Gudhi::coxeter_triangulation::Cell_complex< Out_simplex_map_ > Class Template Reference

A class that constructs the cell complex from the output provided by the class Gudhi::coxeter_triangulation::Manifold_tracing. More...

Public Types
using	Simplex_handle = typename Out_simplex_map_::key_type
	Type of a simplex in the ambient triangulation. Is a model of the concept SimplexInCoxeterTriangulation.
using	Hasse_cell = Gudhi::Hasse_diagram::Hasse_diagram_cell< int, double, bool >
	Type of a cell in the cell complex. Always is Gudhi::Hasse_cell from the Hasse diagram module. The additional information is the boolean that is true if and only if the cell lies on the boundary.
using	Simplex_cell_map = std::map< Simplex_handle, Hasse_cell *, Simplex_comparator< Simplex_handle > >
	Type of a map from permutahedral representations of simplices in the ambient triangulation to the corresponding cells in the cell complex of some specific dimension.
using	Simplex_cell_maps = std::vector< Simplex_cell_map >
	Type of a vector of maps from permutahedral representations of simplices in the ambient triangulation to the corresponding cells in the cell complex of various dimensions.
using	Cell_simplex_map = std::map< Hasse_cell *, Simplex_handle >
	Type of a map from cells in the cell complex to the permutahedral representations of the corresponding simplices in the ambient triangulation.
using	Cell_point_map = std::map< Hasse_cell *, Eigen::VectorXd >
	Type of a map from vertex cells in the cell complex to the permutahedral representations of their Cartesian coordinates.

Public Member Functions
void	construct_complex (const Out_simplex_map_ &out_simplex_map)
	Constructs the the cell complex that approximates an \(m\)-dimensional manifold without boundary embedded in the \( d \)-dimensional Euclidean space from the output of the class Gudhi::Manifold_tracing. More...
void	construct_complex (const Out_simplex_map_ &out_simplex_map, std::size_t limit_dimension)
	Constructs the skeleton of the cell complex that approximates an \(m\)-dimensional manifold without boundary embedded in the \(d\)-dimensional Euclidean space up to a limit dimension from the output of the class Gudhi::Manifold_tracing. More...
void	construct_complex (const Out_simplex_map_ &interior_simplex_map, const Out_simplex_map_ &boundary_simplex_map)
	Constructs the the cell complex that approximates an \(m\)-dimensional manifold with boundary embedded in the \( d \)-dimensional Euclidean space from the output of the class Gudhi::Manifold_tracing. More...
void	construct_complex (const Out_simplex_map_ &interior_simplex_map, const Out_simplex_map_ &boundary_simplex_map, std::size_t limit_dimension)
	Constructs the skeleton of the cell complex that approximates an \(m\)-dimensional manifold with boundary embedded in the \(d\)-dimensional Euclidean space up to a limit dimension from the output of the class Gudhi::Manifold_tracing. More...
std::size_t	intrinsic_dimension () const
	Returns the dimension of the cell complex.
const Simplex_cell_maps &	interior_simplex_cell_maps () const
	Returns a vector of maps from the cells of various dimensions in the interior of the cell complex of type Gudhi::Hasse_cell to the permutahedral representations of the corresponding simplices in the ambient triangulation.
const Simplex_cell_maps &	boundary_simplex_cell_maps () const
	Returns a vector of maps from the cells of various dimensions on the boundary of the cell complex of type Gudhi::Hasse_cell to the permutahedral representations of the corresponding simplices in the ambient triangulation.
const Simplex_cell_map &	interior_simplex_cell_map (std::size_t cell_d) const
	Returns a map from the cells of a given dimension in the interior of the cell complex of type Gudhi::Hasse_cell to the permutahedral representations of the corresponding simplices in the ambient triangulation. More...
const Simplex_cell_map &	boundary_simplex_cell_map (std::size_t cell_d) const
	Returns a map from the cells of a given dimension on the boundary of the cell complex of type Gudhi::Hasse_cell to the permutahedral representations of the corresponding simplices in the ambient triangulation. More...
const Cell_simplex_map &	cell_simplex_map () const
	Returns a map from the cells in the cell complex of type Gudhi::Hasse_cell to the permutahedral representations of the corresponding simplices in the ambient triangulation.
const Cell_point_map &	cell_point_map () const
	Returns a map from the vertex cells in the cell complex of type Gudhi::Hasse_cell to their Cartesian coordinates.
	Cell_complex (std::size_t intrinsic_dimension)
	Constructor for the class Cell_complex. More...

Detailed Description

template<class Out_simplex_map_>
class Gudhi::coxeter_triangulation::Cell_complex< Out_simplex_map_ >

A class that constructs the cell complex from the output provided by the class Gudhi::coxeter_triangulation::Manifold_tracing.

