Classes
class	Abstract_simplicial_chain_complex
	The class `Abstract_simplicial_chain_complex` represents (topological) chain complexes associated to abstract simplicial complexes. More...

class	Cub_object_io
	The class `Cub_object_io` is an intermediate IO class, used to load binary volumes and produce cubical complexes. More...

class	Cubical_chain_complex
	The class `Cubical_chain_complex` represents (topological) chain complexes associated to cubical complexes. More...

class	Duality_cubical_complex_tools
	The class `Duality_cubical_complex_tools` is dedicated to Alexander duality for 3D binary volumes. More...

class	Duality_simplicial_complex_tools
	The class `Duality_simplicial_complex_tools` is dedicated to Alexander duality for 3D surface meshes. More...

class	Filtration_core
	The class `Filtration_core` implements data structures and methods required by the `Filtration` concept. More...

class	Filtration_lower_star
	The class `Filtration_lower_star` implements the lower star filtration on a given complex implementing the concept `AbstractChainComplex`. More...

class	Hdvf
	The class `Hdvf` implements homology and cohomology computation via homological discrete vector fields (HDVF for short). More...

class	Hdvf_core
	The class `Hdvf_core` is the core implementation of homological discrete vector fields (HDVF for short). More...

class	Hdvf_duality
	The class `Hdvf_duality` is the implementation of homological discrete vector fields (HDVF for short) for Alexander duality computation. More...

class	Hdvf_persistence
	The class `Hdvf_persistence` computes persistent homology using HDVFs. More...

class	Icosphere_object_io

struct	IONodeType
	The class `IONodeType` implements a simple data type used to import vertices coordinates (nodes) in various dimensions. More...

class	Mesh_object_io
	The class `Mesh_object_io` is an intermediate IO class, used to load triangular/tetraedral meshes and produce simplicial complexes. More...

struct	PairCell
	Structure to represent data for HDVF operations (pairs of cells). More...

class	Simplex
	The class `Simplex` is used by the class `Abstract_simplicial_chain_complex` to implement the structure de simplex (i.e. cells of a simplicial complex). More...

class	Simplicial_chain_complex
	The class `Simplicial_chain_complex` refines the `Abstract_simplicial_chain_complex` class by assigning coordinates to vertices (i.e. 0-simplices). More...

class	Sub_chain_complex_mask
	The class `Sub_chain_complex_mask` is a technical class implementing a sub chain complex. More...

class	Tet_object_io

class	Z2
	The class `Z2` implements the concept `Ring` with the field \(\mathbb Z/2\mathbb Z\). More...

class	Zp
	The class `Zp` implements the concept `Ring` with the field \(\mathbb Z/p\mathbb Z\). More...

Typedefs
typedef std::vector< size_t >	IOCubCellType
	Type of cells coordinates in Cub_object_io (Khalimsky or voxel coordinates)

typedef std::vector< IOCubCellType >	IOCubChainType
	Type of pre-chains in Cub_object_io (list of cells without coefficients).

typedef std::pair< size_t, size_t >	FiltrIndexPerInterval
	Type to store persistent intervals filtration indices (birth/death indices)

typedef std::pair< size_t, int >	CellDim
	Type for indexing uniquely a cell.

typedef std::pair< CellDim, CellDim >	CellsPerInterval
	Type for describing the pair of cells associated to a persistence interval:

template<typename DegType >
using	DegreePerIntervalT = std::pair< DegType, DegType >
	Template for persistent intervals degrees (birth/death degrees)

template<typename DegType >
using	PerHoleT = std::tuple< FiltrIndexPerInterval, CellsPerInterval, DegreePerIntervalT< DegType > >
	Template for (full) persistent interval data:

typedef std::set< size_t >	IOCellType
	Type of cells of Mesh_object_io.

typedef std::vector< IOCellType >	IOChainType
	Type of pre-chains in Mesh_object_io (list of cells without coefficients).

Enumerations
enum	FlagType { PRIMARY , SECONDARY , CRITICAL , NONE }
	HDVF Enum for the label of cells. More...

Functions
ostream &	operator<< (ostream &out, std::vector< size_t > c)

template<typename ComplexType >
std::function< double(size_t)>	deg_fun (const ComplexType &complex, std::function< double(const vector< double > &)> &f)
	Degree function from a coordinates to scalar map.

template<typename CoefType , typename ComplexType , template< typename, int > typename _ChainType = OSM::Sparse_chain, template< typename, int > typename _SparseMatrixType = OSM::Sparse_matrix, typename VertexIdType = size_t>
void	hdvf_geometric_chain_complex_output_vtk (Hdvf_core< CoefType, ComplexType, _ChainType, _SparseMatrixType > &hdvf, ComplexType &complex, string filename="test", bool co_faces=false)
	Exports all the `Hdvf` information of a geometric chain complex to vtk files.

