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Diffstat (limited to 'eigen/unsupported/test/EulerAngles.cpp')
-rw-r--r-- | eigen/unsupported/test/EulerAngles.cpp | 292 |
1 files changed, 292 insertions, 0 deletions
diff --git a/eigen/unsupported/test/EulerAngles.cpp b/eigen/unsupported/test/EulerAngles.cpp new file mode 100644 index 0000000..79ee728 --- /dev/null +++ b/eigen/unsupported/test/EulerAngles.cpp @@ -0,0 +1,292 @@ +// 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; + +// Unfortunately, we need to specialize it in order to work. (We could add it in main.h test framework) +template <typename Scalar, class System> +bool verifyIsApprox(const Eigen::EulerAngles<Scalar, System>& a, const Eigen::EulerAngles<Scalar, System>& b) +{ + return verifyIsApprox(a.angles(), b.angles()); +} + +// Verify that x is in the approxed range [a, b] +#define VERIFY_APPROXED_RANGE(a, x, b) \ + do { \ + VERIFY_IS_APPROX_OR_LESS_THAN(a, x); \ + VERIFY_IS_APPROX_OR_LESS_THAN(x, b); \ + } while(0) + +const char X = EULER_X; +const char Y = EULER_Y; +const char Z = EULER_Z; + +template<typename Scalar, class EulerSystem> +void verify_euler(const EulerAngles<Scalar, EulerSystem>& e) +{ + 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; + + const Scalar ONE = Scalar(1); + const Scalar HALF_PI = Scalar(EIGEN_PI / 2); + const Scalar PI = Scalar(EIGEN_PI); + + // It's very important calc the acceptable precision depending on the distance from the pole. + const Scalar longitudeRadius = std::abs( + EulerSystem::IsTaitBryan ? + std::cos(e.beta()) : + std::sin(e.beta()) + ); + Scalar precision = test_precision<Scalar>() / longitudeRadius; + + Scalar betaRangeStart, betaRangeEnd; + if (EulerSystem::IsTaitBryan) + { + betaRangeStart = -HALF_PI; + betaRangeEnd = HALF_PI; + } + else + { + if (!EulerSystem::IsBetaOpposite) + { + betaRangeStart = 0; + betaRangeEnd = PI; + } + else + { + betaRangeStart = -PI; + betaRangeEnd = 0; + } + } + + const Vector3 I = EulerAnglesType::AlphaAxisVector(); + const Vector3 J = EulerAnglesType::BetaAxisVector(); + const Vector3 K = EulerAnglesType::GammaAxisVector(); + + // Is approx checks + VERIFY(e.isApprox(e)); + VERIFY_IS_APPROX(e, e); + VERIFY_IS_NOT_APPROX(e, EulerAnglesType(e.alpha() + ONE, e.beta() + ONE, e.gamma() + ONE)); + + const Matrix3 m(e); + VERIFY_IS_APPROX(Scalar(m.determinant()), ONE); + + EulerAnglesType ebis(m); + + // When no roll(acting like polar representation), we have the best precision. + // One of those cases is when the Euler angles are on the pole, and because it's singular case, + // the computation returns no roll. + if (ebis.beta() == 0) + precision = test_precision<Scalar>(); + + // Check that eabis in range + VERIFY_APPROXED_RANGE(-PI, ebis.alpha(), PI); + VERIFY_APPROXED_RANGE(betaRangeStart, ebis.beta(), betaRangeEnd); + VERIFY_APPROXED_RANGE(-PI, ebis.gamma(), PI); + + const Matrix3 mbis(AngleAxisType(ebis.alpha(), I) * AngleAxisType(ebis.beta(), J) * AngleAxisType(ebis.gamma(), K)); + VERIFY_IS_APPROX(Scalar(mbis.determinant()), ONE); + VERIFY_IS_APPROX(mbis, ebis.toRotationMatrix()); + /*std::cout << "===================\n" << + "e: " << e << std::endl << + "eabis: " << eabis.transpose() << std::endl << + "m: " << m << std::endl << + "mbis: " << mbis << std::endl << + "X: " << (m * Vector3::UnitX()).transpose() << std::endl << + "X: " << (mbis * Vector3::UnitX()).transpose() << std::endl;*/ + VERIFY(m.isApprox(mbis, precision)); + + // Test if ea and eabis are the same + // Need to check both singular and non-singular cases + // There are two singular cases. + // 1. When I==K and sin(ea(1)) == 0 + // 2. When I!