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1862 lines
56 KiB
1862 lines
56 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', './Matrix3-ea964448', './defaultValue-135942ca', './Check-40d84a28', './Transforms-ac2d28a9', './Math-efde0c7b'], (function (exports, Matrix3, defaultValue, Check, Transforms, Math$1) { 'use strict';
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/**
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* Defines functions for 2nd order polynomial functions of one variable with only real coefficients.
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*
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* @namespace QuadraticRealPolynomial
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*/
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const QuadraticRealPolynomial = {};
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/**
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* Provides the discriminant of the quadratic equation from the supplied coefficients.
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*
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* @param {Number} a The coefficient of the 2nd order monomial.
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* @param {Number} b The coefficient of the 1st order monomial.
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* @param {Number} c The coefficient of the 0th order monomial.
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* @returns {Number} The value of the discriminant.
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*/
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QuadraticRealPolynomial.computeDiscriminant = function (a, b, c) {
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//>>includeStart('debug', pragmas.debug);
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if (typeof a !== "number") {
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throw new Check.DeveloperError("a is a required number.");
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}
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if (typeof b !== "number") {
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throw new Check.DeveloperError("b is a required number.");
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}
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if (typeof c !== "number") {
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throw new Check.DeveloperError("c is a required number.");
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}
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//>>includeEnd('debug');
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const discriminant = b * b - 4.0 * a * c;
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return discriminant;
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};
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function addWithCancellationCheck$1(left, right, tolerance) {
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const difference = left + right;
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if (
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Math$1.CesiumMath.sign(left) !== Math$1.CesiumMath.sign(right) &&
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Math.abs(difference / Math.max(Math.abs(left), Math.abs(right))) < tolerance
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) {
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return 0.0;
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}
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return difference;
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}
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/**
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* Provides the real valued roots of the quadratic polynomial with the provided coefficients.
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*
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* @param {Number} a The coefficient of the 2nd order monomial.
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* @param {Number} b The coefficient of the 1st order monomial.
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* @param {Number} c The coefficient of the 0th order monomial.
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* @returns {Number[]} The real valued roots.
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*/
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QuadraticRealPolynomial.computeRealRoots = function (a, b, c) {
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//>>includeStart('debug', pragmas.debug);
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if (typeof a !== "number") {
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throw new Check.DeveloperError("a is a required number.");
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}
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if (typeof b !== "number") {
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throw new Check.DeveloperError("b is a required number.");
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}
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if (typeof c !== "number") {
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throw new Check.DeveloperError("c is a required number.");
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}
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//>>includeEnd('debug');
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let ratio;
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if (a === 0.0) {
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if (b === 0.0) {
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// Constant function: c = 0.
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return [];
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}
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// Linear function: b * x + c = 0.
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return [-c / b];
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} else if (b === 0.0) {
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if (c === 0.0) {
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// 2nd order monomial: a * x^2 = 0.
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return [0.0, 0.0];
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}
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const cMagnitude = Math.abs(c);
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const aMagnitude = Math.abs(a);
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if (
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cMagnitude < aMagnitude &&
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cMagnitude / aMagnitude < Math$1.CesiumMath.EPSILON14
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) {
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// c ~= 0.0.
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// 2nd order monomial: a * x^2 = 0.
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return [0.0, 0.0];
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} else if (
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cMagnitude > aMagnitude &&
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aMagnitude / cMagnitude < Math$1.CesiumMath.EPSILON14
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) {
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// a ~= 0.0.
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// Constant function: c = 0.
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return [];
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}
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// a * x^2 + c = 0
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ratio = -c / a;
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if (ratio < 0.0) {
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// Both roots are complex.
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return [];
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}
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// Both roots are real.
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const root = Math.sqrt(ratio);
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return [-root, root];
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} else if (c === 0.0) {
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// a * x^2 + b * x = 0
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ratio = -b / a;
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if (ratio < 0.0) {
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return [ratio, 0.0];
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}
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return [0.0, ratio];
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}
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// a * x^2 + b * x + c = 0
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const b2 = b * b;
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const four_ac = 4.0 * a * c;
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const radicand = addWithCancellationCheck$1(b2, -four_ac, Math$1.CesiumMath.EPSILON14);
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if (radicand < 0.0) {
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// Both roots are complex.
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return [];
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}
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const q =
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-0.5 *
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addWithCancellationCheck$1(
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b,
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Math$1.CesiumMath.sign(b) * Math.sqrt(radicand),
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Math$1.CesiumMath.EPSILON14
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);
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if (b > 0.0) {
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return [q / a, c / q];
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}
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return [c / q, q / a];
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};
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var QuadraticRealPolynomial$1 = QuadraticRealPolynomial;
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/**
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* Defines functions for 3rd order polynomial functions of one variable with only real coefficients.
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*
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* @namespace CubicRealPolynomial
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*/
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const CubicRealPolynomial = {};
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/**
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* Provides the discriminant of the cubic equation from the supplied coefficients.
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*
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* @param {Number} a The coefficient of the 3rd order monomial.
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* @param {Number} b The coefficient of the 2nd order monomial.
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* @param {Number} c The coefficient of the 1st order monomial.
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* @param {Number} d The coefficient of the 0th order monomial.
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* @returns {Number} The value of the discriminant.
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*/
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CubicRealPolynomial.computeDiscriminant = function (a, b, c, d) {
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//>>includeStart('debug', pragmas.debug);
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if (typeof a !== "number") {
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throw new Check.DeveloperError("a is a required number.");
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}
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if (typeof b !== "number") {
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throw new Check.DeveloperError("b is a required number.");
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}
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if (typeof c !== "number") {
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throw new Check.DeveloperError("c is a required number.");
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}
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if (typeof d !== "number") {
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throw new Check.DeveloperError("d is a required number.");
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}
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//>>includeEnd('debug');
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const a2 = a * a;
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const b2 = b * b;
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const c2 = c * c;
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const d2 = d * d;
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const discriminant =
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18.0 * a * b * c * d +
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b2 * c2 -
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27.0 * a2 * d2 -
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4.0 * (a * c2 * c + b2 * b * d);
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return discriminant;
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};
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function computeRealRoots(a, b, c, d) {
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const A = a;
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const B = b / 3.0;
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const C = c / 3.0;
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const D = d;
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const AC = A * C;
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const BD = B * D;
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const B2 = B * B;
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const C2 = C * C;
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const delta1 = A * C - B2;
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const delta2 = A * D - B * C;
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const delta3 = B * D - C2;
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const discriminant = 4.0 * delta1 * delta3 - delta2 * delta2;
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let temp;
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let temp1;
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if (discriminant < 0.0) {
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let ABar;
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let CBar;
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let DBar;
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if (B2 * BD >= AC * C2) {
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ABar = A;
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CBar = delta1;
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DBar = -2.0 * B * delta1 + A * delta2;
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} else {
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ABar = D;
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CBar = delta3;
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DBar = -D * delta2 + 2.0 * C * delta3;
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}
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const s = DBar < 0.0 ? -1.0 : 1.0; // This is not Math.Sign()!
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const temp0 = -s * Math.abs(ABar) * Math.sqrt(-discriminant);
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temp1 = -DBar + temp0;
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const x = temp1 / 2.0;
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const p = x < 0.0 ? -Math.pow(-x, 1.0 / 3.0) : Math.pow(x, 1.0 / 3.0);
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const q = temp1 === temp0 ? -p : -CBar / p;
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temp = CBar <= 0.0 ? p + q : -DBar / (p * p + q * q + CBar);
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if (B2 * BD >= AC * C2) {
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return [(temp - B) / A];
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}
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return [-D / (temp + C)];
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}
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const CBarA = delta1;
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const DBarA = -2.0 * B * delta1 + A * delta2;
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const CBarD = delta3;
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const DBarD = -D * delta2 + 2.0 * C * delta3;
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const squareRootOfDiscriminant = Math.sqrt(discriminant);
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const halfSquareRootOf3 = Math.sqrt(3.0) / 2.0;
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let theta = Math.abs(Math.atan2(A * squareRootOfDiscriminant, -DBarA) / 3.0);
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temp = 2.0 * Math.sqrt(-CBarA);
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let cosine = Math.cos(theta);
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temp1 = temp * cosine;
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let temp3 = temp * (-cosine / 2.0 - halfSquareRootOf3 * Math.sin(theta));
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const numeratorLarge = temp1 + temp3 > 2.0 * B ? temp1 - B : temp3 - B;
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const denominatorLarge = A;
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const root1 = numeratorLarge / denominatorLarge;
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theta = Math.abs(Math.atan2(D * squareRootOfDiscriminant, -DBarD) / 3.0);
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temp = 2.0 * Math.sqrt(-CBarD);
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cosine = Math.cos(theta);
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temp1 = temp * cosine;
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temp3 = temp * (-cosine / 2.0 - halfSquareRootOf3 * Math.sin(theta));
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const numeratorSmall = -D;
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const denominatorSmall = temp1 + temp3 < 2.0 * C ? temp1 + C : temp3 + C;
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const root3 = numeratorSmall / denominatorSmall;
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const E = denominatorLarge * denominatorSmall;
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const F =
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-numeratorLarge * denominatorSmall - denominatorLarge * numeratorSmall;
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const G = numeratorLarge * numeratorSmall;
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const root2 = (C * F - B * G) / (-B * F + C * E);
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if (root1 <= root2) {
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if (root1 <= root3) {
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if (root2 <= root3) {
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return [root1, root2, root3];
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}
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return [root1, root3, root2];
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}
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return [root3, root1, root2];
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}
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if (root1 <= root3) {
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return [root2, root1, root3];
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}
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if (root2 <= root3) {
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return [root2, root3, root1];
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}
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return [root3, root2, root1];
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}
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/**
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* Provides the real valued roots of the cubic polynomial with the provided coefficients.
