qd-changjing/public/static/Build/CesiumUnminified/Workers/Matrix2-265d9610.js.map

{"version":3,"file":"Matrix2-265d9610.js","sources":["../../../../Source/Core/Cartesian3.js","../../../../Source/Core/scaleToGeodeticSurface.js","../../../../Source/Core/Cartographic.js","../../../../Source/Core/Ellipsoid.js","../../../../Source/Core/Matrix3.js","../../../../Source/Core/Cartesian4.js","../../../../Source/Core/Matrix4.js","../../../../Source/Core/Rectangle.js","../../../../Source/Core/Cartesian2.js","../../../../Source/Core/Matrix2.js"],"sourcesContent":["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 3D Cartesian point.\n * @alias Cartesian3\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 *\n * @see Cartesian2\n * @see Cartesian4\n * @see Packable\n */\nfunction Cartesian3(x, y, z) {\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/**\n * Converts the provided Spherical into Cartesian3 coordinates.\n *\n * @param {Spherical} spherical The Spherical to be converted to Cartesian3.\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.fromSpherical = function (spherical, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.object(\"spherical\", spherical);\n  //>>includeEnd('debug');\n\n  if (!defined(result)) {\n    result = new Cartesian3();\n  }\n\n  const clock = spherical.clock;\n  const cone = spherical.cone;\n  const magnitude = defaultValue(spherical.magnitude, 1.0);\n  const radial = magnitude * Math.sin(cone);\n  result.x = radial * Math.cos(clock);\n  result.y = radial * Math.sin(clock);\n  result.z = magnitude * Math.cos(cone);\n  return result;\n};\n\n/**\n * Creates a Cartesian3 instance from x, y and z 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 {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.fromElements = function (x, y, z, result) {\n  if (!defined(result)) {\n    return new Cartesian3(x, y, z);\n  }\n\n  result.x = x;\n  result.y = y;\n  result.z = z;\n  return result;\n};\n\n/**\n * Duplicates a Cartesian3 instance.\n *\n * @param {Cartesian3} cartesian The Cartesian to duplicate.\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. (Returns undefined if cartesian is undefined)\n */\nCartesian3.clone = function (cartesian, result) {\n  if (!defined(cartesian)) {\n    return undefined;\n  }\n  if (!defined(result)) {\n    return new Cartesian3(cartesian.x, cartesian.y, cartesian.z);\n  }\n\n  result.x = cartesian.x;\n  result.y = cartesian.y;\n  result.z = cartesian.z;\n  return result;\n};\n\n/**\n * Creates a Cartesian3 instance from an existing Cartesian4.  This simply takes the\n * x, y, and z properties of the Cartesian4 and drops w.\n * @function\n *\n * @param {Cartesian4} cartesian The Cartesian4 instance to create a Cartesian3 instance from.\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.fromCartesian4 = Cartesian3.clone;\n\n/**\n * The number of elements used to pack the object into an array.\n * @type {Number}\n */\nCartesian3.packedLength = 3;\n\n/**\n * Stores the provided instance into the provided array.\n *\n * @param {Cartesian3} 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 */\nCartesian3.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\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 {Cartesian3} [result] The object into which to store the result.\n * @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if one was not provided.\n */\nCartesian3.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 Cartesian3();\n  }\n  result.x = array[startingIndex++];\n  result.y = array[startingIndex++];\n  result.z = array[startingIndex];\n  return result;\n};\n\n/**\n * Flattens an array of Cartesian3s into an array of components.\n *\n * @param {Cartesian3[]} 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 * 3 components, else a {@link DeveloperError} will be thrown. If it is a regular array, it will be resized to have (array.length * 3) elements.\n * @returns {Number[]} The packed array.\n */\nCartesian3.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 * 3;\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 * 3 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    Cartesian3.pack(array[i], result, i * 3);\n  }\n  return result;\n};\n\n/**\n * Unpacks an array of cartesian components into an array of Cartesian3s.\n *\n * @param {Number[]} array The array of components to unpack.\n * @param {Cartesian3[]} [result] The array onto which to store the result.\n * @returns {Cartesian3[]} The unpacked array.\n */\nCartesian3.unpackArray = function (array, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.defined(\"array\", array);\n  Check.typeOf.number.greaterThanOrEquals(\"array.length\", array.length, 3);\n  if (array.length % 3 !== 0) {\n    throw new DeveloperError(\"array length must be a multiple of 3.\");\n  }\n  //>>includeEnd('debug');\n\n  const length = array.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 index = i / 3;\n    result[index] = Cartesian3.unpack(array, i, result[index]);\n  }\n  return result;\n};\n\n/**\n * Creates a Cartesian3 from three consecutive elements in an array.\n * @function\n *\n * @param {Number[]} array The array whose three consecutive elements correspond to the x, y, and z components, respectively.\n * @param {Number} [startingIndex=0] The offset into the array of the first element, which corresponds to the x component.\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 *\n * @example\n * // Create a Cartesian3 with (1.0, 2.0, 3.0)\n * const v = [1.0, 2.0, 3.0];\n * const p = Cesium.Cartesian3.fromArray(v);\n *\n * // Create a Cartesian3 with (1.0, 2.0, 3.0) using an offset into an array\n * const v2 = [0.0, 0.0, 1.0, 2.0, 3.0];\n * const p2 = Cesium.Cartesian3.fromArray(v2, 2);\n */\nCartesian3.fromArray = Cartesian3.unpack;\n\n/**\n * Computes the value of the maximum component for the supplied Cartesian.\n *\n * @param {Cartesian3} cartesian The cartesian to use.\n * @returns {Number} The value of the maximum component.\n */\nCartesian3.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);\n};\n\n/**\n * Computes the value of the minimum component for the supplied Cartesian.\n *\n * @param {Cartesian3} cartesian The cartesian to use.\n * @returns {Number} The value of the minimum component.\n */\nCartesian3.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);\n};\n\n/**\n * Compares two Cartesians and computes a Cartesian which contains the minimum components of the supplied Cartesians.\n *\n * @param {Cartesian3} first A cartesian to compare.\n * @param {Cartesian3} second A cartesian to compare.\n * @param {Cartesian3} result The object into which to store the result.\n * @returns {Cartesian3} A cartesian with the minimum components.\n */\nCartesian3.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\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 {Cartesian3} first A cartesian to compare.\n * @param {Cartesian3} second A cartesian to compare.\n * @param {Cartesian3} result The object into which to store the result.\n * @returns {Cartesian3} A cartesian with the maximum components.\n */\nCartesian3.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  return result;\n};\n\n/**\n * Computes the provided Cartesian's squared magnitude.\n *\n * @param {Cartesian3} cartesian The Cartesian instance whose squared magnitude is to be computed.\n * @returns {Number} The squared magnitude.\n */\nCartesian3.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  );\n};\n\n/**\n * Computes the Cartesian's magnitude (length).\n *\n * @param {Cartesian3} cartesian The Cartesian instance whose magnitude is to be computed.\n * @returns {Number} The magnitude.\n */\nCartesian3.magnitude = function (cartesian) {\n  return Math.sqrt(Cartesian3.magnitudeSquared(cartesian));\n};\n\nconst distanceScratch = new Cartesian3();\n\n/**\n * Computes the distance between two points.\n *\n * @param {Cartesian3} left The first point to compute the distance from.\n * @param {Cartesian3} 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.Cartesian3.distance(new Cesium.Cartesian3(1.0, 0.0, 0.0), new Cesium.Cartesian3(2.0, 0.0, 0.0));\n */\nCartesian3.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  Cartesian3.subtract(left, right, distanceScratch);\n  return Cartesian3.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 Cartesian3#distance}.\n *\n * @param {Cartesian3} left The first point to compute the distance from.\n * @param {Cartesian3} 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.Cartesian3.distanceSquared(new Cesium.Cartesian3(1.0, 0.0, 0.0), new Cesium.Cartesian3(3.0, 0.0, 0.0));\n */\nCartesian3.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  Cartesian3.subtract(left, right, distanceScratch);\n  return Cartesian3.magnitudeSquared(distanceScratch);\n};\n\n/**\n * Computes the normalized form of the supplied Cartesian.\n *\n * @param {Cartesian3} cartesian The Cartesian to be normalized.\n * @param {Cartesian3} result The object onto which to store the result.\n * @returns {Cartesian3} The modified result parameter.\n */\nCartesian3.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 = Cartesian3.magnitude(cartesian);\n\n  result.x = cartesian.x / magnitude;\n  result.y = cartesian.y / magnitude;\n  result.z = cartesian.z / magnitude;\n\n  //>>includeStart('debug', pragmas.debug);\n  if (isNaN(result.x) || isNaN(result.y) || isNaN(result.z)) {\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 {Cartesian3} left The first Cartesian.\n * @param {Cartesian3} right The second Cartesian.\n * @returns {Number} The dot product.\n */\nCartesian3.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 + left.z * right.z;\n};\n\n/**\n * Computes the componentwise 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 modified result parameter.\n */\nCartesian3.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  return result;\n};\n\n/**\n * Computes the componentwise quotient 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 modified result parameter.\n */\nCartesian3.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  return result;\n};\n\n/**\n * Computes the componentwise sum 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 modified result parameter.\n */\nCartesian3.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  return result;\n};\n\n/**\n * Computes the componentwise difference 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 modified result parameter.\n */\nCartesian3.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  return result;\n};\n\n/**\n * Multiplies the provided Cartesian componentwise by the provided scalar.\n *\n * @param {Cartesian3} cartesian The Cartesian to be scaled.\n * @param {Number} scalar The scalar to multiply with.\n * @param {Cartesian3} result The object onto which to store the result.\n * @returns {Cartesian3} The modified result parameter.\n */\nCartesian3.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  return result;\n};\n\n/**\n * Divides the provided Cartesian componentwise by the provided scalar.\n *\n * @param {Cartesian3} cartesian The Cartesian to be divided.\n * @param {Number} scalar The scalar to divide by.\n * @param {Cartesian3} result The object onto which to store the result.\n * @returns {Cartesian3} The modified result parameter.\n */\nCartesian3.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  return result;\n};\n\n/**\n * Negates the provided Cartesian.\n *\n * @param {Cartesian3} cartesian The Cartesian to be negated.\n * @param {Cartesian3} result The object onto which to store the result.\n * @returns {Cartesian3} The modified result parameter.\n */\nCartesian3.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  return result;\n};\n\n/**\n * Computes the absolute value of the provided Cartesian.\n *\n * @param {Cartesian3} cartesian The Cartesian whose absolute value is to be computed.\n * @param {Cartesian3} result The object onto which to store the result.\n * @returns {Cartesian3} The modified result parameter.\n */\nCartesian3.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  return result;\n};\n\nconst lerpScratch = new Cartesian3();\n/**\n * Computes the linear interpolation or extrapolation at t using the provided cartesians.\n *\n * @param {Cartesian3} start The value corresponding to t at 0.0.\n * @param {Cartesian3} end The value corresponding to t at 1.0.\n * @param {Number} t The point along t at which to interpolate.\n * @param {Cartesian3} result The object onto which to store the result.\n * @returns {Cartesian3} The modified result parameter.\n */\nCartesian3.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  Cartesian3.multiplyByScalar(end, t, lerpScratch);\n  result = Cartesian3.multiplyByScalar(start, 1.0 - t, result);\n  return Cartesian3.add(lerpScratch, result, result);\n};\n\nconst angleBetweenScratch = new Cartesian3();\nconst angleBetweenScratch2 = new Cartesian3();\n/**\n * Returns the angle, in radians, between the provided Cartesians.\n *\n * @param {Cartesian3} left The first Cartesian.\n * @param {Cartesian3} right The second Cartesian.\n * @returns {Number} The angle between the Cartesians.\n */\nCartesian3.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  Cartesian3.normalize(left, angleBetweenScratch);\n  Cartesian3.normalize(right, angleBetweenScratch2);\n  const cosine = Cartesian3.dot(angleBetweenScratch, angleBetweenScratch2);\n  const sine = Cartesian3.magnitude(\n    Cartesian3.cross(\n      angleBetweenScratch,\n      angleBetweenScratch2,\n      angleBetweenScratch\n    )\n  );\n  return Math.atan2(sine, cosine);\n};\n\nconst mostOrthogonalAxisScratch = new Cartesian3();\n/**\n * Returns the axis that is most orthogonal to the provided Cartesian.\n *\n * @param {Cartesian3} cartesian The Cartesian on which to find the most orthogonal axis.\n * @param {Cartesian3} result The object onto which to store the result.\n * @returns {Cartesian3} The most orthogonal axis.\n */\nCartesian3.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 = Cartesian3.normalize(cartesian, mostOrthogonalAxisScratch);\n  Cartesian3.abs(f, f);\n\n  if (f.x <= f.y) {\n    if (f.x <= f.z) {\n      result = Cartesian3.clone(Cartesian3.UNIT_X, result);\n    } else {\n      result = Cartesian3.clone(Cartesian3.UNIT_Z, result);\n    }\n  } else if (f.y <= f.z) {\n    result = Cartesian3.clone(Cartesian3.UNIT_Y, result);\n  } else {\n    result = Cartesian3.clone(Cartesian3.UNIT_Z, result);\n  }\n\n  return result;\n};\n\n/**\n * Projects vector a onto vector b\n * @param {Cartesian3} a The vector that needs projecting\n * @param {Cartesian3} b The vector to project onto\n * @param {Cartesian3} result The result cartesian\n * @returns {Cartesian3} The modified result parameter\n */\nCartesian3.projectVector = function (a, b, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.defined(\"a\", a);\n  Check.defined(\"b\", b);\n  Check.defined(\"result\", result);\n  //>>includeEnd('debug');\n\n  const scalar = Cartesian3.dot(a, b) / Cartesian3.dot(b, b);\n  return Cartesian3.multiplyByScalar(b, scalar, result);\n};\n\n/**\n * Compares the provided Cartesians componentwise and returns\n * <code>true</code> if they are equal, <code>false</code> otherwise.\n *\n * @param {Cartesian3} [left] The first Cartesian.\n * @param {Cartesian3} [right] The second Cartesian.\n * @returns {Boolean} <code>true</code> if left and right are equal, <code>false</code> 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 * <code>true</code> if they pass an absolute or relative tolerance test,\n * <code>false</code> 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} <code>true</code> if left and right are within the provided epsilon, <code>false</code> 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 * <code>true</code> if they are equal, <code>false</code> otherwise.\n *\n * @param {Cartesian3} [right] The right hand side Cartesian.\n * @returns {Boolean} <code>true</code> if they are equal, <code>false</code> 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 * <code>true</code> if they pass an absolute or relative tolerance test,\n * <code>false</code> 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} <code>true</code> if they are within the provided epsilon, <code>false</code> 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 * <code>true</code> if they are equal, <code>false</code> otherwise.\n *\n * @param {Cartographic} [left] The first cartographic.\n * @param {Cartographic} [right] The second cartographic.\n * @returns {Boolean} <code>true</code> if left and right are equal, <code>false</code> 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 * <code>true</code> if they are within the provided epsilon,\n * <code>false</code> 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} <code>true</code> if left and right are within the provided epsilon, <code>false</code> 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 * <code>true</code> if they are equal, <code>false</code> otherwise.\n *\n * @param {Cartographic} [right] The second cartographic.\n * @returns {Boolean} <code>true</code> if left and right are equal, <code>false</code> 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 * <code>true</code> if they are within the provided epsilon,\n * <code>false</code> otherwise.\n *\n * @param {Cartographic} [right] The second cartographic.\n * @param {Number} [epsilon=0] The epsilon to use for equality testing.\n * @returns {Boolean} <code>true</code> if left and right are within the provided epsilon, <code>false</code> 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 * <code>(x / a)^2 + (y / b)^2 + (z / c)^2 = 1</code>.  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 * <code>true</code> if they are equal, <code>false</code> otherwise.\n *\n * @param {Ellipsoid} [right] The other Ellipsoid.\n * @returns {Boolean} <code>true</code> if they are equal, <code>false</code> 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<number>}\n *\n * @param {Number} [column0Row0=0.0] The value for column 0, row 0.\n * @param {Number} [column1Row0=0.0] The value for column 1, row 0.