// This file is part of Eigen, a lightweight C++ template library // for linear algebra. // // Copyright (C) 2008-2012 Gael Guennebaud <gael.guennebaud@inria.fr> // Copyright (C) 2023 Juraj Oršulić, University of Zagreb <juraj.orsulic@fer.hr> // // 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/. // Silence warnings about using the deprecated non-canonical .eulerAngles(), which are still being tested. #define EIGEN_NO_DEPRECATED_WARNING #include "main.h" #include <Eigen/Geometry> #include <Eigen/LU> #include <Eigen/SVD> template <typename Scalar> void verify_euler(const Matrix<Scalar, 3, 1>& ea, int i, int j, int k) { typedef Matrix<Scalar, 3, 3> Matrix3; typedef Matrix<Scalar, 3, 1> Vector3; typedef AngleAxis<Scalar> AngleAxisx; const Matrix3 m(AngleAxisx(ea[0], Vector3::Unit(i)) * AngleAxisx(ea[1], Vector3::Unit(j)) * AngleAxisx(ea[2], Vector3::Unit(k))); const Scalar kPi = Scalar(EIGEN_PI); // Test non-canonical eulerAngles { Vector3 eabis = m.eulerAngles(i, j, k); Matrix3 mbis(AngleAxisx(eabis[0], Vector3::Unit(i)) * AngleAxisx(eabis[1], Vector3::Unit(j)) * AngleAxisx(eabis[2], Vector3::Unit(k))); VERIFY_IS_APPROX(m, mbis); // approx_or_less_than does not work for 0 VERIFY(0 < eabis[0] || test_isMuchSmallerThan(eabis[0], Scalar(1))); VERIFY_IS_APPROX_OR_LESS_THAN(eabis[0], kPi); VERIFY_IS_APPROX_OR_LESS_THAN(-kPi, eabis[1]); VERIFY_IS_APPROX_OR_LESS_THAN(eabis[1], kPi); VERIFY_IS_APPROX_OR_LESS_THAN(-kPi, eabis[2]); VERIFY_IS_APPROX_OR_LESS_THAN(eabis[2], kPi); } // Test canonicalEulerAngles { Vector3 eabis = m.canonicalEulerAngles(i, j, k); Matrix3 mbis(AngleAxisx(eabis[0], Vector3::Unit(i)) * AngleAxisx(eabis[1], Vector3::Unit(j)) * AngleAxisx(eabis[2], Vector3::Unit(k))); VERIFY_IS_APPROX(m, mbis); VERIFY_IS_APPROX_OR_LESS_THAN(-kPi, eabis[0]); VERIFY_IS_APPROX_OR_LESS_THAN(eabis[0], kPi); if (i != k) { // Tait-Bryan sequence VERIFY_IS_APPROX_OR_LESS_THAN(-Scalar(kPi / 2), eabis[1]); VERIFY_IS_APPROX_OR_LESS_THAN(eabis[1], Scalar(kPi / 2)); } else { // Proper Euler sequence // approx_or_less_than does not work for 0 VERIFY(0 < eabis[1] || test_isMuchSmallerThan(eabis[1], Scalar(1))); VERIFY_IS_APPROX_OR_LESS_THAN(eabis[1], kPi); } VERIFY_IS_APPROX_OR_LESS_THAN(-kPi, eabis[2]); VERIFY_IS_APPROX_OR_LESS_THAN(eabis[2], kPi); } } template <typename Scalar> void check_all_var(const Matrix<Scalar, 3, 1>& ea) { auto verify_permutation = [](const Matrix<Scalar, 3, 1>& eap) { verify_euler(eap, 0, 1, 2); verify_euler(eap, 0, 1, 0); verify_euler(eap, 0, 2, 1); verify_euler(eap, 0, 2, 0); verify_euler(eap, 1, 2, 0); verify_euler(eap, 1, 2, 1); verify_euler(eap, 1, 0, 2); verify_euler(eap, 1, 0, 1); verify_euler(eap, 2, 0, 1); verify_euler(eap, 2, 0, 2); verify_euler(eap, 2, 1, 0); verify_euler(eap, 2, 1, 2); }; int i, j, k; for (i = 0; i < 3; i++) for (j = 0; j < 3; j++) for (k = 0; k < 3; k++) { Matrix<Scalar, 3, 1> eap(ea(i), ea(j), ea(k)); verify_permutation(eap); } } 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> AngleAxisx; const Scalar kPi = Scalar(EIGEN_PI); const Scalar smallVal = static_cast<Scalar>(0.001); Scalar a = internal::random<Scalar>(-kPi, kPi); Quaternionx q1; q1 = AngleAxisx(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 [-pi:pi]x[-pi:pi]x[-pi:pi]. ea = Array3::Random() * kPi; check_all_var(ea); auto test_with_some_zeros = [=](const Vector3& eaz) { check_all_var(eaz); Vector3 ea_glz = eaz; ea_glz[0] = Scalar(0); check_all_var(ea_glz); ea_glz[0] = internal::random<Scalar>(-smallVal, smallVal); check_all_var(ea_glz); ea_glz[2] = Scalar(0); check_all_var(ea_glz); ea_glz[2] = internal::random<Scalar>(-smallVal, smallVal); check_all_var(ea_glz); }; // Check gimbal lock configurations and a bit noisy gimbal locks Vector3 ea_gl = ea; ea_gl[1] = kPi / 2; test_with_some_zeros(ea_gl); ea_gl[1] += internal::random<Scalar>(-smallVal, smallVal); test_with_some_zeros(ea_gl); ea_gl[1] = -kPi / 2; test_with_some_zeros(ea_gl); ea_gl[1] += internal::random<Scalar>(-smallVal, smallVal); test_with_some_zeros(ea_gl); ea_gl[1] = kPi / 2; ea_gl[2] = ea_gl[0]; test_with_some_zeros(ea_gl); ea_gl[1] += internal::random<Scalar>(-smallVal, smallVal); test_with_some_zeros(ea_gl); ea_gl[1] = -kPi / 2; test_with_some_zeros(ea_gl); ea_gl[1] += internal::random<Scalar>(-smallVal, smallVal); test_with_some_zeros(ea_gl); // Similar to above, but with pi instead of pi/2 Vector3 ea_pi = ea; ea_pi[1] = kPi; test_with_some_zeros(ea_gl); ea_pi[1] += internal::random<Scalar>(-smallVal, smallVal); test_with_some_zeros(ea_gl); ea_pi[1] = -kPi; test_with_some_zeros(ea_gl); ea_pi[1] += internal::random<Scalar>(-smallVal, smallVal); test_with_some_zeros(ea_gl); ea_pi[1] = kPi; ea_pi[2] = ea_pi[0]; test_with_some_zeros(ea_gl); ea_pi[1] += internal::random<Scalar>(-smallVal, smallVal); test_with_some_zeros(ea_gl); ea_pi[1] = -kPi; test_with_some_zeros(ea_gl); ea_pi[1] += internal::random<Scalar>(-smallVal, smallVal); test_with_some_zeros(ea_gl); ea[2] = ea[0] = internal::random<Scalar>(0, kPi); check_all_var(ea); ea[0] = ea[1] = internal::random<Scalar>(0, kPi); 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); } EIGEN_DECLARE_TEST(geo_eulerangles) { for (int i = 0; i < g_repeat; i++) { CALL_SUBTEST_1(eulerangles<float>()); CALL_SUBTEST_2(eulerangles<double>()); } }