| // 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>() ); |
| } |
| } |