\n * @param {Number} [column2Row0=0.0] The value for column 2, row 0.\n * @param {Number} [column0Row1=0.0] The value for column 0, row 1.\n * @param {Number} [column1Row1=0.0] The value for column 1, row 1.\n * @param {Number} [column2Row1=0.0] The value for column 2, row 1.\n * @param {Number} [column0Row2=0.0] The value for column 0, row 2.\n * @param {Number} [column1Row2=0.0] The value for column 1, row 2.\n * @param {Number} [column2Row2=0.0] The value for column 2, row 2.\n *\n * @see Matrix3.fromArray\n * @see Matrix3.fromColumnMajorArray\n * @see Matrix3.fromRowMajorArray\n * @see Matrix3.fromQuaternion\n * @see Matrix3.fromHeadingPitchRoll\n * @see Matrix3.fromScale\n * @see Matrix3.fromUniformScale\n * @see Matrix3.fromCrossProduct\n * @see Matrix3.fromRotationX\n * @see Matrix3.fromRotationY\n * @see Matrix3.fromRotationZ\n * @see Matrix2\n * @see Matrix4\n */\nfunction Matrix3(\n  column0Row0,\n  column1Row0,\n  column2Row0,\n  column0Row1,\n  column1Row1,\n  column2Row1,\n  column0Row2,\n  column1Row2,\n  column2Row2\n) {\n  this[0] = defaultValue(column0Row0, 0.0);\n  this[1] = defaultValue(column0Row1, 0.0);\n  this[2] = defaultValue(column0Row2, 0.0);\n  this[3] = defaultValue(column1Row0, 0.0);\n  this[4] = defaultValue(column1Row1, 0.0);\n  this[5] = defaultValue(column1Row2, 0.0);\n  this[6] = defaultValue(column2Row0, 0.0);\n  this[7] = defaultValue(column2Row1, 0.0);\n  this[8] = defaultValue(column2Row2, 0.0);\n}\n\n/**\n * The number of elements used to pack the object into an array.\n * @type {Number}\n */\nMatrix3.packedLength = 9;\n\n/**\n * Stores the provided instance into the provided array.\n *\n * @param {Matrix3} 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 */\nMatrix3.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[0];\n  array[startingIndex++] = value[1];\n  array[startingIndex++] = value[2];\n  array[startingIndex++] = value[3];\n  array[startingIndex++] = value[4];\n  array[startingIndex++] = value[5];\n  array[startingIndex++] = value[6];\n  array[startingIndex++] = value[7];\n  array[startingIndex++] = value[8];\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 {Matrix3} [result] The object into which to store the result.\n * @returns {Matrix3} The modified result parameter or a new Matrix3 instance if one was not provided.\n */\nMatrix3.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 Matrix3();\n  }\n\n  result[0] = array[startingIndex++];\n  result[1] = array[startingIndex++];\n  result[2] = array[startingIndex++];\n  result[3] = array[startingIndex++];\n  result[4] = array[startingIndex++];\n  result[5] = array[startingIndex++];\n  result[6] = array[startingIndex++];\n  result[7] = array[startingIndex++];\n  result[8] = array[startingIndex++];\n  return result;\n};\n\n/**\n * Flattens an array of Matrix3s into an array of components. The components\n * are stored in column-major order.\n *\n * @param {Matrix3[]} array The array of matrices 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 * 9 components, else a {@link DeveloperError} will be thrown. If it is a regular array, it will be resized to have (array.length * 9) elements.\n * @returns {Number[]} The packed array.\n */\nMatrix3.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 * 9;\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 * 9 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    Matrix3.pack(array[i], result, i * 9);\n  }\n  return result;\n};\n\n/**\n * Unpacks an array of column-major matrix components into an array of Matrix3s.\n *\n * @param {Number[]} array The array of components to unpack.\n * @param {Matrix3[]} [result] The array onto which to store the result.\n * @returns {Matrix3[]} The unpacked array.\n */\nMatrix3.unpackArray = function (array, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.defined(\"array\", array);\n  Check.typeOf.number.greaterThanOrEquals(\"array.length\", array.length, 9);\n  if (array.length % 9 !== 0) {\n    throw new DeveloperError(\"array length must be a multiple of 9.\");\n  }\n  //>>includeEnd('debug');\n\n  const length = array.length;\n  if (!defined(result)) {\n    result = new Array(length / 9);\n  } else {\n    result.length = length / 9;\n  }\n\n  for (let i = 0; i < length; i += 9) {\n    const index = i / 9;\n    result[index] = Matrix3.unpack(array, i, result[index]);\n  }\n  return result;\n};\n\n/**\n * Duplicates a Matrix3 instance.\n *\n * @param {Matrix3} matrix The matrix to duplicate.\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. (Returns undefined if matrix is undefined)\n */\nMatrix3.clone = function (matrix, result) {\n  if (!defined(matrix)) {\n    return undefined;\n  }\n  if (!defined(result)) {\n    return new Matrix3(\n      matrix[0],\n      matrix[3],\n      matrix[6],\n      matrix[1],\n      matrix[4],\n      matrix[7],\n      matrix[2],\n      matrix[5],\n      matrix[8]\n    );\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  return result;\n};\n\n/**\n * Creates a Matrix3 from 9 consecutive elements in an array.\n *\n * @param {Number[]} array The array whose 9 consecutive elements correspond to the positions of the matrix.  Assumes column-major order.\n * @param {Number} [startingIndex=0] The offset into the array of the first element, which corresponds to first column first row position in the matrix.\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 *\n * @example\n * // Create the Matrix3:\n * // [1.0, 2.0, 3.0]\n * // [1.0, 2.0, 3.0]\n * // [1.0, 2.0, 3.0]\n *\n * const v = [1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 3.0, 3.0, 3.0];\n * const m = Cesium.Matrix3.fromArray(v);\n *\n * // Create same Matrix3 with using an offset into an array\n * const v2 = [0.0, 0.0, 1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 3.0, 3.0, 3.0];\n * const m2 = Cesium.Matrix3.fromArray(v2, 2);\n */\nMatrix3.fromArray = Matrix3.unpack;\n\n/**\n * Creates a Matrix3 instance from a column-major order array.\n *\n * @param {Number[]} values The column-major order array.\n * @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.\n * @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.\n */\nMatrix3.fromColumnMajorArray = function (values, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.defined(\"values\", values);\n  //>>includeEnd('debug');\n\n  return Matrix3.clone(values, result);\n};\n\n/**\n * Creates a Matrix3 instance from a row-major order array.\n * The resulting matrix will be in column-major order.\n *\n * @param {Number[]} values The row-major order array.\n * @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.\n * @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.\n */\nMatrix3.fromRowMajorArray = function (values, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.defined(\"values\", values);\n  //>>includeEnd('debug');\n\n  if (!defined(result)) {\n    return new Matrix3(\n      values[0],\n      values[1],\n      values[2],\n      values[3],\n      values[4],\n      values[5],\n      values[6],\n      values[7],\n      values[8]\n    );\n  }\n  result[0] = values[0];\n  result[1] = values[3];\n  result[2] = values[6];\n  result[3] = values[1];\n  result[4] = values[4];\n  result[5] = values[7];\n  result[6] = values[2];\n  result[7] = values[5];\n  result[8] = values[8];\n  return result;\n};\n\n/**\n * Computes a 3x3 rotation matrix from the provided quaternion.\n *\n * @param {Quaternion} quaternion the quaternion to use.\n * @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.\n * @returns {Matrix3} The 3x3 rotation matrix from this quaternion.\n */\nMatrix3.fromQuaternion = function (quaternion, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.object(\"quaternion\", quaternion);\n  //>>includeEnd('debug');\n\n  const x2 = quaternion.x * quaternion.x;\n  const xy = quaternion.x * quaternion.y;\n  const xz = quaternion.x * quaternion.z;\n  const xw = quaternion.x * quaternion.w;\n  const y2 = quaternion.y * quaternion.y;\n  const yz = quaternion.y * quaternion.z;\n  const yw = quaternion.y * quaternion.w;\n  const z2 = quaternion.z * quaternion.z;\n  const zw = quaternion.z * quaternion.w;\n  const w2 = quaternion.w * quaternion.w;\n\n  const m00 = x2 - y2 - z2 + w2;\n  const m01 = 2.0 * (xy - zw);\n  const m02 = 2.0 * (xz + yw);\n\n  const m10 = 2.0 * (xy + zw);\n  const m11 = -x2 + y2 - z2 + w2;\n  const m12 = 2.0 * (yz - xw);\n\n  const m20 = 2.0 * (xz - yw);\n  const m21 = 2.0 * (yz + xw);\n  const m22 = -x2 - y2 + z2 + w2;\n\n  if (!defined(result)) {\n    return new Matrix3(m00, m01, m02, m10, m11, m12, m20, m21, m22);\n  }\n  result[0] = m00;\n  result[1] = m10;\n  result[2] = m20;\n  result[3] = m01;\n  result[4] = m11;\n  result[5] = m21;\n  result[6] = m02;\n  result[7] = m12;\n  result[8] = m22;\n  return result;\n};\n\n/**\n * Computes a 3x3 rotation matrix from the provided headingPitchRoll. (see http://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles )\n *\n * @param {HeadingPitchRoll} headingPitchRoll the headingPitchRoll to use.\n * @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.\n * @returns {Matrix3} The 3x3 rotation matrix from this headingPitchRoll.\n */\nMatrix3.fromHeadingPitchRoll = function (headingPitchRoll, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.object(\"headingPitchRoll\", headingPitchRoll);\n  //>>includeEnd('debug');\n\n  const cosTheta = Math.cos(-headingPitchRoll.pitch);\n  const cosPsi = Math.cos(-headingPitchRoll.heading);\n  const cosPhi = Math.cos(headingPitchRoll.roll);\n  const sinTheta = Math.sin(-headingPitchRoll.pitch);\n  const sinPsi = Math.sin(-headingPitchRoll.heading);\n  const sinPhi = Math.sin(headingPitchRoll.roll);\n\n  const m00 = cosTheta * cosPsi;\n  const m01 = -cosPhi * sinPsi + sinPhi * sinTheta * cosPsi;\n  const m02 = sinPhi * sinPsi + cosPhi * sinTheta * cosPsi;\n\n  const m10 = cosTheta * sinPsi;\n  const m11 = cosPhi * cosPsi + sinPhi * sinTheta * sinPsi;\n  const m12 = -sinPhi * cosPsi + cosPhi * sinTheta * sinPsi;\n\n  const m20 = -sinTheta;\n  const m21 = sinPhi * cosTheta;\n  const m22 = cosPhi * cosTheta;\n\n  if (!defined(result)) {\n    return new Matrix3(m00, m01, m02, m10, m11, m12, m20, m21, m22);\n  }\n  result[0] = m00;\n  result[1] = m10;\n  result[2] = m20;\n  result[3] = m01;\n  result[4] = m11;\n  result[5] = m21;\n  result[6] = m02;\n  result[7] = m12;\n  result[8] = m22;\n  return result;\n};\n\n/**\n * Computes a Matrix3 instance representing a non-uniform scale.\n *\n * @param {Cartesian3} scale The x, y, and z scale factors.\n * @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.\n * @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.\n *\n * @example\n * // Creates\n * //   [7.0, 0.0, 0.0]\n * //   [0.0, 8.0, 0.0]\n * //   [0.0, 0.0, 9.0]\n * const m = Cesium.Matrix3.fromScale(new Cesium.Cartesian3(7.0, 8.0, 9.0));\n */\nMatrix3.fromScale = function (scale, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.object(\"scale\", scale);\n  //>>includeEnd('debug');\n\n  if (!defined(result)) {\n    return new Matrix3(scale.x, 0.0, 0.0, 0.0, scale.y, 0.0, 0.0, 0.0, scale.z);\n  }\n\n  result[0] = scale.x;\n  result[1] = 0.0;\n  result[2] = 0.0;\n  result[3] = 0.0;\n  result[4] = scale.y;\n  result[5] = 0.0;\n  result[6] = 0.0;\n  result[7] = 0.0;\n  result[8] = scale.z;\n  return result;\n};\n\n/**\n * Computes a Matrix3 instance representing a uniform scale.\n *\n * @param {Number} scale The uniform scale factor.\n * @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.\n * @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.\n *\n * @example\n * // Creates\n * //   [2.0, 0.0, 0.0]\n * //   [0.0, 2.0, 0.0]\n * //   [0.0, 0.0, 2.0]\n * const m = Cesium.Matrix3.fromUniformScale(2.0);\n */\nMatrix3.fromUniformScale = function (scale, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.number(\"scale\", scale);\n  //>>includeEnd('debug');\n\n  if (!defined(result)) {\n    return new Matrix3(scale, 0.0, 0.0, 0.0, scale, 0.0, 0.0, 0.0, scale);\n  }\n\n  result[0] = scale;\n  result[1] = 0.0;\n  result[2] = 0.0;\n  result[3] = 0.0;\n  result[4] = scale;\n  result[5] = 0.0;\n  result[6] = 0.0;\n  result[7] = 0.0;\n  result[8] = scale;\n  return result;\n};\n\n/**\n * Computes a Matrix3 instance representing the cross product equivalent matrix of a Cartesian3 vector.\n *\n * @param {Cartesian3} vector the vector on the left hand side of the cross product operation.\n * @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.\n * @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.\n *\n * @example\n * // Creates\n * //   [0.0, -9.0,  8.0]\n * //   [9.0,  0.0, -7.0]\n * //   [-8.0, 7.0,  0.0]\n * const m = Cesium.Matrix3.fromCrossProduct(new Cesium.Cartesian3(7.0, 8.0, 9.0));\n */\nMatrix3.fromCrossProduct = function (vector, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.object(\"vector\", vector);\n  //>>includeEnd('debug');\n\n  if (!defined(result)) {\n    return new Matrix3(\n      0.0,\n      -vector.z,\n      vector.y,\n      vector.z,\n      0.0,\n      -vector.x,\n      -vector.y,\n      vector.x,\n      0.0\n    );\n  }\n\n  result[0] = 0.0;\n  result[1] = vector.z;\n  result[2] = -vector.y;\n  result[3] = -vector.z;\n  result[4] = 0.0;\n  result[5] = vector.x;\n  result[6] = vector.y;\n  result[7] = -vector.x;\n  result[8] = 0.0;\n  return result;\n};\n\n/**\n * Creates a rotation matrix around the x-axis.\n *\n * @param {Number} angle The angle, in radians, of the rotation.  Positive angles are counterclockwise.\n * @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.\n * @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.\n *\n * @example\n * // Rotate a point 45 degrees counterclockwise around the x-axis.\n * const p = new Cesium.Cartesian3(5, 6, 7);\n * const m = Cesium.Matrix3.fromRotationX(Cesium.Math.toRadians(45.0));\n * const rotated = Cesium.Matrix3.multiplyByVector(m, p, new Cesium.Cartesian3());\n */\nMatrix3.fromRotationX = function (angle, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.number(\"angle\", angle);\n  //>>includeEnd('debug');\n\n  const cosAngle = Math.cos(angle);\n  const sinAngle = Math.sin(angle);\n\n  if (!defined(result)) {\n    return new Matrix3(\n      1.0,\n      0.0,\n      0.0,\n      0.0,\n      cosAngle,\n      -sinAngle,\n      0.0,\n      sinAngle,\n      cosAngle\n    );\n  }\n\n  result[0] = 1.0;\n  result[1] = 0.0;\n  result[2] = 0.0;\n  result[3] = 0.0;\n  result[4] = cosAngle;\n  result[5] = sinAngle;\n  result[6] = 0.0;\n  result[7] = -sinAngle;\n  result[8] = cosAngle;\n\n  return result;\n};\n\n/**\n * Creates a rotation matrix around the y-axis.\n *\n * @param {Number} angle The angle, in radians, of the rotation.  Positive angles are counterclockwise.\n * @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.\n * @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.\n *\n * @example\n * // Rotate a point 45 degrees counterclockwise around the y-axis.\n * const p = new Cesium.Cartesian3(5, 6, 7);\n * const m = Cesium.Matrix3.fromRotationY(Cesium.Math.toRadians(45.0));\n * const rotated = Cesium.Matrix3.multiplyByVector(m, p, new Cesium.Cartesian3());\n */\nMatrix3.fromRotationY = function (angle, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.number(\"angle\", angle);\n  //>>includeEnd('debug');\n\n  const cosAngle = Math.cos(angle);\n  const sinAngle = Math.sin(angle);\n\n  if (!defined(result)) {\n    return new Matrix3(\n      cosAngle,\n      0.0,\n      sinAngle,\n      0.0,\n      1.0,\n      0.0,\n      -sinAngle,\n      0.0,\n      cosAngle\n    );\n  }\n\n  result[0] = cosAngle;\n  result[1] = 0.0;\n  result[2] = -sinAngle;\n  result[3] = 0.0;\n  result[4] = 1.0;\n  result[5] = 0.0;\n  result[6] = sinAngle;\n  result[7] = 0.0;\n  result[8] = cosAngle;\n\n  return result;\n};\n\n/**\n * Creates a rotation matrix around the z-axis.\n *\n * @param {Number} angle The angle, in radians, of the rotation.  Positive angles are counterclockwise.\n * @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.\n * @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.\n *\n * @example\n * // Rotate a point 45 degrees counterclockwise around the z-axis.\n * const p = new Cesium.Cartesian3(5, 6, 7);\n * const m = Cesium.Matrix3.fromRotationZ(Cesium.Math.toRadians(45.0));\n * const rotated = Cesium.Matrix3.multiplyByVector(m, p, new Cesium.Cartesian3());\n */\nMatrix3.fromRotationZ = function (angle, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.number(\"angle\", angle);\n  //>>includeEnd('debug');\n\n  const cosAngle = Math.cos(angle);\n  const sinAngle = Math.sin(angle);\n\n  if (!defined(result)) {\n    return new Matrix3(\n      cosAngle,\n      -sinAngle,\n      0.0,\n      sinAngle,\n      cosAngle,\n      0.0,\n      0.0,\n      0.0,\n      1.0\n    );\n  }\n\n  result[0] = cosAngle;\n  result[1] = sinAngle;\n  result[2] = 0.0;\n  result[3] = -sinAngle;\n  result[4] = cosAngle;\n  result[5] = 0.0;\n  result[6] = 0.0;\n  result[7] = 0.0;\n  result[8] = 1.0;\n\n  return result;\n};\n\n/**\n * Creates an Array from the provided Matrix3 instance.\n * The array will be in column-major order.\n *\n * @param {Matrix3} matrix The matrix to use..\n * @param {Number[]} [result] The Array onto which to store the result.\n * @returns {Number[]} The modified Array parameter or a new Array instance if one was not provided.\n */\nMatrix3.toArray = function (matrix, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.object(\"matrix\", matrix);\n  //>>includeEnd('debug');\n\n  if (!defined(result)) {\n    return [\n      matrix[0],\n      matrix[1],\n      matrix[2],\n      matrix[3],\n      matrix[4],\n      matrix[5],\n      matrix[6],\n      matrix[7],\n      matrix[8],\n    ];\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  return result;\n};\n\n/**\n * Computes the array index of the element at the provided row and column.\n *\n * @param {Number} column The zero-based index of the column.\n * @param {Number} row The zero-based index of the row.\n * @returns {Number} The index of the element at the provided row and column.