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*
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* @param {Number} a The coefficient of the 3rd order monomial.
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* @param {Number} b The coefficient of the 2nd order monomial.
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* @param {Number} c The coefficient of the 1st order monomial.
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* @param {Number} d The coefficient of the 0th order monomial.
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* @returns {Number[]} The real valued roots.
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*/
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CubicRealPolynomial.computeRealRoots = function (a, b, c, d) {
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//>>includeStart('debug', pragmas.debug);
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if (typeof a !== "number") {
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throw new Check.DeveloperError("a is a required number.");
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}
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if (typeof b !== "number") {
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throw new Check.DeveloperError("b is a required number.");
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}
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if (typeof c !== "number") {
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throw new Check.DeveloperError("c is a required number.");
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}
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if (typeof d !== "number") {
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throw new Check.DeveloperError("d is a required number.");
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}
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//>>includeEnd('debug');
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let roots;
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let ratio;
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if (a === 0.0) {
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// Quadratic function: b * x^2 + c * x + d = 0.
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return QuadraticRealPolynomial$1.computeRealRoots(b, c, d);
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} else if (b === 0.0) {
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if (c === 0.0) {
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if (d === 0.0) {
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// 3rd order monomial: a * x^3 = 0.
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return [0.0, 0.0, 0.0];
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}
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// a * x^3 + d = 0
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ratio = -d / a;
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const root =
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ratio < 0.0 ? -Math.pow(-ratio, 1.0 / 3.0) : Math.pow(ratio, 1.0 / 3.0);
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return [root, root, root];
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} else if (d === 0.0) {
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// x * (a * x^2 + c) = 0.
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roots = QuadraticRealPolynomial$1.computeRealRoots(a, 0, c);
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// Return the roots in ascending order.
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if (roots.Length === 0) {
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return [0.0];
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}
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return [roots[0], 0.0, roots[1]];
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}
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// Deflated cubic polynomial: a * x^3 + c * x + d= 0.
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return computeRealRoots(a, 0, c, d);
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} else if (c === 0.0) {
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if (d === 0.0) {
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// x^2 * (a * x + b) = 0.
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ratio = -b / a;
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if (ratio < 0.0) {
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return [ratio, 0.0, 0.0];
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}
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return [0.0, 0.0, ratio];
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}
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// a * x^3 + b * x^2 + d = 0.
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return computeRealRoots(a, b, 0, d);
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} else if (d === 0.0) {
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// x * (a * x^2 + b * x + c) = 0
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roots = QuadraticRealPolynomial$1.computeRealRoots(a, b, c);
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// Return the roots in ascending order.
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if (roots.length === 0) {
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return [0.0];
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} else if (roots[1] <= 0.0) {
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return [roots[0], roots[1], 0.0];
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} else if (roots[0] >= 0.0) {
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return [0.0, roots[0], roots[1]];
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}
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return [roots[0], 0.0, roots[1]];
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}
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return computeRealRoots(a, b, c, d);
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};
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var CubicRealPolynomial$1 = CubicRealPolynomial;
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|
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/**
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|
* Defines functions for 4th order polynomial functions of one variable with only real coefficients.
|
|
*
|
|
* @namespace QuarticRealPolynomial
|
|
*/
|
|
const QuarticRealPolynomial = {};
|
|
|
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/**
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|
* Provides the discriminant of the quartic equation from the supplied coefficients.
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|
*
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* @param {Number} a The coefficient of the 4th order monomial.
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* @param {Number} b The coefficient of the 3rd order monomial.
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* @param {Number} c The coefficient of the 2nd order monomial.
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* @param {Number} d The coefficient of the 1st order monomial.
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* @param {Number} e The coefficient of the 0th order monomial.
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* @returns {Number} The value of the discriminant.
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|
*/
|
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QuarticRealPolynomial.computeDiscriminant = function (a, b, c, d, e) {
|
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//>>includeStart('debug', pragmas.debug);
|
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if (typeof a !== "number") {
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throw new Check.DeveloperError("a is a required number.");
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|
}
|
|
if (typeof b !== "number") {
|
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throw new Check.DeveloperError("b is a required number.");
|
|
}
|
|
if (typeof c !== "number") {
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throw new Check.DeveloperError("c is a required number.");
|
|
}
|
|
if (typeof d !== "number") {
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throw new Check.DeveloperError("d is a required number.");
|
|
}
|
|
if (typeof e !== "number") {
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throw new Check.DeveloperError("e is a required number.");
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|
}
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//>>includeEnd('debug');
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const a2 = a * a;
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const a3 = a2 * a;
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const b2 = b * b;
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const b3 = b2 * b;
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const c2 = c * c;
|
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const c3 = c2 * c;
|
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const d2 = d * d;
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const d3 = d2 * d;
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const e2 = e * e;
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const e3 = e2 * e;
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|
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const discriminant =
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b2 * c2 * d2 -
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4.0 * b3 * d3 -
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4.0 * a * c3 * d2 +
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18 * a * b * c * d3 -
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27.0 * a2 * d2 * d2 +
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256.0 * a3 * e3 +
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e *
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(18.0 * b3 * c * d -
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4.0 * b2 * c3 +
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16.0 * a * c2 * c2 -
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80.0 * a * b * c2 * d -
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6.0 * a * b2 * d2 +
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144.0 * a2 * c * d2) +
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e2 *
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(144.0 * a * b2 * c -
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27.0 * b2 * b2 -
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128.0 * a2 * c2 -
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192.0 * a2 * b * d);
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return discriminant;
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};
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|
|
function original(a3, a2, a1, a0) {
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const a3Squared = a3 * a3;
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|
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const p = a2 - (3.0 * a3Squared) / 8.0;
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const q = a1 - (a2 * a3) / 2.0 + (a3Squared * a3) / 8.0;
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const r =
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a0 -
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(a1 * a3) / 4.0 +
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(a2 * a3Squared) / 16.0 -
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(3.0 * a3Squared * a3Squared) / 256.0;
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|
|
// Find the roots of the cubic equations: h^6 + 2 p h^4 + (p^2 - 4 r) h^2 - q^2 = 0.
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|
const cubicRoots = CubicRealPolynomial$1.computeRealRoots(
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1.0,
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2.0 * p,
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p * p - 4.0 * r,
|
|
-q * q
|
|
);
|
|
|
|
if (cubicRoots.length > 0) {
|
|
const temp = -a3 / 4.0;
|
|
|
|
// Use the largest positive root.
|
|
const hSquared = cubicRoots[cubicRoots.length - 1];
|
|
|
|
if (Math.abs(hSquared) < Math$1.CesiumMath.EPSILON14) {
|
|
// y^4 + p y^2 + r = 0.
