Homogeneous.h

00001 // This file is part of Eigen, a lightweight C++ template library
00002 // for linear algebra.
00003 //
00004 // Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
00005 //
00006 // This Source Code Form is subject to the terms of the Mozilla
00007 // Public License v. 2.0. If a copy of the MPL was not distributed
00008 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
00009 
00010 #ifndef EIGEN_HOMOGENEOUS_H
00011 #define EIGEN_HOMOGENEOUS_H
00012 
00013 namespace Eigen { 
00014 
00015 /** \geometry_module \ingroup Geometry_Module
00016   *
00017   * \class Homogeneous
00018   *
00019   * \brief Expression of one (or a set of) homogeneous vector(s)
00020   *
00021   * \param MatrixType the type of the object in which we are making homogeneous
00022   *
00023   * This class represents an expression of one (or a set of) homogeneous vector(s).
00024   * It is the return type of MatrixBase::homogeneous() and most of the time
00025   * this is the only way it is used.
00026   *
00027   * \sa MatrixBase::homogeneous()
00028   */
00029 
00030 namespace internal {
00031 
00032 template<typename MatrixType,int Direction>
00033 struct traits<Homogeneous<MatrixType,Direction> >
00034  : traits<MatrixType>
00035 {
00036   typedef typename traits<MatrixType>::StorageKind StorageKind;
00037   typedef typename nested<MatrixType>::type MatrixTypeNested;
00038   typedef typename remove_reference<MatrixTypeNested>::type _MatrixTypeNested;
00039   enum {
00040     RowsPlusOne = (MatrixType::RowsAtCompileTime != Dynamic) ?
00041                   int(MatrixType::RowsAtCompileTime) + 1 : Dynamic,
00042     ColsPlusOne = (MatrixType::ColsAtCompileTime != Dynamic) ?
00043                   int(MatrixType::ColsAtCompileTime) + 1 : Dynamic,
00044     RowsAtCompileTime = Direction==Vertical  ?  RowsPlusOne : MatrixType::RowsAtCompileTime,
00045     ColsAtCompileTime = Direction==Horizontal ? ColsPlusOne : MatrixType::ColsAtCompileTime,
00046     MaxRowsAtCompileTime = RowsAtCompileTime,
00047     MaxColsAtCompileTime = ColsAtCompileTime,
00048     TmpFlags = _MatrixTypeNested::Flags & HereditaryBits,
00049     Flags = ColsAtCompileTime==1 ? (TmpFlags & ~RowMajorBit)
00050           : RowsAtCompileTime==1 ? (TmpFlags | RowMajorBit)
00051           : TmpFlags,
00052     CoeffReadCost = _MatrixTypeNested::CoeffReadCost
00053   };
00054 };
00055 
00056 template<typename MatrixType,typename Lhs> struct homogeneous_left_product_impl;
00057 template<typename MatrixType,typename Rhs> struct homogeneous_right_product_impl;
00058 
00059 } // end namespace internal
00060 
00061 template<typename MatrixType,int _Direction> class Homogeneous 
00062   : internal::no_assignment_operator, public MatrixBase<Homogeneous<MatrixType,_Direction> >
00063 {
00064   public:
00065 
00066     enum { Direction = _Direction };
00067 
00068     typedef MatrixBase<Homogeneous> Base;
00069     EIGEN_DENSE_PUBLIC_INTERFACE(Homogeneous )
00070 
00071     inline Homogeneous (const MatrixType& matrix)
00072       : m_matrix(matrix)
00073     {}
00074 
00075     inline Index rows() const { return m_matrix.rows() + (int(Direction)==Vertical   ? 1 : 0); }
00076     inline Index cols() const { return m_matrix.cols() + (int(Direction)==Horizontal ? 1 : 0); }
00077 
00078     inline Scalar coeff(Index row, Index col) const
00079     {
00080       if(  (int(Direction)==Vertical   && row==m_matrix.rows())
00081         || (int(Direction)==Horizontal && col==m_matrix.cols()))
00082         return Scalar(1);
00083       return m_matrix.coeff(row, col);
00084     }
00085 
00086     template<typename Rhs>
00087     inline const internal::homogeneous_right_product_impl<Homogeneous,Rhs>
00088     operator* (const MatrixBase<Rhs>& rhs) const
00089     {
00090       eigen_assert(int(Direction)==Horizontal);
00091       return internal::homogeneous_right_product_impl<Homogeneous,Rhs>(m_matrix,rhs.derived());
00092     }
00093 
00094     template<typename Lhs> friend
00095     inline const internal::homogeneous_left_product_impl<Homogeneous,Lhs>
00096     operator* (const MatrixBase<Lhs>& lhs, const Homogeneous & rhs)
00097     {
00098       eigen_assert(int(Direction)==Vertical);
00099       return internal::homogeneous_left_product_impl<Homogeneous,Lhs>(lhs.derived(),rhs.m_matrix);
00100     }
00101 
00102     template<typename Scalar, int Dim, int Mode, int Options> friend
00103     inline const internal::homogeneous_left_product_impl<Homogeneous,Transform<Scalar,Dim,Mode,Options> >
