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cgal/Surface_mesh_topology/include/CGAL/Curves_on_surface_topology.h

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// Copyright (c) 2019 CNRS and LIRIS' Establishments (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
// 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.
//
// Licensees holding a valid commercial license may use this file in
// accordance with the commercial license agreement provided with the software.
//
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// $URL$
// $Id$
// SPDX-License-Identifier: GPL-3.0+
//
// Author(s) : Guillaume Damiand <guillaume.damiand@liris.cnrs.fr>
//
#ifndef CGAL_CURVES_ON_SURFACE_TOPOLOGY_H
#define CGAL_CURVES_ON_SURFACE_TOPOLOGY_H 1
// Should be defined before to include Path_on_surface_with_rle.h
// If nothing is defined, use V1
// #define CGAL_PWRLE_TURN_V1 // Compute turns by turning (method of CMap)
// #define CGAL_PWRLE_TURN_V2 // Compute turns by using an id of darts, given by an hash-table (built and given by Curves_on_surface_topology)
#define CGAL_PWRLE_TURN_V3 // Compute turns by using an id of darts, associated in Info of Darts (build by Curves_on_surface_topology)
#include <CGAL/license/Surface_mesh_topology.h>
#include <CGAL/Union_find.h>
#include <CGAL/Random.h>
#include <CGAL/Path_on_surface.h>
#include <CGAL/Surface_mesh_topology/internal/Path_on_surface_with_rle.h>
#include <CGAL/Surface_mesh_topology/internal/Path_generators.h>
#include <CGAL/Combinatorial_map_operations.h>
#include <CGAL/Timer.h>
#include <CGAL/Face_graph_wrapper.h>
#include <boost/unordered_map.hpp>
#include <stack>
#include <iostream>
namespace CGAL {
namespace Surface_mesh_topology {
struct CMap_for_homotopy_tester_items
{
template <class CMap>
struct Dart_wrapper
{
#ifdef CGAL_PWRLE_TURN_V3
typedef std::size_t Dart_info;
#endif // CGAL_PWRLE_TURN_V3
typedef CGAL::cpp11::tuple<> Attributes;
};
};
typedef CGAL::Combinatorial_map<2, CMap_for_homotopy_tester_items>
CMap_for_homotopy_tester;
template<typename Mesh>
class Curves_on_surface_topology
{
public:
typedef typename CMap_for_homotopy_tester::Dart_handle
Dart_handle;
typedef typename CMap_for_homotopy_tester::Dart_const_handle
Dart_const_handle;
typedef CGAL::Union_find<Dart_handle> UFTree;
typedef typename UFTree::handle UFTree_handle;
typedef typename Get_map<Mesh, Mesh>::type Map;
typedef CGAL::Union_find<typename Map::Dart_const_handle> UFTree2;
typedef typename UFTree2::handle UFTree_handle2;
// Associate each dart of the original map, not removed, a pair of darts in the
// reduced map.
typedef boost::unordered_map<typename Map::Dart_const_handle,
std::pair<Dart_const_handle, Dart_const_handle> > TPaths;
#ifdef CGAL_PWRLE_TURN_V2
typedef boost::unordered_map<Dart_const_handle, std::size_t> TDartIds;
#endif //CGAL_PWRLE_TURN_V2
Curves_on_surface_topology(const Mesh& amap, bool display_time=false) :
m_original_map(amap)
{
if (!m_map.is_without_boundary(1))
{
std::cerr<<"ERROR: the given amap has 1-boundaries; "
<<"such a surface is not possible to process here."
<<std::endl;
return;
}
if (!m_map.is_without_boundary(2))
{
std::cerr<<"ERROR: the given amap has 2-boundaries; "
<<"which are not yet considered (but this will be done later)."
<<std::endl;
return;
}
CGAL::Timer t, t2;
if (display_time)
{ t.start(); t2.start(); }
// The mapping between darts of the original map into the copied map.
boost::unordered_map<typename Map::Dart_const_handle, Dart_handle>
origin_to_copy;
// The mapping between darts of the copy into darts of the original map.
boost::unordered_map<Dart_handle, typename Map::Dart_const_handle>
copy_to_origin;
// We copy the original map, while keeping mappings between darts.
