mirror of
https://gitlab.com/libeigen/eigen.git
synced 2025-10-12 08:01:29 +08:00
204 lines
8.1 KiB
C++
204 lines
8.1 KiB
C++
// This file is part of Eigen, a lightweight C++ template library
|
|
// for linear algebra.
|
|
//
|
|
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
|
|
// Copyright (C) 2023 Juraj Oršulić, University of Zagreb <juraj.orsulic@fer.hr>
|
|
//
|
|
// This Source Code Form is subject to the terms of the Mozilla
|
|
// Public License v. 2.0. If a copy of the MPL was not distributed
|
|
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
|
|
|
#ifndef EIGEN_EULERANGLES_H
|
|
#define EIGEN_EULERANGLES_H
|
|
|
|
// IWYU pragma: private
|
|
#include "./InternalHeaderCheck.h"
|
|
|
|
namespace Eigen {
|
|
|
|
/** \geometry_module \ingroup Geometry_Module
|
|
*
|
|
*
|
|
* \returns the canonical Euler-angles of the rotation matrix \c *this using the convention defined by the triplet (\a
|
|
* a0,\a a1,\a a2)
|
|
*
|
|
* Each of the three parameters \a a0,\a a1,\a a2 represents the respective rotation axis as an integer in {0,1,2}.
|
|
* For instance, in:
|
|
* \code Vector3f ea = mat.eulerAngles(2, 0, 2); \endcode
|
|
* "2" represents the z axis and "0" the x axis, etc. The returned angles are such that
|
|
* we have the following equality:
|
|
* \code
|
|
* mat == AngleAxisf(ea[0], Vector3f::UnitZ())
|
|
* * AngleAxisf(ea[1], Vector3f::UnitX())
|
|
* * AngleAxisf(ea[2], Vector3f::UnitZ()); \endcode
|
|
* This corresponds to the right-multiply conventions (with right hand side frames).
|
|
*
|
|
* For Tait-Bryan angle configurations (a0 != a2), the returned angles are in the ranges [-pi:pi]x[-pi/2:pi/2]x[-pi:pi].
|
|
* For proper Euler angle configurations (a0 == a2), the returned angles are in the ranges [-pi:pi]x[0:pi]x[-pi:pi].
|
|
*
|
|
* The approach used is also described here:
|
|
* https://d3cw3dd2w32x2b.cloudfront.net/wp-content/uploads/2012/07/euler-angles.pdf
|
|
*
|
|
* \sa class AngleAxis
|
|
*/
|
|
template <typename Derived>
|
|
EIGEN_DEVICE_FUNC inline Matrix<typename MatrixBase<Derived>::Scalar, 3, 1> MatrixBase<Derived>::canonicalEulerAngles(
|
|
Index a0, Index a1, Index a2) const {
|
|
/* Implemented from Graphics Gems IV */
|
|
EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Derived, 3, 3)
|
|
|
|
Matrix<Scalar, 3, 1> res;
|
|
|
|
const Index odd = ((a0 + 1) % 3 == a1) ? 0 : 1;
|
|
const Index i = a0;
|
|
const Index j = (a0 + 1 + odd) % 3;
|
|
const Index k = (a0 + 2 - odd) % 3;
|
|
|
|
if (a0 == a2) {
|
|
// Proper Euler angles (same first and last axis).
|
|
// The i, j, k indices enable addressing the input matrix as the XYX archetype matrix (see Graphics Gems IV),
|
|
// where e.g. coeff(k, i) means third column, first row in the XYX archetype matrix:
|
|
// c2 s2s1 s2c1
|
|
// s2s3 -c2s1s3 + c1c3 -c2c1s3 - s1c3
|
|
// -s2c3 c2s1c3 + c1s3 c2c1c3 - s1s3
|
|
|
|
// Note: s2 is always positive.
