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_ROTATIONBASE_H
11#define EIGEN_ROTATIONBASE_H
12
13namespace Eigen {
14
15// forward declaration
16namespace internal {
17template<typename RotationDerived, typename MatrixType, bool IsVector=MatrixType::IsVectorAtCompileTime>
18struct rotation_base_generic_product_selector;
19}
20
21/** \class RotationBase
22  *
23  * \brief Common base class for compact rotation representations
24  *
25  * \param Derived is the derived type, i.e., a rotation type
26  * \param _Dim the dimension of the space
27  */
28template<typename Derived, int _Dim>
29class RotationBase
30{
31  public:
32    enum { Dim = _Dim };
33    /** the scalar type of the coefficients */
34    typedef typename internal::traits<Derived>::Scalar Scalar;
35
36    /** corresponding linear transformation matrix type */
37    typedef Matrix<Scalar,Dim,Dim> RotationMatrixType;
38    typedef Matrix<Scalar,Dim,1> VectorType;
39
40  public:
41    inline const Derived& derived() const { return *static_cast<const Derived*>(this); }
42    inline Derived& derived() { return *static_cast<Derived*>(this); }
43
44    /** \returns an equivalent rotation matrix */
45    inline RotationMatrixType toRotationMatrix() const { return derived().toRotationMatrix(); }
46
47    /** \returns an equivalent rotation matrix
48      * This function is added to be conform with the Transform class' naming scheme.
49      */
50    inline RotationMatrixType matrix() const { return derived().toRotationMatrix(); }
51
52    /** \returns the inverse rotation */
53    inline Derived inverse() const { return derived().inverse(); }
54
55    /** \returns the concatenation of the rotation \c *this with a translation \a t */
56    inline Transform<Scalar,Dim,Isometry> operator*(const Translation<Scalar,Dim>& t) const
57    { return Transform<Scalar,Dim,Isometry>(*this) * t; }
58
59    /** \returns the concatenation of the rotation \c *this with a uniform scaling \a s */
60    inline RotationMatrixType operator*(const UniformScaling<Scalar>& s) const
61    { return toRotationMatrix() * s.factor(); }
62
63    /** \returns the concatenation of the rotation \c *this with a generic expression \a e
64      * \a e can be:
65      *  - a DimxDim linear transformation matrix
66      *  - a DimxDim diagonal matrix (axis aligned scaling)
67      *  - a vector of size Dim
68      */
69    template<typename OtherDerived>
70    EIGEN_STRONG_INLINE typename internal::rotation_base_generic_product_selector<Derived,OtherDerived,OtherDerived::IsVectorAtCompileTime>::ReturnType
71    operator*(const EigenBase<OtherDerived>& e) const
72    { return internal::rotation_base_generic_product_selector<Derived,OtherDerived>::run(derived(), e.derived()); }
73
74    /** \returns the concatenation of a linear transformation \a l with the rotation \a r */
75    template<typename OtherDerived> friend
76    inline RotationMatrixType operator*(const EigenBase<OtherDerived>& l, const Derived& r)
77    { return l.derived() * r.toRotationMatrix(); }
78
79    /** \returns the concatenation of a scaling \a l with the rotation \a r */
80    friend inline Transform<Scalar,Dim,Affine> operator*(const DiagonalMatrix<Scalar,Dim>& l, const Derived& r)
81    {
82      Transform<Scalar,Dim,Affine> res(r);
83      res.linear().applyOnTheLeft(l);
84      return res;
85    }
86
87    /** \returns the concatenation of the rotation \c *this with a transformation \a t */
88    template<int Mode, int Options>
89    inline Transform<Scalar,Dim,Mode> operator*(const Transform<Scalar,Dim,Mode,Options>& t) const
90    { return toRotationMatrix() * t; }
91
92    template<typename OtherVectorType>
93    inline VectorType _transformVector(const OtherVectorType& v) const
94    { return toRotationMatrix() * v; }
95};
96
97namespace internal {
98
99// implementation of the generic product rotation * matrix
100template<typename RotationDerived, typename MatrixType>
