1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2009-2010 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_HOMOGENEOUS_H
11 #define EIGEN_HOMOGENEOUS_H
12 
13 namespace Eigen {
14 
15 /** \geometry_module \ingroup Geometry_Module
16   *
17   * \class Homogeneous
18   *
19   * \brief Expression of one (or a set of) homogeneous vector(s)
20   *
21   * \param MatrixType the type of the object in which we are making homogeneous
22   *
23   * This class represents an expression of one (or a set of) homogeneous vector(s).
24   * It is the return type of MatrixBase::homogeneous() and most of the time
25   * this is the only way it is used.
26   *
27   * \sa MatrixBase::homogeneous()
28   */
29 
30 namespace internal {
31 
32 template<typename MatrixType,int Direction>
33 struct traits<Homogeneous<MatrixType,Direction> >
34  : traits<MatrixType>
35 {
36   typedef typename traits<MatrixType>::StorageKind StorageKind;
37   typedef typename nested<MatrixType>::type MatrixTypeNested;
38   typedef typename remove_reference<MatrixTypeNested>::type _MatrixTypeNested;
39   enum {
40     RowsPlusOne = (MatrixType::RowsAtCompileTime != Dynamic) ?
41                   int(MatrixType::RowsAtCompileTime) + 1 : Dynamic,
42     ColsPlusOne = (MatrixType::ColsAtCompileTime != Dynamic) ?
43                   int(MatrixType::ColsAtCompileTime) + 1 : Dynamic,
44     RowsAtCompileTime = Direction==Vertical  ?  RowsPlusOne : MatrixType::RowsAtCompileTime,
45     ColsAtCompileTime = Direction==Horizontal ? ColsPlusOne : MatrixType::ColsAtCompileTime,
46     MaxRowsAtCompileTime = RowsAtCompileTime,
47     MaxColsAtCompileTime = ColsAtCompileTime,
48     TmpFlags = _MatrixTypeNested::Flags & HereditaryBits,
49     Flags = ColsAtCompileTime==1 ? (TmpFlags & ~RowMajorBit)
50           : RowsAtCompileTime==1 ? (TmpFlags | RowMajorBit)
51           : TmpFlags,
52     CoeffReadCost = _MatrixTypeNested::CoeffReadCost
53   };
54 };
55 
56 template<typename MatrixType,typename Lhs> struct homogeneous_left_product_impl;
57 template<typename MatrixType,typename Rhs> struct homogeneous_right_product_impl;
58 
59 } // end namespace internal
60 
61 template<typename MatrixType,int _Direction> class Homogeneous
62   : internal::no_assignment_operator, public MatrixBase<Homogeneous<MatrixType,_Direction> >
63 {
64   public:
65 
66     enum { Direction = _Direction };
67 
68     typedef MatrixBase<Homogeneous> Base;
69     EIGEN_DENSE_PUBLIC_INTERFACE(Homogeneous)
70 
71     inline Homogeneous(const MatrixType& matrix)
72       : m_matrix(matrix)
73     {}
74 
75     inline Index rows() const { return m_matrix.rows() + (int(Direction)==Vertical   ? 1 : 0); }
76     inline Index cols() const { return m_matrix.cols() + (int(Direction)==Horizontal ? 1 : 0); }
77 
78     inline Scalar coeff(Index row, Index col) const
79     {
80       if(  (int(Direction)==Vertical   && row==m_matrix.rows())
81         || (int(Direction)==Horizontal && col==m_matrix.cols()))
82         return 1;
83       return m_matrix.coeff(row, col);
84     }
85 
86     template<typename Rhs>
87     inline const internal::homogeneous_right_product_impl<Homogeneous,Rhs>
88     operator* (const MatrixBase<Rhs>& rhs) const
89     {
90       eigen_assert(int(Direction)==Horizontal);
91       return internal::homogeneous_right_product_impl<Homogeneous,Rhs>(m_matrix,rhs.derived());
92     }
93 
94     template<typename Lhs> friend
95     inline const internal::homogeneous_left_product_impl<Homogeneous,Lhs>
96     operator* (const MatrixBase<Lhs>& lhs, const Homogeneous& rhs)
97     {
98       eigen_assert(int(Direction)==Vertical);
99       return internal::homogeneous_left_product_impl<Homogeneous,Lhs>(lhs.derived(),rhs.m_matrix);
100     }
101 
102     template<typename Scalar, int Dim, int Mode, int Options> friend
103     inline const internal::homogeneous_left_product_impl<Homogeneous,Transform<Scalar,Dim,Mode,Options> >
104     operator* (const Transform<Scalar,Dim,Mode,Options>& lhs, const Homogeneous& rhs)
105     {
106       eigen_assert(int(Direction)==Vertical);
107       return internal::homogeneous_left_product_impl<Homogeneous,Transform<Scalar,Dim,Mode,Options> >(lhs,rhs.m_matrix);
