1// This file is part of Eigen, a lightweight C++ template library
2// for linear algebra.
3//
4// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
5//
6// This Source Code Form is subject to the terms of the Mozilla
7// Public License v. 2.0. If a copy of the MPL was not distributed
8// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
9
10#ifndef EIGEN_EULERANGLES_H
11#define EIGEN_EULERANGLES_H
12
13namespace Eigen {
14
15/** \geometry_module \ingroup Geometry_Module
16  *
17  *
18  * \returns the Euler-angles of the rotation matrix \c *this using the convention defined by the triplet (\a a0,\a a1,\a a2)
19  *
20  * Each of the three parameters \a a0,\a a1,\a a2 represents the respective rotation axis as an integer in {0,1,2}.
21  * For instance, in:
22  * \code Vector3f ea = mat.eulerAngles(2, 0, 2); \endcode
23  * "2" represents the z axis and "0" the x axis, etc. The returned angles are such that
24  * we have the following equality:
25  * \code
26  * mat == AngleAxisf(ea[0], Vector3f::UnitZ())
27  *      * AngleAxisf(ea[1], Vector3f::UnitX())
28  *      * AngleAxisf(ea[2], Vector3f::UnitZ()); \endcode
29  * This corresponds to the right-multiply conventions (with right hand side frames).
30  *
31  * The returned angles are in the ranges [0:pi]x[-pi:pi]x[-pi:pi].
32  *
33  * \sa class AngleAxis
34  */
35template<typename Derived>
36inline Matrix<typename MatrixBase<Derived>::Scalar,3,1>
37MatrixBase<Derived>::eulerAngles(Index a0, Index a1, Index a2) const
38{
39  using std::atan2;
40  using std::sin;
41  using std::cos;
42  /* Implemented from Graphics Gems IV */
43  EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Derived,3,3)
44
45  Matrix<Scalar,3,1> res;
46  typedef Matrix<typename Derived::Scalar,2,1> Vector2;
47
48  const Index odd = ((a0+1)%3 == a1) ? 0 : 1;
49  const Index i = a0;
50  const Index j = (a0 + 1 + odd)%3;
51  const Index k = (a0 + 2 - odd)%3;
52
53  if (a0==a2)
54  {
55    res[0] = atan2(coeff(j,i), coeff(k,i));
56    if((odd && res[0]<Scalar(0)) || ((!odd) && res[0]>Scalar(0)))
57    {
58      res[0] = (res[0] > Scalar(0)) ? res[0] - Scalar(M_PI) : res[0] + Scalar(M_PI);
59      Scalar s2 = Vector2(coeff(j,i), coeff(k,i)).norm();
60      res[1] = -atan2(s2, coeff(i,i));
61    }
62    else
63    {
64      Scalar s2 = Vector2(coeff(j,i), coeff(k,i)).norm();
65      res[1] = atan2(s2, coeff(i,i));
66    }
67
68    // With a=(0,1,0), we have i=0; j=1; k=2, and after computing the first two angles,
69    // we can compute their respective rotation, and apply its inverse to M. Since the result must
70    // be a rotation around x, we have:
71    //
72    //  c2  s1.s2 c1.s2                   1  0   0
73    //  0   c1    -s1       *    M    =   0  c3  s3
74    //  -s2 s1.c2 c1.c2                   0 -s3  c3
75    //
76    //  Thus:  m11.c1 - m21.s1 = c3  &   m12.c1 - m22.s1 = s3
77
78    Scalar s1 = sin(res[0]);
79    Scalar c1 = cos(res[0]);
80    res[2] = atan2(c1*coeff(j,k)-s1*coeff(k,k), c1*coeff(j,j) - s1 * coeff(k,j));
81  }
82  else
83  {
84    res[0] = atan2(coeff(j,k), coeff(k,k));
85    Scalar c2 = Vector2(coeff(i,i), coeff(i,j)).norm();
86    if((odd && res[0]<Scalar(0)) || ((!odd) && res[0]>Scalar(0))) {
87      res[0] = (res[0] > Scalar(0)) ? res[0] - Scalar(M_PI) : res[0] + Scalar(M_PI);
88      res[1] = atan2(-coeff(i,k), -c2);
89    }
90    else
91      res[1] = atan2(-coeff(i,k), c2);
92    Scalar s1 = sin(res[0]);
93    Scalar c1 = cos(res[0]);
94    res[2] = atan2(s1*coeff(k,i)-c1*coeff(j,i), c1*coeff(j,j) - s1 * coeff(k,j));
95  }
96  if (!odd)
97    res = -res;
98
99  return res;
100}
101
102} // end namespace Eigen
103
104#endif // EIGEN_EULERANGLES_H
105