\n *\n * @exception {DeveloperError} row must be 0, 1, or 2.\n * @exception {DeveloperError} column must be 0, 1, or 2.\n *\n * @example\n * const myMatrix = new Cesium.Matrix3();\n * const column1Row0Index = Cesium.Matrix3.getElementIndex(1, 0);\n * const column1Row0 = myMatrix[column1Row0Index]\n * myMatrix[column1Row0Index] = 10.0;\n */\nMatrix3.getElementIndex = function (column, row) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.number.greaterThanOrEquals(\"row\", row, 0);\n  Check.typeOf.number.lessThanOrEquals(\"row\", row, 2);\n  Check.typeOf.number.greaterThanOrEquals(\"column\", column, 0);\n  Check.typeOf.number.lessThanOrEquals(\"column\", column, 2);\n  //>>includeEnd('debug');\n\n  return column * 3 + row;\n};\n\n/**\n * Retrieves a copy of the matrix column at the provided index as a Cartesian3 instance.\n *\n * @param {Matrix3} matrix The matrix to use.\n * @param {Number} index The zero-based index of the column to retrieve.\n * @param {Cartesian3} result The object onto which to store the result.\n * @returns {Cartesian3} The modified result parameter.\n *\n * @exception {DeveloperError} index must be 0, 1, or 2.\n */\nMatrix3.getColumn = function (matrix, index, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.object(\"matrix\", matrix);\n  Check.typeOf.number.greaterThanOrEquals(\"index\", index, 0);\n  Check.typeOf.number.lessThanOrEquals(\"index\", index, 2);\n  Check.typeOf.object(\"result\", result);\n  //>>includeEnd('debug');\n\n  const startIndex = index * 3;\n  const x = matrix[startIndex];\n  const y = matrix[startIndex + 1];\n  const z = matrix[startIndex + 2];\n\n  result.x = x;\n  result.y = y;\n  result.z = z;\n  return result;\n};\n\n/**\n * Computes a new matrix that replaces the specified column in the provided matrix with the provided Cartesian3 instance.\n *\n * @param {Matrix3} matrix The matrix to use.\n * @param {Number} index The zero-based index of the column to set.\n * @param {Cartesian3} cartesian The Cartesian whose values will be assigned to the specified column.\n * @param {Matrix3} result The object onto which to store the result.\n * @returns {Matrix3} The modified result parameter.\n *\n * @exception {DeveloperError} index must be 0, 1, or 2.\n */\nMatrix3.setColumn = function (matrix, index, cartesian, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.object(\"matrix\", matrix);\n  Check.typeOf.number.greaterThanOrEquals(\"index\", index, 0);\n  Check.typeOf.number.lessThanOrEquals(\"index\", index, 2);\n  Check.typeOf.object(\"cartesian\", cartesian);\n  Check.typeOf.object(\"result\", result);\n  //>>includeEnd('debug');\n\n  result = Matrix3.clone(matrix, result);\n  const startIndex = index * 3;\n  result[startIndex] = cartesian.x;\n  result[startIndex + 1] = cartesian.y;\n  result[startIndex + 2] = cartesian.z;\n  return result;\n};\n\n/**\n * Retrieves a copy of the matrix row at the provided index as a Cartesian3 instance.\n *\n * @param {Matrix3} matrix The matrix to use.\n * @param {Number} index The zero-based index of the row to retrieve.\n * @param {Cartesian3} result The object onto which to store the result.\n * @returns {Cartesian3} The modified result parameter.\n *\n * @exception {DeveloperError} index must be 0, 1, or 2.\n */\nMatrix3.getRow = function (matrix, index, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.object(\"matrix\", matrix);\n  Check.typeOf.number.greaterThanOrEquals(\"index\", index, 0);\n  Check.typeOf.number.lessThanOrEquals(\"index\", index, 2);\n  Check.typeOf.object(\"result\", result);\n  //>>includeEnd('debug');\n\n  const x = matrix[index];\n  const y = matrix[index + 3];\n  const z = matrix[index + 6];\n\n  result.x = x;\n  result.y = y;\n  result.z = z;\n  return result;\n};\n\n/**\n * Computes a new matrix that replaces the specified row in the provided matrix with the provided Cartesian3 instance.\n *\n * @param {Matrix3} matrix The matrix to use.\n * @param {Number} index The zero-based index of the row to set.\n * @param {Cartesian3} cartesian The Cartesian whose values will be assigned to the specified row.\n * @param {Matrix3} result The object onto which to store the result.\n * @returns {Matrix3} The modified result parameter.\n *\n * @exception {DeveloperError} index must be 0, 1, or 2.\n */\nMatrix3.setRow = function (matrix, index, cartesian, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.object(\"matrix\", matrix);\n  Check.typeOf.number.greaterThanOrEquals(\"index\", index, 0);\n  Check.typeOf.number.lessThanOrEquals(\"index\", index, 2);\n  Check.typeOf.object(\"cartesian\", cartesian);\n  Check.typeOf.object(\"result\", result);\n  //>>includeEnd('debug');\n\n  result = Matrix3.clone(matrix, result);\n  result[index] = cartesian.x;\n  result[index + 3] = cartesian.y;\n  result[index + 6] = cartesian.z;\n  return result;\n};\n\nconst scaleScratch1 = new Cartesian3();\n\n/**\n * Computes a new matrix that replaces the scale with the provided scale.\n * This assumes the matrix is an affine transformation.\n *\n * @param {Matrix3} matrix The matrix to use.\n * @param {Cartesian3} scale The scale that replaces the scale of the provided matrix.\n * @param {Matrix3} result The object onto which to store the result.\n * @returns {Matrix3} The modified result parameter.\n *\n * @see Matrix3.setUniformScale\n * @see Matrix3.fromScale\n * @see Matrix3.fromUniformScale\n * @see Matrix3.multiplyByScale\n * @see Matrix3.multiplyByUniformScale\n * @see Matrix3.getScale\n */\nMatrix3.setScale = 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 existingScale = Matrix3.getScale(matrix, scaleScratch1);\n  const scaleRatioX = scale.x / existingScale.x;\n  const scaleRatioY = scale.y / existingScale.y;\n  const scaleRatioZ = scale.z / existingScale.z;\n\n  result[0] = matrix[0] * scaleRatioX;\n  result[1] = matrix[1] * scaleRatioX;\n  result[2] = matrix[2] * scaleRatioX;\n  result[3] = matrix[3] * scaleRatioY;\n  result[4] = matrix[4] * scaleRatioY;\n  result[5] = matrix[5] * scaleRatioY;\n  result[6] = matrix[6] * scaleRatioZ;\n  result[7] = matrix[7] * scaleRatioZ;\n  result[8] = matrix[8] * scaleRatioZ;\n\n  return result;\n};\n\nconst scaleScratch2 = new Cartesian3();\n\n/**\n * Computes a new matrix that replaces the scale with the provided uniform scale.\n * This assumes the matrix is an affine transformation.\n *\n * @param {Matrix3} matrix The matrix to use.\n * @param {Number} scale The uniform scale that replaces the scale of the provided matrix.\n * @param {Matrix3} result The object onto which to store the result.\n * @returns {Matrix3} The modified result parameter.\n *\n * @see Matrix3.setScale\n * @see Matrix3.fromScale\n * @see Matrix3.fromUniformScale\n * @see Matrix3.multiplyByScale\n * @see Matrix3.multiplyByUniformScale\n * @see Matrix3.getScale\n */\nMatrix3.setUniformScale = 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  const existingScale = Matrix3.getScale(matrix, scaleScratch2);\n  const scaleRatioX = scale / existingScale.x;\n  const scaleRatioY = scale / existingScale.y;\n  const scaleRatioZ = scale / existingScale.z;\n\n  result[0] = matrix[0] * scaleRatioX;\n  result[1] = matrix[1] * scaleRatioX;\n  result[2] = matrix[2] * scaleRatioX;\n  result[3] = matrix[3] * scaleRatioY;\n  result[4] = matrix[4] * scaleRatioY;\n  result[5] = matrix[5] * scaleRatioY;\n  result[6] = matrix[6] * scaleRatioZ;\n  result[7] = matrix[7] * scaleRatioZ;\n  result[8] = matrix[8] * scaleRatioZ;\n\n  return result;\n};\n\nconst scratchColumn = new Cartesian3();\n\n/**\n * Extracts the non-uniform scale assuming the matrix is an affine transformation.\n *\n * @param {Matrix3} matrix The matrix.\n * @param {Cartesian3} result The object onto which to store the result.\n * @returns {Cartesian3} The modified result parameter.\n *\n * @see Matrix3.multiplyByScale\n * @see Matrix3.multiplyByUniformScale\n * @see Matrix3.fromScale\n * @see Matrix3.fromUniformScale\n * @see Matrix3.setScale\n * @see Matrix3.setUniformScale\n */\nMatrix3.getScale = 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 = Cartesian3.magnitude(\n    Cartesian3.fromElements(matrix[0], matrix[1], matrix[2], scratchColumn)\n  );\n  result.y = Cartesian3.magnitude(\n    Cartesian3.fromElements(matrix[3], matrix[4], matrix[5], scratchColumn)\n  );\n  result.z = Cartesian3.magnitude(\n    Cartesian3.fromElements(matrix[6], matrix[7], matrix[8], scratchColumn)\n  );\n  return result;\n};\n\nconst scaleScratch3 = new Cartesian3();\n\n/**\n * Computes the maximum scale assuming the matrix is an affine transformation.\n * The maximum scale is the maximum length of the column vectors.\n *\n * @param {Matrix3} matrix The matrix.\n * @returns {Number} The maximum scale.\n */\nMatrix3.getMaximumScale = function (matrix) {\n  Matrix3.getScale(matrix, scaleScratch3);\n  return Cartesian3.maximumComponent(scaleScratch3);\n};\n\nconst scaleScratch4 = new Cartesian3();\n\n/**\n * Sets the rotation assuming the matrix is an affine transformation.\n *\n * @param {Matrix3} matrix The matrix.\n * @param {Matrix3} rotation The rotation matrix.\n * @returns {Matrix3} The modified result parameter.\n *\n * @see Matrix3.getRotation\n */\nMatrix3.setRotation = function (matrix, rotation, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.object(\"matrix\", matrix);\n  Check.typeOf.object(\"result\", result);\n  //>>includeEnd('debug');\n\n  const scale = Matrix3.getScale(matrix, scaleScratch4);\n\n  result[0] = rotation[0] * scale.x;\n  result[1] = rotation[1] * scale.x;\n  result[2] = rotation[2] * scale.x;\n  result[3] = rotation[3] * scale.y;\n  result[4] = rotation[4] * scale.y;\n  result[5] = rotation[5] * scale.y;\n  result[6] = rotation[6] * scale.z;\n  result[7] = rotation[7] * scale.z;\n  result[8] = rotation[8] * scale.z;\n\n  return result;\n};\n\nconst scaleScratch5 = new Cartesian3();\n\n/**\n * Extracts the rotation matrix assuming the matrix is an affine transformation.\n *\n * @param {Matrix3} matrix The matrix.\n * @param {Matrix3} result The object onto which to store the result.\n * @returns {Matrix3} The modified result parameter.\n *\n * @see Matrix3.setRotation\n */\nMatrix3.getRotation = 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 scale = Matrix3.getScale(matrix, scaleScratch5);\n\n  result[0] = matrix[0] / scale.x;\n  result[1] = matrix[1] / scale.x;\n  result[2] = matrix[2] / scale.x;\n  result[3] = matrix[3] / scale.y;\n  result[4] = matrix[4] / scale.y;\n  result[5] = matrix[5] / scale.y;\n  result[6] = matrix[6] / scale.z;\n  result[7] = matrix[7] / scale.z;\n  result[8] = matrix[8] / scale.z;\n\n  return result;\n};\n\n/**\n * Computes the product of two matrices.\n *\n * @param {Matrix3} left The first matrix.\n * @param {Matrix3} right The second matrix.\n * @param {Matrix3} result The object onto which to store the result.\n * @returns {Matrix3} The modified result parameter.\n */\nMatrix3.multiply = 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 column0Row0 =\n    left[0] * right[0] + left[3] * right[1] + left[6] * right[2];\n  const column0Row1 =\n    left[1] * right[0] + left[4] * right[1] + left[7] * right[2];\n  const column0Row2 =\n    left[2] * right[0] + left[5] * right[1] + left[8] * right[2];\n\n  const column1Row0 =\n    left[0] * right[3] + left[3] * right[4] + left[6] * right[5];\n  const column1Row1 =\n    left[1] * right[3] + left[4] * right[4] + left[7] * right[5];\n  const column1Row2 =\n    left[2] * right[3] + left[5] * right[4] + left[8] * right[5];\n\n  const column2Row0 =\n    left[0] * right[6] + left[3] * right[7] + left[6] * right[8];\n  const column2Row1 =\n    left[1] * right[6] + left[4] * right[7] + left[7] * right[8];\n  const column2Row2 =\n    left[2] * right[6] + left[5] * right[7] + left[8] * right[8];\n\n  result[0] = column0Row0;\n  result[1] = column0Row1;\n  result[2] = column0Row2;\n  result[3] = column1Row0;\n  result[4] = column1Row1;\n  result[5] = column1Row2;\n  result[6] = column2Row0;\n  result[7] = column2Row1;\n  result[8] = column2Row2;\n  return result;\n};\n\n/**\n * Computes the sum of two matrices.\n *\n * @param {Matrix3} left The first matrix.\n * @param {Matrix3} right The second matrix.\n * @param {Matrix3} result The object onto which to store the result.\n * @returns {Matrix3} The modified result parameter.\n */\nMatrix3.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[0] = left[0] + right[0];\n  result[1] = left[1] + right[1];\n  result[2] = left[2] + right[2];\n  result[3] = left[3] + right[3];\n  result[4] = left[4] + right[4];\n  result[5] = left[5] + right[5];\n  result[6] = left[6] + right[6];\n  result[7] = left[7] + right[7];\n  result[8] = left[8] + right[8];\n  return result;\n};\n\n/**\n * Computes the difference of two matrices.\n *\n * @param {Matrix3} left The first matrix.\n * @param {Matrix3} right The second matrix.\n * @param {Matrix3} result The object onto which to store the result.\n * @returns {Matrix3} The modified result parameter.\n */\nMatrix3.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[0] = left[0] - right[0];\n  result[1] = left[1] - right[1];\n  result[2] = left[2] - right[2];\n  result[3] = left[3] - right[3];\n  result[4] = left[4] - right[4];\n  result[5] = left[5] - right[5];\n  result[6] = left[6] - right[6];\n  result[7] = left[7] - right[7];\n  result[8] = left[8] - right[8];\n  return result;\n};\n\n/**\n * Computes the product of a matrix and a column vector.\n *\n * @param {Matrix3} matrix The matrix.\n * @param {Cartesian3} cartesian The column.\n * @param {Cartesian3} result The object onto which to store the result.\n * @returns {Cartesian3} The modified result parameter.\n */\nMatrix3.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\n  const x = matrix[0] * vX + matrix[3] * vY + matrix[6] * vZ;\n  const y = matrix[1] * vX + matrix[4] * vY + matrix[7] * vZ;\n  const z = matrix[2] * vX + matrix[5] * vY + matrix[8] * 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 scalar.\n *\n * @param {Matrix3} matrix The matrix.\n * @param {Number} scalar The number to multiply by.\n * @param {Matrix3} result The object onto which to store the result.\n * @returns {Matrix3} The modified result parameter.\n */\nMatrix3.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  return result;\n};\n\n/**\n * Computes the product of a matrix times a (non-uniform) scale, as if the scale were a scale matrix.\n *\n * @param {Matrix3} matrix The matrix on the left-hand side.\n * @param {Number} scale The non-uniform scale on the right-hand side.\n * @param {Matrix3} result The object onto which to store the result.\n * @returns {Matrix3} The modified result parameter.\n *\n *\n * @example\n * // Instead of Cesium.Matrix3.multiply(m, Cesium.Matrix3.fromScale(scale), m);\n * Cesium.Matrix3.multiplyByScale(m, scale, m);\n *\n * @see Matrix3.multiplyByUniformScale\n * @see Matrix3.fromScale\n * @see Matrix3.fromUniformScale\n * @see Matrix3.setScale\n * @see Matrix3.setUniformScale\n * @see Matrix3.getScale\n */\nMatrix3.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  result[0] = matrix[0] * scale.x;\n  result[1] = matrix[1] * scale.x;\n  result[2] = matrix[2] * scale.x;\n  result[3] = matrix[3] * scale.y;\n  result[4] = matrix[4] * scale.y;\n  result[5] = matrix[5] * scale.y;\n  result[6] = matrix[6] * scale.z;\n  result[7] = matrix[7] * scale.z;\n  result[8] = matrix[8] * scale.z;\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 {Matrix3} matrix The matrix on the left-hand side.\n * @param {Number} scale The uniform scale on the right-hand side.\n * @param {Matrix3} result The object onto which to store the result.\n * @returns {Matrix3} The modified result parameter.\n *\n * @example\n * // Instead of Cesium.Matrix3.multiply(m, Cesium.Matrix3.fromUniformScale(scale), m);\n * Cesium.Matrix3.multiplyByUniformScale(m, scale, m);\n *\n * @see Matrix3.multiplyByScale\n * @see Matrix3.fromScale\n * @see Matrix3.fromUniformScale\n * @see Matrix3.setScale\n * @see Matrix3.setUniformScale\n * @see Matrix3.getScale\n */\nMatrix3.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] * scale;\n  result[4] = matrix[4] * scale;\n  result[5] = matrix[5] * scale;\n  result[6] = matrix[6] * scale;\n  result[7] = matrix[7] * scale;\n  result[8] = matrix[8] * scale;\n\n  return result;\n};\n\n/**\n * Creates a negated copy of the provided matrix.\n *\n * @param {Matrix3} matrix The matrix to negate.\n * @param {Matrix3} result The object onto which to store the result.\n * @returns {Matrix3} The modified result parameter.\n */\nMatrix3.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  return result;\n};\n\n/**\n * Computes the transpose of the provided matrix.\n *\n * @param {Matrix3} matrix The matrix to transpose.\n * @param {Matrix3} result The object onto which to store the result.\n * @returns {Matrix3} The modified result parameter.\n */\nMatrix3.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 column0Row0 = matrix[0];\n  const column0Row1 = matrix[3];\n  const column0Row2 = matrix[6];\n  const column1Row0 = matrix[1];\n  const column1Row1 = matrix[4];\n  const column1Row2 = matrix[7];\n  const column2Row0 = matrix[2];\n  const column2Row1 = matrix[5];\n  const column2Row2 = matrix[8];\n\n  result[0] = column0Row0;\n  result[1] = column0Row1;\n  result[2] = column0Row2;\n  result[3] = column1Row0;\n  result[4] = column1Row1;\n  result[5] = column1Row2;\n  result[6] = column2Row0;\n  result[7] = column2Row1;\n  result[8] = column2Row2;\n  return result;\n};\n\nfunction computeFrobeniusNorm(matrix) {\n  let norm = 0.0;\n  for (let i = 0; i < 9; ++i) {\n    const temp = matrix[i];\n    norm += temp * temp;\n  }\n\n  return Math.sqrt(norm);\n}\n\nconst rowVal = [1, 0, 0];\nconst colVal = [2, 2, 1];\n\nfunction offDiagonalFrobeniusNorm(matrix) {\n  // Computes the \"off-diagonal\" Frobenius norm.\n  // Assumes matrix is symmetric.\n\n  let norm = 0.0;\n  for (let i = 0; i < 3; ++i) {\n    const temp = matrix[Matrix3.getElementIndex(colVal[i], rowVal[i])];\n    norm += 2.0 * temp * temp;\n  }\n\n  return Math.sqrt(norm);\n}\n\nfunction shurDecomposition(matrix, result) {\n  // This routine was created based upon Matrix Computations, 3rd ed., by Golub and Van Loan,\n  // section 8.4.2 The 2by2 Symmetric Schur Decomposition.