108     }
109 
110   protected:
111     typename MatrixType::Nested m_matrix;
112 };
113 
114 /** \geometry_module
115   *
116   * \return an expression of the equivalent homogeneous vector
117   *
118   * \only_for_vectors
119   *
120   * Example: \include MatrixBase_homogeneous.cpp
121   * Output: \verbinclude MatrixBase_homogeneous.out
122   *
123   * \sa class Homogeneous
124   */
125 template<typename Derived>
126 inline typename MatrixBase<Derived>::HomogeneousReturnType
127 MatrixBase<Derived>::homogeneous() const
128 {
129   EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
130   return derived();
131 }
132 
133 /** \geometry_module
134   *
135   * \returns a matrix expression of homogeneous column (or row) vectors
136   *
137   * Example: \include VectorwiseOp_homogeneous.cpp
138   * Output: \verbinclude VectorwiseOp_homogeneous.out
139   *
140   * \sa MatrixBase::homogeneous() */
141 template<typename ExpressionType, int Direction>
142 inline Homogeneous<ExpressionType,Direction>
143 VectorwiseOp<ExpressionType,Direction>::homogeneous() const
144 {
145   return _expression();
146 }
147 
148 /** \geometry_module
149   *
150   * \returns an expression of the homogeneous normalized vector of \c *this
151   *
152   * Example: \include MatrixBase_hnormalized.cpp
153   * Output: \verbinclude MatrixBase_hnormalized.out
154   *
155   * \sa VectorwiseOp::hnormalized() */
156 template<typename Derived>
157 inline const typename MatrixBase<Derived>::HNormalizedReturnType
158 MatrixBase<Derived>::hnormalized() const
159 {
160   EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
161   return ConstStartMinusOne(derived(),0,0,
162     ColsAtCompileTime==1?size()-1:1,
163     ColsAtCompileTime==1?1:size()-1) / coeff(size()-1);
164 }
165 
166 /** \geometry_module
167   *
168   * \returns an expression of the homogeneous normalized vector of \c *this
169   *
170   * Example: \include DirectionWise_hnormalized.cpp
171   * Output: \verbinclude DirectionWise_hnormalized.out
172   *
173   * \sa MatrixBase::hnormalized() */
174 template<typename ExpressionType, int Direction>
175 inline const typename VectorwiseOp<ExpressionType,Direction>::HNormalizedReturnType
176 VectorwiseOp<ExpressionType,Direction>::hnormalized() const
177 {
178   return HNormalized_Block(_expression(),0,0,
179       Direction==Vertical   ? _expression().rows()-1 : _expression().rows(),
180       Direction==Horizontal ? _expression().cols()-1 : _expression().cols()).cwiseQuotient(
181       Replicate<HNormalized_Factors,
182                 Direction==Vertical   ? HNormalized_SizeMinusOne : 1,
183                 Direction==Horizontal ? HNormalized_SizeMinusOne : 1>
184         (HNormalized_Factors(_expression(),
185           Direction==Vertical    ? _expression().rows()-1:0,
186           Direction==Horizontal  ? _expression().cols()-1:0,
187           Direction==Vertical    ? 1 : _expression().rows(),
188           Direction==Horizontal  ? 1 : _expression().cols()),
189          Direction==Vertical   ? _expression().rows()-1 : 1,
190          Direction==Horizontal ? _expression().cols()-1 : 1));
191 }
192 
193 namespace internal {
194 
195 template<typename MatrixOrTransformType>
196 struct take_matrix_for_product
197 {
198   typedef MatrixOrTransformType type;
199   static const type& run(const type &x) { return x; }
200 };
201 
202 template<typename Scalar, int Dim, int Mode,int Options>
203 struct take_matrix_for_product<Transform<Scalar, Dim, Mode, Options> >
204 {
205   typedef Transform<Scalar, Dim, Mode, Options> TransformType;
206   typedef typename internal::add_const<typename TransformType::ConstAffinePart>::type type;
207   static type run (const TransformType& x) { return x.affine(); }
208 };
209 
210 template<typename Scalar, int Dim, int Options>
211 struct take_matrix_for_product<Transform<Scalar, Dim, Projective, Options> >
212 {
213   typedef Transform<Scalar, Dim, Projective, Options> TransformType;
214   typedef typename TransformType::MatrixType type;
215   static const type& run (const TransformType& x) { return x.matrix(); }
216 };
217 
218 template<typename MatrixType,typename Lhs>
