 * 6378137.0,\n 6356752.3142451793 * 6356752.3142451793\n);\n\n/**\n * Returns a Cartesian3 position from longitude and latitude values given in radians.\n *\n * @param {Number} longitude The longitude, in radians\n * @param {Number} latitude The latitude, in radians\n * @param {Number} [height=0.0] The height, in meters, above the ellipsoid.\n * @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the position lies.\n * @param {Cartesian3} [result] The object onto which to store the result.\n * @returns {Cartesian3} The position\n *\n * @example\n * const position = Cesium.Cartesian3.fromRadians(-2.007, 0.645);\n */\nCartesian3.fromRadians = function (\n longitude,\n latitude,\n height,\n ellipsoid,\n result\n) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.number(\"longitude\", longitude);\n Check.typeOf.number(\"latitude\", latitude);\n //>>includeEnd('debug');\n\n height = defaultValue(height, 0.0);\n const radiiSquared = defined(ellipsoid)\n ? ellipsoid.radiiSquared\n : wgs84RadiiSquared;\n\n const cosLatitude = Math.cos(latitude);\n scratchN.x = cosLatitude * Math.cos(longitude);\n scratchN.y = cosLatitude * Math.sin(longitude);\n scratchN.z = Math.sin(latitude);\n scratchN = Cartesian3.normalize(scratchN, scratchN);\n\n Cartesian3.multiplyComponents(radiiSquared, scratchN, scratchK);\n const gamma = Math.sqrt(Cartesian3.dot(scratchN, scratchK));\n scratchK = Cartesian3.divideByScalar(scratchK, gamma, scratchK);\n scratchN = Cartesian3.multiplyByScalar(scratchN, height, scratchN);\n\n if (!defined(result)) {\n result = new Cartesian3();\n }\n return Cartesian3.add(scratchK, scratchN, result);\n};\n\n/**\n * Returns an array of Cartesian3 positions given an array of longitude and latitude values given in degrees.\n *\n * @param {Number[]} coordinates A list of longitude and latitude values. Values alternate [longitude, latitude, longitude, latitude...].\n * @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the coordinates lie.\n * @param {Cartesian3[]} [result] An array of Cartesian3 objects to store the result.\n * @returns {Cartesian3[]} The array of positions.\n *\n * @example\n * const positions = Cesium.Cartesian3.fromDegreesArray([-115.0, 37.0, -107.0, 33.0]);\n */\nCartesian3.fromDegreesArray = function (coordinates, ellipsoid, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.defined(\"coordinates\", coordinates);\n if (coordinates.length < 2 || coordinates.length % 2 !== 0) {\n throw new DeveloperError(\n \"the number of coordinates must be a multiple of 2 and at least 2\"\n );\n }\n //>>includeEnd('debug');\n\n const length = coordinates.length;\n if (!defined(result)) {\n result = new Array(length / 2);\n } else {\n result.length = length / 2;\n }\n\n for (let i = 0; i < length; i += 2) {\n const longitude = coordinates[i];\n const latitude = coordinates[i + 1];\n const index = i / 2;\n result[index] = Cartesian3.fromDegrees(\n longitude,\n latitude,\n 0,\n ellipsoid,\n result[index]\n );\n }\n\n return result;\n};\n\n/**\n * Returns an array of Cartesian3 positions given an array of longitude and latitude values given in radians.\n *\n * @param {Number[]} coordinates A list of longitude and latitude values. Values alternate [longitude, latitude, longitude, latitude...].\n * @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the coordinates lie.\n * @param {Cartesian3[]} [result] An array of Cartesian3 objects to store the result.\n * @returns {Cartesian3[]} The array of positions.\n *\n * @example\n * const positions = Cesium.Cartesian3.fromRadiansArray([-2.007, 0.645, -1.867, .575]);\n */\nCartesian3.fromRadiansArray = function (coordinates, ellipsoid, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.defined(\"coordinates\", coordinates);\n if (coordinates.length < 2 || coordinates.length % 2 !== 0) {\n throw new DeveloperError(\n \"the number of coordinates must be a multiple of 2 and at least 2\"\n );\n }\n //>>includeEnd('debug');\n\n const length = coordinates.length;\n if (!defined(result)) {\n result = new Array(length / 2);\n } else {\n result.length = length / 2;\n }\n\n for (let i = 0; i < length; i += 2) {\n const longitude = coordinates[i];\n const latitude = coordinates[i + 1];\n const index = i / 2;\n result[index] = Cartesian3.fromRadians(\n longitude,\n latitude,\n 0,\n ellipsoid,\n result[index]\n );\n }\n\n return result;\n};\n\n/**\n * Returns an array of Cartesian3 positions given an array of longitude, latitude and height values where longitude and latitude are given in degrees.\n *\n * @param {Number[]} coordinates A list of longitude, latitude and height values. Values alternate [longitude, latitude, height, longitude, latitude, height...].\n * @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the position lies.\n * @param {Cartesian3[]} [result] An array of Cartesian3 objects to store the result.\n * @returns {Cartesian3[]} The array of positions.\n *\n * @example\n * const positions = Cesium.Cartesian3.fromDegreesArrayHeights([-115.0, 37.0, 100000.0, -107.0, 33.0, 150000.0]);\n */\nCartesian3.fromDegreesArrayHeights = function (coordinates, ellipsoid, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.defined(\"coordinates\", coordinates);\n if (coordinates.length < 3 || coordinates.length % 3 !== 0) {\n throw new DeveloperError(\n \"the number of coordinates must be a multiple of 3 and at least 3\"\n );\n }\n //>>includeEnd('debug');\n\n const length = coordinates.length;\n if (!defined(result)) {\n result = new Array(length / 3);\n } else {\n result.length = length / 3;\n }\n\n for (let i = 0; i < length; i += 3) {\n const longitude = coordinates[i];\n const latitude = coordinates[i + 1];\n const height = coordinates[i + 2];\n const index = i / 3;\n result[index] = Cartesian3.fromDegrees(\n longitude,\n latitude,\n height,\n ellipsoid,\n result[index]\n );\n }\n\n return result;\n};\n\n/**\n * Returns an array of Cartesian3 positions given an array of longitude, latitude and height values where longitude and latitude are given in radians.\n *\n * @param {Number[]} coordinates A list of longitude, latitude and height values. Values alternate [longitude, latitude, height, longitude, latitude, height...].\n * @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the position lies.\n * @param {Cartesian3[]} [result] An array of Cartesian3 objects to store the result.\n * @returns {Cartesian3[]} The array of positions.\n *\n * @example\n * const positions = Cesium.Cartesian3.fromRadiansArrayHeights([-2.007, 0.645, 100000.0, -1.867, .575, 150000.0]);\n */\nCartesian3.fromRadiansArrayHeights = function (coordinates, ellipsoid, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.defined(\"coordinates\", coordinates);\n if (coordinates.length < 3 || coordinates.length % 3 !== 0) {\n throw new DeveloperError(\n \"the number of coordinates must be a multiple of 3 and at least 3\"\n );\n }\n //>>includeEnd('debug');\n\n const length = coordinates.length;\n if (!defined(result)) {\n result = new Array(length / 3);\n } else {\n result.length = length / 3;\n }\n\n for (let i = 0; i < length; i += 3) {\n const longitude = coordinates[i];\n const latitude = coordinates[i + 1];\n const height = coordinates[i + 2];\n const index = i / 3;\n result[index] = Cartesian3.fromRadians(\n longitude,\n latitude,\n height,\n ellipsoid,\n result[index]\n );\n }\n\n return result;\n};\n\n/**\n * An immutable Cartesian3 instance initialized to (0.0, 0.0, 0.0).\n *\n * @type {Cartesian3}\n * @constant\n */\nCartesian3.ZERO = Object.freeze(new Cartesian3(0.0, 0.0, 0.0));\n\n/**\n * An immutable Cartesian3 instance initialized to (1.0, 1.0, 1.0).\n *\n * @type {Cartesian3}\n * @constant\n */\nCartesian3.ONE = Object.freeze(new Cartesian3(1.0, 1.0, 1.0));\n\n/**\n * An immutable Cartesian3 instance initialized to (1.0, 0.0, 0.0).\n *\n * @type {Cartesian3}\n * @constant\n */\nCartesian3.UNIT_X = Object.freeze(new Cartesian3(1.0, 0.0, 0.0));\n\n/**\n * An immutable Cartesian3 instance initialized to (0.0, 1.0, 0.0).\n *\n * @type {Cartesian3}\n * @constant\n */\nCartesian3.UNIT_Y = Object.freeze(new Cartesian3(0.0, 1.0, 0.0));\n\n/**\n * An immutable Cartesian3 instance initialized to (0.0, 0.0, 1.0).\n *\n * @type {Cartesian3}\n * @constant\n */\nCartesian3.UNIT_Z = Object.freeze(new Cartesian3(0.0, 0.0, 1.0));\n\n/**\n * Duplicates this Cartesian3 instance.\n *\n * @param {Cartesian3} [result] The object onto which to store the result.\n * @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if one was not provided.\n */\nCartesian3.prototype.clone = function (result) {\n return Cartesian3.clone(this, result);\n};\n\n/**\n * Compares this Cartesian against the provided Cartesian componentwise and returns\n * true if they are equal, false otherwise.\n *\n * @param {Cartesian3} [right] The right hand side Cartesian.\n * @returns {Boolean} true if they are equal, false otherwise.\n */\nCartesian3.prototype.equals = function (right) {\n return Cartesian3.equals(this, right);\n};\n\n/**\n * Compares this Cartesian against the provided Cartesian componentwise and returns\n * true if they pass an absolute or relative tolerance test,\n * false otherwise.\n *\n * @param {Cartesian3} [right] The right hand side Cartesian.\n * @param {Number} [relativeEpsilon=0] The relative epsilon tolerance to use for equality testing.\n * @param {Number} [absoluteEpsilon=relativeEpsilon] The absolute epsilon tolerance to use for equality testing.\n * @returns {Boolean} true if they are within the provided epsilon, false otherwise.\n */\nCartesian3.prototype.equalsEpsilon = function (\n right,\n relativeEpsilon,\n absoluteEpsilon\n) {\n return Cartesian3.equalsEpsilon(\n this,\n right,\n relativeEpsilon,\n absoluteEpsilon\n );\n};\n\n/**\n * Creates a string representing this Cartesian in the format '(x, y, z)'.\n *\n * @returns {String} A string representing this Cartesian in the format '(x, y, z)'.\n */\nCartesian3.prototype.toString = function () {\n return `(${this.x}, ${this.y}, ${this.z})`;\n};\nexport default Cartesian3;\n","import Cartesian3 from \"./Cartesian3.js\";\nimport defined from \"./defined.js\";\nimport DeveloperError from \"./DeveloperError.js\";\nimport CesiumMath from \"./Math.js\";\n\nconst scaleToGeodeticSurfaceIntersection = new Cartesian3();\nconst scaleToGeodeticSurfaceGradient = new Cartesian3();\n\n/**\n * Scales the provided Cartesian position along the geodetic surface normal\n * so that it is on the surface of this ellipsoid. If the position is\n * at the center of the ellipsoid, this function returns undefined.\n *\n * @param {Cartesian3} cartesian The Cartesian position to scale.\n * @param {Cartesian3} oneOverRadii One over radii of the ellipsoid.\n * @param {Cartesian3} oneOverRadiiSquared One over radii squared of the ellipsoid.\n * @param {Number} centerToleranceSquared Tolerance for closeness to the center.\n * @param {Cartesian3} [result] The object onto which to store the result.\n * @returns {Cartesian3} The modified result parameter, a new Cartesian3 instance if none was provided, or undefined if the position is at the center.\n *\n * @function scaleToGeodeticSurface\n *\n * @private\n */\nfunction scaleToGeodeticSurface(\n cartesian,\n oneOverRadii,\n oneOverRadiiSquared,\n centerToleranceSquared,\n result\n) {\n //>>includeStart('debug', pragmas.debug);\n if (!defined(cartesian)) {\n throw new DeveloperError(\"cartesian is required.\");\n }\n if (!defined(oneOverRadii)) {\n throw new DeveloperError(\"oneOverRadii is required.\");\n }\n if (!defined(oneOverRadiiSquared)) {\n throw new DeveloperError(\"oneOverRadiiSquared is required.\");\n }\n if (!defined(centerToleranceSquared)) {\n throw new DeveloperError(\"centerToleranceSquared is required.\");\n }\n //>>includeEnd('debug');\n\n const positionX = cartesian.x;\n const positionY = cartesian.y;\n const positionZ = cartesian.z;\n\n const oneOverRadiiX = oneOverRadii.x;\n const oneOverRadiiY = oneOverRadii.y;\n const oneOverRadiiZ = oneOverRadii.z;\n\n const x2 = positionX * positionX * oneOverRadiiX * oneOverRadiiX;\n const y2 = positionY * positionY * oneOverRadiiY * oneOverRadiiY;\n const z2 = positionZ * positionZ * oneOverRadiiZ * oneOverRadiiZ;\n\n // Compute the squared ellipsoid norm.\n const squaredNorm = x2 + y2 + z2;\n const ratio = Math.sqrt(1.0 / squaredNorm);\n\n // As an initial approximation, assume that the radial intersection is the projection point.\n const intersection = Cartesian3.multiplyByScalar(\n cartesian,\n ratio,\n scaleToGeodeticSurfaceIntersection\n );\n\n // If the position is near the center, the iteration will not converge.\n if (squaredNorm < centerToleranceSquared) {\n return !isFinite(ratio)\n ? undefined\n : Cartesian3.clone(intersection, result);\n }\n\n const oneOverRadiiSquaredX = oneOverRadiiSquared.x;\n const oneOverRadiiSquaredY = oneOverRadiiSquared.y;\n const oneOverRadiiSquaredZ = oneOverRadiiSquared.z;\n\n // Use the gradient at the intersection point in place of the true unit normal.\n // The difference in magnitude will be absorbed in the multiplier.\n const gradient = scaleToGeodeticSurfaceGradient;\n gradient.x = intersection.x * oneOverRadiiSquaredX * 2.0;\n gradient.y = intersection.y * oneOverRadiiSquaredY * 2.0;\n gradient.z = intersection.z * oneOverRadiiSquaredZ * 2.0;\n\n // Compute the initial guess at the normal vector multiplier, lambda.\n let lambda =\n ((1.0 - ratio) * Cartesian3.magnitude(cartesian)) /\n (0.5 * Cartesian3.magnitude(gradient));\n let correction = 0.0;\n\n let func;\n let denominator;\n let xMultiplier;\n let yMultiplier;\n let zMultiplier;\n let xMultiplier2;\n let yMultiplier2;\n let zMultiplier2;\n let xMultiplier3;\n let yMultiplier3;\n let zMultiplier3;\n\n do {\n lambda -= correction;\n\n xMultiplier = 1.0 / (1.0 + lambda * oneOverRadiiSquaredX);\n yMultiplier = 1.0 / (1.0 + lambda * oneOverRadiiSquaredY);\n zMultiplier = 1.0 / (1.0 + lambda * oneOverRadiiSquaredZ);\n\n xMultiplier2 = xMultiplier * xMultiplier;\n yMultiplier2 = yMultiplier * yMultiplier;\n zMultiplier2 = zMultiplier * zMultiplier;\n\n xMultiplier3 = xMultiplier2 * xMultiplier;\n yMultiplier3 = yMultiplier2 * yMultiplier;\n zMultiplier3 = zMultiplier2 * zMultiplier;\n\n func = x2 * xMultiplier2 + y2 * yMultiplier2 + z2 * zMultiplier2 - 1.0;\n\n // \"denominator\" here refers to the use of this expression in the velocity and acceleration\n // computations in the sections to follow.\n denominator =\n x2 * xMultiplier3 * oneOverRadiiSquaredX +\n y2 * yMultiplier3 * oneOverRadiiSquaredY +\n z2 * zMultiplier3 * oneOverRadiiSquaredZ;\n\n const derivative = -2.0 * denominator;\n\n correction = func / derivative;\n } while (Math.abs(func) > CesiumMath.EPSILON12);\n\n if (!defined(result)) {\n return new Cartesian3(\n positionX * xMultiplier,\n positionY * yMultiplier,\n positionZ * zMultiplier\n );\n }\n result.x = positionX * xMultiplier;\n result.y = positionY * yMultiplier;\n result.z = positionZ * zMultiplier;\n return result;\n}\nexport default scaleToGeodeticSurface;\n","import Cartesian3 from \"./Cartesian3.js\";\nimport Check from \"./Check.js\";\nimport defaultValue from \"./defaultValue.js\";\nimport defined from \"./defined.js\";\nimport CesiumMath from \"./Math.js\";\nimport scaleToGeodeticSurface from \"./scaleToGeodeticSurface.js\";\n\n/**\n * A position defined by longitude, latitude, and height.\n * @alias Cartographic\n * @constructor\n *\n * @param {Number} [longitude=0.0] The longitude, in radians.\n * @param {Number} [latitude=0.0] The latitude, in radians.\n * @param {Number} [height=0.0] The height, in meters, above the ellipsoid.\n *\n * @see Ellipsoid\n */\nfunction Cartographic(longitude, latitude, height) {\n /**\n * The longitude, in radians.\n * @type {Number}\n * @default 0.0\n */\n this.longitude = defaultValue(longitude, 0.0);\n\n /**\n * The latitude, in radians.\n * @type {Number}\n * @default 0.0\n */\n this.latitude = defaultValue(latitude, 0.0);\n\n /**\n * The height, in meters, above the ellipsoid.\n * @type {Number}\n * @default 0.0\n */\n this.height = defaultValue(height, 0.0);\n}\n\n/**\n * Creates a new Cartographic instance from longitude and latitude\n * specified in radians.\n *\n * @param {Number} longitude The longitude, in radians.\n * @param {Number} latitude The latitude, in radians.\n * @param {Number} [height=0.0] The height, in meters, above the ellipsoid.\n * @param {Cartographic} [result] The object onto which to store the result.\n * @returns {Cartographic} The modified result parameter or a new Cartographic instance if one was not provided.\n */\nCartographic.fromRadians = function (longitude, latitude, height, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.number(\"longitude\", longitude);\n Check.typeOf.number(\"latitude\", latitude);\n //>>includeEnd('debug');\n\n height = defaultValue(height, 0.0);\n\n if (!defined(result)) {\n return new Cartographic(longitude, latitude, height);\n }\n\n result.longitude = longitude;\n result.latitude = latitude;\n result.height = height;\n return result;\n};\n\n/**\n * Creates a new Cartographic instance from longitude and latitude\n * specified in degrees. The values in the resulting object will\n * be in radians.\n *\n * @param {Number} longitude The longitude, in degrees.\n * @param {Number} latitude The latitude, in degrees.\n * @param {Number} [height=0.0] The height, in meters, above the ellipsoid.\n * @param {Cartographic} [result] The object onto which to store the result.\n * @returns {Cartographic} The modified result parameter or a new Cartographic instance if one was not provided.\n */\nCartographic.fromDegrees = function (longitude, latitude, height, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.number(\"longitude\", longitude);\n Check.typeOf.number(\"latitude\", latitude);\n //>>includeEnd('debug');\n longitude = CesiumMath.toRadians(longitude);\n latitude = CesiumMath.toRadians(latitude);\n\n return Cartographic.fromRadians(longitude, latitude, height, result);\n};\n\nconst cartesianToCartographicN = new Cartesian3();\nconst cartesianToCartographicP = new Cartesian3();\nconst cartesianToCartographicH = new Cartesian3();\nconst wgs84OneOverRadii = new Cartesian3(\n 1.0 / 6378137.0,\n 1.0 / 6378137.0,\n 1.0 / 6356752.3142451793\n);\nconst wgs84OneOverRadiiSquared = new Cartesian3(\n 1.0 / (6378137.0 * 6378137.0),\n 1.0 / (6378137.0 * 6378137.0),\n 1.0 / (6356752.3142451793 * 6356752.3142451793)\n);\nconst wgs84CenterToleranceSquared = CesiumMath.EPSILON1;\n\n/**\n * Creates a new Cartographic instance from a Cartesian position. The values in the\n * resulting object will be in radians.\n *\n * @param {Cartesian3} cartesian The Cartesian position to convert to cartographic representation.\n * @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the position lies.\n * @param {Cartographic} [result] The object onto which to store the result.\n * @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.\n */\nCartographic.fromCartesian = function (cartesian, ellipsoid, result) {\n const oneOverRadii = defined(ellipsoid)\n ? ellipsoid.oneOverRadii\n : wgs84OneOverRadii;\n const oneOverRadiiSquared = defined(ellipsoid)\n ? ellipsoid.oneOverRadiiSquared\n : wgs84OneOverRadiiSquared;\n const centerToleranceSquared = defined(ellipsoid)\n ? ellipsoid._centerToleranceSquared\n : wgs84CenterToleranceSquared;\n\n //`cartesian is required.` is thrown from scaleToGeodeticSurface\n const p = scaleToGeodeticSurface(\n cartesian,\n oneOverRadii,\n oneOverRadiiSquared,\n centerToleranceSquared,\n cartesianToCartographicP\n );\n\n if (!defined(p)) {\n return undefined;\n }\n\n let n = Cartesian3.multiplyComponents(\n p,\n oneOverRadiiSquared,\n cartesianToCartographicN\n );\n n = Cartesian3.normalize(n, n);\n\n const h = Cartesian3.subtract(cartesian, p, cartesianToCartographicH);\n\n const longitude = Math.atan2(n.y, n.x);\n const latitude = Math.asin(n.z);\n const height =\n CesiumMath.sign(Cartesian3.dot(h, cartesian)) * Cartesian3.magnitude(h);\n\n if (!defined(result)) {\n return new Cartographic(longitude, latitude, height);\n }\n result.longitude = longitude;\n result.latitude = latitude;\n result.height = height;\n return result;\n};\n\n/**\n * Creates a new Cartesian3 instance from a Cartographic input. The values in the inputted\n * object should be in radians.\n *\n * @param {Cartographic} cartographic Input to be converted into a Cartesian3 output.\n * @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the position lies.\n * @param {Cartesian3} [result] The object onto which to store the result.\n * @returns {Cartesian3} The position\n */\nCartographic.toCartesian = function (cartographic, ellipsoid, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.defined(\"cartographic\", cartographic);\n //>>includeEnd('debug');\n\n return Cartesian3.fromRadians(\n cartographic.longitude,\n cartographic.latitude,\n cartographic.height,\n ellipsoid,\n result\n );\n};\n\n/**\n * Duplicates a Cartographic instance.\n *\n * @param {Cartographic} cartographic The cartographic to duplicate.\n * @param {Cartographic} [result] The object onto which to store the result.\n * @returns {Cartographic} The modified result parameter or a new Cartographic instance if one was not provided. (Returns undefined if cartographic is undefined)\n */\nCartographic.clone = function (cartographic, result) {\n if (!defined(cartographic)) {\n return undefined;\n }\n if (!defined(result)) {\n return new Cartographic(\n cartographic.longitude,\n cartographic.latitude,\n cartographic.height\n );\n }\n result.longitude = cartographic.longitude;\n result.latitude = cartographic.latitude;\n result.height = cartographic.height;\n return result;\n};\n\n/**\n * Compares the provided cartographics componentwise and returns\n * true if they are equal, false otherwise.\n *\n * @param {Cartographic} [left] The first cartographic.\n * @param {Cartographic} [right] The second cartographic.\n * @returns {Boolean} true if left and right are equal, false otherwise.\n */\nCartographic.equals = function (left, right) {\n return (\n left === right ||\n (defined(left) &&\n defined(right) &&\n left.longitude === right.longitude &&\n left.latitude === right.latitude &&\n left.height === right.height)\n );\n};\n\n/**\n * Compares the provided cartographics componentwise and returns\n * true if they are within the provided epsilon,\n * false otherwise.\n *\n * @param {Cartographic} [left] The first cartographic.\n * @param {Cartographic} [right] The second cartographic.\n * @param {Number} [epsilon=0] The epsilon to use for equality testing.\n * @returns {Boolean} true if left and right are within the provided epsilon, false otherwise.\n */\nCartographic.equalsEpsilon = function (left, right, epsilon) {\n epsilon = defaultValue(epsilon, 0);\n\n return (\n left === right ||\n (defined(left) &&\n defined(right) &&\n Math.abs(left.longitude - right.longitude) <= epsilon &&\n Math.abs(left.latitude - right.latitude) <= epsilon &&\n Math.abs(left.height - right.height) <= epsilon)\n );\n};\n\n/**\n * An immutable Cartographic instance initialized to (0.0, 0.0, 0.0).\n *\n * @type {Cartographic}\n * @constant\n */\nCartographic.ZERO = Object.freeze(new Cartographic(0.0, 0.0, 0.0));\n\n/**\n * Duplicates this instance.\n *\n * @param {Cartographic} [result] The object onto which to store the result.\n * @returns {Cartographic} The modified result parameter or a new Cartographic instance if one was not provided.