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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 
13 namespace 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   */
35 template<typename Derived>
36 inline Matrix<typename MatrixBase<Derived>::Scalar,3,1>
eulerAngles(Index a0,Index a1,Index a2)37 MatrixBase<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