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- // This file is part of Eigen, a lightweight C++ template library
- // for linear algebra.
- //
- // Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
- //
- // This Source Code Form is subject to the terms of the Mozilla
- // Public License v. 2.0. If a copy of the MPL was not distributed
- // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
- #ifndef EIGEN_HOMOGENEOUS_H
- #define EIGEN_HOMOGENEOUS_H
- namespace Eigen {
- /** \geometry_module \ingroup Geometry_Module
- *
- * \class Homogeneous
- *
- * \brief Expression of one (or a set of) homogeneous vector(s)
- *
- * \param MatrixType the type of the object in which we are making homogeneous
- *
- * This class represents an expression of one (or a set of) homogeneous vector(s).
- * It is the return type of MatrixBase::homogeneous() and most of the time
- * this is the only way it is used.
- *
- * \sa MatrixBase::homogeneous()
- */
- namespace internal {
- template<typename MatrixType,int Direction>
- struct traits<Homogeneous<MatrixType,Direction> >
- : traits<MatrixType>
- {
- typedef typename traits<MatrixType>::StorageKind StorageKind;
- typedef typename ref_selector<MatrixType>::type MatrixTypeNested;
- typedef typename remove_reference<MatrixTypeNested>::type _MatrixTypeNested;
- enum {
- RowsPlusOne = (MatrixType::RowsAtCompileTime != Dynamic) ?
- int(MatrixType::RowsAtCompileTime) + 1 : Dynamic,
- ColsPlusOne = (MatrixType::ColsAtCompileTime != Dynamic) ?
- int(MatrixType::ColsAtCompileTime) + 1 : Dynamic,
- RowsAtCompileTime = Direction==Vertical ? RowsPlusOne : MatrixType::RowsAtCompileTime,
- ColsAtCompileTime = Direction==Horizontal ? ColsPlusOne : MatrixType::ColsAtCompileTime,
- MaxRowsAtCompileTime = RowsAtCompileTime,
- MaxColsAtCompileTime = ColsAtCompileTime,
- TmpFlags = _MatrixTypeNested::Flags & HereditaryBits,
- Flags = ColsAtCompileTime==1 ? (TmpFlags & ~RowMajorBit)
- : RowsAtCompileTime==1 ? (TmpFlags | RowMajorBit)
- : TmpFlags
- };
- };
- template<typename MatrixType,typename Lhs> struct homogeneous_left_product_impl;
- template<typename MatrixType,typename Rhs> struct homogeneous_right_product_impl;
- } // end namespace internal
- template<typename MatrixType,int _Direction> class Homogeneous
- : public MatrixBase<Homogeneous<MatrixType,_Direction> >, internal::no_assignment_operator
- {
- public:
- typedef MatrixType NestedExpression;
- enum { Direction = _Direction };
- typedef MatrixBase<Homogeneous> Base;
- EIGEN_DENSE_PUBLIC_INTERFACE(Homogeneous)
- EIGEN_DEVICE_FUNC explicit inline Homogeneous(const MatrixType& matrix)
- : m_matrix(matrix)
- {}
- EIGEN_DEVICE_FUNC inline Index rows() const { return m_matrix.rows() + (int(Direction)==Vertical ? 1 : 0); }
- EIGEN_DEVICE_FUNC inline Index cols() const { return m_matrix.cols() + (int(Direction)==Horizontal ? 1 : 0); }
-
- EIGEN_DEVICE_FUNC const NestedExpression& nestedExpression() const { return m_matrix; }
- template<typename Rhs>
- EIGEN_DEVICE_FUNC inline const Product<Homogeneous,Rhs>
- operator* (const MatrixBase<Rhs>& rhs) const
- {
- eigen_assert(int(Direction)==Horizontal);
- return Product<Homogeneous,Rhs>(*this,rhs.derived());
- }
- template<typename Lhs> friend
- EIGEN_DEVICE_FUNC inline const Product<Lhs,Homogeneous>
- operator* (const MatrixBase<Lhs>& lhs, const Homogeneous& rhs)
- {
- eigen_assert(int(Direction)==Vertical);
- return Product<Lhs,Homogeneous>(lhs.derived(),rhs);
- }
- template<typename Scalar, int Dim, int Mode, int Options> friend
- EIGEN_DEVICE_FUNC inline const Product<Transform<Scalar,Dim,Mode,Options>, Homogeneous >
- operator* (const Transform<Scalar,Dim,Mode,Options>& lhs, const Homogeneous& rhs)
- {
- eigen_assert(int(Direction)==Vertical);
- return Product<Transform<Scalar,Dim,Mode,Options>, Homogeneous>(lhs,rhs);
- }
- template<typename Func>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename internal::result_of<Func(Scalar,Scalar)>::type
- redux(const Func& func) const
- {
- return func(m_matrix.redux(func), Scalar(1));
- }
- protected:
- typename MatrixType::Nested m_matrix;
- };
- /** \geometry_module \ingroup Geometry_Module
- *
- * \returns a vector expression that is one longer than the vector argument, with the value 1 symbolically appended as the last coefficient.