\n */\nCartographic.prototype.clone = function (result) {\n return Cartographic.clone(this, result);\n};\n\n/**\n * Compares the provided against this cartographic componentwise and returns\n * true if they are equal, false otherwise.\n *\n * @param {Cartographic} [right] The second cartographic.\n * @returns {Boolean} true if left and right are equal, false otherwise.\n */\nCartographic.prototype.equals = function (right) {\n return Cartographic.equals(this, right);\n};\n\n/**\n * Compares the provided against this cartographic componentwise and returns\n * true if they are within the provided epsilon,\n * false otherwise.\n *\n * @param {Cartographic} [right] The second cartographic.\n * @param {Number} [epsilon=0] The epsilon to use for equality testing.\n * @returns {Boolean} true if left and right are within the provided epsilon, false otherwise.\n */\nCartographic.prototype.equalsEpsilon = function (right, epsilon) {\n return Cartographic.equalsEpsilon(this, right, epsilon);\n};\n\n/**\n * Creates a string representing this cartographic in the format '(longitude, latitude, height)'.\n *\n * @returns {String} A string representing the provided cartographic in the format '(longitude, latitude, height)'.\n */\nCartographic.prototype.toString = function () {\n return `(${this.longitude}, ${this.latitude}, ${this.height})`;\n};\nexport default Cartographic;\n","import Cartesian3 from \"./Cartesian3.js\";\nimport Cartographic from \"./Cartographic.js\";\nimport Check from \"./Check.js\";\nimport defaultValue from \"./defaultValue.js\";\nimport defined from \"./defined.js\";\nimport DeveloperError from \"./DeveloperError.js\";\nimport CesiumMath from \"./Math.js\";\nimport scaleToGeodeticSurface from \"./scaleToGeodeticSurface.js\";\n\nfunction initialize(ellipsoid, x, y, z) {\n x = defaultValue(x, 0.0);\n y = defaultValue(y, 0.0);\n z = defaultValue(z, 0.0);\n\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.number.greaterThanOrEquals(\"x\", x, 0.0);\n Check.typeOf.number.greaterThanOrEquals(\"y\", y, 0.0);\n Check.typeOf.number.greaterThanOrEquals(\"z\", z, 0.0);\n //>>includeEnd('debug');\n\n ellipsoid._radii = new Cartesian3(x, y, z);\n\n ellipsoid._radiiSquared = new Cartesian3(x * x, y * y, z * z);\n\n ellipsoid._radiiToTheFourth = new Cartesian3(\n x * x * x * x,\n y * y * y * y,\n z * z * z * z\n );\n\n ellipsoid._oneOverRadii = new Cartesian3(\n x === 0.0 ? 0.0 : 1.0 / x,\n y === 0.0 ? 0.0 : 1.0 / y,\n z === 0.0 ? 0.0 : 1.0 / z\n );\n\n ellipsoid._oneOverRadiiSquared = new Cartesian3(\n x === 0.0 ? 0.0 : 1.0 / (x * x),\n y === 0.0 ? 0.0 : 1.0 / (y * y),\n z === 0.0 ? 0.0 : 1.0 / (z * z)\n );\n\n ellipsoid._minimumRadius = Math.min(x, y, z);\n\n ellipsoid._maximumRadius = Math.max(x, y, z);\n\n ellipsoid._centerToleranceSquared = CesiumMath.EPSILON1;\n\n if (ellipsoid._radiiSquared.z !== 0) {\n ellipsoid._squaredXOverSquaredZ =\n ellipsoid._radiiSquared.x / ellipsoid._radiiSquared.z;\n }\n}\n\n/**\n * A quadratic surface defined in Cartesian coordinates by the equation\n * (x / a)^2 + (y / b)^2 + (z / c)^2 = 1. Primarily used\n * by Cesium to represent the shape of planetary bodies.\n *\n * Rather than constructing this object directly, one of the provided\n * constants is normally used.\n * @alias Ellipsoid\n * @constructor\n *\n * @param {Number} [x=0] The radius in the x direction.\n * @param {Number} [y=0] The radius in the y direction.\n * @param {Number} [z=0] The radius in the z direction.\n *\n * @exception {DeveloperError} All radii components must be greater than or equal to zero.\n *\n * @see Ellipsoid.fromCartesian3\n * @see Ellipsoid.WGS84\n * @see Ellipsoid.UNIT_SPHERE\n */\nfunction Ellipsoid(x, y, z) {\n this._radii = undefined;\n this._radiiSquared = undefined;\n this._radiiToTheFourth = undefined;\n this._oneOverRadii = undefined;\n this._oneOverRadiiSquared = undefined;\n this._minimumRadius = undefined;\n this._maximumRadius = undefined;\n this._centerToleranceSquared = undefined;\n this._squaredXOverSquaredZ = undefined;\n\n initialize(this, x, y, z);\n}\n\nObject.defineProperties(Ellipsoid.prototype, {\n /**\n * Gets the radii of the ellipsoid.\n * @memberof Ellipsoid.prototype\n * @type {Cartesian3}\n * @readonly\n */\n radii: {\n get: function () {\n return this._radii;\n },\n },\n /**\n * Gets the squared radii of the ellipsoid.\n * @memberof Ellipsoid.prototype\n * @type {Cartesian3}\n * @readonly\n */\n radiiSquared: {\n get: function () {\n return this._radiiSquared;\n },\n },\n /**\n * Gets the radii of the ellipsoid raise to the fourth power.\n * @memberof Ellipsoid.prototype\n * @type {Cartesian3}\n * @readonly\n */\n radiiToTheFourth: {\n get: function () {\n return this._radiiToTheFourth;\n },\n },\n /**\n * Gets one over the radii of the ellipsoid.\n * @memberof Ellipsoid.prototype\n * @type {Cartesian3}\n * @readonly\n */\n oneOverRadii: {\n get: function () {\n return this._oneOverRadii;\n },\n },\n /**\n * Gets one over the squared radii of the ellipsoid.\n * @memberof Ellipsoid.prototype\n * @type {Cartesian3}\n * @readonly\n */\n oneOverRadiiSquared: {\n get: function () {\n return this._oneOverRadiiSquared;\n },\n },\n /**\n * Gets the minimum radius of the ellipsoid.\n * @memberof Ellipsoid.prototype\n * @type {Number}\n * @readonly\n */\n minimumRadius: {\n get: function () {\n return this._minimumRadius;\n },\n },\n /**\n * Gets the maximum radius of the ellipsoid.\n * @memberof Ellipsoid.prototype\n * @type {Number}\n * @readonly\n */\n maximumRadius: {\n get: function () {\n return this._maximumRadius;\n },\n },\n});\n\n/**\n * Duplicates an Ellipsoid instance.\n *\n * @param {Ellipsoid} ellipsoid The ellipsoid to duplicate.\n * @param {Ellipsoid} [result] The object onto which to store the result, or undefined if a new\n * instance should be created.\n * @returns {Ellipsoid} The cloned Ellipsoid. (Returns undefined if ellipsoid is undefined)\n */\nEllipsoid.clone = function (ellipsoid, result) {\n if (!defined(ellipsoid)) {\n return undefined;\n }\n const radii = ellipsoid._radii;\n\n if (!defined(result)) {\n return new Ellipsoid(radii.x, radii.y, radii.z);\n }\n\n Cartesian3.clone(radii, result._radii);\n Cartesian3.clone(ellipsoid._radiiSquared, result._radiiSquared);\n Cartesian3.clone(ellipsoid._radiiToTheFourth, result._radiiToTheFourth);\n Cartesian3.clone(ellipsoid._oneOverRadii, result._oneOverRadii);\n Cartesian3.clone(ellipsoid._oneOverRadiiSquared, result._oneOverRadiiSquared);\n result._minimumRadius = ellipsoid._minimumRadius;\n result._maximumRadius = ellipsoid._maximumRadius;\n result._centerToleranceSquared = ellipsoid._centerToleranceSquared;\n\n return result;\n};\n\n/**\n * Computes an Ellipsoid from a Cartesian specifying the radii in x, y, and z directions.\n *\n * @param {Cartesian3} [cartesian=Cartesian3.ZERO] The ellipsoid's radius in the x, y, and z directions.\n * @param {Ellipsoid} [result] The object onto which to store the result, or undefined if a new\n * instance should be created.\n * @returns {Ellipsoid} A new Ellipsoid instance.\n *\n * @exception {DeveloperError} All radii components must be greater than or equal to zero.\n *\n * @see Ellipsoid.WGS84\n * @see Ellipsoid.UNIT_SPHERE\n */\nEllipsoid.fromCartesian3 = function (cartesian, result) {\n if (!defined(result)) {\n result = new Ellipsoid();\n }\n\n if (!defined(cartesian)) {\n return result;\n }\n\n initialize(result, cartesian.x, cartesian.y, cartesian.z);\n return result;\n};\n\n/**\n * An Ellipsoid instance initialized to the WGS84 standard.\n *\n * @type {Ellipsoid}\n * @constant\n */\nEllipsoid.WGS84 = Object.freeze(\n new Ellipsoid(6378137.0, 6378137.0, 6356752.3142451793)\n);\n\n/**\n * An Ellipsoid instance initialized to radii of (1.0, 1.0, 1.0).\n *\n * @type {Ellipsoid}\n * @constant\n */\nEllipsoid.UNIT_SPHERE = Object.freeze(new Ellipsoid(1.0, 1.0, 1.0));\n\n/**\n * An Ellipsoid instance initialized to a sphere with the lunar radius.\n *\n * @type {Ellipsoid}\n * @constant\n */\nEllipsoid.MOON = Object.freeze(\n new Ellipsoid(\n CesiumMath.LUNAR_RADIUS,\n CesiumMath.LUNAR_RADIUS,\n CesiumMath.LUNAR_RADIUS\n )\n);\n\n/**\n * Duplicates an Ellipsoid instance.\n *\n * @param {Ellipsoid} [result] The object onto which to store the result, or undefined if a new\n * instance should be created.\n * @returns {Ellipsoid} The cloned Ellipsoid.\n */\nEllipsoid.prototype.clone = function (result) {\n return Ellipsoid.clone(this, result);\n};\n\n/**\n * The number of elements used to pack the object into an array.\n * @type {Number}\n */\nEllipsoid.packedLength = Cartesian3.packedLength;\n\n/**\n * Stores the provided instance into the provided array.\n *\n * @param {Ellipsoid} value The value to pack.\n * @param {Number[]} array The array to pack into.\n * @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.\n *\n * @returns {Number[]} The array that was packed into\n */\nEllipsoid.pack = function (value, array, startingIndex) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"value\", value);\n Check.defined(\"array\", array);\n //>>includeEnd('debug');\n\n startingIndex = defaultValue(startingIndex, 0);\n\n Cartesian3.pack(value._radii, array, startingIndex);\n\n return array;\n};\n\n/**\n * Retrieves an instance from a packed array.\n *\n * @param {Number[]} array The packed array.\n * @param {Number} [startingIndex=0] The starting index of the element to be unpacked.\n * @param {Ellipsoid} [result] The object into which to store the result.\n * @returns {Ellipsoid} The modified result parameter or a new Ellipsoid instance if one was not provided.\n */\nEllipsoid.unpack = function (array, startingIndex, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.defined(\"array\", array);\n //>>includeEnd('debug');\n\n startingIndex = defaultValue(startingIndex, 0);\n\n const radii = Cartesian3.unpack(array, startingIndex);\n return Ellipsoid.fromCartesian3(radii, result);\n};\n\n/**\n * Computes the unit vector directed from the center of this ellipsoid toward the provided Cartesian position.\n * @function\n *\n * @param {Cartesian3} cartesian The Cartesian for which to to determine the geocentric normal.\n * @param {Cartesian3} [result] The object onto which to store the result.\n * @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if none was provided.\n */\nEllipsoid.prototype.geocentricSurfaceNormal = Cartesian3.normalize;\n\n/**\n * Computes the normal of the plane tangent to the surface of the ellipsoid at the provided position.\n *\n * @param {Cartographic} cartographic The cartographic position for which to to determine the geodetic normal.\n * @param {Cartesian3} [result] The object onto which to store the result.\n * @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if none was provided.\n */\nEllipsoid.prototype.geodeticSurfaceNormalCartographic = function (\n cartographic,\n result\n) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"cartographic\", cartographic);\n //>>includeEnd('debug');\n\n const longitude = cartographic.longitude;\n const latitude = cartographic.latitude;\n const cosLatitude = Math.cos(latitude);\n\n const x = cosLatitude * Math.cos(longitude);\n const y = cosLatitude * Math.sin(longitude);\n const z = Math.sin(latitude);\n\n if (!defined(result)) {\n result = new Cartesian3();\n }\n result.x = x;\n result.y = y;\n result.z = z;\n return Cartesian3.normalize(result, result);\n};\n\n/**\n * Computes the normal of the plane tangent to the surface of the ellipsoid at the provided position.\n *\n * @param {Cartesian3} cartesian The Cartesian position for which to to determine the surface normal.\n * @param {Cartesian3} [result] The object onto which to store the result.\n * @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if none was provided, or undefined if a normal cannot be found.\n */\nEllipsoid.prototype.geodeticSurfaceNormal = function (cartesian, result) {\n if (\n Cartesian3.equalsEpsilon(cartesian, Cartesian3.ZERO, CesiumMath.EPSILON14)\n ) {\n return undefined;\n }\n if (!defined(result)) {\n result = new Cartesian3();\n }\n result = Cartesian3.multiplyComponents(\n cartesian,\n this._oneOverRadiiSquared,\n result\n );\n return Cartesian3.normalize(result, result);\n};\n\nconst cartographicToCartesianNormal = new Cartesian3();\nconst cartographicToCartesianK = new Cartesian3();\n\n/**\n * Converts the provided cartographic to Cartesian representation.\n *\n * @param {Cartographic} cartographic The cartographic position.\n * @param {Cartesian3} [result] The object onto which to store the result.\n * @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if none was provided.\n *\n * @example\n * //Create a Cartographic and determine it's Cartesian representation on a WGS84 ellipsoid.\n * const position = new Cesium.Cartographic(Cesium.Math.toRadians(21), Cesium.Math.toRadians(78), 5000);\n * const cartesianPosition = Cesium.Ellipsoid.WGS84.cartographicToCartesian(position);\n */\nEllipsoid.prototype.cartographicToCartesian = function (cartographic, result) {\n //`cartographic is required` is thrown from geodeticSurfaceNormalCartographic.\n const n = cartographicToCartesianNormal;\n const k = cartographicToCartesianK;\n this.geodeticSurfaceNormalCartographic(cartographic, n);\n Cartesian3.multiplyComponents(this._radiiSquared, n, k);\n const gamma = Math.sqrt(Cartesian3.dot(n, k));\n Cartesian3.divideByScalar(k, gamma, k);\n Cartesian3.multiplyByScalar(n, cartographic.height, n);\n\n if (!defined(result)) {\n result = new Cartesian3();\n }\n return Cartesian3.add(k, n, result);\n};\n\n/**\n * Converts the provided array of cartographics to an array of Cartesians.\n *\n * @param {Cartographic[]} cartographics An array of cartographic positions.\n * @param {Cartesian3[]} [result] The object onto which to store the result.\n * @returns {Cartesian3[]} The modified result parameter or a new Array instance if none was provided.\n *\n * @example\n * //Convert an array of Cartographics and determine their Cartesian representation on a WGS84 ellipsoid.\n * const positions = [new Cesium.Cartographic(Cesium.Math.toRadians(21), Cesium.Math.toRadians(78), 0),\n * new Cesium.Cartographic(Cesium.Math.toRadians(21.321), Cesium.Math.toRadians(78.123), 100),\n * new Cesium.Cartographic(Cesium.Math.toRadians(21.645), Cesium.Math.toRadians(78.456), 250)];\n * const cartesianPositions = Cesium.Ellipsoid.WGS84.cartographicArrayToCartesianArray(positions);\n */\nEllipsoid.prototype.cartographicArrayToCartesianArray = function (\n cartographics,\n result\n) {\n //>>includeStart('debug', pragmas.debug);\n Check.defined(\"cartographics\", cartographics);\n //>>includeEnd('debug')\n\n const length = cartographics.length;\n if (!defined(result)) {\n result = new Array(length);\n } else {\n result.length = length;\n }\n for (let i = 0; i < length; i++) {\n result[i] = this.cartographicToCartesian(cartographics[i], result[i]);\n }\n return result;\n};\n\nconst cartesianToCartographicN = new Cartesian3();\nconst cartesianToCartographicP = new Cartesian3();\nconst cartesianToCartographicH = new Cartesian3();\n\n/**\n * Converts the provided cartesian to cartographic representation.\n * The cartesian is undefined at the center of the ellipsoid.\n *\n * @param {Cartesian3} cartesian The Cartesian position to convert to cartographic representation.\n * @param {Cartographic} [result] The object onto which to store the result.\n * @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.\n *\n * @example\n * //Create a Cartesian and determine it's Cartographic representation on a WGS84 ellipsoid.\n * const position = new Cesium.Cartesian3(17832.12, 83234.52, 952313.73);\n * const cartographicPosition = Cesium.Ellipsoid.WGS84.cartesianToCartographic(position);\n */\nEllipsoid.prototype.cartesianToCartographic = function (cartesian, result) {\n //`cartesian is required.` is thrown from scaleToGeodeticSurface\n const p = this.scaleToGeodeticSurface(cartesian, cartesianToCartographicP);\n\n if (!defined(p)) {\n return undefined;\n }\n\n const n = this.geodeticSurfaceNormal(p, cartesianToCartographicN);\n const h = Cartesian3.subtract(cartesian, p, cartesianToCartographicH);\n\n const longitude = Math.atan2(n.y, n.x);\n const latitude = Math.asin(n.z);\n const height =\n CesiumMath.sign(Cartesian3.dot(h, cartesian)) * Cartesian3.magnitude(h);\n\n if (!defined(result)) {\n return new Cartographic(longitude, latitude, height);\n }\n result.longitude = longitude;\n result.latitude = latitude;\n result.height = height;\n return result;\n};\n\n/**\n * Converts the provided array of cartesians to an array of cartographics.\n *\n * @param {Cartesian3[]} cartesians An array of Cartesian positions.\n * @param {Cartographic[]} [result] The object onto which to store the result.\n * @returns {Cartographic[]} The modified result parameter or a new Array instance if none was provided.\n *\n * @example\n * //Create an array of Cartesians and determine their Cartographic representation on a WGS84 ellipsoid.\n * const positions = [new Cesium.Cartesian3(17832.12, 83234.52, 952313.73),\n * new Cesium.Cartesian3(17832.13, 83234.53, 952313.73),\n * new Cesium.Cartesian3(17832.14, 83234.54, 952313.73)]\n * const cartographicPositions = Cesium.Ellipsoid.WGS84.cartesianArrayToCartographicArray(positions);\n */\nEllipsoid.prototype.cartesianArrayToCartographicArray = function (\n cartesians,\n result\n) {\n //>>includeStart('debug', pragmas.debug);\n Check.defined(\"cartesians\", cartesians);\n //>>includeEnd('debug');\n\n const length = cartesians.length;\n if (!defined(result)) {\n result = new Array(length);\n } else {\n result.length = length;\n }\n for (let i = 0; i < length; ++i) {\n result[i] = this.cartesianToCartographic(cartesians[i], result[i]);\n }\n return result;\n};\n\n/**\n * Scales the provided Cartesian position along the geodetic surface normal\n * so that it is on the surface of this ellipsoid. If the position is\n * at the center of the ellipsoid, this function returns undefined.\n *\n * @param {Cartesian3} cartesian The Cartesian position to scale.\n * @param {Cartesian3} [result] The object onto which to store the result.\n * @returns {Cartesian3} The modified result parameter, a new Cartesian3 instance if none was provided, or undefined if the position is at the center.\n */\nEllipsoid.prototype.scaleToGeodeticSurface = function (cartesian, result) {\n return scaleToGeodeticSurface(\n cartesian,\n this._oneOverRadii,\n this._oneOverRadiiSquared,\n this._centerToleranceSquared,\n result\n );\n};\n\n/**\n * Scales the provided Cartesian position along the geocentric surface normal\n * so that it is on the surface of this ellipsoid.\n *\n * @param {Cartesian3} cartesian The Cartesian position to scale.\n * @param {Cartesian3} [result] The object onto which to store the result.\n * @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if none was provided.\n */\nEllipsoid.prototype.scaleToGeocentricSurface = function (cartesian, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"cartesian\", cartesian);\n //>>includeEnd('debug');\n\n if (!defined(result)) {\n result = new Cartesian3();\n }\n\n const positionX = cartesian.x;\n const positionY = cartesian.y;\n const positionZ = cartesian.z;\n const oneOverRadiiSquared = this._oneOverRadiiSquared;\n\n const beta =\n 1.0 /\n Math.sqrt(\n positionX * positionX * oneOverRadiiSquared.x +\n positionY * positionY * oneOverRadiiSquared.y +\n positionZ * positionZ * oneOverRadiiSquared.z\n );\n\n return Cartesian3.multiplyByScalar(cartesian, beta, result);\n};\n\n/**\n * Transforms a Cartesian X, Y, Z position to the ellipsoid-scaled space by multiplying\n * its components by the result of {@link Ellipsoid#oneOverRadii}.\n *\n * @param {Cartesian3} position The position to transform.\n * @param {Cartesian3} [result] The position to which to copy the result, or undefined to create and\n * return a new instance.\n * @returns {Cartesian3} The position expressed in the scaled space. The returned instance is the\n * one passed as the result parameter if it is not undefined, or a new instance of it is.\n */\nEllipsoid.prototype.transformPositionToScaledSpace = function (\n position,\n result\n) {\n if (!defined(result)) {\n result = new Cartesian3();\n }\n\n return Cartesian3.multiplyComponents(position, this._oneOverRadii, result);\n};\n\n/**\n * Transforms a Cartesian X, Y, Z position from the ellipsoid-scaled space by multiplying\n * its components by the result of {@link Ellipsoid#radii}.\n *\n * @param {Cartesian3} position The position to transform.\n * @param {Cartesian3} [result] The position to which to copy the result, or undefined to create and\n * return a new instance.\n * @returns {Cartesian3} The position expressed in the unscaled space. The returned instance is the\n * one passed as the result parameter if it is not undefined, or a new instance of it is.\n */\nEllipsoid.prototype.transformPositionFromScaledSpace = function (\n position,\n result\n) {\n if (!defined(result)) {\n result = new Cartesian3();\n }\n\n return Cartesian3.multiplyComponents(position, this._radii, result);\n};\n\n/**\n * Compares this Ellipsoid against the provided Ellipsoid componentwise and returns\n * true if they are equal, false otherwise.\n *\n * @param {Ellipsoid} [right] The other Ellipsoid.\n * @returns {Boolean} true if they are equal, false otherwise.\n */\nEllipsoid.prototype.equals = function (right) {\n return (\n this === right ||\n (defined(right) && Cartesian3.equals(this._radii, right._radii))\n );\n};\n\n/**\n * Creates a string representing this Ellipsoid in the format '(radii.x, radii.y, radii.z)'.\n *\n * @returns {String} A string representing this ellipsoid in the format '(radii.x, radii.y, radii.z)'.\n */\nEllipsoid.prototype.toString = function () {\n return this._radii.toString();\n};\n\n/**\n * Computes a point which is the intersection of the surface normal with the z-axis.\n *\n * @param {Cartesian3} position the position. must be on the surface of the ellipsoid.\n * @param {Number} [buffer = 0.0] A buffer to subtract from the ellipsoid size when checking if the point is inside the ellipsoid.\n * 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.\n * In WGS84 datum, intersection point is at max z = +-42841.31151331382 (0.673% of z-axis).\n * Intersection point could be outside the ellipsoid if the ratio of MajorAxis / AxisOfRotation is bigger than the square root of 2\n * @param {Cartesian3} [result] The cartesian to which to copy the result, or undefined to create and\n * return a new instance.\n * @returns {Cartesian3 | undefined} the intersection point if it's inside the ellipsoid, undefined otherwise\n *\n * @exception {DeveloperError} position is required.\n * @exception {DeveloperError} Ellipsoid must be an ellipsoid of revolution (radii.x == radii.y).\n * @exception {DeveloperError} Ellipsoid.radii.z must be greater than 0.\n */\nEllipsoid.prototype.getSurfaceNormalIntersectionWithZAxis = function (\n position,\n buffer,\n result\n) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"position\", position);\n\n if (\n !CesiumMath.equalsEpsilon(\n this._radii.x,\n this._radii.y,\n CesiumMath.EPSILON15\n )\n ) {\n throw new DeveloperError(\n \"Ellipsoid must be an ellipsoid of revolution (radii.x == radii.y)\"\n );\n }\n\n Check.typeOf.number.greaterThan(\"Ellipsoid.radii.z\", this._radii.z, 0);\n //>>includeEnd('debug');\n\n buffer = defaultValue(buffer, 0.0);\n\n const squaredXOverSquaredZ = this._squaredXOverSquaredZ;\n\n if (!defined(result)) {\n result = new Cartesian3();\n }\n\n result.x = 0.0;\n result.y = 0.0;\n result.z = position.z * (1 - squaredXOverSquaredZ);\n\n if (Math.abs(result.z) >= this._radii.z - buffer) {\n return undefined;\n }\n\n return result;\n};\n\nconst abscissas = [\n 0.14887433898163,\n 0.43339539412925,\n 0.67940956829902,\n 0.86506336668898,\n 0.97390652851717,\n 0.0,\n];\nconst weights = [\n 0.29552422471475,\n 0.26926671930999,\n 0.21908636251598,\n 0.14945134915058,\n 0.066671344308684,\n 0.0,\n];\n\n/**\n * Compute the 10th order Gauss-Legendre Quadrature of the given definite integral.