Searching...
No Matches
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.

## ◆ 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.

## ◆ 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.
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_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.
Examples
cell_complex_from_basic_circle_manifold.cpp.

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