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July 19, 2022 16:06
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Bezier code for path planning
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| // https://github.com/Rezonality/mutils/blob/6adc3fa9d160f455092637032cb6fcd6162d0b93/include/mutils/math/math_utils.h#L124 | |
| template <typename T> | |
| inline T Bezier(float t, T p0, T p1, T p2, T p3) { | |
| return std::pow(1 - t, 3) * p0 + 3 * std::pow(1 - t, 2) * t * p1 + 3 * (1 - t) * (t * t) * p2 + std::pow(t, 3) * p3; | |
| } | |
| template <typename T> | |
| inline T BezierPt(float t, T p0, T p1, T p2, T p3) | |
| { | |
| return T(Bezier(t, p0.x(), p1.x(), p2.x(), p3.x()), Bezier(t, p0.y(), p1.y(), p2.y(), p3.y())); | |
| } | |
| template <typename T> | |
| inline T BezierDerivative(float t, T p0, T p1, T p2, T p3) | |
| { | |
| return 3 * pow(1 - t, 2) * (p1 - p0) + 6 * (1 - t) * t * (p2 - p1) + 3 * (t * t) * (p3 - p2); | |
| } | |
| template <typename T> | |
| inline T BezierDerivativeVec(float t, const T& p0, const T& p1, const T& p2, const T& p3) | |
| { | |
| return T(BezierDerivative(t, p0.x(), p1.x(), p2.x(), p3.x()), BezierDerivative(t, p0.y(), p1.y(), p2.y(), p3.y())); | |
| } | |
| template <typename T> | |
| inline T BezierSecondDerivative(float t, T p0, T p1, T p2, T p3) | |
| { | |
| return 6 * (1 - t) * (p2 - 2*p1 + p0) + 6 * t * (p3 - 2 * p2 + p1); | |
| } | |
| // Tangent | |
| template <typename T> | |
| inline T BezierSecondDerivativeVec(float t, const T& p0, const T& p1, const T& p2, const T& p3) | |
| { | |
| return T(BezierSecondDerivative(t, p0.x(), p1.x(), p2.x(), p3.x()), BezierSecondDerivative(t, p0.y(), p1.y(), p2.y(), p3.y())); | |
| } | |
| // https://math24.net/curvature-radius.html | |
| template <typename T> | |
| inline double CalcCurvature(float t, const T& p0, const T& p1, const T& p2, const T& p3) { | |
| auto first_dir = BezierDerivativeVec(t, p0, p1, p2, p3); | |
| auto second_dir = BezierSecondDerivativeVec(t, p0, p1, p2, p3); | |
| double k = fabs(first_dir.x() * second_dir.y() - first_dir.y() * second_dir.x()) / | |
| std::pow(first_dir.x() * first_dir.x() + first_dir.y() * first_dir.y(), 3. / 2); | |
| double radius_of_curvature = 1.0 / k; | |
| return radius_of_curvature; | |
| } | |
| template <typename T> | |
| inline double computeCurvature(T p0, T p1, T p2) { | |
| double dx1 = p1.x() - p0.x(); | |
| double dy1 = p1.y() - p0.y(); | |
| double dx2 = p2.x() - p0.x(); | |
| double dy2 = p2.y() - p0.y(); | |
| double area = 0.5 * (dx1 * dy2 - dy1 * dx2); | |
| double len0 = p0.DistanceTo2D(p1); | |
| double len1 = p1.DistanceTo2D(p2); | |
| double len2 = p2.DistanceTo2D(p0); | |
| return 4 * area / (len0 * len1 * len2); | |
| } |
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