\n *\n * @param {Number} a The lower bound for the integration.\n * @param {Number} b The upper bound for the integration.\n * @param {Ellipsoid~RealValuedScalarFunction} func The function to integrate.\n * @returns {Number} The value of the integral of the given function over the given domain.\n *\n * @private\n */\nfunction gaussLegendreQuadrature(a, b, func) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.number(\"a\", a);\n Check.typeOf.number(\"b\", b);\n Check.typeOf.func(\"func\", func);\n //>>includeEnd('debug');\n\n // The range is half of the normal range since the five weights add to one (ten weights add to two).\n // The values of the abscissas are multiplied by two to account for this.\n const xMean = 0.5 * (b + a);\n const xRange = 0.5 * (b - a);\n\n let sum = 0.0;\n for (let i = 0; i < 5; i++) {\n const dx = xRange * abscissas[i];\n sum += weights[i] * (func(xMean + dx) + func(xMean - dx));\n }\n\n // Scale the sum to the range of x.\n sum *= xRange;\n return sum;\n}\n\n/**\n * A real valued scalar function.\n * @callback Ellipsoid~RealValuedScalarFunction\n *\n * @param {Number} x The value used to evaluate the function.\n * @returns {Number} The value of the function at x.\n *\n * @private\n */\n\n/**\n * Computes an approximation of the surface area of a rectangle on the surface of an ellipsoid using\n * Gauss-Legendre 10th order quadrature.\n *\n * @param {Rectangle} rectangle The rectangle used for computing the surface area.\n * @returns {Number} The approximate area of the rectangle on the surface of this ellipsoid.\n */\nEllipsoid.prototype.surfaceArea = function (rectangle) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"rectangle\", rectangle);\n //>>includeEnd('debug');\n const minLongitude = rectangle.west;\n let maxLongitude = rectangle.east;\n const minLatitude = rectangle.south;\n const maxLatitude = rectangle.north;\n\n while (maxLongitude < minLongitude) {\n maxLongitude += CesiumMath.TWO_PI;\n }\n\n const radiiSquared = this._radiiSquared;\n const a2 = radiiSquared.x;\n const b2 = radiiSquared.y;\n const c2 = radiiSquared.z;\n const a2b2 = a2 * b2;\n return gaussLegendreQuadrature(minLatitude, maxLatitude, function (lat) {\n // phi represents the angle measured from the north pole\n // sin(phi) = sin(pi / 2 - lat) = cos(lat), cos(phi) is similar\n const sinPhi = Math.cos(lat);\n const cosPhi = Math.sin(lat);\n return (\n Math.cos(lat) *\n gaussLegendreQuadrature(minLongitude, maxLongitude, function (lon) {\n const cosTheta = Math.cos(lon);\n const sinTheta = Math.sin(lon);\n return Math.sqrt(\n a2b2 * cosPhi * cosPhi +\n c2 *\n (b2 * cosTheta * cosTheta + a2 * sinTheta * sinTheta) *\n sinPhi *\n sinPhi\n );\n })\n );\n });\n};\n\nexport default Ellipsoid;\n","import Cartesian3 from \"./Cartesian3.js\";\nimport Check from \"./Check.js\";\nimport defaultValue from \"./defaultValue.js\";\nimport defined from \"./defined.js\";\nimport DeveloperError from \"./DeveloperError.js\";\nimport CesiumMath from \"./Math.js\";\n\n/**\n * A 3x3 matrix, indexable as a column-major order array.\n * Constructor parameters are in row-major order for code readability.\n * @alias Matrix3\n * @constructor\n * @implements {ArrayLike\n * Returns a diagonal matrix and unitary matrix such that:\n * matrix = unitary matrix * diagonal matrix * transpose(unitary matrix)\n *
\n * The values along the diagonal of the diagonal matrix are the eigenvalues. The columns\n * of the unitary matrix are the corresponding eigenvectors.\n *
\n *\n * @param {Matrix3} matrix The matrix to decompose into diagonal and unitary matrix. Expected to be symmetric.\n * @param {Object} [result] An object with unitary and diagonal properties which are matrices onto which to store the result.\n * @returns {Object} An object with unitary and diagonal properties which are the unitary and diagonal matrices, respectively.\n *\n * @example\n * const a = //... symetric matrix\n * const result = {\n * unitary : new Cesium.Matrix3(),\n * diagonal : new Cesium.Matrix3()\n * };\n * Cesium.Matrix3.computeEigenDecomposition(a, result);\n *\n * const unitaryTranspose = Cesium.Matrix3.transpose(result.unitary, new Cesium.Matrix3());\n * const b = Cesium.Matrix3.multiply(result.unitary, result.diagonal, new Cesium.Matrix3());\n * Cesium.Matrix3.multiply(b, unitaryTranspose, b); // b is now equal to a\n *\n * const lambda = Cesium.Matrix3.getColumn(result.diagonal, 0, new Cesium.Cartesian3()).x; // first eigenvalue\n * const v = Cesium.Matrix3.getColumn(result.unitary, 0, new Cesium.Cartesian3()); // first eigenvector\n * const c = Cesium.Cartesian3.multiplyByScalar(v, lambda, new Cesium.Cartesian3()); // equal to Cesium.Matrix3.multiplyByVector(a, v)\n */\nMatrix3.computeEigenDecomposition = function (matrix, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"matrix\", matrix);\n //>>includeEnd('debug');\n\n // This routine was created based upon Matrix Computations, 3rd ed., by Golub and Van Loan,\n // section 8.4.3 The Classical Jacobi Algorithm\n\n const tolerance = CesiumMath.EPSILON20;\n const maxSweeps = 10;\n\n let count = 0;\n let sweep = 0;\n\n if (!defined(result)) {\n result = {};\n }\n\n const unitaryMatrix = (result.unitary = Matrix3.clone(\n Matrix3.IDENTITY,\n result.unitary\n ));\n const diagMatrix = (result.diagonal = Matrix3.clone(matrix, result.diagonal));\n\n const epsilon = tolerance * computeFrobeniusNorm(diagMatrix);\n\n while (sweep < maxSweeps && offDiagonalFrobeniusNorm(diagMatrix) > epsilon) {\n shurDecomposition(diagMatrix, jMatrix);\n Matrix3.transpose(jMatrix, jMatrixTranspose);\n Matrix3.multiply(diagMatrix, jMatrix, diagMatrix);\n Matrix3.multiply(jMatrixTranspose, diagMatrix, diagMatrix);\n Matrix3.multiply(unitaryMatrix, jMatrix, unitaryMatrix);\n\n if (++count > 2) {\n ++sweep;\n count = 0;\n }\n }\n\n return result;\n};\n\n/**\n * Computes a matrix, which contains the absolute (unsigned) values of the provided matrix's elements.\n *\n * @param {Matrix3} matrix The matrix with signed elements.\n * @param {Matrix3} result The object onto which to store the result.\n * @returns {Matrix3} The modified result parameter.\n */\nMatrix3.abs = function (matrix, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"matrix\", matrix);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n result[0] = Math.abs(matrix[0]);\n result[1] = Math.abs(matrix[1]);\n result[2] = Math.abs(matrix[2]);\n result[3] = Math.abs(matrix[3]);\n result[4] = Math.abs(matrix[4]);\n result[5] = Math.abs(matrix[5]);\n result[6] = Math.abs(matrix[6]);\n result[7] = Math.abs(matrix[7]);\n result[8] = Math.abs(matrix[8]);\n\n return result;\n};\n\n/**\n * Computes the determinant of the provided matrix.\n *\n * @param {Matrix3} matrix The matrix to use.\n * @returns {Number} The value of the determinant of the matrix.\n */\nMatrix3.determinant = function (matrix) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"matrix\", matrix);\n //>>includeEnd('debug');\n\n const m11 = matrix[0];\n const m21 = matrix[3];\n const m31 = matrix[6];\n const m12 = matrix[1];\n const m22 = matrix[4];\n const m32 = matrix[7];\n const m13 = matrix[2];\n const m23 = matrix[5];\n const m33 = matrix[8];\n\n return (\n m11 * (m22 * m33 - m23 * m32) +\n m12 * (m23 * m31 - m21 * m33) +\n m13 * (m21 * m32 - m22 * m31)\n );\n};\n\n/**\n * Computes the inverse of the provided matrix.\n *\n * @param {Matrix3} matrix The matrix to invert.\n * @param {Matrix3} result The object onto which to store the result.\n * @returns {Matrix3} The modified result parameter.\n *\n * @exception {DeveloperError} matrix is not invertible.\n */\nMatrix3.inverse = function (matrix, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"matrix\", matrix);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n const m11 = matrix[0];\n const m21 = matrix[1];\n const m31 = matrix[2];\n const m12 = matrix[3];\n const m22 = matrix[4];\n const m32 = matrix[5];\n const m13 = matrix[6];\n const m23 = matrix[7];\n const m33 = matrix[8];\n\n const determinant = Matrix3.determinant(matrix);\n\n //>>includeStart('debug', pragmas.debug);\n if (Math.abs(determinant) <= CesiumMath.EPSILON15) {\n throw new DeveloperError(\"matrix is not invertible\");\n }\n //>>includeEnd('debug');\n\n result[0] = m22 * m33 - m23 * m32;\n result[1] = m23 * m31 - m21 * m33;\n result[2] = m21 * m32 - m22 * m31;\n result[3] = m13 * m32 - m12 * m33;\n result[4] = m11 * m33 - m13 * m31;\n result[5] = m12 * m31 - m11 * m32;\n result[6] = m12 * m23 - m13 * m22;\n result[7] = m13 * m21 - m11 * m23;\n result[8] = m11 * m22 - m12 * m21;\n\n const scale = 1.0 / determinant;\n return Matrix3.multiplyByScalar(result, scale, result);\n};\n\nconst scratchTransposeMatrix = new Matrix3();\n\n/**\n * Computes the inverse transpose of a matrix.\n *\n * @param {Matrix3} matrix The matrix to transpose and invert.\n * @param {Matrix3} result The object onto which to store the result.\n * @returns {Matrix3} The modified result parameter.\n */\nMatrix3.inverseTranspose = function (matrix, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"matrix\", matrix);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n return Matrix3.inverse(\n Matrix3.transpose(matrix, scratchTransposeMatrix),\n result\n );\n};\n\n/**\n * Compares the provided matrices componentwise and returns\n *true if they are equal, false otherwise.\n *\n * @param {Matrix3} [left] The first matrix.\n * @param {Matrix3} [right] The second matrix.\n * @returns {Boolean} true if left and right are equal, false otherwise.\n */\nMatrix3.equals = function (left, right) {\n return (\n left === right ||\n (defined(left) &&\n defined(right) &&\n left[0] === right[0] &&\n left[1] === right[1] &&\n left[2] === right[2] &&\n left[3] === right[3] &&\n left[4] === right[4] &&\n left[5] === right[5] &&\n left[6] === right[6] &&\n left[7] === right[7] &&\n left[8] === right[8])\n );\n};\n\n/**\n * Compares the provided matrices componentwise and returns\n * true if they are within the provided epsilon,\n * false otherwise.\n *\n * @param {Matrix3} [left] The first matrix.\n * @param {Matrix3} [right] The second matrix.\n * @param {Number} [epsilon=0] The epsilon to use for equality testing.\n * @returns {Boolean} true if left and right are within the provided epsilon, false otherwise.\n */\nMatrix3.equalsEpsilon = function (left, right, epsilon) {\n epsilon = defaultValue(epsilon, 0);\n\n return (\n left === right ||\n (defined(left) &&\n defined(right) &&\n Math.abs(left[0] - right[0]) <= epsilon &&\n Math.abs(left[1] - right[1]) <= epsilon &&\n Math.abs(left[2] - right[2]) <= epsilon &&\n Math.abs(left[3] - right[3]) <= epsilon &&\n Math.abs(left[4] - right[4]) <= epsilon &&\n Math.abs(left[5] - right[5]) <= epsilon &&\n Math.abs(left[6] - right[6]) <= epsilon &&\n Math.abs(left[7] - right[7]) <= epsilon &&\n Math.abs(left[8] - right[8]) <= epsilon)\n );\n};\n\n/**\n * An immutable Matrix3 instance initialized to the identity matrix.\n *\n * @type {Matrix3}\n * @constant\n */\nMatrix3.IDENTITY = Object.freeze(\n new Matrix3(1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0)\n);\n\n/**\n * An immutable Matrix3 instance initialized to the zero matrix.\n *\n * @type {Matrix3}\n * @constant\n */\nMatrix3.ZERO = Object.freeze(\n new Matrix3(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0)\n);\n\n/**\n * The index into Matrix3 for column 0, row 0.\n *\n * @type {Number}\n * @constant\n */\nMatrix3.COLUMN0ROW0 = 0;\n\n/**\n * The index into Matrix3 for column 0, row 1.\n *\n * @type {Number}\n * @constant\n */\nMatrix3.COLUMN0ROW1 = 1;\n\n/**\n * The index into Matrix3 for column 0, row 2.\n *\n * @type {Number}\n * @constant\n */\nMatrix3.COLUMN0ROW2 = 2;\n\n/**\n * The index into Matrix3 for column 1, row 0.\n *\n * @type {Number}\n * @constant\n */\nMatrix3.COLUMN1ROW0 = 3;\n\n/**\n * The index into Matrix3 for column 1, row 1.\n *\n * @type {Number}\n * @constant\n */\nMatrix3.COLUMN1ROW1 = 4;\n\n/**\n * The index into Matrix3 for column 1, row 2.\n *\n * @type {Number}\n * @constant\n */\nMatrix3.COLUMN1ROW2 = 5;\n\n/**\n * The index into Matrix3 for column 2, row 0.\n *\n * @type {Number}\n * @constant\n */\nMatrix3.COLUMN2ROW0 = 6;\n\n/**\n * The index into Matrix3 for column 2, row 1.\n *\n * @type {Number}\n * @constant\n */\nMatrix3.COLUMN2ROW1 = 7;\n\n/**\n * The index into Matrix3 for column 2, row 2.\n *\n * @type {Number}\n * @constant\n */\nMatrix3.COLUMN2ROW2 = 8;\n\nObject.defineProperties(Matrix3.prototype, {\n /**\n * Gets the number of items in the collection.\n * @memberof Matrix3.prototype\n *\n * @type {Number}\n */\n length: {\n get: function () {\n return Matrix3.packedLength;\n },\n },\n});\n\n/**\n * Duplicates the provided Matrix3 instance.\n *\n * @param {Matrix3} [result] The object onto which to store the result.\n * @returns {Matrix3} The modified result parameter or a new Matrix3 instance if one was not provided.\n */\nMatrix3.prototype.clone = function (result) {\n return Matrix3.clone(this, result);\n};\n\n/**\n * Compares this matrix to the provided matrix componentwise and returns\n * true if they are equal, false otherwise.\n *\n * @param {Matrix3} [right] The right hand side matrix.\n * @returns {Boolean} true if they are equal, false otherwise.\n */\nMatrix3.prototype.equals = function (right) {\n return Matrix3.equals(this, right);\n};\n\n/**\n * @private\n */\nMatrix3.equalsArray = function (matrix, array, offset) {\n return (\n matrix[0] === array[offset] &&\n matrix[1] === array[offset + 1] &&\n matrix[2] === array[offset + 2] &&\n matrix[3] === array[offset + 3] &&\n matrix[4] === array[offset + 4] &&\n matrix[5] === array[offset + 5] &&\n matrix[6] === array[offset + 6] &&\n matrix[7] === array[offset + 7] &&\n matrix[8] === array[offset + 8]\n );\n};\n\n/**\n * Compares this matrix to the provided matrix componentwise and returns\n * true if they are within the provided epsilon,\n * false otherwise.\n *\n * @param {Matrix3} [right] The right hand side matrix.\n * @param {Number} [epsilon=0] The epsilon to use for equality testing.\n * @returns {Boolean} true if they are within the provided epsilon, false otherwise.\n */\nMatrix3.prototype.equalsEpsilon = function (right, epsilon) {\n return Matrix3.equalsEpsilon(this, right, epsilon);\n};\n\n/**\n * Creates a string representing this Matrix with each row being\n * on a separate line and in the format '(column0, column1, column2)'.\n *\n * @returns {String} A string representing the provided Matrix with each row being on a separate line and in the format '(column0, column1, column2)'.\n */\nMatrix3.prototype.toString = function () {\n return (\n `(${this[0]}, ${this[3]}, ${this[6]})\\n` +\n `(${this[1]}, ${this[4]}, ${this[7]})\\n` +\n `(${this[2]}, ${this[5]}, ${this[8]})`\n );\n};\nexport default Matrix3;\n","import Check from \"./Check.js\";\nimport defaultValue from \"./defaultValue.js\";\nimport defined from \"./defined.js\";\nimport DeveloperError from \"./DeveloperError.js\";\nimport CesiumMath from \"./Math.js\";\n\n/**\n * A 4D Cartesian point.\n * @alias Cartesian4\n * @constructor\n *\n * @param {Number} [x=0.0] The X component.\n * @param {Number} [y=0.0] The Y component.\n * @param {Number} [z=0.0] The Z component.\n * @param {Number} [w=0.0] The W component.\n *\n * @see Cartesian2\n * @see Cartesian3\n * @see Packable\n */\nfunction Cartesian4(x, y, z, w) {\n /**\n * The X component.\n * @type {Number}\n * @default 0.0\n */\n this.x = defaultValue(x, 0.0);\n\n /**\n * The Y component.\n * @type {Number}\n * @default 0.0\n */\n this.y = defaultValue(y, 0.0);\n\n /**\n * The Z component.\n * @type {Number}\n * @default 0.0\n */\n this.z = defaultValue(z, 0.0);\n\n /**\n * The W component.\n * @type {Number}\n * @default 0.0\n */\n this.w = defaultValue(w, 0.0);\n}\n\n/**\n * Creates a Cartesian4 instance from x, y, z and w coordinates.\n *\n * @param {Number} x The x coordinate.\n * @param {Number} y The y coordinate.\n * @param {Number} z The z coordinate.\n * @param {Number} w The w coordinate.\n * @param {Cartesian4} [result] The object onto which to store the result.\n * @returns {Cartesian4} The modified result parameter or a new Cartesian4 instance if one was not provided.\n */\nCartesian4.fromElements = function (x, y, z, w, result) {\n if (!defined(result)) {\n return new Cartesian4(x, y, z, w);\n }\n\n result.x = x;\n result.y = y;\n result.z = z;\n result.w = w;\n return result;\n};\n\n/**\n * Creates a Cartesian4 instance from a {@link Color}. red, green, blue,\n * and alpha map to x, y, z, and w, respectively.\n *\n * @param {Color} color The source color.\n * @param {Cartesian4} [result] The object onto which to store the result.\n * @returns {Cartesian4} The modified result parameter or a new Cartesian4 instance if one was not provided.\n */\nCartesian4.fromColor = function (color, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"color\", color);\n //>>includeEnd('debug');\n if (!defined(result)) {\n return new Cartesian4(color.red, color.green, color.blue, color.alpha);\n }\n\n result.x = color.red;\n result.y = color.green;\n result.z = color.blue;\n result.w = color.alpha;\n return result;\n};\n\n/**\n * Duplicates a Cartesian4 instance.\n *\n * @param {Cartesian4} cartesian The Cartesian to duplicate.\n * @param {Cartesian4} [result] The object onto which to store the result.\n * @returns {Cartesian4} The modified result parameter or a new Cartesian4 instance if one was not provided. (Returns undefined if cartesian is undefined)\n */\nCartesian4.clone = function (cartesian, result) {\n if (!defined(cartesian)) {\n return undefined;\n }\n\n if (!defined(result)) {\n return new Cartesian4(cartesian.x, cartesian.y, cartesian.z, cartesian.w);\n }\n\n result.x = cartesian.x;\n result.y = cartesian.y;\n result.z = cartesian.z;\n result.w = cartesian.w;\n return result;\n};\n\n/**\n * The number of elements used to pack the object into an array.\n * @type {Number}\n */\nCartesian4.packedLength = 4;\n\n/**\n * Stores the provided instance into the provided array.\n *\n * @param {Cartesian4} value The value to pack.\n * @param {Number[]} array The array to pack into.\n * @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.\n *\n * @returns {Number[]} The array that was packed into\n */\nCartesian4.pack = function (value, array, startingIndex) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"value\", value);\n Check.defined(\"array\", array);\n //>>includeEnd('debug');\n\n startingIndex = defaultValue(startingIndex, 0);\n\n array[startingIndex++] = value.x;\n array[startingIndex++] = value.y;\n array[startingIndex++] = value.z;\n array[startingIndex] = value.w;\n\n return array;\n};\n\n/**\n * Retrieves an instance from a packed array.\n *\n * @param {Number[]} array The packed array.\n * @param {Number} [startingIndex=0] The starting index of the element to be unpacked.\n * @param {Cartesian4} [result] The object into which to store the result.\n * @returns {Cartesian4} The modified result parameter or a new Cartesian4 instance if one was not provided.\n */\nCartesian4.unpack = function (array, startingIndex, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.defined(\"array\", array);\n //>>includeEnd('debug');\n\n startingIndex = defaultValue(startingIndex, 0);\n\n if (!defined(result)) {\n result = new Cartesian4();\n }\n result.x = array[startingIndex++];\n result.y = array[startingIndex++];\n result.z = array[startingIndex++];\n result.w = array[startingIndex];\n return result;\n};\n\n/**\n * Flattens an array of Cartesian4s into an array of components.\n *\n * @param {Cartesian4[]} array The array of cartesians to pack.\n * @param {Number[]} [result] The array onto which to store the result. If this is a typed array, it must have array.length * 4 components, else a {@link DeveloperError} will be thrown. If it is a regular array, it will be resized to have (array.length * 4) elements.\n * @returns {Number[]} The packed array.\n */\nCartesian4.packArray = function (array, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.defined(\"array\", array);\n //>>includeEnd('debug');\n\n const length = array.length;\n const resultLength = length * 4;\n if (!defined(result)) {\n result = new Array(resultLength);\n } else if (!Array.isArray(result) && result.length !== resultLength) {\n //>>includeStart('debug', pragmas.debug);\n throw new DeveloperError(\n \"If result is a typed array, it must have exactly array.length * 4 elements\"\n );\n //>>includeEnd('debug');\n } else if (result.length !== resultLength) {\n result.length = resultLength;\n }\n\n for (let i = 0; i < length; ++i) {\n Cartesian4.pack(array[i], result, i * 4);\n }\n return result;\n};\n\n/**\n * Unpacks an array of cartesian components into an array of Cartesian4s.\n *\n * @param {Number[]} array The array of components to unpack.\n * @param {Cartesian4[]} [result] The array onto which to store the result.\n * @returns {Cartesian4[]} The unpacked array.\n */\nCartesian4.unpackArray = function (array, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.defined(\"array\", array);\n Check.typeOf.number.greaterThanOrEquals(\"array.length\", array.length, 4);\n if (array.length % 4 !== 0) {\n throw new DeveloperError(\"array length must be a multiple of 4.\");\n }\n //>>includeEnd('debug');\n\n const length = array.length;\n if (!defined(result)) {\n result = new Array(length / 4);\n } else {\n result.length = length / 4;\n }\n\n for (let i = 0; i < length; i += 4) {\n const index = i / 4;\n result[index] = Cartesian4.unpack(array, i, result[index]);\n }\n return result;\n};\n\n/**\n * Creates a Cartesian4 from four consecutive elements in an array.\n * @function\n *\n * @param {Number[]} array The array whose four consecutive elements correspond to the x, y, z, and w components, respectively.\n * @param {Number} [startingIndex=0] The offset into the array of the first element, which corresponds to the x component.\n * @param {Cartesian4} [result] The object onto which to store the result.\n * @returns {Cartesian4} The modified result parameter or a new Cartesian4 instance if one was not provided.\n *\n * @example\n * // Create a Cartesian4 with (1.0, 2.0, 3.0, 4.0)\n * const v = [1.0, 2.0, 3.0, 4.0];\n * const p = Cesium.Cartesian4.fromArray(v);\n *\n * // Create a Cartesian4 with (1.0, 2.0, 3.0, 4.0) using an offset into an array\n * const v2 = [0.0, 0.0, 1.0, 2.0, 3.0, 4.0];\n * const p2 = Cesium.Cartesian4.fromArray(v2, 2);\n */\nCartesian4.fromArray = Cartesian4.unpack;\n\n/**\n * Computes the value of the maximum component for the supplied Cartesian.\n *\n * @param {Cartesian4} cartesian The cartesian to use.\n * @returns {Number} The value of the maximum component.\n */\nCartesian4.maximumComponent = function (cartesian) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"cartesian\", cartesian);\n //>>includeEnd('debug');\n\n return Math.max(cartesian.x, cartesian.y, cartesian.z, cartesian.w);\n};\n\n/**\n * Computes the value of the minimum component for the supplied Cartesian.\n *\n * @param {Cartesian4} cartesian The cartesian to use.