1 // This file is part of Eigen, a lightweight C++ template library 2 // for linear algebra. 3 // 4 // Copyright (C) 2015 Tal Hadad <tal_hd (at) hotmail.com> 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 12 #include <unsupported/Eigen/EulerAngles> 13 14 using namespace Eigen; 15 16 template<typename EulerSystem, typename Scalar> 17 void verify_euler_ranged(const Matrix<Scalar,3,1>& ea, 18 bool positiveRangeAlpha, bool positiveRangeBeta, bool positiveRangeGamma) 19 { 20 typedef EulerAngles<Scalar, EulerSystem> EulerAnglesType; 21 typedef Matrix<Scalar,3,3> Matrix3; 22 typedef Matrix<Scalar,3,1> Vector3; 23 typedef Quaternion<Scalar> QuaternionType; 24 typedef AngleAxis<Scalar> AngleAxisType; 25 using std::abs; 26 27 Scalar alphaRangeStart, alphaRangeEnd; 28 Scalar betaRangeStart, betaRangeEnd; 29 Scalar gammaRangeStart, gammaRangeEnd; 30 31 if (positiveRangeAlpha) 32 { 33 alphaRangeStart = Scalar(0); 34 alphaRangeEnd = Scalar(2 * EIGEN_PI); 35 } 36 else 37 { 38 alphaRangeStart = -Scalar(EIGEN_PI); 39 alphaRangeEnd = Scalar(EIGEN_PI); 40 } 41 42 if (positiveRangeBeta) 43 { 44 betaRangeStart = Scalar(0); 45 betaRangeEnd = Scalar(2 * EIGEN_PI); 46 } 47 else 48 { 49 betaRangeStart = -Scalar(EIGEN_PI); 50 betaRangeEnd = Scalar(EIGEN_PI); 51 } 52 53 if (positiveRangeGamma) 54 { 55 gammaRangeStart = Scalar(0); 56 gammaRangeEnd = Scalar(2 * EIGEN_PI); 57 } 58 else 59 { 60 gammaRangeStart = -Scalar(EIGEN_PI); 61 gammaRangeEnd = Scalar(EIGEN_PI); 62 } 63 64 const int i = EulerSystem::AlphaAxisAbs - 1; 65 const int j = EulerSystem::BetaAxisAbs - 1; 66 const int k = EulerSystem::GammaAxisAbs - 1; 67 68 const int iFactor = EulerSystem::IsAlphaOpposite ? -1 : 1; 69 const int jFactor = EulerSystem::IsBetaOpposite ? -1 : 1; 70 const int kFactor = EulerSystem::IsGammaOpposite ? -1 : 1; 71 72 const Vector3 I = EulerAnglesType::AlphaAxisVector(); 73 const Vector3 J = EulerAnglesType::BetaAxisVector(); 74 const Vector3 K = EulerAnglesType::GammaAxisVector(); 75 76 EulerAnglesType e(ea[0], ea[1], ea[2]); 77 78 Matrix3 m(e); 79 Vector3 eabis = EulerAnglesType(m, positiveRangeAlpha, positiveRangeBeta, positiveRangeGamma).angles(); 80 81 // Check that eabis in range 82 VERIFY(alphaRangeStart <= eabis[0] && eabis[0] <= alphaRangeEnd); 83 VERIFY(betaRangeStart <= eabis[1] && eabis[1] <= betaRangeEnd); 84 VERIFY(gammaRangeStart <= eabis[2] && eabis[2] <= gammaRangeEnd); 85 86 Vector3 eabis2 = m.eulerAngles(i, j, k); 87 88 // Invert the relevant axes 89 eabis2[0] *= iFactor; 90 eabis2[1] *= jFactor; 91 eabis2[2] *= kFactor; 92 93 // Saturate the angles to the correct range 94 if (positiveRangeAlpha && (eabis2[0] < 0)) 95 eabis2[0] += Scalar(2 * EIGEN_PI); 96 if (positiveRangeBeta && (eabis2[1] < 0)) 97 eabis2[1] += Scalar(2 * EIGEN_PI); 98 if (positiveRangeGamma && (eabis2[2] < 0)) 99 eabis2[2] += Scalar(2 * EIGEN_PI); 100 101 VERIFY_IS_APPROX(eabis, eabis2);// Verify that our estimation is the same as m.eulerAngles() is 102 103 Matrix3 mbis(AngleAxisType(eabis[0], I) * AngleAxisType(eabis[1], J) * AngleAxisType(eabis[2], K)); 104 VERIFY_IS_APPROX(m, mbis); 105 106 // Tests that are only relevant for no possitive range 107 if (!(positiveRangeAlpha || positiveRangeBeta || positiveRangeGamma)) 108 { 109 /* If I==K, and ea[1]==0, then there no unique solution. */ 110 /* The remark apply in the case where I!