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 
13 namespace Eigen {
14 
15 // forward declaration
16 namespace internal {
17 template<typename RotationDerived, typename MatrixType, bool IsVector=MatrixType::IsVectorAtCompileTime>
18 struct rotation_base_generic_product_selector;
19 }
20 
21 /** \class RotationBase
22   *
23   * \brief Common base class for compact rotation representations
24   *
25   * \tparam Derived is the derived type, i.e., a rotation type
26   * \tparam _Dim the dimension of the space
27   */
28 template<typename Derived, int _Dim>
29 class 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:
derived()41     EIGEN_DEVICE_FUNC inline const Derived& derived() const { return *static_cast<const Derived*>(this); }
derived()42     EIGEN_DEVICE_FUNC inline Derived& derived() { return *static_cast<Derived*>(this); }
43 
44     /** \returns an equivalent rotation matrix */
toRotationMatrix()45     EIGEN_DEVICE_FUNC 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       */
matrix()50     EIGEN_DEVICE_FUNC inline RotationMatrixType matrix() const { return derived().toRotationMatrix(); }
51 
52     /** \returns the inverse rotation */
inverse()53     EIGEN_DEVICE_FUNC inline Derived inverse() const { return derived().inverse(); }
54 
55     /** \returns the concatenation of the rotation \c *this with a translation \a t */
56     EIGEN_DEVICE_FUNC 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     EIGEN_DEVICE_FUNC 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_DEVICE_FUNC 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     EIGEN_DEVICE_FUNC 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     EIGEN_DEVICE_FUNC 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     EIGEN_DEVICE_FUNC inline Transform<Scalar,Dim,Mode> operator*(const Transform<Scalar,Dim,Mode,Options>& t) const
90     { return toRotationMatrix() * t; }
91 
92     template<typename OtherVectorType>
_transformVector(const OtherVectorType & v)93     EIGEN_DEVICE_FUNC inline VectorType _transformVector(const OtherVectorType& v) const
94     { return toRotationMatrix() * v; }
95 };
96 
97 namespace internal {
98 
99 // implementation of the generic product rotation * matrix
100 template<typename RotationDerived, typename MatrixType>
101 struct rotation_base_generic_product_selector<RotationDerived,MatrixType,false>
102 {
103   enum { Dim = RotationDerived::Dim };
104   typedef Matrix<typename RotationDerived::Scalar,Dim,Dim> ReturnType;
105   EIGEN_DEVICE_FUNC static inline ReturnType run(const RotationDerived& r, const MatrixType& m)
106   { return r.toRotationMatrix() * m; }
107 };
108 
109 template<typename RotationDerived, typename Scalar, int Dim, int MaxDim>
110 struct rotation_base_generic_product_selector< RotationDerived, DiagonalMatrix<Scalar,Dim,MaxDim>, false >
111 {
112   typedef Transform<Scalar,Dim,Affine> ReturnType;
113   EIGEN_DEVICE_FUNC 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 
121 template<typename RotationDerived,typename OtherVectorType>
122 struct rotation_base_generic_product_selector<RotationDerived,OtherVectorType,true>
123 {
124   enum { Dim = RotationDerived::Dim };
125   typedef Matrix<typename RotationDerived::Scalar,Dim,1> ReturnType;
126   EIGEN_DEVICE_FUNC 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   */
138 template<typename _Scalar, int _Rows, int _Cols, int _Storage, int _MaxRows, int _MaxCols>
139 template<typename OtherDerived>
140 EIGEN_DEVICE_FUNC Matrix<_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   */
151 template<typename _Scalar, int _Rows, int _Cols, int _Storage, int _MaxRows, int _MaxCols>
152 template<typename OtherDerived>
153 EIGEN_DEVICE_FUNC Matrix<_Scalar, _Rows, _Cols, _Storage, _MaxRows, _MaxCols>&
154 Matrix<_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 
161 namespace internal {
162 
163 /** \internal
164   *
165   * Helper function to return an arbitrary rotation object to a rotation matrix.
166   *
167   * \tparam Scalar the numeric type of the matrix coefficients
168   * \tparam 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   */
181 template<typename Scalar, int Dim>
182 EIGEN_DEVICE_FUNC static 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 
188 template<typename Scalar, int Dim, typename OtherDerived>
189 EIGEN_DEVICE_FUNC static inline Matrix<Scalar,Dim,Dim> toRotationMatrix(const RotationBase<OtherDerived,Dim>& r)
190 {
191   return r.toRotationMatrix();
192 }
193 
194 template<typename Scalar, int Dim, typename OtherDerived>
195 EIGEN_DEVICE_FUNC static 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