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4308 lines
142 KiB
4308 lines
142 KiB
/**
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* @license
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* Cesium - https://github.com/CesiumGS/cesium
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* Version 1.99
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*
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* Copyright 2011-2022 Cesium Contributors
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*
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* Columbus View (Pat. Pend.)
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*
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* Portions licensed separately.
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* See https://github.com/CesiumGS/cesium/blob/main/LICENSE.md for full licensing details.
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*/
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define(['exports', './Check-40d84a28', './defaultValue-135942ca', './Math-efde0c7b'], (function (exports, Check, defaultValue, Math$1) { 'use strict';
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/**
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* A 3D Cartesian point.
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* @alias Cartesian3
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* @constructor
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*
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* @param {Number} [x=0.0] The X component.
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* @param {Number} [y=0.0] The Y component.
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* @param {Number} [z=0.0] The Z component.
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*
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* @see Cartesian2
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* @see Cartesian4
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* @see Packable
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*/
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function Cartesian3(x, y, z) {
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/**
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* The X component.
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* @type {Number}
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* @default 0.0
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*/
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this.x = defaultValue.defaultValue(x, 0.0);
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/**
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* The Y component.
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* @type {Number}
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* @default 0.0
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*/
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this.y = defaultValue.defaultValue(y, 0.0);
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/**
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* The Z component.
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* @type {Number}
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* @default 0.0
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*/
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this.z = defaultValue.defaultValue(z, 0.0);
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}
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/**
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* Converts the provided Spherical into Cartesian3 coordinates.
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*
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* @param {Spherical} spherical The Spherical to be converted to Cartesian3.
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* @param {Cartesian3} [result] The object onto which to store the result.
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* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if one was not provided.
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*/
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Cartesian3.fromSpherical = function (spherical, result) {
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//>>includeStart('debug', pragmas.debug);
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Check.Check.typeOf.object("spherical", spherical);
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//>>includeEnd('debug');
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if (!defaultValue.defined(result)) {
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result = new Cartesian3();
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}
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const clock = spherical.clock;
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const cone = spherical.cone;
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const magnitude = defaultValue.defaultValue(spherical.magnitude, 1.0);
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const radial = magnitude * Math.sin(cone);
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result.x = radial * Math.cos(clock);
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result.y = radial * Math.sin(clock);
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result.z = magnitude * Math.cos(cone);
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return result;
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};
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/**
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* Creates a Cartesian3 instance from x, y and z coordinates.
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*
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* @param {Number} x The x coordinate.
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* @param {Number} y The y coordinate.
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* @param {Number} z The z coordinate.
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* @param {Cartesian3} [result] The object onto which to store the result.
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* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if one was not provided.
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*/
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Cartesian3.fromElements = function (x, y, z, result) {
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if (!defaultValue.defined(result)) {
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return new Cartesian3(x, y, z);
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}
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result.x = x;
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result.y = y;
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result.z = z;
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return result;
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};
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/**
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* Duplicates a Cartesian3 instance.
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*
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* @param {Cartesian3} cartesian The Cartesian to duplicate.
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* @param {Cartesian3} [result] The object onto which to store the result.
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* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if one was not provided. (Returns undefined if cartesian is undefined)
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*/
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Cartesian3.clone = function (cartesian, result) {
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if (!defaultValue.defined(cartesian)) {
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return undefined;
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}
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if (!defaultValue.defined(result)) {
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return new Cartesian3(cartesian.x, cartesian.y, cartesian.z);
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}
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result.x = cartesian.x;
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result.y = cartesian.y;
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result.z = cartesian.z;
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return result;
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};
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/**
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* Creates a Cartesian3 instance from an existing Cartesian4. This simply takes the
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* x, y, and z properties of the Cartesian4 and drops w.
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* @function
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*
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* @param {Cartesian4} cartesian The Cartesian4 instance to create a Cartesian3 instance from.
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* @param {Cartesian3} [result] The object onto which to store the result.
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* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if one was not provided.
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*/
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Cartesian3.fromCartesian4 = Cartesian3.clone;
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/**
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* The number of elements used to pack the object into an array.
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* @type {Number}
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*/
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Cartesian3.packedLength = 3;
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/**
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* Stores the provided instance into the provided array.
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*
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* @param {Cartesian3} value The value to pack.
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* @param {Number[]} array The array to pack into.
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* @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
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*
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* @returns {Number[]} The array that was packed into
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*/
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Cartesian3.pack = function (value, array, startingIndex) {
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//>>includeStart('debug', pragmas.debug);
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Check.Check.typeOf.object("value", value);
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Check.Check.defined("array", array);
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//>>includeEnd('debug');
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startingIndex = defaultValue.defaultValue(startingIndex, 0);
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array[startingIndex++] = value.x;
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array[startingIndex++] = value.y;
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array[startingIndex] = value.z;
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return array;
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};
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/**
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* Retrieves an instance from a packed array.
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*
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* @param {Number[]} array The packed array.
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* @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
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* @param {Cartesian3} [result] The object into which to store the result.
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* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if one was not provided.
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*/
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Cartesian3.unpack = function (array, startingIndex, result) {
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//>>includeStart('debug', pragmas.debug);
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Check.Check.defined("array", array);
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//>>includeEnd('debug');
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startingIndex = defaultValue.defaultValue(startingIndex, 0);
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if (!defaultValue.defined(result)) {
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result = new Cartesian3();
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}
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result.x = array[startingIndex++];
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result.y = array[startingIndex++];
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result.z = array[startingIndex];
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return result;
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};
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/**
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* Flattens an array of Cartesian3s into an array of components.
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*
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* @param {Cartesian3[]} array The array of cartesians to pack.
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* @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.
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* @returns {Number[]} The packed array.
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*/
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Cartesian3.packArray = function (array, result) {
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//>>includeStart('debug', pragmas.debug);
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Check.Check.defined("array", array);
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//>>includeEnd('debug');
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const length = array.length;
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const resultLength = length * 3;
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if (!defaultValue.defined(result)) {
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result = new Array(resultLength);
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} else if (!Array.isArray(result) && result.length !== resultLength) {
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//>>includeStart('debug', pragmas.debug);
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throw new Check.DeveloperError(
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"If result is a typed array, it must have exactly array.length * 3 elements"
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);
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//>>includeEnd('debug');
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} else if (result.length !== resultLength) {
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result.length = resultLength;
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}
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for (let i = 0; i < length; ++i) {
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Cartesian3.pack(array[i], result, i * 3);
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}
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return result;
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};
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/**
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* Unpacks an array of cartesian components into an array of Cartesian3s.
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*
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* @param {Number[]} array The array of components to unpack.
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* @param {Cartesian3[]} [result] The array onto which to store the result.
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* @returns {Cartesian3[]} The unpacked array.
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*/
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Cartesian3.unpackArray = function (array, result) {
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//>>includeStart('debug', pragmas.debug);
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Check.Check.defined("array", array);
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Check.Check.typeOf.number.greaterThanOrEquals("array.length", array.length, 3);
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if (array.length % 3 !== 0) {
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throw new Check.DeveloperError("array length must be a multiple of 3.");
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}
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//>>includeEnd('debug');
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const length = array.length;
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if (!defaultValue.defined(result)) {
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result = new Array(length / 3);
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} else {
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result.length = length / 3;
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}
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for (let i = 0; i < length; i += 3) {
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const index = i / 3;
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result[index] = Cartesian3.unpack(array, i, result[index]);
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}
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return result;
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};
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/**
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* Creates a Cartesian3 from three consecutive elements in an array.
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* @function
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*
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* @param {Number[]} array The array whose three consecutive elements correspond to the x, y, and z components, respectively.
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* @param {Number} [startingIndex=0] The offset into the array of the first element, which corresponds to the x component.
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* @param {Cartesian3} [result] The object onto which to store the result.
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* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if one was not provided.
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*
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* @example
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* // Create a Cartesian3 with (1.0, 2.0, 3.0)
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* const v = [1.0, 2.0, 3.0];
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* const p = Cesium.Cartesian3.fromArray(v);
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*
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* // Create a Cartesian3 with (1.0, 2.0, 3.0) using an offset into an array
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* const v2 = [0.0, 0.0, 1.0, 2.0, 3.0];
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* const p2 = Cesium.Cartesian3.fromArray(v2, 2);
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*/
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Cartesian3.fromArray = Cartesian3.unpack;
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/**
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* Computes the value of the maximum component for the supplied Cartesian.
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*
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* @param {Cartesian3} cartesian The cartesian to use.
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* @returns {Number} The value of the maximum component.
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*/
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Cartesian3.maximumComponent = function (cartesian) {
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//>>includeStart('debug', pragmas.debug);
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Check.Check.typeOf.object("cartesian", cartesian);
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//>>includeEnd('debug');
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return Math.max(cartesian.x, cartesian.y, cartesian.z);
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};
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/**
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* Computes the value of the minimum component for the supplied Cartesian.
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*
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* @param {Cartesian3} cartesian The cartesian to use.
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* @returns {Number} The value of the minimum component.
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*/
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Cartesian3.minimumComponent = function (cartesian) {
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//>>includeStart('debug', pragmas.debug);
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Check.Check.typeOf.object("cartesian", cartesian);
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//>>includeEnd('debug');
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return Math.min(cartesian.x, cartesian.y, cartesian.z);
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};
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/**
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* Compares two Cartesians and computes a Cartesian which contains the minimum components of the supplied Cartesians.
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*
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* @param {Cartesian3} first A cartesian to compare.
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* @param {Cartesian3} second A cartesian to compare.
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* @param {Cartesian3} result The object into which to store the result.
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* @returns {Cartesian3} A cartesian with the minimum components.
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*/
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Cartesian3.minimumByComponent = function (first, second, result) {
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//>>includeStart('debug', pragmas.debug);
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Check.Check.typeOf.object("first", first);
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Check.Check.typeOf.object("second", second);
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Check.Check.typeOf.object("result", result);
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//>>includeEnd('debug');
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result.x = Math.min(first.x, second.x);
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result.y = Math.min(first.y, second.y);
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result.z = Math.min(first.z, second.z);
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return result;
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};
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/**
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* Compares two Cartesians and computes a Cartesian which contains the maximum components of the supplied Cartesians.
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*
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* @param {Cartesian3} first A cartesian to compare.
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* @param {Cartesian3} second A cartesian to compare.
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* @param {Cartesian3} result The object into which to store the result.
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* @returns {Cartesian3} A cartesian with the maximum components.
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*/
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Cartesian3.maximumByComponent = function (first, second, result) {
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//>>includeStart('debug', pragmas.debug);
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Check.Check.typeOf.object("first", first);
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Check.Check.typeOf.object("second", second);
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Check.Check.typeOf.object("result", result);
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//>>includeEnd('debug');
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result.x = Math.max(first.x, second.x);
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result.y = Math.max(first.y, second.y);
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result.z = Math.max(first.z, second.z);
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return result;
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};
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/**
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* Constrain a value to lie between two values.
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*
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* @param {Cartesian3} cartesian The value to clamp.
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* @param {Cartesian3} min The minimum bound.
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* @param {Cartesian3} max The maximum bound.
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* @param {Cartesian3} result The object into which to store the result.
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* @returns {Cartesian3} The clamped value such that min <= value <= max.
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*/
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Cartesian3.clamp = function (value, min, max, result) {
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//>>includeStart('debug', pragmas.debug);
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Check.Check.typeOf.object("value", value);
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Check.Check.typeOf.object("min", min);
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Check.Check.typeOf.object("max", max);
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Check.Check.typeOf.object("result", result);
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//>>includeEnd('debug');
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const x = Math$1.CesiumMath.clamp(value.x, min.x, max.x);
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const y = Math$1.CesiumMath.clamp(value.y, min.y, max.y);
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const z = Math$1.CesiumMath.clamp(value.z, min.z, max.z);
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result.x = x;
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result.y = y;
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result.z = z;
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return result;
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};
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/**
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* Computes the provided Cartesian's squared magnitude.
|
|
*
|
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* @param {Cartesian3} cartesian The Cartesian instance whose squared magnitude is to be computed.
|
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* @returns {Number} The squared magnitude.
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*/
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Cartesian3.magnitudeSquared = function (cartesian) {
|
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//>>includeStart('debug', pragmas.debug);
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Check.Check.typeOf.object("cartesian", cartesian);
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//>>includeEnd('debug');
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|
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return (
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cartesian.x * cartesian.x +
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cartesian.y * cartesian.y +
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cartesian.z * cartesian.z
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);
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};
|
|
|
|
/**
|
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* Computes the Cartesian's magnitude (length).
|
|
*
|
|
* @param {Cartesian3} cartesian The Cartesian instance whose magnitude is to be computed.
|
|
* @returns {Number} The magnitude.
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|
*/
|
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Cartesian3.magnitude = function (cartesian) {
|
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return Math.sqrt(Cartesian3.magnitudeSquared(cartesian));
|
|
};
|
|
|
|
const distanceScratch = new Cartesian3();
|
|
|
|
/**
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|
* Computes the distance between two points.
|
|
*
|
|
* @param {Cartesian3} left The first point to compute the distance from.
|
|
* @param {Cartesian3} right The second point to compute the distance to.
|
|
* @returns {Number} The distance between two points.
|
|
*
|
|
* @example
|
|
* // Returns 1.0
|
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* const d = Cesium.Cartesian3.distance(new Cesium.Cartesian3(1.0, 0.0, 0.0), new Cesium.Cartesian3(2.0, 0.0, 0.0));
|
|
*/
|
|
Cartesian3.distance = function (left, right) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("left", left);
|
|
Check.Check.typeOf.object("right", right);
|
|
//>>includeEnd('debug');
|
|
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|
Cartesian3.subtract(left, right, distanceScratch);
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|
return Cartesian3.magnitude(distanceScratch);
|
|
};
|
|
|
|
/**
|
|
* Computes the squared distance between two points. Comparing squared distances
|
|
* using this function is more efficient than comparing distances using {@link Cartesian3#distance}.
|
|
*
|
|
* @param {Cartesian3} left The first point to compute the distance from.
|
|
* @param {Cartesian3} right The second point to compute the distance to.
|
|
* @returns {Number} The distance between two points.
|
|
*
|
|
* @example
|
|
* // Returns 4.0, not 2.0
|
|
* const d = Cesium.Cartesian3.distanceSquared(new Cesium.Cartesian3(1.0, 0.0, 0.0), new Cesium.Cartesian3(3.0, 0.0, 0.0));
|
|
*/
|
|
Cartesian3.distanceSquared = function (left, right) {
|
|
//>>includeStart('debug', pragmas.debug);
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|
Check.Check.typeOf.object("left", left);
|
|
Check.Check.typeOf.object("right", right);
|
|
//>>includeEnd('debug');
|
|
|
|
Cartesian3.subtract(left, right, distanceScratch);
|
|
return Cartesian3.magnitudeSquared(distanceScratch);
|
|
};
|
|
|
|
/**
|
|
* Computes the normalized form of the supplied Cartesian.
|
|
*
|
|
* @param {Cartesian3} cartesian The Cartesian to be normalized.
|
|
* @param {Cartesian3} result The object onto which to store the result.
|
|
* @returns {Cartesian3} The modified result parameter.
|
|
*/
|
|
Cartesian3.normalize = function (cartesian, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("cartesian", cartesian);
|
|
Check.Check.typeOf.object("result", result);
|
|
//>>includeEnd('debug');
|
|
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|
const magnitude = Cartesian3.magnitude(cartesian);
|
|
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|
result.x = cartesian.x / magnitude;
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|
result.y = cartesian.y / magnitude;
|
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result.z = cartesian.z / magnitude;
|
|
|
|
//>>includeStart('debug', pragmas.debug);
|
|
if (isNaN(result.x) || isNaN(result.y) || isNaN(result.z)) {
|
|
throw new Check.DeveloperError("normalized result is not a number");
|
|
}
|
|
//>>includeEnd('debug');
|
|
|
|
return result;
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};
|
|
|
|
/**
|
|
* Computes the dot (scalar) product of two Cartesians.
|
|
*
|
|
* @param {Cartesian3} left The first Cartesian.
|
|
* @param {Cartesian3} right The second Cartesian.
|
|
* @returns {Number} The dot product.
|
|
*/
|
|
Cartesian3.dot = function (left, right) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("left", left);
|
|
Check.Check.typeOf.object("right", right);
|
|
//>>includeEnd('debug');
|
|
|
|
return left.x * right.x + left.y * right.y + left.z * right.z;
|
|
};
|
|
|
|
/**
|
|
* Computes the componentwise product of two Cartesians.
|
|
*
|
|
* @param {Cartesian3} left The first Cartesian.
|
|
* @param {Cartesian3} right The second Cartesian.
|
|
* @param {Cartesian3} result The object onto which to store the result.
|
|
* @returns {Cartesian3} The modified result parameter.
|
|
*/
|
|
Cartesian3.multiplyComponents = function (left, right, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("left", left);
|
|
Check.Check.typeOf.object("right", right);
|
|
Check.Check.typeOf.object("result", result);
|
|
//>>includeEnd('debug');
|
|
|
|
result.x = left.x * right.x;
|
|
result.y = left.y * right.y;
|
|
result.z = left.z * right.z;
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Computes the componentwise quotient of two Cartesians.
|
|
*
|
|
* @param {Cartesian3} left The first Cartesian.
|
|
* @param {Cartesian3} right The second Cartesian.
|
|
* @param {Cartesian3} result The object onto which to store the result.
|
|
* @returns {Cartesian3} The modified result parameter.
|
|
*/
|
|
Cartesian3.divideComponents = function (left, right, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("left", left);
|
|
Check.Check.typeOf.object("right", right);
|
|
Check.Check.typeOf.object("result", result);
|
|
//>>includeEnd('debug');
|
|
|
|
result.x = left.x / right.x;
|
|
result.y = left.y / right.y;
|
|
result.z = left.z / right.z;
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Computes the componentwise sum of two Cartesians.
|
|
*
|
|
* @param {Cartesian3} left The first Cartesian.
|
|
* @param {Cartesian3} right The second Cartesian.
|
|
* @param {Cartesian3} result The object onto which to store the result.
|
|
* @returns {Cartesian3} The modified result parameter.
|
|
*/
|
|
Cartesian3.add = function (left, right, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("left", left);
|
|
Check.Check.typeOf.object("right", right);
|
|
Check.Check.typeOf.object("result", result);
|
|
//>>includeEnd('debug');
|
|
|
|
result.x = left.x + right.x;
|
|
result.y = left.y + right.y;
|
|
result.z = left.z + right.z;
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Computes the componentwise difference of two Cartesians.
|
|
*
|
|
* @param {Cartesian3} left The first Cartesian.
|
|
* @param {Cartesian3} right The second Cartesian.
|
|
* @param {Cartesian3} result The object onto which to store the result.
|
|
* @returns {Cartesian3} The modified result parameter.
|
|
*/
|
|
Cartesian3.subtract = function (left, right, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("left", left);
|
|
Check.Check.typeOf.object("right", right);
|
|
Check.Check.typeOf.object("result", result);
|
|
//>>includeEnd('debug');
|
|
|
|
result.x = left.x - right.x;
|
|
result.y = left.y - right.y;
|
|
result.z = left.z - right.z;
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Multiplies the provided Cartesian componentwise by the provided scalar.
|
|
*
|
|
* @param {Cartesian3} cartesian The Cartesian to be scaled.
|
|
* @param {Number} scalar The scalar to multiply with.
|
|
* @param {Cartesian3} result The object onto which to store the result.
|
|
* @returns {Cartesian3} The modified result parameter.
|
|
*/
|
|
Cartesian3.multiplyByScalar = function (cartesian, scalar, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("cartesian", cartesian);
|
|
Check.Check.typeOf.number("scalar", scalar);
|
|
Check.Check.typeOf.object("result", result);
|
|
//>>includeEnd('debug');
|
|
|
|
result.x = cartesian.x * scalar;
|
|
result.y = cartesian.y * scalar;
|
|
result.z = cartesian.z * scalar;
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Divides the provided Cartesian componentwise by the provided scalar.
|
|
*
|
|
* @param {Cartesian3} cartesian The Cartesian to be divided.
|
|
* @param {Number} scalar The scalar to divide by.
|
|
* @param {Cartesian3} result The object onto which to store the result.
|
|
* @returns {Cartesian3} The modified result parameter.
|
|
*/
|
|
Cartesian3.divideByScalar = function (cartesian, scalar, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("cartesian", cartesian);
|
|
Check.Check.typeOf.number("scalar", scalar);
|
|
Check.Check.typeOf.object("result", result);
|
|
//>>includeEnd('debug');
|
|
|
|
result.x = cartesian.x / scalar;
|
|
result.y = cartesian.y / scalar;
|
|
result.z = cartesian.z / scalar;
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Negates the provided Cartesian.
|
|
*
|
|
* @param {Cartesian3} cartesian The Cartesian to be negated.