// m_map.copy(m_original_map, &origin_to_copy, &copy_to_origin);
if (display_time)
{
t2.stop();
std::cout<<"[TIME] Copy map: "<<t2.time()<<" seconds"<<std::endl;
t2.reset(); t2.start();
}
// We reserve the two marks (used to mark darts in m_original_map that
// belong to T or to L)
m_mark_T=m_original_map.get_new_mark();
m_mark_L=m_original_map.get_new_mark();
/* std::cout<<"Number of darts in m_map: "<<m_map.number_of_darts()
<<"; number of darts in origin_to_copy: "<<origin_to_copy.size()
<<"; number of darts in copy_to_origin: "<<copy_to_origin.size()
<<std::endl; */
// 1) We simplify m_map in a surface with only one vertex
surface_simplification_in_one_vertex(origin_to_copy, copy_to_origin);
if (display_time)
{
t2.stop();
std::cout<<"[TIME] Simplification in one vertex: "
<<t2.time()<<" seconds"<<std::endl;
t2.reset(); t2.start();
}
#ifdef CGAL_TRACE_CMAP_TOOLS
std::cout<<"All non loop contracted: ";
m_map.display_characteristics(std::cout) << ", valid="
<< m_map.is_valid() << std::endl;
/* std::cout<<"Number of darts in m_map: "<<m_map.number_of_darts()
<<"; number of darts in origin_to_copy: "<<origin_to_copy.size()
<<"; number of darts in copy_to_origin: "<<copy_to_origin.size()
<<std::endl; */
#endif
// 2) Now we compute each length two path associated with each edge that does
// not belong to the spanning tree (which are thus all the survival edges).
compute_length_two_paths(origin_to_copy);
if (display_time)
{
t2.stop();
std::cout<<"[TIME] Computation of length two paths: "
<<t2.time()<<" seconds"<<std::endl;
t2.reset(); t2.start();
}
/* std::cout<<"Number of darts in m_map: "<<m_map.number_of_darts()
<<"; number of darts in origin_to_copy: "<<origin_to_copy.size()
<<"; number of darts in copy_to_origin: "<<copy_to_origin.size()
<<std::endl; */
/* std::cout<<"Paths are all valid 1 ? "<<(are_paths_valid()?"YES":"NO")
<<std::endl; */
// 3) We simplify m_map in a surface with only one face
surface_simplification_in_one_face(origin_to_copy, copy_to_origin);
if (display_time)
{
t2.stop();
std::cout<<"[TIME] Simplification in one face: "
<<t2.time()<<" seconds"<<std::endl;
t2.reset(); t2.start();
}
#ifdef CGAL_TRACE_CMAP_TOOLS
std::cout<<"All faces merges: ";
m_map.display_characteristics(std::cout) << ", valid="
<< m_map.is_valid() << std::endl;
/* std::cout<<"Number of darts in m_map: "<<m_map.number_of_darts()
<<"; number of darts in origin_to_copy: "<<origin_to_copy.size()
<<"; number of darts in copy_to_origin: "<<copy_to_origin.size()
<<std::endl; */
#endif
if (!m_map.is_empty()) // m_map is_empty if the surface is a sphere
{
// 4) And we quadrangulate the face, except for the torus surfaces
if (m_map.darts().size()!=4)
{
surface_quadrangulate();
if (display_time)
{
t2.stop();
std::cout<<"[TIME] Face quadrangulation: "
<<t2.time()<<" seconds"<<std::endl;
t2.reset(); t2.start();
}
}
// Now we label all the darts of the reduced map, to allow the computation
// of turns in constant time: only for methods V2 and V3
#if defined(CGAL_PWRLE_TURN_V2) || defined(CGAL_PWRLE_TURN_V3)
CGAL_assertion(m_map.number_of_darts()%2==0);
Dart_handle dh1=m_map.darts().begin();
Dart_handle dh2=m_map.template beta<2>(dh1);
