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 template<typename Derived>
32 inline Matrix<typename MatrixBase<Derived>::Scalar,3,1>
eulerAngles(Index a0,Index a1,Index a2)33 MatrixBase<Derived>::eulerAngles(Index a0, Index a1, Index a2) const
34 {
35 /* Implemented from Graphics Gems IV */
36 EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Derived,3,3)
37
38 Matrix<Scalar,3,1> res;
39 typedef Matrix<typename Derived::Scalar,2,1> Vector2;
40 const Scalar epsilon = NumTraits<Scalar>::dummy_precision();
41
42 const Index odd = ((a0+1)%3 == a1) ? 0 : 1;
43 const Index i = a0;
44 const Index j = (a0 + 1 + odd)%3;
45 const Index k = (a0 + 2 - odd)%3;
46
47 if (a0==a2)
48 {
49 Scalar s = Vector2(coeff(j,i) , coeff(k,i)).norm();
50 res[1] = internal::atan2(s, coeff(i,i));
51 if (s > epsilon)
52 {
53 res[0] = internal::atan2(coeff(j,i), coeff(k,i));
54 res[2] = internal::atan2(coeff(i,j),-coeff(i,k));
55 }
56 else
57 {
58 res[0] = Scalar(0);
59 res[2] = (coeff(i,i)>0?1:-1)*internal::atan2(-coeff(k,j), coeff(j,j));
60 }
61 }
62 else
63 {
64 Scalar c = Vector2(coeff(i,i) , coeff(i,j)).norm();
65 res[1] = internal::atan2(-coeff(i,k), c);
66 if (c > epsilon)
67 {
68 res[0] = internal::atan2(coeff(j,k), coeff(k,k));
69 res[2] = internal::atan2(coeff(i,j), coeff(i,i));
70 }
71 else
72 {
73 res[0] = Scalar(0);
74 res[2] = (coeff(i,k)>0?1:-1)*internal::atan2(-coeff(k,j), coeff(j,j));
75 }
76 }
77 if (!odd)
78 res = -res;
79 return res;
80 }
81
82 } // end namespace Eigen
83
84 #endif // EIGEN_EULERANGLES_H
85