|
|
* @param {Cartesian3} result The object onto which to store the result.
|
|
* @returns {Cartesian3} The modified result parameter.
|
|
*/
|
|
Cartesian3.negate = function (cartesian, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("cartesian", cartesian);
|
|
Check.Check.typeOf.object("result", result);
|
|
//>>includeEnd('debug');
|
|
|
|
result.x = -cartesian.x;
|
|
result.y = -cartesian.y;
|
|
result.z = -cartesian.z;
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Computes the absolute value of the provided Cartesian.
|
|
*
|
|
* @param {Cartesian3} cartesian The Cartesian whose absolute value is to be computed.
|
|
* @param {Cartesian3} result The object onto which to store the result.
|
|
* @returns {Cartesian3} The modified result parameter.
|
|
*/
|
|
Cartesian3.abs = function (cartesian, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("cartesian", cartesian);
|
|
Check.Check.typeOf.object("result", result);
|
|
//>>includeEnd('debug');
|
|
|
|
result.x = Math.abs(cartesian.x);
|
|
result.y = Math.abs(cartesian.y);
|
|
result.z = Math.abs(cartesian.z);
|
|
return result;
|
|
};
|
|
|
|
const lerpScratch = new Cartesian3();
|
|
/**
|
|
* Computes the linear interpolation or extrapolation at t using the provided cartesians.
|
|
*
|
|
* @param {Cartesian3} start The value corresponding to t at 0.0.
|
|
* @param {Cartesian3} end The value corresponding to t at 1.0.
|
|
* @param {Number} t The point along t at which to interpolate.
|
|
* @param {Cartesian3} result The object onto which to store the result.
|
|
* @returns {Cartesian3} The modified result parameter.
|
|
*/
|
|
Cartesian3.lerp = function (start, end, t, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("start", start);
|
|
Check.Check.typeOf.object("end", end);
|
|
Check.Check.typeOf.number("t", t);
|
|
Check.Check.typeOf.object("result", result);
|
|
//>>includeEnd('debug');
|
|
|
|
Cartesian3.multiplyByScalar(end, t, lerpScratch);
|
|
result = Cartesian3.multiplyByScalar(start, 1.0 - t, result);
|
|
return Cartesian3.add(lerpScratch, result, result);
|
|
};
|
|
|
|
const angleBetweenScratch = new Cartesian3();
|
|
const angleBetweenScratch2 = new Cartesian3();
|
|
/**
|
|
* Returns the angle, in radians, between the provided Cartesians.
|
|
*
|
|
* @param {Cartesian3} left The first Cartesian.
|
|
* @param {Cartesian3} right The second Cartesian.
|
|
* @returns {Number} The angle between the Cartesians.
|
|
*/
|
|
Cartesian3.angleBetween = function (left, right) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("left", left);
|
|
Check.Check.typeOf.object("right", right);
|
|
//>>includeEnd('debug');
|
|
|
|
Cartesian3.normalize(left, angleBetweenScratch);
|
|
Cartesian3.normalize(right, angleBetweenScratch2);
|
|
const cosine = Cartesian3.dot(angleBetweenScratch, angleBetweenScratch2);
|
|
const sine = Cartesian3.magnitude(
|
|
Cartesian3.cross(
|
|
angleBetweenScratch,
|
|
angleBetweenScratch2,
|
|
angleBetweenScratch
|
|
)
|
|
);
|
|
return Math.atan2(sine, cosine);
|
|
};
|
|
|
|
const mostOrthogonalAxisScratch = new Cartesian3();
|
|
/**
|
|
* Returns the axis that is most orthogonal to the provided Cartesian.
|
|
*
|
|
* @param {Cartesian3} cartesian The Cartesian on which to find the most orthogonal axis.
|
|
* @param {Cartesian3} result The object onto which to store the result.
|
|
* @returns {Cartesian3} The most orthogonal axis.
|
|
*/
|
|
Cartesian3.mostOrthogonalAxis = function (cartesian, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("cartesian", cartesian);
|
|
Check.Check.typeOf.object("result", result);
|
|
//>>includeEnd('debug');
|
|
|
|
const f = Cartesian3.normalize(cartesian, mostOrthogonalAxisScratch);
|
|
Cartesian3.abs(f, f);
|
|
|
|
if (f.x <= f.y) {
|
|
if (f.x <= f.z) {
|
|
result = Cartesian3.clone(Cartesian3.UNIT_X, result);
|
|
} else {
|
|
result = Cartesian3.clone(Cartesian3.UNIT_Z, result);
|
|
}
|
|
} else if (f.y <= f.z) {
|
|
result = Cartesian3.clone(Cartesian3.UNIT_Y, result);
|
|
} else {
|
|
result = Cartesian3.clone(Cartesian3.UNIT_Z, result);
|
|
}
|
|
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Projects vector a onto vector b
|
|
* @param {Cartesian3} a The vector that needs projecting
|
|
* @param {Cartesian3} b The vector to project onto
|
|
* @param {Cartesian3} result The result cartesian
|
|
* @returns {Cartesian3} The modified result parameter
|
|
*/
|
|
Cartesian3.projectVector = function (a, b, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.defined("a", a);
|
|
Check.Check.defined("b", b);
|
|
Check.Check.defined("result", result);
|
|
//>>includeEnd('debug');
|
|
|
|
const scalar = Cartesian3.dot(a, b) / Cartesian3.dot(b, b);
|
|
return Cartesian3.multiplyByScalar(b, scalar, result);
|
|
};
|
|
|
|
/**
|
|
* Compares the provided Cartesians componentwise and returns
|
|
* <code>true</code> if they are equal, <code>false</code> otherwise.
|
|
*
|
|
* @param {Cartesian3} [left] The first Cartesian.
|
|
* @param {Cartesian3} [right] The second Cartesian.
|
|
* @returns {Boolean} <code>true</code> if left and right are equal, <code>false</code> otherwise.
|
|
*/
|
|
Cartesian3.equals = function (left, right) {
|
|
return (
|
|
left === right ||
|
|
(defaultValue.defined(left) &&
|
|
defaultValue.defined(right) &&
|
|
left.x === right.x &&
|
|
left.y === right.y &&
|
|
left.z === right.z)
|
|
);
|
|
};
|
|
|
|
/**
|
|
* @private
|
|
*/
|
|
Cartesian3.equalsArray = function (cartesian, array, offset) {
|
|
return (
|
|
cartesian.x === array[offset] &&
|
|
cartesian.y === array[offset + 1] &&
|
|
cartesian.z === array[offset + 2]
|
|
);
|
|
};
|
|
|
|
/**
|
|
* Compares the provided Cartesians componentwise and returns
|
|
* <code>true</code> if they pass an absolute or relative tolerance test,
|
|
* <code>false</code> otherwise.
|
|
*
|
|
* @param {Cartesian3} [left] The first Cartesian.
|
|
* @param {Cartesian3} [right] The second Cartesian.
|
|
* @param {Number} [relativeEpsilon=0] The relative epsilon tolerance to use for equality testing.
|
|
* @param {Number} [absoluteEpsilon=relativeEpsilon] The absolute epsilon tolerance to use for equality testing.
|
|
* @returns {Boolean} <code>true</code> if left and right are within the provided epsilon, <code>false</code> otherwise.
|
|
*/
|
|
Cartesian3.equalsEpsilon = function (
|
|
left,
|
|
right,
|
|
relativeEpsilon,
|
|
absoluteEpsilon
|
|
) {
|
|
return (
|
|
left === right ||
|
|
(defaultValue.defined(left) &&
|
|
defaultValue.defined(right) &&
|
|
Math$1.CesiumMath.equalsEpsilon(
|
|
left.x,
|
|
right.x,
|
|
relativeEpsilon,
|
|
absoluteEpsilon
|
|
) &&
|
|
Math$1.CesiumMath.equalsEpsilon(
|
|
left.y,
|
|
right.y,
|
|
relativeEpsilon,
|
|
absoluteEpsilon
|
|
) &&
|
|
Math$1.CesiumMath.equalsEpsilon(
|
|
left.z,
|
|
right.z,
|
|
relativeEpsilon,
|
|
absoluteEpsilon
|
|
))
|
|
);
|
|
};
|
|
|
|
/**
|
|
* Computes the cross (outer) product of two Cartesians.
|
|
*
|
|
* @param {Cartesian3} left The first Cartesian.
|
|
* @param {Cartesian3} right The second Cartesian.
|
|
* @param {Cartesian3} result The object onto which to store the result.
|
|
* @returns {Cartesian3} The cross product.
|
|
*/
|
|
Cartesian3.cross = function (left, right, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("left", left);
|
|
Check.Check.typeOf.object("right", right);
|
|
Check.Check.typeOf.object("result", result);
|
|
//>>includeEnd('debug');
|
|
|
|
const leftX = left.x;
|
|
const leftY = left.y;
|
|
const leftZ = left.z;
|
|
const rightX = right.x;
|
|
const rightY = right.y;
|
|
const rightZ = right.z;
|
|
|
|
const x = leftY * rightZ - leftZ * rightY;
|
|
const y = leftZ * rightX - leftX * rightZ;
|
|
const z = leftX * rightY - leftY * rightX;
|
|
|
|
result.x = x;
|
|
result.y = y;
|
|
result.z = z;
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Computes the midpoint between the right and left Cartesian.
|
|
* @param {Cartesian3} left The first Cartesian.
|
|
* @param {Cartesian3} right The second Cartesian.
|
|
* @param {Cartesian3} result The object onto which to store the result.
|
|
* @returns {Cartesian3} The midpoint.
|
|
*/
|
|
Cartesian3.midpoint = function (left, right, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("left", left);
|
|
Check.Check.typeOf.object("right", right);
|
|
Check.Check.typeOf.object("result", result);
|
|
//>>includeEnd('debug');
|
|
|
|
result.x = (left.x + right.x) * 0.5;
|
|
result.y = (left.y + right.y) * 0.5;
|
|
result.z = (left.z + right.z) * 0.5;
|
|
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Returns a Cartesian3 position from longitude and latitude values given in degrees.
|
|
*
|
|
* @param {Number} longitude The longitude, in degrees
|
|
* @param {Number} latitude The latitude, in degrees
|
|
* @param {Number} [height=0.0] The height, in meters, above the ellipsoid.
|
|
* @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the position lies.
|
|
* @param {Cartesian3} [result] The object onto which to store the result.
|
|
* @returns {Cartesian3} The position
|
|
*
|
|
* @example
|
|
* const position = Cesium.Cartesian3.fromDegrees(-115.0, 37.0);
|
|
*/
|
|
Cartesian3.fromDegrees = function (
|
|
longitude,
|
|
latitude,
|
|
height,
|
|
ellipsoid,
|
|
result
|
|
) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.number("longitude", longitude);
|
|
Check.Check.typeOf.number("latitude", latitude);
|
|
//>>includeEnd('debug');
|
|
|
|
longitude = Math$1.CesiumMath.toRadians(longitude);
|
|
latitude = Math$1.CesiumMath.toRadians(latitude);
|
|
return Cartesian3.fromRadians(longitude, latitude, height, ellipsoid, result);
|
|
};
|
|
|
|
let scratchN = new Cartesian3();
|
|
let scratchK = new Cartesian3();
|
|
const wgs84RadiiSquared = new Cartesian3(
|
|
6378137.0 * 6378137.0,
|
|
6378137.0 * 6378137.0,
|
|
6356752.3142451793 * 6356752.3142451793
|
|
);
|
|
|
|
/**
|
|
* Returns a Cartesian3 position from longitude and latitude values given in radians.
|
|
*
|
|
* @param {Number} longitude The longitude, in radians
|
|
* @param {Number} latitude The latitude, in radians
|
|
* @param {Number} [height=0.0] The height, in meters, above the ellipsoid.
|
|
* @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the position lies.
|
|
* @param {Cartesian3} [result] The object onto which to store the result.
|
|
* @returns {Cartesian3} The position
|
|
*
|
|
* @example
|
|
* const position = Cesium.Cartesian3.fromRadians(-2.007, 0.645);
|
|
*/
|
|
Cartesian3.fromRadians = function (
|
|
longitude,
|
|
latitude,
|
|
height,
|
|
ellipsoid,
|
|
result
|
|
) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.number("longitude", longitude);
|
|
Check.Check.typeOf.number("latitude", latitude);
|
|
//>>includeEnd('debug');
|
|
|
|
height = defaultValue.defaultValue(height, 0.0);
|
|
const radiiSquared = defaultValue.defined(ellipsoid)
|
|
? ellipsoid.radiiSquared
|
|
: wgs84RadiiSquared;
|
|
|
|
const cosLatitude = Math.cos(latitude);
|
|
scratchN.x = cosLatitude * Math.cos(longitude);
|
|
scratchN.y = cosLatitude * Math.sin(longitude);
|
|
scratchN.z = Math.sin(latitude);
|
|
scratchN = Cartesian3.normalize(scratchN, scratchN);
|
|
|
|
Cartesian3.multiplyComponents(radiiSquared, scratchN, scratchK);
|
|
const gamma = Math.sqrt(Cartesian3.dot(scratchN, scratchK));
|
|
scratchK = Cartesian3.divideByScalar(scratchK, gamma, scratchK);
|
|
scratchN = Cartesian3.multiplyByScalar(scratchN, height, scratchN);
|
|
|
|
if (!defaultValue.defined(result)) {
|
|
result = new Cartesian3();
|
|
}
|
|
return Cartesian3.add(scratchK, scratchN, result);
|
|
};
|
|
|
|
/**
|
|
* Returns an array of Cartesian3 positions given an array of longitude and latitude values given in degrees.
|
|
*
|
|
* @param {Number[]} coordinates A list of longitude and latitude values. Values alternate [longitude, latitude, longitude, latitude...].
|
|
* @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the coordinates lie.
|
|
* @param {Cartesian3[]} [result] An array of Cartesian3 objects to store the result.
|
|
* @returns {Cartesian3[]} The array of positions.
|
|
*
|
|
* @example
|
|
* const positions = Cesium.Cartesian3.fromDegreesArray([-115.0, 37.0, -107.0, 33.0]);
|
|
*/
|
|
Cartesian3.fromDegreesArray = function (coordinates, ellipsoid, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.defined("coordinates", coordinates);
|
|
if (coordinates.length < 2 || coordinates.length % 2 !== 0) {
|
|
throw new Check.DeveloperError(
|
|
"the number of coordinates must be a multiple of 2 and at least 2"
|
|
);
|
|
}
|
|
//>>includeEnd('debug');
|
|
|
|
const length = coordinates.length;
|
|
if (!defaultValue.defined(result)) {
|
|
result = new Array(length / 2);
|
|
} else {
|
|
result.length = length / 2;
|
|
}
|
|
|
|
for (let i = 0; i < length; i += 2) {
|
|
const longitude = coordinates[i];
|
|
const latitude = coordinates[i + 1];
|
|
const index = i / 2;
|
|
result[index] = Cartesian3.fromDegrees(
|
|
longitude,
|
|
latitude,
|
|
0,
|
|
ellipsoid,
|
|
result[index]
|
|
);
|
|
}
|
|
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Returns an array of Cartesian3 positions given an array of longitude and latitude values given in radians.
|
|
*
|
|
* @param {Number[]} coordinates A list of longitude and latitude values. Values alternate [longitude, latitude, longitude, latitude...].
|
|
* @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the coordinates lie.
|
|
* @param {Cartesian3[]} [result] An array of Cartesian3 objects to store the result.
|
|
* @returns {Cartesian3[]} The array of positions.
|
|
*
|
|
* @example
|
|
* const positions = Cesium.Cartesian3.fromRadiansArray([-2.007, 0.645, -1.867, .575]);
|
|
*/
|
|
Cartesian3.fromRadiansArray = function (coordinates, ellipsoid, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.defined("coordinates", coordinates);
|
|
if (coordinates.length < 2 || coordinates.length % 2 !== 0) {
|
|
throw new Check.DeveloperError(
|
|
"the number of coordinates must be a multiple of 2 and at least 2"
|
|
);
|
|
}
|
|
//>>includeEnd('debug');
|
|
|
|
const length = coordinates.length;
|
|
if (!defaultValue.defined(result)) {
|
|
result = new Array(length / 2);
|
|
} else {
|
|
result.length = length / 2;
|
|
}
|
|
|
|
for (let i = 0; i < length; i += 2) {
|
|
const longitude = coordinates[i];
|
|
const latitude = coordinates[i + 1];
|
|
const index = i / 2;
|
|
result[index] = Cartesian3.fromRadians(
|
|
longitude,
|
|
latitude,
|
|
0,
|
|
ellipsoid,
|
|
result[index]
|
|
);
|
|
}
|
|
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Returns an array of Cartesian3 positions given an array of longitude, latitude and height values where longitude and latitude are given in degrees.
|
|
*
|
|
* @param {Number[]} coordinates A list of longitude, latitude and height values. Values alternate [longitude, latitude, height, longitude, latitude, height...].
|
|
* @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the position lies.
|
|
* @param {Cartesian3[]} [result] An array of Cartesian3 objects to store the result.
|
|
* @returns {Cartesian3[]} The array of positions.
|
|
*
|
|
* @example
|
|
* const positions = Cesium.Cartesian3.fromDegreesArrayHeights([-115.0, 37.0, 100000.0, -107.0, 33.0, 150000.0]);
|
|
*/
|
|
Cartesian3.fromDegreesArrayHeights = function (coordinates, ellipsoid, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.defined("coordinates", coordinates);
|
|
if (coordinates.length < 3 || coordinates.length % 3 !== 0) {
|
|
throw new Check.DeveloperError(
|
|
"the number of coordinates must be a multiple of 3 and at least 3"
|
|
);
|
|
}
|
|
//>>includeEnd('debug');
|
|
|
|
const length = coordinates.length;
|
|
if (!defaultValue.defined(result)) {
|
|
result = new Array(length / 3);
|
|
} else {
|
|
result.length = length / 3;
|
|
}
|
|
|
|
for (let i = 0; i < length; i += 3) {
|
|
const longitude = coordinates[i];
|
|
const latitude = coordinates[i + 1];
|
|
const height = coordinates[i + 2];
|
|
const index = i / 3;
|
|
result[index] = Cartesian3.fromDegrees(
|
|
longitude,
|
|
latitude,
|
|
height,
|
|
ellipsoid,
|
|
result[index]
|
|
);
|
|
}
|
|
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Returns an array of Cartesian3 positions given an array of longitude, latitude and height values where longitude and latitude are given in radians.
|
|
*
|
|
* @param {Number[]} coordinates A list of longitude, latitude and height values. Values alternate [longitude, latitude, height, longitude, latitude, height...].
|
|
* @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the position lies.
|
|
* @param {Cartesian3[]} [result] An array of Cartesian3 objects to store the result.
|
|
* @returns {Cartesian3[]} The array of positions.
|
|
*
|
|
* @example
|
|
* const positions = Cesium.Cartesian3.fromRadiansArrayHeights([-2.007, 0.645, 100000.0, -1.867, .575, 150000.0]);
|
|
*/
|
|
Cartesian3.fromRadiansArrayHeights = function (coordinates, ellipsoid, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.defined("coordinates", coordinates);
|
|
if (coordinates.length < 3 || coordinates.length % 3 !== 0) {
|
|
throw new Check.DeveloperError(
|
|
"the number of coordinates must be a multiple of 3 and at least 3"
|
|
);
|
|
}
|
|
//>>includeEnd('debug');
|
|
|
|
const length = coordinates.length;
|
|
if (!defaultValue.defined(result)) {
|
|
result = new Array(length / 3);
|
|
} else {
|
|
result.length = length / 3;
|
|
}
|
|
|
|
for (let i = 0; i < length; i += 3) {
|
|
const longitude = coordinates[i];
|
|
const latitude = coordinates[i + 1];
|
|
const height = coordinates[i + 2];
|
|
const index = i / 3;
|
|
result[index] = Cartesian3.fromRadians(
|
|
longitude,
|
|
latitude,
|
|
height,
|
|
ellipsoid,
|
|
result[index]
|
|
);
|
|
}
|
|
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* An immutable Cartesian3 instance initialized to (0.0, 0.0, 0.0).
|
|
*
|
|
* @type {Cartesian3}
|
|
* @constant
|
|
*/
|
|
Cartesian3.ZERO = Object.freeze(new Cartesian3(0.0, 0.0, 0.0));
|
|
|
|
/**
|
|
* An immutable Cartesian3 instance initialized to (1.0, 1.0, 1.0).
|
|
*
|
|
* @type {Cartesian3}
|
|
* @constant
|
|
*/
|
|
Cartesian3.ONE = Object.freeze(new Cartesian3(1.0, 1.0, 1.0));
|
|
|
|
/**
|
|
* An immutable Cartesian3 instance initialized to (1.0, 0.0, 0.0).