std::size_t id=0;
for(; dh1!=NULL; dh1=(dh1==dh2?NULL:dh2)) // We have two vertices to process
{
Dart_handle cur_dh=dh1;
do
{
#ifdef CGAL_PWRLE_TURN_V2
m_dart_ids[cur_dh]=id++;
#else // CGAL_PWRLE_TURN_V2
// Here we use CGAL_PWRLE_TURN_V3
m_map.info(cur_dh)=id++;
#endif // CGAL_PWRLE_TURN_V2
cur_dh=m_map.template beta<2, 1>(cur_dh);
}
while(cur_dh!=dh1);
}
if (display_time)
{
t2.stop();
std::cout<<"[TIME] Label darts: "<<t2.time()<<" seconds"<<std::endl;
}
#endif // defined(CGAL_PWRLE_TURN_V2) || defined(CGAL_PWRLE_TURN_V3)
}
#ifdef CGAL_TRACE_CMAP_TOOLS
std::cout<<"After quadrangulation: ";
m_map.display_characteristics(std::cout) << ", valid="
<< m_map.is_valid() << std::endl;
std::cout<<"Paths are all valid ? "<<(are_paths_valid()?"YES":"NO")
<<std::endl;
auto marktemp=m_map.get_new_mark();
Dart_handle dh2=NULL;
for (auto it=m_map.darts().begin(); it!=m_map.darts().end(); ++it)
{
if (!m_map.is_marked(it, marktemp))
{
std::cout<<"Degree="<<CGAL::template degree<Map, 0>(m_map, it)<<std::endl;
std::cout<<"Co-degree="<<CGAL::template codegree<Map, 2>(m_map, it)<<std::endl;
dh2=it;
do
{
m_map.mark(dh2, marktemp);
std::cout<<m_map.darts().index(dh2)<<" "
<<m_map.darts().index(m_map.template beta<0>(dh2))<<std::endl;
dh2=m_map.template beta<0,2>(dh2);
}
while(dh2!=it);
}
}
m_map.free_mark(marktemp);
m_map.display_darts(std::cout);
#endif
if (display_time)
{
t.stop();
std::cout<<"[TIME] Total time for computation of reduced map: "
<<t.time()<<" seconds"<<std::endl;
}
CGAL_assertion(m_map.darts().size()==4 || are_paths_valid()); // Because torus is a special case
}
~Curves_on_surface_topology()
{
m_original_map.free_mark(m_mark_T);
m_original_map.free_mark(m_mark_L);
}
/// @return true iff 'path' is contractible.
bool is_contractible(const Path_on_surface<Mesh>& p,
bool display_time=false) const
{
if (p.is_empty())
{ return true; }
if (!p.is_closed())
{
std::cerr<<"Error: is_contractible requires a closed path."<<std::endl;
return false;
}
if (m_map.is_empty())
{ return true; } // A closed path on a sphere is always contractible.
CGAL::Timer t;
if (display_time)
{ t.start(); }
bool res=false;
if (m_map.number_of_darts()==4)
{ // Case of torus
Path_on_surface<CMap_for_homotopy_tester>
pt=transform_original_path_into_quad_surface_for_torus(p);
int a, b;
count_edges_of_path_on_torus(pt, a, b);
res=(a==0 && b==0);
}
else
{
internal::Path_on_surface_with_rle<CMap_for_homotopy_tester>
pt=transform_original_path_into_quad_surface_with_rle(p);
pt.canonize();
res=pt.is_empty();
}
if (display_time)
{
t.stop();
std::cout<<"[TIME] is_contractible: "<<t.time()<<" seconds"
<<std::endl;
}
return res;
}
/// @return true iff 'path1' and 'path2' are freely homotopic.
bool are_freely_homotopic(const Path_on_surface<Mesh>& p1,
const Path_on_surface<Mesh>& p2,
bool display_time=false) const
{
if (p1.is_empty() && p2.is_empty()) { return true; }
if ((!p1.is_empty() && !p1.is_closed()) ||
(!p2.is_empty() && !p2.is_closed()))
{
std::cerr<<"Error: are_freely_homotopic requires two closed paths."
<<std::endl;
return false;
}
// Here we have two non empty closed paths.
if (m_map.is_empty())
{ return true; } // Two closed paths on a sphere are always homotopic.
