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
15/** \geometry_module \ingroup Geometry_Module
16  *
17  * \class AngleAxis
18  *
19  * \brief Represents a 3D rotation as a rotation angle around an arbitrary 3D axis
20  *
21  * \param _Scalar the scalar type, i.e., the type of the coefficients.
22  *
23  * \warning When setting up an AngleAxis object, the axis vector \b must \b be \b normalized.
24  *
25  * The following two typedefs are provided for convenience:
26  * \li \c AngleAxisf for \c float
27  * \li \c AngleAxisd for \c double
28  *
29  * Combined with MatrixBase::Unit{X,Y,Z}, AngleAxis can be used to easily
30  * mimic Euler-angles. Here is an example:
31  * \include AngleAxis_mimic_euler.cpp
32  * Output: \verbinclude AngleAxis_mimic_euler.out
33  *
34  * \note This class is not aimed to be used to store a rotation transformation,
35  * but rather to make easier the creation of other rotation (Quaternion, rotation Matrix)
36  * and transformation objects.
37  *
38  * \sa class Quaternion, class Transform, MatrixBase::UnitX()
39  */
40
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{
51  typedef RotationBase<AngleAxis<_Scalar>,3> Base;
52
53public:
54
55  using Base::operator*;
56
57  enum { Dim = 3 };
58  /** the scalar type of the coefficients */
59  typedef _Scalar Scalar;
60  typedef Matrix<Scalar,3,3> Matrix3;
61  typedef Matrix<Scalar,3,1> Vector3;
62  typedef Quaternion<Scalar> QuaternionType;
63
64protected:
65
66  Vector3 m_axis;
67  Scalar m_angle;
68
69public:
70
71  /** Default constructor without initialization. */
72  EIGEN_DEVICE_FUNC AngleAxis() {}
73  /** Constructs and initialize the angle-axis rotation from an \a angle in radian
74    * and an \a axis which \b must \b be \b normalized.
75    *
76    * \warning If the \a axis vector is not normalized, then the angle-axis object
77    *          represents an invalid rotation. */
78  template<typename Derived>
79  EIGEN_DEVICE_FUNC
80  inline AngleAxis(const Scalar& angle, const MatrixBase<Derived>& axis) : m_axis(axis), m_angle(angle) {}
81  /** Constructs and initialize the angle-axis rotation from a quaternion \a q.
82    * This function implicitly normalizes the quaternion \a q.
83    */
84  template<typename QuatDerived>
85  EIGEN_DEVICE_FUNC inline explicit AngleAxis(const QuaternionBase<QuatDerived>& q) { *this = q; }
86  /** Constructs and initialize the angle-axis rotation from a 3x3 rotation matrix. */
87  template<typename Derived>
88  EIGEN_DEVICE_FUNC inline explicit AngleAxis(const MatrixBase<Derived>& m) { *this = m; }
89
90  /** \returns the value of the rotation angle in radian */
91  EIGEN_DEVICE_FUNC Scalar angle() const { return m_angle; }
92  /** \returns a read-write reference to the stored angle in radian */
93  EIGEN_DEVICE_FUNC Scalar& angle() { return m_angle; }
94
95  /** \returns the rotation axis */
96  EIGEN_DEVICE_FUNC const Vector3& axis() const { return m_axis; }
97  /** \returns a read-write reference to the stored rotation axis.
98    *
99    * \warning The rotation axis must remain a \b unit vector.
100    */
101  EIGEN_DEVICE_FUNC Vector3& axis() { return m_axis; }
102
103  /** Concatenates two rotations */
104  EIGEN_DEVICE_FUNC inline QuaternionType operator* (const AngleAxis& other) const
105  { return QuaternionType(*this) * QuaternionType(other); }
106
107  /** Concatenates two rotations */
108  EIGEN_DEVICE_FUNC inline QuaternionType operator* (const QuaternionType& other) const
109  { return QuaternionType(*this) * other; }
110
111  /** Concatenates two rotations */
112  friend EIGEN_DEVICE_FUNC inline QuaternionType operator* (const QuaternionType& a, const AngleAxis& b)
113  { return a * QuaternionType(b); }
114
115  /** \returns the inverse rotation, i.e., an angle-axis with opposite rotation angle */
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
128  /** \returns \c *this with scalar type casted to \a NewScalarType
129    *
130    * Note that if \a NewScalarType is equal to the current scalar type of \c *this
131    * then this function smartly returns a const reference to \c *this.
132    */
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
137  /** Copy constructor with scalar type conversion */
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
147  /** \returns \c true if \c *this is approximately equal to \a other, within the precision
148    * determined by \a prec.
149    *
150    * \sa MatrixBase::isApprox() */
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
155/** \ingroup Geometry_Module
156  * single precision angle-axis type */
157typedef AngleAxis<float> AngleAxisf;
158/** \ingroup Geometry_Module
159  * double precision angle-axis type */
160typedef AngleAxis<double> AngleAxisd;
161
162/** Set \c *this from a \b unit quaternion.
163  *
164  * The resulting axis is normalized, and the computed angle is in the [0,pi] range.
165  *
166  * This function implicitly normalizes the quaternion \a q.
167  */
168template<typename Scalar>
169template<typename QuatDerived>
170EIGEN_DEVICE_FUNC AngleAxis<Scalar>& AngleAxis<Scalar>::operator=(const QuaternionBase<QuatDerived>& q)
171{
172  EIGEN_USING_STD_MATH(atan2)
173  EIGEN_USING_STD_MATH(abs)
174  Scalar n = q.vec().norm();
175  if(n<NumTraits<Scalar>::epsilon())
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() < 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
193/** Set \c *this from a 3x3 rotation matrix \a mat.
194  */
195template<typename Scalar>
196template<typename Derived>
197EIGEN_DEVICE_FUNC AngleAxis<Scalar>& AngleAxis<Scalar>::operator=(const MatrixBase<Derived>& mat)
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
204/**
205* \brief Sets \c *this from a 3x3 rotation matrix.
206**/
207template<typename Scalar>
208template<typename Derived>
209EIGEN_DEVICE_FUNC AngleAxis<Scalar>& AngleAxis<Scalar>::fromRotationMatrix(const MatrixBase<Derived>& mat)
210{
211  return *this = QuaternionType(mat);
212}
213
214/** Constructs and \returns an equivalent 3x3 rotation matrix.
215  */
216template<typename Scalar>
217typename AngleAxis<Scalar>::Matrix3
218EIGEN_DEVICE_FUNC AngleAxis<Scalar>::toRotationMatrix(void) const
219{
220  EIGEN_USING_STD_MATH(sin)
221  EIGEN_USING_STD_MATH(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
248