|
|
*
|
|
* @type {Cartesian3}
|
|
* @constant
|
|
*/
|
|
Cartesian3.UNIT_X = Object.freeze(new Cartesian3(1.0, 0.0, 0.0));
|
|
|
|
/**
|
|
* An immutable Cartesian3 instance initialized to (0.0, 1.0, 0.0).
|
|
*
|
|
* @type {Cartesian3}
|
|
* @constant
|
|
*/
|
|
Cartesian3.UNIT_Y = Object.freeze(new Cartesian3(0.0, 1.0, 0.0));
|
|
|
|
/**
|
|
* An immutable Cartesian3 instance initialized to (0.0, 0.0, 1.0).
|
|
*
|
|
* @type {Cartesian3}
|
|
* @constant
|
|
*/
|
|
Cartesian3.UNIT_Z = Object.freeze(new Cartesian3(0.0, 0.0, 1.0));
|
|
|
|
/**
|
|
* Duplicates this Cartesian3 instance.
|
|
*
|
|
* @param {Cartesian3} [result] The object onto which to store the result.
|
|
* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if one was not provided.
|
|
*/
|
|
Cartesian3.prototype.clone = function (result) {
|
|
return Cartesian3.clone(this, result);
|
|
};
|
|
|
|
/**
|
|
* Compares this Cartesian against the provided Cartesian componentwise and returns
|
|
* <code>true</code> if they are equal, <code>false</code> otherwise.
|
|
*
|
|
* @param {Cartesian3} [right] The right hand side Cartesian.
|
|
* @returns {Boolean} <code>true</code> if they are equal, <code>false</code> otherwise.
|
|
*/
|
|
Cartesian3.prototype.equals = function (right) {
|
|
return Cartesian3.equals(this, right);
|
|
};
|
|
|
|
/**
|
|
* Compares this Cartesian against the provided Cartesian componentwise and returns
|
|
* <code>true</code> if they pass an absolute or relative tolerance test,
|
|
* <code>false</code> otherwise.
|
|
*
|
|
* @param {Cartesian3} [right] The right hand side Cartesian.
|
|
* @param {Number} [relativeEpsilon=0] The relative epsilon tolerance to use for equality testing.
|
|
* @param {Number} [absoluteEpsilon=relativeEpsilon] The absolute epsilon tolerance to use for equality testing.
|
|
* @returns {Boolean} <code>true</code> if they are within the provided epsilon, <code>false</code> otherwise.
|
|
*/
|
|
Cartesian3.prototype.equalsEpsilon = function (
|
|
right,
|
|
relativeEpsilon,
|
|
absoluteEpsilon
|
|
) {
|
|
return Cartesian3.equalsEpsilon(
|
|
this,
|
|
right,
|
|
relativeEpsilon,
|
|
absoluteEpsilon
|
|
);
|
|
};
|
|
|
|
/**
|
|
* Creates a string representing this Cartesian in the format '(x, y, z)'.
|
|
*
|
|
* @returns {String} A string representing this Cartesian in the format '(x, y, z)'.
|
|
*/
|
|
Cartesian3.prototype.toString = function () {
|
|
return `(${this.x}, ${this.y}, ${this.z})`;
|
|
};
|
|
|
|
const scaleToGeodeticSurfaceIntersection = new Cartesian3();
|
|
const scaleToGeodeticSurfaceGradient = new Cartesian3();
|
|
|
|
/**
|
|
* Scales the provided Cartesian position along the geodetic surface normal
|
|
* so that it is on the surface of this ellipsoid. If the position is
|
|
* at the center of the ellipsoid, this function returns undefined.
|
|
*
|
|
* @param {Cartesian3} cartesian The Cartesian position to scale.
|
|
* @param {Cartesian3} oneOverRadii One over radii of the ellipsoid.
|
|
* @param {Cartesian3} oneOverRadiiSquared One over radii squared of the ellipsoid.
|
|
* @param {Number} centerToleranceSquared Tolerance for closeness to the center.
|
|
* @param {Cartesian3} [result] The object onto which to store the result.
|
|
* @returns {Cartesian3} The modified result parameter, a new Cartesian3 instance if none was provided, or undefined if the position is at the center.
|
|
*
|
|
* @function scaleToGeodeticSurface
|
|
*
|
|
* @private
|
|
*/
|
|
function scaleToGeodeticSurface(
|
|
cartesian,
|
|
oneOverRadii,
|
|
oneOverRadiiSquared,
|
|
centerToleranceSquared,
|
|
result
|
|
) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
if (!defaultValue.defined(cartesian)) {
|
|
throw new Check.DeveloperError("cartesian is required.");
|
|
}
|
|
if (!defaultValue.defined(oneOverRadii)) {
|
|
throw new Check.DeveloperError("oneOverRadii is required.");
|
|
}
|
|
if (!defaultValue.defined(oneOverRadiiSquared)) {
|
|
throw new Check.DeveloperError("oneOverRadiiSquared is required.");
|
|
}
|
|
if (!defaultValue.defined(centerToleranceSquared)) {
|
|
throw new Check.DeveloperError("centerToleranceSquared is required.");
|
|
}
|
|
//>>includeEnd('debug');
|
|
|
|
const positionX = cartesian.x;
|
|
const positionY = cartesian.y;
|
|
const positionZ = cartesian.z;
|
|
|
|
const oneOverRadiiX = oneOverRadii.x;
|
|
const oneOverRadiiY = oneOverRadii.y;
|
|
const oneOverRadiiZ = oneOverRadii.z;
|
|
|
|
const x2 = positionX * positionX * oneOverRadiiX * oneOverRadiiX;
|
|
const y2 = positionY * positionY * oneOverRadiiY * oneOverRadiiY;
|
|
const z2 = positionZ * positionZ * oneOverRadiiZ * oneOverRadiiZ;
|
|
|
|
// Compute the squared ellipsoid norm.
|
|
const squaredNorm = x2 + y2 + z2;
|
|
const ratio = Math.sqrt(1.0 / squaredNorm);
|
|
|
|
// As an initial approximation, assume that the radial intersection is the projection point.
|
|
const intersection = Cartesian3.multiplyByScalar(
|
|
cartesian,
|
|
ratio,
|
|
scaleToGeodeticSurfaceIntersection
|
|
);
|
|
|
|
// If the position is near the center, the iteration will not converge.
|
|
if (squaredNorm < centerToleranceSquared) {
|
|
return !isFinite(ratio)
|
|
? undefined
|
|
: Cartesian3.clone(intersection, result);
|
|
}
|
|
|
|
const oneOverRadiiSquaredX = oneOverRadiiSquared.x;
|
|
const oneOverRadiiSquaredY = oneOverRadiiSquared.y;
|
|
const oneOverRadiiSquaredZ = oneOverRadiiSquared.z;
|
|
|
|
// Use the gradient at the intersection point in place of the true unit normal.
|
|
// The difference in magnitude will be absorbed in the multiplier.
|
|
const gradient = scaleToGeodeticSurfaceGradient;
|
|
gradient.x = intersection.x * oneOverRadiiSquaredX * 2.0;
|
|
gradient.y = intersection.y * oneOverRadiiSquaredY * 2.0;
|
|
gradient.z = intersection.z * oneOverRadiiSquaredZ * 2.0;
|
|
|
|
// Compute the initial guess at the normal vector multiplier, lambda.
|
|
let lambda =
|
|
((1.0 - ratio) * Cartesian3.magnitude(cartesian)) /
|
|
(0.5 * Cartesian3.magnitude(gradient));
|
|
let correction = 0.0;
|
|
|
|
let func;
|
|
let denominator;
|
|
let xMultiplier;
|
|
let yMultiplier;
|
|
let zMultiplier;
|
|
let xMultiplier2;
|
|
let yMultiplier2;
|
|
let zMultiplier2;
|
|
let xMultiplier3;
|
|
let yMultiplier3;
|
|
let zMultiplier3;
|
|
|
|
do {
|
|
lambda -= correction;
|
|
|
|
xMultiplier = 1.0 / (1.0 + lambda * oneOverRadiiSquaredX);
|
|
yMultiplier = 1.0 / (1.0 + lambda * oneOverRadiiSquaredY);
|
|
zMultiplier = 1.0 / (1.0 + lambda * oneOverRadiiSquaredZ);
|
|
|
|
xMultiplier2 = xMultiplier * xMultiplier;
|
|
yMultiplier2 = yMultiplier * yMultiplier;
|
|
zMultiplier2 = zMultiplier * zMultiplier;
|
|
|
|
xMultiplier3 = xMultiplier2 * xMultiplier;
|
|
yMultiplier3 = yMultiplier2 * yMultiplier;
|
|
zMultiplier3 = zMultiplier2 * zMultiplier;
|
|
|
|
func = x2 * xMultiplier2 + y2 * yMultiplier2 + z2 * zMultiplier2 - 1.0;
|
|
|
|
// "denominator" here refers to the use of this expression in the velocity and acceleration
|
|
// computations in the sections to follow.
|
|
denominator =
|
|
x2 * xMultiplier3 * oneOverRadiiSquaredX +
|
|
y2 * yMultiplier3 * oneOverRadiiSquaredY +
|
|
z2 * zMultiplier3 * oneOverRadiiSquaredZ;
|
|
|
|
const derivative = -2.0 * denominator;
|
|
|
|
correction = func / derivative;
|
|
} while (Math.abs(func) > Math$1.CesiumMath.EPSILON12);
|
|
|
|
if (!defaultValue.defined(result)) {
|
|
return new Cartesian3(
|
|
positionX * xMultiplier,
|
|
positionY * yMultiplier,
|
|
positionZ * zMultiplier
|
|
);
|
|
}
|
|
result.x = positionX * xMultiplier;
|
|
result.y = positionY * yMultiplier;
|
|
result.z = positionZ * zMultiplier;
|
|
return result;
|
|
}
|
|
|
|
/**
|
|
* A position defined by longitude, latitude, and height.
|
|
* @alias Cartographic
|
|
* @constructor
|
|
*
|
|
* @param {Number} [longitude=0.0] The longitude, in radians.
|
|
* @param {Number} [latitude=0.0] The latitude, in radians.
|
|
* @param {Number} [height=0.0] The height, in meters, above the ellipsoid.
|
|
*
|
|
* @see Ellipsoid
|
|
*/
|
|
function Cartographic(longitude, latitude, height) {
|
|
/**
|
|
* The longitude, in radians.
|
|
* @type {Number}
|
|
* @default 0.0
|
|
*/
|
|
this.longitude = defaultValue.defaultValue(longitude, 0.0);
|
|
|
|
/**
|
|
* The latitude, in radians.
|
|
* @type {Number}
|
|
* @default 0.0
|
|
*/
|
|
this.latitude = defaultValue.defaultValue(latitude, 0.0);
|
|
|
|
/**
|
|
* The height, in meters, above the ellipsoid.
|
|
* @type {Number}
|
|
* @default 0.0
|
|
*/
|
|
this.height = defaultValue.defaultValue(height, 0.0);
|
|
}
|
|
|
|
/**
|
|
* Creates a new Cartographic instance from longitude and latitude
|
|
* specified in radians.
|
|
*
|
|
* @param {Number} longitude The longitude, in radians.
|
|
* @param {Number} latitude The latitude, in radians.
|
|
* @param {Number} [height=0.0] The height, in meters, above the ellipsoid.
|
|
* @param {Cartographic} [result] The object onto which to store the result.
|
|
* @returns {Cartographic} The modified result parameter or a new Cartographic instance if one was not provided.
|
|
*/
|
|
Cartographic.fromRadians = function (longitude, latitude, height, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.number("longitude", longitude);
|
|
Check.Check.typeOf.number("latitude", latitude);
|
|
//>>includeEnd('debug');
|
|
|
|
height = defaultValue.defaultValue(height, 0.0);
|
|
|
|
if (!defaultValue.defined(result)) {
|
|
return new Cartographic(longitude, latitude, height);
|
|
}
|
|
|
|
result.longitude = longitude;
|
|
result.latitude = latitude;
|
|
result.height = height;
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Creates a new Cartographic instance from longitude and latitude
|
|
* specified in degrees. The values in the resulting object will
|
|
* be in radians.
|
|
*
|
|
* @param {Number} longitude The longitude, in degrees.
|
|
* @param {Number} latitude The latitude, in degrees.
|
|
* @param {Number} [height=0.0] The height, in meters, above the ellipsoid.
|
|
* @param {Cartographic} [result] The object onto which to store the result.
|
|
* @returns {Cartographic} The modified result parameter or a new Cartographic instance if one was not provided.
|
|
*/
|
|
Cartographic.fromDegrees = function (longitude, latitude, height, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.number("longitude", longitude);
|
|
Check.Check.typeOf.number("latitude", latitude);
|
|
//>>includeEnd('debug');
|
|
longitude = Math$1.CesiumMath.toRadians(longitude);
|
|
latitude = Math$1.CesiumMath.toRadians(latitude);
|
|
|
|
return Cartographic.fromRadians(longitude, latitude, height, result);
|
|
};
|
|
|
|
const cartesianToCartographicN$1 = new Cartesian3();
|
|
const cartesianToCartographicP$1 = new Cartesian3();
|
|
const cartesianToCartographicH$1 = new Cartesian3();
|
|
const wgs84OneOverRadii = new Cartesian3(
|
|
1.0 / 6378137.0,
|
|
1.0 / 6378137.0,
|
|
1.0 / 6356752.3142451793
|
|
);
|
|
const wgs84OneOverRadiiSquared = new Cartesian3(
|
|
1.0 / (6378137.0 * 6378137.0),
|
|
1.0 / (6378137.0 * 6378137.0),
|
|
1.0 / (6356752.3142451793 * 6356752.3142451793)
|
|
);
|
|
const wgs84CenterToleranceSquared = Math$1.CesiumMath.EPSILON1;
|
|
|
|
/**
|
|
* Creates a new Cartographic instance from a Cartesian position. The values in the
|
|
* resulting object will be in radians.
|
|
*
|
|
* @param {Cartesian3} cartesian The Cartesian position to convert to cartographic representation.
|
|
* @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the position lies.
|
|
* @param {Cartographic} [result] The object onto which to store the result.
|
|
* @returns {Cartographic} The modified result parameter, new Cartographic instance if none was provided, or undefined if the cartesian is at the center of the ellipsoid.
|
|
*/
|
|
Cartographic.fromCartesian = function (cartesian, ellipsoid, result) {
|
|
const oneOverRadii = defaultValue.defined(ellipsoid)
|
|
? ellipsoid.oneOverRadii
|
|
: wgs84OneOverRadii;
|
|
const oneOverRadiiSquared = defaultValue.defined(ellipsoid)
|
|
? ellipsoid.oneOverRadiiSquared
|
|
: wgs84OneOverRadiiSquared;
|
|
const centerToleranceSquared = defaultValue.defined(ellipsoid)
|
|
? ellipsoid._centerToleranceSquared
|
|
: wgs84CenterToleranceSquared;
|
|
|
|
//`cartesian is required.` is thrown from scaleToGeodeticSurface
|
|
const p = scaleToGeodeticSurface(
|
|
cartesian,
|
|
oneOverRadii,
|
|
oneOverRadiiSquared,
|
|
centerToleranceSquared,
|
|
cartesianToCartographicP$1
|
|
);
|
|
|
|
if (!defaultValue.defined(p)) {
|
|
return undefined;
|
|
}
|
|
|
|
let n = Cartesian3.multiplyComponents(
|
|
p,
|
|
oneOverRadiiSquared,
|
|
cartesianToCartographicN$1
|
|
);
|
|
n = Cartesian3.normalize(n, n);
|
|
|
|
const h = Cartesian3.subtract(cartesian, p, cartesianToCartographicH$1);
|
|
|
|
const longitude = Math.atan2(n.y, n.x);
|
|
const latitude = Math.asin(n.z);
|
|
const height =
|
|
Math$1.CesiumMath.sign(Cartesian3.dot(h, cartesian)) * Cartesian3.magnitude(h);
|
|
|
|
if (!defaultValue.defined(result)) {
|
|
return new Cartographic(longitude, latitude, height);
|
|
}
|
|
result.longitude = longitude;
|
|
result.latitude = latitude;
|
|
result.height = height;
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Creates a new Cartesian3 instance from a Cartographic input. The values in the inputted
|
|
* object should be in radians.
|
|
*
|
|
* @param {Cartographic} cartographic Input to be converted into a Cartesian3 output.
|
|
* @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the position lies.
|
|
* @param {Cartesian3} [result] The object onto which to store the result.
|
|
* @returns {Cartesian3} The position
|
|
*/
|
|
Cartographic.toCartesian = function (cartographic, ellipsoid, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.defined("cartographic", cartographic);
|
|
//>>includeEnd('debug');
|
|
|
|
return Cartesian3.fromRadians(
|
|
cartographic.longitude,
|
|
cartographic.latitude,
|
|
cartographic.height,
|
|
ellipsoid,
|
|
result
|
|
);
|
|
};
|
|
|
|
/**
|
|
* Duplicates a Cartographic instance.
|
|
*
|
|
* @param {Cartographic} cartographic The cartographic to duplicate.
|
|
* @param {Cartographic} [result] The object onto which to store the result.
|
|
* @returns {Cartographic} The modified result parameter or a new Cartographic instance if one was not provided. (Returns undefined if cartographic is undefined)
|
|
*/
|
|
Cartographic.clone = function (cartographic, result) {
|
|
if (!defaultValue.defined(cartographic)) {
|
|
return undefined;
|
|
}
|
|
if (!defaultValue.defined(result)) {
|
|
return new Cartographic(
|
|
cartographic.longitude,
|
|
cartographic.latitude,
|
|
cartographic.height
|
|
);
|
|
}
|
|
result.longitude = cartographic.longitude;
|
|
result.latitude = cartographic.latitude;
|
|
result.height = cartographic.height;
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Compares the provided cartographics componentwise and returns
|
|
* <code>true</code> if they are equal, <code>false</code> otherwise.
|
|
*
|
|
* @param {Cartographic} [left] The first cartographic.
|
|
* @param {Cartographic} [right] The second cartographic.
|
|
* @returns {Boolean} <code>true</code> if left and right are equal, <code>false</code> otherwise.
|
|
*/
|
|
Cartographic.equals = function (left, right) {
|
|
return (
|
|
left === right ||
|
|
(defaultValue.defined(left) &&
|
|
defaultValue.defined(right) &&
|
|
left.longitude === right.longitude &&
|
|
left.latitude === right.latitude &&
|
|
left.height === right.height)
|
|
);
|
|
};
|
|
|
|
/**
|
|
* Compares the provided cartographics componentwise and returns
|
|
* <code>true</code> if they are within the provided epsilon,
|
|
* <code>false</code> otherwise.
|
|
*
|
|
* @param {Cartographic} [left] The first cartographic.
|
|
* @param {Cartographic} [right] The second cartographic.
|
|
* @param {Number} [epsilon=0] The epsilon to use for equality testing.
|
|
* @returns {Boolean} <code>true</code> if left and right are within the provided epsilon, <code>false</code> otherwise.
|
|
*/
|
|
Cartographic.equalsEpsilon = function (left, right, epsilon) {
|
|
epsilon = defaultValue.defaultValue(epsilon, 0);
|
|
|
|
return (
|
|
left === right ||
|
|
(defaultValue.defined(left) &&
|
|
defaultValue.defined(right) &&
|
|
Math.abs(left.longitude - right.longitude) <= epsilon &&
|
|
Math.abs(left.latitude - right.latitude) <= epsilon &&
|
|
Math.abs(left.height - right.height) <= epsilon)
|
|
);
|
|
};
|
|
|
|
/**
|
|
* An immutable Cartographic instance initialized to (0.0, 0.0, 0.0).
|
|
*
|
|
* @type {Cartographic}
|
|
* @constant
|
|
*/
|
|
Cartographic.ZERO = Object.freeze(new Cartographic(0.0, 0.0, 0.0));
|
|
|
|
/**
|
|
* Duplicates this instance.
|
|
*
|
|
* @param {Cartographic} [result] The object onto which to store the result.
|
|
* @returns {Cartographic} The modified result parameter or a new Cartographic instance if one was not provided.
|
|
*/
|
|
Cartographic.prototype.clone = function (result) {
|
|
return Cartographic.clone(this, result);
|
|
};
|
|
|
|
/**
|
|
* Compares the provided against this cartographic componentwise and returns
|
|
* <code>true</code> if they are equal, <code>false</code> otherwise.
|
|
*
|
|
* @param {Cartographic} [right] The second cartographic.
|
|
* @returns {Boolean} <code>true</code> if left and right are equal, <code>false</code> otherwise.
|
|
*/
|
|
Cartographic.prototype.equals = function (right) {
|
|
return Cartographic.equals(this, right);
|
|
};
|
|
|
|
/**
|
|
* Compares the provided against this cartographic componentwise and returns
|
|
* <code>true</code> if they are within the provided epsilon,
|
|
* <code>false</code> otherwise.