CGAL::Timer t;
if (display_time)
{ t.start(); }
bool res=false;
if (m_map.number_of_darts()==4)
{ // Case of torus
Path_on_surface<CMap_for_homotopy_tester>
pt1=transform_original_path_into_quad_surface_for_torus(p1);
Path_on_surface<CMap_for_homotopy_tester>
pt2=transform_original_path_into_quad_surface_for_torus(p2);
int a1, a2, b1, b2;
count_edges_of_path_on_torus(pt1, a1, b1);
count_edges_of_path_on_torus(pt2, a2, b2);
res=(a1==a2 && b1==b2);
}
else
{
internal::Path_on_surface_with_rle<CMap_for_homotopy_tester>
pt1=transform_original_path_into_quad_surface_with_rle(p1);
internal::Path_on_surface_with_rle<CMap_for_homotopy_tester>
pt2=transform_original_path_into_quad_surface_with_rle(p2);
pt1.canonize();
pt2.canonize();
res=(pt1==pt2); // Do here to be counted in the computation time
#ifdef CGAL_TRACE_PATH_TESTS
std::cout<<"Length of reduced paths: "<<pt1.length()<<" and "
<<pt2.length()<<std::endl;
#endif
/* std::cout<<"path1="<<Path_on_surface<CMap_for_homotopy_tester>(path1)<<std::endl
<<"path2="<<Path_on_surface<CMap_for_homotopy_tester>(path2)<<std::endl;
Path_on_surface<CMap_for_homotopy_tester>(path1).display_pos_and_neg_turns(); std::cout<<std::endl;
Path_on_surface<CMap_for_homotopy_tester>(path2).display_pos_and_neg_turns(); std::cout<<std::endl;
path1.display_pos_and_neg_turns(); std::cout<<std::endl;
path2.display_pos_and_neg_turns(); std::cout<<std::endl; */
}
if (display_time)
{
t.stop();
std::cout<<"[TIME] are_freely_homotopic: "<<t.time()<<" seconds"<<std::endl;
}
return res;
}
/// @return true iff 'path1' and 'path2' are base point freely homotopic.
bool are_base_point_homotopic(const Path_on_surface<Mesh>& p1,
const Path_on_surface<Mesh>& p2,
bool display_time=false) const
{
if (p1.is_empty() && p2.is_empty()) { return true; }
if (p1.is_empty() || p2.is_empty()) { return false; }
if (!m_original_map.template belong_to_same_cell<0>(p1.front(), p2.front()) ||
!m_original_map.template belong_to_same_cell<0>(m_original_map.other_extremity(p1.back()),
m_original_map.other_extremity(p2.back())))
{
std::cerr<<"Error: are_base_point_homotopic requires two paths that"
<<" share the same vertices as extremities."<<std::endl;
return false;
}
if (m_map.is_empty())
{ return true; } // Two paths on a sphere are always base_point_homotopic.
CGAL::Timer t;
if (display_time)
{ t.start(); }
Path_on_surface<Mesh> path=p1;
Path_on_surface<Mesh> path2=p2; path2.reverse();
path+=path2;
bool res=is_contractible(path);
if (display_time)
{
t.stop();
std::cout<<"[TIME] are_base_point_homotopic: "<<t.time()<<" seconds."
<<std::endl;
}
return res;
}
const CMap_for_homotopy_tester& get_map() const
{ return m_map; }
protected:
void count_edges_of_path_on_torus
(const Path_on_surface<CMap_for_homotopy_tester>& path,
int& a, int& b) const
{
CGAL_assertion(m_map.number_of_darts()==4);
Dart_const_handle dha=m_map.darts().begin();
Dart_const_handle dhb=m_map.template beta<1>(dha);
a=0; b=0;
for (std::size_t i=0; i<path.length(); ++i)
{
if (path[i]==dha) { ++a; }
else if (path[i]==m_map.template beta<2>(dha)) { --a; }
else if (path[i]==dhb) { ++b; }
else if (path[i]==m_map.template beta<2>(dhb)) { --b; }
}
}
Path_on_surface<CMap_for_homotopy_tester>
transform_original_path_into_quad_surface_for_torus(const Path_on_surface<Mesh>& path) const
{
CGAL_assertion(m_map.number_of_darts()==4);
Path_on_surface<CMap_for_homotopy_tester> res(m_map);
if (path.is_empty()) return res;
Dart_const_handle cur;
for (std::size_t i=0; i<path.length(); ++i)
{
if (!m_original_map.is_marked(path[i], m_mark_T))
{
cur=get_first_dart_of_the_path(path[i], false);
while(cur!=get_second_dart_of_the_path(path[i], false))
{
res.push_back(cur, false);
cur=m_map.template beta<1>(cur);
}
}
}
res.update_is_closed();
CGAL_assertion(res.is_empty() || res.is_closed());
