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Yousef Khadadeh
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include/Eigen/src/Geometry/EulerAngles.h
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include/Eigen/src/Geometry/EulerAngles.h
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// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
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// Copyright (C) 2023 Juraj Oršulić, University of Zagreb <juraj.orsulic@fer.hr>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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#ifndef EIGEN_EULERANGLES_H
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#define EIGEN_EULERANGLES_H
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// IWYU pragma: private
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#include "./InternalHeaderCheck.h"
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namespace Eigen {
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/** \geometry_module \ingroup Geometry_Module
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*
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*
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* \returns the canonical Euler-angles of the rotation matrix \c *this using the convention defined by the triplet (\a
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* a0,\a a1,\a a2)
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*
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* Each of the three parameters \a a0,\a a1,\a a2 represents the respective rotation axis as an integer in {0,1,2}.
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* For instance, in:
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* \code Vector3f ea = mat.eulerAngles(2, 0, 2); \endcode
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* "2" represents the z axis and "0" the x axis, etc. The returned angles are such that
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* we have the following equality:
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* \code
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* mat == AngleAxisf(ea[0], Vector3f::UnitZ())
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* * AngleAxisf(ea[1], Vector3f::UnitX())
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* * AngleAxisf(ea[2], Vector3f::UnitZ()); \endcode
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* This corresponds to the right-multiply conventions (with right hand side frames).
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*
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* For Tait-Bryan angle configurations (a0 != a2), the returned angles are in the ranges [-pi:pi]x[-pi/2:pi/2]x[-pi:pi].
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* For proper Euler angle configurations (a0 == a2), the returned angles are in the ranges [-pi:pi]x[0:pi]x[-pi:pi].
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*
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* The approach used is also described here:
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* https://d3cw3dd2w32x2b.cloudfront.net/wp-content/uploads/2012/07/euler-angles.pdf
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*
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* \sa class AngleAxis
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*/
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template <typename Derived>
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EIGEN_DEVICE_FUNC inline Matrix<typename MatrixBase<Derived>::Scalar, 3, 1> MatrixBase<Derived>::canonicalEulerAngles(
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Index a0, Index a1, Index a2) const {
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/* Implemented from Graphics Gems IV */
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EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Derived, 3, 3)
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Matrix<Scalar, 3, 1> res;
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const Index odd = ((a0 + 1) % 3 == a1) ? 0 : 1;
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const Index i = a0;
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const Index j = (a0 + 1 + odd) % 3;
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const Index k = (a0 + 2 - odd) % 3;
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if (a0 == a2) {
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// Proper Euler angles (same first and last axis).
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// The i, j, k indices enable addressing the input matrix as the XYX archetype matrix (see Graphics Gems IV),
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// where e.g. coeff(k, i) means third column, first row in the XYX archetype matrix:
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// c2 s2s1 s2c1
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// s2s3 -c2s1s3 + c1c3 -c2c1s3 - s1c3
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// -s2c3 c2s1c3 + c1s3 c2c1c3 - s1s3
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// Note: s2 is always positive.
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Scalar s2 = numext::hypot(coeff(j, i), coeff(k, i));
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if (odd) {
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res[0] = numext::atan2(coeff(j, i), coeff(k, i));
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// s2 is always positive, so res[1] will be within the canonical [0, pi] range
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res[1] = numext::atan2(s2, coeff(i, i));
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} else {
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// In the !odd case, signs of all three angles are flipped at the very end. To keep the solution within the
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// canonical range, we flip the solution and make res[1] always negative here (since s2 is always positive,
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// -atan2(s2, c2) will always be negative). The final flip at the end due to !odd will thus make res[1] positive
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// and canonical. NB: in the general case, there are two correct solutions, but only one is canonical. For proper
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// Euler angles, flipping from one solution to the other involves flipping the sign of the second angle res[1] and
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// adding/subtracting pi to the first and third angles. The addition/subtraction of pi to the first angle res[0]
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// is handled here by flipping the signs of arguments to atan2, while the calculation of the third angle does not
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// need special adjustment since it uses the adjusted res[0] as the input and produces a correct result.
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res[0] = numext::atan2(-coeff(j, i), -coeff(k, i));
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res[1] = -numext::atan2(s2, coeff(i, i));
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}
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// With a=(0,1,0), we have i=0; j=1; k=2, and after computing the first two angles,
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// we can compute their respective rotation, and apply its inverse to M. Since the result must
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// be a rotation around x, we have:
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//
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// c2 s1.s2 c1.s2 1 0 0
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// 0 c1 -s1 * M = 0 c3 s3
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// -s2 s1.c2 c1.c2 0 -s3 c3
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//
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// Thus: m11.c1 - m21.s1 = c3 & m12.c1 - m22.s1 = s3
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Scalar s1 = numext::sin(res[0]);
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Scalar c1 = numext::cos(res[0]);
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res[2] = numext::atan2(c1 * coeff(j, k) - s1 * coeff(k, k), c1 * coeff(j, j) - s1 * coeff(k, j));
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} else {
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// Tait-Bryan angles (all three axes are different; typically used for yaw-pitch-roll calculations).