\n  //\n  // The routine takes a matrix, which is assumed to be symmetric, and\n  // finds the largest off-diagonal term, and then creates\n  // a matrix (result) which can be used to help reduce it\n\n  const tolerance = CesiumMath.EPSILON15;\n\n  let maxDiagonal = 0.0;\n  let rotAxis = 1;\n\n  // find pivot (rotAxis) based on max diagonal of matrix\n  for (let i = 0; i < 3; ++i) {\n    const temp = Math.abs(\n      matrix[Matrix3.getElementIndex(colVal[i], rowVal[i])]\n    );\n    if (temp > maxDiagonal) {\n      rotAxis = i;\n      maxDiagonal = temp;\n    }\n  }\n\n  let c = 1.0;\n  let s = 0.0;\n\n  const p = rowVal[rotAxis];\n  const q = colVal[rotAxis];\n\n  if (Math.abs(matrix[Matrix3.getElementIndex(q, p)]) > tolerance) {\n    const qq = matrix[Matrix3.getElementIndex(q, q)];\n    const pp = matrix[Matrix3.getElementIndex(p, p)];\n    const qp = matrix[Matrix3.getElementIndex(q, p)];\n\n    const tau = (qq - pp) / 2.0 / qp;\n    let t;\n\n    if (tau < 0.0) {\n      t = -1.0 / (-tau + Math.sqrt(1.0 + tau * tau));\n    } else {\n      t = 1.0 / (tau + Math.sqrt(1.0 + tau * tau));\n    }\n\n    c = 1.0 / Math.sqrt(1.0 + t * t);\n    s = t * c;\n  }\n\n  result = Matrix3.clone(Matrix3.IDENTITY, result);\n\n  result[Matrix3.getElementIndex(p, p)] = result[\n    Matrix3.getElementIndex(q, q)\n  ] = c;\n  result[Matrix3.getElementIndex(q, p)] = s;\n  result[Matrix3.getElementIndex(p, q)] = -s;\n\n  return result;\n}\n\nconst jMatrix = new Matrix3();\nconst jMatrixTranspose = new Matrix3();\n\n/**\n * Computes the eigenvectors and eigenvalues of a symmetric matrix.\n * <p>\n * Returns a diagonal matrix and unitary matrix such that:\n * <code>matrix = unitary matrix * diagonal matrix * transpose(unitary matrix)</code>\n * </p>\n * <p>\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 * </p>\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 * <code>true</code> if they are equal, <code>false</code> otherwise.\n *\n * @param {Matrix3} [left] The first matrix.\n * @param {Matrix3} [right] The second matrix.\n * @returns {Boolean} <code>true</code> if left and right are equal, <code>false</code> 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 * <code>true</code> if they are within the provided epsilon,\n * <code>false</code> 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} <code>true</code> if left and right are within the provided epsilon, <code>false</code> 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 * <code>true</code> if they are equal, <code>false</code> otherwise.\n *\n * @param {Matrix3} [right] The right hand side matrix.\n * @returns {Boolean} <code>true</code> if they are equal, <code>false</code> 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 * <code>true</code> if they are within the provided epsilon,\n * <code>false</code> 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} <code>true</code> if they are within the provided epsilon, <code>false</code> 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}. <code>red</code>, <code>green</code>, <code>blue</code>,\n * and <code>alpha</code> map to <code>x</code>, <code>y</code>, <code>z</code>, and <code>w</code>, 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 * <code>true</code> if they are equal, <code>false</code> otherwise.\n *\n * @param {Cartesian4} [left] The first Cartesian.\n * @param {Cartesian4} [right] The second Cartesian.\n * @returns {Boolean} <code>true</code> if left and right are equal, <code>false</code> 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 * <code>true</code> if they pass an absolute or relative tolerance test,\n * <code>false</code> 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} <code>true</code> if left and right are within the provided epsilon, <code>false</code> 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 * <code>true</code> if they are equal, <code>false</code> otherwise.\n *\n * @param {Cartesian4} [right] The right hand side Cartesian.\n * @returns {Boolean} <code>true</code> if they are equal, <code>false</code> 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 * <code>true</code> if they pass an absolute or relative tolerance test,\n * <code>false</code> 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} <code>true</code> if they are within the provided epsilon, <code>false</code> 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<number>}\n *\n * @param {Number} [column0Row0=0.0] The value for column 0, row 0.\n * @param {Number} [column1Row0=0.0] The value for column 1, row 0.\n * @param {Number} [column2Row0=0.0] The value for column 2, row 0.\n * @param {Number} [column3Row0=0.0] The value for column 3, row 0.\n * @param {Number} [column0Row1=0.0] The value for column 0, row 1.\n * @param {Number} [column1Row1=0.0] The value for column 1, row 1.\n * @param {Number} [column2Row1=0.0] The value for column 2, row 1.\n * @param {Number} [column3Row1=0.0] The value for column 3, row 1.\n * @param {Number} [column0Row2=0.0] The value for column 0, row 2.\n * @param {Number} [column1Row2=0.0] The value for column 1, row 2.\n * @param {Number} [column2Row2=0.0] The value for column 2, row 2.\n * @param {Number} [column3Row2=0.0] The value for column 3, row 2.\n * @param {Number} [column0Row3=0.0] The value for column 0, row 3.\n * @param {Number} [column1Row3=0.0] The value for column 1, row 3.\n * @param {Number} [column2Row3=0.0] The value for column 2, row 3.\n * @param {Number} [column3Row3=0.0] The value for column 3, row 3.\n *\n * @see Matrix4.fromArray\n * @see Matrix4.fromColumnMajorArray\n * @see Matrix4.fromRowMajorArray\n * @see Matrix4.fromRotationTranslation\n * @see Matrix4.fromTranslationQuaternionRotationScale\n * @see Matrix4.fromTranslationRotationScale\n * @see Matrix4.fromTranslation\n * @see Matrix4.fromScale\n * @see Matrix4.fromUniformScale\n * @see Matrix4.fromRotation\n * @see Matrix4.fromCamera\n * @see Matrix4.computePerspectiveFieldOfView\n * @see Matrix4.computeOrthographicOffCenter\n * @see Matrix4.computePerspectiveOffCenter\n * @see Matrix4.computeInfinitePerspectiveOffCenter\n * @see Matrix4.computeViewportTransformation\n * @see Matrix4.computeView\n * @see Matrix2\n * @see Matrix3\n * @see Packable\n */\nfunction Matrix4(\n  column0Row0,\n  column1Row0,\n  column2Row0,\n  column3Row0,\n  column0Row1,\n  column1Row1,\n  column2Row1,\n  column3Row1,\n  column0Row2,\n  column1Row2,\n  column2Row2,\n  column3Row2,\n  column0Row3,\n  column1Row3,\n  column2Row3,\n  column3Row3\n) {\n  this[0] = defaultValue(column0Row0, 0.0);\n  this[1] = defaultValue(column0Row1, 0.0);\n  this[2] = defaultValue(column0Row2, 0.0);\n  this[3] = defaultValue(column0Row3, 0.0);\n  this[4] = defaultValue(column1Row0, 0.0);\n  this[5] = defaultValue(column1Row1, 0.0);\n  this[6] = defaultValue(column1Row2, 0.0);\n  this[7] = defaultValue(column1Row3, 0.0);\n  this[8] = defaultValue(column2Row0, 0.0);\n  this[9] = defaultValue(column2Row1, 0.0);\n  this[10] = defaultValue(column2Row2, 0.0);\n  this[11] = defaultValue(column2Row3, 0.0);\n  this[12] = defaultValue(column3Row0, 0.0);\n  this[13] = defaultValue(column3Row1, 0.0);\n  this[14] = defaultValue(column3Row2, 0.0);\n  this[15] = defaultValue(column3Row3, 0.0);\n}\n\n/**\n * The number of elements used to pack the object into an array.\n * @type {Number}\n */\nMatrix4.packedLength = 16;\n\n/**\n * Stores the provided instance into the provided array.\n *\n * @param {Matrix4} 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 */\nMatrix4.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[0];\n  array[startingIndex++] = value[1];\n  array[startingIndex++] = value[2];\n  array[startingIndex++] = value[3];\n  array[startingIndex++] = value[4];\n  array[startingIndex++] = value[5];\n  array[startingIndex++] = value[6];\n  array[startingIndex++] = value[7];\n  array[startingIndex++] = value[8];\n  array[startingIndex++] = value[9];\n  array[startingIndex++] = value[10];\n  array[startingIndex++] = value[11];\n  array[startingIndex++] = value[12];\n  array[startingIndex++] = value[13];\n  array[startingIndex++] = value[14];\n  array[startingIndex] = value[15];\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 {Matrix4} [result] The object into which to store the result.\n * @returns {Matrix4} The modified result parameter or a new Matrix4 instance if one was not provided.\n */\nMatrix4.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 Matrix4();\n  }\n\n  result[0] = array[startingIndex++];\n  result[1] = array[startingIndex++];\n  result[2] = array[startingIndex++];\n  result[3] = array[startingIndex++];\n  result[4] = array[startingIndex++];\n  result[5] = array[startingIndex++];\n  result[6] = array[startingIndex++];\n  result[7] = array[startingIndex++];\n  result[8] = array[startingIndex++];\n  result[9] = array[startingIndex++];\n  result[10] = array[startingIndex++];\n  result[11] = array[startingIndex++];\n  result[12] = array[startingIndex++];\n  result[13] = array[startingIndex++];\n  result[14] = array[startingIndex++];\n  result[15] = array[startingIndex];\n  return result;\n};\n\n/**\n * Flattens an array of Matrix4s into an array of components. The components\n * are stored in column-major order.\n *\n * @param {Matrix4[]} array The array of matrices 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 * 16 components, else a {@link DeveloperError} will be thrown. If it is a regular array, it will be resized to have (array.length * 16) elements.\n * @returns {Number[]} The packed array.\n */\nMatrix4.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 * 16;\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 * 16 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    Matrix4.pack(array[i], result, i * 16);\n  }\n  return result;\n};\n\n/**\n * Unpacks an array of column-major matrix components into an array of Matrix4s.\n *\n * @param {Number[]} array The array of components to unpack.\n * @param {Matrix4[]} [result] The array onto which to store the result.\n * @returns {Matrix4[]} The unpacked array.\n */\nMatrix4.unpackArray = function (array, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.defined(\"array\", array);\n  Check.typeOf.number.greaterThanOrEquals(\"array.length\", array.length, 16);\n  if (array.length % 16 !== 0) {\n    throw new DeveloperError(\"array length must be a multiple of 16.\");\n  }\n  //>>includeEnd('debug');\n\n  const length = array.length;\n  if (!defined(result)) {\n    result = new Array(length / 16);\n  } else {\n    result.length = length / 16;\n  }\n\n  for (let i = 0; i < length; i += 16) {\n    const index = i / 16;\n    result[index] = Matrix4.unpack(array, i, result[index]);\n  }\n  return result;\n};\n\n/**\n * Duplicates a Matrix4 instance.\n *\n * @param {Matrix4} matrix The matrix to duplicate.\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. (Returns undefined if matrix is undefined)\n */\nMatrix4.clone = function (matrix, result) {\n  if (!defined(matrix)) {\n    return undefined;\n  }\n  if (!defined(result)) {\n    return new Matrix4(\n      matrix[0],\n      matrix[4],\n      matrix[8],\n      matrix[12],\n      matrix[1],\n      matrix[5],\n      matrix[9],\n      matrix[13],\n      matrix[2],\n      matrix[6],\n      matrix[10],\n      matrix[14],\n      matrix[3],\n      matrix[7],\n      matrix[11],\n      matrix[15]\n    );\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 * Creates a Matrix4 from 16 consecutive elements in an array.\n * @function\n *\n * @param {Number[]} array The array whose 16 consecutive elements correspond to the positions of the matrix.  Assumes column-major order.\n * @param {Number} [startingIndex=0] The offset into the array of the first element, which corresponds to first column first row position in the matrix.\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 *\n * @example\n * // Create the Matrix4:\n * // [1.0, 2.0, 3.0, 4.0]\n * // [1.0, 2.0, 3.0, 4.0]\n * // [1.0, 2.0, 3.0, 4.0]\n * // [1.0, 2.0, 3.0, 4.0]\n *\n * const v = [1.0, 1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 2.0, 3.0, 3.0, 3.0, 3.0, 4.0, 4.0, 4.0, 4.0];\n * const m = Cesium.Matrix4.fromArray(v);\n *\n * // Create same Matrix4 with using an offset into an array\n * const v2 = [0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 2.0, 3.0, 3.0, 3.0, 3.0, 4.0, 4.0, 4.0, 4.0];\n * const m2 = Cesium.Matrix4.fromArray(v2, 2);\n */\nMatrix4.fromArray = Matrix4.unpack;\n\n/**\n * Computes a Matrix4 instance from a column-major order array.\n *\n * @param {Number[]} values The column-major order array.\n * @param {Matrix4} [result] The object in which the result will be stored, if undefined a new instance will be created.\n * @returns {Matrix4} The modified result parameter, or a new Matrix4 instance if one was not provided.\n */\nMatrix4.fromColumnMajorArray = function (values, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.defined(\"values\", values);\n  //>>includeEnd('debug');\n\n  return Matrix4.clone(values, result);\n};\n\n/**\n * Computes a Matrix4 instance from a row-major order array.\n * The resulting matrix will be in column-major order.\n *\n * @param {Number[]} values The row-major order array.\n * @param {Matrix4} [result] The object in which the result will be stored, if undefined a new instance will be created.\n * @returns {Matrix4} The modified result parameter, or a new Matrix4 instance if one was not provided.\n */\nMatrix4.fromRowMajorArray = function (values, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.defined(\"values\", values);\n  //>>includeEnd('debug');\n\n  if (!defined(result)) {\n    return new Matrix4(\n      values[0],\n      values[1],\n      values[2],\n      values[3],\n      values[4],\n      values[5],\n      values[6],\n      values[7],\n      values[8],\n      values[9],\n      values[10],\n      values[11],\n      values[12],\n      values[13],\n      values[14],\n      values[15]\n    );\n  }\n  result[0] = values[0];\n  result[1] = values[4];\n  result[2] = values[8];\n  result[3] = values[12];\n  result[4] = values[1];\n  result[5] = values[5];\n  result[6] = values[9];\n  result[7] = values[13];\n  result[8] = values[2];\n  result[9] = values[6];\n  result[10] = values[10];\n  result[11] = values[14];\n  result[12] = values[3];\n  result[13] = values[7];\n  result[14] = values[11];\n  result[15] = values[15];\n  return result;\n};\n\n/**\n * Computes a Matrix4 instance from a Matrix3 representing the rotation\n * and a Cartesian3 representing the translation.\n *\n * @param {Matrix3} rotation The upper left portion of the matrix representing the rotation.\n * @param {Cartesian3} [translation=Cartesian3.ZERO] The upper right portion of the matrix representing the translation.\n * @param {Matrix4} [result] The object in which the result will be stored, if undefined a new instance will be created.\n * @returns {Matrix4} The modified result parameter, or a new Matrix4 instance if one was not provided.\n */\nMatrix4.fromRotationTranslation = function (rotation, translation, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.object(\"rotation\", rotation);\n  //>>includeEnd('debug');\n\n  translation = defaultValue(translation, Cartesian3.ZERO);\n\n  if (!defined(result)) {\n    return new Matrix4(\n      rotation[0],\n      rotation[3],\n      rotation[6],\n      translation.x,\n      rotation[1],\n      rotation[4],\n      rotation[7],\n      translation.y,\n      rotation[2],\n      rotation[5],\n      rotation[8],\n      translation.z,\n      0.0,\n      0.0,\n      0.0,\n      1.0\n    );\n  }\n\n  result[0] = rotation[0];\n  result[1] = rotation[1];\n  result[2] = rotation[2];\n  result[3] = 0.0;\n  result[4] = rotation[3];\n  result[5] = rotation[4];\n  result[6] = rotation[5];\n  result[7] = 0.0;\n  result[8] = rotation[6];\n  result[9] = rotation[7];\n  result[10] = rotation[8];\n  result[11] = 0.0;\n  result[12] = translation.x;\n  result[13] = translation.y;\n  result[14] = translation.z;\n  result[15] = 1.0;\n  return result;\n};\n\n/**\n * Computes a Matrix4 instance from a translation, rotation, and scale (TRS)\n * representation with the rotation represented as a quaternion.\n *\n * @param {Cartesian3} translation The translation transformation.\n * @param {Quaternion} rotation The rotation transformation.\n * @param {Cartesian3} scale The non-uniform scale transformation.\n * @param {Matrix4} [result] The object in which the result will be stored, if undefined a new instance will be created.\n * @returns {Matrix4} The modified result parameter, or a new Matrix4 instance if one was not provided.\n *\n * @example\n * const result = Cesium.Matrix4.fromTranslationQuaternionRotationScale(\n *   new Cesium.Cartesian3(1.0, 2.0, 3.0), // translation\n *   Cesium.Quaternion.IDENTITY,           // rotation\n *   new Cesium.Cartesian3(7.0, 8.0, 9.0), // scale\n *   result);\n */\nMatrix4.fromTranslationQuaternionRotationScale = function (\n  translation,\n  rotation,\n  scale,\n  result\n) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.object(\"translation\", translation);\n  Check.typeOf.object(\"rotation\", rotation);\n  Check.typeOf.object(\"scale\", scale);\n  //>>includeEnd('debug');\n\n  if (!defined(result)) {\n    result = new Matrix4();\n  }\n\n  const scaleX = scale.x;\n  const scaleY = scale.y;\n  const scaleZ = scale.z;\n\n  const x2 = rotation.x * rotation.x;\n  const xy = rotation.x * rotation.y;\n  const xz = rotation.x * rotation.z;\n  const xw = rotation.x * rotation.w;\n  const y2 = rotation.y * rotation.y;\n  const yz = rotation.y * rotation.z;\n  const yw = rotation.y * rotation.w;\n  const z2 = rotation.z * rotation.z;\n  const zw = rotation.z * rotation.w;\n  const w2 = rotation.w * rotation.w;\n\n  const m00 = x2 - y2 - z2 + w2;\n  const m01 = 2.0 * (xy - zw);\n  const m02 = 2.0 * (xz + yw);\n\n  const m10 = 2.0 * (xy + zw);\n  const m11 = -x2 + y2 - z2 + w2;\n  const m12 = 2.0 * (yz - xw);\n\n  const m20 = 2.0 * (xz - yw);\n  const m21 = 2.0 * (yz + xw);\n  const m22 = -x2 - y2 + z2 + w2;\n\n  result[0] = m00 * scaleX;\n  result[1] = m10 * scaleX;\n  result[2] = m20 * scaleX;\n  result[3] = 0.0;\n  result[4] = m01 * scaleY;\n  result[5] = m11 * scaleY;\n  result[6] = m21 * scaleY;\n  result[7] = 0.0;\n  result[8] = m02 * scaleZ;\n  result[9] = m12 * scaleZ;\n  result[10] = m22 * scaleZ;\n  result[11] = 0.0;\n  result[12] = translation.x;\n  result[13] = translation.y;\n  result[14] = translation.z;\n  result[15] = 1.0;\n\n  return result;\n};\n\n/**\n * Creates a Matrix4 instance from a {@link TranslationRotationScale} instance.