Aim: DiscreteExteriorCalculus represents a calculus in the dec package. This is the main structure in the dec package. This is used to describe the space on which the dec is build and to compute various operators. Once operators or kforms are created, this structure should not be modified. More...

#include <DGtal/dec/DiscreteExteriorCalculus.h>

Data Structures
struct	Property
	Holds size 'primal_size', 'dual_size', 'index' and 'flipped' for each cell of the DEC object. To avoid inserting both positive and negative cells in a DEC object, only non signed cells are stored internally. More...

Public Types
typedef DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >	Self

typedef TLinearAlgebraBackend	LinearAlgebraBackend

typedef LinearAlgebraBackend::DenseVector::Index	Index

typedef LinearAlgebraBackend::DenseVector::Scalar	Scalar

typedef LinearAlgebraBackend::DenseVector	DenseVector

typedef LinearAlgebraBackend::DenseMatrix	DenseMatrix

typedef LinearAlgebraBackend::SparseMatrix	SparseMatrix

typedef DGtal::KhalimskySpaceND< dimAmbient, TInteger >	KSpace

typedef KSpace::Cell	Cell

typedef KSpace::SCell	SCell

typedef KSpace::Point	Point

typedef boost::unordered_map< Cell, Property >	Properties

typedef std::vector< SCell >	SCells

typedef boost::array< SCells, dimEmbedded+1 >	IndexedSCells

typedef VectorField< Self, PRIMAL >	PrimalVectorField

typedef VectorField< Self, DUAL >	DualVectorField

typedef KForm< Self, 0, PRIMAL >	PrimalForm0

typedef KForm< Self, 1, PRIMAL >	PrimalForm1

typedef KForm< Self, 2, PRIMAL >	PrimalForm2

typedef KForm< Self, 3, PRIMAL >	PrimalForm3

typedef KForm< Self, 0, DUAL >	DualForm0

typedef KForm< Self, 1, DUAL >	DualForm1

typedef KForm< Self, 2, DUAL >	DualForm2

typedef KForm< Self, 3, DUAL >	DualForm3

typedef LinearOperator< Self, 0, PRIMAL, 1, PRIMAL >	PrimalDerivative0

typedef LinearOperator< Self, 1, PRIMAL, 2, PRIMAL >	PrimalDerivative1

typedef LinearOperator< Self, 2, PRIMAL, 3, PRIMAL >	PrimalDerivative2

typedef LinearOperator< Self, 0, DUAL, 1, DUAL >	DualDerivative0

typedef LinearOperator< Self, 1, DUAL, 2, DUAL >	DualDerivative1

typedef LinearOperator< Self, 2, DUAL, 3, DUAL >	DualDerivative2

typedef LinearOperator< Self, 1, PRIMAL, 0, PRIMAL >	PrimalAntiderivative1

typedef LinearOperator< Self, 2, PRIMAL, 1, PRIMAL >	PrimalAntiderivative2

typedef LinearOperator< Self, 3, PRIMAL, 2, PRIMAL >	PrimalAntiderivative3

typedef LinearOperator< Self, 1, DUAL, 0, DUAL >	DualAntiderivative1

typedef LinearOperator< Self, 2, DUAL, 1, DUAL >	DualAntiderivative2

typedef LinearOperator< Self, 3, DUAL, 2, DUAL >	DualAntiderivative3

typedef LinearOperator< Self, 0, PRIMAL, dimEmbedded-0, DUAL >	PrimalHodge0

typedef LinearOperator< Self, 1, PRIMAL, dimEmbedded-1, DUAL >	PrimalHodge1

typedef LinearOperator< Self, 2, PRIMAL, dimEmbedded-2, DUAL >	PrimalHodge2

typedef LinearOperator< Self, 3, PRIMAL, dimEmbedded-3, DUAL >	PrimalHodge3

typedef LinearOperator< Self, 0, DUAL, dimEmbedded-0, PRIMAL >	DualHodge0

typedef LinearOperator< Self, 1, DUAL, dimEmbedded-1, PRIMAL >	DualHodge1

typedef LinearOperator< Self, 2, DUAL, dimEmbedded-2, PRIMAL >	DualHodge2

typedef LinearOperator< Self, 3, DUAL, dimEmbedded-3, PRIMAL >	DualHodge3

typedef LinearOperator< Self, 0, PRIMAL, 0, PRIMAL >	PrimalIdentity0

typedef LinearOperator< Self, 1, PRIMAL, 1, PRIMAL >	PrimalIdentity1

typedef LinearOperator< Self, 2, PRIMAL, 2, PRIMAL >	PrimalIdentity2

typedef LinearOperator< Self, 3, PRIMAL, 3, PRIMAL >	PrimalIdentity3

typedef LinearOperator< Self, 0, DUAL, 0, DUAL >	DualIdentity0

typedef LinearOperator< Self, 1, DUAL, 1, DUAL >	DualIdentity1

typedef LinearOperator< Self, 2, DUAL, 2, DUAL >	DualIdentity2

typedef LinearOperator< Self, 3, DUAL, 3, DUAL >	DualIdentity3

typedef Properties::const_iterator	ConstIterator

typedef Properties::iterator	Iterator

Public Member Functions
	BOOST_CONCEPT_ASSERT ((concepts::CInteger< TInteger >))