101struct rotation_base_generic_product_selector<RotationDerived,MatrixType,false>
102{
103  enum { Dim = RotationDerived::Dim };
104  typedef Matrix<typename RotationDerived::Scalar,Dim,Dim> ReturnType;
105  static inline ReturnType run(const RotationDerived& r, const MatrixType& m)
106  { return r.toRotationMatrix() * m; }
107};
108
109template<typename RotationDerived, typename Scalar, int Dim, int MaxDim>
110struct rotation_base_generic_product_selector< RotationDerived, DiagonalMatrix<Scalar,Dim,MaxDim>, false >
111{
112  typedef Transform<Scalar,Dim,Affine> ReturnType;
113  static inline ReturnType run(const RotationDerived& r, const DiagonalMatrix<Scalar,Dim,MaxDim>& m)
114  {
115    ReturnType res(r);
116    res.linear() *= m;
117    return res;
118  }
119};
120
121template<typename RotationDerived,typename OtherVectorType>
122struct rotation_base_generic_product_selector<RotationDerived,OtherVectorType,true>
123{
124  enum { Dim = RotationDerived::Dim };
125  typedef Matrix<typename RotationDerived::Scalar,Dim,1> ReturnType;
126  static EIGEN_STRONG_INLINE ReturnType run(const RotationDerived& r, const OtherVectorType& v)
127  {
128    return r._transformVector(v);
129  }
130};
131
132} // end namespace internal
133
134/** \geometry_module
135  *
136  * \brief Constructs a Dim x Dim rotation matrix from the rotation \a r
137  */
138template<typename _Scalar, int _Rows, int _Cols, int _Storage, int _MaxRows, int _MaxCols>
139template<typename OtherDerived>
140Matrix<_Scalar, _Rows, _Cols, _Storage, _MaxRows, _MaxCols>
141::Matrix(const RotationBase<OtherDerived,ColsAtCompileTime>& r)
142{
143  EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Matrix,int(OtherDerived::Dim),int(OtherDerived::Dim))
144  *this = r.toRotationMatrix();
145}
146
147/** \geometry_module
148  *
149  * \brief Set a Dim x Dim rotation matrix from the rotation \a r
150  */
151template<typename _Scalar, int _Rows, int _Cols, int _Storage, int _MaxRows, int _MaxCols>
152template<typename OtherDerived>
153Matrix<_Scalar, _Rows, _Cols, _Storage, _MaxRows, _MaxCols>&
154Matrix<_Scalar, _Rows, _Cols, _Storage, _MaxRows, _MaxCols>
155::operator=(const RotationBase<OtherDerived,ColsAtCompileTime>& r)
156{
157  EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Matrix,int(OtherDerived::Dim),int(OtherDerived::Dim))
158  return *this = r.toRotationMatrix();
159}
160
161namespace internal {
162
163/** \internal
164  *
165  * Helper function to return an arbitrary rotation object to a rotation matrix.
166  *
167  * \param Scalar the numeric type of the matrix coefficients
168  * \param Dim the dimension of the current space
169  *
170  * It returns a Dim x Dim fixed size matrix.
171  *
172  * Default specializations are provided for:
173  *   - any scalar type (2D),
174  *   - any matrix expression,
175  *   - any type based on RotationBase (e.g., Quaternion, AngleAxis, Rotation2D)
176  *
177  * Currently toRotationMatrix is only used by Transform.
178  *
179  * \sa class Transform, class Rotation2D, class Quaternion, class AngleAxis
180  */
181template<typename Scalar, int Dim>
182static inline Matrix<Scalar,2,2> toRotationMatrix(const Scalar& s)
183{
184  EIGEN_STATIC_ASSERT(Dim==2,YOU_MADE_A_PROGRAMMING_MISTAKE)
185  return Rotation2D<Scalar>(s).toRotationMatrix();
186}
187
188template<typename Scalar, int Dim, typename OtherDerived>
189static inline Matrix<Scalar,Dim,Dim> toRotationMatrix(const RotationBase<OtherDerived,Dim>& r)
190{
191  return r.toRotationMatrix();
192}
193
194template<typename Scalar, int Dim, typename OtherDerived>
195static inline const MatrixBase<OtherDerived>& toRotationMatrix(const MatrixBase<OtherDerived>& mat)
196{
197  EIGEN_STATIC_ASSERT(OtherDerived::RowsAtCompileTime==Dim && OtherDerived::ColsAtCompileTime==Dim,
198    YOU_MADE_A_PROGRAMMING_MISTAKE)
199  return mat;
200}
201
202} // end namespace internal
203
204} // end namespace Eigen
205
206#endif // EIGEN_ROTATIONBASE_H
207