|
|
const roots = QuadraticRealPolynomial$1.computeRealRoots(1.0, p, r);
|
|
|
|
if (roots.length === 2) {
|
|
const root0 = roots[0];
|
|
const root1 = roots[1];
|
|
|
|
let y;
|
|
if (root0 >= 0.0 && root1 >= 0.0) {
|
|
const y0 = Math.sqrt(root0);
|
|
const y1 = Math.sqrt(root1);
|
|
|
|
return [temp - y1, temp - y0, temp + y0, temp + y1];
|
|
} else if (root0 >= 0.0 && root1 < 0.0) {
|
|
y = Math.sqrt(root0);
|
|
return [temp - y, temp + y];
|
|
} else if (root0 < 0.0 && root1 >= 0.0) {
|
|
y = Math.sqrt(root1);
|
|
return [temp - y, temp + y];
|
|
}
|
|
}
|
|
return [];
|
|
} else if (hSquared > 0.0) {
|
|
const h = Math.sqrt(hSquared);
|
|
|
|
const m = (p + hSquared - q / h) / 2.0;
|
|
const n = (p + hSquared + q / h) / 2.0;
|
|
|
|
// Now solve the two quadratic factors: (y^2 + h y + m)(y^2 - h y + n);
|
|
const roots1 = QuadraticRealPolynomial$1.computeRealRoots(1.0, h, m);
|
|
const roots2 = QuadraticRealPolynomial$1.computeRealRoots(1.0, -h, n);
|
|
|
|
if (roots1.length !== 0) {
|
|
roots1[0] += temp;
|
|
roots1[1] += temp;
|
|
|
|
if (roots2.length !== 0) {
|
|
roots2[0] += temp;
|
|
roots2[1] += temp;
|
|
|
|
if (roots1[1] <= roots2[0]) {
|
|
return [roots1[0], roots1[1], roots2[0], roots2[1]];
|
|
} else if (roots2[1] <= roots1[0]) {
|
|
return [roots2[0], roots2[1], roots1[0], roots1[1]];
|
|
} else if (roots1[0] >= roots2[0] && roots1[1] <= roots2[1]) {
|
|
return [roots2[0], roots1[0], roots1[1], roots2[1]];
|
|
} else if (roots2[0] >= roots1[0] && roots2[1] <= roots1[1]) {
|
|
return [roots1[0], roots2[0], roots2[1], roots1[1]];
|
|
} else if (roots1[0] > roots2[0] && roots1[0] < roots2[1]) {
|
|
return [roots2[0], roots1[0], roots2[1], roots1[1]];
|
|
}
|
|
return [roots1[0], roots2[0], roots1[1], roots2[1]];
|
|
}
|
|
return roots1;
|
|
}
|
|
|
|
if (roots2.length !== 0) {
|
|
roots2[0] += temp;
|
|
roots2[1] += temp;
|
|
|
|
return roots2;
|
|
}
|
|
return [];
|
|
}
|
|
}
|
|
return [];
|
|
}
|
|
|
|
function neumark(a3, a2, a1, a0) {
|
|
const a1Squared = a1 * a1;
|
|
const a2Squared = a2 * a2;
|
|
const a3Squared = a3 * a3;
|
|
|
|
const p = -2.0 * a2;
|
|
const q = a1 * a3 + a2Squared - 4.0 * a0;
|
|
const r = a3Squared * a0 - a1 * a2 * a3 + a1Squared;
|
|
|
|
const cubicRoots = CubicRealPolynomial$1.computeRealRoots(1.0, p, q, r);
|
|
|
|
if (cubicRoots.length > 0) {
|
|
// Use the most positive root
|
|
const y = cubicRoots[0];
|
|
|
|
const temp = a2 - y;
|
|
const tempSquared = temp * temp;
|
|
|
|
const g1 = a3 / 2.0;
|
|
const h1 = temp / 2.0;
|
|
|
|
const m = tempSquared - 4.0 * a0;
|
|
const mError = tempSquared + 4.0 * Math.abs(a0);
|
|
|
|
const n = a3Squared - 4.0 * y;
|
|
const nError = a3Squared + 4.0 * Math.abs(y);
|
|
|
|
let g2;
|
|
let h2;
|
|
|
|
if (y < 0.0 || m * nError < n * mError) {
|
|
const squareRootOfN = Math.sqrt(n);
|
|
g2 = squareRootOfN / 2.0;
|
|
h2 = squareRootOfN === 0.0 ? 0.0 : (a3 * h1 - a1) / squareRootOfN;
|
|
} else {
|
|
const squareRootOfM = Math.sqrt(m);
|
|
g2 = squareRootOfM === 0.0 ? 0.0 : (a3 * h1 - a1) / squareRootOfM;
|
|
h2 = squareRootOfM / 2.0;
|
|
}
|
|
|
|
let G;
|
|
let g;
|
|
if (g1 === 0.0 && g2 === 0.0) {
|
|
G = 0.0;
|
|
g = 0.0;
|
|
} else if (Math$1.CesiumMath.sign(g1) === Math$1.CesiumMath.sign(g2)) {
|
|
G = g1 + g2;
|
|
g = y / G;
|
|
} else {
|
|
g = g1 - g2;
|
|
G = y / g;
|
|
}
|
|
|
|
let H;
|
|
let h;
|
|
if (h1 === 0.0 && h2 === 0.0) {
|
|
H = 0.0;
|
|
h = 0.0;
|
|
} else if (Math$1.CesiumMath.sign(h1) === Math$1.CesiumMath.sign(h2)) {
|
|
H = h1 + h2;
|
|
h = a0 / H;
|
|
} else {
|
|
h = h1 - h2;
|
|
H = a0 / h;
|
|
}
|
|
|
|
// Now solve the two quadratic factors: (y^2 + G y + H)(y^2 + g y + h);
|
|
const roots1 = QuadraticRealPolynomial$1.computeRealRoots(1.0, G, H);
|
|
const roots2 = QuadraticRealPolynomial$1.computeRealRoots(1.0, g, h);
|
|
|
|
if (roots1.length !== 0) {
|
|
if (roots2.length !== 0) {
|
|
if (roots1[1] <= roots2[0]) {
|
|
return [roots1[0], roots1[1], roots2[0], roots2[1]];
|
|
} else if (roots2[1] <= roots1[0]) {
|
|
return [roots2[0], roots2[1], roots1[0], roots1[1]];
|
|
} else if (roots1[0] >= roots2[0] && roots1[1] <= roots2[1]) {
|
|
return [roots2[0], roots1[0], roots1[1], roots2[1]];
|
|
} else if (roots2[0] >= roots1[0] && roots2[1] <= roots1[1]) {
|
|
return [roots1[0], roots2[0], roots2[1], roots1[1]];
|
|
} else if (roots1[0] > roots2[0] && roots1[0] < roots2[1]) {
|
|
return [roots2[0], roots1[0], roots2[1], roots1[1]];
|
|
}
|
|
return [roots1[0], roots2[0], roots1[1], roots2[1]];
|
|
}
|
|
return roots1;
|
|
}
|
|
if (roots2.length !== 0) {
|
|
return roots2;
|
|
}
|
|
}
|
|
return [];
|
|
}
|
|
|
|
/**
|
|
* Provides the real valued roots of the quartic polynomial with the provided coefficients.
|
|
*
|
|
* @param {Number} a The coefficient of the 4th order monomial.
|
|
* @param {Number} b The coefficient of the 3rd order monomial.
|
|
* @param {Number} c The coefficient of the 2nd order monomial.
|
|
* @param {Number} d The coefficient of the 1st order monomial.
|
|
* @param {Number} e The coefficient of the 0th order monomial.
|
|
* @returns {Number[]} The real valued roots.
|
|
*/
|
|
QuarticRealPolynomial.computeRealRoots = function (a, b, c, d, e) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
if (typeof a !== "number") {
|
|
throw new Check.DeveloperError("a is a required number.");
|
|
}
|
|
if (typeof b !== "number") {
|
|
throw new Check.DeveloperError("b is a required number.");
|
|
}
|
|
if (typeof c !== "number") {
|
|
throw new Check.DeveloperError("c is a required number.");
|
|
}
|
|
if (typeof d !== "number") {
|
|
throw new Check.DeveloperError("d is a required number.");
|
|
}
|
|
if (typeof e !== "number") {
|
|
throw new Check.DeveloperError("e is a required number.");
|
|
}
|
|
//>>includeEnd('debug');
|
|
|
|
if (Math.abs(a) < Math$1.CesiumMath.EPSILON15) {
|
|
return CubicRealPolynomial$1.computeRealRoots(b, c, d, e);
|
|
}
|
|
const a3 = b / a;
|
|
const a2 = c / a;
|
|
const a1 = d / a;
|
|
const a0 = e / a;
|
|
|
|
let k = a3 < 0.0 ? 1 : 0;
|
|
k += a2 < 0.0 ? k + 1 : k;
|
|
k += a1 < 0.0 ? k + 1 : k;
|
|
k += a0 < 0.0 ? k + 1 : k;
|
|
|
|
switch (k) {
|
|
case 0:
|
|
return original(a3, a2, a1, a0);
|
|
case 1:
|
|
return neumark(a3, a2, a1, a0);
|
|
case 2:
|
|
return neumark(a3, a2, a1, a0);
|
|
case 3:
|
|
return original(a3, a2, a1, a0);
|
|
case 4:
|
|
return original(a3, a2, a1, a0);
|
|
case 5:
|
|
return neumark(a3, a2, a1, a0);
|
|
case 6:
|
|
return original(a3, a2, a1, a0);
|
|
case 7:
|
|
return original(a3, a2, a1, a0);
|
|
case 8:
|
|
return neumark(a3, a2, a1, a0);
|
|
case 9:
|
|
return original(a3, a2, a1, a0);
|
|
case 10:
|
|
return original(a3, a2, a1, a0);
|
|
case 11:
|
|
return neumark(a3, a2, a1, a0);
|
|
case 12:
|
|
return original(a3, a2, a1, a0);
|
|
case 13:
|
|
return original(a3, a2, a1, a0);
|
|
case 14:
|
|
return original(a3, a2, a1, a0);
|
|
case 15:
|
|
return original(a3, a2, a1, a0);
|
|
default:
|
|
return undefined;
|
|
}
|
|
};
|
|
var QuarticRealPolynomial$1 = QuarticRealPolynomial;
|
|
|
|
/**
|
|
* Represents a ray that extends infinitely from the provided origin in the provided direction.
|
|
* @alias Ray
|
|
* @constructor
|
|
*
|
|
* @param {Cartesian3} [origin=Cartesian3.ZERO] The origin of the ray.
|
|
* @param {Cartesian3} [direction=Cartesian3.ZERO] The direction of the ray.