00104     operator* (const Transform<Scalar,Dim,Mode,Options> & lhs, const Homogeneous & rhs)
00105     {
00106       eigen_assert(int(Direction)==Vertical);
00107       return internal::homogeneous_left_product_impl<Homogeneous,Transform<Scalar,Dim,Mode,Options> >(lhs,rhs.m_matrix);
00108     }
00109 
00110   protected:
00111     typename MatrixType::Nested m_matrix;
00112 };
00113 
00114 /** \geometry_module
00115   *
00116   * \return an expression of the equivalent homogeneous vector
00117   *
00118   * \only_for_vectors
00119   *
00120   * Example: \include MatrixBase_homogeneous.cpp
00121   * Output: \verbinclude MatrixBase_homogeneous.out
00122   *
00123   * \sa class Homogeneous
00124   */
00125 template<typename Derived>
00126 inline typename MatrixBase<Derived>::HomogeneousReturnType 
00127 MatrixBase<Derived>::homogeneous () const
00128 {
00129   EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
00130   return derived();
00131 }
00132 
00133 /** \geometry_module
00134   *
00135   * \returns a matrix expression of homogeneous column (or row) vectors
00136   *
00137   * Example: \include VectorwiseOp_homogeneous.cpp
00138   * Output: \verbinclude VectorwiseOp_homogeneous.out
00139   *
00140   * \sa MatrixBase::homogeneous() */
00141 template<typename ExpressionType, int Direction>
00142 inline Homogeneous<ExpressionType,Direction> 
00143 VectorwiseOp<ExpressionType,Direction>::homogeneous () const
00144 {
00145   return _expression();
00146 }
00147 
00148 /** \geometry_module
00149   *
00150   * \returns an expression of the homogeneous normalized vector of \c *this
00151   *
00152   * Example: \include MatrixBase_hnormalized.cpp
00153   * Output: \verbinclude MatrixBase_hnormalized.out
00154   *
00155   * \sa VectorwiseOp::hnormalized() */
00156 template<typename Derived>
00157 inline const typename MatrixBase<Derived>::HNormalizedReturnType
00158 MatrixBase<Derived>::hnormalized () const
00159 {
00160   EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
00161   return ConstStartMinusOne(derived(),0,0,
00162     ColsAtCompileTime==1?size()-1:1,
00163     ColsAtCompileTime==1?1:size()-1) / coeff(size()-1);
00164 }
00165 
00166 /** \geometry_module
00167   *
00168   * \returns an expression of the homogeneous normalized vector of \c *this
00169   *
00170   * Example: \include DirectionWise_hnormalized.cpp
00171   * Output: \verbinclude DirectionWise_hnormalized.out
00172   *
00173   * \sa MatrixBase::hnormalized() */
00174 template<typename ExpressionType, int Direction>
00175 inline const typename VectorwiseOp<ExpressionType,Direction>::HNormalizedReturnType
00176 VectorwiseOp<ExpressionType,Direction>::hnormalized () const
00177 {
00178   return HNormalized_Block(_expression(),0,0,
00179       Direction==Vertical   ? _expression().rows()-1 : _expression().rows(),
00180       Direction==Horizontal ? _expression().cols()-1 : _expression().cols()).cwiseQuotient(
00181       Replicate<HNormalized_Factors,
00182                 Direction==Vertical   ? HNormalized_SizeMinusOne : 1,
00183                 Direction==Horizontal ? HNormalized_SizeMinusOne : 1>
00184         (HNormalized_Factors(_expression(),
00185           Direction==Vertical    ? _expression().rows()-1:0,
00186           Direction==Horizontal  ? _expression().cols()-1:0,
00187           Direction==Vertical    ? 1 : _expression().rows(),
00188           Direction==Horizontal  ? 1 : _expression().cols()),
00189          Direction==Vertical   ? _expression().rows()-1 : 1,
00190          Direction==Horizontal ? _expression().cols()-1 : 1));
00191 }
00192 
00193 namespace internal {
00194 
00195 template<typename MatrixOrTransformType>
00196 struct take_matrix_for_product
00197 {
00198   typedef MatrixOrTransformType type;
00199   static const type& run(const type &x) { return x; }
00200 };
00201 
00202 template<typename Scalar, int Dim, int Mode,int Options>
00203 struct take_matrix_for_product<Transform<Scalar, Dim, Mode, Options> >
00204 {
00205   typedef Transform<Scalar, Dim, Mode, Options> TransformType;
00206   typedef typename internal::add_const<typename TransformType::ConstAffinePart>::type type;
00207   static type run (const TransformType& x) { return x.affine(); }
00208 };
00209 
00210 template<typename Scalar, int Dim, int Options>
00211 struct take_matrix_for_product<Transform<Scalar, Dim, Projective, Options> >
00212 {
00213   typedef Transform<Scalar, Dim, Projective, Options> TransformType;
00214   typedef typename TransformType::MatrixType type;
