text: // 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);
  }
  
  void test_geo_eulerangles()
  {
    for(int i = 0; i < g_repeat; i++) {
      CALL_SUBTEST_1( eulerangles<float>() );
      CALL_SUBTEST_2( eulerangles<double>() );
    }
  }
  