- *
- * This can be used to convert affine coordinates to homogeneous coordinates.
- *
- * \only_for_vectors
- *
- * Example: \include MatrixBase_homogeneous.cpp
- * Output: \verbinclude MatrixBase_homogeneous.out
- *
- * \sa VectorwiseOp::homogeneous(), class Homogeneous
- */
- template<typename Derived>
- EIGEN_DEVICE_FUNC inline typename MatrixBase<Derived>::HomogeneousReturnType
- MatrixBase<Derived>::homogeneous() const
- {
- EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
- return HomogeneousReturnType(derived());
- }
- /** \geometry_module \ingroup Geometry_Module
- *
- * \returns an expression where the value 1 is symbolically appended as the final coefficient to each column (or row) of the matrix.
- *
- * This can be used to convert affine coordinates to homogeneous coordinates.
- *
- * Example: \include VectorwiseOp_homogeneous.cpp
- * Output: \verbinclude VectorwiseOp_homogeneous.out
- *
- * \sa MatrixBase::homogeneous(), class Homogeneous */
- template<typename ExpressionType, int Direction>
- EIGEN_DEVICE_FUNC inline Homogeneous<ExpressionType,Direction>
- VectorwiseOp<ExpressionType,Direction>::homogeneous() const
- {
- return HomogeneousReturnType(_expression());
- }
- /** \geometry_module \ingroup Geometry_Module
- *
- * \brief homogeneous normalization
- *
- * \returns a vector expression of the N-1 first coefficients of \c *this divided by that last coefficient.
- *
- * This can be used to convert homogeneous coordinates to affine coordinates.
- *
- * It is essentially a shortcut for:
- * \code
- this->head(this->size()-1)/this->coeff(this->size()-1);
- \endcode
- *
- * Example: \include MatrixBase_hnormalized.cpp
- * Output: \verbinclude MatrixBase_hnormalized.out
- *
- * \sa VectorwiseOp::hnormalized() */
- template<typename Derived>
- EIGEN_DEVICE_FUNC inline const typename MatrixBase<Derived>::HNormalizedReturnType
- MatrixBase<Derived>::hnormalized() const
- {
- EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
- return ConstStartMinusOne(derived(),0,0,
- ColsAtCompileTime==1?size()-1:1,
- ColsAtCompileTime==1?1:size()-1) / coeff(size()-1);
- }
- /** \geometry_module \ingroup Geometry_Module
- *
- * \brief column or row-wise homogeneous normalization
- *
- * \returns an expression of the first N-1 coefficients of each column (or row) of \c *this divided by the last coefficient of each column (or row).
- *
- * This can be used to convert homogeneous coordinates to affine coordinates.
- *
- * It is conceptually equivalent to calling MatrixBase::hnormalized() to each column (or row) of \c *this.