219 struct traits<homogeneous_left_product_impl<Homogeneous<MatrixType,Vertical>,Lhs> >
220 {
221   typedef typename take_matrix_for_product<Lhs>::type LhsMatrixType;
222   typedef typename remove_all<MatrixType>::type MatrixTypeCleaned;
223   typedef typename remove_all<LhsMatrixType>::type LhsMatrixTypeCleaned;
224   typedef typename make_proper_matrix_type<
225                  typename traits<MatrixTypeCleaned>::Scalar,
226                  LhsMatrixTypeCleaned::RowsAtCompileTime,
227                  MatrixTypeCleaned::ColsAtCompileTime,
228                  MatrixTypeCleaned::PlainObject::Options,
229                  LhsMatrixTypeCleaned::MaxRowsAtCompileTime,
230                  MatrixTypeCleaned::MaxColsAtCompileTime>::type ReturnType;
231 };
232 
233 template<typename MatrixType,typename Lhs>
234 struct homogeneous_left_product_impl<Homogeneous<MatrixType,Vertical>,Lhs>
235   : public ReturnByValue<homogeneous_left_product_impl<Homogeneous<MatrixType,Vertical>,Lhs> >
236 {
237   typedef typename traits<homogeneous_left_product_impl>::LhsMatrixType LhsMatrixType;
238   typedef typename remove_all<LhsMatrixType>::type LhsMatrixTypeCleaned;
239   typedef typename remove_all<typename LhsMatrixTypeCleaned::Nested>::type LhsMatrixTypeNested;
240   typedef typename MatrixType::Index Index;
241   homogeneous_left_product_impl(const Lhs& lhs, const MatrixType& rhs)
242     : m_lhs(take_matrix_for_product<Lhs>::run(lhs)),
243       m_rhs(rhs)
244   {}
245 
246   inline Index rows() const { return m_lhs.rows(); }
247   inline Index cols() const { return m_rhs.cols(); }
248 
249   template<typename Dest> void evalTo(Dest& dst) const
250   {
251     // FIXME investigate how to allow lazy evaluation of this product when possible
252     dst = Block<const LhsMatrixTypeNested,
253               LhsMatrixTypeNested::RowsAtCompileTime,
254               LhsMatrixTypeNested::ColsAtCompileTime==Dynamic?Dynamic:LhsMatrixTypeNested::ColsAtCompileTime-1>
255             (m_lhs,0,0,m_lhs.rows(),m_lhs.cols()-1) * m_rhs;
256     dst += m_lhs.col(m_lhs.cols()-1).rowwise()
257             .template replicate<MatrixType::ColsAtCompileTime>(m_rhs.cols());
258   }
259 
260   typename LhsMatrixTypeCleaned::Nested m_lhs;
261   typename MatrixType::Nested m_rhs;
262 };
263 
264 template<typename MatrixType,typename Rhs>
265 struct traits<homogeneous_right_product_impl<Homogeneous<MatrixType,Horizontal>,Rhs> >
266 {
267   typedef typename make_proper_matrix_type<typename traits<MatrixType>::Scalar,
268                  MatrixType::RowsAtCompileTime,
269                  Rhs::ColsAtCompileTime,
270                  MatrixType::PlainObject::Options,
271                  MatrixType::MaxRowsAtCompileTime,
272                  Rhs::MaxColsAtCompileTime>::type ReturnType;
273 };
274 
275 template<typename MatrixType,typename Rhs>
276 struct homogeneous_right_product_impl<Homogeneous<MatrixType,Horizontal>,Rhs>
277   : public ReturnByValue<homogeneous_right_product_impl<Homogeneous<MatrixType,Horizontal>,Rhs> >
278 {
279   typedef typename remove_all<typename Rhs::Nested>::type RhsNested;
280   typedef typename MatrixType::Index Index;
281   homogeneous_right_product_impl(const MatrixType& lhs, const Rhs& rhs)
282     : m_lhs(lhs), m_rhs(rhs)
283   {}
284 
285   inline Index rows() const { return m_lhs.rows(); }
286   inline Index cols() const { return m_rhs.cols(); }
287 
288   template<typename Dest> void evalTo(Dest& dst) const
289   {
290     // FIXME investigate how to allow lazy evaluation of this product when possible
291     dst = m_lhs * Block<const RhsNested,
292                         RhsNested::RowsAtCompileTime==Dynamic?Dynamic:RhsNested::RowsAtCompileTime-1,
293                         RhsNested::ColsAtCompileTime>
294             (m_rhs,0,0,m_rhs.rows()-1,m_rhs.cols());
295     dst += m_rhs.row(m_rhs.rows()-1).colwise()
296             .template replicate<MatrixType::RowsAtCompileTime>(m_lhs.rows());
297   }
298 
299   typename MatrixType::Nested m_lhs;
300   typename Rhs::Nested m_rhs;
301 };
302 
303 } // end namespace internal
304 
305 } // end namespace Eigen
306 
307 #endif // EIGEN_HOMOGENEOUS_H
308