|
|
*/
|
|
function Ray(origin, direction) {
|
|
direction = Matrix3.Cartesian3.clone(defaultValue.defaultValue(direction, Matrix3.Cartesian3.ZERO));
|
|
if (!Matrix3.Cartesian3.equals(direction, Matrix3.Cartesian3.ZERO)) {
|
|
Matrix3.Cartesian3.normalize(direction, direction);
|
|
}
|
|
|
|
/**
|
|
* The origin of the ray.
|
|
* @type {Cartesian3}
|
|
* @default {@link Cartesian3.ZERO}
|
|
*/
|
|
this.origin = Matrix3.Cartesian3.clone(defaultValue.defaultValue(origin, Matrix3.Cartesian3.ZERO));
|
|
|
|
/**
|
|
* The direction of the ray.
|
|
* @type {Cartesian3}
|
|
*/
|
|
this.direction = direction;
|
|
}
|
|
|
|
/**
|
|
* Duplicates a Ray instance.
|
|
*
|
|
* @param {Ray} ray The ray to duplicate.
|
|
* @param {Ray} [result] The object onto which to store the result.
|
|
* @returns {Ray} The modified result parameter or a new Ray instance if one was not provided. (Returns undefined if ray is undefined)
|
|
*/
|
|
Ray.clone = function (ray, result) {
|
|
if (!defaultValue.defined(ray)) {
|
|
return undefined;
|
|
}
|
|
if (!defaultValue.defined(result)) {
|
|
return new Ray(ray.origin, ray.direction);
|
|
}
|
|
result.origin = Matrix3.Cartesian3.clone(ray.origin);
|
|
result.direction = Matrix3.Cartesian3.clone(ray.direction);
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Computes the point along the ray given by r(t) = o + t*d,
|
|
* where o is the origin of the ray and d is the direction.
|
|
*
|
|
* @param {Ray} ray The ray.
|
|
* @param {Number} t A scalar value.
|
|
* @param {Cartesian3} [result] The object in which the result will be stored.
|
|
* @returns {Cartesian3} The modified result parameter, or a new instance if none was provided.
|
|
*
|
|
* @example
|
|
* //Get the first intersection point of a ray and an ellipsoid.
|
|
* const intersection = Cesium.IntersectionTests.rayEllipsoid(ray, ellipsoid);
|
|
* const point = Cesium.Ray.getPoint(ray, intersection.start);
|
|
*/
|
|
Ray.getPoint = function (ray, t, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.object("ray", ray);
|
|
Check.Check.typeOf.number("t", t);
|
|
//>>includeEnd('debug');
|
|
|
|
if (!defaultValue.defined(result)) {
|
|
result = new Matrix3.Cartesian3();
|
|
}
|
|
|
|
result = Matrix3.Cartesian3.multiplyByScalar(ray.direction, t, result);
|
|
return Matrix3.Cartesian3.add(ray.origin, result, result);
|
|
};
|
|
|
|
/**
|
|
* Functions for computing the intersection between geometries such as rays, planes, triangles, and ellipsoids.
|
|
*
|
|
* @namespace IntersectionTests
|
|
*/
|
|
const IntersectionTests = {};
|
|
|
|
/**
|
|
* Computes the intersection of a ray and a plane.
|
|
*
|
|
* @param {Ray} ray The ray.
|
|
* @param {Plane} plane The plane.
|
|
* @param {Cartesian3} [result] The object onto which to store the result.
|
|
* @returns {Cartesian3} The intersection point or undefined if there is no intersections.
|
|
*/
|
|
IntersectionTests.rayPlane = function (ray, plane, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
if (!defaultValue.defined(ray)) {
|
|
throw new Check.DeveloperError("ray is required.");
|
|
}
|
|
if (!defaultValue.defined(plane)) {
|
|
throw new Check.DeveloperError("plane is required.");
|
|
}
|
|
//>>includeEnd('debug');
|
|
|
|
if (!defaultValue.defined(result)) {
|
|
result = new Matrix3.Cartesian3();
|
|
}
|
|
|
|
const origin = ray.origin;
|
|
const direction = ray.direction;
|
|
const normal = plane.normal;
|
|
const denominator = Matrix3.Cartesian3.dot(normal, direction);
|
|
|
|
if (Math.abs(denominator) < Math$1.CesiumMath.EPSILON15) {
|
|
// Ray is parallel to plane. The ray may be in the polygon's plane.
|
|
return undefined;
|
|
}
|
|
|
|
const t = (-plane.distance - Matrix3.Cartesian3.dot(normal, origin)) / denominator;
|
|
|
|
if (t < 0) {
|
|
return undefined;
|
|
}
|
|
|
|
result = Matrix3.Cartesian3.multiplyByScalar(direction, t, result);
|
|
return Matrix3.Cartesian3.add(origin, result, result);
|
|
};
|
|
|
|
const scratchEdge0 = new Matrix3.Cartesian3();
|
|
const scratchEdge1 = new Matrix3.Cartesian3();
|
|
const scratchPVec = new Matrix3.Cartesian3();
|
|
const scratchTVec = new Matrix3.Cartesian3();
|
|
const scratchQVec = new Matrix3.Cartesian3();
|
|
|
|
/**
|
|
* Computes the intersection of a ray and a triangle as a parametric distance along the input ray. The result is negative when the triangle is behind the ray.
|
|
*
|
|
* Implements {@link https://cadxfem.org/inf/Fast%20MinimumStorage%20RayTriangle%20Intersection.pdf|
|
|
* Fast Minimum Storage Ray/Triangle Intersection} by Tomas Moller and Ben Trumbore.
|
|
*
|
|
* @memberof IntersectionTests
|
|
*
|
|
* @param {Ray} ray The ray.
|
|
* @param {Cartesian3} p0 The first vertex of the triangle.
|
|
* @param {Cartesian3} p1 The second vertex of the triangle.
|
|
* @param {Cartesian3} p2 The third vertex of the triangle.
|
|
* @param {Boolean} [cullBackFaces=false] If <code>true</code>, will only compute an intersection with the front face of the triangle
|
|
* and return undefined for intersections with the back face.
|
|
* @returns {Number} The intersection as a parametric distance along the ray, or undefined if there is no intersection.
|
|
*/
|
|
IntersectionTests.rayTriangleParametric = function (
|
|
ray,
|
|
p0,
|
|
p1,
|
|
p2,
|
|
cullBackFaces
|
|
) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
if (!defaultValue.defined(ray)) {
|
|
throw new Check.DeveloperError("ray is required.");
|
|
}
|
|
if (!defaultValue.defined(p0)) {
|
|
throw new Check.DeveloperError("p0 is required.");
|
|
}
|
|
if (!defaultValue.defined(p1)) {
|
|
throw new Check.DeveloperError("p1 is required.");
|
|
}
|
|
if (!defaultValue.defined(p2)) {
|
|
throw new Check.DeveloperError("p2 is required.");
|
|
}
|
|
//>>includeEnd('debug');
|
|
|
|
cullBackFaces = defaultValue.defaultValue(cullBackFaces, false);
|
|
|
|
const origin = ray.origin;
|
|
const direction = ray.direction;
|
|
|
|
const edge0 = Matrix3.Cartesian3.subtract(p1, p0, scratchEdge0);
|
|
const edge1 = Matrix3.Cartesian3.subtract(p2, p0, scratchEdge1);
|
|
|
|
const p = Matrix3.Cartesian3.cross(direction, edge1, scratchPVec);
|
|
const det = Matrix3.Cartesian3.dot(edge0, p);
|
|
|
|
let tvec;
|
|
let q;
|
|
|
|
let u;
|
|
let v;
|
|
let t;
|
|
|
|
if (cullBackFaces) {
|
|
if (det < Math$1.CesiumMath.EPSILON6) {
|
|
return undefined;
|
|
}
|
|
|
|
tvec = Matrix3.Cartesian3.subtract(origin, p0, scratchTVec);
|
|
u = Matrix3.Cartesian3.dot(tvec, p);
|
|
if (u < 0.0 || u > det) {
|
|
return undefined;
|
|
}
|
|
|
|
q = Matrix3.Cartesian3.cross(tvec, edge0, scratchQVec);
|
|
|
|
v = Matrix3.Cartesian3.dot(direction, q);
|
|
if (v < 0.0 || u + v > det) {
|
|
return undefined;
|
|
}
|
|
|
|
t = Matrix3.Cartesian3.dot(edge1, q) / det;
|
|
} else {
|
|
if (Math.abs(det) < Math$1.CesiumMath.EPSILON6) {
|
|
return undefined;
|
|
}
|
|
const invDet = 1.0 / det;
|
|
|
|
tvec = Matrix3.Cartesian3.subtract(origin, p0, scratchTVec);
|
|
u = Matrix3.Cartesian3.dot(tvec, p) * invDet;
|
|
if (u < 0.0 || u > 1.0) {
|
|
return undefined;
|
|
}
|
|
|
|
q = Matrix3.Cartesian3.cross(tvec, edge0, scratchQVec);
|
|
|
|
v = Matrix3.Cartesian3.dot(direction, q) * invDet;
|
|
if (v < 0.0 || u + v > 1.0) {
|
|
return undefined;
|
|
}
|
|
|
|
t = Matrix3.Cartesian3.dot(edge1, q) * invDet;
|
|
}
|
|
|
|
return t;
|
|
};
|
|
|
|
/**
|
|
* Computes the intersection of a ray and a triangle as a Cartesian3 coordinate.