00215   static const type& run (const TransformType& x) { return x.matrix(); }
00216 };
00217 
00218 template<typename MatrixType,typename Lhs>
00219 struct traits<homogeneous_left_product_impl<Homogeneous<MatrixType,Vertical>,Lhs> >
00220 {
00221   typedef typename take_matrix_for_product<Lhs>::type LhsMatrixType;
00222   typedef typename remove_all<MatrixType>::type MatrixTypeCleaned;
00223   typedef typename remove_all<LhsMatrixType>::type LhsMatrixTypeCleaned;
00224   typedef typename make_proper_matrix_type<
00225                  typename traits<MatrixTypeCleaned>::Scalar,
00226                  LhsMatrixTypeCleaned::RowsAtCompileTime,
00227                  MatrixTypeCleaned::ColsAtCompileTime,
00228                  MatrixTypeCleaned::PlainObject::Options,
00229                  LhsMatrixTypeCleaned::MaxRowsAtCompileTime,
00230                  MatrixTypeCleaned::MaxColsAtCompileTime>::type ReturnType;
00231 };
00232 
00233 template<typename MatrixType,typename Lhs>
00234 struct homogeneous_left_product_impl<Homogeneous<MatrixType,Vertical>,Lhs>
00235   : public ReturnByValue<homogeneous_left_product_impl<Homogeneous<MatrixType,Vertical>,Lhs> >
00236 {
00237   typedef typename traits<homogeneous_left_product_impl>::LhsMatrixType LhsMatrixType;
00238   typedef typename remove_all<LhsMatrixType>::type LhsMatrixTypeCleaned;
00239   typedef typename remove_all<typename LhsMatrixTypeCleaned::Nested>::type LhsMatrixTypeNested;
00240   typedef typename MatrixType::Index Index;
00241   homogeneous_left_product_impl(const Lhs& lhs, const MatrixType& rhs)
00242     : m_lhs(take_matrix_for_product<Lhs>::run(lhs)),
00243       m_rhs(rhs)
00244   {}
00245 
00246   inline Index rows() const { return m_lhs.rows(); }
00247   inline Index cols() const { return m_rhs.cols(); }
00248 
00249   template<typename Dest> void evalTo(Dest& dst) const
00250   {
00251     // FIXME investigate how to allow lazy evaluation of this product when possible
00252     dst = Block<const LhsMatrixTypeNested,
00253               LhsMatrixTypeNested::RowsAtCompileTime,
00254               LhsMatrixTypeNested::ColsAtCompileTime==Dynamic?Dynamic:LhsMatrixTypeNested::ColsAtCompileTime-1>
00255             (m_lhs,0,0,m_lhs.rows(),m_lhs.cols()-1) * m_rhs;
00256     dst += m_lhs.col(m_lhs.cols()-1).rowwise()
00257             .template replicate<MatrixType::ColsAtCompileTime>(m_rhs.cols());
00258   }
00259 
00260   typename LhsMatrixTypeCleaned::Nested m_lhs;
00261   typename MatrixType::Nested m_rhs;
00262 };
00263 
00264 template<typename MatrixType,typename Rhs>
00265 struct traits<homogeneous_right_product_impl<Homogeneous<MatrixType,Horizontal>,Rhs> >
00266 {
00267   typedef typename make_proper_matrix_type<typename traits<MatrixType>::Scalar,
00268                  MatrixType::RowsAtCompileTime,
00269                  Rhs::ColsAtCompileTime,
00270                  MatrixType::PlainObject::Options,
00271                  MatrixType::MaxRowsAtCompileTime,
00272                  Rhs::MaxColsAtCompileTime>::type ReturnType;
00273 };
00274 
00275 template<typename MatrixType,typename Rhs>
00276 struct homogeneous_right_product_impl<Homogeneous<MatrixType,Horizontal>,Rhs>
00277   : public ReturnByValue<homogeneous_right_product_impl<Homogeneous<MatrixType,Horizontal>,Rhs> >
00278 {
00279   typedef typename remove_all<typename Rhs::Nested>::type RhsNested;
00280   typedef typename MatrixType::Index Index;
00281   homogeneous_right_product_impl(const MatrixType& lhs, const Rhs& rhs)
00282     : m_lhs(lhs), m_rhs(rhs)
00283   {}
00284 
00285   inline Index rows() const { return m_lhs.rows(); }
00286   inline Index cols() const { return m_rhs.cols(); }
00287 
00288   template<typename Dest> void evalTo(Dest& dst) const
00289   {
00290     // FIXME investigate how to allow lazy evaluation of this product when possible
00291     dst = m_lhs * Block<const RhsNested,
00292                         RhsNested::RowsAtCompileTime==Dynamic?Dynamic:RhsNested::RowsAtCompileTime-1,
00293                         RhsNested::ColsAtCompileTime>
00294             (m_rhs,0,0,m_rhs.rows()-1,m_rhs.cols());
00295     dst += m_rhs.row(m_rhs.rows()-1).colwise()
00296             .template replicate<MatrixType::RowsAtCompileTime>(m_lhs.rows());
00297   }
00298 
00299   typename MatrixType::Nested m_lhs;
00300   typename Rhs::Nested m_rhs;
00301 };
00302 
00303 } // end namespace internal
00304 
00305 } // end namespace Eigen
00306 
00307 #endif // EIGEN_HOMOGENEOUS_H