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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2012 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// 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 <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;
using std::abs;
Matrix3 m(AngleAxisx(ea[0], Vector3::Unit(i)) * AngleAxisx(ea[1], Vector3::Unit(j)) * AngleAxisx(ea[2], Vector3::Unit(k)));
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);
/* 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)));
VERIFY_IS_APPROX_OR_LESS_THAN(eabis[0], Scalar(EIGEN_PI));
VERIFY_IS_APPROX_OR_LESS_THAN(-Scalar(EIGEN_PI), eabis[1]);
VERIFY_IS_APPROX_OR_LESS_THAN(eabis[1], Scalar(EIGEN_PI));
VERIFY_IS_APPROX_OR_LESS_THAN(-Scalar(EIGEN_PI), eabis[2]);
VERIFY_IS_APPROX_OR_LESS_THAN(eabis[2], Scalar(EIGEN_PI));
}
template<typename Scalar> void check_all_var(const Matrix<Scalar,3,1>& ea)
{
verify_euler(ea, 0,1,2);
verify_euler(ea, 0,1,0);
verify_euler(ea, 0,2,1);
verify_euler(ea, 0,2,0);
verify_euler(ea, 1,2,0);
verify_euler(ea, 1,2,1);
verify_euler(ea, 1,0,2);
verify_euler(ea, 1,0,1);
verify_euler(ea, 2,0,1);
verify_euler(ea, 2,0,2);
verify_euler(ea, 2,1,0);
verify_euler(ea, 2,1,2);
}
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;
Scalar a = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_PI));
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 [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);
}
EIGEN_DECLARE_TEST(geo_eulerangles)
{
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1( eulerangles<float>() );
CALL_SUBTEST_2( eulerangles<double>() );
}
}
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