// This file is part of Eigen, a lightweight C++ template library // for linear algebra. // // Copyright (C) 2015 Tal Hadad <tal_hd@hotmail.com> // // 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/. #include "main.h" #include <unsupported/Eigen/EulerAngles> using namespace Eigen; template<typename EulerSystem, typename Scalar> void verify_euler_ranged(const Matrix<Scalar,3,1>& ea, bool positiveRangeAlpha, bool positiveRangeBeta, bool positiveRangeGamma) { typedef EulerAngles<Scalar, EulerSystem> EulerAnglesType; typedef Matrix<Scalar,3,3> Matrix3; typedef Matrix<Scalar,3,1> Vector3; typedef Quaternion<Scalar> QuaternionType; typedef AngleAxis<Scalar> AngleAxisType; using std::abs; Scalar alphaRangeStart, alphaRangeEnd; Scalar betaRangeStart, betaRangeEnd; Scalar gammaRangeStart, gammaRangeEnd; if (positiveRangeAlpha) { alphaRangeStart = Scalar(0); alphaRangeEnd = Scalar(2 * EIGEN_PI); } else { alphaRangeStart = -Scalar(EIGEN_PI); alphaRangeEnd = Scalar(EIGEN_PI); } if (positiveRangeBeta) { betaRangeStart = Scalar(0); betaRangeEnd = Scalar(2 * EIGEN_PI); } else { betaRangeStart = -Scalar(EIGEN_PI); betaRangeEnd = Scalar(EIGEN_PI); } if (positiveRangeGamma) { gammaRangeStart = Scalar(0); gammaRangeEnd = Scalar(2 * EIGEN_PI); } else { gammaRangeStart = -Scalar(EIGEN_PI); gammaRangeEnd = Scalar(EIGEN_PI); } const int i = EulerSystem::AlphaAxisAbs - 1; const int j = EulerSystem::BetaAxisAbs - 1; const int k = EulerSystem::GammaAxisAbs - 1; const int iFactor = EulerSystem::IsAlphaOpposite ? -1 : 1; const int jFactor = EulerSystem::IsBetaOpposite ? -1 : 1; const int kFactor = EulerSystem::IsGammaOpposite ? -1 : 1; const Vector3 I = EulerAnglesType::AlphaAxisVector(); const Vector3 J = EulerAnglesType::BetaAxisVector(); const Vector3 K = EulerAnglesType::GammaAxisVector(); EulerAnglesType e(ea[0], ea[1], ea[2]); Matrix3 m(e); Vector3 eabis = EulerAnglesType(m, positiveRangeAlpha, positiveRangeBeta, positiveRangeGamma).angles(); // Check that eabis in range VERIFY(alphaRangeStart <= eabis[0] && eabis[0] <= alphaRangeEnd); VERIFY(betaRangeStart <= eabis[1] && eabis[1] <= betaRangeEnd); VERIFY(gammaRangeStart <= eabis[2] && eabis[2] <= gammaRangeEnd); Vector3 eabis2 = m.eulerAngles(i, j, k); // Invert the relevant axes eabis2[0] *= iFactor; eabis2[1] *= jFactor; eabis2[2] *= kFactor; // Saturate the angles to the correct range if (positiveRangeAlpha && (eabis2[0] < 0)) eabis2[0] += Scalar(2 * EIGEN_PI); if (positiveRangeBeta && (eabis2[1] < 0)) eabis2[1] += Scalar(2 * EIGEN_PI); if (positiveRangeGamma && (eabis2[2] < 0)) eabis2[2] += Scalar(2 * EIGEN_PI); VERIFY_IS_APPROX(eabis, eabis2);// Verify that our estimation is the same as m.eulerAngles() is Matrix3 mbis(AngleAxisType(eabis[0], I) * AngleAxisType(eabis[1], J) * AngleAxisType(eabis[2], K)); VERIFY_IS_APPROX(m, mbis); // Tests that are only relevant for no possitive range if (!