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// 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).
*
* The returned angles are in the ranges [0:pi]x[-pi:pi]x[-pi:pi].
*
* \sa class AngleAxis
*/
template<typename Derived>
inline Matrix<typename MatrixBase<Derived>::Scalar,3,1>
MatrixBase<Derived>::eulerAngles(Index a0, Index a1, Index a2) const
{
using std::atan2;
using std::sin;
using std::cos;
/* 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 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)
{
res[0] = atan2(coeff(j,i), coeff(k,i));
if((odd && res[0]<Scalar(0)) || ((!odd) && res[0]>Scalar(0)))
{
res[0] = (res[0] > Scalar(0)) ? res[0] - Scalar(M_PI) : res[0] + Scalar(M_PI);
Scalar s2 = Vector2(coeff(j,i), coeff(k,i)).norm();
res[1] = -atan2(s2, coeff(i,i));
}
else
{
Scalar s2 = Vector2(coeff(j,i), coeff(k,i)).norm();
res[1] = atan2(s2, coeff(i,i));
}
// With a=(0,1,0), we have i=0; j=1; k=2, and after computing the first two angles,
// we can compute their respective rotation, and apply its inverse to M. Since the result must
// be a rotation around x, we have:
//
// c2 s1.s2 c1.s2 1 0 0
// 0 c1 -s1 * M = 0 c3 s3
// -s2 s1.c2 c1.c2 0 -s3 c3
//
// Thus: m11.c1 - m21.s1 = c3 & m12.c1 - m22.s1 = s3
Scalar s1 = sin(res[0]);
Scalar c1 = cos(res[0]);
res[2] = atan2(c1*coeff(j,k)-s1*coeff(k,k), c1*coeff(j,j) - s1 * coeff(k,j));
}
else
{
res[0] = atan2(coeff(j,k), coeff(k,k));
Scalar c2 = Vector2(coeff(i,i), coeff(i,j)).norm();
if((odd && res[0]<Scalar(0)) || ((!odd) && res[0]>Scalar(0))) {
res[0] = (res[0] > Scalar(0)) ? res[0] - Scalar(M_PI) : res[0] + Scalar(M_PI);
res[1] = atan2(-coeff(i,k), -c2);
}
else
res[1] = atan2(-coeff(i,k), c2);
Scalar s1 = sin(res[0]);
Scalar c1 = cos(res[0]);
res[2] = atan2(s1*coeff(k,i)-c1*coeff(j,i), c1*coeff(j,j) - s1 * coeff(k,j));
}
if (!odd)
res = -res;
return res;
}
} // end namespace Eigen
#endif // EIGEN_EULERANGLES_H
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