=K, and |ea[1]| is close to pi/2. */ 111 if( (i!=k || ea[1]!=0) && (i==k || !internal::isApprox(abs(ea[1]),Scalar(EIGEN_PI/2),test_precision<Scalar>())) ) 112 VERIFY((ea-eabis).norm() <= test_precision<Scalar>()); 113 114 // approx_or_less_than does not work for 0 115 VERIFY(0 < eabis[0] || test_isMuchSmallerThan(eabis[0], Scalar(1))); 116 } 117 118 // Quaternions 119 QuaternionType q(e); 120 eabis = EulerAnglesType(q, positiveRangeAlpha, positiveRangeBeta, positiveRangeGamma).angles(); 121 VERIFY_IS_APPROX(eabis, eabis2);// Verify that the euler angles are still the same 122 } 123 124 template<typename EulerSystem, typename Scalar> 125 void verify_euler(const Matrix<Scalar,3,1>& ea) 126 { 127 verify_euler_ranged<EulerSystem>(ea, false, false, false); 128 verify_euler_ranged<EulerSystem>(ea, false, false, true); 129 verify_euler_ranged<EulerSystem>(ea, false, true, false); 130 verify_euler_ranged<EulerSystem>(ea, false, true, true); 131 verify_euler_ranged<EulerSystem>(ea, true, false, false); 132 verify_euler_ranged<EulerSystem>(ea, true, false, true); 133 verify_euler_ranged<EulerSystem>(ea, true, true, false); 134 verify_euler_ranged<EulerSystem>(ea, true, true, true); 135 } 136 137 template<typename Scalar> void check_all_var(const Matrix<Scalar,3,1>& ea) 138 { 139 verify_euler<EulerSystemXYZ>(ea); 140 verify_euler<EulerSystemXYX>(ea); 141 verify_euler<EulerSystemXZY>(ea); 142 verify_euler<EulerSystemXZX>(ea); 143 144 verify_euler<EulerSystemYZX>(ea); 145 verify_euler<EulerSystemYZY>(ea); 146 verify_euler<EulerSystemYXZ>(ea); 147 verify_euler<EulerSystemYXY>(ea); 148 149 verify_euler<EulerSystemZXY>(ea); 150 verify_euler<EulerSystemZXZ>(ea); 151 verify_euler<EulerSystemZYX>(ea); 152 verify_euler<EulerSystemZYZ>(ea); 153 } 154 155 template<typename Scalar> void eulerangles() 156 { 157 typedef Matrix<Scalar,3,3> Matrix3; 158 typedef Matrix<Scalar,3,1> Vector3; 159 typedef Array<Scalar,3,1> Array3; 160 typedef Quaternion<Scalar> Quaternionx; 161 typedef AngleAxis<Scalar> AngleAxisType; 162 163 Scalar a = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_PI)); 164 Quaternionx q1; 165 q1 = AngleAxisType(a, Vector3::Random().normalized()); 166 Matrix3 m; 167 m = q1; 168 169 Vector3 ea = m.eulerAngles(0,1,2); 170 check_all_var(ea); 171 ea = m.eulerAngles(0,1,0); 172 check_all_var(ea); 173 174 // Check with purely random Quaternion: 175 q1.coeffs() = Quaternionx::Coefficients::Random().normalized(); 176 m = q1; 177 ea = m.eulerAngles(0,1,2); 178 check_all_var(ea); 179 ea = m.eulerAngles(0,1,0); 180 check_all_var(ea); 181 182 // Check with random angles in range [0:pi]x[-pi:pi]x[-pi:pi]. 183 ea = (Array3::Random() + Array3(1,0,0))*Scalar(EIGEN_PI)*Array3(0.5,1,1); 184 check_all_var(ea); 185 186 ea[2] = ea[0] = internal::random<Scalar>(0,Scalar(EIGEN_PI)); 187 check_all_var(ea); 188 189 ea[0] = ea[1] = internal::random<Scalar>(0,Scalar(EIGEN_PI)); 190 check_all_var(ea); 191 192 ea[1] = 0; 193 check_all_var(ea); 194 195 ea.head(2).setZero(); 196 check_all_var(ea); 197 198 ea.setZero(); 199 check_all_var(ea); 200 } 201 202 void test_EulerAngles() 203 { 204 for(int i = 0; i < g_repeat; i++) { 205 CALL_SUBTEST_1( eulerangles<float>() ); 206 CALL_SUBTEST_2( eulerangles<double>() ); 207 } 208 } 209
