1 // This file is part of Eigen, a lightweight C++ template library 2 // for linear algebra. 3 // 4 // Copyright (C) 2008-2012 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 #include "main.h" 11 #include <Eigen/Geometry> 12 #include <Eigen/LU> 13 #include <Eigen/SVD> 14 15 16 template<typename Scalar> 17 void verify_euler(const Matrix<Scalar,3,1>& ea, int i, int j, int k) 18 { 19 typedef Matrix<Scalar,3,3> Matrix3; 20 typedef Matrix<Scalar,3,1> Vector3; 21 typedef AngleAxis<Scalar> AngleAxisx; 22 using std::abs; 23 Matrix3 m(AngleAxisx(ea[0], Vector3::Unit(i)) * AngleAxisx(ea[1], Vector3::Unit(j)) * AngleAxisx(ea[2], Vector3::Unit(k))); 24 Vector3 eabis = m.eulerAngles(i, j, k); 25 Matrix3 mbis(AngleAxisx(eabis[0], Vector3::Unit(i)) * AngleAxisx(eabis[1], Vector3::Unit(j)) * AngleAxisx(eabis[2], Vector3::Unit(k))); 26 VERIFY_IS_APPROX(m, mbis); 27 /* If I==K, and ea[1]==0, then there no unique solution. */ 28 /* The remark apply in the case where I!=K, and |ea[1]| is close to pi/2. */ 29 if( (i!=k || ea[1]!=0) && (i==k || !internal::isApprox(abs(ea[1]),Scalar(EIGEN_PI/2),test_precision<Scalar>())) ) 30 VERIFY((ea-eabis).norm() <= test_precision<Scalar>()); 31 32 // approx_or_less_than does not work for 0 33 VERIFY(0 < eabis[0] || test_isMuchSmallerThan(eabis[0], Scalar(1))); 34 VERIFY_IS_APPROX_OR_LESS_THAN(eabis[0], Scalar(EIGEN_PI)); 35 VERIFY_IS_APPROX_OR_LESS_THAN(-Scalar(EIGEN_PI), eabis[1]); 36 VERIFY_IS_APPROX_OR_LESS_THAN(eabis[1], Scalar(EIGEN_PI)); 37 VERIFY_IS_APPROX_OR_LESS_THAN(-Scalar(EIGEN_PI), eabis[2]); 38 VERIFY_IS_APPROX_OR_LESS_THAN(eabis[2], Scalar(EIGEN_PI)); 39 } 40 41 template<typename Scalar> void check_all_var(const Matrix<Scalar,3,1>& ea) 42 { 43 verify_euler(ea, 0,1,2); 44 verify_euler(ea, 0,1,0); 45 verify_euler(ea, 0,2,1); 46 verify_euler(ea, 0,2,0); 47 48 verify_euler(ea, 1,2,0); 49 verify_euler(ea, 1,2,1); 50 verify_euler(ea, 1,0,2); 51 verify_euler(ea, 1,0,1); 52 53 verify_euler(ea, 2,0,1); 54 verify_euler(ea, 2,0,2); 55 verify_euler(ea, 2,1,0); 56 verify_euler(ea, 2,1,2); 57 } 58 59 template<typename Scalar> void eulerangles() 60 { 61 typedef Matrix<Scalar,3,3> Matrix3; 62 typedef Matrix<Scalar,3,1> Vector3; 63 typedef Array<Scalar,3,1> Array3; 64 typedef Quaternion<Scalar> Quaternionx; 65 typedef AngleAxis<Scalar> AngleAxisx; 66 67 Scalar a = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_PI)); 68 Quaternionx q1; 69 q1 = AngleAxisx(a, Vector3::Random().normalized()); 70 Matrix3 m; 71 m = q1; 72 73 Vector3 ea = m.eulerAngles(0,1,2); 74 check_all_var(ea); 75 ea = m.eulerAngles(0,1,0); 76 check_all_var(ea); 77 78 // Check with purely random Quaternion: 79 q1.coeffs() = Quaternionx::Coefficients::Random().normalized(); 80 m = q1; 81 ea = m.eulerAngles(0,1,2); 82 check_all_var(ea); 83 ea = m.eulerAngles(0,1,0); 84 check_all_var(ea); 85 86 // Check with random angles in range [0:pi]x[-pi:pi]x[-pi:pi]. 87 ea = (Array3::Random() + Array3(1,0,0))*Scalar(EIGEN_PI)*Array3(0.5,1,1); 88 check_all_var(ea); 89 90 ea[2] = ea[0] = internal::random<Scalar>(0,Scalar(EIGEN_PI)); 91 check_all_var(ea); 92 93 ea[0] = ea[1] = internal::random<Scalar>(0,Scalar(EIGEN_PI)); 94 check_all_var(ea); 95 96 ea[1] = 0; 97 check_all_var(ea); 98 99 ea.head(2).setZero(); 100 check_all_var(ea); 101 102 ea.setZero(); 103 check_all_var(ea); 104 } 105 106 void test_geo_eulerangles() 107 { 108 for(int i = 0; i < g_repeat; i++) { 109 CALL_SUBTEST_1( eulerangles<float>() ); 110 CALL_SUBTEST_2( eulerangles<double>() ); 111 } 112 } 113
