CGAL::Homological_discrete_vector_field Namespace Reference

Classes
class	Abstract_simplicial_chain_complex
	The class Abstract_simplicial_chain_complex represents (topological) chain complexes associated to abstract simplicial complexes. More...
struct	Cell_pair
	Structure to represent data for HDVF operations (pairs of cells). More...
class	Complex_duality_data_t
	Type returned by dualize_complex(). 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 (over a ring of coefficients which should actually be a field). More...
struct	Hdvf_traits_2
	The class Hdvf_traits_2 implements the HDVFTraits concept for 2D data, using a geometric kernel K. More...
struct	Hdvf_traits_3
	The class Hdvf_traits_3 implements the HDVFTraits concept for 3D data, using a geometric kernel K. More...
struct	Hdvf_traits_d
	The class Hdvf_traits_d implements the HDVFTraits concept for dD data, using a geometric kernel K. More...
class	Icosphere_object_io
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...
class	Simplex
	The class Simplex is used by the class Abstract_simplicial_chain_complex to represent a 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	Surface_mesh_io
	The class Surface_mesh_io is an intermediate IO class, used to load a triangle mesh and produce simplicial complexes. More...
class	Tet_object_io
class	Triangulation_3_io
	The class Triangulation_3_io is an intermediate IO class, used to load a Triangulation_3 and produce simplicial complexes. 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< std::size_t, int >	Cell
	Type for indexing uniquely a cell.
typedef std::vector< size_t >	Io_cell_type
	Type of cells of Mesh_object_io.
typedef std::vector< Io_cell_type >	Io_chain_type
	Type of pre-chains in Mesh_object_io (list of cells without coefficients).

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

Functions
template<typename CoefficientRing >
std::ostream &	operator<< (std::ostream &out, const Abstract_simplicial_chain_complex< CoefficientRing > &complex)
template<typename CoefficientRing , typename Traits >
std::ostream &	operator<< (std::ostream &out, const Cubical_chain_complex< CoefficientRing, Traits > &complex)
template<typename ChainComplex , typename P >
std::function< double(size_t)>	degree_function (const ChainComplex &complex, const std::function< double(const P &)> &f)
	Degree function from a coordinates to scalar map.
std::ostream &	operator<< (std::ostream &out, const std::vector< Cell_pair > &pairs)
	Overload of operator<< for Cell_pair type.
template<typename ChainComplex , typename Degree , typename Filtration_ >
std::ostream &	operator<< (std::ostream &out_stream, const typename Hdvf_persistence< ChainComplex, Degree, Filtration_ >::Persistence_interval &hole)
std::ostream &	operator<< (std::ostream &out, const Cell_pair &p)
template<typename ChainComplex >
void	interaction_loop (Hdvf< ChainComplex > &hdvf, ChainComplex &complex, const std::function< void(Hdvf< ChainComplex > &hdvf, ChainComplex &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)
template<typename Traits >
size_t	read_nodes (const std::string &filename, std::vector< typename Traits::Point > *nodes, bool adapt=false)
	Load nodes from a .nodes file.

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

Cell

typedef std::pair<std::size_t, int> CGAL::Homological_discrete_vector_field::Cell

Type for indexing uniquely a cell.

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

Io_cell_type

typedef std::vector<size_t> CGAL::Homological_discrete_vector_field::Io_cell_type

Type of cells of Mesh_object_io.

Sorted vector of the vertex indices.

Enumeration Type Documentation

PSC_flag

enum CGAL::Homological_discrete_vector_field::PSC_flag

HDVF Enum for the label of cells.

Enumerator
PRIMARY
SECONDARY
CRITICAL
NONE

Function Documentation

interaction_loop()

template<typename ChainComplex >

void CGAL::Homological_discrete_vector_field::interaction_loop	(	Hdvf< ChainComplex > &	hdvf,
		ChainComplex &	complex,
		const std::function< void(Hdvf< ChainComplex > &hdvf, ChainComplex &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).

read_nodes()

template<typename Traits >

size_t CGAL::Homological_discrete_vector_field::read_nodes	(	const std::string &	filename,
		std::vector< typename Traits::Point > *	nodes,
		bool	adapt = false
	)

Load nodes from a .nodes file.

Load vertices coordinates from a .nodes file.

Parameters

filename	Name of the input file.
nodes	Pointer to a vector of points into which nodes are outputed.
adapt	If fill is false, nodes must have the same dimension as the traits Point, if true, nodes dimension can be lower (and missing coordinates are filled with zeros) or higher (and coordinates are truncated to the traits dimension).

Variable Documentation

f_x

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

Initial value:

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

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

f_y

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

Initial value:

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

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

f_z

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

Initial value:

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

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