|
|
*
|
|
* Implements {@link https://cadxfem.org/inf/Fast%20MinimumStorage%20RayTriangle%20Intersection.pdf|
|
|
* Fast Minimum Storage Ray/Triangle Intersection} by Tomas Moller and Ben Trumbore.
|
|
*
|
|
* @memberof IntersectionTests
|
|
*
|
|
* @param {Ray} ray The ray.
|
|
* @param {Cartesian3} p0 The first vertex of the triangle.
|
|
* @param {Cartesian3} p1 The second vertex of the triangle.
|
|
* @param {Cartesian3} p2 The third vertex of the triangle.
|
|
* @param {Boolean} [cullBackFaces=false] If <code>true</code>, will only compute an intersection with the front face of the triangle
|
|
* and return undefined for intersections with the back face.
|
|
* @param {Cartesian3} [result] The <code>Cartesian3</code> onto which to store the result.
|
|
* @returns {Cartesian3} The intersection point or undefined if there is no intersections.
|
|
*/
|
|
IntersectionTests.rayTriangle = function (
|
|
ray,
|
|
p0,
|
|
p1,
|
|
p2,
|
|
cullBackFaces,
|
|
result
|
|
) {
|
|
const t = IntersectionTests.rayTriangleParametric(
|
|
ray,
|
|
p0,
|
|
p1,
|
|
p2,
|
|
cullBackFaces
|
|
);
|
|
if (!defaultValue.defined(t) || t < 0.0) {
|
|
return undefined;
|
|
}
|
|
|
|
if (!defaultValue.defined(result)) {
|
|
result = new Matrix3.Cartesian3();
|
|
}
|
|
|
|
Matrix3.Cartesian3.multiplyByScalar(ray.direction, t, result);
|
|
return Matrix3.Cartesian3.add(ray.origin, result, result);
|
|
};
|
|
|
|
const scratchLineSegmentTriangleRay = new Ray();
|
|
|
|
/**
|
|
* Computes the intersection of a line segment and a triangle.
|
|
* @memberof IntersectionTests
|
|
*
|
|
* @param {Cartesian3} v0 The an end point of the line segment.
|
|
* @param {Cartesian3} v1 The other end point of the line segment.
|
|
* @param {Cartesian3} p0 The first vertex of the triangle.
|
|
* @param {Cartesian3} p1 The second vertex of the triangle.
|
|
* @param {Cartesian3} p2 The third vertex of the triangle.
|
|
* @param {Boolean} [cullBackFaces=false] If <code>true</code>, will only compute an intersection with the front face of the triangle
|
|
* and return undefined for intersections with the back face.
|
|
* @param {Cartesian3} [result] The <code>Cartesian3</code> onto which to store the result.
|
|
* @returns {Cartesian3} The intersection point or undefined if there is no intersections.
|
|
*/
|
|
IntersectionTests.lineSegmentTriangle = function (
|
|
v0,
|
|
v1,
|
|
p0,
|
|
p1,
|
|
p2,
|
|
cullBackFaces,
|
|
result
|
|
) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
if (!defaultValue.defined(v0)) {
|
|
throw new Check.DeveloperError("v0 is required.");
|
|
}
|
|
if (!defaultValue.defined(v1)) {
|
|
throw new Check.DeveloperError("v1 is required.");
|
|
}
|
|
if (!defaultValue.defined(p0)) {
|
|
throw new Check.DeveloperError("p0 is required.");
|
|
}
|
|
if (!defaultValue.defined(p1)) {
|
|
throw new Check.DeveloperError("p1 is required.");
|
|
}
|
|
if (!defaultValue.defined(p2)) {
|
|
throw new Check.DeveloperError("p2 is required.");
|
|
}
|
|
//>>includeEnd('debug');
|
|
|
|
const ray = scratchLineSegmentTriangleRay;
|
|
Matrix3.Cartesian3.clone(v0, ray.origin);
|
|
Matrix3.Cartesian3.subtract(v1, v0, ray.direction);
|
|
Matrix3.Cartesian3.normalize(ray.direction, ray.direction);
|
|
|
|
const t = IntersectionTests.rayTriangleParametric(
|
|
ray,
|
|
p0,
|
|
p1,
|
|
p2,
|
|
cullBackFaces
|
|
);
|
|
if (!defaultValue.defined(t) || t < 0.0 || t > Matrix3.Cartesian3.distance(v0, v1)) {
|
|
return undefined;
|
|
}
|
|
|
|
if (!defaultValue.defined(result)) {
|
|
result = new Matrix3.Cartesian3();
|
|
}
|
|
|
|
Matrix3.Cartesian3.multiplyByScalar(ray.direction, t, result);
|
|
return Matrix3.Cartesian3.add(ray.origin, result, result);
|
|
};
|
|
|
|
function solveQuadratic(a, b, c, result) {
|
|
const det = b * b - 4.0 * a * c;
|
|
if (det < 0.0) {
|
|
return undefined;
|
|
} else if (det > 0.0) {
|
|
const denom = 1.0 / (2.0 * a);
|
|
const disc = Math.sqrt(det);
|
|
const root0 = (-b + disc) * denom;
|
|
const root1 = (-b - disc) * denom;
|
|
|
|
if (root0 < root1) {
|
|
result.root0 = root0;
|
|
result.root1 = root1;
|
|
} else {
|
|
result.root0 = root1;
|
|
result.root1 = root0;
|
|
}
|
|
|
|
return result;
|
|
}
|
|
|
|
const root = -b / (2.0 * a);
|
|
if (root === 0.0) {
|
|
return undefined;
|
|
}
|
|
|
|
result.root0 = result.root1 = root;
|
|
return result;
|
|
}
|
|
|
|
const raySphereRoots = {
|
|
root0: 0.0,
|
|
root1: 0.0,
|
|
};
|
|
|
|
function raySphere(ray, sphere, result) {
|
|
if (!defaultValue.defined(result)) {
|
|
result = new Transforms.Interval();
|
|
}
|
|
|
|
const origin = ray.origin;
|
|
const direction = ray.direction;
|
|
|
|
const center = sphere.center;
|
|
const radiusSquared = sphere.radius * sphere.radius;
|
|
|
|
const diff = Matrix3.Cartesian3.subtract(origin, center, scratchPVec);
|
|
|
|
const a = Matrix3.Cartesian3.dot(direction, direction);
|
|
const b = 2.0 * Matrix3.Cartesian3.dot(direction, diff);
|
|
const c = Matrix3.Cartesian3.magnitudeSquared(diff) - radiusSquared;
|
|
|
|
const roots = solveQuadratic(a, b, c, raySphereRoots);
|
|
if (!defaultValue.defined(roots)) {
|
|
return undefined;
|
|
}
|
|
|
|
result.start = roots.root0;
|
|
result.stop = roots.root1;
|
|
return result;
|
|
}
|
|
|
|
/**
|
|
* Computes the intersection points of a ray with a sphere.
|
|
* @memberof IntersectionTests
|
|
*
|
|
* @param {Ray} ray The ray.
|
|
* @param {BoundingSphere} sphere The sphere.
|
|
* @param {Interval} [result] The result onto which to store the result.
|
|
* @returns {Interval} The interval containing scalar points along the ray or undefined if there are no intersections.
|
|
*/
|
|
IntersectionTests.raySphere = function (ray, sphere, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
if (!defaultValue.defined(ray)) {
|
|
throw new Check.DeveloperError("ray is required.");
|
|
}
|
|
if (!defaultValue.defined(sphere)) {
|
|
throw new Check.DeveloperError("sphere is required.");
|
|
}
|
|
//>>includeEnd('debug');
|
|
|
|
result = raySphere(ray, sphere, result);
|
|
if (!defaultValue.defined(result) || result.stop < 0.0) {
|
|
return undefined;
|
|
}
|
|
|
|
result.start = Math.max(result.start, 0.0);
|
|
return result;
|
|
};
|
|
|
|
const scratchLineSegmentRay = new Ray();
|
|
|
|
/**
|
|
* Computes the intersection points of a line segment with a sphere.
|
|
* @memberof IntersectionTests
|
|
*
|
|
* @param {Cartesian3} p0 An end point of the line segment.
|
|
* @param {Cartesian3} p1 The other end point of the line segment.
|
|
* @param {BoundingSphere} sphere The sphere.
|
|
* @param {Interval} [result] The result onto which to store the result.
|
|
* @returns {Interval} The interval containing scalar points along the ray or undefined if there are no intersections.
