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Eigen  3.4.0
 
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AngleAxis.h
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_ANGLEAXIS_H
11#define EIGEN_ANGLEAXIS_H
12
13namespace Eigen {
14
41namespace internal {
42template<typename _Scalar> struct traits<AngleAxis<_Scalar> >
43{
44 typedef _Scalar Scalar;
45};
46}
47
48template<typename _Scalar>
49class AngleAxis : public RotationBase<AngleAxis<_Scalar>,3>
50{
52
53public:
54
55 using Base::operator*;
56
57 enum { Dim = 3 };
59 typedef _Scalar Scalar;
63
64protected:
65
66 Vector3 m_axis;
67 Scalar m_angle;
68
69public:
70
72 EIGEN_DEVICE_FUNC AngleAxis() {}
78 template<typename Derived>
79 EIGEN_DEVICE_FUNC
80 inline AngleAxis(const Scalar& angle, const MatrixBase<Derived>& axis) : m_axis(axis), m_angle(angle) {}
84 template<typename QuatDerived>
85 EIGEN_DEVICE_FUNC inline explicit AngleAxis(const QuaternionBase<QuatDerived>& q) { *this = q; }
87 template<typename Derived>
88 EIGEN_DEVICE_FUNC inline explicit AngleAxis(const MatrixBase<Derived>& m) { *this = m; }
89
91 EIGEN_DEVICE_FUNC Scalar angle() const { return m_angle; }
93 EIGEN_DEVICE_FUNC Scalar& angle() { return m_angle; }
94
96 EIGEN_DEVICE_FUNC const Vector3& axis() const { return m_axis; }
101 EIGEN_DEVICE_FUNC Vector3& axis() { return m_axis; }
102
104 EIGEN_DEVICE_FUNC inline QuaternionType operator* (const AngleAxis& other) const
105 { return QuaternionType(*this) * QuaternionType(other); }
106
108 EIGEN_DEVICE_FUNC inline QuaternionType operator* (const QuaternionType& other) const
109 { return QuaternionType(*this) * other; }
110
112 friend EIGEN_DEVICE_FUNC inline QuaternionType operator* (const QuaternionType& a, const AngleAxis& b)
113 { return a * QuaternionType(b); }
114
116 EIGEN_DEVICE_FUNC AngleAxis inverse() const
117 { return AngleAxis(-m_angle, m_axis); }
118
119 template<class QuatDerived>
120 EIGEN_DEVICE_FUNC AngleAxis& operator=(const QuaternionBase<QuatDerived>& q);
121 template<typename Derived>
122 EIGEN_DEVICE_FUNC AngleAxis& operator=(const MatrixBase<Derived>& m);
123
124 template<typename Derived>
125 EIGEN_DEVICE_FUNC AngleAxis& fromRotationMatrix(const MatrixBase<Derived>& m);
126 EIGEN_DEVICE_FUNC Matrix3 toRotationMatrix(void) const;
127
133 template<typename NewScalarType>
134 EIGEN_DEVICE_FUNC inline typename internal::cast_return_type<AngleAxis,AngleAxis<NewScalarType> >::type cast() const
135 { return typename internal::cast_return_type<AngleAxis,AngleAxis<NewScalarType> >::type(*this); }
136
138 template<typename OtherScalarType>
139 EIGEN_DEVICE_FUNC inline explicit AngleAxis(const AngleAxis<OtherScalarType>& other)
140 {
141 m_axis = other.axis().template cast<Scalar>();
142 m_angle = Scalar(other.angle());
143 }
144
145 EIGEN_DEVICE_FUNC static inline const AngleAxis Identity() { return AngleAxis(Scalar(0), Vector3::UnitX()); }
146
151 EIGEN_DEVICE_FUNC bool isApprox(const AngleAxis& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
152 { return m_axis.isApprox(other.m_axis, prec) && internal::isApprox(m_angle,other.m_angle, prec); }
153};
154
161
168template<typename Scalar>
169template<typename QuatDerived>
171{
172 EIGEN_USING_STD(atan2)
173 EIGEN_USING_STD(abs)
174 Scalar n = q.vec().norm();
176 n = q.vec().stableNorm();
177
178 if (n != Scalar(0))
179 {
180 m_angle = Scalar(2)*atan2(n, abs(q.w()));
181 if(q.w() < Scalar(0))