- *
- * Example: \include DirectionWise_hnormalized.cpp
- * Output: \verbinclude DirectionWise_hnormalized.out
- *
- * \sa MatrixBase::hnormalized() */
- template<typename ExpressionType, int Direction>
- EIGEN_DEVICE_FUNC inline const typename VectorwiseOp<ExpressionType,Direction>::HNormalizedReturnType
- VectorwiseOp<ExpressionType,Direction>::hnormalized() const
- {
- return HNormalized_Block(_expression(),0,0,
- Direction==Vertical ? _expression().rows()-1 : _expression().rows(),
- Direction==Horizontal ? _expression().cols()-1 : _expression().cols()).cwiseQuotient(
- Replicate<HNormalized_Factors,
- Direction==Vertical ? HNormalized_SizeMinusOne : 1,
- Direction==Horizontal ? HNormalized_SizeMinusOne : 1>
- (HNormalized_Factors(_expression(),
- Direction==Vertical ? _expression().rows()-1:0,
- Direction==Horizontal ? _expression().cols()-1:0,
- Direction==Vertical ? 1 : _expression().rows(),
- Direction==Horizontal ? 1 : _expression().cols()),
- Direction==Vertical ? _expression().rows()-1 : 1,
- Direction==Horizontal ? _expression().cols()-1 : 1));
- }
- namespace internal {
- template<typename MatrixOrTransformType>
- struct take_matrix_for_product
- {
- typedef MatrixOrTransformType type;
- EIGEN_DEVICE_FUNC static const type& run(const type &x) { return x; }
- };
- template<typename Scalar, int Dim, int Mode,int Options>
- struct take_matrix_for_product<Transform<Scalar, Dim, Mode, Options> >
- {
- typedef Transform<Scalar, Dim, Mode, Options> TransformType;
- typedef typename internal::add_const<typename TransformType::ConstAffinePart>::type type;
- EIGEN_DEVICE_FUNC static type run (const TransformType& x) { return x.affine(); }
- };
- template<typename Scalar, int Dim, int Options>
- struct take_matrix_for_product<Transform<Scalar, Dim, Projective, Options> >
- {
- typedef Transform<Scalar, Dim, Projective, Options> TransformType;
- typedef typename TransformType::MatrixType type;
- EIGEN_DEVICE_FUNC static const type& run (const TransformType& x) { return x.matrix(); }
- };
- template<typename MatrixType,typename Lhs>
- struct traits<homogeneous_left_product_impl<Homogeneous<MatrixType,Vertical>,Lhs> >
- {
- typedef typename take_matrix_for_product<Lhs>::type LhsMatrixType;
- typedef typename remove_all<MatrixType>::type MatrixTypeCleaned;
- typedef typename remove_all<LhsMatrixType>::type LhsMatrixTypeCleaned;
- typedef typename make_proper_matrix_type<
- typename traits<MatrixTypeCleaned>::Scalar,
- LhsMatrixTypeCleaned::RowsAtCompileTime,
- MatrixTypeCleaned::ColsAtCompileTime,
- MatrixTypeCleaned::PlainObject::Options,
- LhsMatrixTypeCleaned::MaxRowsAtCompileTime,
- MatrixTypeCleaned::MaxColsAtCompileTime>::type ReturnType;
- };
- template<typename MatrixType,typename Lhs>
- struct homogeneous_left_product_impl<Homogeneous<MatrixType,Vertical>,Lhs>
- : public ReturnByValue<homogeneous_left_product_impl<Homogeneous<MatrixType,Vertical>,Lhs> >
- {
- typedef typename traits<homogeneous_left_product_impl>::LhsMatrixType LhsMatrixType;
- typedef typename remove_all<LhsMatrixType>::type LhsMatrixTypeCleaned;
- typedef typename remove_all<typename LhsMatrixTypeCleaned::Nested>::type LhsMatrixTypeNested;
- EIGEN_DEVICE_FUNC homogeneous_left_product_impl(const Lhs& lhs, const MatrixType& rhs)
- : m_lhs(take_matrix_for_product<Lhs>::run(lhs)),
- m_rhs(rhs)
- {}
- EIGEN_DEVICE_FUNC inline Index rows() const { return m_lhs.rows(); }
