Eigen/src/Geometry/EulerAngles.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 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/.

#ifndef EIGEN_EULERANGLES_H
#define EIGEN_EULERANGLES_H

namespace Eigen { 

/** \geometry_module \ingroup Geometry_Module
  *
  *
  * \returns the Euler-angles of the rotation matrix \c *this using the convention defined by the triplet (\a a0,\a a1,\a a2)
  *
  * Each of the three parameters \a a0,\a a1,\a a2 represents the respective rotation axis as an integer in {0,1,2}.
  * For instance, in:
  * \code Vector3f ea = mat.eulerAngles(2, 0, 2); \endcode
  * "2" represents the z axis and "0" the x axis, etc. The returned angles are such that
  * we have the following equality:
  * \code
  * mat == AngleAxisf(ea[0], Vector3f::UnitZ())
  *      * AngleAxisf(ea[1], Vector3f::UnitX())
  *      * AngleAxisf(ea[2], Vector3f::UnitZ()); \endcode
  * This corresponds to the right-multiply conventions (with right hand side frames).
  */
template<typename Derived>
inline Matrix<typename MatrixBase<Derived>::Scalar,3,1>
MatrixBase<Derived>::eulerAngles(Index a0, Index a1, Index a2) const
{
  /* Implemented from Graphics Gems IV */
  EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Derived,3,3)

  Matrix<Scalar,3,1> res;
  typedef Matrix<typename Derived::Scalar,2,1> Vector2;
  const Scalar epsilon = NumTraits<Scalar>::dummy_precision();

  const Index odd = ((a0+1)%3 == a1) ? 0 : 1;
  const Index i = a0;
  const Index j = (a0 + 1 + odd)%3;
  const Index k = (a0 + 2 - odd)%3;

  if (a0==a2)
  {
    Scalar s = Vector2(coeff(j,i) , coeff(k,i)).norm();
    res[1] = internal::atan2(s, coeff(i,i));
    if (s > epsilon)
    {
      res[0] = internal::atan2(coeff(j,i), coeff(k,i));
      res[2] = internal::atan2(coeff(i,j),-coeff(i,k));
    }
    else
    {
      res[0] = Scalar(0);
      res[2] = (coeff(i,i)>0?1:-1)*internal::atan2(-coeff(k,j), coeff(j,j));
    }
  }
  else
  {
    Scalar c = Vector2(coeff(i,i) , coeff(i,j)).norm();
    res[1] = internal::atan2(-coeff(i,k), c);
    if (c > epsilon)
    {
      res[0] = internal::atan2(coeff(j,k), coeff(k,k));
      res[2] = internal::atan2(coeff(i,j), coeff(i,i));
    }
    else
    {
      res[0] = Scalar(0);
      res[2] = (coeff(i,k)>0?1:-1)*internal::atan2(-coeff(k,j), coeff(j,j));
    }
  }
  if (!odd)
    res = -res;
  return res;
}

} // end namespace Eigen

#endif // EIGEN_EULERANGLES_H