182 n = -n;
183 m_axis = q.vec() / n;
184 }
185 else
186 {
187 m_angle = Scalar(0);
188 m_axis << Scalar(1), Scalar(0), Scalar(0);
189 }
190 return *this;
191}
192
195template<typename Scalar>
196template<typename Derived>
198{
199 // Since a direct conversion would not be really faster,
200 // let's use the robust Quaternion implementation:
201 return *this = QuaternionType(mat);
202}
203
207template<typename Scalar>
208template<typename Derived>
210{
211 return *this = QuaternionType(mat);
212}
213
216template<typename Scalar>
218EIGEN_DEVICE_FUNC AngleAxis<Scalar>::toRotationMatrix(void) const
219{
220 EIGEN_USING_STD(sin)
221 EIGEN_USING_STD(cos)
222 Matrix3 res;
223 Vector3 sin_axis = sin(m_angle) * m_axis;
224 Scalar c = cos(m_angle);
225 Vector3 cos1_axis = (Scalar(1)-c) * m_axis;
226
227 Scalar tmp;
228 tmp = cos1_axis.x() * m_axis.y();
229 res.coeffRef(0,1) = tmp - sin_axis.z();
230 res.coeffRef(1,0) = tmp + sin_axis.z();
231
232 tmp = cos1_axis.x() * m_axis.z();
233 res.coeffRef(0,2) = tmp + sin_axis.y();
234 res.coeffRef(2,0) = tmp - sin_axis.y();
235
236 tmp = cos1_axis.y() * m_axis.z();
237 res.coeffRef(1,2) = tmp - sin_axis.x();
238 res.coeffRef(2,1) = tmp + sin_axis.x();
239
240 res.diagonal() = (cos1_axis.cwiseProduct(m_axis)).array() + c;
241
242 return res;
243}
244
245} // end namespace Eigen
246
247#endif // EIGEN_ANGLEAXIS_H
Represents a 3D rotation as a rotation angle around an arbitrary 3D axis.
Definition: AngleAxis.h:50
AngleAxis()
Definition: AngleAxis.h:72
Scalar & angle()
Definition: AngleAxis.h:93
Vector3 & axis()
Definition: AngleAxis.h:101
AngleAxis(const MatrixBase< Derived > &m)
Definition: AngleAxis.h:88
Scalar angle() const
Definition: AngleAxis.h:91
AngleAxis(const AngleAxis< OtherScalarType > &other)
Definition: AngleAxis.h:139
AngleAxis(const Scalar &angle, const MatrixBase< Derived > &axis)
Definition: AngleAxis.h:80
internal::cast_return_type< AngleAxis, AngleAxis< NewScalarType > >::type cast() const
Definition: AngleAxis.h:134
bool isApprox(const AngleAxis &other, const typename NumTraits< Scalar >::Real &prec=NumTraits< Scalar >::dummy_precision()) const
Definition: AngleAxis.h:151
const Vector3 & axis() const
Definition: AngleAxis.h:96
_Scalar Scalar
Definition: AngleAxis.h:59
friend QuaternionType operator*(const QuaternionType &a, const AngleAxis &b)
Definition: AngleAxis.h:112
Matrix3 toRotationMatrix(void) const
Definition: AngleAxis.h:218
AngleAxis inverse() const
Definition: AngleAxis.h:116
AngleAxis(const QuaternionBase< QuatDerived > &q)
Definition: AngleAxis.h:85
Base class for all dense matrices, vectors, and expressions.
Definition: MatrixBase.h:50
The matrix class, also used for vectors and row-vectors.
Definition: Matrix.h:180
Scalar & coeffRef(Index rowId, Index colId)
Definition: PlainObjectBase.h:175
Base class for quaternion expressions.
Definition: Quaternion.h:36
const VectorBlock< const Coefficients, 3 > vec() const
Definition: Quaternion.h:84
CoeffReturnType w() const
Definition: Quaternion.h:72
The quaternion class used to represent 3D orientations and rotations.
Definition: Quaternion.h:274
Common base class for compact rotation representations.
Definition: RotationBase.h:30
Namespace containing all symbols from the Eigen library.
Definition: Core:141
Holds information about the various numeric (i.e. scalar) types allowed by Eigen.
Definition: NumTraits.h:233