- EIGEN_DEVICE_FUNC inline Index cols() const { return m_rhs.cols(); }
- template<typename Dest> EIGEN_DEVICE_FUNC void evalTo(Dest& dst) const
- {
- // FIXME investigate how to allow lazy evaluation of this product when possible
- dst = Block<const LhsMatrixTypeNested,
- LhsMatrixTypeNested::RowsAtCompileTime,
- LhsMatrixTypeNested::ColsAtCompileTime==Dynamic?Dynamic:LhsMatrixTypeNested::ColsAtCompileTime-1>
- (m_lhs,0,0,m_lhs.rows(),m_lhs.cols()-1) * m_rhs;
- dst += m_lhs.col(m_lhs.cols()-1).rowwise()
- .template replicate<MatrixType::ColsAtCompileTime>(m_rhs.cols());
- }
- typename LhsMatrixTypeCleaned::Nested m_lhs;
- typename MatrixType::Nested m_rhs;
- };
- template<typename MatrixType,typename Rhs>
- struct traits<homogeneous_right_product_impl<Homogeneous<MatrixType,Horizontal>,Rhs> >
- {
- typedef typename make_proper_matrix_type<typename traits<MatrixType>::Scalar,
- MatrixType::RowsAtCompileTime,
- Rhs::ColsAtCompileTime,
- MatrixType::PlainObject::Options,
- MatrixType::MaxRowsAtCompileTime,
- Rhs::MaxColsAtCompileTime>::type ReturnType;
- };
- template<typename MatrixType,typename Rhs>
- struct homogeneous_right_product_impl<Homogeneous<MatrixType,Horizontal>,Rhs>
- : public ReturnByValue<homogeneous_right_product_impl<Homogeneous<MatrixType,Horizontal>,Rhs> >
- {
- typedef typename remove_all<typename Rhs::Nested>::type RhsNested;
- EIGEN_DEVICE_FUNC homogeneous_right_product_impl(const MatrixType& lhs, const Rhs& rhs)
- : m_lhs(lhs), m_rhs(rhs)
- {}
- EIGEN_DEVICE_FUNC inline Index rows() const { return m_lhs.rows(); }
- EIGEN_DEVICE_FUNC inline Index cols() const { return m_rhs.cols(); }
- template<typename Dest> EIGEN_DEVICE_FUNC void evalTo(Dest& dst) const
- {
- // FIXME investigate how to allow lazy evaluation of this product when possible
- dst = m_lhs * Block<const RhsNested,
- RhsNested::RowsAtCompileTime==Dynamic?Dynamic:RhsNested::RowsAtCompileTime-1,
- RhsNested::ColsAtCompileTime>
- (m_rhs,0,0,m_rhs.rows()-1,m_rhs.cols());
- dst += m_rhs.row(m_rhs.rows()-1).colwise()
- .template replicate<MatrixType::RowsAtCompileTime>(m_lhs.rows());
- }
- typename MatrixType::Nested m_lhs;
- typename Rhs::Nested m_rhs;
- };
- template<typename ArgType,int Direction>
- struct evaluator_traits<Homogeneous<ArgType,Direction> >
- {
- typedef typename storage_kind_to_evaluator_kind<typename ArgType::StorageKind>::Kind Kind;
- typedef HomogeneousShape Shape;
- };
- template<> struct AssignmentKind<DenseShape,HomogeneousShape> { typedef Dense2Dense Kind; };
- template<typename ArgType,int Direction>
- struct unary_evaluator<Homogeneous<ArgType,Direction>, IndexBased>
- : evaluator<typename Homogeneous<ArgType,Direction>::PlainObject >
- {
- typedef Homogeneous<ArgType,Direction> XprType;
- typedef typename XprType::PlainObject PlainObject;
- typedef evaluator<PlainObject> Base;
- EIGEN_DEVICE_FUNC explicit unary_evaluator(const XprType& op)
- : Base(), m_temp(op)
- {
- ::new (static_cast<Base*>(this)) Base(m_temp);
- }
- protected:
- PlainObject m_temp;
- };
- // dense = homogeneous
- template< typename DstXprType, typename ArgType, typename Scalar>
- struct Assignment<DstXprType, Homogeneous<ArgType,Vertical>, internal::assign_op<Scalar,typename ArgType::Scalar>, Dense2Dense>
- {
- typedef Homogeneous<ArgType,Vertical> SrcXprType;
- EIGEN_DEVICE_FUNC static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,typename ArgType::Scalar> &)
- {
- Index dstRows = src.rows();
- Index dstCols = src.cols();