|
|
*
|
|
* @param {Cartographic} [right] The second cartographic.
|
|
* @param {Number} [epsilon=0] The epsilon to use for equality testing.
|
|
* @returns {Boolean} <code>true</code> if left and right are within the provided epsilon, <code>false</code> otherwise.
|
|
*/
|
|
Cartographic.prototype.equalsEpsilon = function (right, epsilon) {
|
|
return Cartographic.equalsEpsilon(this, right, epsilon);
|
|
};
|
|
|
|
/**
|
|
* Creates a string representing this cartographic in the format '(longitude, latitude, height)'.
|
|
*
|
|
* @returns {String} A string representing the provided cartographic in the format '(longitude, latitude, height)'.
|
|
*/
|
|
Cartographic.prototype.toString = function () {
|
|
return `(${this.longitude}, ${this.latitude}, ${this.height})`;
|
|
};
|
|
|
|
function initialize(ellipsoid, x, y, z) {
|
|
x = defaultValue.defaultValue(x, 0.0);
|
|
y = defaultValue.defaultValue(y, 0.0);
|
|
z = defaultValue.defaultValue(z, 0.0);
|
|
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.number.greaterThanOrEquals("x", x, 0.0);
|
|
Check.Check.typeOf.number.greaterThanOrEquals("y", y, 0.0);
|
|
Check.Check.typeOf.number.greaterThanOrEquals("z", z, 0.0);
|
|
//>>includeEnd('debug');
|
|
|
|
ellipsoid._radii = new Cartesian3(x, y, z);
|
|
|
|
ellipsoid._radiiSquared = new Cartesian3(x * x, y * y, z * z);
|
|
|
|
ellipsoid._radiiToTheFourth = new Cartesian3(
|
|
x * x * x * x,
|
|
y * y * y * y,
|
|
z * z * z * z
|
|
);
|
|
|
|
ellipsoid._oneOverRadii = new Cartesian3(
|
|
x === 0.0 ? 0.0 : 1.0 / x,
|
|
y === 0.0 ? 0.0 : 1.0 / y,
|
|
z === 0.0 ? 0.0 : 1.0 / z
|
|
);
|
|
|
|
ellipsoid._oneOverRadiiSquared = new Cartesian3(
|
|
x === 0.0 ? 0.0 : 1.0 / (x * x),
|
|
y === 0.0 ? 0.0 : 1.0 / (y * y),
|
|
z === 0.0 ? 0.0 : 1.0 / (z * z)
|
|
);
|
|
|
|
ellipsoid._minimumRadius = Math.min(x, y, z);
|
|
|
|
ellipsoid._maximumRadius = Math.max(x, y, z);
|
|
|
|
ellipsoid._centerToleranceSquared = Math$1.CesiumMath.EPSILON1;
|
|
|
|
if (ellipsoid._radiiSquared.z !== 0) {
|
|
ellipsoid._squaredXOverSquaredZ =
|
|
ellipsoid._radiiSquared.x / ellipsoid._radiiSquared.z;
|
|
}
|
|
}
|
|
|
|
/**
|
|
* A quadratic surface defined in Cartesian coordinates by the equation
|
|
* <code>(x / a)^2 + (y / b)^2 + (z / c)^2 = 1</code>. Primarily used
|
|
* by Cesium to represent the shape of planetary bodies.
|
|
*
|
|
* Rather than constructing this object directly, one of the provided
|
|
* constants is normally used.
|
|
* @alias Ellipsoid
|
|
* @constructor
|
|
*
|
|
* @param {Number} [x=0] The radius in the x direction.
|
|
* @param {Number} [y=0] The radius in the y direction.
|
|
* @param {Number} [z=0] The radius in the z direction.
|
|
*
|
|
* @exception {DeveloperError} All radii components must be greater than or equal to zero.
|
|
*
|
|
* @see Ellipsoid.fromCartesian3
|
|
* @see Ellipsoid.WGS84
|
|
* @see Ellipsoid.UNIT_SPHERE
|
|
*/
|
|
function Ellipsoid(x, y, z) {
|
|
this._radii = undefined;
|
|
this._radiiSquared = undefined;
|
|
this._radiiToTheFourth = undefined;
|
|
this._oneOverRadii = undefined;
|
|
this._oneOverRadiiSquared = undefined;
|
|
this._minimumRadius = undefined;
|
|
this._maximumRadius = undefined;
|
|
this._centerToleranceSquared = undefined;
|
|
this._squaredXOverSquaredZ = undefined;
|
|
|
|
initialize(this, x, y, z);
|
|
}
|
|
|
|
Object.defineProperties(Ellipsoid.prototype, {
|
|
/**
|
|
* Gets the radii of the ellipsoid.
|
|
* @memberof Ellipsoid.prototype
|
|
* @type {Cartesian3}
|
|
* @readonly
|
|
*/
|
|
radii: {
|
|
get: function () {
|
|
return this._radii;
|
|
},
|
|
},
|
|
/**
|
|
* Gets the squared radii of the ellipsoid.
|
|
* @memberof Ellipsoid.prototype
|
|
* @type {Cartesian3}
|
|
* @readonly
|
|
*/
|
|
radiiSquared: {
|
|
get: function () {
|
|
return this._radiiSquared;
|
|
},
|
|
},
|
|
/**
|
|
* Gets the radii of the ellipsoid raise to the fourth power.
|
|
* @memberof Ellipsoid.prototype
|
|
* @type {Cartesian3}
|
|
* @readonly
|
|
*/
|
|
radiiToTheFourth: {
|
|
get: function () {
|
|
return this._radiiToTheFourth;
|
|
},
|
|
},
|
|
/**
|
|
* Gets one over the radii of the ellipsoid.
|
|
* @memberof Ellipsoid.prototype
|
|
* @type {Cartesian3}
|
|
* @readonly
|
|
*/
|
|
oneOverRadii: {
|
|
get: function () {
|
|
return this._oneOverRadii;
|
|
},
|
|
},
|
|
/**
|
|
* Gets one over the squared radii of the ellipsoid.
|
|
* @memberof Ellipsoid.prototype
|
|
* @type {Cartesian3}
|
|
* @readonly
|
|
*/
|
|
oneOverRadiiSquared: {
|
|
get: function () {
|
|
return this._oneOverRadiiSquared;
|
|
},
|
|
},
|
|
/**
|
|
* Gets the minimum radius of the ellipsoid.
|
|
* @memberof Ellipsoid.prototype
|
|
* @type {Number}
|
|
* @readonly
|
|
*/
|
|
minimumRadius: {
|
|
get: function () {
|
|
return this._minimumRadius;
|
|
},
|
|
},
|
|
/**
|
|
* Gets the maximum radius of the ellipsoid.
|
|
* @memberof Ellipsoid.prototype
|
|
* @type {Number}
|
|
* @readonly
|
|
*/
|
|
maximumRadius: {
|
|
get: function () {
|
|
return this._maximumRadius;
|
|
},
|
|
},
|
|
});
|
|
|
|
/**
|
|
* Duplicates an Ellipsoid instance.
|
|
*
|
|
* @param {Ellipsoid} ellipsoid The ellipsoid to duplicate.
|
|
* @param {Ellipsoid} [result] The object onto which to store the result, or undefined if a new
|
|
* instance should be created.
|
|
* @returns {Ellipsoid} The cloned Ellipsoid. (Returns undefined if ellipsoid is undefined)
|
|
*/
|
|
Ellipsoid.clone = function (ellipsoid, result) {
|
|
if (!defaultValue.defined(ellipsoid)) {
|
|
return undefined;
|
|
}
|
|
const radii = ellipsoid._radii;
|
|
|
|
if (!defaultValue.defined(result)) {
|
|
return new Ellipsoid(radii.x, radii.y, radii.z);
|
|
}
|
|
|
|
Cartesian3.clone(radii, result._radii);
|
|
Cartesian3.clone(ellipsoid._radiiSquared, result._radiiSquared);
|
|
Cartesian3.clone(ellipsoid._radiiToTheFourth, result._radiiToTheFourth);
|
|
Cartesian3.clone(ellipsoid._oneOverRadii, result._oneOverRadii);
|
|
Cartesian3.clone(ellipsoid._oneOverRadiiSquared, result._oneOverRadiiSquared);
|
|
result._minimumRadius = ellipsoid._minimumRadius;
|
|
result._maximumRadius = ellipsoid._maximumRadius;
|
|
result._centerToleranceSquared = ellipsoid._centerToleranceSquared;
|
|
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Computes an Ellipsoid from a Cartesian specifying the radii in x, y, and z directions.
|
|
*
|
|
* @param {Cartesian3} [cartesian=Cartesian3.ZERO] The ellipsoid's radius in the x, y, and z directions.
|
|
* @param {Ellipsoid} [result] The object onto which to store the result, or undefined if a new
|
|
* instance should be created.
|
|
* @returns {Ellipsoid} A new Ellipsoid instance.
|
|
*
|
|
* @exception {DeveloperError} All radii components must be greater than or equal to zero.
|
|
*
|
|
* @see Ellipsoid.WGS84
|
|
* @see Ellipsoid.UNIT_SPHERE
|
|
*/
|
|
Ellipsoid.fromCartesian3 = function (cartesian, result) {
|
|
if (!defaultValue.defined(result)) {
|
|
result = new Ellipsoid();
|
|
}
|
|
|
|
if (!defaultValue.defined(cartesian)) {
|
|
return result;
|
|
}
|
|
|
|
initialize(result, cartesian.x, cartesian.y, cartesian.z);
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* An Ellipsoid instance initialized to the WGS84 standard.
|
|
*
|
|
* @type {Ellipsoid}
|
|
* @constant
|
|
*/
|
|
Ellipsoid.WGS84 = Object.freeze(
|
|
new Ellipsoid(6378137.0, 6378137.0, 6356752.3142451793)
|
|
);
|
|
|
|
/**
|
|
* An Ellipsoid instance initialized to radii of (1.0, 1.0, 1.0).
|
|
*
|
|
* @type {Ellipsoid}
|
|
* @constant
|
|
*/
|
|
Ellipsoid.UNIT_SPHERE = Object.freeze(new Ellipsoid(1.0, 1.0, 1.0));
|
|
|
|
/**
|
|
* An Ellipsoid instance initialized to a sphere with the lunar radius.
|
|
*
|
|
* @type {Ellipsoid}
|
|
* @constant
|
|
*/
|
|
Ellipsoid.MOON = Object.freeze(
|
|
new Ellipsoid(
|
|
Math$1.CesiumMath.LUNAR_RADIUS,
|
|
Math$1.CesiumMath.LUNAR_RADIUS,
|
|
Math$1.CesiumMath.LUNAR_RADIUS
|
|
)
|
|
);
|
|
|
|
/**
|
|
* Duplicates an Ellipsoid instance.
|
|
*
|
|
* @param {Ellipsoid} [result] The object onto which to store the result, or undefined if a new
|
|
* instance should be created.
|
|
* @returns {Ellipsoid} The cloned Ellipsoid.
|
|
*/
|
|
Ellipsoid.prototype.clone = function (result) {
|
|
return Ellipsoid.clone(this, result);
|
|
};
|
|
|
|
/**
|
|
* The number of elements used to pack the object into an array.
|
|
* @type {Number}
|
|
*/
|
|
Ellipsoid.packedLength = Cartesian3.packedLength;
|
|
|
|
/**
|
|
* Stores the provided instance into the provided array.
|
|
*
|
|
* @param {Ellipsoid} value The value to pack.
|
|
* @param {Number[]} array The array to pack into.
|
|
* @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
|
|
*
|
|
* @returns {Number[]} The array that was packed into
|
|
*/
|
|
Ellipsoid.pack = function (value, array, startingIndex) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("value", value);
|
|
Check.Check.defined("array", array);
|
|
//>>includeEnd('debug');
|
|
|
|
startingIndex = defaultValue.defaultValue(startingIndex, 0);
|
|
|
|
Cartesian3.pack(value._radii, array, startingIndex);
|
|
|
|
return array;
|
|
};
|
|
|
|
/**
|
|
* Retrieves an instance from a packed array.
|
|
*
|
|
* @param {Number[]} array The packed array.
|
|
* @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
|
|
* @param {Ellipsoid} [result] The object into which to store the result.
|
|
* @returns {Ellipsoid} The modified result parameter or a new Ellipsoid instance if one was not provided.
|
|
*/
|
|
Ellipsoid.unpack = function (array, startingIndex, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.defined("array", array);
|
|
//>>includeEnd('debug');
|
|
|
|
startingIndex = defaultValue.defaultValue(startingIndex, 0);
|
|
|
|
const radii = Cartesian3.unpack(array, startingIndex);
|
|
return Ellipsoid.fromCartesian3(radii, result);
|
|
};
|
|
|
|
/**
|
|
* Computes the unit vector directed from the center of this ellipsoid toward the provided Cartesian position.
|
|
* @function
|
|
*
|
|
* @param {Cartesian3} cartesian The Cartesian for which to to determine the geocentric normal.
|
|
* @param {Cartesian3} [result] The object onto which to store the result.
|
|
* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if none was provided.
|
|
*/
|
|
Ellipsoid.prototype.geocentricSurfaceNormal = Cartesian3.normalize;
|
|
|
|
/**
|
|
* Computes the normal of the plane tangent to the surface of the ellipsoid at the provided position.
|
|
*
|
|
* @param {Cartographic} cartographic The cartographic position for which to to determine the geodetic normal.
|
|
* @param {Cartesian3} [result] The object onto which to store the result.
|
|
* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if none was provided.
|
|
*/
|
|
Ellipsoid.prototype.geodeticSurfaceNormalCartographic = function (
|
|
cartographic,
|
|
result
|
|
) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("cartographic", cartographic);
|
|
//>>includeEnd('debug');
|
|
|
|
const longitude = cartographic.longitude;
|
|
const latitude = cartographic.latitude;
|
|
const cosLatitude = Math.cos(latitude);
|
|
|
|
const x = cosLatitude * Math.cos(longitude);
|
|
const y = cosLatitude * Math.sin(longitude);
|
|
const z = Math.sin(latitude);
|
|
|
|
if (!defaultValue.defined(result)) {
|
|
result = new Cartesian3();
|
|
}
|
|
result.x = x;
|
|
result.y = y;
|
|
result.z = z;
|
|
return Cartesian3.normalize(result, result);
|
|
};
|
|
|
|
/**
|
|
* Computes the normal of the plane tangent to the surface of the ellipsoid at the provided position.
|
|
*
|
|
* @param {Cartesian3} cartesian The Cartesian position for which to to determine the surface normal.
|
|
* @param {Cartesian3} [result] The object onto which to store the result.
|
|
* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if none was provided, or undefined if a normal cannot be found.
|
|
*/
|
|
Ellipsoid.prototype.geodeticSurfaceNormal = function (cartesian, result) {
|
|
if (
|
|
Cartesian3.equalsEpsilon(cartesian, Cartesian3.ZERO, Math$1.CesiumMath.EPSILON14)
|
|
) {
|
|
return undefined;
|
|
}
|
|
if (!defaultValue.defined(result)) {
|
|
result = new Cartesian3();
|
|
}
|
|
result = Cartesian3.multiplyComponents(
|
|
cartesian,
|
|
this._oneOverRadiiSquared,
|
|
result
|
|
);
|
|
return Cartesian3.normalize(result, result);
|
|
};
|
|
|
|
const cartographicToCartesianNormal = new Cartesian3();
|
|
const cartographicToCartesianK = new Cartesian3();
|
|
|
|
/**
|
|
* Converts the provided cartographic to Cartesian representation.
|
|
*
|
|
* @param {Cartographic} cartographic The cartographic position.
|
|
* @param {Cartesian3} [result] The object onto which to store the result.
|
|
* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if none was provided.
|
|
*
|
|
* @example
|
|
* //Create a Cartographic and determine it's Cartesian representation on a WGS84 ellipsoid.
|
|
* const position = new Cesium.Cartographic(Cesium.Math.toRadians(21), Cesium.Math.toRadians(78), 5000);
|
|
* const cartesianPosition = Cesium.Ellipsoid.WGS84.cartographicToCartesian(position);
|
|
*/
|
|
Ellipsoid.prototype.cartographicToCartesian = function (cartographic, result) {
|
|
//`cartographic is required` is thrown from geodeticSurfaceNormalCartographic.
|
|
const n = cartographicToCartesianNormal;
|
|
const k = cartographicToCartesianK;
|
|
this.geodeticSurfaceNormalCartographic(cartographic, n);
|
|
Cartesian3.multiplyComponents(this._radiiSquared, n, k);
|
|
const gamma = Math.sqrt(Cartesian3.dot(n, k));
|
|
Cartesian3.divideByScalar(k, gamma, k);
|
|
Cartesian3.multiplyByScalar(n, cartographic.height, n);
|
|
|
|
if (!defaultValue.defined(result)) {
|
|
result = new Cartesian3();
|
|
}
|
|
return Cartesian3.add(k, n, result);
|
|
};
|
|
|
|
/**
|
|
* Converts the provided array of cartographics to an array of Cartesians.
|
|
*
|
|
* @param {Cartographic[]} cartographics An array of cartographic positions.
|
|
* @param {Cartesian3[]} [result] The object onto which to store the result.
|
|
* @returns {Cartesian3[]} The modified result parameter or a new Array instance if none was provided.
|
|
*
|
|
* @example
|
|
* //Convert an array of Cartographics and determine their Cartesian representation on a WGS84 ellipsoid.
|
|
* const positions = [new Cesium.Cartographic(Cesium.Math.toRadians(21), Cesium.Math.toRadians(78), 0),
|
|
* new Cesium.Cartographic(Cesium.Math.toRadians(21.321), Cesium.Math.toRadians(78.123), 100),
|
|
* new Cesium.Cartographic(Cesium.Math.toRadians(21.645), Cesium.Math.toRadians(78.456), 250)];
|
|
* const cartesianPositions = Cesium.Ellipsoid.WGS84.cartographicArrayToCartesianArray(positions);
|
|
*/
|
|
Ellipsoid.prototype.cartographicArrayToCartesianArray = function (
|
|
cartographics,
|
|
result
|
|
) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.defined("cartographics", cartographics);
|
|
//>>includeEnd('debug')
|
|
|
|
const length = cartographics.length;
|
|
if (!defaultValue.defined(result)) {
|
|
result = new Array(length);
|
|
} else {
|
|
result.length = length;
|
|
}
|
|
for (let i = 0; i < length; i++) {
|
|
result[i] = this.cartographicToCartesian(cartographics[i], result[i]);
|
|
}
|
|
return result;
|
|
};
|
|
|
|
const cartesianToCartographicN = new Cartesian3();
|
|
const cartesianToCartographicP = new Cartesian3();
|
|
const cartesianToCartographicH = new Cartesian3();
|
|
|
|
/**
|
|
* Converts the provided cartesian to cartographic representation.
|
|
* The cartesian is undefined at the center of the ellipsoid.
|
|
*
|
|
* @param {Cartesian3} cartesian The Cartesian position to convert to cartographic representation.
|
|
* @param {Cartographic} [result] The object onto which to store the result.
|
|
* @returns {Cartographic} The modified result parameter, new Cartographic instance if none was provided, or undefined if the cartesian is at the center of the ellipsoid.
|
|
*
|
|
* @example
|
|
* //Create a Cartesian and determine it's Cartographic representation on a WGS84 ellipsoid.
|
|
* const position = new Cesium.Cartesian3(17832.12, 83234.52, 952313.73);
|
|
* const cartographicPosition = Cesium.Ellipsoid.WGS84.cartesianToCartographic(position);
|
|
*/
|
|
Ellipsoid.prototype.cartesianToCartographic = function (cartesian, result) {
|
|
//`cartesian is required.` is thrown from scaleToGeodeticSurface
|
|
const p = this.scaleToGeodeticSurface(cartesian, cartesianToCartographicP);
|
|
|
|
if (!defaultValue.defined(p)) {
|
|
return undefined;
|
|
}
|
|
|
|
const n = this.geodeticSurfaceNormal(p, cartesianToCartographicN);
|
|
const h = Cartesian3.subtract(cartesian, p, cartesianToCartographicH);
|
|
|
|
const longitude = Math.atan2(n.y, n.x);
|
|
const latitude = Math.asin(n.z);
|
|
const height =
|
|
Math$1.CesiumMath.sign(Cartesian3.dot(h, cartesian)) * Cartesian3.magnitude(h);
|
|
|
|
if (!defaultValue.defined(result)) {
|
|
return new Cartographic(longitude, latitude, height);
|
|
}
|
|
result.longitude = longitude;
|
|
result.latitude = latitude;
|
|
result.height = height;
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Converts the provided array of cartesians to an array of cartographics.