	BOOST_CONCEPT_ASSERT ((concepts::CDynamicVector< DenseVector >))

	BOOST_CONCEPT_ASSERT ((concepts::CDynamicMatrix< DenseMatrix >))

	BOOST_CONCEPT_ASSERT ((concepts::CDynamicMatrix< SparseMatrix >))

	BOOST_CONCEPT_ASSERT ((concepts::CLinearAlgebra< DenseVector, SparseMatrix >))

	BOOST_CONCEPT_ASSERT ((concepts::CLinearAlgebra< DenseVector, DenseMatrix >))

	BOOST_STATIC_ASSERT ((boost::is_same< Dimension, Order >::value))

	BOOST_STATIC_ASSERT ((dimAmbient >=dimEmbedded))

	BOOST_STATIC_CONSTANT (Dimension, dimensionEmbedded=dimEmbedded)

	BOOST_STATIC_CONSTANT (Dimension, dimensionAmbient=dimAmbient)

	DiscreteExteriorCalculus ()

template<typename TDomain >
void	initKSpace (ConstAlias< TDomain > domain)

ConstIterator	begin () const

ConstIterator	end () const

Iterator	begin ()

Iterator	end ()

void	selfDisplay (std::ostream &out) const

std::string	className () const

bool	insertSCell (const SCell &signed_cell)

bool	insertSCell (const SCell &signed_cell, const Scalar &primal_size, const Scalar &dual_size)

bool	eraseCell (const Cell &cell)

void	updateIndexes ()

const Properties &	getProperties () const

template<Order order, Duality duality>
const SCells &	getIndexedSCells () const

template<Order order, Duality duality, typename TConstIterator >
LinearOperator< Self, order, duality, order, duality >	reorder (const TConstIterator &begin_range, const TConstIterator &end_range) const

template<Order order, Duality duality>
LinearOperator< Self, order, duality, order, duality >	identity () const

template<Order order, Duality duality>
LinearOperator< Self, order, duality, order+1, duality >	derivative () const

template<Order order, Duality duality>
LinearOperator< Self, order, duality, order-1, duality >	antiderivative () const

template<Duality duality>
LinearOperator< Self, 0, duality, 0, duality >	laplace () const

template<Duality duality>
LinearOperator< Self, 0, duality, 0, duality >	heatLaplace (const typename DenseVector::Scalar &h, const typename DenseVector::Scalar &t, const typename DenseVector::Scalar &K) const

template<Order order, Duality duality>
LinearOperator< Self, order, duality, dimEmbedded-order, OppositeDuality< duality >::duality >	hodge () const

template<Duality duality>
KForm< Self, 1, duality >	flat (const VectorField< Self, duality > &vector_field) const

template<Duality duality>
LinearOperator< Self, 0, duality, 1, duality >	flatDirectional (const Dimension &dir) const

template<Duality duality>
VectorField< Self, duality >	sharp (const KForm< Self, 1, duality > &one_form) const

template<Duality duality>
LinearOperator< Self, 1, duality, 0, duality >	sharpDirectional (const Dimension &dir) const

SCell	getSCell (const Order &order, const Duality &duality, const Index &index) const

bool	isCellFlipped (const Cell &cell) const

bool	containsCell (const Cell &cell) const

Index	getCellIndex (const Cell &cell) const

Index	kFormLength (const Order &order, const Duality &duality) const

Order	actualOrder (const Order &order, const Duality &duality) const

Scalar	hodgeSign (const Cell &cell, const Duality &duality) const

Dimension	edgeDirection (const Cell &cell, const Duality &duality) const

void	resetSizes ()

bool	isValid () const

Data Fields
KSpace	myKSpace

Private Member Functions
void	updateCachedOperators ()

template<Duality duality>
void	updateFlatOperator ()

template<Duality duality>
void	updateSharpOperator ()

Private Attributes
Properties	myCellProperties

IndexedSCells	myIndexSignedCells

boost::array< boost::array< SparseMatrix, dimAmbient >, 2 >	myFlatOperatorMatrixes

boost::array< boost::array< SparseMatrix, dimAmbient >, 2 >	mySharpOperatorMatrixes

bool	myCachedOperatorsNeedUpdate

bool	myIndexesNeedUpdate

Friends
class	DiscreteExteriorCalculusFactory< TLinearAlgebraBackend, TInteger >

Detailed Description

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend, typename TInteger = DGtal::int32_t>
class DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >

Aim: DiscreteExteriorCalculus represents a calculus in the dec package. This is the main structure in the dec package. This is used to describe the space on which the dec is build and to compute various operators. Once operators or kforms are created, this structure should not be modified.

