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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra. Eigen itself is part of the KDE project.
//
// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#ifndef EIGEN_EULERANGLES_H
#define EIGEN_EULERANGLES_H
template<typename Other,
int OtherRows=Other::RowsAtCompileTime,
int OtherCols=Other::ColsAtCompileTime>
struct ei_eulerangles_assign_impl;
// enum {
// XYZ,
// XYX,
//
//
// };
/** \class EulerAngles
*
* \brief Represents a rotation in a 3 dimensional space as three Euler angles
*
* \param _Scalar the scalar type, i.e., the type of the angles.
*
* \sa class Quaternion, class AngleAxis, class Transform
*/
template<typename _Scalar>
class EulerAngles
{
public:
enum { Dim = 3 };
/** the scalar type of the coefficients */
typedef _Scalar Scalar;
typedef Matrix<Scalar,3,3> Matrix3;
typedef Matrix<Scalar,3,1> Vector3;
typedef Quaternion<Scalar> QuaternionType;
typedef AngleAxis<Scalar> AngleAxisType;
protected:
Vector3 m_angles;
public:
EulerAngles() {}
inline EulerAngles(Scalar a0, Scalar a1, Scalar a2) : m_angles(a0, a1, a2) {}
inline EulerAngles(const QuaternionType& q) { *this = q; }
inline EulerAngles(const AngleAxisType& aa) { *this = aa; }
template<typename Derived>
inline EulerAngles(const MatrixBase<Derived>& m) { *this = m; }
Scalar angle(int i) const { return m_angles.coeff(i); }
Scalar& angle(int i) { return m_angles.coeffRef(i); }
const Vector3& coeffs() const { return m_angles; }
Vector3& coeffs() { return m_angles; }
EulerAngles& operator=(const QuaternionType& q);
EulerAngles& operator=(const AngleAxisType& ea);
template<typename Derived>
EulerAngles& operator=(const MatrixBase<Derived>& m);
template<typename Derived>
EulerAngles& fromRotationMatrix(const MatrixBase<Derived>& m);
Matrix3 toRotationMatrix(void) const;
};
/** Set \c *this from a quaternion.
* The axis is normalized.
*/
template<typename Scalar>
EulerAngles<Scalar>& EulerAngles<Scalar>::operator=(const QuaternionType& q)
{
Scalar y2 = q.y() * q.y();
m_angles.coeffRef(0) = std::atan2(2*(q.w()*q.x() + q.y()*q.z()), (1 - 2*(q.x()*q.x() + y2)));
m_angles.coeffRef(1) = std::asin( 2*(q.w()*q.y() - q.z()*q.x()));
m_angles.coeffRef(2) = std::atan2(2*(q.w()*q.z() + q.x()*q.y()), (1 - 2*(y2 + q.z()*q.z())));
return *this;
}
/** Set \c *this from Euler angles \a ea.
*/
template<typename Scalar>
EulerAngles<Scalar>& EulerAngles<Scalar>::operator=(const AngleAxisType& aa)
{
return *this = QuaternionType(aa);
}
/** Set \c *this from the expression \a xpr:
* - if \a xpr is a 3x1 vector, then \a xpr is assumed to be a vector of angles
* - if \a xpr is a 3x3 matrix, then \a xpr is assumed to be rotation matrix
* and \a xpr is converted to Euler angles
*/
template<typename Scalar>
template<typename Derived>
EulerAngles<Scalar>& EulerAngles<Scalar>::operator=(const MatrixBase<Derived>& other)
{
ei_eulerangles_assign_impl<Derived>::run(*this,other.derived());
return *this;
}
/** Constructs and \returns an equivalent 3x3 rotation matrix.
*/
template<typename Scalar>
typename EulerAngles<Scalar>::Matrix3
EulerAngles<Scalar>::toRotationMatrix(void) const
{
Vector3 c = m_angles.cwise().cos();
Vector3 s = m_angles.cwise().sin();
return Matrix3() <<
c.y()*c.z(), -c.y()*s.z(), s.y(),
c.z()*s.x()*s.y()+c.x()*s.z(), c.x()*c.z()-s.x()*s.y()*s.z(), -c.y()*s.x(),
-c.x()*c.z()*s.y()+s.x()*s.z(), c.z()*s.x()+c.x()*s.y()*s.z(), c.x()*c.y();
}
// set from a rotation matrix
template<typename Other>
struct ei_eulerangles_assign_impl<Other,3,3>
{
typedef typename Other::Scalar Scalar;
inline static void run(EulerAngles<Scalar>& ea, const Other& mat)
{
// mat = cy*cz -cy*sz sy
// cz*sx*sy+cx*sz cx*cz-sx*sy*sz -cy*sx
// -cx*cz*sy+sx*sz cz*sx+cx*sy*sz cx*cy
ea.angle(1) = std::asin(mat.coeff(0,2));
ea.angle(0) = std::atan2(-mat.coeff(1,2),mat.coeff(2,2));
ea.angle(2) = std::atan2(-mat.coeff(0,1),mat.coeff(0,0));
}
};
// set from a vector of angles
template<typename Other>
struct ei_eulerangles_assign_impl<Other,3,1>
{
typedef typename Other::Scalar Scalar;
inline static void run(EulerAngles<Scalar>& ea, const Other& vec)
{
ea.coeffs() = vec;
}
};
#endif // EIGEN_EULERANGLES_H
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