\n *\n * @param {TranslationRotationScale} translationRotationScale The instance.\n * @param {Matrix4} [result] The object in which the result will be stored, if undefined a new instance will be created.\n * @returns {Matrix4} The modified result parameter, or a new Matrix4 instance if one was not provided.\n */\nMatrix4.fromTranslationRotationScale = function (\n  translationRotationScale,\n  result\n) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.object(\"translationRotationScale\", translationRotationScale);\n  //>>includeEnd('debug');\n\n  return Matrix4.fromTranslationQuaternionRotationScale(\n    translationRotationScale.translation,\n    translationRotationScale.rotation,\n    translationRotationScale.scale,\n    result\n  );\n};\n\n/**\n * Creates a Matrix4 instance from a Cartesian3 representing the translation.\n *\n * @param {Cartesian3} translation The upper right portion of the matrix representing the translation.\n * @param {Matrix4} [result] The object in which the result will be stored, if undefined a new instance will be created.\n * @returns {Matrix4} The modified result parameter, or a new Matrix4 instance if one was not provided.\n *\n * @see Matrix4.multiplyByTranslation\n */\nMatrix4.fromTranslation = function (translation, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.object(\"translation\", translation);\n  //>>includeEnd('debug');\n\n  return Matrix4.fromRotationTranslation(Matrix3.IDENTITY, translation, result);\n};\n\n/**\n * Computes a Matrix4 instance representing a non-uniform scale.\n *\n * @param {Cartesian3} scale The x, y, and z scale factors.\n * @param {Matrix4} [result] The object in which the result will be stored, if undefined a new instance will be created.\n * @returns {Matrix4} The modified result parameter, or a new Matrix4 instance if one was not provided.\n *\n * @example\n * // Creates\n * //   [7.0, 0.0, 0.0, 0.0]\n * //   [0.0, 8.0, 0.0, 0.0]\n * //   [0.0, 0.0, 9.0, 0.0]\n * //   [0.0, 0.0, 0.0, 1.0]\n * const m = Cesium.Matrix4.fromScale(new Cesium.Cartesian3(7.0, 8.0, 9.0));\n */\nMatrix4.fromScale = function (scale, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.object(\"scale\", scale);\n  //>>includeEnd('debug');\n\n  if (!defined(result)) {\n    return new Matrix4(\n      scale.x,\n      0.0,\n      0.0,\n      0.0,\n      0.0,\n      scale.y,\n      0.0,\n      0.0,\n      0.0,\n      0.0,\n      scale.z,\n      0.0,\n      0.0,\n      0.0,\n      0.0,\n      1.0\n    );\n  }\n\n  result[0] = scale.x;\n  result[1] = 0.0;\n  result[2] = 0.0;\n  result[3] = 0.0;\n  result[4] = 0.0;\n  result[5] = scale.y;\n  result[6] = 0.0;\n  result[7] = 0.0;\n  result[8] = 0.0;\n  result[9] = 0.0;\n  result[10] = scale.z;\n  result[11] = 0.0;\n  result[12] = 0.0;\n  result[13] = 0.0;\n  result[14] = 0.0;\n  result[15] = 1.0;\n  return result;\n};\n\n/**\n * Computes a Matrix4 instance representing a uniform scale.\n *\n * @param {Number} scale The uniform scale factor.\n * @param {Matrix4} [result] The object in which the result will be stored, if undefined a new instance will be created.\n * @returns {Matrix4} The modified result parameter, or a new Matrix4 instance if one was not provided.\n *\n * @example\n * // Creates\n * //   [2.0, 0.0, 0.0, 0.0]\n * //   [0.0, 2.0, 0.0, 0.0]\n * //   [0.0, 0.0, 2.0, 0.0]\n * //   [0.0, 0.0, 0.0, 1.0]\n * const m = Cesium.Matrix4.fromUniformScale(2.0);\n */\nMatrix4.fromUniformScale = function (scale, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.number(\"scale\", scale);\n  //>>includeEnd('debug');\n\n  if (!defined(result)) {\n    return new Matrix4(\n      scale,\n      0.0,\n      0.0,\n      0.0,\n      0.0,\n      scale,\n      0.0,\n      0.0,\n      0.0,\n      0.0,\n      scale,\n      0.0,\n      0.0,\n      0.0,\n      0.0,\n      1.0\n    );\n  }\n\n  result[0] = scale;\n  result[1] = 0.0;\n  result[2] = 0.0;\n  result[3] = 0.0;\n  result[4] = 0.0;\n  result[5] = scale;\n  result[6] = 0.0;\n  result[7] = 0.0;\n  result[8] = 0.0;\n  result[9] = 0.0;\n  result[10] = scale;\n  result[11] = 0.0;\n  result[12] = 0.0;\n  result[13] = 0.0;\n  result[14] = 0.0;\n  result[15] = 1.0;\n  return result;\n};\n\n/**\n * Creates a rotation matrix.\n *\n * @param {Matrix3} rotation The rotation matrix.\n * @param {Matrix4} [result] The object in which the result will be stored, if undefined a new instance will be created.\n * @returns {Matrix4} The modified result parameter, or a new Matrix4 instance if one was not provided.\n */\nMatrix4.fromRotation = function (rotation, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.object(\"rotation\", rotation);\n  //>>includeEnd('debug');\n\n  if (!defined(result)) {\n    result = new Matrix4();\n  }\n  result[0] = rotation[0];\n  result[1] = rotation[1];\n  result[2] = rotation[2];\n  result[3] = 0.0;\n\n  result[4] = rotation[3];\n  result[5] = rotation[4];\n  result[6] = rotation[5];\n  result[7] = 0.0;\n\n  result[8] = rotation[6];\n  result[9] = rotation[7];\n  result[10] = rotation[8];\n  result[11] = 0.0;\n\n  result[12] = 0.0;\n  result[13] = 0.0;\n  result[14] = 0.0;\n  result[15] = 1.0;\n\n  return result;\n};\n\nconst fromCameraF = new Cartesian3();\nconst fromCameraR = new Cartesian3();\nconst fromCameraU = new Cartesian3();\n\n/**\n * Computes a Matrix4 instance from a Camera.\n *\n * @param {Camera} camera The camera to use.\n * @param {Matrix4} [result] The object in which the result will be stored, if undefined a new instance will be created.\n * @returns {Matrix4} The modified result parameter, or a new Matrix4 instance if one was not provided.\n */\nMatrix4.fromCamera = function (camera, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.object(\"camera\", camera);\n  //>>includeEnd('debug');\n\n  const position = camera.position;\n  const direction = camera.direction;\n  const up = camera.up;\n\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.object(\"camera.position\", position);\n  Check.typeOf.object(\"camera.direction\", direction);\n  Check.typeOf.object(\"camera.up\", up);\n  //>>includeEnd('debug');\n\n  Cartesian3.normalize(direction, fromCameraF);\n  Cartesian3.normalize(\n    Cartesian3.cross(fromCameraF, up, fromCameraR),\n    fromCameraR\n  );\n  Cartesian3.normalize(\n    Cartesian3.cross(fromCameraR, fromCameraF, fromCameraU),\n    fromCameraU\n  );\n\n  const sX = fromCameraR.x;\n  const sY = fromCameraR.y;\n  const sZ = fromCameraR.z;\n  const fX = fromCameraF.x;\n  const fY = fromCameraF.y;\n  const fZ = fromCameraF.z;\n  const uX = fromCameraU.x;\n  const uY = fromCameraU.y;\n  const uZ = fromCameraU.z;\n  const positionX = position.x;\n  const positionY = position.y;\n  const positionZ = position.z;\n  const t0 = sX * -positionX + sY * -positionY + sZ * -positionZ;\n  const t1 = uX * -positionX + uY * -positionY + uZ * -positionZ;\n  const t2 = fX * positionX + fY * positionY + fZ * positionZ;\n\n  // The code below this comment is an optimized\n  // version of the commented lines.\n  // Rather that create two matrices and then multiply,\n  // we just bake in the multiplcation as part of creation.\n  // const rotation = new Matrix4(\n  //                 sX,  sY,  sZ, 0.0,\n  //                 uX,  uY,  uZ, 0.0,\n  //                -fX, -fY, -fZ, 0.0,\n  //                 0.0,  0.0,  0.0, 1.0);\n  // const translation = new Matrix4(\n  //                 1.0, 0.0, 0.0, -position.x,\n  //                 0.0, 1.0, 0.0, -position.y,\n  //                 0.0, 0.0, 1.0, -position.z,\n  //                 0.0, 0.0, 0.0, 1.0);\n  // return rotation.multiply(translation);\n  if (!defined(result)) {\n    return new Matrix4(\n      sX,\n      sY,\n      sZ,\n      t0,\n      uX,\n      uY,\n      uZ,\n      t1,\n      -fX,\n      -fY,\n      -fZ,\n      t2,\n      0.0,\n      0.0,\n      0.0,\n      1.0\n    );\n  }\n  result[0] = sX;\n  result[1] = uX;\n  result[2] = -fX;\n  result[3] = 0.0;\n  result[4] = sY;\n  result[5] = uY;\n  result[6] = -fY;\n  result[7] = 0.0;\n  result[8] = sZ;\n  result[9] = uZ;\n  result[10] = -fZ;\n  result[11] = 0.0;\n  result[12] = t0;\n  result[13] = t1;\n  result[14] = t2;\n  result[15] = 1.0;\n  return result;\n};\n\n/**\n * Computes a Matrix4 instance representing a perspective transformation matrix.\n *\n * @param {Number} fovY The field of view along the Y axis in radians.\n * @param {Number} aspectRatio The aspect ratio.\n * @param {Number} near The distance to the near plane in meters.\n * @param {Number} far The distance to the far plane in meters.\n * @param {Matrix4} result The object in which the result will be stored.\n * @returns {Matrix4} The modified result parameter.\n *\n * @exception {DeveloperError} fovY must be in (0, PI].\n * @exception {DeveloperError} aspectRatio must be greater than zero.\n * @exception {DeveloperError} near must be greater than zero.\n * @exception {DeveloperError} far must be greater than zero.\n */\nMatrix4.computePerspectiveFieldOfView = function (\n  fovY,\n  aspectRatio,\n  near,\n  far,\n  result\n) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.number.greaterThan(\"fovY\", fovY, 0.0);\n  Check.typeOf.number.lessThan(\"fovY\", fovY, Math.PI);\n  Check.typeOf.number.greaterThan(\"near\", near, 0.0);\n  Check.typeOf.number.greaterThan(\"far\", far, 0.0);\n  Check.typeOf.object(\"result\", result);\n  //>>includeEnd('debug');\n\n  const bottom = Math.tan(fovY * 0.5);\n\n  const column1Row1 = 1.0 / bottom;\n  const column0Row0 = column1Row1 / aspectRatio;\n  const column2Row2 = (far + near) / (near - far);\n  const column3Row2 = (2.0 * far * near) / (near - far);\n\n  result[0] = column0Row0;\n  result[1] = 0.0;\n  result[2] = 0.0;\n  result[3] = 0.0;\n  result[4] = 0.0;\n  result[5] = column1Row1;\n  result[6] = 0.0;\n  result[7] = 0.0;\n  result[8] = 0.0;\n  result[9] = 0.0;\n  result[10] = column2Row2;\n  result[11] = -1.0;\n  result[12] = 0.0;\n  result[13] = 0.0;\n  result[14] = column3Row2;\n  result[15] = 0.0;\n  return result;\n};\n\n/**\n * Computes a Matrix4 instance representing an orthographic transformation matrix.\n *\n * @param {Number} left The number of meters to the left of the camera that will be in view.\n * @param {Number} right The number of meters to the right of the camera that will be in view.\n * @param {Number} bottom The number of meters below of the camera that will be in view.\n * @param {Number} top The number of meters above of the camera that will be in view.\n * @param {Number} near The distance to the near plane in meters.\n * @param {Number} far The distance to the far plane in meters.\n * @param {Matrix4} result The object in which the result will be stored.\n * @returns {Matrix4} The modified result parameter.\n */\nMatrix4.computeOrthographicOffCenter = function (\n  left,\n  right,\n  bottom,\n  top,\n  near,\n  far,\n  result\n) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.number(\"left\", left);\n  Check.typeOf.number(\"right\", right);\n  Check.typeOf.number(\"bottom\", bottom);\n  Check.typeOf.number(\"top\", top);\n  Check.typeOf.number(\"near\", near);\n  Check.typeOf.number(\"far\", far);\n  Check.typeOf.object(\"result\", result);\n  //>>includeEnd('debug');\n\n  let a = 1.0 / (right - left);\n  let b = 1.0 / (top - bottom);\n  let c = 1.0 / (far - near);\n\n  const tx = -(right + left) * a;\n  const ty = -(top + bottom) * b;\n  const tz = -(far + near) * c;\n  a *= 2.0;\n  b *= 2.0;\n  c *= -2.0;\n\n  result[0] = a;\n  result[1] = 0.0;\n  result[2] = 0.0;\n  result[3] = 0.0;\n  result[4] = 0.0;\n  result[5] = b;\n  result[6] = 0.0;\n  result[7] = 0.0;\n  result[8] = 0.0;\n  result[9] = 0.0;\n  result[10] = c;\n  result[11] = 0.0;\n  result[12] = tx;\n  result[13] = ty;\n  result[14] = tz;\n  result[15] = 1.0;\n  return result;\n};\n\n/**\n * Computes a Matrix4 instance representing an off center perspective transformation.\n *\n * @param {Number} left The number of meters to the left of the camera that will be in view.\n * @param {Number} right The number of meters to the right of the camera that will be in view.\n * @param {Number} bottom The number of meters below of the camera that will be in view.\n * @param {Number} top The number of meters above of the camera that will be in view.\n * @param {Number} near The distance to the near plane in meters.\n * @param {Number} far The distance to the far plane in meters.\n * @param {Matrix4} result The object in which the result will be stored.\n * @returns {Matrix4} The modified result parameter.\n */\nMatrix4.computePerspectiveOffCenter = function (\n  left,\n  right,\n  bottom,\n  top,\n  near,\n  far,\n  result\n) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.number(\"left\", left);\n  Check.typeOf.number(\"right\", right);\n  Check.typeOf.number(\"bottom\", bottom);\n  Check.typeOf.number(\"top\", top);\n  Check.typeOf.number(\"near\", near);\n  Check.typeOf.number(\"far\", far);\n  Check.typeOf.object(\"result\", result);\n  //>>includeEnd('debug');\n\n  const column0Row0 = (2.0 * near) / (right - left);\n  const column1Row1 = (2.0 * near) / (top - bottom);\n  const column2Row0 = (right + left) / (right - left);\n  const column2Row1 = (top + bottom) / (top - bottom);\n  const column2Row2 = -(far + near) / (far - near);\n  const column2Row3 = -1.0;\n  const column3Row2 = (-2.0 * far * near) / (far - near);\n\n  result[0] = column0Row0;\n  result[1] = 0.0;\n  result[2] = 0.0;\n  result[3] = 0.0;\n  result[4] = 0.0;\n  result[5] = column1Row1;\n  result[6] = 0.0;\n  result[7] = 0.0;\n  result[8] = column2Row0;\n  result[9] = column2Row1;\n  result[10] = column2Row2;\n  result[11] = column2Row3;\n  result[12] = 0.0;\n  result[13] = 0.0;\n  result[14] = column3Row2;\n  result[15] = 0.0;\n  return result;\n};\n\n/**\n * Computes a Matrix4 instance representing an infinite off center perspective transformation.\n *\n * @param {Number} left The number of meters to the left of the camera that will be in view.\n * @param {Number} right The number of meters to the right of the camera that will be in view.\n * @param {Number} bottom The number of meters below of the camera that will be in view.\n * @param {Number} top The number of meters above of the camera that will be in view.\n * @param {Number} near The distance to the near plane in meters.\n * @param {Matrix4} result The object in which the result will be stored.\n * @returns {Matrix4} The modified result parameter.\n */\nMatrix4.computeInfinitePerspectiveOffCenter = function (\n  left,\n  right,\n  bottom,\n  top,\n  near,\n  result\n) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.number(\"left\", left);\n  Check.typeOf.number(\"right\", right);\n  Check.typeOf.number(\"bottom\", bottom);\n  Check.typeOf.number(\"top\", top);\n  Check.typeOf.number(\"near\", near);\n  Check.typeOf.object(\"result\", result);\n  //>>includeEnd('debug');\n\n  const column0Row0 = (2.0 * near) / (right - left);\n  const column1Row1 = (2.0 * near) / (top - bottom);\n  const column2Row0 = (right + left) / (right - left);\n  const column2Row1 = (top + bottom) / (top - bottom);\n  const column2Row2 = -1.0;\n  const column2Row3 = -1.0;\n  const column3Row2 = -2.0 * near;\n\n  result[0] = column0Row0;\n  result[1] = 0.0;\n  result[2] = 0.0;\n  result[3] = 0.0;\n  result[4] = 0.0;\n  result[5] = column1Row1;\n  result[6] = 0.0;\n  result[7] = 0.0;\n  result[8] = column2Row0;\n  result[9] = column2Row1;\n  result[10] = column2Row2;\n  result[11] = column2Row3;\n  result[12] = 0.0;\n  result[13] = 0.0;\n  result[14] = column3Row2;\n  result[15] = 0.0;\n  return result;\n};\n\n/**\n * Computes a Matrix4 instance that transforms from normalized device coordinates to window coordinates.\n *\n * @param {Object} [viewport = { x : 0.0, y : 0.0, width : 0.0, height : 0.0 }] The viewport's corners as shown in Example 1.\n * @param {Number} [nearDepthRange=0.0] The near plane distance in window coordinates.\n * @param {Number} [farDepthRange=1.0] The far plane distance in window coordinates.\n * @param {Matrix4} [result] The object in which the result will be stored.\n * @returns {Matrix4} The modified result parameter.\n *\n * @example\n * // Create viewport transformation using an explicit viewport and depth range.\n * const m = Cesium.Matrix4.computeViewportTransformation({\n *     x : 0.0,\n *     y : 0.0,\n *     width : 1024.0,\n *     height : 768.0\n * }, 0.0, 1.0, new Cesium.Matrix4());\n */\nMatrix4.computeViewportTransformation = function (\n  viewport,\n  nearDepthRange,\n  farDepthRange,\n  result\n) {\n  if (!defined(result)) {\n    result = new Matrix4();\n  }\n\n  viewport = defaultValue(viewport, defaultValue.EMPTY_OBJECT);\n  const x = defaultValue(viewport.x, 0.0);\n  const y = defaultValue(viewport.y, 0.0);\n  const width = defaultValue(viewport.width, 0.0);\n  const height = defaultValue(viewport.height, 0.0);\n  nearDepthRange = defaultValue(nearDepthRange, 0.0);\n  farDepthRange = defaultValue(farDepthRange, 1.0);\n\n  const halfWidth = width * 0.5;\n  const halfHeight = height * 0.5;\n  const halfDepth = (farDepthRange - nearDepthRange) * 0.5;\n\n  const column0Row0 = halfWidth;\n  const column1Row1 = halfHeight;\n  const column2Row2 = halfDepth;\n  const column3Row0 = x + halfWidth;\n  const column3Row1 = y + halfHeight;\n  const column3Row2 = nearDepthRange + halfDepth;\n  const column3Row3 = 1.0;\n\n  result[0] = column0Row0;\n  result[1] = 0.0;\n  result[2] = 0.0;\n  result[3] = 0.0;\n  result[4] = 0.0;\n  result[5] = column1Row1;\n  result[6] = 0.0;\n  result[7] = 0.0;\n  result[8] = 0.0;\n  result[9] = 0.0;\n  result[10] = column2Row2;\n  result[11] = 0.0;\n  result[12] = column3Row0;\n  result[13] = column3Row1;\n  result[14] = column3Row2;\n  result[15] = column3Row3;\n\n  return result;\n};\n\n/**\n * Computes a Matrix4 instance that transforms from world space to view space.