|
|
*/
|
|
IntersectionTests.lineSegmentSphere = function (p0, p1, sphere, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
if (!defaultValue.defined(p0)) {
|
|
throw new Check.DeveloperError("p0 is required.");
|
|
}
|
|
if (!defaultValue.defined(p1)) {
|
|
throw new Check.DeveloperError("p1 is required.");
|
|
}
|
|
if (!defaultValue.defined(sphere)) {
|
|
throw new Check.DeveloperError("sphere is required.");
|
|
}
|
|
//>>includeEnd('debug');
|
|
|
|
const ray = scratchLineSegmentRay;
|
|
Matrix3.Cartesian3.clone(p0, ray.origin);
|
|
const direction = Matrix3.Cartesian3.subtract(p1, p0, ray.direction);
|
|
|
|
const maxT = Matrix3.Cartesian3.magnitude(direction);
|
|
Matrix3.Cartesian3.normalize(direction, direction);
|
|
|
|
result = raySphere(ray, sphere, result);
|
|
if (!defaultValue.defined(result) || result.stop < 0.0 || result.start > maxT) {
|
|
return undefined;
|
|
}
|
|
|
|
result.start = Math.max(result.start, 0.0);
|
|
result.stop = Math.min(result.stop, maxT);
|
|
return result;
|
|
};
|
|
|
|
const scratchQ = new Matrix3.Cartesian3();
|
|
const scratchW = new Matrix3.Cartesian3();
|
|
|
|
/**
|
|
* Computes the intersection points of a ray with an ellipsoid.
|
|
*
|
|
* @param {Ray} ray The ray.
|
|
* @param {Ellipsoid} ellipsoid The ellipsoid.
|
|
* @returns {Interval} The interval containing scalar points along the ray or undefined if there are no intersections.
|
|
*/
|
|
IntersectionTests.rayEllipsoid = function (ray, ellipsoid) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
if (!defaultValue.defined(ray)) {
|
|
throw new Check.DeveloperError("ray is required.");
|
|
}
|
|
if (!defaultValue.defined(ellipsoid)) {
|
|
throw new Check.DeveloperError("ellipsoid is required.");
|
|
}
|
|
//>>includeEnd('debug');
|
|
|
|
const inverseRadii = ellipsoid.oneOverRadii;
|
|
const q = Matrix3.Cartesian3.multiplyComponents(inverseRadii, ray.origin, scratchQ);
|
|
const w = Matrix3.Cartesian3.multiplyComponents(
|
|
inverseRadii,
|
|
ray.direction,
|
|
scratchW
|
|
);
|
|
|
|
const q2 = Matrix3.Cartesian3.magnitudeSquared(q);
|
|
const qw = Matrix3.Cartesian3.dot(q, w);
|
|
|
|
let difference, w2, product, discriminant, temp;
|
|
|
|
if (q2 > 1.0) {
|
|
// Outside ellipsoid.
|
|
if (qw >= 0.0) {
|
|
// Looking outward or tangent (0 intersections).
|
|
return undefined;
|
|
}
|
|
|
|
// qw < 0.0.
|
|
const qw2 = qw * qw;
|
|
difference = q2 - 1.0; // Positively valued.
|
|
w2 = Matrix3.Cartesian3.magnitudeSquared(w);
|
|
product = w2 * difference;
|
|
|
|
if (qw2 < product) {
|
|
// Imaginary roots (0 intersections).
|
|
return undefined;
|
|
} else if (qw2 > product) {
|
|
// Distinct roots (2 intersections).
|
|
discriminant = qw * qw - product;
|
|
temp = -qw + Math.sqrt(discriminant); // Avoid cancellation.
|
|
const root0 = temp / w2;
|
|
const root1 = difference / temp;
|
|
if (root0 < root1) {
|
|
return new Transforms.Interval(root0, root1);
|
|
}
|
|
|
|
return {
|
|
start: root1,
|
|
stop: root0,
|
|
};
|
|
}
|
|
// qw2 == product. Repeated roots (2 intersections).
|
|
const root = Math.sqrt(difference / w2);
|
|
return new Transforms.Interval(root, root);
|
|
} else if (q2 < 1.0) {
|
|
// Inside ellipsoid (2 intersections).
|
|
difference = q2 - 1.0; // Negatively valued.
|
|
w2 = Matrix3.Cartesian3.magnitudeSquared(w);
|
|
product = w2 * difference; // Negatively valued.
|
|
|
|
discriminant = qw * qw - product;
|
|
temp = -qw + Math.sqrt(discriminant); // Positively valued.
|
|
return new Transforms.Interval(0.0, temp / w2);
|
|
}
|
|
// q2 == 1.0. On ellipsoid.
|
|
if (qw < 0.0) {
|
|
// Looking inward.
|
|
w2 = Matrix3.Cartesian3.magnitudeSquared(w);
|
|
return new Transforms.Interval(0.0, -qw / w2);
|
|
}
|
|
|
|
// qw >= 0.0. Looking outward or tangent.
|
|
return undefined;
|
|
};
|
|
|
|
function addWithCancellationCheck(left, right, tolerance) {
|
|
const difference = left + right;
|
|
if (
|
|
Math$1.CesiumMath.sign(left) !== Math$1.CesiumMath.sign(right) &&
|
|
Math.abs(difference / Math.max(Math.abs(left), Math.abs(right))) < tolerance
|
|
) {
|
|
return 0.0;
|
|
}
|
|
|
|
return difference;
|
|
}
|
|
|
|
function quadraticVectorExpression(A, b, c, x, w) {
|
|
const xSquared = x * x;
|
|
const wSquared = w * w;
|
|
|
|
const l2 = (A[Matrix3.Matrix3.COLUMN1ROW1] - A[Matrix3.Matrix3.COLUMN2ROW2]) * wSquared;
|
|
const l1 =
|
|
w *
|
|
(x *
|
|
addWithCancellationCheck(
|
|
A[Matrix3.Matrix3.COLUMN1ROW0],
|
|
A[Matrix3.Matrix3.COLUMN0ROW1],
|
|
Math$1.CesiumMath.EPSILON15
|
|
) +
|
|
b.y);
|
|
const l0 =
|
|
A[Matrix3.Matrix3.COLUMN0ROW0] * xSquared +
|
|
A[Matrix3.Matrix3.COLUMN2ROW2] * wSquared +
|
|
x * b.x +
|
|
c;
|
|
|
|
const r1 =
|
|
wSquared *
|
|
addWithCancellationCheck(
|
|
A[Matrix3.Matrix3.COLUMN2ROW1],
|
|
A[Matrix3.Matrix3.COLUMN1ROW2],
|
|
Math$1.CesiumMath.EPSILON15
|
|
);
|
|
const r0 =
|
|
w *
|
|
(x *
|
|
addWithCancellationCheck(A[Matrix3.Matrix3.COLUMN2ROW0], A[Matrix3.Matrix3.COLUMN0ROW2]) +
|
|
b.z);
|
|
|
|
let cosines;
|
|
const solutions = [];
|
|
if (r0 === 0.0 && r1 === 0.0) {
|
|
cosines = QuadraticRealPolynomial$1.computeRealRoots(l2, l1, l0);
|
|
if (cosines.length === 0) {
|
|
return solutions;
|
|
}
|
|
|
|
const cosine0 = cosines[0];
|
|
const sine0 = Math.sqrt(Math.max(1.0 - cosine0 * cosine0, 0.0));
|
|
solutions.push(new Matrix3.Cartesian3(x, w * cosine0, w * -sine0));
|
|
solutions.push(new Matrix3.Cartesian3(x, w * cosine0, w * sine0));
|
|
|
|
if (cosines.length === 2) {
|
|
const cosine1 = cosines[1];
|
|
const sine1 = Math.sqrt(Math.max(1.0 - cosine1 * cosine1, 0.0));
|
|
solutions.push(new Matrix3.Cartesian3(x, w * cosine1, w * -sine1));
|
|
solutions.push(new Matrix3.Cartesian3(x, w * cosine1, w * sine1));
|
|
}
|
|
|
|
return solutions;
|
|
}
|
|
|
|
const r0Squared = r0 * r0;
|
|
const r1Squared = r1 * r1;
|
|
const l2Squared = l2 * l2;
|
|
const r0r1 = r0 * r1;
|
|
|
|
const c4 = l2Squared + r1Squared;
|
|
const c3 = 2.0 * (l1 * l2 + r0r1);
|
|
const c2 = 2.0 * l0 * l2 + l1 * l1 - r1Squared + r0Squared;
|
|
const c1 = 2.0 * (l0 * l1 - r0r1);
|
|
const c0 = l0 * l0 - r0Squared;
|
|
|
|
if (c4 === 0.0 && c3 === 0.0 && c2 === 0.0 && c1 === 0.0) {
|
|
return solutions;
|
|
}
|
|
|
|
cosines = QuarticRealPolynomial$1.computeRealRoots(c4, c3, c2, c1, c0);
|
|
const length = cosines.length;
|
|
if (length === 0) {
|
|
return solutions;
|
|
}
|
|
|
|
for (let i = 0; i < length; ++i) {
|
|
const cosine = cosines[i];
|
|
const cosineSquared = cosine * cosine;
|
|
const sineSquared = Math.max(1.0 - cosineSquared, 0.0);
|
|
const sine = Math.sqrt(sineSquared);
|
|
|
|
//const left = l2 * cosineSquared + l1 * cosine + l0;
|
|
let left;
|
|
if (Math$1.CesiumMath.sign(l2) === Math$1.CesiumMath.sign(l0)) {
|
|
left = addWithCancellationCheck(
|
|
l2 * cosineSquared + l0,
|
|
l1 * cosine,
|
|
Math$1.CesiumMath.EPSILON12
|
|
);
|
|
} else if (Math$1.CesiumMath.sign(l0) === Math$1.CesiumMath.sign(l1 * cosine)) {
|
|
left = addWithCancellationCheck(
|
|
l2 * cosineSquared,
|
|
l1 * cosine + l0,
|
|
Math$1.CesiumMath.EPSILON12
|
|
);
|
|
} else {
|
|
left = addWithCancellationCheck(
|
|
l2 * cosineSquared + l1 * cosine,
|
|
l0,
|
|
Math$1.CesiumMath.EPSILON12
|
|
);
|
|
}
|
|
|
|
const right = addWithCancellationCheck(
|
|
r1 * cosine,
|
|
r0,
|
|
Math$1.CesiumMath.EPSILON15
|
|
);
|
|
const product = left * right;
|
|
|
|
if (product < 0.0) {
|
|
solutions.push(new Matrix3.Cartesian3(x, w * cosine, w * sine));
|
|
} else if (product > 0.0) {
|
|
solutions.push(new Matrix3.Cartesian3(x, w * cosine, w * -sine));
|
|
} else if (sine !== 0.0) {
|
|
solutions.push(new Matrix3.Cartesian3(x, w * cosine, w * -sine));
|
|
solutions.push(new Matrix3.Cartesian3(x, w * cosine, w * sine));
|
|
++i;
|
|
} else {
|
|
solutions.push(new Matrix3.Cartesian3(x, w * cosine, w * sine));
|
|
}
|
|
}
|
|
|
|
return solutions;
|
|
}
|
|
|
|
const firstAxisScratch = new Matrix3.Cartesian3();
|
|
const secondAxisScratch = new Matrix3.Cartesian3();
|
|
const thirdAxisScratch = new Matrix3.Cartesian3();
|
|
const referenceScratch = new Matrix3.Cartesian3();
|
|
const bCart = new Matrix3.Cartesian3();
|
|
const bScratch = new Matrix3.Matrix3();
|
|
const btScratch = new Matrix3.Matrix3();
|
|
const diScratch = new Matrix3.Matrix3();
|
|
const dScratch = new Matrix3.Matrix3();
|
|
const cScratch = new Matrix3.Matrix3();
|
|
const tempMatrix = new Matrix3.Matrix3();
|
|
const aScratch = new Matrix3.Matrix3();
|
|
const sScratch = new Matrix3.Cartesian3();
|
|
const closestScratch = new Matrix3.Cartesian3();
|
|
const surfPointScratch = new Matrix3.Cartographic();
|
|
|
|
/**
|
|
* Provides the point along the ray which is nearest to the ellipsoid.
