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cell_complex_from_basic_circle_manifold.cpp
#include <iostream>
#include <gudhi/Coxeter_triangulation.h>
#include <gudhi/Implicit_manifold_intersection_oracle.h> // for Gudhi::coxeter_triangulation::make_oracle
#include <gudhi/Manifold_tracing.h>
#include <gudhi/Coxeter_triangulation/Cell_complex/Cell_complex.h>
#include <gudhi/Functions/Function_Sm_in_Rd.h>
using namespace Gudhi::coxeter_triangulation;
int main(int argc, char** argv) {
// Oracle is a circle of radius 1
// Define a Coxeter triangulation.
Coxeter_triangulation<> cox_tr(oracle.amb_d());
// Theory forbids that a vertex of the triangulation lies exactly on the circle.
// Add some offset to avoid algorithm degeneracies.
cox_tr.change_offset(-Eigen::VectorXd::Random(oracle.amb_d()));
// For a better manifold approximation, one can change the circle radius value or change the linear transformation
// matrix.
// The number of points and edges will increase with a better resolution.
//cox_tr.change_matrix(0.5 * cox_tr.matrix());
// Manifold tracing algorithm
using Out_simplex_map = typename Manifold_tracing<Coxeter_triangulation<> >::Out_simplex_map;
std::vector<Eigen::VectorXd> seed_points(1, oracle.seed());
Out_simplex_map interior_simplex_map;
manifold_tracing_algorithm(seed_points, cox_tr, oracle, interior_simplex_map);
// Constructing the cell complex
std::size_t intr_d = oracle.amb_d() - oracle.cod_d();
Cell_complex<Out_simplex_map> cell_complex(intr_d);
cell_complex.construct_complex(interior_simplex_map);
// List of Hasse_cell pointers to retrieve vertices values from edges
std::map<Cell_complex<Out_simplex_map>::Hasse_cell*, std::size_t> vi_map;
std::size_t index = 0;
std::clog << "Vertices:" << std::endl;
for (const auto& cp_pair : cell_complex.cell_point_map()) {
std::clog << index << " : (" << cp_pair.second(0) << ", " << cp_pair.second(1) << ")" << std::endl;
vi_map.emplace(cp_pair.first, index++);
}
std::clog << "Edges:" << std::endl;
for (const auto& sc_pair : cell_complex.interior_simplex_cell_map(1)) {
Cell_complex<Out_simplex_map>::Hasse_cell* edge_cell = sc_pair.second;
for (const auto& vi_pair : edge_cell->get_boundary()) std::clog << vi_map[vi_pair.first] << " ";
std::clog << std::endl;
}
return 0;
}
Data structure to store a cell in a Hasse diagram.
Definition: Hasse_diagram_cell.h:49
A class that constructs the cell complex from the output provided by the class Gudhi::coxeter_triangu...
Definition: Cell_complex.h:38
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 ...
Definition: Cell_complex.h:315
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::...
Definition: Cell_complex.h:289
void construct_complex(const Out_simplex_map_ &out_simplex_map)
Constructs the the cell complex that approximates an -dimensional manifold without boundary embedded ...
Definition: Cell_complex.h:199
A class that stores Coxeter triangulation of type . This triangulation has the greatest simplex quali...
Definition: Coxeter_triangulation.h:45
void change_offset(const Eigen::VectorXd &offset)
Change the offset vector to a given value.
Definition: Freudenthal_triangulation.h:113
A class that assembles methods for manifold tracing algorithm.
Definition: Manifold_tracing.h:39
A class for the function that defines an m-dimensional implicit sphere embedded in the d-dimensional ...
Definition: Function_Sm_in_Rd.h:27