\n *\n * @param {Cartesian3} position The position of the camera.\n * @param {Cartesian3} direction The forward direction.\n * @param {Cartesian3} up The up direction.\n * @param {Cartesian3} right The right direction.\n * @param {Matrix4} result The object in which the result will be stored.\n * @returns {Matrix4} The modified result parameter.\n */\nMatrix4.computeView = function (position, direction, up, right, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.object(\"position\", position);\n  Check.typeOf.object(\"direction\", direction);\n  Check.typeOf.object(\"up\", up);\n  Check.typeOf.object(\"right\", right);\n  Check.typeOf.object(\"result\", result);\n  //>>includeEnd('debug');\n\n  result[0] = right.x;\n  result[1] = up.x;\n  result[2] = -direction.x;\n  result[3] = 0.0;\n  result[4] = right.y;\n  result[5] = up.y;\n  result[6] = -direction.y;\n  result[7] = 0.0;\n  result[8] = right.z;\n  result[9] = up.z;\n  result[10] = -direction.z;\n  result[11] = 0.0;\n  result[12] = -Cartesian3.dot(right, position);\n  result[13] = -Cartesian3.dot(up, position);\n  result[14] = Cartesian3.dot(direction, position);\n  result[15] = 1.0;\n  return result;\n};\n\n/**\n * Computes an Array from the provided Matrix4 instance.\n * The array will be in column-major order.\n *\n * @param {Matrix4} matrix The matrix to use..\n * @param {Number[]} [result] The Array onto which to store the result.\n * @returns {Number[]} The modified Array parameter or a new Array instance if one was not provided.\n *\n * @example\n * //create an array from an instance of Matrix4\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 * const a = Cesium.Matrix4.toArray(m);\n *\n * // m remains the same\n * //creates a = [10.0, 11.0, 12.0, 13.0, 14.0, 15.0, 16.0, 17.0, 18.0, 19.0, 20.0, 21.0, 22.0, 23.0, 24.0, 25.0]\n */\nMatrix4.toArray = function (matrix, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.object(\"matrix\", matrix);\n  //>>includeEnd('debug');\n\n  if (!defined(result)) {\n    return [\n      matrix[0],\n      matrix[1],\n      matrix[2],\n      matrix[3],\n      matrix[4],\n      matrix[5],\n      matrix[6],\n      matrix[7],\n      matrix[8],\n      matrix[9],\n      matrix[10],\n      matrix[11],\n      matrix[12],\n      matrix[13],\n      matrix[14],\n      matrix[15],\n    ];\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 array index of the element at the provided row and column.\n *\n * @param {Number} row The zero-based index of the row.\n * @param {Number} column The zero-based index of the column.\n * @returns {Number} The index of the element at the provided row and column.\n *\n * @exception {DeveloperError} row must be 0, 1, 2, or 3.\n * @exception {DeveloperError} column must be 0, 1, 2, or 3.\n *\n * @example\n * const myMatrix = new Cesium.Matrix4();\n * const column1Row0Index = Cesium.Matrix4.getElementIndex(1, 0);\n * const column1Row0 = myMatrix[column1Row0Index];\n * myMatrix[column1Row0Index] = 10.0;\n */\nMatrix4.getElementIndex = function (column, row) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.number.greaterThanOrEquals(\"row\", row, 0);\n  Check.typeOf.number.lessThanOrEquals(\"row\", row, 3);\n\n  Check.typeOf.number.greaterThanOrEquals(\"column\", column, 0);\n  Check.typeOf.number.lessThanOrEquals(\"column\", column, 3);\n  //>>includeEnd('debug');\n\n  return column * 4 + row;\n};\n\n/**\n * Retrieves a copy of the matrix column at the provided index as a Cartesian4 instance.\n *\n * @param {Matrix4} matrix The matrix to use.\n * @param {Number} index The zero-based index of the column to retrieve.\n * @param {Cartesian4} result The object onto which to store the result.\n * @returns {Cartesian4} The modified result parameter.\n *\n * @exception {DeveloperError} index must be 0, 1, 2, or 3.\n *\n * @example\n * //returns a Cartesian4 instance with values from the specified column\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 * //Example 1: Creates an instance of Cartesian\n * const a = Cesium.Matrix4.getColumn(m, 2, new Cesium.Cartesian4());\n *\n * @example\n * //Example 2: Sets values for Cartesian instance\n * const a = new Cesium.Cartesian4();\n * Cesium.Matrix4.getColumn(m, 2, a);\n *\n * // a.x = 12.0; a.y = 16.0; a.z = 20.0; a.w = 24.0;\n */\nMatrix4.getColumn = function (matrix, index, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.object(\"matrix\", matrix);\n\n  Check.typeOf.number.greaterThanOrEquals(\"index\", index, 0);\n  Check.typeOf.number.lessThanOrEquals(\"index\", index, 3);\n\n  Check.typeOf.object(\"result\", result);\n  //>>includeEnd('debug');\n\n  const startIndex = index * 4;\n  const x = matrix[startIndex];\n  const y = matrix[startIndex + 1];\n  const z = matrix[startIndex + 2];\n  const w = matrix[startIndex + 3];\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 a new matrix that replaces the specified column in the provided matrix with the provided Cartesian4 instance.\n *\n * @param {Matrix4} matrix The matrix to use.\n * @param {Number} index The zero-based index of the column to set.\n * @param {Cartesian4} cartesian The Cartesian whose values will be assigned to the specified column.\n * @param {Matrix4} result The object onto which to store the result.\n * @returns {Matrix4} The modified result parameter.\n *\n * @exception {DeveloperError} index must be 0, 1, 2, or 3.\n *\n * @example\n * //creates a new Matrix4 instance with new column values from the Cartesian4 instance\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.setColumn(m, 2, new Cesium.Cartesian4(99.0, 98.0, 97.0, 96.0), new Cesium.Matrix4());\n *\n * // m remains the same\n * // a = [10.0, 11.0, 99.0, 13.0]\n * //     [14.0, 15.0, 98.0, 17.0]\n * //     [18.0, 19.0, 97.0, 21.0]\n * //     [22.0, 23.0, 96.0, 25.0]\n */\nMatrix4.setColumn = function (matrix, index, cartesian, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.object(\"matrix\", matrix);\n\n  Check.typeOf.number.greaterThanOrEquals(\"index\", index, 0);\n  Check.typeOf.number.lessThanOrEquals(\"index\", index, 3);\n\n  Check.typeOf.object(\"cartesian\", cartesian);\n  Check.typeOf.object(\"result\", result);\n  //>>includeEnd('debug');\n\n  result = Matrix4.clone(matrix, result);\n  const startIndex = index * 4;\n  result[startIndex] = cartesian.x;\n  result[startIndex + 1] = cartesian.y;\n  result[startIndex + 2] = cartesian.z;\n  result[startIndex + 3] = cartesian.w;\n  return result;\n};\n\n/**\n * Retrieves a copy of the matrix row at the provided index as a Cartesian4 instance.\n *\n * @param {Matrix4} matrix The matrix to use.\n * @param {Number} index The zero-based index of the row to retrieve.\n * @param {Cartesian4} result The object onto which to store the result.\n * @returns {Cartesian4} The modified result parameter.\n *\n * @exception {DeveloperError} index must be 0, 1, 2, or 3.\n *\n * @example\n * //returns a Cartesian4 instance with values from the specified column\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 * //Example 1: Returns an instance of Cartesian\n * const a = Cesium.Matrix4.getRow(m, 2, new Cesium.Cartesian4());\n *\n * @example\n * //Example 2: Sets values for a Cartesian instance\n * const a = new Cesium.Cartesian4();\n * Cesium.Matrix4.getRow(m, 2, a);\n *\n * // a.x = 18.0; a.y = 19.0; a.z = 20.0; a.w = 21.0;\n */\nMatrix4.getRow = function (matrix, index, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.object(\"matrix\", matrix);\n\n  Check.typeOf.number.greaterThanOrEquals(\"index\", index, 0);\n  Check.typeOf.number.lessThanOrEquals(\"index\", index, 3);\n\n  Check.typeOf.object(\"result\", result);\n  //>>includeEnd('debug');\n\n  const x = matrix[index];\n  const y = matrix[index + 4];\n  const z = matrix[index + 8];\n  const w = matrix[index + 12];\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 a new matrix that replaces the specified row in the provided matrix with the provided Cartesian4 instance.\n *\n * @param {Matrix4} matrix The matrix to use.\n * @param {Number} index The zero-based index of the row to set.\n * @param {Cartesian4} cartesian The Cartesian whose values will be assigned to the specified row.\n * @param {Matrix4} result The object onto which to store the result.\n * @returns {Matrix4} The modified result parameter.\n *\n * @exception {DeveloperError} index must be 0, 1, 2, or 3.\n *\n * @example\n * //create a new Matrix4 instance with new row values from the Cartesian4 instance\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.setRow(m, 2, new Cesium.Cartesian4(99.0, 98.0, 97.0, 96.0), 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 * //     [99.0, 98.0, 97.0, 96.0]\n * //     [22.0, 23.0, 24.0, 25.0]\n */\nMatrix4.setRow = function (matrix, index, cartesian, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.object(\"matrix\", matrix);\n\n  Check.typeOf.number.greaterThanOrEquals(\"index\", index, 0);\n  Check.typeOf.number.lessThanOrEquals(\"index\", index, 3);\n\n  Check.typeOf.object(\"cartesian\", cartesian);\n  Check.typeOf.object(\"result\", result);\n  //>>includeEnd('debug');\n\n  result = Matrix4.clone(matrix, result);\n  result[index] = cartesian.x;\n  result[index + 4] = cartesian.y;\n  result[index + 8] = cartesian.z;\n  result[index + 12] = cartesian.w;\n  return result;\n};\n\n/**\n * Computes a new matrix that replaces the translation in the rightmost column of the provided\n * matrix with the provided translation. This assumes the matrix is an affine transformation.\n *\n * @param {Matrix4} matrix The matrix to use.\n * @param {Cartesian3} translation The translation that replaces the translation of the provided matrix.\n * @param {Matrix4} result The object onto which to store the result.\n * @returns {Matrix4} The modified result parameter.\n */\nMatrix4.setTranslation = 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  result[0] = matrix[0];\n  result[1] = matrix[1];\n  result[2] = matrix[2];\n  result[3] = matrix[3];\n\n  result[4] = matrix[4];\n  result[5] = matrix[5];\n  result[6] = matrix[6];\n  result[7] = matrix[7];\n\n  result[8] = matrix[8];\n  result[9] = matrix[9];\n  result[10] = matrix[10];\n  result[11] = matrix[11];\n\n  result[12] = translation.x;\n  result[13] = translation.y;\n  result[14] = translation.z;\n  result[15] = matrix[15];\n\n  return result;\n};\n\nconst scaleScratch1 = new Cartesian3();\n\n/**\n * Computes a new matrix that replaces the scale with the provided scale.\n * This assumes the matrix is an affine transformation.\n *\n * @param {Matrix4} matrix The matrix to use.\n * @param {Cartesian3} scale The scale that replaces the scale of the provided matrix.\n * @param {Matrix4} result The object onto which to store the result.\n * @returns {Matrix4} The modified result parameter.\n *\n * @see Matrix4.setUniformScale\n * @see Matrix4.fromScale\n * @see Matrix4.fromUniformScale\n * @see Matrix4.multiplyByScale\n * @see Matrix4.multiplyByUniformScale\n * @see Matrix4.getScale\n */\nMatrix4.setScale = 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 existingScale = Matrix4.getScale(matrix, scaleScratch1);\n  const scaleRatioX = scale.x / existingScale.x;\n  const scaleRatioY = scale.y / existingScale.y;\n  const scaleRatioZ = scale.z / existingScale.y;\n\n  result[0] = matrix[0] * scaleRatioX;\n  result[1] = matrix[1] * scaleRatioX;\n  result[2] = matrix[2] * scaleRatioX;\n  result[3] = matrix[3];\n\n  result[4] = matrix[4] * scaleRatioY;\n  result[5] = matrix[5] * scaleRatioY;\n  result[6] = matrix[6] * scaleRatioY;\n  result[7] = matrix[7];\n\n  result[8] = matrix[8] * scaleRatioZ;\n  result[9] = matrix[9] * scaleRatioZ;\n  result[10] = matrix[10] * scaleRatioZ;\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\nconst scaleScratch2 = new Cartesian3();\n\n/**\n * Computes a new matrix that replaces the scale with the provided uniform scale.\n * This assumes the matrix is an affine transformation.\n *\n * @param {Matrix4} matrix The matrix to use.\n * @param {Number} scale The uniform scale that replaces the scale of the provided matrix.\n * @param {Matrix4} result The object onto which to store the result.\n * @returns {Matrix4} The modified result parameter.\n *\n * @see Matrix4.setScale\n * @see Matrix4.fromScale\n * @see Matrix4.fromUniformScale\n * @see Matrix4.multiplyByScale\n * @see Matrix4.multiplyByUniformScale\n * @see Matrix4.getScale\n */\nMatrix4.setUniformScale = 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  const existingScale = Matrix4.getScale(matrix, scaleScratch2);\n  const scaleRatioX = scale / existingScale.x;\n  const scaleRatioY = scale / existingScale.y;\n  const scaleRatioZ = scale / existingScale.z;\n\n  result[0] = matrix[0] * scaleRatioX;\n  result[1] = matrix[1] * scaleRatioX;\n  result[2] = matrix[2] * scaleRatioX;\n  result[3] = matrix[3];\n\n  result[4] = matrix[4] * scaleRatioY;\n  result[5] = matrix[5] * scaleRatioY;\n  result[6] = matrix[6] * scaleRatioY;\n  result[7] = matrix[7];\n\n  result[8] = matrix[8] * scaleRatioZ;\n  result[9] = matrix[9] * scaleRatioZ;\n  result[10] = matrix[10] * scaleRatioZ;\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\nconst scratchColumn = new Cartesian3();\n\n/**\n * Extracts the non-uniform scale assuming the matrix is an affine transformation.\n *\n * @param {Matrix4} matrix The matrix.\n * @param {Cartesian3} result The object onto which to store the result.\n * @returns {Cartesian3} The modified result parameter\n *\n * @see Matrix4.multiplyByScale\n * @see Matrix4.multiplyByUniformScale\n * @see Matrix4.fromScale\n * @see Matrix4.fromUniformScale\n * @see Matrix4.setScale\n * @see Matrix4.setUniformScale\n */\nMatrix4.getScale = 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 = Cartesian3.magnitude(\n    Cartesian3.fromElements(matrix[0], matrix[1], matrix[2], scratchColumn)\n  );\n  result.y = Cartesian3.magnitude(\n    Cartesian3.fromElements(matrix[4], matrix[5], matrix[6], scratchColumn)\n  );\n  result.z = Cartesian3.magnitude(\n    Cartesian3.fromElements(matrix[8], matrix[9], matrix[10], scratchColumn)\n  );\n  return result;\n};\n\nconst scaleScratch3 = new Cartesian3();\n\n/**\n * Computes the maximum scale assuming the matrix is an affine transformation.\n * The maximum scale is the maximum length of the column vectors in the upper-left\n * 3x3 matrix.\n *\n * @param {Matrix4} matrix The matrix.\n * @returns {Number} The maximum scale.\n */\nMatrix4.getMaximumScale = function (matrix) {\n  Matrix4.getScale(matrix, scaleScratch3);\n  return Cartesian3.maximumComponent(scaleScratch3);\n};\n\nconst scaleScratch4 = new Cartesian3();\n\n/**\n * Sets the rotation assuming the matrix is an affine transformation.\n *\n * @param {Matrix4} matrix The matrix.\n * @param {Matrix4} rotation The rotation matrix.\n * @returns {Matrix4} The modified result parameter.\n *\n * @see Matrix4.fromRotation\n * @see Matrix4.getRotation\n */\nMatrix4.setRotation = function (matrix, rotation, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.object(\"matrix\", matrix);\n  Check.typeOf.object(\"result\", result);\n  //>>includeEnd('debug');\n\n  const scale = Matrix4.getScale(matrix, scaleScratch4);\n\n  result[0] = rotation[0] * scale.x;\n  result[1] = rotation[1] * scale.x;\n  result[2] = rotation[2] * scale.x;\n  result[3] = matrix[3];\n\n  result[4] = rotation[3] * scale.y;\n  result[5] = rotation[4] * scale.y;\n  result[6] = rotation[5] * scale.y;\n  result[7] = matrix[7];\n\n  result[8] = rotation[6] * scale.z;\n  result[9] = rotation[7] * scale.z;\n  result[10] = rotation[8] * scale.z;\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\nconst scaleScratch5 = new Cartesian3();\n\n/**\n * Extracts the rotation matrix assuming the matrix is an affine transformation.\n *\n * @param {Matrix4} matrix The matrix.\n * @param {Matrix4} result The object onto which to store the result.\n * @returns {Matrix4} The modified result parameter.\n *\n * @see Matrix4.setRotation\n * @see Matrix4.fromRotation\n */\nMatrix4.getRotation = 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 scale = Matrix4.getScale(matrix, scaleScratch5);\n\n  result[0] = matrix[0] / scale.x;\n  result[1] = matrix[1] / scale.x;\n  result[2] = matrix[2] / scale.x;\n\n  result[3] = matrix[4] / scale.y;\n  result[4] = matrix[5] / scale.y;\n  result[5] = matrix[6] / scale.y;\n\n  result[6] = matrix[8] / scale.z;\n  result[7] = matrix[9] / scale.z;\n  result[8] = matrix[10] / scale.z;\n\n  return result;\n};\n\n/**\n * Computes the product of two matrices.\n *\n * @param {Matrix4} left The first matrix.\n * @param {Matrix4} right The second matrix.\n * @param {Matrix4} result The object onto which to store the result.\n * @returns {Matrix4} The modified result parameter.