=K and cos(ea(1)) == 0 + + // TODO: Make this test work well, and use range saturation function. + /*// 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_IS_APPROX(ea, eabis);*/ + + // Quaternions + const QuaternionType q(e); + ebis = q; + const QuaternionType qbis(ebis); + VERIFY(internal::isApprox<Scalar>(std::abs(q.dot(qbis)), ONE, precision)); + //VERIFY_IS_APPROX(eabis, eabis2);// Verify that the euler angles are still the same + + // A suggestion for simple product test when will be supported. + /*EulerAnglesType e2(PI/2, PI/2, PI/2); + Matrix3 m2(e2); + VERIFY_IS_APPROX(e*e2, m*m2);*/ +} + +template<signed char A, signed char B, signed char C, typename Scalar> +void verify_euler_vec(const Matrix<Scalar,3,1>& ea) +{ + verify_euler(EulerAngles<Scalar, EulerSystem<A, B, C> >(ea[0], ea[1], ea[2])); +} + +template<signed char A, signed char B, signed char C, typename Scalar> +void verify_euler_all_neg(const Matrix<Scalar,3,1>& ea) +{ + verify_euler_vec<+A,+B,+C>(ea); + verify_euler_vec<+A,+B,-C>(ea); + verify_euler_vec<+A,-B,+C>(ea); + verify_euler_vec<+A,-B,-C>(ea); + + verify_euler_vec<-A,+B,+C>(ea); + verify_euler_vec<-A,+B,-C>(ea); + verify_euler_vec<-A,-B,+C>(ea); + verify_euler_vec<-A,-B,-C>(ea); +} + +template<typename Scalar> void check_all_var(const Matrix<Scalar,3,1>& ea) +{ + verify_euler_all_neg<X,Y,Z>(ea); + verify_euler_all_neg<X,Y,X>(ea); + verify_euler_all_neg<X,Z,Y>(ea); + verify_euler_all_neg<X,Z,X>(ea); + + verify_euler_all_neg<Y,Z,X>(ea); + verify_euler_all_neg<Y,Z,Y>(ea); + verify_euler_all_neg<Y,X,Z>(ea); + verify_euler_all_neg<Y,X,Y>(ea); + + verify_euler_all_neg<Z,X,Y>(ea); + verify_euler_all_neg<Z,X,Z>(ea); + verify_euler_all_neg<Z,Y,X>(ea); + verify_euler_all_neg<Z,Y,Z>(ea); +} + +template<typename Scalar> void check_singular_cases(const Scalar& singularBeta) +{ + typedef Matrix<Scalar,3,1> Vector3; + const Scalar PI = Scalar(EIGEN_PI); + + for (Scalar epsilon = NumTraits<Scalar>::epsilon(); epsilon < 1; epsilon *= Scalar(1.2)) + { + check_all_var(Vector3(PI/4, singularBeta, PI/3)); + check_all_var(Vector3(PI/4, singularBeta - epsilon, PI/3)); + check_all_var(Vector3(PI/4, singularBeta - Scalar(1.5)*epsilon, PI/3)); + check_all_var(Vector3(PI/4, singularBeta - 2*epsilon, PI/3)); + check_all_var(Vector3(PI*Scalar(0.8), singularBeta - epsilon, Scalar(0.9)*PI)); + check_all_var(Vector3(PI*Scalar(-0.9), singularBeta + epsilon, PI*Scalar(0.3))); + check_all_var(Vector3(PI*Scalar(-0.6), singularBeta + Scalar(1.5)*epsilon, PI*Scalar(0.3))); + check_all_var(Vector3(PI*Scalar(-0.5), singularBeta + 2*epsilon, PI*Scalar(0.4))); + check_all_var(Vector3(PI*Scalar(0.9), singularBeta + epsilon, Scalar(0.8)*PI)); + } + + // This one for sanity, it had a problem with near pole cases in float scalar. + check_all_var(Vector3(PI*Scalar(0.8), singularBeta - Scalar(1E-6), Scalar(0.9)*PI)); +} + +template<typename Scalar> void eulerangles_manual() +{ + typedef Matrix<Scalar,3,1> Vector3; + const Vector3 Zero = Vector3::Zero(); + const Scalar PI = Scalar(EIGEN_PI); + + check_all_var(Zero); + + // singular cases + check_singular_cases(PI/2); + check_singular_cases(-PI/2); + + check_singular_cases(Scalar(0)); + check_singular_cases(Scalar(-0)); + + check_singular_cases(PI); + check_singular_cases(-PI); + + // non-singular cases + VectorXd alpha = VectorXd::LinSpaced(Eigen::Sequential, 20, Scalar(-0.99) * PI, PI); + VectorXd beta = VectorXd::LinSpaced(Eigen::Sequential, 20, Scalar(-0.49) * PI, Scalar(0.49) * PI); + VectorXd gamma = VectorXd::LinSpaced(Eigen::Sequential, 20, Scalar(-0.99) * PI, PI); + for (int i = 0; i < alpha.size(); ++i) { + for (int j = 0; j < beta.size(); ++j) { + for (int k = 0; k < gamma.size(); ++k) { + check_all_var(Vector3d(alpha(i), beta(j), gamma(k))); + } + } + } +} + +template<typename Scalar> void eulerangles_rand() +{ + 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() +{ + // Simple cast test + EulerAnglesXYZd onesEd(1, 1, 1); + EulerAnglesXYZf onesEf = onesEd.cast<float>(); + VERIFY_IS_APPROX(onesEd, onesEf.cast<double>()); + + CALL_SUBTEST_1( eulerangles_manual<float>() ); + CALL_SUBTEST_2( eulerangles_manual<double>() ); + + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_3( eulerangles_rand<float>() ); + CALL_SUBTEST_4( eulerangles_rand<double>() ); + } + + // TODO: Add tests for auto diff + // TODO: Add tests for complex numbers +} |