1 // This file is part of Eigen, a lightweight C++ template library 2 // for linear algebra. 3 // 4 // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud (at) inria.fr> 5 // 6 // This Source Code Form is subject to the terms of the Mozilla 7 // Public License v. 2.0. If a copy of the MPL was not distributed 8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 9 10 #ifndef EIGEN_EULERANGLES_H 11 #define EIGEN_EULERANGLES_H 12 13 namespace Eigen { 14 15 /** \geometry_module \ingroup Geometry_Module 16 * 17 * 18 * \returns the Euler-angles of the rotation matrix \c *this using the convention defined by the triplet (\a a0,\a a1,\a a2) 19 * 20 * Each of the three parameters \a a0,\a a1,\a a2 represents the respective rotation axis as an integer in {0,1,2}. 21 * For instance, in: 22 * \code Vector3f ea = mat.eulerAngles(2, 0, 2); \endcode 23 * "2" represents the z axis and "0" the x axis, etc. The returned angles are such that 24 * we have the following equality: 25 * \code 26 * mat == AngleAxisf(ea[0], Vector3f::UnitZ()) 27 * * AngleAxisf(ea[1], Vector3f::UnitX()) 28 * * AngleAxisf(ea[2], Vector3f::UnitZ()); \endcode 29 * This corresponds to the right-multiply conventions (with right hand side frames). 30 * 31 * The returned angles are in the ranges [0:pi]x[-pi:pi]x[-pi:pi]. 32 * 33 * \sa class AngleAxis 34 */ 35 template<typename Derived> 36 inline Matrix<typename MatrixBase<Derived>::Scalar,3,1> 37 MatrixBase<Derived>::eulerAngles(Index a0, Index a1, Index a2) const 38 { 39 using std::atan2; 40 using std::sin; 41 using std::cos; 42 /* Implemented from Graphics Gems IV */ 43 EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Derived,3,3) 44 45 Matrix<Scalar,3,1> res; 46 typedef Matrix<typename Derived::Scalar,2,1> Vector2; 47 48 const Index odd = ((a0+1)%3 == a1) ? 0 : 1; 49 const Index i = a0; 50 const Index j = (a0 + 1 + odd)%3; 51 const Index k = (a0 + 2 - odd)%3; 52 53 if (a0==a2) 54 { 55 res[0] = atan2(coeff(j,i), coeff(k,i)); 56 if((odd && res[0]<Scalar(0)) || ((!odd) && res[0]>Scalar(0))) 57 { 58 res[0] = (res[0] > Scalar(0)) ? res[0] - Scalar(M_PI) : res[0] + Scalar(M_PI); 59 Scalar s2 = Vector2(coeff(j,i), coeff(k,i)).norm(); 60 res[1] = -atan2(s2, coeff(i,i)); 61 } 62 else 63 { 64 Scalar s2 = Vector2(coeff(j,i), coeff(k,i)).norm(); 65 res[1] = atan2(s2, coeff(i,i)); 66 } 67 68 // With a=(0,1,0), we have i=0; j=1; k=2, and after computing the first two angles, 69 // we can compute their respective rotation, and apply its inverse to M. Since the result must 70 // be a rotation around x, we have: 71 // 72 // c2 s1.s2 c1.s2 1 0 0 73 // 0 c1 -s1 * M = 0 c3 s3 74 // -s2 s1.c2 c1.c2 0 -s3 c3 75 // 76 // Thus: m11.c1 - m21.s1 = c3 & m12.c1 - m22.s1 = s3 77 78 Scalar s1 = sin(res[0]); 79 Scalar c1 = cos(res[0]); 80 res[2] = atan2(c1*coeff(j,k)-s1*coeff(k,k), c1*coeff(j,j) - s1 * coeff(k,j)); 81 } 82 else 83 { 84 res[0] = atan2(coeff(j,k), coeff(k,k)); 85 Scalar c2 = Vector2(coeff(i,i), coeff(i,j)).norm(); 86 if((odd && res[0]<Scalar(0)) || ((!odd) && res[0]>Scalar(0))) { 87 res[0] = (res[0] > Scalar(0)) ? res[0] - Scalar(M_PI) : res[0] + Scalar(M_PI); 88 res[1] = atan2(-coeff(i,k), -c2); 89 } 90 else 91 res[1] = atan2(-coeff(i,k), c2); 92 Scalar s1 = sin(res[0]); 93 Scalar c1 = cos(res[0]); 94 res[2] = atan2(s1*coeff(k,i)-c1*coeff(j,i), c1*coeff(j,j) - s1 * coeff(k,j)); 95 } 96 if (!odd) 97 res = -res; 98 99 return res; 100 } 101 102 } // end namespace Eigen 103 104 #endif // EIGEN_EULERANGLES_H 105