\n */\nMatrix4.multiply = 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 left0 = left[0];\n  const left1 = left[1];\n  const left2 = left[2];\n  const left3 = left[3];\n  const left4 = left[4];\n  const left5 = left[5];\n  const left6 = left[6];\n  const left7 = left[7];\n  const left8 = left[8];\n  const left9 = left[9];\n  const left10 = left[10];\n  const left11 = left[11];\n  const left12 = left[12];\n  const left13 = left[13];\n  const left14 = left[14];\n  const left15 = left[15];\n\n  const right0 = right[0];\n  const right1 = right[1];\n  const right2 = right[2];\n  const right3 = right[3];\n  const right4 = right[4];\n  const right5 = right[5];\n  const right6 = right[6];\n  const right7 = right[7];\n  const right8 = right[8];\n  const right9 = right[9];\n  const right10 = right[10];\n  const right11 = right[11];\n  const right12 = right[12];\n  const right13 = right[13];\n  const right14 = right[14];\n  const right15 = right[15];\n\n  const column0Row0 =\n    left0 * right0 + left4 * right1 + left8 * right2 + left12 * right3;\n  const column0Row1 =\n    left1 * right0 + left5 * right1 + left9 * right2 + left13 * right3;\n  const column0Row2 =\n    left2 * right0 + left6 * right1 + left10 * right2 + left14 * right3;\n  const column0Row3 =\n    left3 * right0 + left7 * right1 + left11 * right2 + left15 * right3;\n\n  const column1Row0 =\n    left0 * right4 + left4 * right5 + left8 * right6 + left12 * right7;\n  const column1Row1 =\n    left1 * right4 + left5 * right5 + left9 * right6 + left13 * right7;\n  const column1Row2 =\n    left2 * right4 + left6 * right5 + left10 * right6 + left14 * right7;\n  const column1Row3 =\n    left3 * right4 + left7 * right5 + left11 * right6 + left15 * right7;\n\n  const column2Row0 =\n    left0 * right8 + left4 * right9 + left8 * right10 + left12 * right11;\n  const column2Row1 =\n    left1 * right8 + left5 * right9 + left9 * right10 + left13 * right11;\n  const column2Row2 =\n    left2 * right8 + left6 * right9 + left10 * right10 + left14 * right11;\n  const column2Row3 =\n    left3 * right8 + left7 * right9 + left11 * right10 + left15 * right11;\n\n  const column3Row0 =\n    left0 * right12 + left4 * right13 + left8 * right14 + left12 * right15;\n  const column3Row1 =\n    left1 * right12 + left5 * right13 + left9 * right14 + left13 * right15;\n  const column3Row2 =\n    left2 * right12 + left6 * right13 + left10 * right14 + left14 * right15;\n  const column3Row3 =\n    left3 * right12 + left7 * right13 + left11 * right14 + left15 * right15;\n\n  result[0] = column0Row0;\n  result[1] = column0Row1;\n  result[2] = column0Row2;\n  result[3] = column0Row3;\n  result[4] = column1Row0;\n  result[5] = column1Row1;\n  result[6] = column1Row2;\n  result[7] = column1Row3;\n  result[8] = column2Row0;\n  result[9] = column2Row1;\n  result[10] = column2Row2;\n  result[11] = column2Row3;\n  result[12] = column3Row0;\n  result[13] = column3Row1;\n  result[14] = column3Row2;\n  result[15] = column3Row3;\n  return result;\n};\n\n/**\n * Computes the sum of two matrices.\n *\n * @param {Matrix4} left The first matrix.\n * @param {Matrix4} right The second matrix.\n * @param {Matrix4} result The object onto which to store the result.\n * @returns {Matrix4} The modified result parameter.\n */\nMatrix4.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[0] = left[0] + right[0];\n  result[1] = left[1] + right[1];\n  result[2] = left[2] + right[2];\n  result[3] = left[3] + right[3];\n  result[4] = left[4] + right[4];\n  result[5] = left[5] + right[5];\n  result[6] = left[6] + right[6];\n  result[7] = left[7] + right[7];\n  result[8] = left[8] + right[8];\n  result[9] = left[9] + right[9];\n  result[10] = left[10] + right[10];\n  result[11] = left[11] + right[11];\n  result[12] = left[12] + right[12];\n  result[13] = left[13] + right[13];\n  result[14] = left[14] + right[14];\n  result[15] = left[15] + right[15];\n  return result;\n};\n\n/**\n * Computes the difference of two matrices.\n *\n * @param {Matrix4} left The first matrix.\n * @param {Matrix4} right The second matrix.\n * @param {Matrix4} result The object onto which to store the result.\n * @returns {Matrix4} The modified result parameter.\n */\nMatrix4.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[0] = left[0] - right[0];\n  result[1] = left[1] - right[1];\n  result[2] = left[2] - right[2];\n  result[3] = left[3] - right[3];\n  result[4] = left[4] - right[4];\n  result[5] = left[5] - right[5];\n  result[6] = left[6] - right[6];\n  result[7] = left[7] - right[7];\n  result[8] = left[8] - right[8];\n  result[9] = left[9] - right[9];\n  result[10] = left[10] - right[10];\n  result[11] = left[11] - right[11];\n  result[12] = left[12] - right[12];\n  result[13] = left[13] - right[13];\n  result[14] = left[14] - right[14];\n  result[15] = left[15] - right[15];\n  return result;\n};\n\n/**\n * Computes the product of two matrices assuming the matrices are affine transformation matrices,\n * where the upper left 3x3 elements are any matrix, and\n * 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 product for general 4x4\n * matrices using {@link Matrix4.multiply}.\n *\n * @param {Matrix4} left The first matrix.\n * @param {Matrix4} right The second matrix.\n * @param {Matrix4} result The object onto which to store the result.\n * @returns {Matrix4} The modified result parameter.\n *\n * @example\n * const m1 = new Cesium.Matrix4(1.0, 6.0, 7.0, 0.0, 2.0, 5.0, 8.0, 0.0, 3.0, 4.0, 9.0, 0.0, 0.0, 0.0, 0.0, 1.0);\n * const m2 = Cesium.Transforms.eastNorthUpToFixedFrame(new Cesium.Cartesian3(1.0, 1.0, 1.0));\n * const m3 = Cesium.Matrix4.multiplyTransformation(m1, m2, new Cesium.Matrix4());\n */\nMatrix4.multiplyTransformation = 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 left0 = left[0];\n  const left1 = left[1];\n  const left2 = left[2];\n  const left4 = left[4];\n  const left5 = left[5];\n  const left6 = left[6];\n  const left8 = left[8];\n  const left9 = left[9];\n  const left10 = left[10];\n  const left12 = left[12];\n  const left13 = left[13];\n  const left14 = left[14];\n\n  const right0 = right[0];\n  const right1 = right[1];\n  const right2 = right[2];\n  const right4 = right[4];\n  const right5 = right[5];\n  const right6 = right[6];\n  const right8 = right[8];\n  const right9 = right[9];\n  const right10 = right[10];\n  const right12 = right[12];\n  const right13 = right[13];\n  const right14 = right[14];\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  const column3Row0 =\n    left0 * right12 + left4 * right13 + left8 * right14 + left12;\n  const column3Row1 =\n    left1 * right12 + left5 * right13 + left9 * right14 + left13;\n  const column3Row2 =\n    left2 * right12 + left6 * right13 + left10 * right14 + left14;\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] = column3Row0;\n  result[13] = column3Row1;\n  result[14] = column3Row2;\n  result[15] = 1.0;\n  return result;\n};\n\n/**\n * Multiplies a transformation matrix (with a bottom row of <code>[0.0, 0.0, 0.0, 1.0]</code>)\n * by a 3x3 rotation matrix.  This is an optimization\n * for <code>Matrix4.multiply(m, Matrix4.fromRotationTranslation(rotation), m);</code> 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 <code>[0.0, 0.0, 0.0, 1.0]</code>)\n * by an implicit translation matrix defined by a {@link Cartesian3}.  This is an optimization\n * for <code>Matrix4.multiply(m, Matrix4.fromTranslation(position), m);</code> 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 <code>[0.0, 0.0, 0.0, 1.0]</code>)\n * by an implicit non-uniform scale matrix. This is an optimization\n * for <code>Matrix4.multiply(m, Matrix4.fromUniformScale(scale), m);</code>, where\n * <code>m</code> 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 <code>w</code> 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 <code>w</code> 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 * <code>true</code> if they are equal, <code>false</code> otherwise.\n *\n * @param {Matrix4} [left] The first matrix.\n * @param {Matrix4} [right] The second matrix.\n * @returns {Boolean} <code>true</code> if left and right are equal, <code>false</code> 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 * <code>true</code> if they are within the provided epsilon,\n * <code>false</code> 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} <code>true</code> if left and right are within the provided epsilon, <code>false</code> 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 * <code>true</code> if they are equal, <code>false</code> otherwise.\n *\n * @param {Matrix4} [right] The right hand side matrix.\n * @returns {Boolean} <code>true</code> if they are equal, <code>false</code> 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 * <code>true</code> if they are within the provided epsilon,\n * <code>false</code> 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} <code>true</code> if they are within the provided epsilon, <code>false</code> 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 * <code>true</code> if they pass an absolute or relative tolerance test,\n * <code>false</code> 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} <code>true</code> if left and right are within the provided epsilon, <code>false</code> 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 * <code>true</code> if they are equal, <code>false</code> otherwise.\n *\n * @param {Rectangle} [other] The Rectangle to compare.\n * @returns {Boolean} <code>true</code> if the Rectangles are equal, <code>false</code> otherwise.\n */\nRectangle.prototype.equals = function (other) {\n  return Rectangle.equals(this, other);\n};\n\n/**\n * Compares the provided rectangles and returns <code>true</code> if they are equal,\n * <code>false</code> otherwise.\n *\n * @param {Rectangle} [left] The first Rectangle.\n * @param {Rectangle} [right] The second Rectangle.\n * @returns {Boolean} <code>true</code> if left and right are equal; otherwise <code>false</code>.\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 * <code>true</code> if they are within the provided epsilon,\n * <code>false</code> 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} <code>true</code> if the Rectangles are within the provided epsilon, <code>false</code> 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} <code>north</code> must be in the interval [<code>-Pi/2</code>, <code>Pi/2</code>].\n * @exception {DeveloperError} <code>south</code> must be in the interval [<code>-Pi/2</code>, <code>Pi/2</code>].\n * @exception {DeveloperError} <code>east</code> must be in the interval [<code>-Pi</code>, <code>Pi</code>].\n * @exception {DeveloperError} <code>west</code> must be in the interval [<code>-Pi</code>, <code>Pi</code>].\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 * <code>true</code> if they are equal, <code>false</code> otherwise.\n *\n * @param {Cartesian2} [left] The first Cartesian.\n * @param {Cartesian2} [right] The second Cartesian.\n * @returns {Boolean} <code>true</code> if left and right are equal, <code>false</code> 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 * <code>true</code> if they pass an absolute or relative tolerance test,\n * <code>false</code> 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} <code>true</code> if left and right are within the provided epsilon, <code>false</code> 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 * <code>true</code> if they are equal, <code>false</code> otherwise.\n *\n * @param {Cartesian2} [right] The right hand side Cartesian.\n * @returns {Boolean} <code>true</code> if they are equal, <code>false</code> 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 * <code>true</code> if they pass an absolute or relative tolerance test,\n * <code>false</code> 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} <code>true</code> if they are within the provided epsilon, <code>false</code> 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 {ArrayLike<number>}\n *\n * @param {Number} [column0Row0=0.0] The value for column 0, row 0.\n * @param {Number} [column1Row0=0.0] The value for column 1, row 0.\n * @param {Number} [column0Row1=0.0] The value for column 0, row 1.\n * @param {Number} [column1Row1=0.0] The value for column 1, row 1.\n *\n * @see Matrix2.fromArray\n * @see Matrix2.fromColumnMajorArray\n * @see Matrix2.fromRowMajorArray\n * @see Matrix2.fromScale\n * @see Matrix2.fromUniformScale\n * @see Matrix2.fromRotation\n * @see Matrix3\n * @see Matrix4\n */\nfunction Matrix2(column0Row0, column1Row0, column0Row1, column1Row1) {\n  this[0] = defaultValue(column0Row0, 0.0);\n  this[1] = defaultValue(column0Row1, 0.0);\n  this[2] = defaultValue(column1Row0, 0.0);\n  this[3] = defaultValue(column1Row1, 0.0);\n}\n\n/**\n * The number of elements used to pack the object into an array.\n * @type {Number}\n */\nMatrix2.packedLength = 4;\n\n/**\n * Stores the provided instance into the provided array.\n *\n * @param {Matrix2} 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 */\nMatrix2.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[0];\n  array[startingIndex++] = value[1];\n  array[startingIndex++] = value[2];\n  array[startingIndex++] = value[3];\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 {Matrix2} [result] The object into which to store the result.\n * @returns {Matrix2} The modified result parameter or a new Matrix2 instance if one was not provided.\n */\nMatrix2.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 Matrix2();\n  }\n\n  result[0] = array[startingIndex++];\n  result[1] = array[startingIndex++];\n  result[2] = array[startingIndex++];\n  result[3] = array[startingIndex++];\n  return result;\n};\n\n/**\n * Flattens an array of Matrix2s into an array of components. The components\n * are stored in column-major order.\n *\n * @param {Matrix2[]} array The array of matrices 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 */\nMatrix2.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    Matrix2.pack(array[i], result, i * 4);\n  }\n  return result;\n};\n\n/**\n * Unpacks an array of column-major matrix components into an array of Matrix2s.\n *\n * @param {Number[]} array The array of components to unpack.\n * @param {Matrix2[]} [result] The array onto which to store the result.\n * @returns {Matrix2[]} The unpacked array.\n */\nMatrix2.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] = Matrix2.unpack(array, i, result[index]);\n  }\n  return result;\n};\n\n/**\n * Duplicates a Matrix2 instance.\n *\n * @param {Matrix2} matrix The matrix to duplicate.\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. (Returns undefined if matrix is undefined)\n */\nMatrix2.clone = function (matrix, result) {\n  if (!defined(matrix)) {\n    return undefined;\n  }\n  if (!defined(result)) {\n    return new Matrix2(matrix[0], matrix[2], matrix[1], matrix[3]);\n  }\n  result[0] = matrix[0];\n  result[1] = matrix[1];\n  result[2] = matrix[2];\n  result[3] = matrix[3];\n  return result;\n};\n\n/**\n * Creates a Matrix2 from 4 consecutive elements in an array.\n *\n * @param {Number[]} array The array whose 4 consecutive elements correspond to the positions of the matrix.  Assumes column-major order.\n * @param {Number} [startingIndex=0] The offset into the array of the first element, which corresponds to first column first row position in the matrix.\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 *\n * @example\n * // Create the Matrix2:\n * // [1.0, 2.0]\n * // [1.0, 2.0]\n *\n * const v = [1.0, 1.0, 2.0, 2.0];\n * const m = Cesium.Matrix2.fromArray(v);\n *\n * // Create same Matrix2 with using an offset into an array\n * const v2 = [0.0, 0.0, 1.0, 1.0, 2.0, 2.0];\n * const m2 = Cesium.Matrix2.fromArray(v2, 2);\n */\nMatrix2.fromArray = Matrix2.unpack;\n/**\n * Creates a Matrix2 instance from a column-major order array.\n *\n * @param {Number[]} values The column-major order array.\n * @param {Matrix2} [result] The object in which the result will be stored, if undefined a new instance will be created.\n * @returns {Matrix2} The modified result parameter, or a new Matrix2 instance if one was not provided.\n */\nMatrix2.fromColumnMajorArray = function (values, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.defined(\"values\", values);\n  //>>includeEnd('debug');\n\n  return Matrix2.clone(values, result);\n};\n\n/**\n * Creates a Matrix2 instance from a row-major order array.\n * The resulting matrix will be in column-major order.\n *\n * @param {Number[]} values The row-major order array.\n * @param {Matrix2} [result] The object in which the result will be stored, if undefined a new instance will be created.\n * @returns {Matrix2} The modified result parameter, or a new Matrix2 instance if one was not provided.\n */\nMatrix2.fromRowMajorArray = function (values, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.defined(\"values\", values);\n  //>>includeEnd('debug');\n\n  if (!defined(result)) {\n    return new Matrix2(values[0], values[1], values[2], values[3]);\n  }\n  result[0] = values[0];\n  result[1] = values[2];\n  result[2] = values[1];\n  result[3] = values[3];\n  return result;\n};\n\n/**\n * Computes a Matrix2 instance representing a non-uniform scale.\n *\n * @param {Cartesian2} scale The x and y scale factors.\n * @param {Matrix2} [result] The object in which the result will be stored, if undefined a new instance will be created.\n * @returns {Matrix2} The modified result parameter, or a new Matrix2 instance if one was not provided.\n *\n * @example\n * // Creates\n * //   [7.0, 0.0]\n * //   [0.0, 8.0]\n * const m = Cesium.Matrix2.fromScale(new Cesium.Cartesian2(7.0, 8.0));\n */\nMatrix2.fromScale = function (scale, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.object(\"scale\", scale);\n  //>>includeEnd('debug');\n\n  if (!defined(result)) {\n    return new Matrix2(scale.x, 0.0, 0.0, scale.y);\n  }\n\n  result[0] = scale.x;\n  result[1] = 0.0;\n  result[2] = 0.0;\n  result[3] = scale.y;\n  return result;\n};\n\n/**\n * Computes a Matrix2 instance representing a uniform scale.\n *\n * @param {Number} scale The uniform scale factor.\n * @param {Matrix2} [result] The object in which the result will be stored, if undefined a new instance will be created.\n * @returns {Matrix2} The modified result parameter, or a new Matrix2 instance if one was not provided.\n *\n * @example\n * // Creates\n * //   [2.0, 0.0]\n * //   [0.0, 2.0]\n * const m = Cesium.Matrix2.fromUniformScale(2.0);\n */\nMatrix2.fromUniformScale = function (scale, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.number(\"scale\", scale);\n  //>>includeEnd('debug');\n\n  if (!defined(result)) {\n    return new Matrix2(scale, 0.0, 0.0, scale);\n  }\n\n  result[0] = scale;\n  result[1] = 0.0;\n  result[2] = 0.0;\n  result[3] = scale;\n  return result;\n};\n\n/**\n * Creates a rotation matrix.\n *\n * @param {Number} angle The angle, in radians, of the rotation.  Positive angles are counterclockwise.