|
|
*
|
|
* @param {Cartesian3[]} cartesians An array of Cartesian positions.
|
|
* @param {Cartographic[]} [result] The object onto which to store the result.
|
|
* @returns {Cartographic[]} The modified result parameter or a new Array instance if none was provided.
|
|
*
|
|
* @example
|
|
* //Create an array of Cartesians and determine their Cartographic representation on a WGS84 ellipsoid.
|
|
* const positions = [new Cesium.Cartesian3(17832.12, 83234.52, 952313.73),
|
|
* new Cesium.Cartesian3(17832.13, 83234.53, 952313.73),
|
|
* new Cesium.Cartesian3(17832.14, 83234.54, 952313.73)]
|
|
* const cartographicPositions = Cesium.Ellipsoid.WGS84.cartesianArrayToCartographicArray(positions);
|
|
*/
|
|
Ellipsoid.prototype.cartesianArrayToCartographicArray = function (
|
|
cartesians,
|
|
result
|
|
) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.defined("cartesians", cartesians);
|
|
//>>includeEnd('debug');
|
|
|
|
const length = cartesians.length;
|
|
if (!defaultValue.defined(result)) {
|
|
result = new Array(length);
|
|
} else {
|
|
result.length = length;
|
|
}
|
|
for (let i = 0; i < length; ++i) {
|
|
result[i] = this.cartesianToCartographic(cartesians[i], result[i]);
|
|
}
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Scales the provided Cartesian position along the geodetic surface normal
|
|
* so that it is on the surface of this ellipsoid. If the position is
|
|
* at the center of the ellipsoid, this function returns undefined.
|
|
*
|
|
* @param {Cartesian3} cartesian The Cartesian position to scale.
|
|
* @param {Cartesian3} [result] The object onto which to store the result.
|
|
* @returns {Cartesian3} The modified result parameter, a new Cartesian3 instance if none was provided, or undefined if the position is at the center.
|
|
*/
|
|
Ellipsoid.prototype.scaleToGeodeticSurface = function (cartesian, result) {
|
|
return scaleToGeodeticSurface(
|
|
cartesian,
|
|
this._oneOverRadii,
|
|
this._oneOverRadiiSquared,
|
|
this._centerToleranceSquared,
|
|
result
|
|
);
|
|
};
|
|
|
|
/**
|
|
* Scales the provided Cartesian position along the geocentric surface normal
|
|
* so that it is on the surface of this ellipsoid.
|
|
*
|
|
* @param {Cartesian3} cartesian The Cartesian position to scale.
|
|
* @param {Cartesian3} [result] The object onto which to store the result.
|
|
* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if none was provided.
|
|
*/
|
|
Ellipsoid.prototype.scaleToGeocentricSurface = function (cartesian, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("cartesian", cartesian);
|
|
//>>includeEnd('debug');
|
|
|
|
if (!defaultValue.defined(result)) {
|
|
result = new Cartesian3();
|
|
}
|
|
|
|
const positionX = cartesian.x;
|
|
const positionY = cartesian.y;
|
|
const positionZ = cartesian.z;
|
|
const oneOverRadiiSquared = this._oneOverRadiiSquared;
|
|
|
|
const beta =
|
|
1.0 /
|
|
Math.sqrt(
|
|
positionX * positionX * oneOverRadiiSquared.x +
|
|
positionY * positionY * oneOverRadiiSquared.y +
|
|
positionZ * positionZ * oneOverRadiiSquared.z
|
|
);
|
|
|
|
return Cartesian3.multiplyByScalar(cartesian, beta, result);
|
|
};
|
|
|
|
/**
|
|
* Transforms a Cartesian X, Y, Z position to the ellipsoid-scaled space by multiplying
|
|
* its components by the result of {@link Ellipsoid#oneOverRadii}.
|
|
*
|
|
* @param {Cartesian3} position The position to transform.
|
|
* @param {Cartesian3} [result] The position to which to copy the result, or undefined to create and
|
|
* return a new instance.
|
|
* @returns {Cartesian3} The position expressed in the scaled space. The returned instance is the
|
|
* one passed as the result parameter if it is not undefined, or a new instance of it is.
|
|
*/
|
|
Ellipsoid.prototype.transformPositionToScaledSpace = function (
|
|
position,
|
|
result
|
|
) {
|
|
if (!defaultValue.defined(result)) {
|
|
result = new Cartesian3();
|
|
}
|
|
|
|
return Cartesian3.multiplyComponents(position, this._oneOverRadii, result);
|
|
};
|
|
|
|
/**
|
|
* Transforms a Cartesian X, Y, Z position from the ellipsoid-scaled space by multiplying
|
|
* its components by the result of {@link Ellipsoid#radii}.
|
|
*
|
|
* @param {Cartesian3} position The position to transform.
|
|
* @param {Cartesian3} [result] The position to which to copy the result, or undefined to create and
|
|
* return a new instance.
|
|
* @returns {Cartesian3} The position expressed in the unscaled space. The returned instance is the
|
|
* one passed as the result parameter if it is not undefined, or a new instance of it is.
|
|
*/
|
|
Ellipsoid.prototype.transformPositionFromScaledSpace = function (
|
|
position,
|
|
result
|
|
) {
|
|
if (!defaultValue.defined(result)) {
|
|
result = new Cartesian3();
|
|
}
|
|
|
|
return Cartesian3.multiplyComponents(position, this._radii, result);
|
|
};
|
|
|
|
/**
|
|
* Compares this Ellipsoid against the provided Ellipsoid componentwise and returns
|
|
* <code>true</code> if they are equal, <code>false</code> otherwise.
|
|
*
|
|
* @param {Ellipsoid} [right] The other Ellipsoid.
|
|
* @returns {Boolean} <code>true</code> if they are equal, <code>false</code> otherwise.
|
|
*/
|
|
Ellipsoid.prototype.equals = function (right) {
|
|
return (
|
|
this === right ||
|
|
(defaultValue.defined(right) && Cartesian3.equals(this._radii, right._radii))
|
|
);
|
|
};
|
|
|
|
/**
|
|
* Creates a string representing this Ellipsoid in the format '(radii.x, radii.y, radii.z)'.
|
|
*
|
|
* @returns {String} A string representing this ellipsoid in the format '(radii.x, radii.y, radii.z)'.
|
|
*/
|
|
Ellipsoid.prototype.toString = function () {
|
|
return this._radii.toString();
|
|
};
|
|
|
|
/**
|
|
* Computes a point which is the intersection of the surface normal with the z-axis.
|
|
*
|
|
* @param {Cartesian3} position the position. must be on the surface of the ellipsoid.
|
|
* @param {Number} [buffer = 0.0] A buffer to subtract from the ellipsoid size when checking if the point is inside the ellipsoid.
|
|
* In earth case, with common earth datums, there is no need for this buffer since the intersection point is always (relatively) very close to the center.
|
|
* In WGS84 datum, intersection point is at max z = +-42841.31151331382 (0.673% of z-axis).
|
|
* Intersection point could be outside the ellipsoid if the ratio of MajorAxis / AxisOfRotation is bigger than the square root of 2
|
|
* @param {Cartesian3} [result] The cartesian to which to copy the result, or undefined to create and
|
|
* return a new instance.
|
|
* @returns {Cartesian3 | undefined} the intersection point if it's inside the ellipsoid, undefined otherwise
|
|
*
|
|
* @exception {DeveloperError} position is required.
|
|
* @exception {DeveloperError} Ellipsoid must be an ellipsoid of revolution (radii.x == radii.y).
|
|
* @exception {DeveloperError} Ellipsoid.radii.z must be greater than 0.
|
|
*/
|
|
Ellipsoid.prototype.getSurfaceNormalIntersectionWithZAxis = function (
|
|
position,
|
|
buffer,
|
|
result
|
|
) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("position", position);
|
|
|
|
if (
|
|
!Math$1.CesiumMath.equalsEpsilon(
|
|
this._radii.x,
|
|
this._radii.y,
|
|
Math$1.CesiumMath.EPSILON15
|
|
)
|
|
) {
|
|
throw new Check.DeveloperError(
|
|
"Ellipsoid must be an ellipsoid of revolution (radii.x == radii.y)"
|
|
);
|
|
}
|
|
|
|
Check.Check.typeOf.number.greaterThan("Ellipsoid.radii.z", this._radii.z, 0);
|
|
//>>includeEnd('debug');
|
|
|
|
buffer = defaultValue.defaultValue(buffer, 0.0);
|
|
|
|
const squaredXOverSquaredZ = this._squaredXOverSquaredZ;
|
|
|
|
if (!defaultValue.defined(result)) {
|
|
result = new Cartesian3();
|
|
}
|
|
|
|
result.x = 0.0;
|
|
result.y = 0.0;
|
|
result.z = position.z * (1 - squaredXOverSquaredZ);
|
|
|
|
if (Math.abs(result.z) >= this._radii.z - buffer) {
|
|
return undefined;
|
|
}
|
|
|
|
return result;
|
|
};
|
|
|
|
const abscissas = [
|
|
0.14887433898163,
|
|
0.43339539412925,
|
|
0.67940956829902,
|
|
0.86506336668898,
|
|
0.97390652851717,
|
|
0.0,
|
|
];
|
|
const weights = [
|
|
0.29552422471475,
|
|
0.26926671930999,
|
|
0.21908636251598,
|
|
0.14945134915058,
|
|
0.066671344308684,
|
|
0.0,
|
|
];
|
|
|
|
/**
|
|
* Compute the 10th order Gauss-Legendre Quadrature of the given definite integral.
|
|
*
|
|
* @param {Number} a The lower bound for the integration.
|
|
* @param {Number} b The upper bound for the integration.
|
|
* @param {Ellipsoid~RealValuedScalarFunction} func The function to integrate.
|
|
* @returns {Number} The value of the integral of the given function over the given domain.
|
|
*
|
|
* @private
|
|
*/
|
|
function gaussLegendreQuadrature(a, b, func) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.number("a", a);
|
|
Check.Check.typeOf.number("b", b);
|
|
Check.Check.typeOf.func("func", func);
|
|
//>>includeEnd('debug');
|
|
|
|
// The range is half of the normal range since the five weights add to one (ten weights add to two).
|
|
// The values of the abscissas are multiplied by two to account for this.
|
|
const xMean = 0.5 * (b + a);
|
|
const xRange = 0.5 * (b - a);
|
|
|
|
let sum = 0.0;
|
|
for (let i = 0; i < 5; i++) {
|
|
const dx = xRange * abscissas[i];
|
|
sum += weights[i] * (func(xMean + dx) + func(xMean - dx));
|
|
}
|
|
|
|
// Scale the sum to the range of x.
|
|
sum *= xRange;
|
|
return sum;
|
|
}
|
|
|
|
/**
|
|
* A real valued scalar function.
|
|
* @callback Ellipsoid~RealValuedScalarFunction
|
|
*
|
|
* @param {Number} x The value used to evaluate the function.
|
|
* @returns {Number} The value of the function at x.
|
|
*
|
|
* @private
|
|
*/
|
|
|
|
/**
|
|
* Computes an approximation of the surface area of a rectangle on the surface of an ellipsoid using
|
|
* Gauss-Legendre 10th order quadrature.
|
|
*
|
|
* @param {Rectangle} rectangle The rectangle used for computing the surface area.
|
|
* @returns {Number} The approximate area of the rectangle on the surface of this ellipsoid.
|
|
*/
|
|
Ellipsoid.prototype.surfaceArea = function (rectangle) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("rectangle", rectangle);
|
|
//>>includeEnd('debug');
|
|
const minLongitude = rectangle.west;
|
|
let maxLongitude = rectangle.east;
|
|
const minLatitude = rectangle.south;
|
|
const maxLatitude = rectangle.north;
|
|
|
|
while (maxLongitude < minLongitude) {
|
|
maxLongitude += Math$1.CesiumMath.TWO_PI;
|
|
}
|
|
|
|
const radiiSquared = this._radiiSquared;
|
|
const a2 = radiiSquared.x;
|
|
const b2 = radiiSquared.y;
|
|
const c2 = radiiSquared.z;
|
|
const a2b2 = a2 * b2;
|
|
return gaussLegendreQuadrature(minLatitude, maxLatitude, function (lat) {
|
|
// phi represents the angle measured from the north pole
|
|
// sin(phi) = sin(pi / 2 - lat) = cos(lat), cos(phi) is similar
|
|
const sinPhi = Math.cos(lat);
|
|
const cosPhi = Math.sin(lat);
|
|
return (
|
|
Math.cos(lat) *
|
|
gaussLegendreQuadrature(minLongitude, maxLongitude, function (lon) {
|
|
const cosTheta = Math.cos(lon);
|
|
const sinTheta = Math.sin(lon);
|
|
return Math.sqrt(
|
|
a2b2 * cosPhi * cosPhi +
|
|
c2 *
|
|
(b2 * cosTheta * cosTheta + a2 * sinTheta * sinTheta) *
|
|
sinPhi *
|
|
sinPhi
|
|
);
|
|
})
|
|
);
|
|
});
|
|
};
|
|
|
|
/**
|
|
* A 3x3 matrix, indexable as a column-major order array.
|
|
* Constructor parameters are in row-major order for code readability.
|
|
* @alias Matrix3
|
|
* @constructor
|
|
* @implements {ArrayLike<number>}
|
|
*
|
|
* @param {Number} [column0Row0=0.0] The value for column 0, row 0.
|
|
* @param {Number} [column1Row0=0.0] The value for column 1, row 0.
|
|
* @param {Number} [column2Row0=0.0] The value for column 2, row 0.
|
|
* @param {Number} [column0Row1=0.0] The value for column 0, row 1.
|
|
* @param {Number} [column1Row1=0.0] The value for column 1, row 1.
|
|
* @param {Number} [column2Row1=0.0] The value for column 2, row 1.
|
|
* @param {Number} [column0Row2=0.0] The value for column 0, row 2.
|
|
* @param {Number} [column1Row2=0.0] The value for column 1, row 2.
|
|
* @param {Number} [column2Row2=0.0] The value for column 2, row 2.
|
|
*
|
|
* @see Matrix3.fromArray
|
|
* @see Matrix3.fromColumnMajorArray
|
|
* @see Matrix3.fromRowMajorArray
|
|
* @see Matrix3.fromQuaternion
|
|
* @see Matrix3.fromHeadingPitchRoll
|
|
* @see Matrix3.fromScale
|
|
* @see Matrix3.fromUniformScale
|
|
* @see Matrix3.fromCrossProduct
|
|
* @see Matrix3.fromRotationX
|
|
* @see Matrix3.fromRotationY
|
|
* @see Matrix3.fromRotationZ
|
|
* @see Matrix2
|
|
* @see Matrix4
|
|
*/
|
|
function Matrix3(
|
|
column0Row0,
|
|
column1Row0,
|
|
column2Row0,
|
|
column0Row1,
|
|
column1Row1,
|
|
column2Row1,
|
|
column0Row2,
|
|
column1Row2,
|
|
column2Row2
|
|
) {
|
|
this[0] = defaultValue.defaultValue(column0Row0, 0.0);
|
|
this[1] = defaultValue.defaultValue(column0Row1, 0.0);
|
|
this[2] = defaultValue.defaultValue(column0Row2, 0.0);
|
|
this[3] = defaultValue.defaultValue(column1Row0, 0.0);
|
|
this[4] = defaultValue.defaultValue(column1Row1, 0.0);
|
|
this[5] = defaultValue.defaultValue(column1Row2, 0.0);
|
|
this[6] = defaultValue.defaultValue(column2Row0, 0.0);
|
|
this[7] = defaultValue.defaultValue(column2Row1, 0.0);
|
|
this[8] = defaultValue.defaultValue(column2Row2, 0.0);
|
|
}
|
|
|
|
/**
|
|
* The number of elements used to pack the object into an array.
|
|
* @type {Number}
|
|
*/
|
|
Matrix3.packedLength = 9;
|
|
|
|
/**
|
|
* Stores the provided instance into the provided array.
|
|
*
|
|
* @param {Matrix3} value The value to pack.
|
|
* @param {Number[]} array The array to pack into.
|
|
* @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
|
|
*
|
|
* @returns {Number[]} The array that was packed into
|
|
*/
|
|
Matrix3.pack = function (value, array, startingIndex) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("value", value);
|
|
Check.Check.defined("array", array);
|
|
//>>includeEnd('debug');
|
|
|
|
startingIndex = defaultValue.defaultValue(startingIndex, 0);
|
|
|
|
array[startingIndex++] = value[0];
|
|
array[startingIndex++] = value[1];
|
|
array[startingIndex++] = value[2];
|
|
array[startingIndex++] = value[3];
|
|
array[startingIndex++] = value[4];
|
|
array[startingIndex++] = value[5];
|
|
array[startingIndex++] = value[6];
|
|
array[startingIndex++] = value[7];
|
|
array[startingIndex++] = value[8];
|
|
|
|
return array;
|
|
};
|
|
|
|
/**
|
|
* Retrieves an instance from a packed array.
|
|
*
|
|
* @param {Number[]} array The packed array.
|
|
* @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
|
|
* @param {Matrix3} [result] The object into which to store the result.
|
|
* @returns {Matrix3} The modified result parameter or a new Matrix3 instance if one was not provided.
|
|
*/
|
|
Matrix3.unpack = function (array, startingIndex, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.defined("array", array);
|
|
//>>includeEnd('debug');
|
|
|
|
startingIndex = defaultValue.defaultValue(startingIndex, 0);
|
|
|
|
if (!defaultValue.defined(result)) {
|
|
result = new Matrix3();
|
|
}
|
|
|
|
result[0] = array[startingIndex++];
|
|
result[1] = array[startingIndex++];
|
|
result[2] = array[startingIndex++];
|
|
result[3] = array[startingIndex++];
|
|
result[4] = array[startingIndex++];
|
|
result[5] = array[startingIndex++];
|
|
result[6] = array[startingIndex++];
|
|
result[7] = array[startingIndex++];
|
|
result[8] = array[startingIndex++];
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Flattens an array of Matrix3s into an array of components. The components
|
|
* are stored in column-major order.
|
|
*
|
|
* @param {Matrix3[]} array The array of matrices to pack.
|
|
* @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.
|
|
* @returns {Number[]} The packed array.
|
|
*/
|
|
Matrix3.packArray = function (array, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.defined("array", array);
|
|
//>>includeEnd('debug');
|
|
|
|
const length = array.length;
|
|
const resultLength = length * 9;
|
|
if (!defaultValue.defined(result)) {
|
|
result = new Array(resultLength);
|
|
} else if (!Array.isArray(result) && result.length !== resultLength) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
throw new Check.DeveloperError(
|
|
"If result is a typed array, it must have exactly array.length * 9 elements"
|
|
);
|
|
//>>includeEnd('debug');
|
|
} else if (result.length !== resultLength) {
|
|
result.length = resultLength;
|
|
}
|
|
|
|
for (let i = 0; i < length; ++i) {
|
|
Matrix3.pack(array[i], result, i * 9);
|
|
}
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Unpacks an array of column-major matrix components into an array of Matrix3s.
|
|
*
|
|
* @param {Number[]} array The array of components to unpack.
|
|
* @param {Matrix3[]} [result] The array onto which to store the result.
|
|
* @returns {Matrix3[]} The unpacked array.
|
|
*/
|
|
Matrix3.unpackArray = function (array, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.defined("array", array);
|
|
Check.Check.typeOf.number.greaterThanOrEquals("array.length", array.length, 9);
|
|
if (array.length % 9 !== 0) {
|
|
throw new Check.DeveloperError("array length must be a multiple of 9.");
|
|
}
|
|
//>>includeEnd('debug');
|
|
|
|
const length = array.length;
|
|
if (!defaultValue.defined(result)) {
|
|
result = new Array(length / 9);
|
|
} else {
|
|
result.length = length / 9;
|
|
}
|
|
|
|
for (let i = 0; i < length; i += 9) {
|
|
const index = i / 9;
|
|
result[index] = Matrix3.unpack(array, i, result[index]);
|
|
}
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Duplicates a Matrix3 instance.
|
|
*
|
|
* @param {Matrix3} matrix The matrix to duplicate.
|
|
* @param {Matrix3} [result] The object onto which to store the result.
|
|
* @returns {Matrix3} The modified result parameter or a new Matrix3 instance if one was not provided. (Returns undefined if matrix is undefined)
|
|
*/
|
|
Matrix3.clone = function (matrix, result) {
|
|
if (!defaultValue.defined(matrix)) {
|
|
return undefined;
|
|
}
|
|
if (!defaultValue.defined(result)) {
|
|
return new Matrix3(
|
|
matrix[0],
|
|
matrix[3],
|
|
matrix[6],
|
|
matrix[1],
|
|
matrix[4],
|
|
matrix[7],
|
|
matrix[2],
|
|
matrix[5],
|
|
matrix[8]
|
|
);
|
|
}
|
|
result[0] = matrix[0];
|
|
result[1] = matrix[1];
|
|
result[2] = matrix[2];
|
|
result[3] = matrix[3];
|
|
result[4] = matrix[4];
|
|
result[5] = matrix[5];
|
|
result[6] = matrix[6];
|
|
result[7] = matrix[7];
|
|
result[8] = matrix[8];
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Creates a Matrix3 from 9 consecutive elements in an array.