Description of template class 'DiscreteExteriorCalculus'

Template Parameters

dimEmbedded	dimension of emmbedded manifold.
dimAmbient	dimension of ambient manifold.
TLinearAlgebraBackend	linear algebra backend used (i.e. EigenSparseLinearAlgebraBackend).
TInteger	integer type forwarded to khalimsky space.

Examples: dec/exampleDECSurface.cpp, dec/exampleDiscreteExteriorCalculusChladni.cpp, dec/exampleDiscreteExteriorCalculusSolve.cpp, dec/exampleDiscreteExteriorCalculusUsage.cpp, dec/exampleHeatLaplace.cpp, and dec/examplePropagation.cpp.

Definition at line 97 of file DiscreteExteriorCalculus.h.

Member Typedef Documentation

◆ Cell

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef KSpace::Cell DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::Cell

Definition at line 132 of file DiscreteExteriorCalculus.h.

◆ ConstIterator

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef Properties::const_iterator DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::ConstIterator

Const iterator typedef.

Definition at line 253 of file DiscreteExteriorCalculus.h.

◆ DenseMatrix

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef LinearAlgebraBackend::DenseMatrix DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::DenseMatrix

Definition at line 110 of file DiscreteExteriorCalculus.h.

◆ DenseVector

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef LinearAlgebraBackend::DenseVector DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::DenseVector

Definition at line 109 of file DiscreteExteriorCalculus.h.

◆ DualAntiderivative1

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef LinearOperator<Self, 1, DUAL, 0, DUAL> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::DualAntiderivative1

Definition at line 205 of file DiscreteExteriorCalculus.h.

◆ DualAntiderivative2

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef LinearOperator<Self, 2, DUAL, 1, DUAL> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::DualAntiderivative2

Definition at line 206 of file DiscreteExteriorCalculus.h.

◆ DualAntiderivative3

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef LinearOperator<Self, 3, DUAL, 2, DUAL> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::DualAntiderivative3

Definition at line 207 of file DiscreteExteriorCalculus.h.

◆ DualDerivative0

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef LinearOperator<Self, 0, DUAL, 1, DUAL> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::DualDerivative0

Definition at line 195 of file DiscreteExteriorCalculus.h.

◆ DualDerivative1

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef LinearOperator<Self, 1, DUAL, 2, DUAL> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::DualDerivative1

Definition at line 196 of file DiscreteExteriorCalculus.h.

◆ DualDerivative2

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef LinearOperator<Self, 2, DUAL, 3, DUAL> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::DualDerivative2

Definition at line 197 of file DiscreteExteriorCalculus.h.

◆ DualForm0

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef KForm<Self, 0, DUAL> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::DualForm0

Definition at line 184 of file DiscreteExteriorCalculus.h.

◆ DualForm1

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef KForm<Self, 1, DUAL> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::DualForm1

Definition at line 185 of file DiscreteExteriorCalculus.h.

◆ DualForm2

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef KForm<Self, 2, DUAL> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::DualForm2

Definition at line 186 of file DiscreteExteriorCalculus.h.

◆ DualForm3

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef KForm<Self, 3, DUAL> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::DualForm3

Definition at line 187 of file DiscreteExteriorCalculus.h.

◆ DualHodge0

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef LinearOperator<Self, 0, DUAL, dimEmbedded-0, PRIMAL> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::DualHodge0

Definition at line 216 of file DiscreteExteriorCalculus.h.

◆ DualHodge1

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef LinearOperator<Self, 1, DUAL, dimEmbedded-1, PRIMAL> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::DualHodge1

Definition at line 217 of file DiscreteExteriorCalculus.h.

◆ DualHodge2

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef LinearOperator<Self, 2, DUAL, dimEmbedded-2, PRIMAL> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::DualHodge2

Definition at line 218 of file DiscreteExteriorCalculus.h.