\n * @param {Matrix2} [result] The object in which the result will be stored, if undefined a new instance will be created.\n * @returns {Matrix2} The modified result parameter, or a new Matrix2 instance if one was not provided.\n *\n * @example\n * // Rotate a point 45 degrees counterclockwise.\n * const p = new Cesium.Cartesian2(5, 6);\n * const m = Cesium.Matrix2.fromRotation(Cesium.Math.toRadians(45.0));\n * const rotated = Cesium.Matrix2.multiplyByVector(m, p, new Cesium.Cartesian2());\n */\nMatrix2.fromRotation = function (angle, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.number(\"angle\", angle);\n  //>>includeEnd('debug');\n\n  const cosAngle = Math.cos(angle);\n  const sinAngle = Math.sin(angle);\n\n  if (!defined(result)) {\n    return new Matrix2(cosAngle, -sinAngle, sinAngle, cosAngle);\n  }\n  result[0] = cosAngle;\n  result[1] = sinAngle;\n  result[2] = -sinAngle;\n  result[3] = cosAngle;\n  return result;\n};\n\n/**\n * Creates an Array from the provided Matrix2 instance.\n * The array will be in column-major order.\n *\n * @param {Matrix2} matrix The matrix to use..\n * @param {Number[]} [result] The Array onto which to store the result.\n * @returns {Number[]} The modified Array parameter or a new Array instance if one was not provided.\n */\nMatrix2.toArray = function (matrix, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.object(\"matrix\", matrix);\n  //>>includeEnd('debug');\n\n  if (!defined(result)) {\n    return [matrix[0], matrix[1], matrix[2], matrix[3]];\n  }\n  result[0] = matrix[0];\n  result[1] = matrix[1];\n  result[2] = matrix[2];\n  result[3] = matrix[3];\n  return result;\n};\n\n/**\n * Computes the array index of the element at the provided row and column.\n *\n * @param {Number} row The zero-based index of the row.\n * @param {Number} column The zero-based index of the column.\n * @returns {Number} The index of the element at the provided row and column.\n *\n * @exception {DeveloperError} row must be 0 or 1.\n * @exception {DeveloperError} column must be 0 or 1.\n *\n * @example\n * const myMatrix = new Cesium.Matrix2();\n * const column1Row0Index = Cesium.Matrix2.getElementIndex(1, 0);\n * const column1Row0 = myMatrix[column1Row0Index]\n * myMatrix[column1Row0Index] = 10.0;\n */\nMatrix2.getElementIndex = function (column, row) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.number.greaterThanOrEquals(\"row\", row, 0);\n  Check.typeOf.number.lessThanOrEquals(\"row\", row, 1);\n\n  Check.typeOf.number.greaterThanOrEquals(\"column\", column, 0);\n  Check.typeOf.number.lessThanOrEquals(\"column\", column, 1);\n  //>>includeEnd('debug');\n\n  return column * 2 + row;\n};\n\n/**\n * Retrieves a copy of the matrix column at the provided index as a Cartesian2 instance.\n *\n * @param {Matrix2} matrix The matrix to use.\n * @param {Number} index The zero-based index of the column to retrieve.\n * @param {Cartesian2} result The object onto which to store the result.\n * @returns {Cartesian2} The modified result parameter.\n *\n * @exception {DeveloperError} index must be 0 or 1.\n */\nMatrix2.getColumn = function (matrix, index, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.object(\"matrix\", matrix);\n\n  Check.typeOf.number.greaterThanOrEquals(\"index\", index, 0);\n  Check.typeOf.number.lessThanOrEquals(\"index\", index, 1);\n\n  Check.typeOf.object(\"result\", result);\n  //>>includeEnd('debug');\n\n  const startIndex = index * 2;\n  const x = matrix[startIndex];\n  const y = matrix[startIndex + 1];\n\n  result.x = x;\n  result.y = y;\n  return result;\n};\n\n/**\n * Computes a new matrix that replaces the specified column in the provided matrix with the provided Cartesian2 instance.\n *\n * @param {Matrix2} matrix The matrix to use.\n * @param {Number} index The zero-based index of the column to set.\n * @param {Cartesian2} cartesian The Cartesian whose values will be assigned to the specified column.\n * @param {Cartesian2} result The object onto which to store the result.\n * @returns {Matrix2} The modified result parameter.\n *\n * @exception {DeveloperError} index must be 0 or 1.\n */\nMatrix2.setColumn = function (matrix, index, cartesian, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.object(\"matrix\", matrix);\n\n  Check.typeOf.number.greaterThanOrEquals(\"index\", index, 0);\n  Check.typeOf.number.lessThanOrEquals(\"index\", index, 1);\n\n  Check.typeOf.object(\"cartesian\", cartesian);\n  Check.typeOf.object(\"result\", result);\n  //>>includeEnd('debug');\n\n  result = Matrix2.clone(matrix, result);\n  const startIndex = index * 2;\n  result[startIndex] = cartesian.x;\n  result[startIndex + 1] = cartesian.y;\n  return result;\n};\n\n/**\n * Retrieves a copy of the matrix row at the provided index as a Cartesian2 instance.\n *\n * @param {Matrix2} matrix The matrix to use.\n * @param {Number} index The zero-based index of the row to retrieve.\n * @param {Cartesian2} result The object onto which to store the result.\n * @returns {Cartesian2} The modified result parameter.\n *\n * @exception {DeveloperError} index must be 0 or 1.\n */\nMatrix2.getRow = function (matrix, index, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.object(\"matrix\", matrix);\n\n  Check.typeOf.number.greaterThanOrEquals(\"index\", index, 0);\n  Check.typeOf.number.lessThanOrEquals(\"index\", index, 1);\n\n  Check.typeOf.object(\"result\", result);\n  //>>includeEnd('debug');\n\n  const x = matrix[index];\n  const y = matrix[index + 2];\n\n  result.x = x;\n  result.y = y;\n  return result;\n};\n\n/**\n * Computes a new matrix that replaces the specified row in the provided matrix with the provided Cartesian2 instance.\n *\n * @param {Matrix2} matrix The matrix to use.\n * @param {Number} index The zero-based index of the row to set.\n * @param {Cartesian2} cartesian The Cartesian whose values will be assigned to the specified row.\n * @param {Matrix2} result The object onto which to store the result.\n * @returns {Matrix2} The modified result parameter.\n *\n * @exception {DeveloperError} index must be 0 or 1.\n */\nMatrix2.setRow = function (matrix, index, cartesian, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.object(\"matrix\", matrix);\n\n  Check.typeOf.number.greaterThanOrEquals(\"index\", index, 0);\n  Check.typeOf.number.lessThanOrEquals(\"index\", index, 1);\n\n  Check.typeOf.object(\"cartesian\", cartesian);\n  Check.typeOf.object(\"result\", result);\n  //>>includeEnd('debug');\n\n  result = Matrix2.clone(matrix, result);\n  result[index] = cartesian.x;\n  result[index + 2] = cartesian.y;\n  return result;\n};\n\nconst scaleScratch1 = new Cartesian2();\n\n/**\n * Computes a new matrix that replaces the scale with the provided scale.\n * This assumes the matrix is an affine transformation.\n *\n * @param {Matrix2} matrix The matrix to use.\n * @param {Cartesian2} scale The scale that replaces the scale of the provided matrix.\n * @param {Matrix2} result The object onto which to store the result.\n * @returns {Matrix2} The modified result parameter.\n *\n * @see Matrix2.setUniformScale\n * @see Matrix2.fromScale\n * @see Matrix2.fromUniformScale\n * @see Matrix2.multiplyByScale\n * @see Matrix2.multiplyByUniformScale\n * @see Matrix2.getScale\n */\nMatrix2.setScale = 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 existingScale = Matrix2.getScale(matrix, scaleScratch1);\n  const scaleRatioX = scale.x / existingScale.x;\n  const scaleRatioY = scale.y / existingScale.y;\n\n  result[0] = matrix[0] * scaleRatioX;\n  result[1] = matrix[1] * scaleRatioX;\n  result[2] = matrix[2] * scaleRatioY;\n  result[3] = matrix[3] * scaleRatioY;\n\n  return result;\n};\n\nconst scaleScratch2 = new Cartesian2();\n\n/**\n * Computes a new matrix that replaces the scale with the provided uniform scale.\n * This assumes the matrix is an affine transformation.\n *\n * @param {Matrix2} matrix The matrix to use.\n * @param {Number} scale The uniform scale that replaces the scale of the provided matrix.\n * @param {Matrix2} result The object onto which to store the result.\n * @returns {Matrix2} The modified result parameter.\n *\n * @see Matrix2.setScale\n * @see Matrix2.fromScale\n * @see Matrix2.fromUniformScale\n * @see Matrix2.multiplyByScale\n * @see Matrix2.multiplyByUniformScale\n * @see Matrix2.getScale\n */\nMatrix2.setUniformScale = 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  const existingScale = Matrix2.getScale(matrix, scaleScratch2);\n  const scaleRatioX = scale / existingScale.x;\n  const scaleRatioY = scale / existingScale.y;\n\n  result[0] = matrix[0] * scaleRatioX;\n  result[1] = matrix[1] * scaleRatioX;\n  result[2] = matrix[2] * scaleRatioY;\n  result[3] = matrix[3] * scaleRatioY;\n\n  return result;\n};\n\nconst scratchColumn = new Cartesian2();\n\n/**\n * Extracts the non-uniform scale assuming the matrix is an affine transformation.\n *\n * @param {Matrix2} matrix The matrix.\n * @param {Cartesian2} result The object onto which to store the result.\n * @returns {Cartesian2} The modified result parameter.\n *\n * @see Matrix2.multiplyByScale\n * @see Matrix2.multiplyByUniformScale\n * @see Matrix2.fromScale\n * @see Matrix2.fromUniformScale\n * @see Matrix2.setScale\n * @see Matrix2.setUniformScale\n */\nMatrix2.getScale = 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 = Cartesian2.magnitude(\n    Cartesian2.fromElements(matrix[0], matrix[1], scratchColumn)\n  );\n  result.y = Cartesian2.magnitude(\n    Cartesian2.fromElements(matrix[2], matrix[3], scratchColumn)\n  );\n  return result;\n};\n\nconst scaleScratch3 = new Cartesian2();\n\n/**\n * Computes the maximum scale assuming the matrix is an affine transformation.\n * The maximum scale is the maximum length of the column vectors.\n *\n * @param {Matrix2} matrix The matrix.\n * @returns {Number} The maximum scale.\n */\nMatrix2.getMaximumScale = function (matrix) {\n  Matrix2.getScale(matrix, scaleScratch3);\n  return Cartesian2.maximumComponent(scaleScratch3);\n};\n\nconst scaleScratch4 = new Cartesian2();\n\n/**\n * Sets the rotation assuming the matrix is an affine transformation.\n *\n * @param {Matrix2} matrix The matrix.\n * @param {Matrix2} rotation The rotation matrix.\n * @returns {Matrix2} The modified result parameter.\n *\n * @see Matrix2.fromRotation\n * @see Matrix2.getRotation\n */\nMatrix2.setRotation = function (matrix, rotation, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.object(\"matrix\", matrix);\n  Check.typeOf.object(\"result\", result);\n  //>>includeEnd('debug');\n\n  const scale = Matrix2.getScale(matrix, scaleScratch4);\n\n  result[0] = rotation[0] * scale.x;\n  result[1] = rotation[1] * scale.x;\n  result[2] = rotation[2] * scale.y;\n  result[3] = rotation[3] * scale.y;\n\n  return result;\n};\n\nconst scaleScratch5 = new Cartesian2();\n\n/**\n * Extracts the rotation matrix assuming the matrix is an affine transformation.\n *\n * @param {Matrix2} matrix The matrix.\n * @param {Matrix2} result The object onto which to store the result.\n * @returns {Matrix2} The modified result parameter.\n *\n * @see Matrix2.setRotation\n * @see Matrix2.fromRotation\n */\nMatrix2.getRotation = 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 scale = Matrix2.getScale(matrix, scaleScratch5);\n\n  result[0] = matrix[0] / scale.x;\n  result[1] = matrix[1] / scale.x;\n  result[2] = matrix[2] / scale.y;\n  result[3] = matrix[3] / scale.y;\n\n  return result;\n};\n\n/**\n * Computes the product of two matrices.\n *\n * @param {Matrix2} left The first matrix.\n * @param {Matrix2} right The second matrix.\n * @param {Matrix2} result The object onto which to store the result.\n * @returns {Matrix2} The modified result parameter.\n */\nMatrix2.multiply = 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 column0Row0 = left[0] * right[0] + left[2] * right[1];\n  const column1Row0 = left[0] * right[2] + left[2] * right[3];\n  const column0Row1 = left[1] * right[0] + left[3] * right[1];\n  const column1Row1 = left[1] * right[2] + left[3] * right[3];\n\n  result[0] = column0Row0;\n  result[1] = column0Row1;\n  result[2] = column1Row0;\n  result[3] = column1Row1;\n  return result;\n};\n\n/**\n * Computes the sum of two matrices.\n *\n * @param {Matrix2} left The first matrix.\n * @param {Matrix2} right The second matrix.\n * @param {Matrix2} result The object onto which to store the result.\n * @returns {Matrix2} The modified result parameter.\n */\nMatrix2.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[0] = left[0] + right[0];\n  result[1] = left[1] + right[1];\n  result[2] = left[2] + right[2];\n  result[3] = left[3] + right[3];\n  return result;\n};\n\n/**\n * Computes the difference of two matrices.\n *\n * @param {Matrix2} left The first matrix.\n * @param {Matrix2} right The second matrix.\n * @param {Matrix2} result The object onto which to store the result.\n * @returns {Matrix2} The modified result parameter.\n */\nMatrix2.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[0] = left[0] - right[0];\n  result[1] = left[1] - right[1];\n  result[2] = left[2] - right[2];\n  result[3] = left[3] - right[3];\n  return result;\n};\n\n/**\n * Computes the product of a matrix and a column vector.\n *\n * @param {Matrix2} matrix The matrix.\n * @param {Cartesian2} cartesian The column.\n * @param {Cartesian2} result The object onto which to store the result.\n * @returns {Cartesian2} The modified result parameter.\n */\nMatrix2.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 x = matrix[0] * cartesian.x + matrix[2] * cartesian.y;\n  const y = matrix[1] * cartesian.x + matrix[3] * cartesian.y;\n\n  result.x = x;\n  result.y = y;\n  return result;\n};\n\n/**\n * Computes the product of a matrix and a scalar.\n *\n * @param {Matrix2} matrix The matrix.\n * @param {Number} scalar The number to multiply by.\n * @param {Matrix2} result The object onto which to store the result.\n * @returns {Matrix2} The modified result parameter.\n */\nMatrix2.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  return result;\n};\n\n/**\n * Computes the product of a matrix times a (non-uniform) scale, as if the scale were a scale matrix.\n *\n * @param {Matrix2} matrix The matrix on the left-hand side.\n * @param {Number} scale The non-uniform scale on the right-hand side.\n * @param {Matrix2} result The object onto which to store the result.\n * @returns {Matrix2} The modified result parameter.\n *\n *\n * @example\n * // Instead of Cesium.Matrix2.multiply(m, Cesium.Matrix2.fromScale(scale), m);\n * Cesium.Matrix2.multiplyByScale(m, scale, m);\n *\n * @see Matrix2.multiplyByUniformScale\n * @see Matrix2.fromScale\n * @see Matrix2.fromUniformScale\n * @see Matrix2.setScale\n * @see Matrix2.setUniformScale\n * @see Matrix2.getScale\n */\nMatrix2.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  result[0] = matrix[0] * scale.x;\n  result[1] = matrix[1] * scale.x;\n  result[2] = matrix[2] * scale.y;\n  result[3] = matrix[3] * scale.y;\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 {Matrix2} matrix The matrix on the left-hand side.\n * @param {Number} scale The uniform scale on the right-hand side.\n * @param {Matrix2} result The object onto which to store the result.\n * @returns {Matrix2} The modified result parameter.\n *\n * @example\n * // Instead of Cesium.Matrix2.multiply(m, Cesium.Matrix2.fromUniformScale(scale), m);\n * Cesium.Matrix2.multiplyByUniformScale(m, scale, m);\n *\n * @see Matrix2.multiplyByScale\n * @see Matrix2.fromScale\n * @see Matrix2.fromUniformScale\n * @see Matrix2.setScale\n * @see Matrix2.setUniformScale\n * @see Matrix2.getScale\n */\nMatrix2.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] * scale;\n\n  return result;\n};\n\n/**\n * Creates a negated copy of the provided matrix.\n *\n * @param {Matrix2} matrix The matrix to negate.\n * @param {Matrix2} result The object onto which to store the result.\n * @returns {Matrix2} The modified result parameter.\n */\nMatrix2.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  return result;\n};\n\n/**\n * Computes the transpose of the provided matrix.\n *\n * @param {Matrix2} matrix The matrix to transpose.\n * @param {Matrix2} result The object onto which to store the result.\n * @returns {Matrix2} The modified result parameter.\n */\nMatrix2.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 column0Row0 = matrix[0];\n  const column0Row1 = matrix[2];\n  const column1Row0 = matrix[1];\n  const column1Row1 = matrix[3];\n\n  result[0] = column0Row0;\n  result[1] = column0Row1;\n  result[2] = column1Row0;\n  result[3] = column1Row1;\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 {Matrix2} matrix The matrix with signed elements.\n * @param {Matrix2} result The object onto which to store the result.\n * @returns {Matrix2} The modified result parameter.\n */\nMatrix2.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\n  return result;\n};\n\n/**\n * Compares the provided matrices componentwise and returns\n * <code>true</code> if they are equal, <code>false</code> otherwise.\n *\n * @param {Matrix2} [left] The first matrix.\n * @param {Matrix2} [right] The second matrix.\n * @returns {Boolean} <code>true</code> if left and right are equal, <code>false</code> 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 * <code>true</code> if they are within the provided epsilon,\n * <code>false</code> 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} <code>true</code> if left and right are within the provided epsilon, <code>false</code> 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 * <code>true</code> if they are equal, <code>false</code> otherwise.\n *\n * @param {Matrix2} [right] The right hand side matrix.\n * @returns {Boolean} <code>true</code> if they are equal, <code>false</code> 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 * <code>true</code> if they are within the provided epsilon,\n * <code>false</code> 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} <code>true</code> if they are within the provided epsilon, <code>false</code> 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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