|
|
*
|
|
* @function
|
|
* @param {Number[]} array The array whose 9 consecutive elements correspond to the positions of the matrix. Assumes column-major order.
|
|
* @param {Number} [startingIndex=0] The offset into the array of the first element, which corresponds to first column first row position in the matrix.
|
|
* @param {Matrix3} [result] The object onto which to store the result.
|
|
* @returns {Matrix3} The modified result parameter or a new Matrix3 instance if one was not provided.
|
|
*
|
|
* @example
|
|
* // Create the Matrix3:
|
|
* // [1.0, 2.0, 3.0]
|
|
* // [1.0, 2.0, 3.0]
|
|
* // [1.0, 2.0, 3.0]
|
|
*
|
|
* const v = [1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 3.0, 3.0, 3.0];
|
|
* const m = Cesium.Matrix3.fromArray(v);
|
|
*
|
|
* // Create same Matrix3 with using an offset into an array
|
|
* const v2 = [0.0, 0.0, 1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 3.0, 3.0, 3.0];
|
|
* const m2 = Cesium.Matrix3.fromArray(v2, 2);
|
|
*/
|
|
Matrix3.fromArray = Matrix3.unpack;
|
|
|
|
/**
|
|
* Creates a Matrix3 instance from a column-major order array.
|
|
*
|
|
* @param {Number[]} values The column-major order array.
|
|
* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
|
|
* @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
|
|
*/
|
|
Matrix3.fromColumnMajorArray = function (values, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.defined("values", values);
|
|
//>>includeEnd('debug');
|
|
|
|
return Matrix3.clone(values, result);
|
|
};
|
|
|
|
/**
|
|
* Creates a Matrix3 instance from a row-major order array.
|
|
* The resulting matrix will be in column-major order.
|
|
*
|
|
* @param {Number[]} values The row-major order array.
|
|
* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
|
|
* @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
|
|
*/
|
|
Matrix3.fromRowMajorArray = function (values, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.defined("values", values);
|
|
//>>includeEnd('debug');
|
|
|
|
if (!defaultValue.defined(result)) {
|
|
return new Matrix3(
|
|
values[0],
|
|
values[1],
|
|
values[2],
|
|
values[3],
|
|
values[4],
|
|
values[5],
|
|
values[6],
|
|
values[7],
|
|
values[8]
|
|
);
|
|
}
|
|
result[0] = values[0];
|
|
result[1] = values[3];
|
|
result[2] = values[6];
|
|
result[3] = values[1];
|
|
result[4] = values[4];
|
|
result[5] = values[7];
|
|
result[6] = values[2];
|
|
result[7] = values[5];
|
|
result[8] = values[8];
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Computes a 3x3 rotation matrix from the provided quaternion.
|
|
*
|
|
* @param {Quaternion} quaternion the quaternion to use.
|
|
* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
|
|
* @returns {Matrix3} The 3x3 rotation matrix from this quaternion.
|
|
*/
|
|
Matrix3.fromQuaternion = function (quaternion, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("quaternion", quaternion);
|
|
//>>includeEnd('debug');
|
|
|
|
const x2 = quaternion.x * quaternion.x;
|
|
const xy = quaternion.x * quaternion.y;
|
|
const xz = quaternion.x * quaternion.z;
|
|
const xw = quaternion.x * quaternion.w;
|
|
const y2 = quaternion.y * quaternion.y;
|
|
const yz = quaternion.y * quaternion.z;
|
|
const yw = quaternion.y * quaternion.w;
|
|
const z2 = quaternion.z * quaternion.z;
|
|
const zw = quaternion.z * quaternion.w;
|
|
const w2 = quaternion.w * quaternion.w;
|
|
|
|
const m00 = x2 - y2 - z2 + w2;
|
|
const m01 = 2.0 * (xy - zw);
|
|
const m02 = 2.0 * (xz + yw);
|
|
|
|
const m10 = 2.0 * (xy + zw);
|
|
const m11 = -x2 + y2 - z2 + w2;
|
|
const m12 = 2.0 * (yz - xw);
|
|
|
|
const m20 = 2.0 * (xz - yw);
|
|
const m21 = 2.0 * (yz + xw);
|
|
const m22 = -x2 - y2 + z2 + w2;
|
|
|
|
if (!defaultValue.defined(result)) {
|
|
return new Matrix3(m00, m01, m02, m10, m11, m12, m20, m21, m22);
|
|
}
|
|
result[0] = m00;
|
|
result[1] = m10;
|
|
result[2] = m20;
|
|
result[3] = m01;
|
|
result[4] = m11;
|
|
result[5] = m21;
|
|
result[6] = m02;
|
|
result[7] = m12;
|
|
result[8] = m22;
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Computes a 3x3 rotation matrix from the provided headingPitchRoll. (see http://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles )
|
|
*
|
|
* @param {HeadingPitchRoll} headingPitchRoll the headingPitchRoll to use.
|
|
* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
|
|
* @returns {Matrix3} The 3x3 rotation matrix from this headingPitchRoll.
|
|
*/
|
|
Matrix3.fromHeadingPitchRoll = function (headingPitchRoll, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("headingPitchRoll", headingPitchRoll);
|
|
//>>includeEnd('debug');
|
|
|
|
const cosTheta = Math.cos(-headingPitchRoll.pitch);
|
|
const cosPsi = Math.cos(-headingPitchRoll.heading);
|
|
const cosPhi = Math.cos(headingPitchRoll.roll);
|
|
const sinTheta = Math.sin(-headingPitchRoll.pitch);
|
|
const sinPsi = Math.sin(-headingPitchRoll.heading);
|
|
const sinPhi = Math.sin(headingPitchRoll.roll);
|
|
|
|
const m00 = cosTheta * cosPsi;
|
|
const m01 = -cosPhi * sinPsi + sinPhi * sinTheta * cosPsi;
|
|
const m02 = sinPhi * sinPsi + cosPhi * sinTheta * cosPsi;
|
|
|
|
const m10 = cosTheta * sinPsi;
|
|
const m11 = cosPhi * cosPsi + sinPhi * sinTheta * sinPsi;
|
|
const m12 = -sinPhi * cosPsi + cosPhi * sinTheta * sinPsi;
|
|
|
|
const m20 = -sinTheta;
|
|
const m21 = sinPhi * cosTheta;
|
|
const m22 = cosPhi * cosTheta;
|
|
|
|
if (!defaultValue.defined(result)) {
|
|
return new Matrix3(m00, m01, m02, m10, m11, m12, m20, m21, m22);
|
|
}
|
|
result[0] = m00;
|
|
result[1] = m10;
|
|
result[2] = m20;
|
|
result[3] = m01;
|
|
result[4] = m11;
|
|
result[5] = m21;
|
|
result[6] = m02;
|
|
result[7] = m12;
|
|
result[8] = m22;
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Computes a Matrix3 instance representing a non-uniform scale.
|
|
*
|
|
* @param {Cartesian3} scale The x, y, and z scale factors.
|
|
* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
|
|
* @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
|
|
*
|
|
* @example
|
|
* // Creates
|
|
* // [7.0, 0.0, 0.0]
|
|
* // [0.0, 8.0, 0.0]
|
|
* // [0.0, 0.0, 9.0]
|
|
* const m = Cesium.Matrix3.fromScale(new Cesium.Cartesian3(7.0, 8.0, 9.0));
|
|
*/
|
|
Matrix3.fromScale = function (scale, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("scale", scale);
|
|
//>>includeEnd('debug');
|
|
|
|
if (!defaultValue.defined(result)) {
|
|
return new Matrix3(scale.x, 0.0, 0.0, 0.0, scale.y, 0.0, 0.0, 0.0, scale.z);
|
|
}
|
|
|
|
result[0] = scale.x;
|
|
result[1] = 0.0;
|
|
result[2] = 0.0;
|
|
result[3] = 0.0;
|
|
result[4] = scale.y;
|
|
result[5] = 0.0;
|
|
result[6] = 0.0;
|
|
result[7] = 0.0;
|
|
result[8] = scale.z;
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Computes a Matrix3 instance representing a uniform scale.
|
|
*
|
|
* @param {Number} scale The uniform scale factor.
|
|
* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
|
|
* @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
|
|
*
|
|
* @example
|
|
* // Creates
|
|
* // [2.0, 0.0, 0.0]
|
|
* // [0.0, 2.0, 0.0]
|
|
* // [0.0, 0.0, 2.0]
|
|
* const m = Cesium.Matrix3.fromUniformScale(2.0);
|
|
*/
|
|
Matrix3.fromUniformScale = function (scale, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.number("scale", scale);
|
|
//>>includeEnd('debug');
|
|
|
|
if (!defaultValue.defined(result)) {
|
|
return new Matrix3(scale, 0.0, 0.0, 0.0, scale, 0.0, 0.0, 0.0, scale);
|
|
}
|
|
|
|
result[0] = scale;
|
|
result[1] = 0.0;
|
|
result[2] = 0.0;
|
|
result[3] = 0.0;
|
|
result[4] = scale;
|
|
result[5] = 0.0;
|
|
result[6] = 0.0;
|
|
result[7] = 0.0;
|
|
result[8] = scale;
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Computes a Matrix3 instance representing the cross product equivalent matrix of a Cartesian3 vector.
|
|
*
|
|
* @param {Cartesian3} vector the vector on the left hand side of the cross product operation.
|
|
* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
|
|
* @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
|
|
*
|
|
* @example
|
|
* // Creates
|
|
* // [0.0, -9.0, 8.0]
|
|
* // [9.0, 0.0, -7.0]
|
|
* // [-8.0, 7.0, 0.0]
|
|
* const m = Cesium.Matrix3.fromCrossProduct(new Cesium.Cartesian3(7.0, 8.0, 9.0));
|
|
*/
|
|
Matrix3.fromCrossProduct = function (vector, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("vector", vector);
|
|
//>>includeEnd('debug');
|
|
|
|
if (!defaultValue.defined(result)) {
|
|
return new Matrix3(
|
|
0.0,
|
|
-vector.z,
|
|
vector.y,
|
|
vector.z,
|
|
0.0,
|
|
-vector.x,
|
|
-vector.y,
|
|
vector.x,
|
|
0.0
|
|
);
|
|
}
|
|
|
|
result[0] = 0.0;
|
|
result[1] = vector.z;
|
|
result[2] = -vector.y;
|
|
result[3] = -vector.z;
|
|
result[4] = 0.0;
|
|
result[5] = vector.x;
|
|
result[6] = vector.y;
|
|
result[7] = -vector.x;
|
|
result[8] = 0.0;
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Creates a rotation matrix around the x-axis.
|
|
*
|
|
* @param {Number} angle The angle, in radians, of the rotation. Positive angles are counterclockwise.
|
|
* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
|
|
* @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
|
|
*
|
|
* @example
|
|
* // Rotate a point 45 degrees counterclockwise around the x-axis.
|
|
* const p = new Cesium.Cartesian3(5, 6, 7);
|
|
* const m = Cesium.Matrix3.fromRotationX(Cesium.Math.toRadians(45.0));
|
|
* const rotated = Cesium.Matrix3.multiplyByVector(m, p, new Cesium.Cartesian3());
|
|
*/
|
|
Matrix3.fromRotationX = function (angle, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.number("angle", angle);
|
|
//>>includeEnd('debug');
|
|
|
|
const cosAngle = Math.cos(angle);
|
|
const sinAngle = Math.sin(angle);
|
|
|
|
if (!defaultValue.defined(result)) {
|
|
return new Matrix3(
|
|
1.0,
|
|
0.0,
|
|
0.0,
|
|
0.0,
|
|
cosAngle,
|
|
-sinAngle,
|
|
0.0,
|
|
sinAngle,
|
|
cosAngle
|
|
);
|
|
}
|
|
|
|
result[0] = 1.0;
|
|
result[1] = 0.0;
|
|
result[2] = 0.0;
|
|
result[3] = 0.0;
|
|
result[4] = cosAngle;
|
|
result[5] = sinAngle;
|
|
result[6] = 0.0;
|
|
result[7] = -sinAngle;
|
|
result[8] = cosAngle;
|
|
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Creates a rotation matrix around the y-axis.
|
|
*
|
|
* @param {Number} angle The angle, in radians, of the rotation. Positive angles are counterclockwise.
|
|
* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
|
|
* @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
|
|
*
|
|
* @example
|
|
* // Rotate a point 45 degrees counterclockwise around the y-axis.
|
|
* const p = new Cesium.Cartesian3(5, 6, 7);
|
|
* const m = Cesium.Matrix3.fromRotationY(Cesium.Math.toRadians(45.0));
|
|
* const rotated = Cesium.Matrix3.multiplyByVector(m, p, new Cesium.Cartesian3());
|
|
*/
|
|
Matrix3.fromRotationY = function (angle, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.number("angle", angle);
|
|
//>>includeEnd('debug');
|
|
|
|
const cosAngle = Math.cos(angle);
|
|
const sinAngle = Math.sin(angle);
|
|
|
|
if (!defaultValue.defined(result)) {
|
|
return new Matrix3(
|
|
cosAngle,
|
|
0.0,
|
|
sinAngle,
|
|
0.0,
|
|
1.0,
|
|
0.0,
|
|
-sinAngle,
|
|
0.0,
|
|
cosAngle
|
|
);
|
|
}
|
|
|
|
result[0] = cosAngle;
|
|
result[1] = 0.0;
|
|
result[2] = -sinAngle;
|
|
result[3] = 0.0;
|
|
result[4] = 1.0;
|
|
result[5] = 0.0;
|
|
result[6] = sinAngle;
|
|
result[7] = 0.0;
|
|
result[8] = cosAngle;
|
|
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Creates a rotation matrix around the z-axis.
|
|
*
|
|
* @param {Number} angle The angle, in radians, of the rotation. Positive angles are counterclockwise.
|
|
* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
|
|
* @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
|
|
*
|
|
* @example
|
|
* // Rotate a point 45 degrees counterclockwise around the z-axis.
|
|
* const p = new Cesium.Cartesian3(5, 6, 7);
|
|
* const m = Cesium.Matrix3.fromRotationZ(Cesium.Math.toRadians(45.0));
|
|
* const rotated = Cesium.Matrix3.multiplyByVector(m, p, new Cesium.Cartesian3());
|
|
*/
|
|
Matrix3.fromRotationZ = function (angle, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.number("angle", angle);
|
|
//>>includeEnd('debug');
|
|
|
|
const cosAngle = Math.cos(angle);
|
|
const sinAngle = Math.sin(angle);
|
|
|
|
if (!defaultValue.defined(result)) {
|
|
return new Matrix3(
|
|
cosAngle,
|
|
-sinAngle,
|
|
0.0,
|
|
sinAngle,
|
|
cosAngle,
|
|
0.0,
|
|
0.0,
|
|
0.0,
|
|
1.0
|
|
);
|
|
}
|
|
|
|
result[0] = cosAngle;
|
|
result[1] = sinAngle;
|
|
result[2] = 0.0;
|
|
result[3] = -sinAngle;
|
|
result[4] = cosAngle;
|
|
result[5] = 0.0;
|
|
result[6] = 0.0;
|
|
result[7] = 0.0;
|
|
result[8] = 1.0;
|
|
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Creates an Array from the provided Matrix3 instance.
|
|
* The array will be in column-major order.
|
|
*
|
|
* @param {Matrix3} matrix The matrix to use..
|
|
* @param {Number[]} [result] The Array onto which to store the result.
|
|
* @returns {Number[]} The modified Array parameter or a new Array instance if one was not provided.
|
|
*/
|
|
Matrix3.toArray = function (matrix, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("matrix", matrix);
|
|
//>>includeEnd('debug');
|
|
|
|
if (!defaultValue.defined(result)) {
|
|
return [
|
|
matrix[0],
|
|
matrix[1],
|
|
matrix[2],
|
|
matrix[3],
|
|
matrix[4],
|
|
matrix[5],
|
|
matrix[6],
|
|
matrix[7],
|
|
matrix[8],
|
|
];
|
|
}
|
|
result[0] = matrix[0];
|
|
result[1] = matrix[1];
|
|
result[2] = matrix[2];
|
|
result[3] = matrix[3];
|
|
result[4] = matrix[4];
|
|
result[5] = matrix[5];
|
|
result[6] = matrix[6];
|
|
result[7] = matrix[7];
|
|
result[8] = matrix[8];
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Computes the array index of the element at the provided row and column.
|
|
*
|
|
* @param {Number} column The zero-based index of the column.
|
|
* @param {Number} row The zero-based index of the row.
|
|
* @returns {Number} The index of the element at the provided row and column.
|
|
*
|
|
* @exception {DeveloperError} row must be 0, 1, or 2.
|
|
* @exception {DeveloperError} column must be 0, 1, or 2.
|
|
*
|
|
* @example
|
|
* const myMatrix = new Cesium.Matrix3();
|
|
* const column1Row0Index = Cesium.Matrix3.getElementIndex(1, 0);
|
|
* const column1Row0 = myMatrix[column1Row0Index]
|
|
* myMatrix[column1Row0Index] = 10.0;
|
|
*/
|
|
Matrix3.getElementIndex = function (column, row) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.number.greaterThanOrEquals("row", row, 0);
|
|
Check.Check.typeOf.number.lessThanOrEquals("row", row, 2);
|
|
Check.Check.typeOf.number.greaterThanOrEquals("column", column, 0);
|
|
Check.Check.typeOf.number.lessThanOrEquals("column", column, 2);
|
|
//>>includeEnd('debug');
|
|
|
|
return column * 3 + row;
|
|
};
|
|
|
|
/**
|
|
* Retrieves a copy of the matrix column at the provided index as a Cartesian3 instance.
|
|
*
|
|
* @param {Matrix3} matrix The matrix to use.
|
|
* @param {Number} index The zero-based index of the column to retrieve.
|
|
* @param {Cartesian3} result The object onto which to store the result.
|
|
* @returns {Cartesian3} The modified result parameter.
|
|
*
|
|
* @exception {DeveloperError} index must be 0, 1, or 2.
|
|
*/
|
|
Matrix3.getColumn = function (matrix, index, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("matrix", matrix);
|
|
Check.Check.typeOf.number.greaterThanOrEquals("index", index, 0);
|
|
Check.Check.typeOf.number.lessThanOrEquals("index", index, 2);
|
|
Check.Check.typeOf.object("result", result);
|
|
//>>includeEnd('debug');
|
|
|
|
const startIndex = index * 3;
|
|
const x = matrix[startIndex];
|
|
const y = matrix[startIndex + 1];
|
|
const z = matrix[startIndex + 2];
|
|
|
|
result.x = x;
|
|
result.y = y;
|
|
result.z = z;
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Computes a new matrix that replaces the specified column in the provided matrix with the provided Cartesian3 instance.
|
|
*
|
|
* @param {Matrix3} matrix The matrix to use.
|
|
* @param {Number} index The zero-based index of the column to set.
|
|
* @param {Cartesian3} cartesian The Cartesian whose values will be assigned to the specified column.
|
|
* @param {Matrix3} result The object onto which to store the result.
|
|
* @returns {Matrix3} The modified result parameter.
|
|
*
|
|
* @exception {DeveloperError} index must be 0, 1, or 2.
|
|
*/
|
|
Matrix3.setColumn = function (matrix, index, cartesian, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("matrix", matrix);
|
|
Check.Check.typeOf.number.greaterThanOrEquals("index", index, 0);
|
|
Check.Check.typeOf.number.lessThanOrEquals("index", index, 2);
|
|
Check.Check.typeOf.object("cartesian", cartesian);
|
|
Check.Check.typeOf.object("result", result);
|
|
//>>includeEnd('debug');
|
|
|
|
result = Matrix3.clone(matrix, result);
|
|
const startIndex = index * 3;
|
|
result[startIndex] = cartesian.x;
|
|
result[startIndex + 1] = cartesian.y;
|
|
result[startIndex + 2] = cartesian.z;
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Retrieves a copy of the matrix row at the provided index as a Cartesian3 instance.
|
|
*
|
|
* @param {Matrix3} matrix The matrix to use.
|
|
* @param {Number} index The zero-based index of the row to retrieve.
|
|
* @param {Cartesian3} result The object onto which to store the result.
|
|
* @returns {Cartesian3} The modified result parameter.
|
|
*
|
|
* @exception {DeveloperError} index must be 0, 1, or 2.