◆ DualHodge3

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef LinearOperator<Self, 3, DUAL, dimEmbedded-3, PRIMAL> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::DualHodge3

Definition at line 219 of file DiscreteExteriorCalculus.h.

◆ DualIdentity0

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef LinearOperator<Self, 0, DUAL, 0, DUAL> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::DualIdentity0

Definition at line 228 of file DiscreteExteriorCalculus.h.

◆ DualIdentity1

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef LinearOperator<Self, 1, DUAL, 1, DUAL> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::DualIdentity1

Definition at line 229 of file DiscreteExteriorCalculus.h.

◆ DualIdentity2

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef LinearOperator<Self, 2, DUAL, 2, DUAL> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::DualIdentity2

Definition at line 230 of file DiscreteExteriorCalculus.h.

◆ DualIdentity3

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef LinearOperator<Self, 3, DUAL, 3, DUAL> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::DualIdentity3

Definition at line 231 of file DiscreteExteriorCalculus.h.

◆ DualVectorField

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef VectorField<Self, DUAL> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::DualVectorField

Definition at line 175 of file DiscreteExteriorCalculus.h.

◆ Index

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef LinearAlgebraBackend::DenseVector::Index DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::Index

Definition at line 107 of file DiscreteExteriorCalculus.h.

◆ IndexedSCells

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef boost::array<SCells, dimEmbedded+1> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::IndexedSCells

Definition at line 169 of file DiscreteExteriorCalculus.h.

◆ Iterator

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef Properties::iterator DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::Iterator

Iterator typedef.

Definition at line 268 of file DiscreteExteriorCalculus.h.

◆ KSpace

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef DGtal::KhalimskySpaceND<dimAmbient, TInteger> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::KSpace

Definition at line 131 of file DiscreteExteriorCalculus.h.

◆ LinearAlgebraBackend

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef TLinearAlgebraBackend DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::LinearAlgebraBackend

Definition at line 106 of file DiscreteExteriorCalculus.h.

◆ Point

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef KSpace::Point DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::Point

Definition at line 134 of file DiscreteExteriorCalculus.h.

◆ PrimalAntiderivative1

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef LinearOperator<Self, 1, PRIMAL, 0, PRIMAL> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::PrimalAntiderivative1

Antiderivative linear operator typedefs.

Definition at line 202 of file DiscreteExteriorCalculus.h.

◆ PrimalAntiderivative2

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef LinearOperator<Self, 2, PRIMAL, 1, PRIMAL> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::PrimalAntiderivative2

Definition at line 203 of file DiscreteExteriorCalculus.h.

◆ PrimalAntiderivative3

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef LinearOperator<Self, 3, PRIMAL, 2, PRIMAL> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::PrimalAntiderivative3

Definition at line 204 of file DiscreteExteriorCalculus.h.

◆ PrimalDerivative0

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef LinearOperator<Self, 0, PRIMAL, 1, PRIMAL> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::PrimalDerivative0

Derivative linear operator typedefs.

Definition at line 192 of file DiscreteExteriorCalculus.h.

◆ PrimalDerivative1

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef LinearOperator<Self, 1, PRIMAL, 2, PRIMAL> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::PrimalDerivative1

Definition at line 193 of file DiscreteExteriorCalculus.h.

◆ PrimalDerivative2

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef LinearOperator<Self, 2, PRIMAL, 3, PRIMAL> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::PrimalDerivative2

Definition at line 194 of file DiscreteExteriorCalculus.h.

◆ PrimalForm0

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef KForm<Self, 0, PRIMAL> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::PrimalForm0

KForms typedefs.

Definition at line 180 of file DiscreteExteriorCalculus.h.

◆ PrimalForm1

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef KForm<Self, 1, PRIMAL> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::PrimalForm1

Definition at line 181 of file DiscreteExteriorCalculus.h.

◆ PrimalForm2

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef KForm<Self, 2, PRIMAL> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::PrimalForm2

Definition at line 182 of file DiscreteExteriorCalculus.h.

◆ PrimalForm3

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef KForm<Self, 3, PRIMAL> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::PrimalForm3

Definition at line 183 of file DiscreteExteriorCalculus.h.

◆ PrimalHodge0

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef LinearOperator<Self, 0, PRIMAL, dimEmbedded-0, DUAL> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::PrimalHodge0

Hodge duality linear operator typedefs.

Definition at line 212 of file DiscreteExteriorCalculus.h.

◆ PrimalHodge1

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef LinearOperator<Self, 1, PRIMAL, dimEmbedded-1, DUAL> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::PrimalHodge1

Definition at line 213 of file DiscreteExteriorCalculus.h.

