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93 lines
3.2 KiB
93 lines
3.2 KiB
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/****************************************************************************
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Copyright (c) 2022-2023 Xiamen Yaji Software Co., Ltd.
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http://www.cocos.com
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Permission is hereby granted, free of charge, to any person obtaining a copy
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of this software and associated documentation files (the "Software"), to deal
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in the Software without restriction, including without limitation the rights to
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use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
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of the Software, and to permit persons to whom the Software is furnished to do so,
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subject to the following conditions:
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The above copyright notice and this permission notice shall be included in
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all copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
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THE SOFTWARE.
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****************************************************************************/
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#include "PolynomialSolver.h"
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#include <cmath>
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#include "base/std/container/vector.h"
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#include "math/Math.h"
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namespace cc {
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namespace gi {
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float PolynomialSolver::getQuadraticUniqueRoot(float b, float c, float d) {
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// quadratic case
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if (b != 0.0F) {
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// the discriminant should be 0
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return -c / (2.0F * b);
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}
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// linear case
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if (c != 0.0F) {
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return -d / c;
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}
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// never reach here
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return 0.0F;
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}
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float PolynomialSolver::getCubicUniqueRoot(float b, float c, float d) {
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ccstd::vector<float> roots;
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// let x = y - b / 3, convert equation to: y^3 + 3 * p * y + 2 * q = 0
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// where p = c / 3 - b^2 / 9, q = d / 2 + b^3 / 27 - b * c / 6
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const auto offset = -b / 3.0F;
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const auto p = c / 3.0F - (b * b) / 9.0F;
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const auto q = d / 2.0F + (b * b * b) / 27.0F - (b * c) / 6.0F;
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const auto delta = p * p * p + q * q; // discriminant
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if (delta > 0.0F) {
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// only one real root
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const auto sqrtDelta = std::sqrt(delta);
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roots.push_back(std::cbrt(-q + sqrtDelta) + std::cbrt(-q - sqrtDelta));
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} else if (delta < 0.0F) {
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// three different real roots
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const auto angle = std::acos(-q * std::sqrt(-p) / (p * p)) / 3.0F;
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roots.push_back(2.0F * std::sqrt(-p) * std::cos(angle));
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roots.push_back(2.0F * std::sqrt(-p) * std::cos(angle + 2.0F * math::PI / 3.0F));
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roots.push_back(2.0F * std::sqrt(-p) * std::cos(angle + 4.0F * math::PI / 3.0F));
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} else {
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// three real roots, at least two equal roots
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if (q == 0.0F) {
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roots.push_back(0.0F);
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} else {
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const auto root = std::cbrt(q);
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roots.push_back(root);
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roots.push_back(-2.0F * root);
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}
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}
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// return the unique positive root
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for (float root : roots) {
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if (root + offset >= 0.0F) {
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return root + offset;
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}
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}
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// never reach here
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return 0.0;
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}
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} // namespace gi
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} // namespace cc
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