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Diffstat (limited to 'third_party/eigen3/Eigen/src/Geometry/EulerAngles.h')
| -rw-r--r-- | third_party/eigen3/Eigen/src/Geometry/EulerAngles.h | 104 |
1 files changed, 104 insertions, 0 deletions
diff --git a/third_party/eigen3/Eigen/src/Geometry/EulerAngles.h b/third_party/eigen3/Eigen/src/Geometry/EulerAngles.h new file mode 100644 index 0000000000..82802fb43c --- /dev/null +++ b/third_party/eigen3/Eigen/src/Geometry/EulerAngles.h @@ -0,0 +1,104 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr> +// +// 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 + +namespace Eigen { + +/** \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) + * + * 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). + * + * The returned angles are in the ranges [0:pi]x[-pi:pi]x[-pi:pi]. + * + * \sa class AngleAxis + */ +template<typename Derived> +inline Matrix<typename MatrixBase<Derived>::Scalar,3,1> +MatrixBase<Derived>::eulerAngles(Index a0, Index a1, Index a2) const +{ + using std::atan2; + using std::sin; + using std::cos; + /* Implemented from Graphics Gems IV */ + EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Derived,3,3) + + Matrix<Scalar,3,1> res; + typedef Matrix<typename Derived::Scalar,2,1> Vector2; + + 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] = atan2(coeff(j,i), coeff(k,i)); + if((odd && res[0]<Scalar(0)) || ((!odd) && res[0]>Scalar(0))) + { + res[0] = (res[0] > Scalar(0)) ? res[0] - Scalar(M_PI) : res[0] + Scalar(M_PI); + Scalar s2 = Vector2(coeff(j,i), coeff(k,i)).norm(); + res[1] = -atan2(s2, coeff(i,i)); + } + else + { + Scalar s2 = Vector2(coeff(j,i), coeff(k,i)).norm(); + res[1] = 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 = sin(res[0]); + Scalar c1 = cos(res[0]); + res[2] = atan2(c1*coeff(j,k)-s1*coeff(k,k), c1*coeff(j,j) - s1 * coeff(k,j)); + } + else + { + res[0] = atan2(coeff(j,k), coeff(k,k)); + Scalar c2 = Vector2(coeff(i,i), coeff(i,j)).norm(); + if((odd && res[0]<Scalar(0)) || ((!odd) && res[0]>Scalar(0))) { + res[0] = (res[0] > Scalar(0)) ? res[0] - Scalar(M_PI) : res[0] + Scalar(M_PI); + res[1] = atan2(-coeff(i,k), -c2); + } + else + res[1] = atan2(-coeff(i,k), c2); + Scalar s1 = sin(res[0]); + Scalar c1 = cos(res[0]); + res[2] = 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 |