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/*
* Is_manifold.h
* Created on: Jan 28, 2015
* This file is part of the Gudhi Library. The Gudhi library
* (Geometric Understanding in Higher Dimensions) is a generic C++
* library for computational topology.
*
* Author(s): David Salinas
*
* Copyright (C) 2014 INRIA Sophia Antipolis-Mediterranee (France)
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*
*/
#ifndef UTILS_IS_MANIFOLD_H_
#define UTILS_IS_MANIFOLD_H_
#include "utils/UI_utils.h"
#include "utils/Edge_contractor.h"
/**
* Iteratively tries to anticollapse smallest edge non added so far.
* If its link is contractible then no topological change and else possible topological change.
*
* todo do a sparsification with some parameter eps while growing
*/
template<typename SkBlComplex> class Is_manifold {
private:
const SkBlComplex& input_complex_;
typedef typename SkBlComplex::Vertex_handle Vertex_handle;
public:
/*
* return dim the maximum dimension around one simplex and res which is true if the complex is a manifold.
* If the complex has dimension <= 3 then if res is false, the complex is not a manifold.
* For d-manifold with d>=4, res may be false while the complex is a manifold.
*/
Is_manifold(const SkBlComplex& input_complex, unsigned& dim, bool & res) : input_complex_(input_complex) {
res = true;
dim = -1;
if (!input_complex_.empty()) {
for (auto v : input_complex_.vertex_range()) {
dim = local_dimension(v);
break;
}
// check that the link of every vertex is a dim-1 sphere
for (auto v : input_complex_.vertex_range()) {
if (!is_k_sphere(v, dim - 1)) {
res = false;
break;
}
}
}
}
private:
unsigned local_dimension(Vertex_handle v) {
unsigned dim = 0;
for (const auto& s : input_complex_.star_simplex_range(v))
dim = (std::max)(dim, (unsigned) s.dimension());
return dim;
}
bool is_k_sphere(Vertex_handle v, int k) {
auto link = input_complex_.link(v);
Edge_contractor<Complex> contractor(link, link.num_vertices() - 1);
(void)contractor;
return (is_sphere_simplex(link) == k);
}
// A minimal sphere is a complex that contains vertices v1...vn and all faces
// made upon this set except the face {v1,...,vn}
// return -2 if not a minimal sphere
// and d otherwise if complex is a d minimal sphere
template<typename SubComplex>
int is_sphere_simplex(const SubComplex& complex) {
if (complex.empty()) return -1;
if (complex.num_blockers() != 1) return -2;
// necessary and sufficient condition : there exists a unique blocker that passes through all vertices
auto first_blocker = *(complex.const_blocker_range().begin());
if (first_blocker->dimension() + 1 != complex.num_vertices())
return -2;
else
return (first_blocker->dimension() - 1);
}
};
#endif // UTILS_IS_MANIFOLD_H_
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