|
|
Scalar s2 = numext::hypot(coeff(j, i), coeff(k, i));
|
|
if (odd) {
|
|
res[0] = numext::atan2(coeff(j, i), coeff(k, i));
|
|
// s2 is always positive, so res[1] will be within the canonical [0, pi] range
|
|
res[1] = numext::atan2(s2, coeff(i, i));
|
|
} else {
|
|
// In the !odd case, signs of all three angles are flipped at the very end. To keep the solution within the
|
|
// canonical range, we flip the solution and make res[1] always negative here (since s2 is always positive,
|
|
// -atan2(s2, c2) will always be negative). The final flip at the end due to !odd will thus make res[1] positive
|
|
// and canonical. NB: in the general case, there are two correct solutions, but only one is canonical. For proper
|
|
// Euler angles, flipping from one solution to the other involves flipping the sign of the second angle res[1] and
|
|
// adding/subtracting pi to the first and third angles. The addition/subtraction of pi to the first angle res[0]
|
|
// is handled here by flipping the signs of arguments to atan2, while the calculation of the third angle does not
|
|
// need special adjustment since it uses the adjusted res[0] as the input and produces a correct result.
|
|
res[0] = numext::atan2(-coeff(j, i), -coeff(k, i));
|
|
res[1] = -numext::atan2(s2, coeff(i, i));
|
|
}
|
|
|
|
// With a=(0,1,0), we have i=0; j=1; k=2, and after computing the first two angles,
|
|
// we can compute their respective rotation, and apply its inverse to M. Since the result must
|
|
// be a rotation around x, we have:
|
|
//
|
|
// c2 s1.s2 c1.s2 1 0 0
|
|
// 0 c1 -s1 * M = 0 c3 s3
|
|
// -s2 s1.c2 c1.c2 0 -s3 c3
|
|
//
|
|
// Thus: m11.c1 - m21.s1 = c3 & m12.c1 - m22.s1 = s3
|
|
|
|
Scalar s1 = numext::sin(res[0]);
|
|
Scalar c1 = numext::cos(res[0]);
|
|
res[2] = numext::atan2(c1 * coeff(j, k) - s1 * coeff(k, k), c1 * coeff(j, j) - s1 * coeff(k, j));
|
|
} else {
|
|
// Tait-Bryan angles (all three axes are different; typically used for yaw-pitch-roll calculations).
|
|
// The i, j, k indices enable addressing the input matrix as the XYZ archetype matrix (see Graphics Gems IV),
|
|
// where e.g. coeff(k, i) means third column, first row in the XYZ archetype matrix:
|
|
// c2c3 s2s1c3 - c1s3 s2c1c3 + s1s3
|
|
// c2s3 s2s1s3 + c1c3 s2c1s3 - s1c3
|
|
// -s2 c2s1 c2c1
|
|
|
|
res[0] = numext::atan2(coeff(j, k), coeff(k, k));
|
|
|
|
Scalar c2 = numext::hypot(coeff(i, i), coeff(i, j));
|
|
// c2 is always positive, so the following atan2 will always return a result in the correct canonical middle angle
|
|
// range [-pi/2, pi/2]
|
|
res[1] = numext::atan2(-coeff(i, k), c2);
|
|
|
|
Scalar s1 = numext::sin(res[0]);
|
|
Scalar c1 = numext::cos(res[0]);
|
|
res[2] = numext::atan2(s1 * coeff(k, i) - c1 * coeff(j, i), c1 * coeff(j, j) - s1 * coeff(k, j));
|
|
}
|
|
if (!odd) {
|
|
res = -res;
|
|
}
|
|
|
|
return res;
|
|
}
|
|
|
|
/** \geometry_module \ingroup Geometry_Module
|
|
*
|
|
*
|
|
* \returns the Euler-angles of the rotation matrix \c *this using the convention defined by the triplet (\a a0,\a a1,\a
|
|
* a2)
|
|
*
|
|
* NB: The returned angles are in non-canonical ranges [0:pi]x[-pi:pi]x[-pi:pi]. For canonical Tait-Bryan/proper Euler
|
|
* ranges, use canonicalEulerAngles.