|
|
*
|
|
* @param {Ray} ray The ray.
|
|
* @param {Ellipsoid} ellipsoid The ellipsoid.
|
|
* @returns {Cartesian3} The nearest planetodetic point on the ray.
|
|
*/
|
|
IntersectionTests.grazingAltitudeLocation = function (ray, ellipsoid) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
if (!defaultValue.defined(ray)) {
|
|
throw new Check.DeveloperError("ray is required.");
|
|
}
|
|
if (!defaultValue.defined(ellipsoid)) {
|
|
throw new Check.DeveloperError("ellipsoid is required.");
|
|
}
|
|
//>>includeEnd('debug');
|
|
|
|
const position = ray.origin;
|
|
const direction = ray.direction;
|
|
|
|
if (!Matrix3.Cartesian3.equals(position, Matrix3.Cartesian3.ZERO)) {
|
|
const normal = ellipsoid.geodeticSurfaceNormal(position, firstAxisScratch);
|
|
if (Matrix3.Cartesian3.dot(direction, normal) >= 0.0) {
|
|
// The location provided is the closest point in altitude
|
|
return position;
|
|
}
|
|
}
|
|
|
|
const intersects = defaultValue.defined(this.rayEllipsoid(ray, ellipsoid));
|
|
|
|
// Compute the scaled direction vector.
|
|
const f = ellipsoid.transformPositionToScaledSpace(
|
|
direction,
|
|
firstAxisScratch
|
|
);
|
|
|
|
// Constructs a basis from the unit scaled direction vector. Construct its rotation and transpose.
|
|
const firstAxis = Matrix3.Cartesian3.normalize(f, f);
|
|
const reference = Matrix3.Cartesian3.mostOrthogonalAxis(f, referenceScratch);
|
|
const secondAxis = Matrix3.Cartesian3.normalize(
|
|
Matrix3.Cartesian3.cross(reference, firstAxis, secondAxisScratch),
|
|
secondAxisScratch
|
|
);
|
|
const thirdAxis = Matrix3.Cartesian3.normalize(
|
|
Matrix3.Cartesian3.cross(firstAxis, secondAxis, thirdAxisScratch),
|
|
thirdAxisScratch
|
|
);
|
|
const B = bScratch;
|
|
B[0] = firstAxis.x;
|
|
B[1] = firstAxis.y;
|
|
B[2] = firstAxis.z;
|
|
B[3] = secondAxis.x;
|
|
B[4] = secondAxis.y;
|
|
B[5] = secondAxis.z;
|
|
B[6] = thirdAxis.x;
|
|
B[7] = thirdAxis.y;
|
|
B[8] = thirdAxis.z;
|
|
|
|
const B_T = Matrix3.Matrix3.transpose(B, btScratch);
|
|
|
|
// Get the scaling matrix and its inverse.
|
|
const D_I = Matrix3.Matrix3.fromScale(ellipsoid.radii, diScratch);
|
|
const D = Matrix3.Matrix3.fromScale(ellipsoid.oneOverRadii, dScratch);
|
|
|
|
const C = cScratch;
|
|
C[0] = 0.0;
|
|
C[1] = -direction.z;
|
|
C[2] = direction.y;
|
|
C[3] = direction.z;
|
|
C[4] = 0.0;
|
|
C[5] = -direction.x;
|
|
C[6] = -direction.y;
|
|
C[7] = direction.x;
|
|
C[8] = 0.0;
|
|
|
|
const temp = Matrix3.Matrix3.multiply(
|
|
Matrix3.Matrix3.multiply(B_T, D, tempMatrix),
|
|
C,
|
|
tempMatrix
|
|
);
|
|
const A = Matrix3.Matrix3.multiply(
|
|
Matrix3.Matrix3.multiply(temp, D_I, aScratch),
|
|
B,
|
|
aScratch
|
|
);
|
|
const b = Matrix3.Matrix3.multiplyByVector(temp, position, bCart);
|
|
|
|
// Solve for the solutions to the expression in standard form:
|
|
const solutions = quadraticVectorExpression(
|
|
A,
|
|
Matrix3.Cartesian3.negate(b, firstAxisScratch),
|
|
0.0,
|
|
0.0,
|
|
1.0
|
|
);
|
|
|
|
let s;
|
|
let altitude;
|
|
const length = solutions.length;
|
|
if (length > 0) {
|
|
let closest = Matrix3.Cartesian3.clone(Matrix3.Cartesian3.ZERO, closestScratch);
|
|
let maximumValue = Number.NEGATIVE_INFINITY;
|
|
|
|
for (let i = 0; i < length; ++i) {
|
|
s = Matrix3.Matrix3.multiplyByVector(
|
|
D_I,
|
|
Matrix3.Matrix3.multiplyByVector(B, solutions[i], sScratch),
|
|
sScratch
|
|
);
|
|
const v = Matrix3.Cartesian3.normalize(
|
|
Matrix3.Cartesian3.subtract(s, position, referenceScratch),
|
|
referenceScratch
|
|
);
|
|
const dotProduct = Matrix3.Cartesian3.dot(v, direction);
|
|
|
|
if (dotProduct > maximumValue) {
|
|
maximumValue = dotProduct;
|
|
closest = Matrix3.Cartesian3.clone(s, closest);
|
|
}
|
|
}
|
|
|
|
const surfacePoint = ellipsoid.cartesianToCartographic(
|
|
closest,
|
|
surfPointScratch
|
|
);
|
|
maximumValue = Math$1.CesiumMath.clamp(maximumValue, 0.0, 1.0);
|
|
altitude =
|
|
Matrix3.Cartesian3.magnitude(
|
|
Matrix3.Cartesian3.subtract(closest, position, referenceScratch)
|
|
) * Math.sqrt(1.0 - maximumValue * maximumValue);
|
|
altitude = intersects ? -altitude : altitude;
|
|
surfacePoint.height = altitude;
|
|
return ellipsoid.cartographicToCartesian(surfacePoint, new Matrix3.Cartesian3());
|
|
}
|
|
|
|
return undefined;
|
|
};
|
|
|
|
const lineSegmentPlaneDifference = new Matrix3.Cartesian3();
|
|
|
|
/**
|
|
* Computes the intersection of a line segment and a plane.
|
|
*
|
|
* @param {Cartesian3} endPoint0 An end point of the line segment.
|
|
* @param {Cartesian3} endPoint1 The other end point of the line segment.
|
|
* @param {Plane} plane The plane.
|
|
* @param {Cartesian3} [result] The object onto which to store the result.
|
|
* @returns {Cartesian3} The intersection point or undefined if there is no intersection.
