Homological Discrete Vector Fields Reference

Alexandra Bac

The package provides an implementation of Homological Discrete Vector Fields, a framework computing homology and cohomology information (Betti numbers, generators, annotation functions...) for discrete objects (including persistent homology, Alexander duality isomorphism and reduced homology).

Introduced in: CGAL 6.2
BibTeX: cgal:b-hdvf-25b
License: GPL

Classified Reference Pages

Concepts

• AbstractChainComplex

Classes

• CGAL::Homological_discrete_vector_field::Abstract_simplicial_chain_complex

Modules
	Concepts
	Sparse Matrices and Vectors
	Traits Classes
	IO Classes

Classes
class	CGAL::Homological_discrete_vector_field::Abstract_simplicial_chain_complex< CoefficientRing >
	The class Abstract_simplicial_chain_complex represents (topological) chain complexes associated to abstract simplicial complexes. More...
class	CGAL::Homological_discrete_vector_field::Cubical_chain_complex< CoefficientRing, Traits >
	The class Cubical_chain_complex represents (topological) chain complexes associated to cubical complexes. More...
class	CGAL::Homological_discrete_vector_field::Filtration_core< ChainComplex, Degree >
	The class Filtration_core implements data structures and methods required by the Filtration concept. More...
class	CGAL::Homological_discrete_vector_field::Filtration_lower_star< ChainComplex, Degree >
	The class Filtration_lower_star implements the lower star filtration on a given complex implementing the concept AbstractChainComplex. More...
class	CGAL::Homological_discrete_vector_field::Duality_simplicial_complex_tools< CoefficientRing, Traits >
	The class Duality_simplicial_complex_tools is dedicated to Alexander duality for 3D surface meshes. More...
class	CGAL::Homological_discrete_vector_field::Duality_cubical_complex_tools< CoefficientRing, Traits >
	The class Duality_cubical_complex_tools is dedicated to Alexander duality for 3D binary volumes. More...
class	CGAL::Homological_discrete_vector_field::Hdvf< ChainComplex >
	The class Hdvf implements homology and cohomology computation via homological discrete vector fields (HDVF for short). More...
class	CGAL::Homological_discrete_vector_field::Hdvf_core< ChainComplex, ChainType, SparseMatrixType >
	The class Hdvf_core is the core implementation of homological discrete vector fields (HDVF for short). More...
class	CGAL::Homological_discrete_vector_field::Hdvf_duality< ChainComplex >
	The class Hdvf_duality is the implementation of homological discrete vector fields (HDVF for short) for Alexander duality computation. More...
class	CGAL::Homological_discrete_vector_field::Hdvf_persistence< ChainComplex, Degree, Filtration_ >
	The class Hdvf_persistence computes persistent homology using HDVFs (over a ring of coefficients which should actually be a field). More...
class	CGAL::Homological_discrete_vector_field::Mesh_object_io< Traits >
	The class Mesh_object_io is an intermediate IO class, used to load triangular/tetraedral meshes and produce simplicial complexes. More...
class	CGAL::Homological_discrete_vector_field::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	CGAL::Homological_discrete_vector_field::Simplicial_chain_complex< CoefficientRing, Traits >
	The class Simplicial_chain_complex refines the Abstract_simplicial_chain_complex class by assigning coordinates to vertices (i.e. 0-simplices). More...
class	CGAL::Homological_discrete_vector_field::Sub_chain_complex_mask< ChainComplex >
	The class Sub_chain_complex_mask is a technical class implementing a sub chain complex. More...