◆ PrimalHodge2

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef LinearOperator<Self, 2, PRIMAL, dimEmbedded-2, DUAL> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::PrimalHodge2

Definition at line 214 of file DiscreteExteriorCalculus.h.

◆ PrimalHodge3

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef LinearOperator<Self, 3, PRIMAL, dimEmbedded-3, DUAL> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::PrimalHodge3

Definition at line 215 of file DiscreteExteriorCalculus.h.

◆ PrimalIdentity0

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef LinearOperator<Self, 0, PRIMAL, 0, PRIMAL> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::PrimalIdentity0

Identity linear operator typedefs.

Definition at line 224 of file DiscreteExteriorCalculus.h.

◆ PrimalIdentity1

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef LinearOperator<Self, 1, PRIMAL, 1, PRIMAL> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::PrimalIdentity1

Definition at line 225 of file DiscreteExteriorCalculus.h.

◆ PrimalIdentity2

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef LinearOperator<Self, 2, PRIMAL, 2, PRIMAL> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::PrimalIdentity2

Definition at line 226 of file DiscreteExteriorCalculus.h.

◆ PrimalIdentity3

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef LinearOperator<Self, 3, PRIMAL, 3, PRIMAL> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::PrimalIdentity3

Definition at line 227 of file DiscreteExteriorCalculus.h.

◆ PrimalVectorField

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef VectorField<Self, PRIMAL> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::PrimalVectorField

Vector field typedefs.

Definition at line 174 of file DiscreteExteriorCalculus.h.

◆ Properties

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef boost::unordered_map<Cell, Property> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::Properties

Cells properties map typedef.

Definition at line 163 of file DiscreteExteriorCalculus.h.

◆ Scalar

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef LinearAlgebraBackend::DenseVector::Scalar DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::Scalar

Definition at line 108 of file DiscreteExteriorCalculus.h.

◆ SCell

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef KSpace::SCell DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::SCell

Definition at line 133 of file DiscreteExteriorCalculus.h.

◆ SCells

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef std::vector<SCell> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::SCells

Indices to cells map typedefs.

Definition at line 168 of file DiscreteExteriorCalculus.h.

◆ Self

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef DiscreteExteriorCalculus<dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::Self

Definition at line 104 of file DiscreteExteriorCalculus.h.

◆ SparseMatrix

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

typedef LinearAlgebraBackend::SparseMatrix DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::SparseMatrix

Definition at line 111 of file DiscreteExteriorCalculus.h.

Constructor & Destructor Documentation

◆ DiscreteExteriorCalculus()

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::DiscreteExteriorCalculus ( )

Constructor. Initialize empty discrete exterior calculus.

Member Function Documentation

◆ actualOrder()

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

Order DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::actualOrder	(	const Order &	order,
		const Duality &	duality
	)		const

Return actual order of k-forms in the dec package representation. Used internally mostly.

Parameters

order	order.
duality	duality.

Returns: order if primal, dimEmbedded-order if dual.

◆ antiderivative()

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

template<Order order, Duality duality>

LinearOperator< Self, order, duality, order-1, duality > DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::antiderivative ( ) const

Antiderivative operator from order-forms to _(order-1)_-forms.

Template Parameters

order	order of input k-form.
duality	duality of input k-form.

Returns: antiderivative operator.

◆ begin() [1/2]

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

Iterator DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::begin ( )

Begin iterator.

◆ begin() [2/2]

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

ConstIterator DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::begin ( ) const

Begin const iterator.

◆ BOOST_CONCEPT_ASSERT() [1/6]

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::BOOST_CONCEPT_ASSERT ( (concepts::CDynamicMatrix< DenseMatrix >) )

◆ BOOST_CONCEPT_ASSERT() [2/6]

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::BOOST_CONCEPT_ASSERT ( (concepts::CDynamicMatrix< SparseMatrix >) )

◆ BOOST_CONCEPT_ASSERT() [3/6]

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::BOOST_CONCEPT_ASSERT ( (concepts::CDynamicVector< DenseVector >) )

◆ BOOST_CONCEPT_ASSERT() [4/6]

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::BOOST_CONCEPT_ASSERT ( (concepts::CInteger< TInteger >) )

◆ BOOST_CONCEPT_ASSERT() [5/6]

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::BOOST_CONCEPT_ASSERT ( (concepts::CLinearAlgebra< DenseVector, DenseMatrix >) )

◆ BOOST_CONCEPT_ASSERT() [6/6]

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::BOOST_CONCEPT_ASSERT ( (concepts::CLinearAlgebra< DenseVector, SparseMatrix >) )

◆ BOOST_STATIC_ASSERT() [1/2]

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::BOOST_STATIC_ASSERT ( (boost::is_same< Dimension, Order >::value) )

◆ BOOST_STATIC_ASSERT() [2/2]

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::BOOST_STATIC_ASSERT ( (dimAmbient >=dimEmbedded) )

Static dimensions.