- if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))
- dst.resize(dstRows, dstCols);
- dst.template topRows<ArgType::RowsAtCompileTime>(src.nestedExpression().rows()) = src.nestedExpression();
- dst.row(dst.rows()-1).setOnes();
- }
- };
- // dense = homogeneous
- template< typename DstXprType, typename ArgType, typename Scalar>
- struct Assignment<DstXprType, Homogeneous<ArgType,Horizontal>, internal::assign_op<Scalar,typename ArgType::Scalar>, Dense2Dense>
- {
- typedef Homogeneous<ArgType,Horizontal> SrcXprType;
- EIGEN_DEVICE_FUNC static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,typename ArgType::Scalar> &)
- {
- Index dstRows = src.rows();
- Index dstCols = src.cols();
- if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))
- dst.resize(dstRows, dstCols);
- dst.template leftCols<ArgType::ColsAtCompileTime>(src.nestedExpression().cols()) = src.nestedExpression();
- dst.col(dst.cols()-1).setOnes();
- }
- };
- template<typename LhsArg, typename Rhs, int ProductTag>
- struct generic_product_impl<Homogeneous<LhsArg,Horizontal>, Rhs, HomogeneousShape, DenseShape, ProductTag>
- {
- template<typename Dest>
- EIGEN_DEVICE_FUNC static void evalTo(Dest& dst, const Homogeneous<LhsArg,Horizontal>& lhs, const Rhs& rhs)
- {
- homogeneous_right_product_impl<Homogeneous<LhsArg,Horizontal>, Rhs>(lhs.nestedExpression(), rhs).evalTo(dst);
- }
- };
- template<typename Lhs,typename Rhs>
- struct homogeneous_right_product_refactoring_helper
- {
- enum {
- Dim = Lhs::ColsAtCompileTime,
- Rows = Lhs::RowsAtCompileTime
- };
- typedef typename Rhs::template ConstNRowsBlockXpr<Dim>::Type LinearBlockConst;
- typedef typename remove_const<LinearBlockConst>::type LinearBlock;
- typedef typename Rhs::ConstRowXpr ConstantColumn;
- typedef Replicate<const ConstantColumn,Rows,1> ConstantBlock;
- typedef Product<Lhs,LinearBlock,LazyProduct> LinearProduct;
- typedef CwiseBinaryOp<internal::scalar_sum_op<typename Lhs::Scalar,typename Rhs::Scalar>, const LinearProduct, const ConstantBlock> Xpr;
- };
- template<typename Lhs, typename Rhs, int ProductTag>
- struct product_evaluator<Product<Lhs, Rhs, LazyProduct>, ProductTag, HomogeneousShape, DenseShape>
- : public evaluator<typename homogeneous_right_product_refactoring_helper<typename Lhs::NestedExpression,Rhs>::Xpr>
- {
- typedef Product<Lhs, Rhs, LazyProduct> XprType;
- typedef homogeneous_right_product_refactoring_helper<typename Lhs::NestedExpression,Rhs> helper;
- typedef typename helper::ConstantBlock ConstantBlock;
- typedef typename helper::Xpr RefactoredXpr;
- typedef evaluator<RefactoredXpr> Base;
-
- EIGEN_DEVICE_FUNC explicit product_evaluator(const XprType& xpr)
- : Base( xpr.lhs().nestedExpression() .lazyProduct( xpr.rhs().template topRows<helper::Dim>(xpr.lhs().nestedExpression().cols()) )
- + ConstantBlock(xpr.rhs().row(xpr.rhs().rows()-1),xpr.lhs().rows(), 1) )
- {}
- };
- template<typename Lhs, typename RhsArg, int ProductTag>
- struct generic_product_impl<Lhs, Homogeneous<RhsArg,Vertical>, DenseShape, HomogeneousShape, ProductTag>
- {
- template<typename Dest>
- EIGEN_DEVICE_FUNC static void evalTo(Dest& dst, const Lhs& lhs, const Homogeneous<RhsArg,Vertical>& rhs)
- {
- homogeneous_left_product_impl<Homogeneous<RhsArg,Vertical>, Lhs>(lhs, rhs.nestedExpression()).evalTo(dst);
- }
- };
- // TODO: the following specialization is to address a regression from 3.2 to 3.3
- // In the future, this path should be optimized.
