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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...

#include <include/gudhi/Coxeter_triangulation/Cell_complex/Cell_complex.h>

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_mapsinterior_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_mapsboundary_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_mapinterior_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_mapboundary_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_mapcell_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_mapcell_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.
Examples
cell_complex_from_basic_circle_manifold.cpp, manifold_tracing_custom_function.cpp, and manifold_tracing_flat_torus_with_boundary.cpp.

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_dimensionThe 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_dThe 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_mapA 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_mapA 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_mapA 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_mapA 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_dimensionThe 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_mapA map from simplices of dimension \((d-m)\) in the ambient triangulation that intersect the relative interior of the manifold to the intersection points.
Examples
cell_complex_from_basic_circle_manifold.cpp, and manifold_tracing_flat_torus_with_boundary.cpp.

◆ 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_mapA 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_dimensionThe 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_dThe dimension of the cells.
Examples
cell_complex_from_basic_circle_manifold.cpp.

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