template<typename CoefType , typename ComplexType , typename DegType , typename FiltrationType >
void	hdvf_persistence_geometric_chain_complex_output_vtk (Hdvf_persistence< CoefType, ComplexType, DegType, FiltrationType > &per_hdvf, ComplexType &complex, string filename="per", bool co_faces=false)
	Exports all the `HDVF_persistence` information of a geometric chain complex to vtk files.

template<typename CoefType , typename ComplexType , typename VertexIdType = size_t>
void	hdvf_duality_geometric_chain_complex_output_vtk (Hdvf_duality< CoefType, ComplexType > &hdvf, ComplexType &complex, string filename="test", bool co_faces=false)
	Exports all the `HDVF_duality` information of a geometric chain complex to vtk files.

std::ostream &	operator<< (std::ostream &out, const std::vector< PairCell > &pairs)
	Overload of operator<< for PairCell type.

template<typename DegType >
ostream &	operator<< (ostream &out, const PerHoleT< DegType > &hole)
	Overload of the `<<` operator to display persistent intervals (that is PerHoleT).

std::ostream &	operator<< (std::ostream &out, const PairCell &p)

template<typename CoefType , typename ComplexType >
void	interaction_loop (Hdvf< CoefType, ComplexType > &hdvf, ComplexType &complex, const std::function< void(Hdvf< CoefType, ComplexType > &hdvf, ComplexType &complex)> &output_vtk)
	Runs an interaction loop to iterated M, W or MW operations and export the results to vtk.

bool	check_sanity_line (const std::string &line, const std::string &file)

bool	get_next_uncommented_line (std::ifstream &infile, std::string &result)

Mesh_object_io	mesh_BB (const IONodeType &BBmin, const IONodeType &BBmax)

size_t	read_nodes (const std::string &node_file, bool load_nodes, std::vector< IONodeType > *nodes)

Variables
std::function< double(const std::vector< double > &)>	f_x
	For lower star filtration along x: function mapping coordinates to x.

std::function< double(const std::vector< double > &)>	f_y
	For lower star filtration along y: function mapping coordinates to y.

std::function< double(const std::vector< double > &)>	f_z
	For lower star filtration along z: function mapping coordinates to z.

const int	OPT_BND = 0b0001
	HDVF option (compute only reduced boundary).

const int	OPT_F = 0b0010
	HDVF option (compute only reduced boundary and f).

const int	OPT_G = 0b0100
	HDVF option (compute only reduced boundary and g).

const int	OPT_FULL = 0b1000
	HDVF option (compute full reduction).

static std::vector< size_t >	VTK_types_IO = {1, 3, 5, 10}

Typedef Documentation

◆ CellDim

typedef std::pair<size_t, int> CGAL::HDVF::CellDim

Type for indexing uniquely a cell.

First element of the pair: index of the cell.
Second element of the pair: dimension of the cell.

"Infinite cells" are defined as (-1,q+1) where q is the dimension of the chain complex.

◆ CellsPerInterval

typedef std::pair<CellDim, CellDim> CGAL::HDVF::CellsPerInterval

Type for describing the pair of cells associated to a persistence interval:

First element of the pair: cell entailing the birth of the hole.
Second element of the pair: cell entailing the death of the hole.

For infinite intervals, the "infinite cells" is defined as (-1,q+1) where q is the dimension of the chain complex.

◆ DegreePerIntervalT

template<typename DegType >

using CGAL::HDVF::DegreePerIntervalT = typedef std::pair<DegType,DegType>

Template for persistent intervals degrees (birth/death degrees)

For "infinite" intervals borne at degree d, the interval is set to (d,d-1)

◆ FiltrIndexPerInterval

typedef std::pair<size_t, size_t> CGAL::HDVF::FiltrIndexPerInterval

Type to store persistent intervals filtration indices (birth/death indices)

For "infinite" intervals borne at index i, the interval is set to (i,i-1)

◆ PerHoleT

template<typename DegType >

using CGAL::HDVF::PerHoleT = typedef std::tuple<FiltrIndexPerInterval, CellsPerInterval, DegreePerIntervalT<DegType> >

Template for (full) persistent interval data:

First element: persistent interval filtration indices
Second element: persistent interval cells
Third element: persistent interval degrees

Enumeration Type Documentation

◆ FlagType

enum CGAL::HDVF::FlagType

HDVF Enum for the label of cells.

Enumerator
PRIMARY
SECONDARY
CRITICAL
NONE

Function Documentation

◆ hdvf_duality_geometric_chain_complex_output_vtk()

template<typename CoefType , typename ComplexType , typename VertexIdType = size_t>

void CGAL::HDVF::hdvf_duality_geometric_chain_complex_output_vtk	(	Hdvf_duality< CoefType, ComplexType > &	hdvf,
		ComplexType &	complex,
		string	filename = `"test"`,
		bool	co_faces = `false`
	)

Exports all the HDVF_duality information of a geometric chain complex to vtk files.

Export PSC labels and homology/cohomology generators (depending on HDVF options) associated to each persistent intervals to vtk files.