◆ BOOST_STATIC_CONSTANT() [1/2]

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::BOOST_STATIC_CONSTANT	(	Dimension	,
		dimensionAmbient	= `dimAmbient`
	)

◆ BOOST_STATIC_CONSTANT() [2/2]

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::BOOST_STATIC_CONSTANT	(	Dimension	,
		dimensionEmbedded	= `dimEmbedded`
	)

◆ className()

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

std::string DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::className ( ) const

Get class name string "Calculus".

◆ containsCell()

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

bool DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::containsCell ( const Cell & cell ) const

Check is structure contains cell.

Parameters

cell	the tested cell.

◆ derivative()

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

template<Order order, Duality duality>

LinearOperator< Self, order, duality, order+1, duality > DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::derivative ( ) const

Derivative operator from order-forms to _(order+1)_-forms.

Template Parameters

order	order of input k-form.
duality	duality of input k-form.

Returns: derivative operator.

◆ edgeDirection()

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

Dimension DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::edgeDirection	(	const Cell &	cell,
		const Duality &	duality
	)		const

Return edge direction relative to primal.

Parameters

cell	Khalimsky cell.
duality	duality.

◆ end() [1/2]

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

Iterator DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::end ( )

End iterator.

◆ end() [2/2]

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

ConstIterator DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::end ( ) const

End const iterator.

◆ eraseCell()

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

bool DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::eraseCell ( const Cell & cell )

Manually erase cell from calculus. Should call updateIndexes() when structure modification is finished.

Parameters

cell	the cell to be removed.

Returns: true if cell was removed, false if cell was not in calculus.

◆ flat()

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

template<Duality duality>

KForm< Self, 1, duality > DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::flat ( const VectorField< Self, duality > & vector_field ) const

Construct 1-form from vector field.

Template Parameters

duality input vector field and output 1-form duality.

Parameters

vector_field vector field.

Returns: 1-form.

◆ flatDirectional()

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

template<Duality duality>

LinearOperator< Self, 0, duality, 1, duality > DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::flatDirectional ( const Dimension & dir ) const

Get directional flat operator that transforms 0-form containing vector field coordinates along direction dir into 1-form. Invert of sharp(1-form).coordAlongDirection(dir).

Template Parameters

duality input 0-form and output 1-form duality.

Parameters

dir	direction of projection.

Returns: linear operator.

◆ getCellIndex()

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

Index DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::getCellIndex ( const Cell & cell ) const

Get k-form index from cell.

Parameters

cell	Khalimsky cell.

Returns: associated k-form index.

◆ getIndexedSCells()

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

template<Order order, Duality duality>

const SCells & DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::getIndexedSCells ( ) const

Get all signed cells with specific order and duality in index order.

Template Parameters

order	order of signed cells.
duality	duality of signed cells.

Returns: index ordered signed cells.

◆ getProperties()

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

const Properties & DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::getProperties ( ) const

Get all cells properties.

Returns: associative container from Cell to Property.

◆ getSCell()

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

SCell DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::getSCell	(	const Order &	order,
		const Duality &	duality,
		const Index &	index
	)		const

Get signed cell from k-form index.

Parameters

order	k-form order.
duality	k-form duality.
index	index valid on a k-form container.

Returns: associated Khalimsky cell.

◆ heatLaplace()

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

template<Duality duality>

LinearOperator< Self, 0, duality, 0, duality > DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::heatLaplace	(	const typename DenseVector::Scalar &	h,
		const typename DenseVector::Scalar &	t,
		const typename DenseVector::Scalar &	K
	)		const

Convolutional Laplace operator from duality 0-forms to duality 0-forms. See Hands on the Operator in DGtal.

Parameters

h	the grid step
t	the time parameter for the convolution
K	the multiplier for the integration. Must be at least 2.

Returns: Heat Laplace operator.

◆ hodge()

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

template<Order order, Duality duality>

LinearOperator< Self, order, duality, dimEmbedded-order, OppositeDuality< duality >::duality > DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::hodge ( ) const

Hodge operator from duality order-form to opposite duality _(dimEmbedded-order)_-forms.

Template Parameters

order	order of input k-form.
duality	duality of input k-form.

Returns: hodge operator.

◆ hodgeSign()

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

Scalar DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::hodgeSign	(	const Cell &	cell,
		const Duality &	duality
	)		const

Return sign of hodge operator. Used internally mostly.

