EulerAngles.h
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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 
35 template<typename Derived>
38 {
39  using std::atan2;
40  using std::sin;
41  using std::cos;
42  /* Implemented from Graphics Gems IV */
44 
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
USING_NAMESPACE_ACADO IntermediateState sin(const Expression &arg)
internal::traits< Derived >::Index Index
The type of indices.
Definition: DenseBase.h:61
const AutoDiffScalar< Matrix< typename internal::traits< DerTypeA >::Scalar, Dynamic, 1 > > atan2(const AutoDiffScalar< DerTypeA > &a, const AutoDiffScalar< DerTypeB > &b)
iterative scaling algorithm to equilibrate rows and column norms in matrices
Definition: matrix.hpp:471
internal::traits< Derived >::Scalar Scalar
Definition: MatrixBase.h:56
Matrix< Scalar, 3, 1 > eulerAngles(Index a0, Index a1, Index a2) const
Definition: EulerAngles.h:37
IntermediateState cos(const Expression &arg)
#define EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(TYPE, ROWS, COLS)
Definition: StaticAssert.h:146
#define M_PI
Definition: acado_utils.hpp:54
Abstract base class for interfacing tailored matrix-vector operations.


acado
Author(s): Milan Vukov, Rien Quirynen
autogenerated on Mon Jun 10 2019 12:34:33