Parameters

[in]	hdvf	Reference to the HDVF exported.
[in]	complex	Underlying geometric chain complex.
[in]	filename	Prefix of all generated files.
[in]	co_faces	Export the cohomology generator or its co-faces (sometimes more convenient for visualisation).

◆ hdvf_geometric_chain_complex_output_vtk()

template<typename CoefType , typename ComplexType , template< typename, int > typename _ChainType = OSM::Sparse_chain, template< typename, int > typename _SparseMatrixType = OSM::Sparse_matrix, typename VertexIdType = size_t>

void CGAL::HDVF::hdvf_geometric_chain_complex_output_vtk	(	Hdvf_core< CoefType, ComplexType, _ChainType, _SparseMatrixType > &	hdvf,
		ComplexType &	complex,
		string	filename = `"test"`,
		bool	co_faces = `false`
	)

Exports all the Hdvf information of a geometric chain complex to vtk files.

Export PSC labels and homology/cohomology generators (depending on HDVF options) associated to each critical cell to vtk files.

Parameters

[in]	hdvf	Reference to the HDVF exported.
[in]	complex	Underlying geometric chain complex.
[in]	filename	Prefix of all generated files.
[in]	co_faces	Export the cohomology generator or its co-faces (sometimes more convenient for visualisation).

Below, a sample mesh with, (left) homology generators, (right) two examples of cohomology generators (corresponding generators/co-generators bear similar colours):

The same generators displayed through their co-faces:

All homology / cohomology generators:

Examples: HDVF/main_hdvf.cpp.

◆ hdvf_persistence_geometric_chain_complex_output_vtk()

template<typename CoefType , typename ComplexType , typename DegType , typename FiltrationType >

void CGAL::HDVF::hdvf_persistence_geometric_chain_complex_output_vtk	(	Hdvf_persistence< CoefType, ComplexType, DegType, FiltrationType > &	per_hdvf,
		ComplexType &	complex,
		string	filename = `"per"`,
		bool	co_faces = `false`
	)

Exports all the HDVF_persistence information of a geometric chain complex to vtk files.

Export PSC labels and homology/cohomology generators (depending on HDVF options) associated to each persistent intervals to vtk files.

Parameters

[in]	per_hdvf	Reference to the persistent HDVF exported.
[in]	complex	Underlying geometric chain complex.
[in]	filename	Prefix of all generated files.
[in]	co_faces	Export the cohomology generator or its co-faces (sometimes more convenient for visualisation).

◆ interaction_loop()

template<typename CoefType , typename ComplexType >

void CGAL::HDVF::interaction_loop	(	Hdvf< CoefType, ComplexType > &	hdvf,
		ComplexType &	complex,
		const std::function< void(Hdvf< CoefType, ComplexType > &hdvf, ComplexType &complex)> &	output_vtk
	)

Runs an interaction loop to iterated M, W or MW operations and export the results to vtk.

The loop runs until the key Q is pressed. Otherwise, the loop asks for an operation (M, W or MW) and a cell (index and dimension). Then all possible paired cells are listed and the user can chose one of them (or none).

◆ operator<<()

template<typename DegType >

ostream & CGAL::HDVF::operator<<	(	ostream &	out,
		const PerHoleT< DegType > &	hole
	)

Overload of the << operator to display persistent intervals (that is PerHoleT).

Format: birth time (cell, dim) -> death time (cell, dim) / degree duration

Variable Documentation

◆ f_x

std::function<double(const std::vector<double>&)> CGAL::HDVF::f_x

Initial value:

= [](const std::vector<double>& v)
{
    return (v.at(0)) ;
}

For lower star filtration along x: function mapping coordinates to x.

Examples: HDVF/main_per_hdvf.cpp.

◆ f_y

std::function<double(const std::vector<double>&)> CGAL::HDVF::f_y

Initial value:

= [](const std::vector<double>& v)
{
    return (v.at(1)) ;
}

For lower star filtration along y: function mapping coordinates to y.

Examples: HDVF/main_per_hdvf.cpp.

◆ f_z

std::function<double(const std::vector<double>&)> CGAL::HDVF::f_z

Initial value:

= [](const std::vector<double>& v)
{
    return (v.at(2)) ;
}

For lower star filtration along z: function mapping coordinates to z.

Examples: HDVF/main_per_hdvf.cpp.

Classes

Typedefs

Enumerations

Functions

Variables

Typedef Documentation

◆ CellDim

◆ CellsPerInterval

◆ DegreePerIntervalT

◆ FiltrIndexPerInterval

◆ PerHoleT

Enumeration Type Documentation

◆ FlagType

Function Documentation

◆ hdvf_duality_geometric_chain_complex_output_vtk()

◆ hdvf_geometric_chain_complex_output_vtk()

◆ hdvf_persistence_geometric_chain_complex_output_vtk()

◆ interaction_loop()

◆ operator<<()

Variable Documentation

◆ f_x

◆ f_y

◆ f_z