Parameters

cell	Khalimsky cell.
duality	duality.

◆ identity()

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

template<Order order, Duality duality>

LinearOperator< Self, order, duality, order, duality > DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::identity ( ) const

Identity operator from order-forms to order-forms.

Template Parameters

order	input and output order of identity operator.
duality	input and output duality of identity operator.

Returns: identity operator.

◆ initKSpace()

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

template<typename TDomain >

void DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::initKSpace ( ConstAlias< TDomain > domain )

Init Khalimsky space boundaries.

Template Parameters

TDomain type of digital domain.

Parameters

domain domain used to initialize Khalimsky space.

Referenced by test_manual_operators_2d().

◆ insertSCell() [1/2]

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

bool DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::insertSCell ( const SCell & signed_cell )

Manually insert signed cell into calculus with unit primal and dual size. Should call updateIndexes() when structure modification is finished. Be sure to insert all adjacent lower order primal cells.

Parameters

signed_cell the signed cell to be inserted.

Returns: true if cell was not already inserted, false if only cell was already inserted (cell properties are always updated).

◆ insertSCell() [2/2]

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

bool DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::insertSCell	(	const SCell &	signed_cell,
		const Scalar &	primal_size,
		const Scalar &	dual_size
	)

Manually insert signed cell into calculus. Should call updateIndexes() when structure modification is finished. Be sure to insert all adjacent lower order primal cells.

Parameters

signed_cell	the signed cell to be inserted.
primal_size	size (length, area, volume, ...) of primal cell. Primal size of 0-cell should be equal to 1.
dual_size	size (length, area, volume, ...) of dual cell. Dual size of n-cell should be equal to 1.

Returns: true if cell was not already inserted, false if only cell was already inserted (cell properties are always updated).

◆ isCellFlipped()

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

bool DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::isCellFlipped ( const Cell & cell ) const

Check if cell is flipped in display.

Parameters

cell	the tested cell.

◆ isValid()

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

bool DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::isValid ( ) const

Checks the validity/consistency of the object.

Returns: 'true' if the object is valid, 'false' otherwise.

◆ kFormLength()

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

Index DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::kFormLength	(	const Order &	order,
		const Duality &	duality
	)		const

Return number of elements in discrete k-form.

Parameters

order	k-form order.
duality	k-form duality.

◆ laplace()

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

template<Duality duality>

LinearOperator< Self, 0, duality, 0, duality > DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::laplace ( ) const

Laplace operator from duality 0-forms to duality 0-forms.

Returns: Laplace operator.

◆ reorder()

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

template<Order order, Duality duality, typename TConstIterator >

LinearOperator< Self, order, duality, order, duality > DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::reorder	(	const TConstIterator &	begin_range,
		const TConstIterator &	end_range
	)		const

Reorder operator from order-forms to order-forms. Reorder indexes from internal index order to iterator range traversal induced order.

Template Parameters

order	input and output order of reorder operator.
duality	input and output duality of reorder operator.
TConstIterator	const iterator to signed cell type.

Returns: identity operator.

◆ resetSizes()

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

void DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::resetSizes ( )

Reset all primal to dual cell sizes to 1.

◆ selfDisplay()

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

void DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::selfDisplay ( std::ostream & out ) const

Writes/Displays the object on an output stream.

Parameters

out	the output stream where the object is written.

◆ sharp()

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

template<Duality duality>

VectorField< Self, duality > DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::sharp ( const KForm< Self, 1, duality > & one_form ) const

Construct vector field from 1-form.

Template Parameters

duality input 1-form and output vector field duality.

Parameters

one_form 1-form.

Returns: vector field.

◆ sharpDirectional()

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

template<Duality duality>

LinearOperator< Self, 1, duality, 0, duality > DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::sharpDirectional ( const Dimension & dir ) const

Get directional sharp operator that transforms 1-form into 0-form containing vector field coordinates along direction dir. Equivalent to sharp(1-form).coordAlongDirection(dir).

Template Parameters

duality input 1-form and output 0-form duality.

Parameters

dir	direction of projection.

Returns: linear operator.

◆ updateCachedOperators()

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

void DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::updateCachedOperators ( )

private

Update sharp and flat operators cache.

◆ updateFlatOperator()

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

template<Duality duality>

void DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::updateFlatOperator ( )

private

Update flat operator cache.

Template Parameters

duality duality of updated flat operator.

◆ updateIndexes()

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

void DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::updateIndexes ( )

Update indexes for all cells. Cell insertion order == index may not be preserved.

◆ updateSharpOperator()

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

template<Duality duality>

void DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::updateSharpOperator ( )

private

Update sharp operator cache.