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// The i, j, k indices enable addressing the input matrix as the XYZ archetype matrix (see Graphics Gems IV),
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// where e.g. coeff(k, i) means third column, first row in the XYZ archetype matrix:
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// c2c3 s2s1c3 - c1s3 s2c1c3 + s1s3
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// c2s3 s2s1s3 + c1c3 s2c1s3 - s1c3
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// -s2 c2s1 c2c1
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res[0] = numext::atan2(coeff(j, k), coeff(k, k));
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Scalar c2 = numext::hypot(coeff(i, i), coeff(i, j));
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// c2 is always positive, so the following atan2 will always return a result in the correct canonical middle angle
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// range [-pi/2, pi/2]
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res[1] = numext::atan2(-coeff(i, k), c2);
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Scalar s1 = numext::sin(res[0]);
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Scalar c1 = numext::cos(res[0]);
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res[2] = numext::atan2(s1 * coeff(k, i) - c1 * coeff(j, i), c1 * coeff(j, j) - s1 * coeff(k, j));
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}
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if (!odd) {
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res = -res;
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}
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return res;
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}
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/** \geometry_module \ingroup Geometry_Module
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*
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*
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* \returns the Euler-angles of the rotation matrix \c *this using the convention defined by the triplet (\a a0,\a a1,\a
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* a2)
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*
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* NB: The returned angles are in non-canonical ranges [0:pi]x[-pi:pi]x[-pi:pi]. For canonical Tait-Bryan/proper Euler
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* ranges, use canonicalEulerAngles.
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*
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* \sa MatrixBase::canonicalEulerAngles
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* \sa class AngleAxis
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*/
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template <typename Derived>
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EIGEN_DEPRECATED EIGEN_DEVICE_FUNC inline Matrix<typename MatrixBase<Derived>::Scalar, 3, 1>
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MatrixBase<Derived>::eulerAngles(Index a0, Index a1, Index a2) const {
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/* Implemented from Graphics Gems IV */
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EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Derived, 3, 3)
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Matrix<Scalar, 3, 1> res;
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const Index odd = ((a0 + 1) % 3 == a1) ? 0 : 1;
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const Index i = a0;
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const Index j = (a0 + 1 + odd) % 3;
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const Index k = (a0 + 2 - odd) % 3;
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if (a0 == a2) {
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res[0] = numext::atan2(coeff(j, i), coeff(k, i));
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if ((odd && res[0] < Scalar(0)) || ((!odd) && res[0] > Scalar(0))) {
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if (res[0] > Scalar(0)) {
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res[0] -= Scalar(EIGEN_PI);
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} else {
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res[0] += Scalar(EIGEN_PI);
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}
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Scalar s2 = numext::hypot(coeff(j, i), coeff(k, i));
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res[1] = -numext::atan2(s2, coeff(i, i));
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} else {
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Scalar s2 = numext::hypot(coeff(j, i), coeff(k, i));
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res[1] = numext::atan2(s2, coeff(i, i));
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}
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// With a=(0,1,0), we have i=0; j=1; k=2, and after computing the first two angles,
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// we can compute their respective rotation, and apply its inverse to M. Since the result must
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// be a rotation around x, we have:
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//
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// c2 s1.s2 c1.s2 1 0 0
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// 0 c1 -s1 * M = 0 c3 s3
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// -s2 s1.c2 c1.c2 0 -s3 c3
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//
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// Thus: m11.c1 - m21.s1 = c3 & m12.c1 - m22.s1 = s3
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Scalar s1 = numext::sin(res[0]);
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Scalar c1 = numext::cos(res[0]);
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res[2] = numext::atan2(c1 * coeff(j, k) - s1 * coeff(k, k), c1 * coeff(j, j) - s1 * coeff(k, j));
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} else {
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res[0] = numext::atan2(coeff(j, k), coeff(k, k));
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Scalar c2 = numext::hypot(coeff(i, i), coeff(i, j));
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if ((odd && res[0] < Scalar(0)) || ((!odd) && res[0] > Scalar(0))) {
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if (res[0] > Scalar(0)) {
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res[0] -= Scalar(EIGEN_PI);
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} else {
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res[0] += Scalar(EIGEN_PI);
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}
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res[1] = numext::atan2(-coeff(i, k), -c2);
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} else {
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res[1] = numext::atan2(-coeff(i, k), c2);
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}
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Scalar s1 = numext::sin(res[0]);
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Scalar c1 = numext::cos(res[0]);
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res[2] = numext::atan2(s1 * coeff(k, i) - c1 * coeff(j, i), c1 * coeff(j, j) - s1 * coeff(k, j));
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}
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if (!odd) {
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res = -res;
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}
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return res;
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}
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} // end namespace Eigen
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#endif // EIGEN_EULERANGLES_H
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