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114 lines
3.6 KiB
114 lines
3.6 KiB
// 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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//
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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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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 Euler-angles of the rotation matrix \c *this using the convention defined by the triplet (\a 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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* The returned angles are in the ranges [0:pi]x[-pi:pi]x[-pi:pi].
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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>
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MatrixBase<Derived>::eulerAngles(Index a0, Index a1, Index a2) const
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{
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EIGEN_USING_STD_MATH(atan2)
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EIGEN_USING_STD_MATH(sin)
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EIGEN_USING_STD_MATH(cos)
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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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typedef Matrix<typename Derived::Scalar,2,1> Vector2;
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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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{
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res[0] = 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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{
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if(res[0] > Scalar(0)) {
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res[0] -= Scalar(EIGEN_PI);
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}
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else {
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res[0] += Scalar(EIGEN_PI);
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}
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Scalar s2 = Vector2(coeff(j,i), coeff(k,i)).norm();
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res[1] = -atan2(s2, coeff(i,i));
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}
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else
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{
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Scalar s2 = Vector2(coeff(j,i), coeff(k,i)).norm();
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res[1] = 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 = sin(res[0]);
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Scalar c1 = cos(res[0]);
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res[2] = atan2(c1*coeff(j,k)-s1*coeff(k,k), c1*coeff(j,j) - s1 * coeff(k,j));
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}
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else
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{
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res[0] = atan2(coeff(j,k), coeff(k,k));
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Scalar c2 = Vector2(coeff(i,i), coeff(i,j)).norm();
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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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}
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else {
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res[0] += Scalar(EIGEN_PI);
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}
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res[1] = atan2(-coeff(i,k), -c2);
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}
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else
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res[1] = atan2(-coeff(i,k), c2);
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Scalar s1 = sin(res[0]);
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Scalar c1 = cos(res[0]);
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res[2] = 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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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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