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 * \tparam Derived is the derived type, i.e., a rotation type
26 * \tparam _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 EIGEN_DEVICE_FUNC inline const Derived& derived() const { return *static_cast<const Derived*>(this); }
42 EIGEN_DEVICE_FUNC inline Derived& derived() { return *static_cast<Derived*>(this); }
43
44 /** \returns an equivalent rotation matrix */
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 */
50 EIGEN_DEVICE_FUNC inline RotationMatrixType matrix() const { return derived().toRotationMatrix(); }
51
52 /** \returns the inverse rotation */
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>
93 EIGEN_DEVICE_FUNC 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 EIGEN_DEVICE_FUNC 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 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
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 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 */
138template<typename _Scalar, int _Rows, int _Cols, int _Storage, int _MaxRows, int _MaxCols>
139template<typename OtherDerived>
140EIGEN_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 */
151template<typename _Scalar, int _Rows, int _Cols, int _Storage, int _MaxRows, int _MaxCols>
152template<typename OtherDerived>
153EIGEN_DEVICE_FUNC Matrix<_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 * \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 */
181template<typename Scalar, int Dim>
182EIGEN_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
188template<typename Scalar, int Dim, typename OtherDerived>
189EIGEN_DEVICE_FUNC static 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>
195EIGEN_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