CGAL_assertion(res.is_valid());
return res;
}
internal::Path_on_surface_with_rle<CMap_for_homotopy_tester>
transform_original_path_into_quad_surface_with_rle
(const Path_on_surface<Mesh>& path) const
{
internal::Path_on_surface_with_rle<CMap_for_homotopy_tester>
res(m_map
#ifdef CGAL_PWRLE_TURN_V2
, m_dart_ids
#endif //CGAL_PWRLE_TURN_V2
);
if (path.is_empty()) return res;
for (std::size_t i=0; i<path.length(); ++i)
{
if (!m_original_map.is_marked(path[i], m_mark_T))
{
res.push_back(get_first_dart_of_the_path(path[i]), false);
res.push_back(get_second_dart_of_the_path(path[i]), false);
}
}
res.update_is_closed();
res.merge_last_flat_with_next_if_possible();
CGAL_assertion(res.is_closed());
CGAL_assertion(res.is_valid());
return res;
}
void initialize_vertices(UFTree2& uftrees,
boost::unordered_map
<typename Map::Dart_const_handle, UFTree_handle2>&
vertices)
{
uftrees.clear();
vertices.clear();
typename Map::size_type treated=m_original_map.get_new_mark();
for (typename Map::Dart_range::const_iterator
it=m_original_map.darts().begin(), itend=m_original_map.darts().end();
it!=itend; ++it)
{
if (!m_original_map.is_marked(it, treated))
{
UFTree_handle2 newuf=uftrees.make_set(it);
for (typename Map::
template Dart_of_cell_range<0>::const_iterator
itv=m_original_map.template darts_of_cell<0>(it).begin(),
itvend=m_original_map.template darts_of_cell<0>(it).end();
itv!=itvend; ++itv)
{
vertices[itv]=newuf;
m_original_map.mark(itv, treated);
}
}
}
m_original_map.free_mark(treated);
}
void initialize_faces(UFTree& uftrees,
boost::unordered_map<Dart_const_handle, UFTree_handle>&
faces)
{
uftrees.clear();
faces.clear();
typename CMap_for_homotopy_tester::size_type
treated=m_map.get_new_mark();
for (typename CMap_for_homotopy_tester::Dart_range::iterator
it=m_map.darts().begin(), itend=m_map.darts().end(); it!=itend;
++it)
{
if (!m_map.is_marked(it, treated))
{
UFTree_handle newuf=uftrees.make_set(it);
Dart_handle cur=it;
do
{
faces[cur]=newuf;
m_map.mark(cur, treated);
cur=m_map.template beta<1>(cur);
}
while (cur!=it);
}
}
m_map.free_mark(treated);
}
UFTree_handle get_uftree(const UFTree& uftrees,
const boost::unordered_map<Dart_const_handle,
UFTree_handle>& mapdhtouf,
Dart_const_handle dh) const
{
CGAL_assertion(dh!=NULL);
CGAL_assertion(mapdhtouf.find(dh)!=mapdhtouf.end());
return uftrees.find(mapdhtouf.find(dh)->second);
}
UFTree_handle2 get_uftree2(const UFTree2& uftrees,
const boost::unordered_map<typename Map::Dart_const_handle,
UFTree_handle2>& mapdhtouf,
typename Map::Dart_const_handle dh) const
{
// CGAL_assertion(dh!=NULL);
CGAL_assertion(mapdhtouf.find(dh)!=mapdhtouf.end());
return uftrees.find(mapdhtouf.find(dh)->second);
}
/// Mark the edge containing adart in the original map.
void mark_edge(const Map& amap, typename Map::Dart_const_handle adart,
std::size_t amark)
{
amap.mark(amap.template beta<2>(adart), amark);
amap.mark(adart, amark);
}
/// Erase the edge given by adart (which belongs to the map m_map) from the
/// associative array copy_to_origin, and erase the corresponding edge
/// (which belongs to the map m_original_map) from the array origin_to_copy
void erase_edge_from_associative_arrays
(Dart_handle adart,
boost::unordered_map<typename Map::Dart_const_handle, Dart_handle>&
origin_to_copy,
boost::unordered_map<Dart_handle, typename Map::Dart_const_handle>&
copy_to_origin)
{
origin_to_copy.erase(m_original_map.template beta<2>
(copy_to_origin[adart]));
origin_to_copy.erase(copy_to_origin[adart]);
copy_to_origin.erase(m_map.template beta<2>(adart));
copy_to_origin.erase(adart);
}
/// Step 1) Transform m_map into an equivalent surface having only one
/// vertex. All edges contracted during this step belong to the spanning
/// tree T, and thus corresponding edges in m_original_map are marked.
