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>
36EIGEN_DEVICE_FUNC inline Matrix<typename MatrixBase<Derived>::Scalar,3,1>
37MatrixBase<Derived>::eulerAngles(Index a0, Index a1, Index a2) const
38{
39 EIGEN_USING_STD_MATH(atan2)
40 EIGEN_USING_STD_MATH(sin)
41 EIGEN_USING_STD_MATH(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 if(res[0] > Scalar(0)) {
59 res[0] -= Scalar(EIGEN_PI);
60 }
61 else {
62 res[0] += Scalar(EIGEN_PI);
63 }
64 Scalar s2 = Vector2(coeff(j,i), coeff(k,i)).norm();
65 res[1] = -atan2(s2, coeff(i,i));
66 }
67 else
68 {
69 Scalar s2 = Vector2(coeff(j,i), coeff(k,i)).norm();
70 res[1] = atan2(s2, coeff(i,i));
71 }
72
73 // With a=(0,1,0), we have i=0; j=1; k=2, and after computing the first two angles,
74 // we can compute their respective rotation, and apply its inverse to M. Since the result must
75 // be a rotation around x, we have:
76 //
77 // c2 s1.s2 c1.s2 1 0 0
78 // 0 c1 -s1 * M = 0 c3 s3
79 // -s2 s1.c2 c1.c2 0 -s3 c3
80 //
81 // Thus: m11.c1 - m21.s1 = c3 & m12.c1 - m22.s1 = s3
82
83 Scalar s1 = sin(res[0]);
84 Scalar c1 = cos(res[0]);
85 res[2] = atan2(c1*coeff(j,k)-s1*coeff(k,k), c1*coeff(j,j) - s1 * coeff(k,j));
86 }
87 else
88 {
89 res[0] = atan2(coeff(j,k), coeff(k,k));
90 Scalar c2 = Vector2(coeff(i,i), coeff(i,j)).norm();
91 if((odd && res[0]<Scalar(0)) || ((!odd) && res[0]>Scalar(0))) {
92 if(res[0] > Scalar(0)) {
93 res[0] -= Scalar(EIGEN_PI);
94 }
95 else {
96 res[0] += Scalar(EIGEN_PI);
97 }
98 res[1] = atan2(-coeff(i,k), -c2);
99 }
100 else
101 res[1] = atan2(-coeff(i,k), c2);
102 Scalar s1 = sin(res[0]);
103 Scalar c1 = cos(res[0]);
104 res[2] = atan2(s1*coeff(k,i)-c1*coeff(j,i), c1*coeff(j,j) - s1 * coeff(k,j));
105 }
106 if (!odd)
107 res = -res;
108
109 return res;
110}
111
112} // end namespace Eigen
113
114#endif // EIGEN_EULERANGLES_H
115