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209 lines
6.3 KiB
209 lines
6.3 KiB
// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2015 Tal Hadad <tal_hd@hotmail.com>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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#include "main.h"
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#include <unsupported/Eigen/EulerAngles>
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using namespace Eigen;
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template<typename EulerSystem, typename Scalar>
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void verify_euler_ranged(const Matrix<Scalar,3,1>& ea,
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bool positiveRangeAlpha, bool positiveRangeBeta, bool positiveRangeGamma)
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{
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typedef EulerAngles<Scalar, EulerSystem> EulerAnglesType;
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typedef Matrix<Scalar,3,3> Matrix3;
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typedef Matrix<Scalar,3,1> Vector3;
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typedef Quaternion<Scalar> QuaternionType;
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typedef AngleAxis<Scalar> AngleAxisType;
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using std::abs;
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Scalar alphaRangeStart, alphaRangeEnd;
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Scalar betaRangeStart, betaRangeEnd;
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Scalar gammaRangeStart, gammaRangeEnd;
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if (positiveRangeAlpha)
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{
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alphaRangeStart = Scalar(0);
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alphaRangeEnd = Scalar(2 * EIGEN_PI);
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}
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else
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{
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alphaRangeStart = -Scalar(EIGEN_PI);
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alphaRangeEnd = Scalar(EIGEN_PI);
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}
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if (positiveRangeBeta)
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{
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betaRangeStart = Scalar(0);
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betaRangeEnd = Scalar(2 * EIGEN_PI);
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}
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else
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{
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betaRangeStart = -Scalar(EIGEN_PI);
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betaRangeEnd = Scalar(EIGEN_PI);
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}
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if (positiveRangeGamma)
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{
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gammaRangeStart = Scalar(0);
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gammaRangeEnd = Scalar(2 * EIGEN_PI);
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}
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else
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{
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gammaRangeStart = -Scalar(EIGEN_PI);
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gammaRangeEnd = Scalar(EIGEN_PI);
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}
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const int i = EulerSystem::AlphaAxisAbs - 1;
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const int j = EulerSystem::BetaAxisAbs - 1;
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const int k = EulerSystem::GammaAxisAbs - 1;
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const int iFactor = EulerSystem::IsAlphaOpposite ? -1 : 1;
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const int jFactor = EulerSystem::IsBetaOpposite ? -1 : 1;
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const int kFactor = EulerSystem::IsGammaOpposite ? -1 : 1;
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const Vector3 I = EulerAnglesType::AlphaAxisVector();
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const Vector3 J = EulerAnglesType::BetaAxisVector();
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const Vector3 K = EulerAnglesType::GammaAxisVector();
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EulerAnglesType e(ea[0], ea[1], ea[2]);
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Matrix3 m(e);
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Vector3 eabis = EulerAnglesType(m, positiveRangeAlpha, positiveRangeBeta, positiveRangeGamma).angles();
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// Check that eabis in range
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VERIFY(alphaRangeStart <= eabis[0] && eabis[0] <= alphaRangeEnd);
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VERIFY(betaRangeStart <= eabis[1] && eabis[1] <= betaRangeEnd);
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VERIFY(gammaRangeStart <= eabis[2] && eabis[2] <= gammaRangeEnd);
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Vector3 eabis2 = m.eulerAngles(i, j, k);
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// Invert the relevant axes
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eabis2[0] *= iFactor;
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eabis2[1] *= jFactor;
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eabis2[2] *= kFactor;
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// Saturate the angles to the correct range
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if (positiveRangeAlpha && (eabis2[0] < 0))
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eabis2[0] += Scalar(2 * EIGEN_PI);
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if (positiveRangeBeta && (eabis2[1] < 0))
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eabis2[1] += Scalar(2 * EIGEN_PI);
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if (positiveRangeGamma && (eabis2[2] < 0))
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eabis2[2] += Scalar(2 * EIGEN_PI);
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VERIFY_IS_APPROX(eabis, eabis2);// Verify that our estimation is the same as m.eulerAngles() is
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Matrix3 mbis(AngleAxisType(eabis[0], I) * AngleAxisType(eabis[1], J) * AngleAxisType(eabis[2], K));
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VERIFY_IS_APPROX(m, mbis);
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// Tests that are only relevant for no possitive range
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if (!(positiveRangeAlpha || positiveRangeBeta || positiveRangeGamma))
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{
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/* If I==K, and ea[1]==0, then there no unique solution. */