|
|
*/
|
|
Matrix3.getRow = function (matrix, index, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("matrix", matrix);
|
|
Check.Check.typeOf.number.greaterThanOrEquals("index", index, 0);
|
|
Check.Check.typeOf.number.lessThanOrEquals("index", index, 2);
|
|
Check.Check.typeOf.object("result", result);
|
|
//>>includeEnd('debug');
|
|
|
|
const x = matrix[index];
|
|
const y = matrix[index + 3];
|
|
const z = matrix[index + 6];
|
|
|
|
result.x = x;
|
|
result.y = y;
|
|
result.z = z;
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Computes a new matrix that replaces the specified row in the provided matrix with the provided Cartesian3 instance.
|
|
*
|
|
* @param {Matrix3} matrix The matrix to use.
|
|
* @param {Number} index The zero-based index of the row to set.
|
|
* @param {Cartesian3} cartesian The Cartesian whose values will be assigned to the specified row.
|
|
* @param {Matrix3} result The object onto which to store the result.
|
|
* @returns {Matrix3} The modified result parameter.
|
|
*
|
|
* @exception {DeveloperError} index must be 0, 1, or 2.
|
|
*/
|
|
Matrix3.setRow = function (matrix, index, cartesian, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("matrix", matrix);
|
|
Check.Check.typeOf.number.greaterThanOrEquals("index", index, 0);
|
|
Check.Check.typeOf.number.lessThanOrEquals("index", index, 2);
|
|
Check.Check.typeOf.object("cartesian", cartesian);
|
|
Check.Check.typeOf.object("result", result);
|
|
//>>includeEnd('debug');
|
|
|
|
result = Matrix3.clone(matrix, result);
|
|
result[index] = cartesian.x;
|
|
result[index + 3] = cartesian.y;
|
|
result[index + 6] = cartesian.z;
|
|
return result;
|
|
};
|
|
|
|
const scaleScratch1 = new Cartesian3();
|
|
|
|
/**
|
|
* Computes a new matrix that replaces the scale with the provided scale.
|
|
* This assumes the matrix is an affine transformation.
|
|
*
|
|
* @param {Matrix3} matrix The matrix to use.
|
|
* @param {Cartesian3} scale The scale that replaces the scale of the provided matrix.
|
|
* @param {Matrix3} result The object onto which to store the result.
|
|
* @returns {Matrix3} The modified result parameter.
|
|
*
|
|
* @see Matrix3.setUniformScale
|
|
* @see Matrix3.fromScale
|
|
* @see Matrix3.fromUniformScale
|
|
* @see Matrix3.multiplyByScale
|
|
* @see Matrix3.multiplyByUniformScale
|
|
* @see Matrix3.getScale
|
|
*/
|
|
Matrix3.setScale = function (matrix, scale, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("matrix", matrix);
|
|
Check.Check.typeOf.object("scale", scale);
|
|
Check.Check.typeOf.object("result", result);
|
|
//>>includeEnd('debug');
|
|
|
|
const existingScale = Matrix3.getScale(matrix, scaleScratch1);
|
|
const scaleRatioX = scale.x / existingScale.x;
|
|
const scaleRatioY = scale.y / existingScale.y;
|
|
const scaleRatioZ = scale.z / existingScale.z;
|
|
|
|
result[0] = matrix[0] * scaleRatioX;
|
|
result[1] = matrix[1] * scaleRatioX;
|
|
result[2] = matrix[2] * scaleRatioX;
|
|
result[3] = matrix[3] * scaleRatioY;
|
|
result[4] = matrix[4] * scaleRatioY;
|
|
result[5] = matrix[5] * scaleRatioY;
|
|
result[6] = matrix[6] * scaleRatioZ;
|
|
result[7] = matrix[7] * scaleRatioZ;
|
|
result[8] = matrix[8] * scaleRatioZ;
|
|
|
|
return result;
|
|
};
|
|
|
|
const scaleScratch2 = new Cartesian3();
|
|
|
|
/**
|
|
* Computes a new matrix that replaces the scale with the provided uniform scale.
|
|
* This assumes the matrix is an affine transformation.
|
|
*
|
|
* @param {Matrix3} matrix The matrix to use.
|
|
* @param {Number} scale The uniform scale that replaces the scale of the provided matrix.
|
|
* @param {Matrix3} result The object onto which to store the result.
|
|
* @returns {Matrix3} The modified result parameter.
|
|
*
|
|
* @see Matrix3.setScale
|
|
* @see Matrix3.fromScale
|
|
* @see Matrix3.fromUniformScale
|
|
* @see Matrix3.multiplyByScale
|
|
* @see Matrix3.multiplyByUniformScale
|
|
* @see Matrix3.getScale
|
|
*/
|
|
Matrix3.setUniformScale = function (matrix, scale, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("matrix", matrix);
|
|
Check.Check.typeOf.number("scale", scale);
|
|
Check.Check.typeOf.object("result", result);
|
|
//>>includeEnd('debug');
|
|
|
|
const existingScale = Matrix3.getScale(matrix, scaleScratch2);
|
|
const scaleRatioX = scale / existingScale.x;
|
|
const scaleRatioY = scale / existingScale.y;
|
|
const scaleRatioZ = scale / existingScale.z;
|
|
|
|
result[0] = matrix[0] * scaleRatioX;
|
|
result[1] = matrix[1] * scaleRatioX;
|
|
result[2] = matrix[2] * scaleRatioX;
|
|
result[3] = matrix[3] * scaleRatioY;
|
|
result[4] = matrix[4] * scaleRatioY;
|
|
result[5] = matrix[5] * scaleRatioY;
|
|
result[6] = matrix[6] * scaleRatioZ;
|
|
result[7] = matrix[7] * scaleRatioZ;
|
|
result[8] = matrix[8] * scaleRatioZ;
|
|
|
|
return result;
|
|
};
|
|
|
|
const scratchColumn = new Cartesian3();
|
|
|
|
/**
|
|
* Extracts the non-uniform scale assuming the matrix is an affine transformation.
|
|
*
|
|
* @param {Matrix3} matrix The matrix.
|
|
* @param {Cartesian3} result The object onto which to store the result.
|
|
* @returns {Cartesian3} The modified result parameter.
|
|
*
|
|
* @see Matrix3.multiplyByScale
|
|
* @see Matrix3.multiplyByUniformScale
|
|
* @see Matrix3.fromScale
|
|
* @see Matrix3.fromUniformScale
|
|
* @see Matrix3.setScale
|
|
* @see Matrix3.setUniformScale
|
|
*/
|
|
Matrix3.getScale = function (matrix, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("matrix", matrix);
|
|
Check.Check.typeOf.object("result", result);
|
|
//>>includeEnd('debug');
|
|
|
|
result.x = Cartesian3.magnitude(
|
|
Cartesian3.fromElements(matrix[0], matrix[1], matrix[2], scratchColumn)
|
|
);
|
|
result.y = Cartesian3.magnitude(
|
|
Cartesian3.fromElements(matrix[3], matrix[4], matrix[5], scratchColumn)
|
|
);
|
|
result.z = Cartesian3.magnitude(
|
|
Cartesian3.fromElements(matrix[6], matrix[7], matrix[8], scratchColumn)
|
|
);
|
|
return result;
|
|
};
|
|
|
|
const scaleScratch3 = new Cartesian3();
|
|
|
|
/**
|
|
* Computes the maximum scale assuming the matrix is an affine transformation.
|
|
* The maximum scale is the maximum length of the column vectors.
|
|
*
|
|
* @param {Matrix3} matrix The matrix.
|
|
* @returns {Number} The maximum scale.
|
|
*/
|
|
Matrix3.getMaximumScale = function (matrix) {
|
|
Matrix3.getScale(matrix, scaleScratch3);
|
|
return Cartesian3.maximumComponent(scaleScratch3);
|
|
};
|
|
|
|
const scaleScratch4 = new Cartesian3();
|
|
|
|
/**
|
|
* Sets the rotation assuming the matrix is an affine transformation.
|
|
*
|
|
* @param {Matrix3} matrix The matrix.
|
|
* @param {Matrix3} rotation The rotation matrix.
|
|
* @returns {Matrix3} The modified result parameter.
|
|
*
|
|
* @see Matrix3.getRotation
|
|
*/
|
|
Matrix3.setRotation = function (matrix, rotation, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("matrix", matrix);
|
|
Check.Check.typeOf.object("result", result);
|
|
//>>includeEnd('debug');
|
|
|
|
const scale = Matrix3.getScale(matrix, scaleScratch4);
|
|
|
|
result[0] = rotation[0] * scale.x;
|
|
result[1] = rotation[1] * scale.x;
|
|
result[2] = rotation[2] * scale.x;
|
|
result[3] = rotation[3] * scale.y;
|
|
result[4] = rotation[4] * scale.y;
|
|
result[5] = rotation[5] * scale.y;
|
|
result[6] = rotation[6] * scale.z;
|
|
result[7] = rotation[7] * scale.z;
|
|
result[8] = rotation[8] * scale.z;
|
|
|
|
return result;
|
|
};
|
|
|
|
const scaleScratch5 = new Cartesian3();
|
|
|
|
/**
|
|
* Extracts the rotation matrix assuming the matrix is an affine transformation.
|
|
*
|
|
* @param {Matrix3} matrix The matrix.
|
|
* @param {Matrix3} result The object onto which to store the result.
|
|
* @returns {Matrix3} The modified result parameter.
|
|
*
|
|
* @see Matrix3.setRotation
|
|
*/
|
|
Matrix3.getRotation = function (matrix, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("matrix", matrix);
|
|
Check.Check.typeOf.object("result", result);
|
|
//>>includeEnd('debug');
|
|
|
|
const scale = Matrix3.getScale(matrix, scaleScratch5);
|
|
|
|
result[0] = matrix[0] / scale.x;
|
|
result[1] = matrix[1] / scale.x;
|
|
result[2] = matrix[2] / scale.x;
|
|
result[3] = matrix[3] / scale.y;
|
|
result[4] = matrix[4] / scale.y;
|
|
result[5] = matrix[5] / scale.y;
|
|
result[6] = matrix[6] / scale.z;
|
|
result[7] = matrix[7] / scale.z;
|
|
result[8] = matrix[8] / scale.z;
|
|
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Computes the product of two matrices.
|
|
*
|
|
* @param {Matrix3} left The first matrix.
|
|
* @param {Matrix3} right The second matrix.
|
|
* @param {Matrix3} result The object onto which to store the result.
|
|
* @returns {Matrix3} The modified result parameter.
|
|
*/
|
|
Matrix3.multiply = function (left, right, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("left", left);
|
|
Check.Check.typeOf.object("right", right);
|
|
Check.Check.typeOf.object("result", result);
|
|
//>>includeEnd('debug');
|
|
|
|
const column0Row0 =
|
|
left[0] * right[0] + left[3] * right[1] + left[6] * right[2];
|
|
const column0Row1 =
|
|
left[1] * right[0] + left[4] * right[1] + left[7] * right[2];
|
|
const column0Row2 =
|
|
left[2] * right[0] + left[5] * right[1] + left[8] * right[2];
|
|
|
|
const column1Row0 =
|
|
left[0] * right[3] + left[3] * right[4] + left[6] * right[5];
|
|
const column1Row1 =
|
|
left[1] * right[3] + left[4] * right[4] + left[7] * right[5];
|
|
const column1Row2 =
|
|
left[2] * right[3] + left[5] * right[4] + left[8] * right[5];
|
|
|
|
const column2Row0 =
|
|
left[0] * right[6] + left[3] * right[7] + left[6] * right[8];
|
|
const column2Row1 =
|
|
left[1] * right[6] + left[4] * right[7] + left[7] * right[8];
|
|
const column2Row2 =
|
|
left[2] * right[6] + left[5] * right[7] + left[8] * right[8];
|
|
|
|
result[0] = column0Row0;
|
|
result[1] = column0Row1;
|
|
result[2] = column0Row2;
|
|
result[3] = column1Row0;
|
|
result[4] = column1Row1;
|
|
result[5] = column1Row2;
|
|
result[6] = column2Row0;
|
|
result[7] = column2Row1;
|
|
result[8] = column2Row2;
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Computes the sum of two matrices.
|
|
*
|
|
* @param {Matrix3} left The first matrix.
|
|
* @param {Matrix3} right The second matrix.
|
|
* @param {Matrix3} result The object onto which to store the result.
|
|
* @returns {Matrix3} The modified result parameter.
|
|
*/
|
|
Matrix3.add = function (left, right, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("left", left);
|
|
Check.Check.typeOf.object("right", right);
|
|
Check.Check.typeOf.object("result", result);
|
|
//>>includeEnd('debug');
|
|
|
|
result[0] = left[0] + right[0];
|
|
result[1] = left[1] + right[1];
|
|
result[2] = left[2] + right[2];
|
|
result[3] = left[3] + right[3];
|
|
result[4] = left[4] + right[4];
|
|
result[5] = left[5] + right[5];
|
|
result[6] = left[6] + right[6];
|
|
result[7] = left[7] + right[7];
|
|
result[8] = left[8] + right[8];
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Computes the difference of two matrices.
|
|
*
|
|
* @param {Matrix3} left The first matrix.
|
|
* @param {Matrix3} right The second matrix.
|
|
* @param {Matrix3} result The object onto which to store the result.
|
|
* @returns {Matrix3} The modified result parameter.
|
|
*/
|
|
Matrix3.subtract = function (left, right, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("left", left);
|
|
Check.Check.typeOf.object("right", right);
|
|
Check.Check.typeOf.object("result", result);
|
|
//>>includeEnd('debug');
|
|
|
|
result[0] = left[0] - right[0];
|
|
result[1] = left[1] - right[1];
|
|
result[2] = left[2] - right[2];
|
|
result[3] = left[3] - right[3];
|
|
result[4] = left[4] - right[4];
|
|
result[5] = left[5] - right[5];
|
|
result[6] = left[6] - right[6];
|
|
result[7] = left[7] - right[7];
|
|
result[8] = left[8] - right[8];
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Computes the product of a matrix and a column vector.
|
|
*
|
|
* @param {Matrix3} matrix The matrix.
|
|
* @param {Cartesian3} cartesian The column.
|
|
* @param {Cartesian3} result The object onto which to store the result.
|
|
* @returns {Cartesian3} The modified result parameter.
|
|
*/
|
|
Matrix3.multiplyByVector = function (matrix, cartesian, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("matrix", matrix);
|
|
Check.Check.typeOf.object("cartesian", cartesian);
|
|
Check.Check.typeOf.object("result", result);
|
|
//>>includeEnd('debug');
|
|
|
|
const vX = cartesian.x;
|
|
const vY = cartesian.y;
|
|
const vZ = cartesian.z;
|
|
|
|
const x = matrix[0] * vX + matrix[3] * vY + matrix[6] * vZ;
|
|
const y = matrix[1] * vX + matrix[4] * vY + matrix[7] * vZ;
|
|
const z = matrix[2] * vX + matrix[5] * vY + matrix[8] * vZ;
|
|
|
|
result.x = x;
|
|
result.y = y;
|
|
result.z = z;
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Computes the product of a matrix and a scalar.
|
|
*
|
|
* @param {Matrix3} matrix The matrix.
|
|
* @param {Number} scalar The number to multiply by.
|
|
* @param {Matrix3} result The object onto which to store the result.
|
|
* @returns {Matrix3} The modified result parameter.
|
|
*/
|
|
Matrix3.multiplyByScalar = function (matrix, scalar, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("matrix", matrix);
|
|
Check.Check.typeOf.number("scalar", scalar);
|
|
Check.Check.typeOf.object("result", result);
|
|
//>>includeEnd('debug');
|
|
|
|
result[0] = matrix[0] * scalar;
|
|
result[1] = matrix[1] * scalar;
|
|
result[2] = matrix[2] * scalar;
|
|
result[3] = matrix[3] * scalar;
|
|
result[4] = matrix[4] * scalar;
|
|
result[5] = matrix[5] * scalar;
|
|
result[6] = matrix[6] * scalar;
|
|
result[7] = matrix[7] * scalar;
|
|
result[8] = matrix[8] * scalar;
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Computes the product of a matrix times a (non-uniform) scale, as if the scale were a scale matrix.
|
|
*
|
|
* @param {Matrix3} matrix The matrix on the left-hand side.
|
|
* @param {Number} scale The non-uniform scale on the right-hand side.
|
|
* @param {Matrix3} result The object onto which to store the result.
|
|
* @returns {Matrix3} The modified result parameter.
|
|
*
|
|
*
|
|
* @example
|
|
* // Instead of Cesium.Matrix3.multiply(m, Cesium.Matrix3.fromScale(scale), m);
|
|
* Cesium.Matrix3.multiplyByScale(m, scale, m);
|
|
*
|
|
* @see Matrix3.multiplyByUniformScale
|
|
* @see Matrix3.fromScale
|
|
* @see Matrix3.fromUniformScale
|
|
* @see Matrix3.setScale
|
|
* @see Matrix3.setUniformScale
|
|
* @see Matrix3.getScale
|
|
*/
|
|
Matrix3.multiplyByScale = function (matrix, scale, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("matrix", matrix);
|
|
Check.Check.typeOf.object("scale", scale);
|
|
Check.Check.typeOf.object("result", result);
|
|
//>>includeEnd('debug');
|
|
|
|
result[0] = matrix[0] * scale.x;
|
|
result[1] = matrix[1] * scale.x;
|
|
result[2] = matrix[2] * scale.x;
|
|
result[3] = matrix[3] * scale.y;
|
|
result[4] = matrix[4] * scale.y;
|
|
result[5] = matrix[5] * scale.y;
|
|
result[6] = matrix[6] * scale.z;
|
|
result[7] = matrix[7] * scale.z;
|
|
result[8] = matrix[8] * scale.z;
|
|
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Computes the product of a matrix times a uniform scale, as if the scale were a scale matrix.
|
|
*
|
|
* @param {Matrix3} matrix The matrix on the left-hand side.
|
|
* @param {Number} scale The uniform scale on the right-hand side.
|
|
* @param {Matrix3} result The object onto which to store the result.
|
|
* @returns {Matrix3} The modified result parameter.
|
|
*
|
|
* @example
|
|
* // Instead of Cesium.Matrix3.multiply(m, Cesium.Matrix3.fromUniformScale(scale), m);
|
|
* Cesium.Matrix3.multiplyByUniformScale(m, scale, m);
|
|
*
|
|
* @see Matrix3.multiplyByScale
|
|
* @see Matrix3.fromScale
|
|
* @see Matrix3.fromUniformScale
|
|
* @see Matrix3.setScale
|
|
* @see Matrix3.setUniformScale
|
|
* @see Matrix3.getScale
|
|
*/
|
|
Matrix3.multiplyByUniformScale = function (matrix, scale, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("matrix", matrix);
|
|
Check.Check.typeOf.number("scale", scale);
|
|
Check.Check.typeOf.object("result", result);
|
|
//>>includeEnd('debug');
|
|
|
|
result[0] = matrix[0] * scale;
|
|
result[1] = matrix[1] * scale;
|
|
result[2] = matrix[2] * scale;
|
|
result[3] = matrix[3] * scale;
|
|
result[4] = matrix[4] * scale;
|
|
result[5] = matrix[5] * scale;
|
|
result[6] = matrix[6] * scale;
|
|
result[7] = matrix[7] * scale;
|
|
result[8] = matrix[8] * scale;
|
|
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Creates a negated copy of the provided matrix.
|
|
*
|
|
* @param {Matrix3} matrix The matrix to negate.
|
|
* @param {Matrix3} result The object onto which to store the result.
|
|
* @returns {Matrix3} The modified result parameter.
|
|
*/
|
|
Matrix3.negate = function (matrix, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("matrix", matrix);
|
|
Check.Check.typeOf.object("result", result);
|
|
//>>includeEnd('debug');
|
|
|
|
result[0] = -matrix[0];
|
|
result[1] = -matrix[1];
|
|
result[2] = -matrix[2];
|
|
result[3] = -matrix[3];
|
|
result[4] = -matrix[4];
|
|
result[5] = -matrix[5];
|
|
result[6] = -matrix[6];
|
|
result[7] = -matrix[7];
|
|
result[8] = -matrix[8];
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Computes the transpose of the provided matrix.
|
|
*
|
|
* @param {Matrix3} matrix The matrix to transpose.
|
|
* @param {Matrix3} result The object onto which to store the result.
|
|
* @returns {Matrix3} The modified result parameter.