\n * @returns {Number} The value of the minimum component.\n */\nCartesian4.minimumComponent = function (cartesian) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"cartesian\", cartesian);\n //>>includeEnd('debug');\n\n return Math.min(cartesian.x, cartesian.y, cartesian.z, cartesian.w);\n};\n\n/**\n * Compares two Cartesians and computes a Cartesian which contains the minimum components of the supplied Cartesians.\n *\n * @param {Cartesian4} first A cartesian to compare.\n * @param {Cartesian4} second A cartesian to compare.\n * @param {Cartesian4} result The object into which to store the result.\n * @returns {Cartesian4} A cartesian with the minimum components.\n */\nCartesian4.minimumByComponent = function (first, second, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"first\", first);\n Check.typeOf.object(\"second\", second);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n result.x = Math.min(first.x, second.x);\n result.y = Math.min(first.y, second.y);\n result.z = Math.min(first.z, second.z);\n result.w = Math.min(first.w, second.w);\n\n return result;\n};\n\n/**\n * Compares two Cartesians and computes a Cartesian which contains the maximum components of the supplied Cartesians.\n *\n * @param {Cartesian4} first A cartesian to compare.\n * @param {Cartesian4} second A cartesian to compare.\n * @param {Cartesian4} result The object into which to store the result.\n * @returns {Cartesian4} A cartesian with the maximum components.\n */\nCartesian4.maximumByComponent = function (first, second, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"first\", first);\n Check.typeOf.object(\"second\", second);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n result.x = Math.max(first.x, second.x);\n result.y = Math.max(first.y, second.y);\n result.z = Math.max(first.z, second.z);\n result.w = Math.max(first.w, second.w);\n\n return result;\n};\n\n/**\n * Computes the provided Cartesian's squared magnitude.\n *\n * @param {Cartesian4} cartesian The Cartesian instance whose squared magnitude is to be computed.\n * @returns {Number} The squared magnitude.\n */\nCartesian4.magnitudeSquared = function (cartesian) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"cartesian\", cartesian);\n //>>includeEnd('debug');\n\n return (\n cartesian.x * cartesian.x +\n cartesian.y * cartesian.y +\n cartesian.z * cartesian.z +\n cartesian.w * cartesian.w\n );\n};\n\n/**\n * Computes the Cartesian's magnitude (length).\n *\n * @param {Cartesian4} cartesian The Cartesian instance whose magnitude is to be computed.\n * @returns {Number} The magnitude.\n */\nCartesian4.magnitude = function (cartesian) {\n return Math.sqrt(Cartesian4.magnitudeSquared(cartesian));\n};\n\nconst distanceScratch = new Cartesian4();\n\n/**\n * Computes the 4-space distance between two points.\n *\n * @param {Cartesian4} left The first point to compute the distance from.\n * @param {Cartesian4} right The second point to compute the distance to.\n * @returns {Number} The distance between two points.\n *\n * @example\n * // Returns 1.0\n * const d = Cesium.Cartesian4.distance(\n * new Cesium.Cartesian4(1.0, 0.0, 0.0, 0.0),\n * new Cesium.Cartesian4(2.0, 0.0, 0.0, 0.0));\n */\nCartesian4.distance = function (left, right) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"left\", left);\n Check.typeOf.object(\"right\", right);\n //>>includeEnd('debug');\n\n Cartesian4.subtract(left, right, distanceScratch);\n return Cartesian4.magnitude(distanceScratch);\n};\n\n/**\n * Computes the squared distance between two points. Comparing squared distances\n * using this function is more efficient than comparing distances using {@link Cartesian4#distance}.\n *\n * @param {Cartesian4} left The first point to compute the distance from.\n * @param {Cartesian4} right The second point to compute the distance to.\n * @returns {Number} The distance between two points.\n *\n * @example\n * // Returns 4.0, not 2.0\n * const d = Cesium.Cartesian4.distance(\n * new Cesium.Cartesian4(1.0, 0.0, 0.0, 0.0),\n * new Cesium.Cartesian4(3.0, 0.0, 0.0, 0.0));\n */\nCartesian4.distanceSquared = function (left, right) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"left\", left);\n Check.typeOf.object(\"right\", right);\n //>>includeEnd('debug');\n\n Cartesian4.subtract(left, right, distanceScratch);\n return Cartesian4.magnitudeSquared(distanceScratch);\n};\n\n/**\n * Computes the normalized form of the supplied Cartesian.\n *\n * @param {Cartesian4} cartesian The Cartesian to be normalized.\n * @param {Cartesian4} result The object onto which to store the result.\n * @returns {Cartesian4} The modified result parameter.\n */\nCartesian4.normalize = function (cartesian, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"cartesian\", cartesian);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n const magnitude = Cartesian4.magnitude(cartesian);\n\n result.x = cartesian.x / magnitude;\n result.y = cartesian.y / magnitude;\n result.z = cartesian.z / magnitude;\n result.w = cartesian.w / magnitude;\n\n //>>includeStart('debug', pragmas.debug);\n if (\n isNaN(result.x) ||\n isNaN(result.y) ||\n isNaN(result.z) ||\n isNaN(result.w)\n ) {\n throw new DeveloperError(\"normalized result is not a number\");\n }\n //>>includeEnd('debug');\n\n return result;\n};\n\n/**\n * Computes the dot (scalar) product of two Cartesians.\n *\n * @param {Cartesian4} left The first Cartesian.\n * @param {Cartesian4} right The second Cartesian.\n * @returns {Number} The dot product.\n */\nCartesian4.dot = function (left, right) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"left\", left);\n Check.typeOf.object(\"right\", right);\n //>>includeEnd('debug');\n\n return (\n left.x * right.x + left.y * right.y + left.z * right.z + left.w * right.w\n );\n};\n\n/**\n * Computes the componentwise product of two Cartesians.\n *\n * @param {Cartesian4} left The first Cartesian.\n * @param {Cartesian4} right The second Cartesian.\n * @param {Cartesian4} result The object onto which to store the result.\n * @returns {Cartesian4} The modified result parameter.\n */\nCartesian4.multiplyComponents = function (left, right, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"left\", left);\n Check.typeOf.object(\"right\", right);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n result.x = left.x * right.x;\n result.y = left.y * right.y;\n result.z = left.z * right.z;\n result.w = left.w * right.w;\n return result;\n};\n\n/**\n * Computes the componentwise quotient of two Cartesians.\n *\n * @param {Cartesian4} left The first Cartesian.\n * @param {Cartesian4} right The second Cartesian.\n * @param {Cartesian4} result The object onto which to store the result.\n * @returns {Cartesian4} The modified result parameter.\n */\nCartesian4.divideComponents = function (left, right, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"left\", left);\n Check.typeOf.object(\"right\", right);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n result.x = left.x / right.x;\n result.y = left.y / right.y;\n result.z = left.z / right.z;\n result.w = left.w / right.w;\n return result;\n};\n\n/**\n * Computes the componentwise sum of two Cartesians.\n *\n * @param {Cartesian4} left The first Cartesian.\n * @param {Cartesian4} right The second Cartesian.\n * @param {Cartesian4} result The object onto which to store the result.\n * @returns {Cartesian4} The modified result parameter.\n */\nCartesian4.add = function (left, right, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"left\", left);\n Check.typeOf.object(\"right\", right);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n result.x = left.x + right.x;\n result.y = left.y + right.y;\n result.z = left.z + right.z;\n result.w = left.w + right.w;\n return result;\n};\n\n/**\n * Computes the componentwise difference of two Cartesians.\n *\n * @param {Cartesian4} left The first Cartesian.\n * @param {Cartesian4} right The second Cartesian.\n * @param {Cartesian4} result The object onto which to store the result.\n * @returns {Cartesian4} The modified result parameter.\n */\nCartesian4.subtract = function (left, right, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"left\", left);\n Check.typeOf.object(\"right\", right);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n result.x = left.x - right.x;\n result.y = left.y - right.y;\n result.z = left.z - right.z;\n result.w = left.w - right.w;\n return result;\n};\n\n/**\n * Multiplies the provided Cartesian componentwise by the provided scalar.\n *\n * @param {Cartesian4} cartesian The Cartesian to be scaled.\n * @param {Number} scalar The scalar to multiply with.\n * @param {Cartesian4} result The object onto which to store the result.\n * @returns {Cartesian4} The modified result parameter.\n */\nCartesian4.multiplyByScalar = function (cartesian, scalar, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"cartesian\", cartesian);\n Check.typeOf.number(\"scalar\", scalar);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n result.x = cartesian.x * scalar;\n result.y = cartesian.y * scalar;\n result.z = cartesian.z * scalar;\n result.w = cartesian.w * scalar;\n return result;\n};\n\n/**\n * Divides the provided Cartesian componentwise by the provided scalar.\n *\n * @param {Cartesian4} cartesian The Cartesian to be divided.\n * @param {Number} scalar The scalar to divide by.\n * @param {Cartesian4} result The object onto which to store the result.\n * @returns {Cartesian4} The modified result parameter.\n */\nCartesian4.divideByScalar = function (cartesian, scalar, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"cartesian\", cartesian);\n Check.typeOf.number(\"scalar\", scalar);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n result.x = cartesian.x / scalar;\n result.y = cartesian.y / scalar;\n result.z = cartesian.z / scalar;\n result.w = cartesian.w / scalar;\n return result;\n};\n\n/**\n * Negates the provided Cartesian.\n *\n * @param {Cartesian4} cartesian The Cartesian to be negated.\n * @param {Cartesian4} result The object onto which to store the result.\n * @returns {Cartesian4} The modified result parameter.\n */\nCartesian4.negate = function (cartesian, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"cartesian\", cartesian);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n result.x = -cartesian.x;\n result.y = -cartesian.y;\n result.z = -cartesian.z;\n result.w = -cartesian.w;\n return result;\n};\n\n/**\n * Computes the absolute value of the provided Cartesian.\n *\n * @param {Cartesian4} cartesian The Cartesian whose absolute value is to be computed.\n * @param {Cartesian4} result The object onto which to store the result.\n * @returns {Cartesian4} The modified result parameter.\n */\nCartesian4.abs = function (cartesian, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"cartesian\", cartesian);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n result.x = Math.abs(cartesian.x);\n result.y = Math.abs(cartesian.y);\n result.z = Math.abs(cartesian.z);\n result.w = Math.abs(cartesian.w);\n return result;\n};\n\nconst lerpScratch = new Cartesian4();\n/**\n * Computes the linear interpolation or extrapolation at t using the provided cartesians.\n *\n * @param {Cartesian4} start The value corresponding to t at 0.0.\n * @param {Cartesian4}end The value corresponding to t at 1.0.\n * @param {Number} t The point along t at which to interpolate.\n * @param {Cartesian4} result The object onto which to store the result.\n * @returns {Cartesian4} The modified result parameter.\n */\nCartesian4.lerp = function (start, end, t, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"start\", start);\n Check.typeOf.object(\"end\", end);\n Check.typeOf.number(\"t\", t);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n Cartesian4.multiplyByScalar(end, t, lerpScratch);\n result = Cartesian4.multiplyByScalar(start, 1.0 - t, result);\n return Cartesian4.add(lerpScratch, result, result);\n};\n\nconst mostOrthogonalAxisScratch = new Cartesian4();\n/**\n * Returns the axis that is most orthogonal to the provided Cartesian.\n *\n * @param {Cartesian4} cartesian The Cartesian on which to find the most orthogonal axis.\n * @param {Cartesian4} result The object onto which to store the result.\n * @returns {Cartesian4} The most orthogonal axis.\n */\nCartesian4.mostOrthogonalAxis = function (cartesian, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"cartesian\", cartesian);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n const f = Cartesian4.normalize(cartesian, mostOrthogonalAxisScratch);\n Cartesian4.abs(f, f);\n\n if (f.x <= f.y) {\n if (f.x <= f.z) {\n if (f.x <= f.w) {\n result = Cartesian4.clone(Cartesian4.UNIT_X, result);\n } else {\n result = Cartesian4.clone(Cartesian4.UNIT_W, result);\n }\n } else if (f.z <= f.w) {\n result = Cartesian4.clone(Cartesian4.UNIT_Z, result);\n } else {\n result = Cartesian4.clone(Cartesian4.UNIT_W, result);\n }\n } else if (f.y <= f.z) {\n if (f.y <= f.w) {\n result = Cartesian4.clone(Cartesian4.UNIT_Y, result);\n } else {\n result = Cartesian4.clone(Cartesian4.UNIT_W, result);\n }\n } else if (f.z <= f.w) {\n result = Cartesian4.clone(Cartesian4.UNIT_Z, result);\n } else {\n result = Cartesian4.clone(Cartesian4.UNIT_W, result);\n }\n\n return result;\n};\n\n/**\n * Compares the provided Cartesians componentwise and returns\n * true if they are equal, false otherwise.\n *\n * @param {Cartesian4} [left] The first Cartesian.\n * @param {Cartesian4} [right] The second Cartesian.\n * @returns {Boolean} true if left and right are equal, false otherwise.\n */\nCartesian4.equals = function (left, right) {\n return (\n left === right ||\n (defined(left) &&\n defined(right) &&\n left.x === right.x &&\n left.y === right.y &&\n left.z === right.z &&\n left.w === right.w)\n );\n};\n\n/**\n * @private\n */\nCartesian4.equalsArray = function (cartesian, array, offset) {\n return (\n cartesian.x === array[offset] &&\n cartesian.y === array[offset + 1] &&\n cartesian.z === array[offset + 2] &&\n cartesian.w === array[offset + 3]\n );\n};\n\n/**\n * Compares the provided Cartesians componentwise and returns\n * true if they pass an absolute or relative tolerance test,\n * false otherwise.\n *\n * @param {Cartesian4} [left] The first Cartesian.\n * @param {Cartesian4} [right] The second Cartesian.\n * @param {Number} [relativeEpsilon=0] The relative epsilon tolerance to use for equality testing.\n * @param {Number} [absoluteEpsilon=relativeEpsilon] The absolute epsilon tolerance to use for equality testing.\n * @returns {Boolean} true if left and right are within the provided epsilon, false otherwise.\n */\nCartesian4.equalsEpsilon = function (\n left,\n right,\n relativeEpsilon,\n absoluteEpsilon\n) {\n return (\n left === right ||\n (defined(left) &&\n defined(right) &&\n CesiumMath.equalsEpsilon(\n left.x,\n right.x,\n relativeEpsilon,\n absoluteEpsilon\n ) &&\n CesiumMath.equalsEpsilon(\n left.y,\n right.y,\n relativeEpsilon,\n absoluteEpsilon\n ) &&\n CesiumMath.equalsEpsilon(\n left.z,\n right.z,\n relativeEpsilon,\n absoluteEpsilon\n ) &&\n CesiumMath.equalsEpsilon(\n left.w,\n right.w,\n relativeEpsilon,\n absoluteEpsilon\n ))\n );\n};\n\n/**\n * An immutable Cartesian4 instance initialized to (0.0, 0.0, 0.0, 0.0).\n *\n * @type {Cartesian4}\n * @constant\n */\nCartesian4.ZERO = Object.freeze(new Cartesian4(0.0, 0.0, 0.0, 0.0));\n\n/**\n * An immutable Cartesian4 instance initialized to (1.0, 1.0, 1.0, 1.0).\n *\n * @type {Cartesian4}\n * @constant\n */\nCartesian4.ONE = Object.freeze(new Cartesian4(1.0, 1.0, 1.0, 1.0));\n\n/**\n * An immutable Cartesian4 instance initialized to (1.0, 0.0, 0.0, 0.0).\n *\n * @type {Cartesian4}\n * @constant\n */\nCartesian4.UNIT_X = Object.freeze(new Cartesian4(1.0, 0.0, 0.0, 0.0));\n\n/**\n * An immutable Cartesian4 instance initialized to (0.0, 1.0, 0.0, 0.0).\n *\n * @type {Cartesian4}\n * @constant\n */\nCartesian4.UNIT_Y = Object.freeze(new Cartesian4(0.0, 1.0, 0.0, 0.0));\n\n/**\n * An immutable Cartesian4 instance initialized to (0.0, 0.0, 1.0, 0.0).\n *\n * @type {Cartesian4}\n * @constant\n */\nCartesian4.UNIT_Z = Object.freeze(new Cartesian4(0.0, 0.0, 1.0, 0.0));\n\n/**\n * An immutable Cartesian4 instance initialized to (0.0, 0.0, 0.0, 1.0).\n *\n * @type {Cartesian4}\n * @constant\n */\nCartesian4.UNIT_W = Object.freeze(new Cartesian4(0.0, 0.0, 0.0, 1.0));\n\n/**\n * Duplicates this Cartesian4 instance.\n *\n * @param {Cartesian4} [result] The object onto which to store the result.\n * @returns {Cartesian4} The modified result parameter or a new Cartesian4 instance if one was not provided.\n */\nCartesian4.prototype.clone = function (result) {\n return Cartesian4.clone(this, result);\n};\n\n/**\n * Compares this Cartesian against the provided Cartesian componentwise and returns\n * true if they are equal, false otherwise.\n *\n * @param {Cartesian4} [right] The right hand side Cartesian.\n * @returns {Boolean} true if they are equal, false otherwise.\n */\nCartesian4.prototype.equals = function (right) {\n return Cartesian4.equals(this, right);\n};\n\n/**\n * Compares this Cartesian against the provided Cartesian componentwise and returns\n * true if they pass an absolute or relative tolerance test,\n * false otherwise.\n *\n * @param {Cartesian4} [right] The right hand side Cartesian.\n * @param {Number} [relativeEpsilon=0] The relative epsilon tolerance to use for equality testing.\n * @param {Number} [absoluteEpsilon=relativeEpsilon] The absolute epsilon tolerance to use for equality testing.\n * @returns {Boolean} true if they are within the provided epsilon, false otherwise.\n */\nCartesian4.prototype.equalsEpsilon = function (\n right,\n relativeEpsilon,\n absoluteEpsilon\n) {\n return Cartesian4.equalsEpsilon(\n this,\n right,\n relativeEpsilon,\n absoluteEpsilon\n );\n};\n\n/**\n * Creates a string representing this Cartesian in the format '(x, y, z, w)'.\n *\n * @returns {String} A string representing the provided Cartesian in the format '(x, y, z, w)'.\n */\nCartesian4.prototype.toString = function () {\n return `(${this.x}, ${this.y}, ${this.z}, ${this.w})`;\n};\n\n// scratchU8Array and scratchF32Array are views into the same buffer\nconst scratchF32Array = new Float32Array(1);\nconst scratchU8Array = new Uint8Array(scratchF32Array.buffer);\n\nconst testU32 = new Uint32Array([0x11223344]);\nconst testU8 = new Uint8Array(testU32.buffer);\nconst littleEndian = testU8[0] === 0x44;\n\n/**\n * Packs an arbitrary floating point value to 4 values representable using uint8.\n *\n * @param {Number} value A floating point number.\n * @param {Cartesian4} [result] The Cartesian4 that will contain the packed float.\n * @returns {Cartesian4} A Cartesian4 representing the float packed to values in x, y, z, and w.\n */\nCartesian4.packFloat = function (value, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.number(\"value\", value);\n //>>includeEnd('debug');\n\n if (!defined(result)) {\n result = new Cartesian4();\n }\n\n // scratchU8Array and scratchF32Array are views into the same buffer\n scratchF32Array[0] = value;\n\n if (littleEndian) {\n result.x = scratchU8Array[0];\n result.y = scratchU8Array[1];\n result.z = scratchU8Array[2];\n result.w = scratchU8Array[3];\n } else {\n // convert from big-endian to little-endian\n result.x = scratchU8Array[3];\n result.y = scratchU8Array[2];\n result.z = scratchU8Array[1];\n result.w = scratchU8Array[0];\n }\n return result;\n};\n\n/**\n * Unpacks a float packed using Cartesian4.packFloat.\n *\n * @param {Cartesian4} packedFloat A Cartesian4 containing a float packed to 4 values representable using uint8.\n * @returns {Number} The unpacked float.\n * @private\n */\nCartesian4.unpackFloat = function (packedFloat) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"packedFloat\", packedFloat);\n //>>includeEnd('debug');\n\n // scratchU8Array and scratchF32Array are views into the same buffer\n if (littleEndian) {\n scratchU8Array[0] = packedFloat.x;\n scratchU8Array[1] = packedFloat.y;\n scratchU8Array[2] = packedFloat.z;\n scratchU8Array[3] = packedFloat.w;\n } else {\n // convert from little-endian to big-endian\n scratchU8Array[0] = packedFloat.w;\n scratchU8Array[1] = packedFloat.z;\n scratchU8Array[2] = packedFloat.y;\n scratchU8Array[3] = packedFloat.x;\n }\n return scratchF32Array[0];\n};\nexport default Cartesian4;\n","import Cartesian3 from \"./Cartesian3.js\";\nimport Cartesian4 from \"./Cartesian4.js\";\nimport Check from \"./Check.js\";\nimport defaultValue from \"./defaultValue.js\";\nimport defined from \"./defined.js\";\nimport DeveloperError from \"./DeveloperError.js\";\nimport CesiumMath from \"./Math.js\";\nimport Matrix3 from \"./Matrix3.js\";\nimport RuntimeError from \"./RuntimeError.js\";\n\n/**\n * A 4x4 matrix, indexable as a column-major order array.\n * Constructor parameters are in row-major order for code readability.\n * @alias Matrix4\n * @constructor\n * @implements {ArrayLike[0.0, 0.0, 0.0, 1.0])\n * by a 3x3 rotation matrix. This is an optimization\n * for Matrix4.multiply(m, Matrix4.fromRotationTranslation(rotation), m); with less allocations and arithmetic operations.\n *\n * @param {Matrix4} matrix The matrix on the left-hand side.\n * @param {Matrix3} rotation The 3x3 rotation matrix on the right-hand side.\n * @param {Matrix4} result The object onto which to store the result.\n * @returns {Matrix4} The modified result parameter.\n *\n * @example\n * // Instead of Cesium.Matrix4.multiply(m, Cesium.Matrix4.fromRotationTranslation(rotation), m);\n * Cesium.Matrix4.multiplyByMatrix3(m, rotation, m);\n */\nMatrix4.multiplyByMatrix3 = function (matrix, rotation, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"matrix\", matrix);\n Check.typeOf.object(\"rotation\", rotation);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n const left0 = matrix[0];\n const left1 = matrix[1];\n const left2 = matrix[2];\n const left4 = matrix[4];\n const left5 = matrix[5];\n const left6 = matrix[6];\n const left8 = matrix[8];\n const left9 = matrix[9];\n const left10 = matrix[10];\n\n const right0 = rotation[0];\n const right1 = rotation[1];\n const right2 = rotation[2];\n const right4 = rotation[3];\n const right5 = rotation[4];\n const right6 = rotation[5];\n const right8 = rotation[6];\n const right9 = rotation[7];\n const right10 = rotation[8];\n\n const column0Row0 = left0 * right0 + left4 * right1 + left8 * right2;\n const column0Row1 = left1 * right0 + left5 * right1 + left9 * right2;\n const column0Row2 = left2 * right0 + left6 * right1 + left10 * right2;\n\n const column1Row0 = left0 * right4 + left4 * right5 + left8 * right6;\n const column1Row1 = left1 * right4 + left5 * right5 + left9 * right6;\n const column1Row2 = left2 * right4 + left6 * right5 + left10 * right6;\n\n const column2Row0 = left0 * right8 + left4 * right9 + left8 * right10;\n const column2Row1 = left1 * right8 + left5 * right9 + left9 * right10;\n const column2Row2 = left2 * right8 + left6 * right9 + left10 * right10;\n\n result[0] = column0Row0;\n result[1] = column0Row1;\n result[2] = column0Row2;\n result[3] = 0.0;\n result[4] = column1Row0;\n result[5] = column1Row1;\n result[6] = column1Row2;\n result[7] = 0.0;\n result[8] = column2Row0;\n result[9] = column2Row1;\n result[10] = column2Row2;\n result[11] = 0.0;\n result[12] = matrix[12];\n result[13] = matrix[13];\n result[14] = matrix[14];\n result[15] = matrix[15];\n return result;\n};\n\n/**\n * Multiplies a transformation matrix (with a bottom row of [0.0, 0.0, 0.0, 1.0])\n * by an implicit translation matrix defined by a {@link Cartesian3}. This is an optimization\n * for Matrix4.multiply(m, Matrix4.fromTranslation(position), m); with less allocations and arithmetic operations.