|
|
*
|
|
* @example
|
|
* const origin = Cesium.Cartesian3.fromDegrees(-75.59777, 40.03883);
|
|
* const normal = ellipsoid.geodeticSurfaceNormal(origin);
|
|
* const plane = Cesium.Plane.fromPointNormal(origin, normal);
|
|
*
|
|
* const p0 = new Cesium.Cartesian3(...);
|
|
* const p1 = new Cesium.Cartesian3(...);
|
|
*
|
|
* // find the intersection of the line segment from p0 to p1 and the tangent plane at origin.
|
|
* const intersection = Cesium.IntersectionTests.lineSegmentPlane(p0, p1, plane);
|
|
*/
|
|
IntersectionTests.lineSegmentPlane = function (
|
|
endPoint0,
|
|
endPoint1,
|
|
plane,
|
|
result
|
|
) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
if (!defaultValue.defined(endPoint0)) {
|
|
throw new Check.DeveloperError("endPoint0 is required.");
|
|
}
|
|
if (!defaultValue.defined(endPoint1)) {
|
|
throw new Check.DeveloperError("endPoint1 is required.");
|
|
}
|
|
if (!defaultValue.defined(plane)) {
|
|
throw new Check.DeveloperError("plane is required.");
|
|
}
|
|
//>>includeEnd('debug');
|
|
|
|
if (!defaultValue.defined(result)) {
|
|
result = new Matrix3.Cartesian3();
|
|
}
|
|
|
|
const difference = Matrix3.Cartesian3.subtract(
|
|
endPoint1,
|
|
endPoint0,
|
|
lineSegmentPlaneDifference
|
|
);
|
|
const normal = plane.normal;
|
|
const nDotDiff = Matrix3.Cartesian3.dot(normal, difference);
|
|
|
|
// check if the segment and plane are parallel
|
|
if (Math.abs(nDotDiff) < Math$1.CesiumMath.EPSILON6) {
|
|
return undefined;
|
|
}
|
|
|
|
const nDotP0 = Matrix3.Cartesian3.dot(normal, endPoint0);
|
|
const t = -(plane.distance + nDotP0) / nDotDiff;
|
|
|
|
// intersection only if t is in [0, 1]
|
|
if (t < 0.0 || t > 1.0) {
|
|
return undefined;
|
|
}
|
|
|
|
// intersection is endPoint0 + t * (endPoint1 - endPoint0)
|
|
Matrix3.Cartesian3.multiplyByScalar(difference, t, result);
|
|
Matrix3.Cartesian3.add(endPoint0, result, result);
|
|
return result;
|
|
};
|
|
|
|
/**
|
|
* Computes the intersection of a triangle and a plane
|
|
*
|
|
* @param {Cartesian3} p0 First point of the triangle
|
|
* @param {Cartesian3} p1 Second point of the triangle
|
|
* @param {Cartesian3} p2 Third point of the triangle
|
|
* @param {Plane} plane Intersection plane
|
|
* @returns {Object} An object with properties <code>positions</code> and <code>indices</code>, which are arrays that represent three triangles that do not cross the plane. (Undefined if no intersection exists)
|
|
*
|
|
* @example
|
|
* const origin = Cesium.Cartesian3.fromDegrees(-75.59777, 40.03883);
|
|
* const normal = ellipsoid.geodeticSurfaceNormal(origin);
|
|
* const plane = Cesium.Plane.fromPointNormal(origin, normal);
|
|
*
|
|
* const p0 = new Cesium.Cartesian3(...);
|
|
* const p1 = new Cesium.Cartesian3(...);
|
|
* const p2 = new Cesium.Cartesian3(...);
|
|
*
|
|
* // convert the triangle composed of points (p0, p1, p2) to three triangles that don't cross the plane
|
|
* const triangles = Cesium.IntersectionTests.trianglePlaneIntersection(p0, p1, p2, plane);
|
|
*/
|
|
IntersectionTests.trianglePlaneIntersection = function (p0, p1, p2, plane) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
if (!defaultValue.defined(p0) || !defaultValue.defined(p1) || !defaultValue.defined(p2) || !defaultValue.defined(plane)) {
|
|
throw new Check.DeveloperError("p0, p1, p2, and plane are required.");
|
|
}
|
|
//>>includeEnd('debug');
|
|
|
|
const planeNormal = plane.normal;
|
|
const planeD = plane.distance;
|
|
const p0Behind = Matrix3.Cartesian3.dot(planeNormal, p0) + planeD < 0.0;
|
|
const p1Behind = Matrix3.Cartesian3.dot(planeNormal, p1) + planeD < 0.0;
|
|
const p2Behind = Matrix3.Cartesian3.dot(planeNormal, p2) + planeD < 0.0;
|
|
// Given these dots products, the calls to lineSegmentPlaneIntersection
|
|
// always have defined results.
|
|
|
|
let numBehind = 0;
|
|
numBehind += p0Behind ? 1 : 0;
|
|
numBehind += p1Behind ? 1 : 0;
|
|
numBehind += p2Behind ? 1 : 0;
|
|
|
|
let u1, u2;
|
|
if (numBehind === 1 || numBehind === 2) {
|
|
u1 = new Matrix3.Cartesian3();
|
|
u2 = new Matrix3.Cartesian3();
|
|
}
|
|
|
|
if (numBehind === 1) {
|
|
if (p0Behind) {
|
|
IntersectionTests.lineSegmentPlane(p0, p1, plane, u1);
|
|
IntersectionTests.lineSegmentPlane(p0, p2, plane, u2);
|
|
|
|
return {
|
|
positions: [p0, p1, p2, u1, u2],
|
|
indices: [
|
|
// Behind
|
|
0,
|
|
3,
|
|
4,
|
|
|
|
// In front
|
|
1,
|
|
2,
|
|
4,
|
|
1,
|
|
4,
|
|
3,
|
|
],
|
|
};
|
|
} else if (p1Behind) {
|
|
IntersectionTests.lineSegmentPlane(p1, p2, plane, u1);
|
|
IntersectionTests.lineSegmentPlane(p1, p0, plane, u2);
|
|
|
|
return {
|
|
positions: [p0, p1, p2, u1, u2],
|
|
indices: [
|
|
// Behind
|
|
1,
|
|
3,
|
|
4,
|
|
|
|
// In front
|
|
2,
|
|
0,
|
|
4,
|
|
2,
|
|
4,
|
|
3,
|
|
],
|
|
};
|
|
} else if (p2Behind) {
|
|
IntersectionTests.lineSegmentPlane(p2, p0, plane, u1);
|
|
IntersectionTests.lineSegmentPlane(p2, p1, plane, u2);
|
|
|
|
return {
|
|
positions: [p0, p1, p2, u1, u2],
|
|
indices: [
|
|
// Behind
|
|
2,
|
|
3,
|
|
4,
|
|
|
|
// In front
|
|
0,
|
|
1,
|
|
4,
|
|
0,
|
|
4,
|
|
3,
|
|
],
|
|
};
|
|
}
|
|
} else if (numBehind === 2) {
|
|
if (!p0Behind) {
|
|
IntersectionTests.lineSegmentPlane(p1, p0, plane, u1);
|
|
IntersectionTests.lineSegmentPlane(p2, p0, plane, u2);
|
|
|
|
return {
|
|
positions: [p0, p1, p2, u1, u2],
|
|
indices: [
|
|
// Behind
|
|
1,
|
|
2,
|
|
4,
|
|
1,
|
|
4,
|
|
3,
|
|
|
|
// In front
|
|
0,
|
|
3,
|
|
4,
|
|
],
|
|
};
|
|
} else if (!p1Behind) {
|
|
IntersectionTests.lineSegmentPlane(p2, p1, plane, u1);
|
|
IntersectionTests.lineSegmentPlane(p0, p1, plane, u2);
|
|
|
|
return {
|
|
positions: [p0, p1, p2, u1, u2],
|
|
indices: [
|
|
// Behind
|
|
2,
|
|
0,
|
|
4,
|
|
2,
|
|
4,
|
|
3,
|
|
|
|
// In front
|
|
1,
|
|
3,
|
|
4,
|
|
],
|
|
};
|
|
} else if (!p2Behind) {
|
|
IntersectionTests.lineSegmentPlane(p0, p2, plane, u1);
|
|
IntersectionTests.lineSegmentPlane(p1, p2, plane, u2);
|
|
|
|
return {
|
|
positions: [p0, p1, p2, u1, u2],
|
|
indices: [
|
|
// Behind
|
|
0,
|
|
1,
|
|
4,
|
|
0,
|
|
4,
|
|
3,
|
|
|
|
// In front
|
|
2,
|
|
3,
|
|
4,
|
|
],
|
|
};
|
|
}
|
|
}
|
|
|
|
// if numBehind is 3, the triangle is completely behind the plane;
|
|
// otherwise, it is completely in front (numBehind is 0).
|
|
return undefined;
|
|
};
|
|
var IntersectionTests$1 = IntersectionTests;
|
|
|
|
exports.IntersectionTests = IntersectionTests$1;
|
|
exports.Ray = Ray;
|
|
|
|
}));
|