|
|
*/
|
|
Matrix3.transpose = function (matrix, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("matrix", matrix);
|
|
Check.Check.typeOf.object("result", result);
|
|
//>>includeEnd('debug');
|
|
|
|
const column0Row0 = matrix[0];
|
|
const column0Row1 = matrix[3];
|
|
const column0Row2 = matrix[6];
|
|
const column1Row0 = matrix[1];
|
|
const column1Row1 = matrix[4];
|
|
const column1Row2 = matrix[7];
|
|
const column2Row0 = matrix[2];
|
|
const column2Row1 = matrix[5];
|
|
const column2Row2 = matrix[8];
|
|
|
|
result[0] = column0Row0;
|
|
result[1] = column0Row1;
|
|
result[2] = column0Row2;
|
|
result[3] = column1Row0;
|
|
result[4] = column1Row1;
|
|
result[5] = column1Row2;
|
|
result[6] = column2Row0;
|
|
result[7] = column2Row1;
|
|
result[8] = column2Row2;
|
|
return result;
|
|
};
|
|
|
|
function computeFrobeniusNorm(matrix) {
|
|
let norm = 0.0;
|
|
for (let i = 0; i < 9; ++i) {
|
|
const temp = matrix[i];
|
|
norm += temp * temp;
|
|
}
|
|
|
|
return Math.sqrt(norm);
|
|
}
|
|
|
|
const rowVal = [1, 0, 0];
|
|
const colVal = [2, 2, 1];
|
|
|
|
function offDiagonalFrobeniusNorm(matrix) {
|
|
// Computes the "off-diagonal" Frobenius norm.
|
|
// Assumes matrix is symmetric.
|
|
|
|
let norm = 0.0;
|
|
for (let i = 0; i < 3; ++i) {
|
|
const temp = matrix[Matrix3.getElementIndex(colVal[i], rowVal[i])];
|
|
norm += 2.0 * temp * temp;
|
|
}
|
|
|
|
return Math.sqrt(norm);
|
|
}
|
|
|
|
function shurDecomposition(matrix, result) {
|
|
// This routine was created based upon Matrix Computations, 3rd ed., by Golub and Van Loan,
|
|
// section 8.4.2 The 2by2 Symmetric Schur Decomposition.
|
|
//
|
|
// The routine takes a matrix, which is assumed to be symmetric, and
|
|
// finds the largest off-diagonal term, and then creates
|
|
// a matrix (result) which can be used to help reduce it
|
|
|
|
const tolerance = Math$1.CesiumMath.EPSILON15;
|
|
|
|
let maxDiagonal = 0.0;
|
|
let rotAxis = 1;
|
|
|
|
// find pivot (rotAxis) based on max diagonal of matrix
|
|
for (let i = 0; i < 3; ++i) {
|
|
const temp = Math.abs(
|
|
matrix[Matrix3.getElementIndex(colVal[i], rowVal[i])]
|
|
);
|
|
if (temp > maxDiagonal) {
|
|
rotAxis = i;
|
|
maxDiagonal = temp;
|
|
}
|
|
}
|
|
|
|
let c = 1.0;
|
|
let s = 0.0;
|
|
|
|
const p = rowVal[rotAxis];
|
|
const q = colVal[rotAxis];
|
|
|
|
if (Math.abs(matrix[Matrix3.getElementIndex(q, p)]) > tolerance) {
|
|
const qq = matrix[Matrix3.getElementIndex(q, q)];
|
|
const pp = matrix[Matrix3.getElementIndex(p, p)];
|
|
const qp = matrix[Matrix3.getElementIndex(q, p)];
|
|
|
|
const tau = (qq - pp) / 2.0 / qp;
|
|
let t;
|
|
|
|
if (tau < 0.0) {
|
|
t = -1.0 / (-tau + Math.sqrt(1.0 + tau * tau));
|
|
} else {
|
|
t = 1.0 / (tau + Math.sqrt(1.0 + tau * tau));
|
|
}
|
|
|
|
c = 1.0 / Math.sqrt(1.0 + t * t);
|
|
s = t * c;
|
|
}
|
|
|
|
result = Matrix3.clone(Matrix3.IDENTITY, result);
|
|
|
|
result[Matrix3.getElementIndex(p, p)] = result[
|
|
Matrix3.getElementIndex(q, q)
|
|
] = c;
|
|
result[Matrix3.getElementIndex(q, p)] = s;
|
|
result[Matrix3.getElementIndex(p, q)] = -s;
|
|
|
|
return result;
|
|
}
|
|
|
|
const jMatrix = new Matrix3();
|
|
const jMatrixTranspose = new Matrix3();
|
|
|
|
/**
|
|
* Computes the eigenvectors and eigenvalues of a symmetric matrix.
|
|
* <p>
|
|
* Returns a diagonal matrix and unitary matrix such that:
|
|
* <code>matrix = unitary matrix * diagonal matrix * transpose(unitary matrix)</code>
|
|
* </p>
|
|
* <p>
|
|
* The values along the diagonal of the diagonal matrix are the eigenvalues. The columns
|
|
* of the unitary matrix are the corresponding eigenvectors.
|
|
* </p>
|
|
*
|
|
* @param {Matrix3} matrix The matrix to decompose into diagonal and unitary matrix. Expected to be symmetric.
|
|
* @param {Object} [result] An object with unitary and diagonal properties which are matrices onto which to store the result.
|
|
* @returns {Object} An object with unitary and diagonal properties which are the unitary and diagonal matrices, respectively.
|
|
*
|
|
* @example
|
|
* const a = //... symetric matrix
|
|
* const result = {
|
|
* unitary : new Cesium.Matrix3(),
|
|
* diagonal : new Cesium.Matrix3()
|
|
* };
|
|
* Cesium.Matrix3.computeEigenDecomposition(a, result);
|
|
*
|
|
* const unitaryTranspose = Cesium.Matrix3.transpose(result.unitary, new Cesium.Matrix3());
|
|
* const b = Cesium.Matrix3.multiply(result.unitary, result.diagonal, new Cesium.Matrix3());
|
|
* Cesium.Matrix3.multiply(b, unitaryTranspose, b); // b is now equal to a
|
|
*
|
|
* const lambda = Cesium.Matrix3.getColumn(result.diagonal, 0, new Cesium.Cartesian3()).x; // first eigenvalue
|
|
* const v = Cesium.Matrix3.getColumn(result.unitary, 0, new Cesium.Cartesian3()); // first eigenvector
|
|
* const c = Cesium.Cartesian3.multiplyByScalar(v, lambda, new Cesium.Cartesian3()); // equal to Cesium.Matrix3.multiplyByVector(a, v)
|
|
*/
|
|
Matrix3.computeEigenDecomposition = function (matrix, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("matrix", matrix);
|
|
//>>includeEnd('debug');
|
|
|
|
// This routine was created based upon Matrix Computations, 3rd ed., by Golub and Van Loan,
|
|
// section 8.4.3 The Classical Jacobi Algorithm
|
|
|
|
const tolerance = Math$1.CesiumMath.EPSILON20;
|
|
const maxSweeps = 10;
|
|
|
|
let count = 0;
|
|
let sweep = 0;
|
|
|
|
if (!defaultValue.defined(result)) {
|
|
result = {};
|
|
}
|
|
|
|
const unitaryMatrix = (result.unitary = Matrix3.clone(
|
|
Matrix3.IDENTITY,
|
|
result.unitary
|
|
));
|
|
const diagMatrix = (result.diagonal = Matrix3.clone(matrix, result.diagonal));
|
|
|
|
const epsilon = tolerance * computeFrobeniusNorm(diagMatrix);
|
|
|
|
while (sweep < maxSweeps && offDiagonalFrobeniusNorm(diagMatrix) > epsilon) {
|
|
shurDecomposition(diagMatrix, jMatrix);
|
|
Matrix3.transpose(jMatrix, jMatrixTranspose);
|
|
Matrix3.multiply(diagMatrix, jMatrix, diagMatrix);
|
|
Matrix3.multiply(jMatrixTranspose, diagMatrix, diagMatrix);
|
|
Matrix3.multiply(unitaryMatrix, jMatrix, unitaryMatrix);
|
|
|
|
if (++count > 2) {
|
|
++sweep;
|
|
count = 0;
|
|
}
|
|
}
|
|
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Computes a matrix, which contains the absolute (unsigned) values of the provided matrix's elements.
|
|
*
|
|
* @param {Matrix3} matrix The matrix with signed elements.
|
|
* @param {Matrix3} result The object onto which to store the result.
|
|
* @returns {Matrix3} The modified result parameter.
|
|
*/
|
|
Matrix3.abs = function (matrix, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("matrix", matrix);
|
|
Check.Check.typeOf.object("result", result);
|
|
//>>includeEnd('debug');
|
|
|
|
result[0] = Math.abs(matrix[0]);
|
|
result[1] = Math.abs(matrix[1]);
|
|
result[2] = Math.abs(matrix[2]);
|
|
result[3] = Math.abs(matrix[3]);
|
|
result[4] = Math.abs(matrix[4]);
|
|
result[5] = Math.abs(matrix[5]);
|
|
result[6] = Math.abs(matrix[6]);
|
|
result[7] = Math.abs(matrix[7]);
|
|
result[8] = Math.abs(matrix[8]);
|
|
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Computes the determinant of the provided matrix.
|
|
*
|
|
* @param {Matrix3} matrix The matrix to use.
|
|
* @returns {Number} The value of the determinant of the matrix.
|
|
*/
|
|
Matrix3.determinant = function (matrix) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("matrix", matrix);
|
|
//>>includeEnd('debug');
|
|
|
|
const m11 = matrix[0];
|
|
const m21 = matrix[3];
|
|
const m31 = matrix[6];
|
|
const m12 = matrix[1];
|
|
const m22 = matrix[4];
|
|
const m32 = matrix[7];
|
|
const m13 = matrix[2];
|
|
const m23 = matrix[5];
|
|
const m33 = matrix[8];
|
|
|
|
return (
|
|
m11 * (m22 * m33 - m23 * m32) +
|
|
m12 * (m23 * m31 - m21 * m33) +
|
|
m13 * (m21 * m32 - m22 * m31)
|
|
);
|
|
};
|
|
|
|
/**
|
|
* Computes the inverse of the provided matrix.
|
|
*
|
|
* @param {Matrix3} matrix The matrix to invert.
|
|
* @param {Matrix3} result The object onto which to store the result.
|
|
* @returns {Matrix3} The modified result parameter.
|
|
*
|
|
* @exception {DeveloperError} matrix is not invertible.
|
|
*/
|
|
Matrix3.inverse = function (matrix, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("matrix", matrix);
|
|
Check.Check.typeOf.object("result", result);
|
|
//>>includeEnd('debug');
|
|
|
|
const m11 = matrix[0];
|
|
const m21 = matrix[1];
|
|
const m31 = matrix[2];
|
|
const m12 = matrix[3];
|
|
const m22 = matrix[4];
|
|
const m32 = matrix[5];
|
|
const m13 = matrix[6];
|
|
const m23 = matrix[7];
|
|
const m33 = matrix[8];
|
|
|
|
const determinant = Matrix3.determinant(matrix);
|
|
|
|
//>>includeStart('debug', pragmas.debug);
|
|
if (Math.abs(determinant) <= Math$1.CesiumMath.EPSILON15) {
|
|
throw new Check.DeveloperError("matrix is not invertible");
|
|
}
|
|
//>>includeEnd('debug');
|
|
|
|
result[0] = m22 * m33 - m23 * m32;
|
|
result[1] = m23 * m31 - m21 * m33;
|
|
result[2] = m21 * m32 - m22 * m31;
|
|
result[3] = m13 * m32 - m12 * m33;
|
|
result[4] = m11 * m33 - m13 * m31;
|
|
result[5] = m12 * m31 - m11 * m32;
|
|
result[6] = m12 * m23 - m13 * m22;
|
|
result[7] = m13 * m21 - m11 * m23;
|
|
result[8] = m11 * m22 - m12 * m21;
|
|
|
|
const scale = 1.0 / determinant;
|
|
return Matrix3.multiplyByScalar(result, scale, result);
|
|
};
|
|
|
|
const scratchTransposeMatrix = new Matrix3();
|
|
|
|
/**
|
|
* Computes the inverse transpose of a matrix.
|
|
*
|
|
* @param {Matrix3} matrix The matrix to transpose and invert.
|
|
* @param {Matrix3} result The object onto which to store the result.
|
|
* @returns {Matrix3} The modified result parameter.
|
|
*/
|
|
Matrix3.inverseTranspose = function (matrix, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("matrix", matrix);
|
|
Check.Check.typeOf.object("result", result);
|
|
//>>includeEnd('debug');
|
|
|
|
return Matrix3.inverse(
|
|
Matrix3.transpose(matrix, scratchTransposeMatrix),
|
|
result
|
|
);
|
|
};
|
|
|
|
/**
|
|
* Compares the provided matrices componentwise and returns
|
|
* <code>true</code> if they are equal, <code>false</code> otherwise.
|
|
*
|
|
* @param {Matrix3} [left] The first matrix.
|
|
* @param {Matrix3} [right] The second matrix.
|
|
* @returns {Boolean} <code>true</code> if left and right are equal, <code>false</code> otherwise.
|
|
*/
|
|
Matrix3.equals = function (left, right) {
|
|
return (
|
|
left === right ||
|
|
(defaultValue.defined(left) &&
|
|
defaultValue.defined(right) &&
|
|
left[0] === right[0] &&
|
|
left[1] === right[1] &&
|
|
left[2] === right[2] &&
|
|
left[3] === right[3] &&
|
|
left[4] === right[4] &&
|
|
left[5] === right[5] &&
|
|
left[6] === right[6] &&
|
|
left[7] === right[7] &&
|
|
left[8] === right[8])
|
|
);
|
|
};
|
|
|
|
/**
|
|
* Compares the provided matrices componentwise and returns
|
|
* <code>true</code> if they are within the provided epsilon,
|
|
* <code>false</code> otherwise.
|
|
*
|
|
* @param {Matrix3} [left] The first matrix.
|
|
* @param {Matrix3} [right] The second matrix.
|
|
* @param {Number} [epsilon=0] The epsilon to use for equality testing.
|
|
* @returns {Boolean} <code>true</code> if left and right are within the provided epsilon, <code>false</code> otherwise.
|
|
*/
|
|
Matrix3.equalsEpsilon = function (left, right, epsilon) {
|
|
epsilon = defaultValue.defaultValue(epsilon, 0);
|
|
|
|
return (
|
|
left === right ||
|
|
(defaultValue.defined(left) &&
|
|
defaultValue.defined(right) &&
|
|
Math.abs(left[0] - right[0]) <= epsilon &&
|
|
Math.abs(left[1] - right[1]) <= epsilon &&
|
|
Math.abs(left[2] - right[2]) <= epsilon &&
|
|
Math.abs(left[3] - right[3]) <= epsilon &&
|
|
Math.abs(left[4] - right[4]) <= epsilon &&
|
|
Math.abs(left[5] - right[5]) <= epsilon &&
|
|
Math.abs(left[6] - right[6]) <= epsilon &&
|
|
Math.abs(left[7] - right[7]) <= epsilon &&
|
|
Math.abs(left[8] - right[8]) <= epsilon)
|
|
);
|
|
};
|
|
|
|
/**
|
|
* An immutable Matrix3 instance initialized to the identity matrix.
|
|
*
|
|
* @type {Matrix3}
|
|
* @constant
|
|
*/
|
|
Matrix3.IDENTITY = Object.freeze(
|
|
new Matrix3(1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0)
|
|
);
|
|
|
|
/**
|
|
* An immutable Matrix3 instance initialized to the zero matrix.
|
|
*
|
|
* @type {Matrix3}
|
|
* @constant
|
|
*/
|
|
Matrix3.ZERO = Object.freeze(
|
|
new Matrix3(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0)
|
|
);
|
|
|
|
/**
|
|
* The index into Matrix3 for column 0, row 0.
|
|
*
|
|
* @type {Number}
|
|
* @constant
|
|
*/
|
|
Matrix3.COLUMN0ROW0 = 0;
|
|
|
|
/**
|
|
* The index into Matrix3 for column 0, row 1.
|
|
*
|
|
* @type {Number}
|
|
* @constant
|
|
*/
|
|
Matrix3.COLUMN0ROW1 = 1;
|
|
|
|
/**
|
|
* The index into Matrix3 for column 0, row 2.
|
|
*
|
|
* @type {Number}
|
|
* @constant
|
|
*/
|
|
Matrix3.COLUMN0ROW2 = 2;
|
|
|
|
/**
|
|
* The index into Matrix3 for column 1, row 0.
|
|
*
|
|
* @type {Number}
|
|
* @constant
|
|
*/
|
|
Matrix3.COLUMN1ROW0 = 3;
|
|
|
|
/**
|
|
* The index into Matrix3 for column 1, row 1.
|
|
*
|
|
* @type {Number}
|
|
* @constant
|
|
*/
|
|
Matrix3.COLUMN1ROW1 = 4;
|
|
|
|
/**
|
|
* The index into Matrix3 for column 1, row 2.
|
|
*
|
|
* @type {Number}
|
|
* @constant
|
|
*/
|
|
Matrix3.COLUMN1ROW2 = 5;
|
|
|
|
/**
|
|
* The index into Matrix3 for column 2, row 0.
|
|
*
|
|
* @type {Number}
|
|
* @constant
|
|
*/
|
|
Matrix3.COLUMN2ROW0 = 6;
|
|
|
|
/**
|
|
* The index into Matrix3 for column 2, row 1.
|
|
*
|
|
* @type {Number}
|
|
* @constant
|
|
*/
|
|
Matrix3.COLUMN2ROW1 = 7;
|
|
|
|
/**
|
|
* The index into Matrix3 for column 2, row 2.
|
|
*
|
|
* @type {Number}
|
|
* @constant
|
|
*/
|
|
Matrix3.COLUMN2ROW2 = 8;
|
|
|
|
Object.defineProperties(Matrix3.prototype, {
|
|
/**
|
|
* Gets the number of items in the collection.
|
|
* @memberof Matrix3.prototype
|
|
*
|
|
* @type {Number}
|
|
*/
|
|
length: {
|
|
get: function () {
|
|
return Matrix3.packedLength;
|
|
},
|
|
},
|
|
});
|
|
|
|
/**
|
|
* Duplicates the provided Matrix3 instance.
|
|
*
|
|
* @param {Matrix3} [result] The object onto which to store the result.
|
|
* @returns {Matrix3} The modified result parameter or a new Matrix3 instance if one was not provided.
|
|
*/
|
|
Matrix3.prototype.clone = function (result) {
|
|
return Matrix3.clone(this, result);
|
|
};
|
|
|
|
/**
|
|
* Compares this matrix to the provided matrix componentwise and returns
|
|
* <code>true</code> if they are equal, <code>false</code> otherwise.
|
|
*
|
|
* @param {Matrix3} [right] The right hand side matrix.
|
|
* @returns {Boolean} <code>true</code> if they are equal, <code>false</code> otherwise.
|
|
*/
|
|
Matrix3.prototype.equals = function (right) {
|
|
return Matrix3.equals(this, right);
|
|
};
|
|
|
|
/**
|
|
* @private
|
|
*/
|
|
Matrix3.equalsArray = function (matrix, array, offset) {
|
|
return (
|
|
matrix[0] === array[offset] &&
|
|
matrix[1] === array[offset + 1] &&
|
|
matrix[2] === array[offset + 2] &&
|
|
matrix[3] === array[offset + 3] &&
|
|
matrix[4] === array[offset + 4] &&
|
|
matrix[5] === array[offset + 5] &&
|
|
matrix[6] === array[offset + 6] &&
|
|
matrix[7] === array[offset + 7] &&
|
|
matrix[8] === array[offset + 8]
|
|
);
|
|
};
|
|
|
|
/**
|
|
* Compares this matrix to the provided matrix componentwise and returns
|
|
* <code>true</code> if they are within the provided epsilon,
|
|
* <code>false</code> otherwise.
|
|
*
|
|
* @param {Matrix3} [right] The right hand side matrix.
|
|
* @param {Number} [epsilon=0] The epsilon to use for equality testing.
|
|
* @returns {Boolean} <code>true</code> if they are within the provided epsilon, <code>false</code> otherwise.
|
|
*/
|
|
Matrix3.prototype.equalsEpsilon = function (right, epsilon) {
|
|
return Matrix3.equalsEpsilon(this, right, epsilon);
|
|
};
|
|
|
|
/**
|
|
* Creates a string representing this Matrix with each row being
|
|
* on a separate line and in the format '(column0, column1, column2)'.
|
|
*
|
|
* @returns {String} A string representing the provided Matrix with each row being on a separate line and in the format '(column0, column1, column2)'.
|
|
*/
|
|
Matrix3.prototype.toString = function () {
|
|
return (
|
|
`(${this[0]}, ${this[3]}, ${this[6]})\n` +
|
|
`(${this[1]}, ${this[4]}, ${this[7]})\n` +
|
|
`(${this[2]}, ${this[5]}, ${this[8]})`
|
|
);
|
|
};
|
|
|
|
exports.Cartesian3 = Cartesian3;
|
|
exports.Cartographic = Cartographic;
|
|
exports.Ellipsoid = Ellipsoid;
|
|
exports.Matrix3 = Matrix3;
|
|
|
|
}));
|