void surface_simplification_in_one_vertex
(boost::unordered_map<typename Map::Dart_const_handle, Dart_handle>&
origin_to_copy,
boost::unordered_map<Dart_handle, typename Map::Dart_const_handle>&
copy_to_origin)
{
UFTree2 uftrees; // uftree of vertices; one tree for each vertex,
// contains one dart of the vertex
boost::unordered_map<typename Map::Dart_const_handle, UFTree_handle2> vertices;
initialize_vertices(uftrees, vertices);
/* m_map.set_automatic_attributes_management(false);
for (typename CMap_for_homotopy_tester::Dart_range::iterator
it=m_map.darts().begin(), itend=m_map.darts().end();
it!=itend; ++it)
{
if (m_map.is_dart_used(it) &&
get_uftree(uftrees, vertices, it)!=
get_uftree(uftrees, vertices, m_map.template beta<2>(it)))
{
mark_edge(m_original_map, copy_to_origin[it], m_mark_T);
erase_edge_from_associative_arrays(it, origin_to_copy, copy_to_origin);
uftrees.unify_sets(get_uftree(uftrees, vertices, it),
get_uftree(uftrees, vertices,
m_map.template beta<2>(it)));
//m_map.template contract_cell<1>(it);
Dart_handle d1=it, d2=m_map.template beta<2>(it);
m_map.template link_beta<1>(m_map.template beta<0>(d1),
m_map.template beta<1>(d1));
m_map.template link_beta<1>(m_map.template beta<0>(d2),
m_map.template beta<1>(d2));
m_map.erase_dart(d1);
m_map.erase_dart(d2);
}
}
m_map.set_automatic_attributes_management(true); */
/* New version that does not need to first copy the map before to simplify it
*/
Dart_handle d1, d2;
for (typename Map::Dart_range::const_iterator
it=m_original_map.darts().begin(), itend=m_original_map.darts().end();
it!=itend; ++it)
{
if (typename Map::Dart_const_handle(it)<m_original_map.template beta<2>(it))
{
if (get_uftree2(uftrees, vertices, it)!=
get_uftree2(uftrees, vertices, m_original_map.template beta<2>(it)))
{
m_original_map.mark(m_original_map.template beta<2>(it), m_mark_T);
m_original_map.mark(it, m_mark_T);
uftrees.unify_sets(get_uftree2(uftrees, vertices, it),
get_uftree2(uftrees, vertices,
m_original_map.template beta<2>(it)));
}
else
{
d1=m_map.create_dart();
d2=m_map.create_dart();
m_map.template basic_link_beta_for_involution<2>(d1, d2);
origin_to_copy[it]=d1;
origin_to_copy[m_original_map.template beta<2>(it)]=d2;
copy_to_origin[d1]=it;
copy_to_origin[d2]=m_original_map.template beta<2>(it);
}
}
}
/// Now we only need to do the basic_link_beta_1
typename Map::Dart_const_handle dd1;
for (typename Map::Dart_range::const_iterator
it=m_original_map.darts().begin(), itend=m_original_map.darts().end();
it!=itend; ++it)
{
if (!m_original_map.is_marked(it, m_mark_T))
{
dd1=m_original_map.template beta<1>(it);
while(m_original_map.is_marked(dd1, m_mark_T))
{ dd1=m_original_map.template beta<1>(dd1); }
m_map.basic_link_beta_1(origin_to_copy[it], origin_to_copy[dd1]);
}
}
}
/// Step 2) Compute, for each edge of m_original_map not in the spanning
/// tree T, the pair of darts of the edge in m_copy. This pair of edges
/// will be updated later (in surface_simplification_in_one_face() and in
/// surface_quadrangulate() )
void compute_length_two_paths
(const boost::unordered_map<typename Map::Dart_const_handle, Dart_handle>&
origin_to_copy)
{
paths.clear();
for (typename Map::Dart_range::const_iterator
it=m_original_map.darts().begin(),
itend=m_original_map.darts().end(); it!=itend; ++it)
{
if (!m_original_map.is_marked(it, m_mark_T))
{
CGAL_assertion(!m_original_map.template is_free<2>(it));
if (typename Map::Dart_const_handle(it)<m_original_map.template beta<2>(it))
{
paths[it]=std::make_pair
(origin_to_copy.at(it),
m_map.template beta<2>(origin_to_copy.at(it)));
CGAL_assertion(paths[it].first!=paths[it].second);
CGAL_assertion(paths[it].first==m_map.template beta<2>(paths[it].second));
}
}
}
#ifdef CGAL_TRACE_CMAP_TOOLS
std::cout<<"Number of darts in paths: "<<paths.size()
<<"; number of darts in m_map: "<<m_map.number_of_darts()
<<std::endl;
#endif
}
/// Step 3) Transform the 2-map into an equivalent surface having only
/// one face. All edges removed during this step belong to the
/// dual spanning tree L (spanning tree of the dual 2-map).