\n *\n * @param {Matrix4} matrix The matrix on the left-hand side.\n * @param {Cartesian3} translation The translation on the right-hand side.\n * @param {Matrix4} result The object onto which to store the result.\n * @returns {Matrix4} The modified result parameter.\n *\n * @example\n * // Instead of Cesium.Matrix4.multiply(m, Cesium.Matrix4.fromTranslation(position), m);\n * Cesium.Matrix4.multiplyByTranslation(m, position, m);\n */\nMatrix4.multiplyByTranslation = function (matrix, translation, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"matrix\", matrix);\n Check.typeOf.object(\"translation\", translation);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n const x = translation.x;\n const y = translation.y;\n const z = translation.z;\n\n const tx = x * matrix[0] + y * matrix[4] + z * matrix[8] + matrix[12];\n const ty = x * matrix[1] + y * matrix[5] + z * matrix[9] + matrix[13];\n const tz = x * matrix[2] + y * matrix[6] + z * matrix[10] + matrix[14];\n\n result[0] = matrix[0];\n result[1] = matrix[1];\n result[2] = matrix[2];\n result[3] = matrix[3];\n result[4] = matrix[4];\n result[5] = matrix[5];\n result[6] = matrix[6];\n result[7] = matrix[7];\n result[8] = matrix[8];\n result[9] = matrix[9];\n result[10] = matrix[10];\n result[11] = matrix[11];\n result[12] = tx;\n result[13] = ty;\n result[14] = tz;\n result[15] = matrix[15];\n return result;\n};\n\n/**\n * Multiplies an affine transformation matrix (with a bottom row of [0.0, 0.0, 0.0, 1.0])\n * by an implicit non-uniform scale matrix. This is an optimization\n * for Matrix4.multiply(m, Matrix4.fromUniformScale(scale), m);, where\n * m must be an affine matrix.\n * This function performs fewer allocations and arithmetic operations.\n *\n * @param {Matrix4} matrix The affine matrix on the left-hand side.\n * @param {Cartesian3} scale The non-uniform scale on the right-hand side.\n * @param {Matrix4} result The object onto which to store the result.\n * @returns {Matrix4} The modified result parameter.\n *\n *\n * @example\n * // Instead of Cesium.Matrix4.multiply(m, Cesium.Matrix4.fromScale(scale), m);\n * Cesium.Matrix4.multiplyByScale(m, scale, m);\n *\n * @see Matrix4.multiplyByUniformScale\n * @see Matrix4.fromScale\n * @see Matrix4.fromUniformScale\n * @see Matrix4.setScale\n * @see Matrix4.setUniformScale\n * @see Matrix4.getScale\n */\nMatrix4.multiplyByScale = function (matrix, scale, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"matrix\", matrix);\n Check.typeOf.object(\"scale\", scale);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n const scaleX = scale.x;\n const scaleY = scale.y;\n const scaleZ = scale.z;\n\n // Faster than Cartesian3.equals\n if (scaleX === 1.0 && scaleY === 1.0 && scaleZ === 1.0) {\n return Matrix4.clone(matrix, result);\n }\n\n result[0] = scaleX * matrix[0];\n result[1] = scaleX * matrix[1];\n result[2] = scaleX * matrix[2];\n result[3] = matrix[3];\n\n result[4] = scaleY * matrix[4];\n result[5] = scaleY * matrix[5];\n result[6] = scaleY * matrix[6];\n result[7] = matrix[7];\n\n result[8] = scaleZ * matrix[8];\n result[9] = scaleZ * matrix[9];\n result[10] = scaleZ * matrix[10];\n result[11] = matrix[11];\n\n result[12] = matrix[12];\n result[13] = matrix[13];\n result[14] = matrix[14];\n result[15] = matrix[15];\n\n return result;\n};\n\n/**\n * Computes the product of a matrix times a uniform scale, as if the scale were a scale matrix.\n *\n * @param {Matrix4} matrix The matrix on the left-hand side.\n * @param {Number} scale The uniform scale on the right-hand side.\n * @param {Matrix4} result The object onto which to store the result.\n * @returns {Matrix4} The modified result parameter.\n *\n * @example\n * // Instead of Cesium.Matrix4.multiply(m, Cesium.Matrix4.fromUniformScale(scale), m);\n * Cesium.Matrix4.multiplyByUniformScale(m, scale, m);\n *\n * @see Matrix4.multiplyByScale\n * @see Matrix4.fromScale\n * @see Matrix4.fromUniformScale\n * @see Matrix4.setScale\n * @see Matrix4.setUniformScale\n * @see Matrix4.getScale\n */\nMatrix4.multiplyByUniformScale = function (matrix, scale, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"matrix\", matrix);\n Check.typeOf.number(\"scale\", scale);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n result[0] = matrix[0] * scale;\n result[1] = matrix[1] * scale;\n result[2] = matrix[2] * scale;\n result[3] = matrix[3];\n\n result[4] = matrix[4] * scale;\n result[5] = matrix[5] * scale;\n result[6] = matrix[6] * scale;\n result[7] = matrix[7];\n\n result[8] = matrix[8] * scale;\n result[9] = matrix[9] * scale;\n result[10] = matrix[10] * scale;\n result[11] = matrix[11];\n\n result[12] = matrix[12];\n result[13] = matrix[13];\n result[14] = matrix[14];\n result[15] = matrix[15];\n\n return result;\n};\n\n/**\n * Computes the product of a matrix and a column vector.\n *\n * @param {Matrix4} matrix The matrix.\n * @param {Cartesian4} cartesian The vector.\n * @param {Cartesian4} result The object onto which to store the result.\n * @returns {Cartesian4} The modified result parameter.\n */\nMatrix4.multiplyByVector = function (matrix, cartesian, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"matrix\", matrix);\n Check.typeOf.object(\"cartesian\", cartesian);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n const vX = cartesian.x;\n const vY = cartesian.y;\n const vZ = cartesian.z;\n const vW = cartesian.w;\n\n const x = matrix[0] * vX + matrix[4] * vY + matrix[8] * vZ + matrix[12] * vW;\n const y = matrix[1] * vX + matrix[5] * vY + matrix[9] * vZ + matrix[13] * vW;\n const z = matrix[2] * vX + matrix[6] * vY + matrix[10] * vZ + matrix[14] * vW;\n const w = matrix[3] * vX + matrix[7] * vY + matrix[11] * vZ + matrix[15] * vW;\n\n result.x = x;\n result.y = y;\n result.z = z;\n result.w = w;\n return result;\n};\n\n/**\n * Computes the product of a matrix and a {@link Cartesian3}. This is equivalent to calling {@link Matrix4.multiplyByVector}\n * with a {@link Cartesian4} with a w component of zero.\n *\n * @param {Matrix4} matrix The matrix.\n * @param {Cartesian3} cartesian The point.\n * @param {Cartesian3} result The object onto which to store the result.\n * @returns {Cartesian3} The modified result parameter.\n *\n * @example\n * const p = new Cesium.Cartesian3(1.0, 2.0, 3.0);\n * const result = Cesium.Matrix4.multiplyByPointAsVector(matrix, p, new Cesium.Cartesian3());\n * // A shortcut for\n * // Cartesian3 p = ...\n * // Cesium.Matrix4.multiplyByVector(matrix, new Cesium.Cartesian4(p.x, p.y, p.z, 0.0), result);\n */\nMatrix4.multiplyByPointAsVector = function (matrix, cartesian, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"matrix\", matrix);\n Check.typeOf.object(\"cartesian\", cartesian);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n const vX = cartesian.x;\n const vY = cartesian.y;\n const vZ = cartesian.z;\n\n const x = matrix[0] * vX + matrix[4] * vY + matrix[8] * vZ;\n const y = matrix[1] * vX + matrix[5] * vY + matrix[9] * vZ;\n const z = matrix[2] * vX + matrix[6] * vY + matrix[10] * vZ;\n\n result.x = x;\n result.y = y;\n result.z = z;\n return result;\n};\n\n/**\n * Computes the product of a matrix and a {@link Cartesian3}. This is equivalent to calling {@link Matrix4.multiplyByVector}\n * with a {@link Cartesian4} with a w component of 1, but returns a {@link Cartesian3} instead of a {@link Cartesian4}.\n *\n * @param {Matrix4} matrix The matrix.\n * @param {Cartesian3} cartesian The point.\n * @param {Cartesian3} result The object onto which to store the result.\n * @returns {Cartesian3} The modified result parameter.\n *\n * @example\n * const p = new Cesium.Cartesian3(1.0, 2.0, 3.0);\n * const result = Cesium.Matrix4.multiplyByPoint(matrix, p, new Cesium.Cartesian3());\n */\nMatrix4.multiplyByPoint = function (matrix, cartesian, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"matrix\", matrix);\n Check.typeOf.object(\"cartesian\", cartesian);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n const vX = cartesian.x;\n const vY = cartesian.y;\n const vZ = cartesian.z;\n\n const x = matrix[0] * vX + matrix[4] * vY + matrix[8] * vZ + matrix[12];\n const y = matrix[1] * vX + matrix[5] * vY + matrix[9] * vZ + matrix[13];\n const z = matrix[2] * vX + matrix[6] * vY + matrix[10] * vZ + matrix[14];\n\n result.x = x;\n result.y = y;\n result.z = z;\n return result;\n};\n\n/**\n * Computes the product of a matrix and a scalar.\n *\n * @param {Matrix4} matrix The matrix.\n * @param {Number} scalar The number to multiply by.\n * @param {Matrix4} result The object onto which to store the result.\n * @returns {Matrix4} The modified result parameter.\n *\n * @example\n * //create a Matrix4 instance which is a scaled version of the supplied Matrix4\n * // m = [10.0, 11.0, 12.0, 13.0]\n * // [14.0, 15.0, 16.0, 17.0]\n * // [18.0, 19.0, 20.0, 21.0]\n * // [22.0, 23.0, 24.0, 25.0]\n *\n * const a = Cesium.Matrix4.multiplyByScalar(m, -2, new Cesium.Matrix4());\n *\n * // m remains the same\n * // a = [-20.0, -22.0, -24.0, -26.0]\n * // [-28.0, -30.0, -32.0, -34.0]\n * // [-36.0, -38.0, -40.0, -42.0]\n * // [-44.0, -46.0, -48.0, -50.0]\n */\nMatrix4.multiplyByScalar = function (matrix, scalar, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"matrix\", matrix);\n Check.typeOf.number(\"scalar\", scalar);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n result[0] = matrix[0] * scalar;\n result[1] = matrix[1] * scalar;\n result[2] = matrix[2] * scalar;\n result[3] = matrix[3] * scalar;\n result[4] = matrix[4] * scalar;\n result[5] = matrix[5] * scalar;\n result[6] = matrix[6] * scalar;\n result[7] = matrix[7] * scalar;\n result[8] = matrix[8] * scalar;\n result[9] = matrix[9] * scalar;\n result[10] = matrix[10] * scalar;\n result[11] = matrix[11] * scalar;\n result[12] = matrix[12] * scalar;\n result[13] = matrix[13] * scalar;\n result[14] = matrix[14] * scalar;\n result[15] = matrix[15] * scalar;\n return result;\n};\n\n/**\n * Computes a negated copy of the provided matrix.\n *\n * @param {Matrix4} matrix The matrix to negate.\n * @param {Matrix4} result The object onto which to store the result.\n * @returns {Matrix4} The modified result parameter.\n *\n * @example\n * //create a new Matrix4 instance which is a negation of a Matrix4\n * // m = [10.0, 11.0, 12.0, 13.0]\n * // [14.0, 15.0, 16.0, 17.0]\n * // [18.0, 19.0, 20.0, 21.0]\n * // [22.0, 23.0, 24.0, 25.0]\n *\n * const a = Cesium.Matrix4.negate(m, new Cesium.Matrix4());\n *\n * // m remains the same\n * // a = [-10.0, -11.0, -12.0, -13.0]\n * // [-14.0, -15.0, -16.0, -17.0]\n * // [-18.0, -19.0, -20.0, -21.0]\n * // [-22.0, -23.0, -24.0, -25.0]\n */\nMatrix4.negate = function (matrix, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"matrix\", matrix);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n result[0] = -matrix[0];\n result[1] = -matrix[1];\n result[2] = -matrix[2];\n result[3] = -matrix[3];\n result[4] = -matrix[4];\n result[5] = -matrix[5];\n result[6] = -matrix[6];\n result[7] = -matrix[7];\n result[8] = -matrix[8];\n result[9] = -matrix[9];\n result[10] = -matrix[10];\n result[11] = -matrix[11];\n result[12] = -matrix[12];\n result[13] = -matrix[13];\n result[14] = -matrix[14];\n result[15] = -matrix[15];\n return result;\n};\n\n/**\n * Computes the transpose of the provided matrix.\n *\n * @param {Matrix4} matrix The matrix to transpose.\n * @param {Matrix4} result The object onto which to store the result.\n * @returns {Matrix4} The modified result parameter.\n *\n * @example\n * //returns transpose of a Matrix4\n * // m = [10.0, 11.0, 12.0, 13.0]\n * // [14.0, 15.0, 16.0, 17.0]\n * // [18.0, 19.0, 20.0, 21.0]\n * // [22.0, 23.0, 24.0, 25.0]\n *\n * const a = Cesium.Matrix4.transpose(m, new Cesium.Matrix4());\n *\n * // m remains the same\n * // a = [10.0, 14.0, 18.0, 22.0]\n * // [11.0, 15.0, 19.0, 23.0]\n * // [12.0, 16.0, 20.0, 24.0]\n * // [13.0, 17.0, 21.0, 25.0]\n */\nMatrix4.transpose = function (matrix, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"matrix\", matrix);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n const matrix1 = matrix[1];\n const matrix2 = matrix[2];\n const matrix3 = matrix[3];\n const matrix6 = matrix[6];\n const matrix7 = matrix[7];\n const matrix11 = matrix[11];\n\n result[0] = matrix[0];\n result[1] = matrix[4];\n result[2] = matrix[8];\n result[3] = matrix[12];\n result[4] = matrix1;\n result[5] = matrix[5];\n result[6] = matrix[9];\n result[7] = matrix[13];\n result[8] = matrix2;\n result[9] = matrix6;\n result[10] = matrix[10];\n result[11] = matrix[14];\n result[12] = matrix3;\n result[13] = matrix7;\n result[14] = matrix11;\n result[15] = matrix[15];\n return result;\n};\n\n/**\n * Computes a matrix, which contains the absolute (unsigned) values of the provided matrix's elements.\n *\n * @param {Matrix4} matrix The matrix with signed elements.\n * @param {Matrix4} result The object onto which to store the result.\n * @returns {Matrix4} The modified result parameter.\n */\nMatrix4.abs = function (matrix, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"matrix\", matrix);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n result[0] = Math.abs(matrix[0]);\n result[1] = Math.abs(matrix[1]);\n result[2] = Math.abs(matrix[2]);\n result[3] = Math.abs(matrix[3]);\n result[4] = Math.abs(matrix[4]);\n result[5] = Math.abs(matrix[5]);\n result[6] = Math.abs(matrix[6]);\n result[7] = Math.abs(matrix[7]);\n result[8] = Math.abs(matrix[8]);\n result[9] = Math.abs(matrix[9]);\n result[10] = Math.abs(matrix[10]);\n result[11] = Math.abs(matrix[11]);\n result[12] = Math.abs(matrix[12]);\n result[13] = Math.abs(matrix[13]);\n result[14] = Math.abs(matrix[14]);\n result[15] = Math.abs(matrix[15]);\n\n return result;\n};\n\n/**\n * Compares the provided matrices componentwise and returns\n * true if they are equal, false otherwise.\n *\n * @param {Matrix4} [left] The first matrix.\n * @param {Matrix4} [right] The second matrix.\n * @returns {Boolean} true if left and right are equal, false otherwise.\n *\n * @example\n * //compares two Matrix4 instances\n *\n * // a = [10.0, 14.0, 18.0, 22.0]\n * // [11.0, 15.0, 19.0, 23.0]\n * // [12.0, 16.0, 20.0, 24.0]\n * // [13.0, 17.0, 21.0, 25.0]\n *\n * // b = [10.0, 14.0, 18.0, 22.0]\n * // [11.0, 15.0, 19.0, 23.0]\n * // [12.0, 16.0, 20.0, 24.0]\n * // [13.0, 17.0, 21.0, 25.0]\n *\n * if(Cesium.Matrix4.equals(a,b)) {\n * console.log(\"Both matrices are equal\");\n * } else {\n * console.log(\"They are not equal\");\n * }\n *\n * //Prints \"Both matrices are equal\" on the console\n */\nMatrix4.equals = function (left, right) {\n // Given that most matrices will be transformation matrices, the elements\n // are tested in order such that the test is likely to fail as early\n // as possible. I _think_ this is just as friendly to the L1 cache\n // as testing in index order. It is certainty faster in practice.\n return (\n left === right ||\n (defined(left) &&\n defined(right) &&\n // Translation\n left[12] === right[12] &&\n left[13] === right[13] &&\n left[14] === right[14] &&\n // Rotation/scale\n left[0] === right[0] &&\n left[1] === right[1] &&\n left[2] === right[2] &&\n left[4] === right[4] &&\n left[5] === right[5] &&\n left[6] === right[6] &&\n left[8] === right[8] &&\n left[9] === right[9] &&\n left[10] === right[10] &&\n // Bottom row\n left[3] === right[3] &&\n left[7] === right[7] &&\n left[11] === right[11] &&\n left[15] === right[15])\n );\n};\n\n/**\n * Compares the provided matrices componentwise and returns\n * true if they are within the provided epsilon,\n * false otherwise.\n *\n * @param {Matrix4} [left] The first matrix.\n * @param {Matrix4} [right] The second matrix.\n * @param {Number} [epsilon=0] The epsilon to use for equality testing.\n * @returns {Boolean} true if left and right are within the provided epsilon, false otherwise.\n *\n * @example\n * //compares two Matrix4 instances\n *\n * // a = [10.5, 14.5, 18.5, 22.5]\n * // [11.5, 15.5, 19.5, 23.5]\n * // [12.5, 16.5, 20.5, 24.5]\n * // [13.5, 17.5, 21.5, 25.5]\n *\n * // b = [10.0, 14.0, 18.0, 22.0]\n * // [11.0, 15.0, 19.0, 23.0]\n * // [12.0, 16.0, 20.0, 24.0]\n * // [13.0, 17.0, 21.0, 25.0]\n *\n * if(Cesium.Matrix4.equalsEpsilon(a,b,0.1)){\n * console.log(\"Difference between both the matrices is less than 0.1\");\n * } else {\n * console.log(\"Difference between both the matrices is not less than 0.1\");\n * }\n *\n * //Prints \"Difference between both the matrices is not less than 0.1\" on the console\n */\nMatrix4.equalsEpsilon = function (left, right, epsilon) {\n epsilon = defaultValue(epsilon, 0);\n\n return (\n left === right ||\n (defined(left) &&\n defined(right) &&\n Math.abs(left[0] - right[0]) <= epsilon &&\n Math.abs(left[1] - right[1]) <= epsilon &&\n Math.abs(left[2] - right[2]) <= epsilon &&\n Math.abs(left[3] - right[3]) <= epsilon &&\n Math.abs(left[4] - right[4]) <= epsilon &&\n Math.abs(left[5] - right[5]) <= epsilon &&\n Math.abs(left[6] - right[6]) <= epsilon &&\n Math.abs(left[7] - right[7]) <= epsilon &&\n Math.abs(left[8] - right[8]) <= epsilon &&\n Math.abs(left[9] - right[9]) <= epsilon &&\n Math.abs(left[10] - right[10]) <= epsilon &&\n Math.abs(left[11] - right[11]) <= epsilon &&\n Math.abs(left[12] - right[12]) <= epsilon &&\n Math.abs(left[13] - right[13]) <= epsilon &&\n Math.abs(left[14] - right[14]) <= epsilon &&\n Math.abs(left[15] - right[15]) <= epsilon)\n );\n};\n\n/**\n * Gets the translation portion of the provided matrix, assuming the matrix is an affine transformation matrix.\n *\n * @param {Matrix4} matrix The matrix to use.\n * @param {Cartesian3} result The object onto which to store the result.\n * @returns {Cartesian3} The modified result parameter.\n */\nMatrix4.getTranslation = function (matrix, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"matrix\", matrix);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n result.x = matrix[12];\n result.y = matrix[13];\n result.z = matrix[14];\n return result;\n};\n\n/**\n * Gets the upper left 3x3 matrix of the provided matrix.\n *\n * @param {Matrix4} matrix The matrix to use.\n * @param {Matrix3} result The object onto which to store the result.\n * @returns {Matrix3} The modified result parameter.\n *\n * @example\n * // returns a Matrix3 instance from a Matrix4 instance\n *\n * // m = [10.0, 14.0, 18.0, 22.0]\n * // [11.0, 15.0, 19.0, 23.0]\n * // [12.0, 16.0, 20.0, 24.0]\n * // [13.0, 17.0, 21.0, 25.0]\n *\n * const b = new Cesium.Matrix3();\n * Cesium.Matrix4.getMatrix3(m,b);\n *\n * // b = [10.0, 14.0, 18.0]\n * // [11.0, 15.0, 19.0]\n * // [12.0, 16.0, 20.0]\n */\nMatrix4.getMatrix3 = function (matrix, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"matrix\", matrix);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n result[0] = matrix[0];\n result[1] = matrix[1];\n result[2] = matrix[2];\n result[3] = matrix[4];\n result[4] = matrix[5];\n result[5] = matrix[6];\n result[6] = matrix[8];\n result[7] = matrix[9];\n result[8] = matrix[10];\n return result;\n};\n\nconst scratchInverseRotation = new Matrix3();\nconst scratchMatrix3Zero = new Matrix3();\nconst scratchBottomRow = new Cartesian4();\nconst scratchExpectedBottomRow = new Cartesian4(0.0, 0.0, 0.0, 1.0);\n\n/**\n * Computes the inverse of the provided matrix using Cramers Rule.\n * If the determinant is zero, the matrix can not be inverted, and an exception is thrown.\n * If the matrix is a proper rigid transformation, it is more efficient\n * to invert it with {@link Matrix4.inverseTransformation}.\n *\n * @param {Matrix4} matrix The matrix to invert.\n * @param {Matrix4} result The object onto which to store the result.\n * @returns {Matrix4} The modified result parameter.\n *\n * @exception {RuntimeError} matrix is not invertible because its determinate is zero.\n */\nMatrix4.inverse = function (matrix, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"matrix\", matrix);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n //\n // Ported from:\n // ftp://download.intel.com/design/PentiumIII/sml/24504301.pdf\n //\n const src0 = matrix[0];\n const src1 = matrix[4];\n const src2 = matrix[8];\n const src3 = matrix[12];\n const src4 = matrix[1];\n const src5 = matrix[5];\n const src6 = matrix[9];\n const src7 = matrix[13];\n const src8 = matrix[2];\n const src9 = matrix[6];\n const src10 = matrix[10];\n const src11 = matrix[14];\n const src12 = matrix[3];\n const src13 = matrix[7];\n const src14 = matrix[11];\n const src15 = matrix[15];\n\n // calculate pairs for first 8 elements (cofactors)\n let tmp0 = src10 * src15;\n let tmp1 = src11 * src14;\n let tmp2 = src9 * src15;\n let tmp3 = src11 * src13;\n let tmp4 = src9 * src14;\n let tmp5 = src10 * src13;\n let tmp6 = src8 * src15;\n let tmp7 = src11 * src12;\n let tmp8 = src8 * src14;\n let tmp9 = src10 * src12;\n let tmp10 = src8 * src13;\n let tmp11 = src9 * src12;\n\n // calculate first 8 elements (cofactors)\n const dst0 =\n tmp0 * src5 +\n tmp3 * src6 +\n tmp4 * src7 -\n (tmp1 * src5 + tmp2 * src6 + tmp5 * src7);\n const dst1 =\n tmp1 * src4 +\n tmp6 * src6 +\n tmp9 * src7 -\n (tmp0 * src4 + tmp7 * src6 + tmp8 * src7);\n const dst2 =\n tmp2 * src4 +\n tmp7 * src5 +\n tmp10 * src7 -\n (tmp3 * src4 + tmp6 * src5 + tmp11 * src7);\n const dst3 =\n tmp5 * src4 +\n tmp8 * src5 +\n tmp11 * src6 -\n (tmp4 * src4 + tmp9 * src5 + tmp10 * src6);\n const dst4 =\n tmp1 * src1 +\n tmp2 * src2 +\n tmp5 * src3 -\n (tmp0 * src1 + tmp3 * src2 + tmp4 * src3);\n const dst5 =\n tmp0 * src0 +\n tmp7 * src2 +\n tmp8 * src3 -\n (tmp1 * src0 + tmp6 * src2 + tmp9 * src3);\n const dst6 =\n tmp3 * src0 +\n tmp6 * src1 +\n tmp11 * src3 -\n (tmp2 * src0 + tmp7 * src1 + tmp10 * src3);\n const dst7 =\n tmp4 * src0 +\n tmp9 * src1 +\n tmp10 * src2 -\n (tmp5 * src0 + tmp8 * src1 + tmp11 * src2);\n\n // calculate pairs for second 8 elements (cofactors)\n tmp0 = src2 * src7;\n tmp1 = src3 * src6;\n tmp2 = src1 * src7;\n tmp3 = src3 * src5;\n tmp4 = src1 * src6;\n tmp5 = src2 * src5;\n tmp6 = src0 * src7;\n tmp7 = src3 * src4;\n tmp8 = src0 * src6;\n tmp9 = src2 * src4;\n tmp10 = src0 * src5;\n tmp11 = src1 * src4;\n\n // calculate second 8 elements (cofactors)\n const dst8 =\n tmp0 * src13 +\n tmp3 * src14 +\n tmp4 * src15 -\n (tmp1 * src13 + tmp2 * src14 + tmp5 * src15);\n const dst9 =\n tmp1 * src12 +\n tmp6 * src14 +\n tmp9 * src15 -\n (tmp0 * src12 + tmp7 * src14 + tmp8 * src15);\n const dst10 =\n tmp2 * src12 +\n tmp7 * src13 +\n tmp10 * src15 -\n (tmp3 * src12 + tmp6 * src13 + tmp11 * src15);\n const dst11 =\n tmp5 * src12 +\n tmp8 * src13 +\n tmp11 * src14 -\n (tmp4 * src12 + tmp9 * src13 + tmp10 * src14);\n const dst12 =\n tmp2 * src10 +\n tmp5 * src11 +\n tmp1 * src9 -\n (tmp4 * src11 + tmp0 * src9 + tmp3 * src10);\n const dst13 =\n tmp8 * src11 +\n tmp0 * src8 +\n tmp7 * src10 -\n (tmp6 * src10 + tmp9 * src11 + tmp1 * src8);\n const dst14 =\n tmp6 * src9 +\n tmp11 * src11 +\n tmp3 * src8 -\n (tmp10 * src11 + tmp2 * src8 + tmp7 * src9);\n const dst15 =\n tmp10 * src10 +\n tmp4 * src8 +\n tmp9 * src9 -\n (tmp8 * src9 + tmp11 * src10 + tmp5 * src8);\n\n // calculate determinant\n let det = src0 * dst0 + src1 * dst1 + src2 * dst2 + src3 * dst3;\n\n if (Math.abs(det) < CesiumMath.EPSILON21) {\n // Special case for a zero scale matrix that can occur, for example,\n // when a model's node has a [0, 0, 0] scale.\n if (\n Matrix3.equalsEpsilon(\n Matrix4.getMatrix3(matrix, scratchInverseRotation),\n scratchMatrix3Zero,\n CesiumMath.EPSILON7\n ) &&\n Cartesian4.equals(\n Matrix4.getRow(matrix, 3, scratchBottomRow),\n scratchExpectedBottomRow\n )\n ) {\n result[0] = 0.0;\n result[1] = 0.0;\n result[2] = 0.0;\n result[3] = 0.0;\n result[4] = 0.0;\n result[5] = 0.0;\n result[6] = 0.0;\n result[7] = 0.0;\n result[8] = 0.0;\n result[9] = 0.0;\n result[10] = 0.0;\n result[11] = 0.0;\n result[12] = -matrix[12];\n result[13] = -matrix[13];\n result[14] = -matrix[14];\n result[15] = 1.0;\n return result;\n }\n\n throw new RuntimeError(\n \"matrix is not invertible because its determinate is zero.\"\n );\n }\n\n // calculate matrix inverse\n det = 1.0 / det;\n\n result[0] = dst0 * det;\n result[1] = dst1 * det;\n result[2] = dst2 * det;\n result[3] = dst3 * det;\n result[4] = dst4 * det;\n result[5] = dst5 * det;\n result[6] = dst6 * det;\n result[7] = dst7 * det;\n result[8] = dst8 * det;\n result[9] = dst9 * det;\n result[10] = dst10 * det;\n result[11] = dst11 * det;\n result[12] = dst12 * det;\n result[13] = dst13 * det;\n result[14] = dst14 * det;\n result[15] = dst15 * det;\n return result;\n};\n\n/**\n * Computes the inverse of the provided matrix assuming it is a proper rigid matrix,\n * where the upper left 3x3 elements are a rotation matrix,\n * and the upper three elements in the fourth column are the translation.\n * The bottom row is assumed to be [0, 0, 0, 1].\n * The matrix is not verified to be in the proper form.\n * This method is faster than computing the inverse for a general 4x4\n * matrix using {@link Matrix4.inverse}.\n *\n * @param {Matrix4} matrix The matrix to invert.\n * @param {Matrix4} result The object onto which to store the result.\n * @returns {Matrix4} The modified result parameter.\n */\nMatrix4.inverseTransformation = function (matrix, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"matrix\", matrix);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n //This function is an optimized version of the below 4 lines.\n //const rT = Matrix3.transpose(Matrix4.getMatrix3(matrix));\n //const rTN = Matrix3.negate(rT);\n //const rTT = Matrix3.multiplyByVector(rTN, Matrix4.getTranslation(matrix));\n //return Matrix4.fromRotationTranslation(rT, rTT, result);\n\n const matrix0 = matrix[0];\n const matrix1 = matrix[1];\n const matrix2 = matrix[2];\n const matrix4 = matrix[4];\n const matrix5 = matrix[5];\n const matrix6 = matrix[6];\n const matrix8 = matrix[8];\n const matrix9 = matrix[9];\n const matrix10 = matrix[10];\n\n const vX = matrix[12];\n const vY = matrix[13];\n const vZ = matrix[14];\n\n const x = -matrix0 * vX - matrix1 * vY - matrix2 * vZ;\n const y = -matrix4 * vX - matrix5 * vY - matrix6 * vZ;\n const z = -matrix8 * vX - matrix9 * vY - matrix10 * vZ;\n\n result[0] = matrix0;\n result[1] = matrix4;\n result[2] = matrix8;\n result[3] = 0.0;\n result[4] = matrix1;\n result[5] = matrix5;\n result[6] = matrix9;\n result[7] = 0.0;\n result[8] = matrix2;\n result[9] = matrix6;\n result[10] = matrix10;\n result[11] = 0.0;\n result[12] = x;\n result[13] = y;\n result[14] = z;\n result[15] = 1.0;\n return result;\n};\n\nconst scratchTransposeMatrix = new Matrix4();\n\n/**\n * Computes the inverse transpose of a matrix.\n *\n * @param {Matrix4} matrix The matrix to transpose and invert.\n * @param {Matrix4} result The object onto which to store the result.\n * @returns {Matrix4} The modified result parameter.\n */\nMatrix4.inverseTranspose = function (matrix, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"matrix\", matrix);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n return Matrix4.inverse(\n Matrix4.transpose(matrix, scratchTransposeMatrix),\n result\n );\n};\n\n/**\n * An immutable Matrix4 instance initialized to the identity matrix.\n *\n * @type {Matrix4}\n * @constant\n */\nMatrix4.IDENTITY = Object.freeze(\n new Matrix4(\n 1.0,\n 0.0,\n 0.0,\n 0.0,\n 0.0,\n 1.0,\n 0.0,\n 0.0,\n 0.0,\n 0.0,\n 1.0,\n 0.0,\n 0.0,\n 0.0,\n 0.0,\n 1.0\n )\n);\n\n/**\n * An immutable Matrix4 instance initialized to the zero matrix.\n *\n * @type {Matrix4}\n * @constant\n */\nMatrix4.ZERO = Object.freeze(\n new Matrix4(\n 0.0,\n 0.0,\n 0.0,\n 0.0,\n 0.0,\n 0.0,\n 0.0,\n 0.0,\n 0.0,\n 0.0,\n 0.0,\n 0.0,\n 0.0,\n 0.0,\n 0.0,\n 0.0\n )\n);\n\n/**\n * The index into Matrix4 for column 0, row 0.\n *\n * @type {Number}\n * @constant\n */\nMatrix4.COLUMN0ROW0 = 0;\n\n/**\n * The index into Matrix4 for column 0, row 1.\n *\n * @type {Number}\n * @constant\n */\nMatrix4.COLUMN0ROW1 = 1;\n\n/**\n * The index into Matrix4 for column 0, row 2.\n *\n * @type {Number}\n * @constant\n */\nMatrix4.COLUMN0ROW2 = 2;\n\n/**\n * The index into Matrix4 for column 0, row 3.\n *\n * @type {Number}\n * @constant\n */\nMatrix4.COLUMN0ROW3 = 3;\n\n/**\n * The index into Matrix4 for column 1, row 0.\n *\n * @type {Number}\n * @constant\n */\nMatrix4.COLUMN1ROW0 = 4;\n\n/**\n * The index into Matrix4 for column 1, row 1.\n *\n * @type {Number}\n * @constant\n */\nMatrix4.COLUMN1ROW1 = 5;\n\n/**\n * The index into Matrix4 for column 1, row 2.\n *\n * @type {Number}\n * @constant\n */\nMatrix4.COLUMN1ROW2 = 6;\n\n/**\n * The index into Matrix4 for column 1, row 3.\n *\n * @type {Number}\n * @constant\n */\nMatrix4.COLUMN1ROW3 = 7;\n\n/**\n * The index into Matrix4 for column 2, row 0.\n *\n * @type {Number}\n * @constant\n */\nMatrix4.COLUMN2ROW0 = 8;\n\n/**\n * The index into Matrix4 for column 2, row 1.\n *\n * @type {Number}\n * @constant\n */\nMatrix4.COLUMN2ROW1 = 9;\n\n/**\n * The index into Matrix4 for column 2, row 2.\n *\n * @type {Number}\n * @constant\n */\nMatrix4.COLUMN2ROW2 = 10;\n\n/**\n * The index into Matrix4 for column 2, row 3.\n *\n * @type {Number}\n * @constant\n */\nMatrix4.COLUMN2ROW3 = 11;\n\n/**\n * The index into Matrix4 for column 3, row 0.\n *\n * @type {Number}\n * @constant\n */\nMatrix4.COLUMN3ROW0 = 12;\n\n/**\n * The index into Matrix4 for column 3, row 1.\n *\n * @type {Number}\n * @constant\n */\nMatrix4.COLUMN3ROW1 = 13;\n\n/**\n * The index into Matrix4 for column 3, row 2.\n *\n * @type {Number}\n * @constant\n */\nMatrix4.COLUMN3ROW2 = 14;\n\n/**\n * The index into Matrix4 for column 3, row 3.\n *\n * @type {Number}\n * @constant\n */\nMatrix4.COLUMN3ROW3 = 15;\n\nObject.defineProperties(Matrix4.prototype, {\n /**\n * Gets the number of items in the collection.\n * @memberof Matrix4.prototype\n *\n * @type {Number}\n */\n length: {\n get: function () {\n return Matrix4.packedLength;\n },\n },\n});\n\n/**\n * Duplicates the provided Matrix4 instance.\n *\n * @param {Matrix4} [result] The object onto which to store the result.\n * @returns {Matrix4} The modified result parameter or a new Matrix4 instance if one was not provided.\n */\nMatrix4.prototype.clone = function (result) {\n return Matrix4.clone(this, result);\n};\n\n/**\n * Compares this matrix to the provided matrix componentwise and returns\n * true if they are equal, false otherwise.\n *\n * @param {Matrix4} [right] The right hand side matrix.\n * @returns {Boolean} true if they are equal, false otherwise.\n */\nMatrix4.prototype.equals = function (right) {\n return Matrix4.equals(this, right);\n};\n\n/**\n * @private\n */\nMatrix4.equalsArray = function (matrix, array, offset) {\n return (\n matrix[0] === array[offset] &&\n matrix[1] === array[offset + 1] &&\n matrix[2] === array[offset + 2] &&\n matrix[3] === array[offset + 3] &&\n matrix[4] === array[offset + 4] &&\n matrix[5] === array[offset + 5] &&\n matrix[6] === array[offset + 6] &&\n matrix[7] === array[offset + 7] &&\n matrix[8] === array[offset + 8] &&\n matrix[9] === array[offset + 9] &&\n matrix[10] === array[offset + 10] &&\n matrix[11] === array[offset + 11] &&\n matrix[12] === array[offset + 12] &&\n matrix[13] === array[offset + 13] &&\n matrix[14] === array[offset + 14] &&\n matrix[15] === array[offset + 15]\n );\n};\n\n/**\n * Compares this matrix to the provided matrix componentwise and returns\n * true if they are within the provided epsilon,\n * false otherwise.\n *\n * @param {Matrix4} [right] The right hand side matrix.\n * @param {Number} [epsilon=0] The epsilon to use for equality testing.\n * @returns {Boolean} true if they are within the provided epsilon, false otherwise.\n */\nMatrix4.prototype.equalsEpsilon = function (right, epsilon) {\n return Matrix4.equalsEpsilon(this, right, epsilon);\n};\n\n/**\n * Computes a string representing this Matrix with each row being\n * on a separate line and in the format '(column0, column1, column2, column3)'.\n *\n * @returns {String} A string representing the provided Matrix with each row being on a separate line and in the format '(column0, column1, column2, column3)'.\n */\nMatrix4.prototype.toString = function () {\n return (\n `(${this[0]}, ${this[4]}, ${this[8]}, ${this[12]})\\n` +\n `(${this[1]}, ${this[5]}, ${this[9]}, ${this[13]})\\n` +\n `(${this[2]}, ${this[6]}, ${this[10]}, ${this[14]})\\n` +\n `(${this[3]}, ${this[7]}, ${this[11]}, ${this[15]})`\n );\n};\nexport default Matrix4;\n","import Cartographic from \"./Cartographic.js\";\nimport Check from \"./Check.js\";\nimport defaultValue from \"./defaultValue.js\";\nimport defined from \"./defined.js\";\nimport Ellipsoid from \"./Ellipsoid.js\";\nimport CesiumMath from \"./Math.js\";\n\n/**\n * A two dimensional region specified as longitude and latitude coordinates.\n *\n * @alias Rectangle\n * @constructor\n *\n * @param {Number} [west=0.0] The westernmost longitude, in radians, in the range [-Pi, Pi].\n * @param {Number} [south=0.0] The southernmost latitude, in radians, in the range [-Pi/2, Pi/2].\n * @param {Number} [east=0.0] The easternmost longitude, in radians, in the range [-Pi, Pi].\n * @param {Number} [north=0.0] The northernmost latitude, in radians, in the range [-Pi/2, Pi/2].\n *\n * @see Packable\n */\nfunction Rectangle(west, south, east, north) {\n /**\n * The westernmost longitude in radians in the range [-Pi, Pi].\n *\n * @type {Number}\n * @default 0.0\n */\n this.west = defaultValue(west, 0.0);\n\n /**\n * The southernmost latitude in radians in the range [-Pi/2, Pi/2].\n *\n * @type {Number}\n * @default 0.0\n */\n this.south = defaultValue(south, 0.0);\n\n /**\n * The easternmost longitude in radians in the range [-Pi, Pi].\n *\n * @type {Number}\n * @default 0.0\n */\n this.east = defaultValue(east, 0.0);\n\n /**\n * The northernmost latitude in radians in the range [-Pi/2, Pi/2].\n *\n * @type {Number}\n * @default 0.0\n */\n this.north = defaultValue(north, 0.0);\n}\n\nObject.defineProperties(Rectangle.prototype, {\n /**\n * Gets the width of the rectangle in radians.\n * @memberof Rectangle.prototype\n * @type {Number}\n * @readonly\n */\n width: {\n get: function () {\n return Rectangle.computeWidth(this);\n },\n },\n\n /**\n * Gets the height of the rectangle in radians.\n * @memberof Rectangle.prototype\n * @type {Number}\n * @readonly\n */\n height: {\n get: function () {\n return Rectangle.computeHeight(this);\n },\n },\n});\n\n/**\n * The number of elements used to pack the object into an array.\n * @type {Number}\n */\nRectangle.packedLength = 4;\n\n/**\n * Stores the provided instance into the provided array.\n *\n * @param {Rectangle} value The value to pack.\n * @param {Number[]} array The array to pack into.\n * @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.\n *\n * @returns {Number[]} The array that was packed into\n */\nRectangle.pack = function (value, array, startingIndex) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"value\", value);\n Check.defined(\"array\", array);\n //>>includeEnd('debug');\n\n startingIndex = defaultValue(startingIndex, 0);\n\n array[startingIndex++] = value.west;\n array[startingIndex++] = value.south;\n array[startingIndex++] = value.east;\n array[startingIndex] = value.north;\n\n return array;\n};\n\n/**\n * Retrieves an instance from a packed array.\n *\n * @param {Number[]} array The packed array.\n * @param {Number} [startingIndex=0] The starting index of the element to be unpacked.\n * @param {Rectangle} [result] The object into which to store the result.\n * @returns {Rectangle} The modified result parameter or a new Rectangle instance if one was not provided.\n */\nRectangle.unpack = function (array, startingIndex, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.defined(\"array\", array);\n //>>includeEnd('debug');\n\n startingIndex = defaultValue(startingIndex, 0);\n\n if (!defined(result)) {\n result = new Rectangle();\n }\n\n result.west = array[startingIndex++];\n result.south = array[startingIndex++];\n result.east = array[startingIndex++];\n result.north = array[startingIndex];\n return result;\n};\n\n/**\n * Computes the width of a rectangle in radians.\n * @param {Rectangle} rectangle The rectangle to compute the width of.\n * @returns {Number} The width.\n */\nRectangle.computeWidth = function (rectangle) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"rectangle\", rectangle);\n //>>includeEnd('debug');\n let east = rectangle.east;\n const west = rectangle.west;\n if (east < west) {\n east += CesiumMath.TWO_PI;\n }\n return east - west;\n};\n\n/**\n * Computes the height of a rectangle in radians.\n * @param {Rectangle} rectangle The rectangle to compute the height of.\n * @returns {Number} The height.\n */\nRectangle.computeHeight = function (rectangle) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"rectangle\", rectangle);\n //>>includeEnd('debug');\n return rectangle.north - rectangle.south;\n};\n\n/**\n * Creates a rectangle given the boundary longitude and latitude in degrees.\n *\n * @param {Number} [west=0.0] The westernmost longitude in degrees in the range [-180.0, 180.0].\n * @param {Number} [south=0.0] The southernmost latitude in degrees in the range [-90.0, 90.0].\n * @param {Number} [east=0.0] The easternmost longitude in degrees in the range [-180.0, 180.0].\n * @param {Number} [north=0.0] The northernmost latitude in degrees in the range [-90.0, 90.0].\n * @param {Rectangle} [result] The object onto which to store the result, or undefined if a new instance should be created.\n * @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided.\n *\n * @example\n * const rectangle = Cesium.Rectangle.fromDegrees(0.0, 20.0, 10.0, 30.0);\n */\nRectangle.fromDegrees = function (west, south, east, north, result) {\n west = CesiumMath.toRadians(defaultValue(west, 0.0));\n south = CesiumMath.toRadians(defaultValue(south, 0.0));\n east = CesiumMath.toRadians(defaultValue(east, 0.0));\n north = CesiumMath.toRadians(defaultValue(north, 0.0));\n\n if (!defined(result)) {\n return new Rectangle(west, south, east, north);\n }\n\n result.west = west;\n result.south = south;\n result.east = east;\n result.north = north;\n\n return result;\n};\n\n/**\n * Creates a rectangle given the boundary longitude and latitude in radians.\n *\n * @param {Number} [west=0.0] The westernmost longitude in radians in the range [-Math.PI, Math.PI].\n * @param {Number} [south=0.0] The southernmost latitude in radians in the range [-Math.PI/2, Math.PI/2].\n * @param {Number} [east=0.0] The easternmost longitude in radians in the range [-Math.PI, Math.PI].\n * @param {Number} [north=0.0] The northernmost latitude in radians in the range [-Math.PI/2, Math.PI/2].\n * @param {Rectangle} [result] The object onto which to store the result, or undefined if a new instance should be created.\n * @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided.\n *\n * @example\n * const rectangle = Cesium.Rectangle.fromRadians(0.0, Math.PI/4, Math.PI/8, 3*Math.PI/4);\n */\nRectangle.fromRadians = function (west, south, east, north, result) {\n if (!defined(result)) {\n return new Rectangle(west, south, east, north);\n }\n\n result.west = defaultValue(west, 0.0);\n result.south = defaultValue(south, 0.0);\n result.east = defaultValue(east, 0.0);\n result.north = defaultValue(north, 0.0);\n\n return result;\n};\n\n/**\n * Creates the smallest possible Rectangle that encloses all positions in the provided array.\n *\n * @param {Cartographic[]} cartographics The list of Cartographic instances.\n * @param {Rectangle} [result] The object onto which to store the result, or undefined if a new instance should be created.\n * @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided.\n */\nRectangle.fromCartographicArray = function (cartographics, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.defined(\"cartographics\", cartographics);\n //>>includeEnd('debug');\n\n let west = Number.MAX_VALUE;\n let east = -Number.MAX_VALUE;\n let westOverIDL = Number.MAX_VALUE;\n let eastOverIDL = -Number.MAX_VALUE;\n let south = Number.MAX_VALUE;\n let north = -Number.MAX_VALUE;\n\n for (let i = 0, len = cartographics.length; i < len; i++) {\n const position = cartographics[i];\n west = Math.min(west, position.longitude);\n east = Math.max(east, position.longitude);\n south = Math.min(south, position.latitude);\n north = Math.max(north, position.latitude);\n\n const lonAdjusted =\n position.longitude >= 0\n ? position.longitude\n : position.longitude + CesiumMath.TWO_PI;\n westOverIDL = Math.min(westOverIDL, lonAdjusted);\n eastOverIDL = Math.max(eastOverIDL, lonAdjusted);\n }\n\n if (east - west > eastOverIDL - westOverIDL) {\n west = westOverIDL;\n east = eastOverIDL;\n\n if (east > CesiumMath.PI) {\n east = east - CesiumMath.TWO_PI;\n }\n if (west > CesiumMath.PI) {\n west = west - CesiumMath.TWO_PI;\n }\n }\n\n if (!defined(result)) {\n return new Rectangle(west, south, east, north);\n }\n\n result.west = west;\n result.south = south;\n result.east = east;\n result.north = north;\n return result;\n};\n\n/**\n * Creates the smallest possible Rectangle that encloses all positions in the provided array.\n *\n * @param {Cartesian3[]} cartesians The list of Cartesian instances.\n * @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid the cartesians are on.\n * @param {Rectangle} [result] The object onto which to store the result, or undefined if a new instance should be created.\n * @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided.\n */\nRectangle.fromCartesianArray = function (cartesians, ellipsoid, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.defined(\"cartesians\", cartesians);\n //>>includeEnd('debug');\n ellipsoid = defaultValue(ellipsoid, Ellipsoid.WGS84);\n\n let west = Number.MAX_VALUE;\n let east = -Number.MAX_VALUE;\n let westOverIDL = Number.MAX_VALUE;\n let eastOverIDL = -Number.MAX_VALUE;\n let south = Number.MAX_VALUE;\n let north = -Number.MAX_VALUE;\n\n for (let i = 0, len = cartesians.length; i < len; i++) {\n const position = ellipsoid.cartesianToCartographic(cartesians[i]);\n west = Math.min(west, position.longitude);\n east = Math.max(east, position.longitude);\n south = Math.min(south, position.latitude);\n north = Math.max(north, position.latitude);\n\n const lonAdjusted =\n position.longitude >= 0\n ? position.longitude\n : position.longitude + CesiumMath.TWO_PI;\n westOverIDL = Math.min(westOverIDL, lonAdjusted);\n eastOverIDL = Math.max(eastOverIDL, lonAdjusted);\n }\n\n if (east - west > eastOverIDL - westOverIDL) {\n west = westOverIDL;\n east = eastOverIDL;\n\n if (east > CesiumMath.PI) {\n east = east - CesiumMath.TWO_PI;\n }\n if (west > CesiumMath.PI) {\n west = west - CesiumMath.TWO_PI;\n }\n }\n\n if (!defined(result)) {\n return new Rectangle(west, south, east, north);\n }\n\n result.west = west;\n result.south = south;\n result.east = east;\n result.north = north;\n return result;\n};\n\n/**\n * Duplicates a Rectangle.\n *\n * @param {Rectangle} rectangle The rectangle to clone.\n * @param {Rectangle} [result] The object onto which to store the result, or undefined if a new instance should be created.\n * @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided. (Returns undefined if rectangle is undefined)\n */\nRectangle.clone = function (rectangle, result) {\n if (!defined(rectangle)) {\n return undefined;\n }\n\n if (!defined(result)) {\n return new Rectangle(\n rectangle.west,\n rectangle.south,\n rectangle.east,\n rectangle.north\n );\n }\n\n result.west = rectangle.west;\n result.south = rectangle.south;\n result.east = rectangle.east;\n result.north = rectangle.north;\n return result;\n};\n\n/**\n * Compares the provided Rectangles componentwise and returns\n * true if they pass an absolute or relative tolerance test,\n * false otherwise.\n *\n * @param {Rectangle} [left] The first Rectangle.\n * @param {Rectangle} [right] The second Rectangle.\n * @param {Number} [absoluteEpsilon=0] The absolute epsilon tolerance to use for equality testing.\n * @returns {Boolean} true if left and right are within the provided epsilon, false otherwise.\n */\nRectangle.equalsEpsilon = function (left, right, absoluteEpsilon) {\n absoluteEpsilon = defaultValue(absoluteEpsilon, 0);\n\n return (\n left === right ||\n (defined(left) &&\n defined(right) &&\n Math.abs(left.west - right.west) <= absoluteEpsilon &&\n Math.abs(left.south - right.south) <= absoluteEpsilon &&\n Math.abs(left.east - right.east) <= absoluteEpsilon &&\n Math.abs(left.north - right.north) <= absoluteEpsilon)\n );\n};\n\n/**\n * Duplicates this Rectangle.\n *\n * @param {Rectangle} [result] The object onto which to store the result.\n * @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided.\n */\nRectangle.prototype.clone = function (result) {\n return Rectangle.clone(this, result);\n};\n\n/**\n * Compares the provided Rectangle with this Rectangle componentwise and returns\n * true if they are equal, false otherwise.\n *\n * @param {Rectangle} [other] The Rectangle to compare.\n * @returns {Boolean} true if the Rectangles are equal, false otherwise.\n */\nRectangle.prototype.equals = function (other) {\n return Rectangle.equals(this, other);\n};\n\n/**\n * Compares the provided rectangles and returns true if they are equal,\n * false otherwise.\n *\n * @param {Rectangle} [left] The first Rectangle.\n * @param {Rectangle} [right] The second Rectangle.\n * @returns {Boolean} true if left and right are equal; otherwise false.\n */\nRectangle.equals = function (left, right) {\n return (\n left === right ||\n (defined(left) &&\n defined(right) &&\n left.west === right.west &&\n left.south === right.south &&\n left.east === right.east &&\n left.north === right.north)\n );\n};\n\n/**\n * Compares the provided Rectangle with this Rectangle componentwise and returns\n * true if they are within the provided epsilon,\n * false otherwise.\n *\n * @param {Rectangle} [other] The Rectangle to compare.\n * @param {Number} [epsilon=0] The epsilon to use for equality testing.\n * @returns {Boolean} true if the Rectangles are within the provided epsilon, false otherwise.\n */\nRectangle.prototype.equalsEpsilon = function (other, epsilon) {\n return Rectangle.equalsEpsilon(this, other, epsilon);\n};\n\n/**\n * Checks a Rectangle's properties and throws if they are not in valid ranges.\n *\n * @param {Rectangle} rectangle The rectangle to validate\n *\n * @exception {DeveloperError} north must be in the interval [-Pi/2, Pi/2].\n * @exception {DeveloperError} south must be in the interval [-Pi/2, Pi/2].\n * @exception {DeveloperError} east must be in the interval [-Pi, Pi].\n * @exception {DeveloperError} west must be in the interval [-Pi, Pi].\n */\nRectangle.validate = function (rectangle) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"rectangle\", rectangle);\n\n const north = rectangle.north;\n Check.typeOf.number.greaterThanOrEquals(\n \"north\",\n north,\n -CesiumMath.PI_OVER_TWO\n );\n Check.typeOf.number.lessThanOrEquals(\"north\", north, CesiumMath.PI_OVER_TWO);\n\n const south = rectangle.south;\n Check.typeOf.number.greaterThanOrEquals(\n \"south\",\n south,\n -CesiumMath.PI_OVER_TWO\n );\n Check.typeOf.number.lessThanOrEquals(\"south\", south, CesiumMath.PI_OVER_TWO);\n\n const west = rectangle.west;\n Check.typeOf.number.greaterThanOrEquals(\"west\", west, -Math.PI);\n Check.typeOf.number.lessThanOrEquals(\"west\", west, Math.PI);\n\n const east = rectangle.east;\n Check.typeOf.number.greaterThanOrEquals(\"east\", east, -Math.PI);\n Check.typeOf.number.lessThanOrEquals(\"east\", east, Math.PI);\n //>>includeEnd('debug');\n};\n\n/**\n * Computes the southwest corner of a rectangle.\n *\n * @param {Rectangle} rectangle The rectangle for which to find the corner\n * @param {Cartographic} [result] The object onto which to store the result.\n * @returns {Cartographic} The modified result parameter or a new Cartographic instance if none was provided.\n */\nRectangle.southwest = function (rectangle, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"rectangle\", rectangle);\n //>>includeEnd('debug');\n\n if (!defined(result)) {\n return new Cartographic(rectangle.west, rectangle.south);\n }\n result.longitude = rectangle.west;\n result.latitude = rectangle.south;\n result.height = 0.0;\n return result;\n};\n\n/**\n * Computes the northwest corner of a rectangle.\n *\n * @param {Rectangle} rectangle The rectangle for which to find the corner\n * @param {Cartographic} [result] The object onto which to store the result.\n * @returns {Cartographic} The modified result parameter or a new Cartographic instance if none was provided.\n */\nRectangle.northwest = function (rectangle, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"rectangle\", rectangle);\n //>>includeEnd('debug');\n\n if (!defined(result)) {\n return new Cartographic(rectangle.west, rectangle.north);\n }\n result.longitude = rectangle.west;\n result.latitude = rectangle.north;\n result.height = 0.0;\n return result;\n};\n\n/**\n * Computes the northeast corner of a rectangle.\n *\n * @param {Rectangle} rectangle The rectangle for which to find the corner\n * @param {Cartographic} [result] The object onto which to store the result.\n * @returns {Cartographic} The modified result parameter or a new Cartographic instance if none was provided.\n */\nRectangle.northeast = function (rectangle, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"rectangle\", rectangle);\n //>>includeEnd('debug');\n\n if (!defined(result)) {\n return new Cartographic(rectangle.east, rectangle.north);\n }\n result.longitude = rectangle.east;\n result.latitude = rectangle.north;\n result.height = 0.0;\n return result;\n};\n\n/**\n * Computes the southeast corner of a rectangle.\n *\n * @param {Rectangle} rectangle The rectangle for which to find the corner\n * @param {Cartographic} [result] The object onto which to store the result.\n * @returns {Cartographic} The modified result parameter or a new Cartographic instance if none was provided.\n */\nRectangle.southeast = function (rectangle, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"rectangle\", rectangle);\n //>>includeEnd('debug');\n\n if (!defined(result)) {\n return new Cartographic(rectangle.east, rectangle.south);\n }\n result.longitude = rectangle.east;\n result.latitude = rectangle.south;\n result.height = 0.0;\n return result;\n};\n\n/**\n * Computes the center of a rectangle.\n *\n * @param {Rectangle} rectangle The rectangle for which to find the center\n * @param {Cartographic} [result] The object onto which to store the result.\n * @returns {Cartographic} The modified result parameter or a new Cartographic instance if none was provided.\n */\nRectangle.center = function (rectangle, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"rectangle\", rectangle);\n //>>includeEnd('debug');\n\n let east = rectangle.east;\n const west = rectangle.west;\n\n if (east < west) {\n east += CesiumMath.TWO_PI;\n }\n\n const longitude = CesiumMath.negativePiToPi((west + east) * 0.5);\n const latitude = (rectangle.south + rectangle.north) * 0.5;\n\n if (!defined(result)) {\n return new Cartographic(longitude, latitude);\n }\n\n result.longitude = longitude;\n result.latitude = latitude;\n result.height = 0.0;\n return result;\n};\n\n/**\n * Computes the intersection of two rectangles. This function assumes that the rectangle's coordinates are\n * latitude and longitude in radians and produces a correct intersection, taking into account the fact that\n * the same angle can be represented with multiple values as well as the wrapping of longitude at the\n * anti-meridian. For a simple intersection that ignores these factors and can be used with projected\n * coordinates, see {@link Rectangle.simpleIntersection}.\n *\n * @param {Rectangle} rectangle On rectangle to find an intersection\n * @param {Rectangle} otherRectangle Another rectangle to find an intersection\n * @param {Rectangle} [result] The object onto which to store the result.\n * @returns {Rectangle|undefined} The modified result parameter, a new Rectangle instance if none was provided or undefined if there is no intersection.\n */\nRectangle.intersection = function (rectangle, otherRectangle, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"rectangle\", rectangle);\n Check.typeOf.object(\"otherRectangle\", otherRectangle);\n //>>includeEnd('debug');\n\n let rectangleEast = rectangle.east;\n let rectangleWest = rectangle.west;\n\n let otherRectangleEast = otherRectangle.east;\n let otherRectangleWest = otherRectangle.west;\n\n if (rectangleEast < rectangleWest && otherRectangleEast > 0.0) {\n rectangleEast += CesiumMath.TWO_PI;\n } else if (otherRectangleEast < otherRectangleWest && rectangleEast > 0.0) {\n otherRectangleEast += CesiumMath.TWO_PI;\n }\n\n if (rectangleEast < rectangleWest && otherRectangleWest < 0.0) {\n otherRectangleWest += CesiumMath.TWO_PI;\n } else if (otherRectangleEast < otherRectangleWest && rectangleWest < 0.0) {\n rectangleWest += CesiumMath.TWO_PI;\n }\n\n const west = CesiumMath.negativePiToPi(\n Math.max(rectangleWest, otherRectangleWest)\n );\n const east = CesiumMath.negativePiToPi(\n Math.min(rectangleEast, otherRectangleEast)\n );\n\n if (\n (rectangle.west < rectangle.east ||\n otherRectangle.west < otherRectangle.east) &&\n east <= west\n ) {\n return undefined;\n }\n\n const south = Math.max(rectangle.south, otherRectangle.south);\n const north = Math.min(rectangle.north, otherRectangle.north);\n\n if (south >= north) {\n return undefined;\n }\n\n if (!defined(result)) {\n return new Rectangle(west, south, east, north);\n }\n result.west = west;\n result.south = south;\n result.east = east;\n result.north = north;\n return result;\n};\n\n/**\n * Computes a simple intersection of two rectangles. Unlike {@link Rectangle.intersection}, this function\n * does not attempt to put the angular coordinates into a consistent range or to account for crossing the\n * anti-meridian. As such, it can be used for rectangles where the coordinates are not simply latitude\n * and longitude (i.e. projected coordinates).\n *\n * @param {Rectangle} rectangle On rectangle to find an intersection\n * @param {Rectangle} otherRectangle Another rectangle to find an intersection\n * @param {Rectangle} [result] The object onto which to store the result.\n * @returns {Rectangle|undefined} The modified result parameter, a new Rectangle instance if none was provided or undefined if there is no intersection.\n */\nRectangle.simpleIntersection = function (rectangle, otherRectangle, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"rectangle\", rectangle);\n Check.typeOf.object(\"otherRectangle\", otherRectangle);\n //>>includeEnd('debug');\n\n const west = Math.max(rectangle.west, otherRectangle.west);\n const south = Math.max(rectangle.south, otherRectangle.south);\n const east = Math.min(rectangle.east, otherRectangle.east);\n const north = Math.min(rectangle.north, otherRectangle.north);\n\n if (south >= north || west >= east) {\n return undefined;\n }\n\n if (!defined(result)) {\n return new Rectangle(west, south, east, north);\n }\n\n result.west = west;\n result.south = south;\n result.east = east;\n result.north = north;\n return result;\n};\n\n/**\n * Computes a rectangle that is the union of two rectangles.\n *\n * @param {Rectangle} rectangle A rectangle to enclose in rectangle.\n * @param {Rectangle} otherRectangle A rectangle to enclose in a rectangle.\n * @param {Rectangle} [result] The object onto which to store the result.\n * @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided.\n */\nRectangle.union = function (rectangle, otherRectangle, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"rectangle\", rectangle);\n Check.typeOf.object(\"otherRectangle\", otherRectangle);\n //>>includeEnd('debug');\n\n if (!defined(result)) {\n result = new Rectangle();\n }\n\n let rectangleEast = rectangle.east;\n let rectangleWest = rectangle.west;\n\n let otherRectangleEast = otherRectangle.east;\n let otherRectangleWest = otherRectangle.west;\n\n if (rectangleEast < rectangleWest && otherRectangleEast > 0.0) {\n rectangleEast += CesiumMath.TWO_PI;\n } else if (otherRectangleEast < otherRectangleWest && rectangleEast > 0.0) {\n otherRectangleEast += CesiumMath.TWO_PI;\n }\n\n if (rectangleEast < rectangleWest && otherRectangleWest < 0.0) {\n otherRectangleWest += CesiumMath.TWO_PI;\n } else if (otherRectangleEast < otherRectangleWest && rectangleWest < 0.0) {\n rectangleWest += CesiumMath.TWO_PI;\n }\n\n const west = CesiumMath.negativePiToPi(\n Math.min(rectangleWest, otherRectangleWest)\n );\n const east = CesiumMath.negativePiToPi(\n Math.max(rectangleEast, otherRectangleEast)\n );\n\n result.west = west;\n result.south = Math.min(rectangle.south, otherRectangle.south);\n result.east = east;\n result.north = Math.max(rectangle.north, otherRectangle.north);\n\n return result;\n};\n\n/**\n * Computes a rectangle by enlarging the provided rectangle until it contains the provided cartographic.\n *\n * @param {Rectangle} rectangle A rectangle to expand.\n * @param {Cartographic} cartographic A cartographic to enclose in a rectangle.\n * @param {Rectangle} [result] The object onto which to store the result.\n * @returns {Rectangle} The modified result parameter or a new Rectangle instance if one was not provided.\n */\nRectangle.expand = function (rectangle, cartographic, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"rectangle\", rectangle);\n Check.typeOf.object(\"cartographic\", cartographic);\n //>>includeEnd('debug');\n\n if (!defined(result)) {\n result = new Rectangle();\n }\n\n result.west = Math.min(rectangle.west, cartographic.longitude);\n result.south = Math.min(rectangle.south, cartographic.latitude);\n result.east = Math.max(rectangle.east, cartographic.longitude);\n result.north = Math.max(rectangle.north, cartographic.latitude);\n\n return result;\n};\n\n/**\n * Returns true if the cartographic is on or inside the rectangle, false otherwise.\n *\n * @param {Rectangle} rectangle The rectangle\n * @param {Cartographic} cartographic The cartographic to test.\n * @returns {Boolean} true if the provided cartographic is inside the rectangle, false otherwise.\n */\nRectangle.contains = function (rectangle, cartographic) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"rectangle\", rectangle);\n Check.typeOf.object(\"cartographic\", cartographic);\n //>>includeEnd('debug');\n\n let longitude = cartographic.longitude;\n const latitude = cartographic.latitude;\n\n const west = rectangle.west;\n let east = rectangle.east;\n\n if (east < west) {\n east += CesiumMath.TWO_PI;\n if (longitude < 0.0) {\n longitude += CesiumMath.TWO_PI;\n }\n }\n return (\n (longitude > west ||\n CesiumMath.equalsEpsilon(longitude, west, CesiumMath.EPSILON14)) &&\n (longitude < east ||\n CesiumMath.equalsEpsilon(longitude, east, CesiumMath.EPSILON14)) &&\n latitude >= rectangle.south &&\n latitude <= rectangle.north\n );\n};\n\nconst subsampleLlaScratch = new Cartographic();\n/**\n * Samples a rectangle so that it includes a list of Cartesian points suitable for passing to\n * {@link BoundingSphere#fromPoints}. Sampling is necessary to account\n * for rectangles that cover the poles or cross the equator.\n *\n * @param {Rectangle} rectangle The rectangle to subsample.\n * @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid to use.\n * @param {Number} [surfaceHeight=0.0] The height of the rectangle above the ellipsoid.\n * @param {Cartesian3[]} [result] The array of Cartesians onto which to store the result.\n * @returns {Cartesian3[]} The modified result parameter or a new Array of Cartesians instances if none was provided.\n */\nRectangle.subsample = function (rectangle, ellipsoid, surfaceHeight, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"rectangle\", rectangle);\n //>>includeEnd('debug');\n\n ellipsoid = defaultValue(ellipsoid, Ellipsoid.WGS84);\n surfaceHeight = defaultValue(surfaceHeight, 0.0);\n\n if (!defined(result)) {\n result = [];\n }\n let length = 0;\n\n const north = rectangle.north;\n const south = rectangle.south;\n const east = rectangle.east;\n const west = rectangle.west;\n\n const lla = subsampleLlaScratch;\n lla.height = surfaceHeight;\n\n lla.longitude = west;\n lla.latitude = north;\n result[length] = ellipsoid.cartographicToCartesian(lla, result[length]);\n length++;\n\n lla.longitude = east;\n result[length] = ellipsoid.cartographicToCartesian(lla, result[length]);\n length++;\n\n lla.latitude = south;\n result[length] = ellipsoid.cartographicToCartesian(lla, result[length]);\n length++;\n\n lla.longitude = west;\n result[length] = ellipsoid.cartographicToCartesian(lla, result[length]);\n length++;\n\n if (north < 0.0) {\n lla.latitude = north;\n } else if (south > 0.0) {\n lla.latitude = south;\n } else {\n lla.latitude = 0.0;\n }\n\n for (let i = 1; i < 8; ++i) {\n lla.longitude = -Math.PI + i * CesiumMath.PI_OVER_TWO;\n if (Rectangle.contains(rectangle, lla)) {\n result[length] = ellipsoid.cartographicToCartesian(lla, result[length]);\n length++;\n }\n }\n\n if (lla.latitude === 0.0) {\n lla.longitude = west;\n result[length] = ellipsoid.cartographicToCartesian(lla, result[length]);\n length++;\n lla.longitude = east;\n result[length] = ellipsoid.cartographicToCartesian(lla, result[length]);\n length++;\n }\n result.length = length;\n return result;\n};\n\n/**\n * Computes a subsection of a rectangle from normalized coordinates in the range [0.0, 1.0].\n *\n * @param {Rectangle} rectangle The rectangle to subsection.\n * @param {Number} westLerp The west interpolation factor in the range [0.0, 1.0]. Must be less than or equal to eastLerp.\n * @param {Number} southLerp The south interpolation factor in the range [0.0, 1.0]. Must be less than or equal to northLerp.\n * @param {Number} eastLerp The east interpolation factor in the range [0.0, 1.0]. Must be greater than or equal to westLerp.\n * @param {Number} northLerp The north interpolation factor in the range [0.0, 1.0]. Must be greater than or equal to southLerp.\n * @param {Rectangle} [result] The object onto which to store the result.\n * @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided.\n */\nRectangle.subsection = function (\n rectangle,\n westLerp,\n southLerp,\n eastLerp,\n northLerp,\n result\n) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"rectangle\", rectangle);\n Check.typeOf.number.greaterThanOrEquals(\"westLerp\", westLerp, 0.0);\n Check.typeOf.number.lessThanOrEquals(\"westLerp\", westLerp, 1.0);\n Check.typeOf.number.greaterThanOrEquals(\"southLerp\", southLerp, 0.0);\n Check.typeOf.number.lessThanOrEquals(\"southLerp\", southLerp, 1.0);\n Check.typeOf.number.greaterThanOrEquals(\"eastLerp\", eastLerp, 0.0);\n Check.typeOf.number.lessThanOrEquals(\"eastLerp\", eastLerp, 1.0);\n Check.typeOf.number.greaterThanOrEquals(\"northLerp\", northLerp, 0.0);\n Check.typeOf.number.lessThanOrEquals(\"northLerp\", northLerp, 1.0);\n\n Check.typeOf.number.lessThanOrEquals(\"westLerp\", westLerp, eastLerp);\n Check.typeOf.number.lessThanOrEquals(\"southLerp\", southLerp, northLerp);\n //>>includeEnd('debug');\n\n if (!defined(result)) {\n result = new Rectangle();\n }\n\n // This function doesn't use CesiumMath.lerp because it has floating point precision problems\n // when the start and end values are the same but the t changes.\n\n if (rectangle.west <= rectangle.east) {\n const width = rectangle.east - rectangle.west;\n result.west = rectangle.west + westLerp * width;\n result.east = rectangle.west + eastLerp * width;\n } else {\n const width = CesiumMath.TWO_PI + rectangle.east - rectangle.west;\n result.west = CesiumMath.negativePiToPi(rectangle.west + westLerp * width);\n result.east = CesiumMath.negativePiToPi(rectangle.west + eastLerp * width);\n }\n const height = rectangle.north - rectangle.south;\n result.south = rectangle.south + southLerp * height;\n result.north = rectangle.south + northLerp * height;\n\n // Fix floating point precision problems when t = 1\n if (westLerp === 1.0) {\n result.west = rectangle.east;\n }\n if (eastLerp === 1.0) {\n result.east = rectangle.east;\n }\n if (southLerp === 1.0) {\n result.south = rectangle.north;\n }\n if (northLerp === 1.0) {\n result.north = rectangle.north;\n }\n\n return result;\n};\n\n/**\n * The largest possible rectangle.\n *\n * @type {Rectangle}\n * @constant\n */\nRectangle.MAX_VALUE = Object.freeze(\n new Rectangle(\n -Math.PI,\n -CesiumMath.PI_OVER_TWO,\n Math.PI,\n CesiumMath.PI_OVER_TWO\n )\n);\nexport default Rectangle;\n","import Check from \"./Check.js\";\nimport defaultValue from \"./defaultValue.js\";\nimport defined from \"./defined.js\";\nimport DeveloperError from \"./DeveloperError.js\";\nimport CesiumMath from \"./Math.js\";\n\n/**\n * A 2D Cartesian point.\n * @alias Cartesian2\n * @constructor\n *\n * @param {Number} [x=0.0] The X component.\n * @param {Number} [y=0.0] The Y component.\n *\n * @see Cartesian3\n * @see Cartesian4\n * @see Packable\n */\nfunction Cartesian2(x, y) {\n /**\n * The X component.\n * @type {Number}\n * @default 0.0\n */\n this.x = defaultValue(x, 0.0);\n\n /**\n * The Y component.\n * @type {Number}\n * @default 0.0\n */\n this.y = defaultValue(y, 0.0);\n}\n\n/**\n * Creates a Cartesian2 instance from x and y coordinates.\n *\n * @param {Number} x The x coordinate.\n * @param {Number} y The y coordinate.\n * @param {Cartesian2} [result] The object onto which to store the result.\n * @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided.\n */\nCartesian2.fromElements = function (x, y, result) {\n if (!defined(result)) {\n return new Cartesian2(x, y);\n }\n\n result.x = x;\n result.y = y;\n return result;\n};\n\n/**\n * Duplicates a Cartesian2 instance.\n *\n * @param {Cartesian2} cartesian The Cartesian to duplicate.\n * @param {Cartesian2} [result] The object onto which to store the result.\n * @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided. (Returns undefined if cartesian is undefined)\n */\nCartesian2.clone = function (cartesian, result) {\n if (!defined(cartesian)) {\n return undefined;\n }\n if (!defined(result)) {\n return new Cartesian2(cartesian.x, cartesian.y);\n }\n\n result.x = cartesian.x;\n result.y = cartesian.y;\n return result;\n};\n\n/**\n * Creates a Cartesian2 instance from an existing Cartesian3. This simply takes the\n * x and y properties of the Cartesian3 and drops z.\n * @function\n *\n * @param {Cartesian3} cartesian The Cartesian3 instance to create a Cartesian2 instance from.\n * @param {Cartesian2} [result] The object onto which to store the result.\n * @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided.\n */\nCartesian2.fromCartesian3 = Cartesian2.clone;\n\n/**\n * Creates a Cartesian2 instance from an existing Cartesian4. This simply takes the\n * x and y properties of the Cartesian4 and drops z and w.\n * @function\n *\n * @param {Cartesian4} cartesian The Cartesian4 instance to create a Cartesian2 instance from.\n * @param {Cartesian2} [result] The object onto which to store the result.\n * @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided.\n */\nCartesian2.fromCartesian4 = Cartesian2.clone;\n\n/**\n * The number of elements used to pack the object into an array.\n * @type {Number}\n */\nCartesian2.packedLength = 2;\n\n/**\n * Stores the provided instance into the provided array.\n *\n * @param {Cartesian2} value The value to pack.\n * @param {Number[]} array The array to pack into.\n * @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.\n *\n * @returns {Number[]} The array that was packed into\n */\nCartesian2.pack = function (value, array, startingIndex) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"value\", value);\n Check.defined(\"array\", array);\n //>>includeEnd('debug');\n\n startingIndex = defaultValue(startingIndex, 0);\n\n array[startingIndex++] = value.x;\n array[startingIndex] = value.y;\n\n return array;\n};\n\n/**\n * Retrieves an instance from a packed array.\n *\n * @param {Number[]} array The packed array.\n * @param {Number} [startingIndex=0] The starting index of the element to be unpacked.\n * @param {Cartesian2} [result] The object into which to store the result.\n * @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided.\n */\nCartesian2.unpack = function (array, startingIndex, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.defined(\"array\", array);\n //>>includeEnd('debug');\n\n startingIndex = defaultValue(startingIndex, 0);\n\n if (!defined(result)) {\n result = new Cartesian2();\n }\n result.x = array[startingIndex++];\n result.y = array[startingIndex];\n return result;\n};\n\n/**\n * Flattens an array of Cartesian2s into an array of components.\n *\n * @param {Cartesian2[]} array The array of cartesians to pack.\n * @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.\n * @returns {Number[]} The packed array.\n */\nCartesian2.packArray = function (array, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.defined(\"array\", array);\n //>>includeEnd('debug');\n\n const length = array.length;\n const resultLength = length * 2;\n if (!defined(result)) {\n result = new Array(resultLength);\n } else if (!Array.isArray(result) && result.length !== resultLength) {\n //>>includeStart('debug', pragmas.debug);\n throw new DeveloperError(\n \"If result is a typed array, it must have exactly array.length * 2 elements\"\n );\n //>>includeEnd('debug');\n } else if (result.length !== resultLength) {\n result.length = resultLength;\n }\n\n for (let i = 0; i < length; ++i) {\n Cartesian2.pack(array[i], result, i * 2);\n }\n return result;\n};\n\n/**\n * Unpacks an array of cartesian components into an array of Cartesian2s.\n *\n * @param {Number[]} array The array of components to unpack.\n * @param {Cartesian2[]} [result] The array onto which to store the result.\n * @returns {Cartesian2[]} The unpacked array.\n */\nCartesian2.unpackArray = function (array, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.defined(\"array\", array);\n Check.typeOf.number.greaterThanOrEquals(\"array.length\", array.length, 2);\n if (array.length % 2 !== 0) {\n throw new DeveloperError(\"array length must be a multiple of 2.\");\n }\n //>>includeEnd('debug');\n\n const length = array.length;\n if (!defined(result)) {\n result = new Array(length / 2);\n } else {\n result.length = length / 2;\n }\n\n for (let i = 0; i < length; i += 2) {\n const index = i / 2;\n result[index] = Cartesian2.unpack(array, i, result[index]);\n }\n return result;\n};\n\n/**\n * Creates a Cartesian2 from two consecutive elements in an array.