Template Parameters

duality duality of updated sharp operator.

Friends And Related Function Documentation

◆ DiscreteExteriorCalculusFactory< TLinearAlgebraBackend, TInteger >

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

friend class DiscreteExteriorCalculusFactory< TLinearAlgebraBackend, TInteger >

friend

Definition at line 620 of file DiscreteExteriorCalculus.h.

Field Documentation

◆ myCachedOperatorsNeedUpdate

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

bool DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::myCachedOperatorsNeedUpdate

private

Cached flat and sharp operators generation flag.

Definition at line 574 of file DiscreteExteriorCalculus.h.

◆ myCellProperties

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

Properties DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::myCellProperties

private

Cells properties.

Definition at line 553 of file DiscreteExteriorCalculus.h.

◆ myFlatOperatorMatrixes

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

boost::array<boost::array<SparseMatrix, dimAmbient>, 2> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::myFlatOperatorMatrixes

private

Cached flat operator matrix.

Definition at line 564 of file DiscreteExteriorCalculus.h.

◆ myIndexesNeedUpdate

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

bool DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::myIndexesNeedUpdate

private

Indexes generation flag.

Definition at line 579 of file DiscreteExteriorCalculus.h.

◆ myIndexSignedCells

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

IndexedSCells DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::myIndexSignedCells

private

Cells indexed by their order. Usefull for finding cell from index and order.

Definition at line 559 of file DiscreteExteriorCalculus.h.

◆ myKSpace

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

KSpace DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::myKSpace

Associated Khalimsky space.

Definition at line 286 of file DiscreteExteriorCalculus.h.

◆ mySharpOperatorMatrixes

template<Dimension dimEmbedded, Dimension dimAmbient, typename TLinearAlgebraBackend , typename TInteger = DGtal::int32_t>

boost::array<boost::array<SparseMatrix, dimAmbient>, 2> DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::mySharpOperatorMatrixes

private

Cached sharp operator matrix.

Definition at line 569 of file DiscreteExteriorCalculus.h.

The documentation for this class was generated from the following file:

DiscreteExteriorCalculus.h

Data Structures

Public Types

Public Member Functions

Data Fields

Private Member Functions

Private Attributes

Friends

Detailed Description

Member Typedef Documentation

◆ Cell

◆ ConstIterator

◆ DenseMatrix

◆ DenseVector

◆ DualAntiderivative1

◆ DualAntiderivative2

◆ DualAntiderivative3

◆ DualDerivative0

◆ DualDerivative1

◆ DualDerivative2

◆ DualForm0

◆ DualForm1

◆ DualForm2

◆ DualForm3

◆ DualHodge0

◆ DualHodge1

◆ DualHodge2

◆ DualHodge3

◆ DualIdentity0

◆ DualIdentity1

◆ DualIdentity2

◆ DualIdentity3

◆ DualVectorField

◆ Index

◆ IndexedSCells

◆ Iterator

◆ KSpace

◆ LinearAlgebraBackend

◆ Point

◆ PrimalAntiderivative1

◆ PrimalAntiderivative2

◆ PrimalAntiderivative3

◆ PrimalDerivative0

◆ PrimalDerivative1

◆ PrimalDerivative2

◆ PrimalForm0

◆ PrimalForm1

◆ PrimalForm2

◆ PrimalForm3

◆ PrimalHodge0

◆ PrimalHodge1

◆ PrimalHodge2

◆ PrimalHodge3

◆ PrimalIdentity0

◆ PrimalIdentity1

◆ PrimalIdentity2

◆ PrimalIdentity3

◆ PrimalVectorField

◆ Properties

◆ Scalar

◆ SCell

◆ SCells

◆ Self

◆ SparseMatrix

Constructor & Destructor Documentation

◆ DiscreteExteriorCalculus()

Member Function Documentation

◆ actualOrder()

◆ antiderivative()

◆ begin() [1/2]

◆ begin() [2/2]

◆ BOOST_CONCEPT_ASSERT() [1/6]

◆ BOOST_CONCEPT_ASSERT() [2/6]

◆ BOOST_CONCEPT_ASSERT() [3/6]

◆ BOOST_CONCEPT_ASSERT() [4/6]

◆ BOOST_CONCEPT_ASSERT() [5/6]

◆ BOOST_CONCEPT_ASSERT() [6/6]

◆ BOOST_STATIC_ASSERT() [1/2]

◆ BOOST_STATIC_ASSERT() [2/2]

◆ BOOST_STATIC_CONSTANT() [1/2]

◆ BOOST_STATIC_CONSTANT() [2/2]