|
|
*
|
|
* \sa MatrixBase::canonicalEulerAngles
|
|
* \sa class AngleAxis
|
|
*/
|
|
template <typename Derived>
|
|
EIGEN_DEVICE_FUNC inline Matrix<typename MatrixBase<Derived>::Scalar, 3, 1> MatrixBase<Derived>::eulerAngles(
|
|
Index a0, Index a1, Index a2) const {
|
|
/* Implemented from Graphics Gems IV */
|
|
EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Derived, 3, 3)
|
|
|
|
Matrix<Scalar, 3, 1> res;
|
|
|
|
const Index odd = ((a0 + 1) % 3 == a1) ? 0 : 1;
|
|
const Index i = a0;
|
|
const Index j = (a0 + 1 + odd) % 3;
|
|
const Index k = (a0 + 2 - odd) % 3;
|
|
|
|
if (a0 == a2) {
|
|
res[0] = numext::atan2(coeff(j, i), coeff(k, i));
|
|
if ((odd && res[0] < Scalar(0)) || ((!odd) && res[0] > Scalar(0))) {
|
|
if (res[0] > Scalar(0)) {
|
|
res[0] -= Scalar(EIGEN_PI);
|
|
} else {
|
|
res[0] += Scalar(EIGEN_PI);
|
|
}
|
|
|
|
Scalar s2 = numext::hypot(coeff(j, i), coeff(k, i));
|
|
res[1] = -numext::atan2(s2, coeff(i, i));
|
|
} else {
|
|
Scalar s2 = numext::hypot(coeff(j, i), coeff(k, i));
|
|
res[1] = numext::atan2(s2, coeff(i, i));
|
|
}
|
|
|
|
// With a=(0,1,0), we have i=0; j=1; k=2, and after computing the first two angles,
|
|
// we can compute their respective rotation, and apply its inverse to M. Since the result must
|
|
// be a rotation around x, we have:
|
|
//
|
|
// c2 s1.s2 c1.s2 1 0 0
|
|
// 0 c1 -s1 * M = 0 c3 s3
|
|
// -s2 s1.c2 c1.c2 0 -s3 c3
|
|
//
|
|
// Thus: m11.c1 - m21.s1 = c3 & m12.c1 - m22.s1 = s3
|
|
|
|
Scalar s1 = numext::sin(res[0]);
|
|
Scalar c1 = numext::cos(res[0]);
|
|
res[2] = numext::atan2(c1 * coeff(j, k) - s1 * coeff(k, k), c1 * coeff(j, j) - s1 * coeff(k, j));
|
|
} else {
|
|
res[0] = numext::atan2(coeff(j, k), coeff(k, k));
|
|
Scalar c2 = numext::hypot(coeff(i, i), coeff(i, j));
|
|
if ((odd && res[0] < Scalar(0)) || ((!odd) && res[0] > Scalar(0))) {
|
|
if (res[0] > Scalar(0)) {
|
|
res[0] -= Scalar(EIGEN_PI);
|
|
} else {
|
|
res[0] += Scalar(EIGEN_PI);
|
|
}
|
|
res[1] = numext::atan2(-coeff(i, k), -c2);
|
|
} else {
|
|
res[1] = numext::atan2(-coeff(i, k), c2);
|
|
}
|
|
Scalar s1 = numext::sin(res[0]);
|
|
Scalar c1 = numext::cos(res[0]);
|
|
res[2] = numext::atan2(s1 * coeff(k, i) - c1 * coeff(j, i), c1 * coeff(j, j) - s1 * coeff(k, j));
|
|
}
|
|
if (!odd) {
|
|
res = -res;
|
|
}
|
|
|
|
return res;
|
|
}
|
|
|
|
} // end namespace Eigen
|
|
|
|
#endif // EIGEN_EULERANGLES_H
|