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