- template<typename Lhs, typename RhsArg, int ProductTag>
- struct generic_product_impl<Lhs, Homogeneous<RhsArg,Vertical>, TriangularShape, HomogeneousShape, ProductTag>
- {
- template<typename Dest>
- static void evalTo(Dest& dst, const Lhs& lhs, const Homogeneous<RhsArg,Vertical>& rhs)
- {
- dst.noalias() = lhs * rhs.eval();
- }
- };
- template<typename Lhs,typename Rhs>
- struct homogeneous_left_product_refactoring_helper
- {
- enum {
- Dim = Rhs::RowsAtCompileTime,
- Cols = Rhs::ColsAtCompileTime
- };
- typedef typename Lhs::template ConstNColsBlockXpr<Dim>::Type LinearBlockConst;
- typedef typename remove_const<LinearBlockConst>::type LinearBlock;
- typedef typename Lhs::ConstColXpr ConstantColumn;
- typedef Replicate<const ConstantColumn,1,Cols> ConstantBlock;
- typedef Product<LinearBlock,Rhs,LazyProduct> LinearProduct;
- typedef CwiseBinaryOp<internal::scalar_sum_op<typename Lhs::Scalar,typename Rhs::Scalar>, const LinearProduct, const ConstantBlock> Xpr;
- };
- template<typename Lhs, typename Rhs, int ProductTag>
- struct product_evaluator<Product<Lhs, Rhs, LazyProduct>, ProductTag, DenseShape, HomogeneousShape>
- : public evaluator<typename homogeneous_left_product_refactoring_helper<Lhs,typename Rhs::NestedExpression>::Xpr>
- {
- typedef Product<Lhs, Rhs, LazyProduct> XprType;
- typedef homogeneous_left_product_refactoring_helper<Lhs,typename Rhs::NestedExpression> helper;
- typedef typename helper::ConstantBlock ConstantBlock;
- typedef typename helper::Xpr RefactoredXpr;
- typedef evaluator<RefactoredXpr> Base;
-
- EIGEN_DEVICE_FUNC explicit product_evaluator(const XprType& xpr)
- : Base( xpr.lhs().template leftCols<helper::Dim>(xpr.rhs().nestedExpression().rows()) .lazyProduct( xpr.rhs().nestedExpression() )
- + ConstantBlock(xpr.lhs().col(xpr.lhs().cols()-1),1,xpr.rhs().cols()) )
- {}
- };
- template<typename Scalar, int Dim, int Mode,int Options, typename RhsArg, int ProductTag>
- struct generic_product_impl<Transform<Scalar,Dim,Mode,Options>, Homogeneous<RhsArg,Vertical>, DenseShape, HomogeneousShape, ProductTag>
- {
- typedef Transform<Scalar,Dim,Mode,Options> TransformType;
- template<typename Dest>
- EIGEN_DEVICE_FUNC static void evalTo(Dest& dst, const TransformType& lhs, const Homogeneous<RhsArg,Vertical>& rhs)
- {
- homogeneous_left_product_impl<Homogeneous<RhsArg,Vertical>, TransformType>(lhs, rhs.nestedExpression()).evalTo(dst);
- }
- };
- template<typename ExpressionType, int Side, bool Transposed>
- struct permutation_matrix_product<ExpressionType, Side, Transposed, HomogeneousShape>
- : public permutation_matrix_product<ExpressionType, Side, Transposed, DenseShape>
- {};
- } // end namespace internal
- } // end namespace Eigen
- #endif // EIGEN_HOMOGENEOUS_H
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