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 // This file is part of Eigen, a lightweight C++ template library // for linear algebra. // // Copyright (C) 2008 Gael Guennebaud // // 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 #include "./InternalHeaderCheck.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 EIGEN_DEVICE_FUNC inline Matrix::Scalar,3,1> MatrixBase::eulerAngles(Index a0, Index a1, Index a2) const { EIGEN_USING_STD(atan2) EIGEN_USING_STD(sin) EIGEN_USING_STD(cos) /* Implemented from Graphics Gems IV */ EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Derived,3,3) Matrix res; typedef Matrix 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))) { if(res[0] > Scalar(0)) { res[0] -= Scalar(EIGEN_PI); } else { res[0] += Scalar(EIGEN_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))) { if(res[0] > Scalar(0)) { res[0] -= Scalar(EIGEN_PI); } else { res[0] += Scalar(EIGEN_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