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>

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.



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...


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

 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_ >
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_ >
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_ >
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 \((dm)\) 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 \((dm+1)\) 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 \((dm)\) 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 \((dm+1)\) 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_ >
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 \((dm)\) 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_ >
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 \((dm)\) 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_ >
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: