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+// 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
+}