The use and interfaces of this cell complex is limited to the Coxeter triangulation implementation.

Template Parameters

Out_simplex_map_

The type of a map from a simplex type that is a model of SimplexInCoxeterTriangulation to Eigen::VectorXd.

Constructor & Destructor Documentation

Cell_complex()

template<class Out_simplex_map_ >

Gudhi::coxeter_triangulation::Cell_complex< Out_simplex_map_ >::Cell_complex ( std::size_t  intrinsic_dimension )

inline

Constructor for the class Cell_complex.

Parameters

[in]

intrinsic_dimension

The dimension of the cell complex.

Member Function Documentation

boundary_simplex_cell_map()

template<class Out_simplex_map_ >

const Simplex_cell_map& Gudhi::coxeter_triangulation::Cell_complex< Out_simplex_map_ >::boundary_simplex_cell_map ( std::size_t  cell_d ) const

inline

Returns a map from the cells of a given dimension on the boundary of the cell complex of type Gudhi::Hasse_cell to the permutahedral representations of the corresponding simplices in the ambient triangulation.

Parameters

[in]

cell_d

The dimension of the cells.

construct_complex() [1/4]

template<class Out_simplex_map_ >

void Gudhi::coxeter_triangulation::Cell_complex< Out_simplex_map_ >::construct_complex ( const Out_simplex_map_ &  interior_simplex_map, const Out_simplex_map_ &  boundary_simplex_map  )

inline

Constructs the the cell complex that approximates an \(m\)-dimensional manifold with boundary embedded in the \( d \)-dimensional Euclidean space from the output of the class Gudhi::Manifold_tracing.

Parameters

[in]	interior_simplex_map	A map from simplices of dimension \((d-m)\) in the ambient triangulation that intersect the relative interior of the manifold to the intersection points.
[in]	boundary_simplex_map	A map from simplices of dimension \((d-m+1)\) in the ambient triangulation that intersect the boundary of the manifold to the intersection points.

construct_complex() [2/4]

template<class Out_simplex_map_ >

void Gudhi::coxeter_triangulation::Cell_complex< Out_simplex_map_ >::construct_complex ( const Out_simplex_map_ &  interior_simplex_map, const Out_simplex_map_ &  boundary_simplex_map, std::size_t  limit_dimension  )

inline

Constructs the skeleton of the cell complex that approximates an \(m\)-dimensional manifold with boundary embedded in the \(d\)-dimensional Euclidean space up to a limit dimension from the output of the class Gudhi::Manifold_tracing.

Parameters

[in]	interior_simplex_map	A map from simplices of dimension \((d-m)\) in the ambient triangulation that intersect the relative interior of the manifold to the intersection points.
[in]	boundary_simplex_map	A map from simplices of dimension \((d-m+1)\) in the ambient triangulation that intersect the boundary of the manifold to the intersection points.
[in]	limit_dimension	The dimension of the constructed skeleton.

construct_complex() [3/4]

template<class Out_simplex_map_ >

void Gudhi::coxeter_triangulation::Cell_complex< Out_simplex_map_ >::construct_complex ( const Out_simplex_map_ &  out_simplex_map )

inline

Constructs the the cell complex that approximates an \(m\)-dimensional manifold without boundary embedded in the \( d \)-dimensional Euclidean space from the output of the class Gudhi::Manifold_tracing.

Parameters

[in]

out_simplex_map

A map from simplices of dimension \((d-m)\) in the ambient triangulation that intersect the relative interior of the manifold to the intersection points.

construct_complex() [4/4]

template<class Out_simplex_map_ >

void Gudhi::coxeter_triangulation::Cell_complex< Out_simplex_map_ >::construct_complex ( const Out_simplex_map_ &  out_simplex_map, std::size_t  limit_dimension  )

inline

Constructs the skeleton of the cell complex that approximates an \(m\)-dimensional manifold without boundary embedded in the \(d\)-dimensional Euclidean space up to a limit dimension from the output of the class Gudhi::Manifold_tracing.

Parameters

[in]	out_simplex_map	A map from simplices of dimension \((d-m)\) in the ambient triangulation that intersect the relative interior of the manifold to the intersection points.
[in]	limit_dimension	The dimension of the constructed skeleton.

interior_simplex_cell_map()

template<class Out_simplex_map_ >

const Simplex_cell_map& Gudhi::coxeter_triangulation::Cell_complex< Out_simplex_map_ >::interior_simplex_cell_map ( std::size_t  cell_d ) const

inline

Returns a map from the cells of a given dimension in the interior of the cell complex of type Gudhi::Hasse_cell to the permutahedral representations of the corresponding simplices in the ambient triangulation.

Parameters

[in]

cell_d

The dimension of the cells.

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

• include/gudhi/Coxeter_triangulation/Cell_complex/Cell_complex.h