\n * @function\n *\n * @param {Number[]} array The array whose two consecutive elements correspond to the x and y components, respectively.\n * @param {Number} [startingIndex=0] The offset into the array of the first element, which corresponds to the x component.\n * @param {Cartesian2} [result] The object onto which to store the result.\n * @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided.\n *\n * @example\n * // Create a Cartesian2 with (1.0, 2.0)\n * const v = [1.0, 2.0];\n * const p = Cesium.Cartesian2.fromArray(v);\n *\n * // Create a Cartesian2 with (1.0, 2.0) using an offset into an array\n * const v2 = [0.0, 0.0, 1.0, 2.0];\n * const p2 = Cesium.Cartesian2.fromArray(v2, 2);\n */\nCartesian2.fromArray = Cartesian2.unpack;\n\n/**\n * Computes the value of the maximum component for the supplied Cartesian.\n *\n * @param {Cartesian2} cartesian The cartesian to use.\n * @returns {Number} The value of the maximum component.\n */\nCartesian2.maximumComponent = function (cartesian) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"cartesian\", cartesian);\n //>>includeEnd('debug');\n\n return Math.max(cartesian.x, cartesian.y);\n};\n\n/**\n * Computes the value of the minimum component for the supplied Cartesian.\n *\n * @param {Cartesian2} cartesian The cartesian to use.\n * @returns {Number} The value of the minimum component.\n */\nCartesian2.minimumComponent = function (cartesian) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"cartesian\", cartesian);\n //>>includeEnd('debug');\n\n return Math.min(cartesian.x, cartesian.y);\n};\n\n/**\n * Compares two Cartesians and computes a Cartesian which contains the minimum components of the supplied Cartesians.\n *\n * @param {Cartesian2} first A cartesian to compare.\n * @param {Cartesian2} second A cartesian to compare.\n * @param {Cartesian2} result The object into which to store the result.\n * @returns {Cartesian2} A cartesian with the minimum components.\n */\nCartesian2.minimumByComponent = function (first, second, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"first\", first);\n Check.typeOf.object(\"second\", second);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n result.x = Math.min(first.x, second.x);\n result.y = Math.min(first.y, second.y);\n\n return result;\n};\n\n/**\n * Compares two Cartesians and computes a Cartesian which contains the maximum components of the supplied Cartesians.\n *\n * @param {Cartesian2} first A cartesian to compare.\n * @param {Cartesian2} second A cartesian to compare.\n * @param {Cartesian2} result The object into which to store the result.\n * @returns {Cartesian2} A cartesian with the maximum components.\n */\nCartesian2.maximumByComponent = function (first, second, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"first\", first);\n Check.typeOf.object(\"second\", second);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n result.x = Math.max(first.x, second.x);\n result.y = Math.max(first.y, second.y);\n return result;\n};\n\n/**\n * Computes the provided Cartesian's squared magnitude.\n *\n * @param {Cartesian2} cartesian The Cartesian instance whose squared magnitude is to be computed.\n * @returns {Number} The squared magnitude.\n */\nCartesian2.magnitudeSquared = function (cartesian) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"cartesian\", cartesian);\n //>>includeEnd('debug');\n\n return cartesian.x * cartesian.x + cartesian.y * cartesian.y;\n};\n\n/**\n * Computes the Cartesian's magnitude (length).\n *\n * @param {Cartesian2} cartesian The Cartesian instance whose magnitude is to be computed.\n * @returns {Number} The magnitude.\n */\nCartesian2.magnitude = function (cartesian) {\n return Math.sqrt(Cartesian2.magnitudeSquared(cartesian));\n};\n\nconst distanceScratch = new Cartesian2();\n\n/**\n * Computes the distance between two points.\n *\n * @param {Cartesian2} left The first point to compute the distance from.\n * @param {Cartesian2} right The second point to compute the distance to.\n * @returns {Number} The distance between two points.\n *\n * @example\n * // Returns 1.0\n * const d = Cesium.Cartesian2.distance(new Cesium.Cartesian2(1.0, 0.0), new Cesium.Cartesian2(2.0, 0.0));\n */\nCartesian2.distance = function (left, right) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"left\", left);\n Check.typeOf.object(\"right\", right);\n //>>includeEnd('debug');\n\n Cartesian2.subtract(left, right, distanceScratch);\n return Cartesian2.magnitude(distanceScratch);\n};\n\n/**\n * Computes the squared distance between two points. Comparing squared distances\n * using this function is more efficient than comparing distances using {@link Cartesian2#distance}.\n *\n * @param {Cartesian2} left The first point to compute the distance from.\n * @param {Cartesian2} right The second point to compute the distance to.\n * @returns {Number} The distance between two points.\n *\n * @example\n * // Returns 4.0, not 2.0\n * const d = Cesium.Cartesian2.distance(new Cesium.Cartesian2(1.0, 0.0), new Cesium.Cartesian2(3.0, 0.0));\n */\nCartesian2.distanceSquared = function (left, right) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"left\", left);\n Check.typeOf.object(\"right\", right);\n //>>includeEnd('debug');\n\n Cartesian2.subtract(left, right, distanceScratch);\n return Cartesian2.magnitudeSquared(distanceScratch);\n};\n\n/**\n * Computes the normalized form of the supplied Cartesian.\n *\n * @param {Cartesian2} cartesian The Cartesian to be normalized.\n * @param {Cartesian2} result The object onto which to store the result.\n * @returns {Cartesian2} The modified result parameter.\n */\nCartesian2.normalize = function (cartesian, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"cartesian\", cartesian);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n const magnitude = Cartesian2.magnitude(cartesian);\n\n result.x = cartesian.x / magnitude;\n result.y = cartesian.y / magnitude;\n\n //>>includeStart('debug', pragmas.debug);\n if (isNaN(result.x) || isNaN(result.y)) {\n throw new DeveloperError(\"normalized result is not a number\");\n }\n //>>includeEnd('debug');\n\n return result;\n};\n\n/**\n * Computes the dot (scalar) product of two Cartesians.\n *\n * @param {Cartesian2} left The first Cartesian.\n * @param {Cartesian2} right The second Cartesian.\n * @returns {Number} The dot product.\n */\nCartesian2.dot = function (left, right) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"left\", left);\n Check.typeOf.object(\"right\", right);\n //>>includeEnd('debug');\n\n return left.x * right.x + left.y * right.y;\n};\n\n/**\n * Computes the magnitude of the cross product that would result from implicitly setting the Z coordinate of the input vectors to 0\n *\n * @param {Cartesian2} left The first Cartesian.\n * @param {Cartesian2} right The second Cartesian.\n * @returns {Number} The cross product.\n */\nCartesian2.cross = function (left, right) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"left\", left);\n Check.typeOf.object(\"right\", right);\n //>>includeEnd('debug');\n\n return left.x * right.y - left.y * right.x;\n};\n\n/**\n * Computes the componentwise product of two Cartesians.\n *\n * @param {Cartesian2} left The first Cartesian.\n * @param {Cartesian2} right The second Cartesian.\n * @param {Cartesian2} result The object onto which to store the result.\n * @returns {Cartesian2} The modified result parameter.\n */\nCartesian2.multiplyComponents = function (left, right, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"left\", left);\n Check.typeOf.object(\"right\", right);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n result.x = left.x * right.x;\n result.y = left.y * right.y;\n return result;\n};\n\n/**\n * Computes the componentwise quotient of two Cartesians.\n *\n * @param {Cartesian2} left The first Cartesian.\n * @param {Cartesian2} right The second Cartesian.\n * @param {Cartesian2} result The object onto which to store the result.\n * @returns {Cartesian2} The modified result parameter.\n */\nCartesian2.divideComponents = function (left, right, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"left\", left);\n Check.typeOf.object(\"right\", right);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n result.x = left.x / right.x;\n result.y = left.y / right.y;\n return result;\n};\n\n/**\n * Computes the componentwise sum of two Cartesians.\n *\n * @param {Cartesian2} left The first Cartesian.\n * @param {Cartesian2} right The second Cartesian.\n * @param {Cartesian2} result The object onto which to store the result.\n * @returns {Cartesian2} The modified result parameter.\n */\nCartesian2.add = function (left, right, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"left\", left);\n Check.typeOf.object(\"right\", right);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n result.x = left.x + right.x;\n result.y = left.y + right.y;\n return result;\n};\n\n/**\n * Computes the componentwise difference of two Cartesians.\n *\n * @param {Cartesian2} left The first Cartesian.\n * @param {Cartesian2} right The second Cartesian.\n * @param {Cartesian2} result The object onto which to store the result.\n * @returns {Cartesian2} The modified result parameter.\n */\nCartesian2.subtract = function (left, right, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"left\", left);\n Check.typeOf.object(\"right\", right);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n result.x = left.x - right.x;\n result.y = left.y - right.y;\n return result;\n};\n\n/**\n * Multiplies the provided Cartesian componentwise by the provided scalar.\n *\n * @param {Cartesian2} cartesian The Cartesian to be scaled.\n * @param {Number} scalar The scalar to multiply with.\n * @param {Cartesian2} result The object onto which to store the result.\n * @returns {Cartesian2} The modified result parameter.\n */\nCartesian2.multiplyByScalar = function (cartesian, scalar, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"cartesian\", cartesian);\n Check.typeOf.number(\"scalar\", scalar);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n result.x = cartesian.x * scalar;\n result.y = cartesian.y * scalar;\n return result;\n};\n\n/**\n * Divides the provided Cartesian componentwise by the provided scalar.\n *\n * @param {Cartesian2} cartesian The Cartesian to be divided.\n * @param {Number} scalar The scalar to divide by.\n * @param {Cartesian2} result The object onto which to store the result.\n * @returns {Cartesian2} The modified result parameter.\n */\nCartesian2.divideByScalar = function (cartesian, scalar, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"cartesian\", cartesian);\n Check.typeOf.number(\"scalar\", scalar);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n result.x = cartesian.x / scalar;\n result.y = cartesian.y / scalar;\n return result;\n};\n\n/**\n * Negates the provided Cartesian.\n *\n * @param {Cartesian2} cartesian The Cartesian to be negated.\n * @param {Cartesian2} result The object onto which to store the result.\n * @returns {Cartesian2} The modified result parameter.\n */\nCartesian2.negate = function (cartesian, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"cartesian\", cartesian);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n result.x = -cartesian.x;\n result.y = -cartesian.y;\n return result;\n};\n\n/**\n * Computes the absolute value of the provided Cartesian.\n *\n * @param {Cartesian2} cartesian The Cartesian whose absolute value is to be computed.\n * @param {Cartesian2} result The object onto which to store the result.\n * @returns {Cartesian2} The modified result parameter.\n */\nCartesian2.abs = function (cartesian, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"cartesian\", cartesian);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n result.x = Math.abs(cartesian.x);\n result.y = Math.abs(cartesian.y);\n return result;\n};\n\nconst lerpScratch = new Cartesian2();\n/**\n * Computes the linear interpolation or extrapolation at t using the provided cartesians.\n *\n * @param {Cartesian2} start The value corresponding to t at 0.0.\n * @param {Cartesian2} end The value corresponding to t at 1.0.\n * @param {Number} t The point along t at which to interpolate.\n * @param {Cartesian2} result The object onto which to store the result.\n * @returns {Cartesian2} The modified result parameter.\n */\nCartesian2.lerp = function (start, end, t, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"start\", start);\n Check.typeOf.object(\"end\", end);\n Check.typeOf.number(\"t\", t);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n Cartesian2.multiplyByScalar(end, t, lerpScratch);\n result = Cartesian2.multiplyByScalar(start, 1.0 - t, result);\n return Cartesian2.add(lerpScratch, result, result);\n};\n\nconst angleBetweenScratch = new Cartesian2();\nconst angleBetweenScratch2 = new Cartesian2();\n/**\n * Returns the angle, in radians, between the provided Cartesians.\n *\n * @param {Cartesian2} left The first Cartesian.\n * @param {Cartesian2} right The second Cartesian.\n * @returns {Number} The angle between the Cartesians.\n */\nCartesian2.angleBetween = function (left, right) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"left\", left);\n Check.typeOf.object(\"right\", right);\n //>>includeEnd('debug');\n\n Cartesian2.normalize(left, angleBetweenScratch);\n Cartesian2.normalize(right, angleBetweenScratch2);\n return CesiumMath.acosClamped(\n Cartesian2.dot(angleBetweenScratch, angleBetweenScratch2)\n );\n};\n\nconst mostOrthogonalAxisScratch = new Cartesian2();\n/**\n * Returns the axis that is most orthogonal to the provided Cartesian.\n *\n * @param {Cartesian2} cartesian The Cartesian on which to find the most orthogonal axis.\n * @param {Cartesian2} result The object onto which to store the result.\n * @returns {Cartesian2} The most orthogonal axis.\n */\nCartesian2.mostOrthogonalAxis = function (cartesian, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"cartesian\", cartesian);\n Check.typeOf.object(\"result\", result);\n //>>includeEnd('debug');\n\n const f = Cartesian2.normalize(cartesian, mostOrthogonalAxisScratch);\n Cartesian2.abs(f, f);\n\n if (f.x <= f.y) {\n result = Cartesian2.clone(Cartesian2.UNIT_X, result);\n } else {\n result = Cartesian2.clone(Cartesian2.UNIT_Y, result);\n }\n\n return result;\n};\n\n/**\n * Compares the provided Cartesians componentwise and returns\n * true if they are equal, false otherwise.\n *\n * @param {Cartesian2} [left] The first Cartesian.\n * @param {Cartesian2} [right] The second Cartesian.\n * @returns {Boolean} true if left and right are equal, false otherwise.\n */\nCartesian2.equals = function (left, right) {\n return (\n left === right ||\n (defined(left) &&\n defined(right) &&\n left.x === right.x &&\n left.y === right.y)\n );\n};\n\n/**\n * @private\n */\nCartesian2.equalsArray = function (cartesian, array, offset) {\n return cartesian.x === array[offset] && cartesian.y === array[offset + 1];\n};\n\n/**\n * Compares the provided Cartesians componentwise and returns\n * true if they pass an absolute or relative tolerance test,\n * false otherwise.\n *\n * @param {Cartesian2} [left] The first Cartesian.\n * @param {Cartesian2} [right] The second Cartesian.\n * @param {Number} [relativeEpsilon=0] The relative epsilon tolerance to use for equality testing.\n * @param {Number} [absoluteEpsilon=relativeEpsilon] The absolute epsilon tolerance to use for equality testing.\n * @returns {Boolean} true if left and right are within the provided epsilon, false otherwise.\n */\nCartesian2.equalsEpsilon = function (\n left,\n right,\n relativeEpsilon,\n absoluteEpsilon\n) {\n return (\n left === right ||\n (defined(left) &&\n defined(right) &&\n CesiumMath.equalsEpsilon(\n left.x,\n right.x,\n relativeEpsilon,\n absoluteEpsilon\n ) &&\n CesiumMath.equalsEpsilon(\n left.y,\n right.y,\n relativeEpsilon,\n absoluteEpsilon\n ))\n );\n};\n\n/**\n * An immutable Cartesian2 instance initialized to (0.0, 0.0).\n *\n * @type {Cartesian2}\n * @constant\n */\nCartesian2.ZERO = Object.freeze(new Cartesian2(0.0, 0.0));\n\n/**\n * An immutable Cartesian2 instance initialized to (1.0, 1.0).\n *\n * @type {Cartesian2}\n * @constant\n */\nCartesian2.ONE = Object.freeze(new Cartesian2(1.0, 1.0));\n\n/**\n * An immutable Cartesian2 instance initialized to (1.0, 0.0).\n *\n * @type {Cartesian2}\n * @constant\n */\nCartesian2.UNIT_X = Object.freeze(new Cartesian2(1.0, 0.0));\n\n/**\n * An immutable Cartesian2 instance initialized to (0.0, 1.0).\n *\n * @type {Cartesian2}\n * @constant\n */\nCartesian2.UNIT_Y = Object.freeze(new Cartesian2(0.0, 1.0));\n\n/**\n * Duplicates this Cartesian2 instance.\n *\n * @param {Cartesian2} [result] The object onto which to store the result.\n * @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided.\n */\nCartesian2.prototype.clone = function (result) {\n return Cartesian2.clone(this, result);\n};\n\n/**\n * Compares this Cartesian against the provided Cartesian componentwise and returns\n * true if they are equal, false otherwise.\n *\n * @param {Cartesian2} [right] The right hand side Cartesian.\n * @returns {Boolean} true if they are equal, false otherwise.\n */\nCartesian2.prototype.equals = function (right) {\n return Cartesian2.equals(this, right);\n};\n\n/**\n * Compares this Cartesian against the provided Cartesian componentwise and returns\n * true if they pass an absolute or relative tolerance test,\n * false otherwise.\n *\n * @param {Cartesian2} [right] The right hand side Cartesian.\n * @param {Number} [relativeEpsilon=0] The relative epsilon tolerance to use for equality testing.\n * @param {Number} [absoluteEpsilon=relativeEpsilon] The absolute epsilon tolerance to use for equality testing.\n * @returns {Boolean} true if they are within the provided epsilon, false otherwise.\n */\nCartesian2.prototype.equalsEpsilon = function (\n right,\n relativeEpsilon,\n absoluteEpsilon\n) {\n return Cartesian2.equalsEpsilon(\n this,\n right,\n relativeEpsilon,\n absoluteEpsilon\n );\n};\n\n/**\n * Creates a string representing this Cartesian in the format '(x, y)'.\n *\n * @returns {String} A string representing the provided Cartesian in the format '(x, y)'.\n */\nCartesian2.prototype.toString = function () {\n return `(${this.x}, ${this.y})`;\n};\nexport default Cartesian2;\n","import Cartesian2 from \"./Cartesian2.js\";\nimport Check from \"./Check.js\";\nimport defaultValue from \"./defaultValue.js\";\nimport defined from \"./defined.js\";\nimport DeveloperError from \"./DeveloperError.js\";\n\n/**\n * A 2x2 matrix, indexable as a column-major order array.\n * Constructor parameters are in row-major order for code readability.\n * @alias Matrix2\n * @constructor\n * @implements {ArrayLiketrue if they are equal, false otherwise.\n *\n * @param {Matrix2} [left] The first matrix.\n * @param {Matrix2} [right] The second matrix.\n * @returns {Boolean} true if left and right are equal, false otherwise.\n */\nMatrix2.equals = function (left, right) {\n return (\n left === right ||\n (defined(left) &&\n defined(right) &&\n left[0] === right[0] &&\n left[1] === right[1] &&\n left[2] === right[2] &&\n left[3] === right[3])\n );\n};\n\n/**\n * @private\n */\nMatrix2.equalsArray = function (matrix, array, offset) {\n return (\n matrix[0] === array[offset] &&\n matrix[1] === array[offset + 1] &&\n matrix[2] === array[offset + 2] &&\n matrix[3] === array[offset + 3]\n );\n};\n\n/**\n * Compares the provided matrices componentwise and returns\n * true if they are within the provided epsilon,\n * false otherwise.\n *\n * @param {Matrix2} [left] The first matrix.\n * @param {Matrix2} [right] The second matrix.\n * @param {Number} [epsilon=0] The epsilon to use for equality testing.\n * @returns {Boolean} true if left and right are within the provided epsilon, false otherwise.\n */\nMatrix2.equalsEpsilon = function (left, right, epsilon) {\n epsilon = defaultValue(epsilon, 0);\n return (\n left === right ||\n (defined(left) &&\n defined(right) &&\n Math.abs(left[0] - right[0]) <= epsilon &&\n Math.abs(left[1] - right[1]) <= epsilon &&\n Math.abs(left[2] - right[2]) <= epsilon &&\n Math.abs(left[3] - right[3]) <= epsilon)\n );\n};\n\n/**\n * An immutable Matrix2 instance initialized to the identity matrix.\n *\n * @type {Matrix2}\n * @constant\n */\nMatrix2.IDENTITY = Object.freeze(new Matrix2(1.0, 0.0, 0.0, 1.0));\n\n/**\n * An immutable Matrix2 instance initialized to the zero matrix.\n *\n * @type {Matrix2}\n * @constant\n */\nMatrix2.ZERO = Object.freeze(new Matrix2(0.0, 0.0, 0.0, 0.0));\n\n/**\n * The index into Matrix2 for column 0, row 0.\n *\n * @type {Number}\n * @constant\n *\n * @example\n * const matrix = new Cesium.Matrix2();\n * matrix[Cesium.Matrix2.COLUMN0ROW0] = 5.0; // set column 0, row 0 to 5.0\n */\nMatrix2.COLUMN0ROW0 = 0;\n\n/**\n * The index into Matrix2 for column 0, row 1.\n *\n * @type {Number}\n * @constant\n *\n * @example\n * const matrix = new Cesium.Matrix2();\n * matrix[Cesium.Matrix2.COLUMN0ROW1] = 5.0; // set column 0, row 1 to 5.0\n */\nMatrix2.COLUMN0ROW1 = 1;\n\n/**\n * The index into Matrix2 for column 1, row 0.\n *\n * @type {Number}\n * @constant\n *\n * @example\n * const matrix = new Cesium.Matrix2();\n * matrix[Cesium.Matrix2.COLUMN1ROW0] = 5.0; // set column 1, row 0 to 5.0\n */\nMatrix2.COLUMN1ROW0 = 2;\n\n/**\n * The index into Matrix2 for column 1, row 1.\n *\n * @type {Number}\n * @constant\n *\n * @example\n * const matrix = new Cesium.Matrix2();\n * matrix[Cesium.Matrix2.COLUMN1ROW1] = 5.0; // set column 1, row 1 to 5.0\n */\nMatrix2.COLUMN1ROW1 = 3;\n\nObject.defineProperties(Matrix2.prototype, {\n /**\n * Gets the number of items in the collection.\n * @memberof Matrix2.prototype\n *\n * @type {Number}\n */\n length: {\n get: function () {\n return Matrix2.packedLength;\n },\n },\n});\n\n/**\n * Duplicates the provided Matrix2 instance.\n *\n * @param {Matrix2} [result] The object onto which to store the result.\n * @returns {Matrix2} The modified result parameter or a new Matrix2 instance if one was not provided.\n */\nMatrix2.prototype.clone = function (result) {\n return Matrix2.clone(this, result);\n};\n\n/**\n * Compares this matrix to the provided matrix componentwise and returns\n * true if they are equal, false otherwise.\n *\n * @param {Matrix2} [right] The right hand side matrix.\n * @returns {Boolean} true if they are equal, false otherwise.\n */\nMatrix2.prototype.equals = function (right) {\n return Matrix2.equals(this, right);\n};\n\n/**\n * Compares this matrix to the provided matrix componentwise and returns\n * true if they are within the provided epsilon,\n * false otherwise.\n *\n * @param {Matrix2} [right] The right hand side matrix.\n * @param {Number} [epsilon=0] The epsilon to use for equality testing.\n * @returns {Boolean} true if they are within the provided epsilon, false otherwise.\n */\nMatrix2.prototype.equalsEpsilon = function (right, epsilon) {\n return Matrix2.equalsEpsilon(this, right, epsilon);\n};\n\n/**\n * Creates a string representing this Matrix with each row being\n * on a separate line and in the format '(column0, column1)'.\n *\n * @returns {String} A string representing the provided Matrix with each row being on a separate line and in the format '(column0, column1)'.\n */\nMatrix2.prototype.toString = function () {\n return `(${this[0]}, ${this[2]})\\n` + `(${this[1]}, ${this[3]})`;\n};\nexport default 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