(positiveRangeAlpha || positiveRangeBeta || positiveRangeGamma)) { /* If I==K, and ea[1]==0, then there no unique solution. */ /* The remark apply in the case where I!=K, and |ea[1]| is close to pi/2. */ if( (i!=k || ea[1]!=0) && (i==k || !internal::isApprox(abs(ea[1]),Scalar(EIGEN_PI/2),test_precision<Scalar>())) ) VERIFY((ea-eabis).norm() <= test_precision<Scalar>()); // approx_or_less_than does not work for 0 VERIFY(0 < eabis[0] || test_isMuchSmallerThan(eabis[0], Scalar(1))); } // Quaternions QuaternionType q(e); eabis = EulerAnglesType(q, positiveRangeAlpha, positiveRangeBeta, positiveRangeGamma).angles(); VERIFY_IS_APPROX(eabis, eabis2);// Verify that the euler angles are still the same } template<typename EulerSystem, typename Scalar> void verify_euler(const Matrix<Scalar,3,1>& ea) { verify_euler_ranged<EulerSystem>(ea, false, false, false); verify_euler_ranged<EulerSystem>(ea, false, false, true); verify_euler_ranged<EulerSystem>(ea, false, true, false); verify_euler_ranged<EulerSystem>(ea, false, true, true); verify_euler_ranged<EulerSystem>(ea, true, false, false); verify_euler_ranged<EulerSystem>(ea, true, false, true); verify_euler_ranged<EulerSystem>(ea, true, true, false); verify_euler_ranged<EulerSystem>(ea, true, true, true); } template<typename Scalar> void check_all_var(const Matrix<Scalar,3,1>& ea) { verify_euler<EulerSystemXYZ>(ea); verify_euler<EulerSystemXYX>(ea); verify_euler<EulerSystemXZY>(ea); verify_euler<EulerSystemXZX>(ea); verify_euler<EulerSystemYZX>(ea); verify_euler<EulerSystemYZY>(ea); verify_euler<EulerSystemYXZ>(ea); verify_euler<EulerSystemYXY>(ea); verify_euler<EulerSystemZXY>(ea); verify_euler<EulerSystemZXZ>(ea); verify_euler<EulerSystemZYX>(ea); verify_euler<EulerSystemZYZ>(ea); } template<typename Scalar> void eulerangles() { typedef Matrix<Scalar,3,3> Matrix3; typedef Matrix<Scalar,3,1> Vector3; typedef Array<Scalar,3,1> Array3; typedef Quaternion<Scalar> Quaternionx; typedef AngleAxis<Scalar> AngleAxisType; Scalar a = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_PI)); Quaternionx q1; q1 = AngleAxisType(a, Vector3::Random().normalized()); Matrix3 m; m = q1; Vector3 ea = m.eulerAngles(0,1,2); check_all_var(ea); ea = m.eulerAngles(0,1,0); check_all_var(ea); // Check with purely random Quaternion: q1.coeffs() = Quaternionx::Coefficients::Random().normalized(); m = q1; ea = m.eulerAngles(0,1,2); check_all_var(ea); ea = m.eulerAngles(0,1,0); check_all_var(ea); // Check with random angles in range [0:pi]x[-pi:pi]x[-pi:pi]. ea = (Array3::Random() + Array3(1,0,0))*Scalar(EIGEN_PI)*Array3(0.5,1,1); check_all_var(ea); ea[2] = ea[0] = internal::random<Scalar>(0,Scalar(EIGEN_PI)); check_all_var(ea); ea[0] = ea[1] = internal::random<Scalar>(0,Scalar(EIGEN_PI)); check_all_var(ea); ea[1] = 0; check_all_var(ea); ea.head(2).setZero(); check_all_var(ea); ea.setZero(); check_all_var(ea); } void test_EulerAngles() { for(int i = 0; i < g_repeat; i++) { CALL_SUBTEST_1( eulerangles<float>() ); CALL_SUBTEST_2( eulerangles<double>() ); } }