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/* The remark apply in the case where I!=K, and |ea[1]| is close to pi/2. */
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if( (i!=k || ea[1]!=0) && (i==k || !internal::isApprox(abs(ea[1]),Scalar(EIGEN_PI/2),test_precision<Scalar>())) )
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VERIFY((ea-eabis).norm() <= test_precision<Scalar>());
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// approx_or_less_than does not work for 0
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VERIFY(0 < eabis[0] || test_isMuchSmallerThan(eabis[0], Scalar(1)));
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}
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// Quaternions
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QuaternionType q(e);
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eabis = EulerAnglesType(q, positiveRangeAlpha, positiveRangeBeta, positiveRangeGamma).angles();
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VERIFY_IS_APPROX(eabis, eabis2);// Verify that the euler angles are still the same
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}
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template<typename EulerSystem, typename Scalar>
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void verify_euler(const Matrix<Scalar,3,1>& ea)
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{
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verify_euler_ranged<EulerSystem>(ea, false, false, false);
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verify_euler_ranged<EulerSystem>(ea, false, false, true);
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verify_euler_ranged<EulerSystem>(ea, false, true, false);
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verify_euler_ranged<EulerSystem>(ea, false, true, true);
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verify_euler_ranged<EulerSystem>(ea, true, false, false);
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verify_euler_ranged<EulerSystem>(ea, true, false, true);
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verify_euler_ranged<EulerSystem>(ea, true, true, false);
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verify_euler_ranged<EulerSystem>(ea, true, true, true);
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}
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template<typename Scalar> void check_all_var(const Matrix<Scalar,3,1>& ea)
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{
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verify_euler<EulerSystemXYZ>(ea);
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verify_euler<EulerSystemXYX>(ea);
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verify_euler<EulerSystemXZY>(ea);
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verify_euler<EulerSystemXZX>(ea);
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verify_euler<EulerSystemYZX>(ea);
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verify_euler<EulerSystemYZY>(ea);
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verify_euler<EulerSystemYXZ>(ea);
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verify_euler<EulerSystemYXY>(ea);
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verify_euler<EulerSystemZXY>(ea);
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verify_euler<EulerSystemZXZ>(ea);
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verify_euler<EulerSystemZYX>(ea);
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verify_euler<EulerSystemZYZ>(ea);
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}
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template<typename Scalar> void eulerangles()
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{
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typedef Matrix<Scalar,3,3> Matrix3;
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typedef Matrix<Scalar,3,1> Vector3;
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typedef Array<Scalar,3,1> Array3;
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typedef Quaternion<Scalar> Quaternionx;
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typedef AngleAxis<Scalar> AngleAxisType;
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Scalar a = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_PI));
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Quaternionx q1;
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q1 = AngleAxisType(a, Vector3::Random().normalized());
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Matrix3 m;
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m = q1;
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Vector3 ea = m.eulerAngles(0,1,2);
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check_all_var(ea);
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ea = m.eulerAngles(0,1,0);
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check_all_var(ea);
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// Check with purely random Quaternion:
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q1.coeffs() = Quaternionx::Coefficients::Random().normalized();
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m = q1;
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ea = m.eulerAngles(0,1,2);
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check_all_var(ea);
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ea = m.eulerAngles(0,1,0);
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check_all_var(ea);
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// Check with random angles in range [0:pi]x[-pi:pi]x[-pi:pi].
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ea = (Array3::Random() + Array3(1,0,0))*Scalar(EIGEN_PI)*Array3(0.5,1,1);
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check_all_var(ea);
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ea[2] = ea[0] = internal::random<Scalar>(0,Scalar(EIGEN_PI));
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check_all_var(ea);
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ea[0] = ea[1] = internal::random<Scalar>(0,Scalar(EIGEN_PI));
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check_all_var(ea);
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ea[1] = 0;
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check_all_var(ea);
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ea.head(2).setZero();
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check_all_var(ea);
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ea.setZero();
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check_all_var(ea);
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}
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void test_EulerAngles()
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{
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for(int i = 0; i < g_repeat; i++) {
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CALL_SUBTEST_1( eulerangles<float>() );
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CALL_SUBTEST_2( eulerangles<double>() );
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}
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}
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