void surface_simplification_in_one_face
(boost::unordered_map<typename Map::Dart_const_handle, Dart_handle>&
origin_to_copy,
boost::unordered_map<Dart_handle, typename Map::Dart_const_handle>&
copy_to_origin)
{
UFTree uftrees; // uftree of faces; one tree for each face,
// contains one dart of the face
boost::unordered_map<Dart_const_handle, UFTree_handle> faces;
initialize_faces(uftrees, faces);
m_map.set_automatic_attributes_management(false);
typename Map::size_type toremove=m_map.get_new_mark();
Dart_handle currentdart=NULL, oppositedart=NULL;
for (typename CMap_for_homotopy_tester::Dart_range::iterator
it=m_map.darts().begin(), itend=m_map.darts().end(); it!=itend;
++it)
{
currentdart=it;
CGAL_assertion(!m_map.template is_free<2>(currentdart)); // TODO later, support opened surfaces
oppositedart=m_map.template beta<2>(currentdart);
if (currentdart<oppositedart && !m_map.is_marked(currentdart, toremove))
{
// We remove degree two edges (we cannot have dangling edges
// because we had previously contracted all the non loop and thus
// we have only one vertex).
if (get_uftree(uftrees, faces, currentdart)!=
get_uftree(uftrees, faces, oppositedart))
{
// We cannot have a dangling edge
CGAL_assertion(m_map.template beta<0>(currentdart)!=oppositedart);
CGAL_assertion(m_map.template beta<1>(currentdart)!=oppositedart);
uftrees.unify_sets(get_uftree(uftrees, faces, currentdart),
get_uftree(uftrees, faces, oppositedart));
m_map.mark(currentdart, toremove);
m_map.mark(oppositedart, toremove);
mark_edge(m_original_map, copy_to_origin[currentdart], m_mark_L);
}
}
}
/* m_map.display_characteristics(std::cout) << ", valid="
<< m_map.is_valid() << std::endl;
m_map.display_darts(std::cout)<<std::endl; */
if (m_map.number_of_marked_darts(toremove)==m_map.number_of_darts())
{
// Case of sphere; all darts are removed.
paths.clear();
m_map.clear();
}
else
{
update_length_two_paths_before_edge_removals(toremove, copy_to_origin);
// We remove all the edges to remove.
for (typename CMap_for_homotopy_tester::Dart_range::iterator
it=m_map.darts().begin(), itend=m_map.darts().end(); it!=itend;
++it)
{
if (m_map.is_dart_used(it) && m_map.is_marked(it, toremove))
{
erase_edge_from_associative_arrays(it, origin_to_copy, copy_to_origin);
// TODO LATER (?) OPTIMIZE AND REPLACE THE REMOVE_CELL CALL BY THE MODIFICATION BY HAND
// OR DEVELOP A SPECIALIZED VERSION OF REMOVE_CELL
m_map.template remove_cell<1>(it);
}
}
}
m_map.set_automatic_attributes_management(true);
m_map.free_mark(toremove);
}
/// Step 4) quadrangulate the surface.
void surface_quadrangulate()
{
// Here the map has only one face and one vertex.
typename Map::size_type oldedges=m_map.get_new_mark();
m_map.negate_mark(oldedges); // now all edges are marked
// 1) We insert a vertex in the face.
// New edges created by the operation are not marked.
m_map.insert_cell_0_in_cell_2(m_map.darts().begin());
// m_map.display_darts(std::cout);
// 2) We update the pair of darts
// std::cout<<"************************************************"<<std::endl;
for (typename TPaths::iterator itp=paths.begin(), itpend=paths.end();
itp!=itpend; ++itp)
{
std::pair<Dart_const_handle, Dart_const_handle>& p=itp->second;
//std::cout<<"Pair: "<<m_map.darts().index(p.first)<<", "
// <<m_map.darts().index(p.second)<<std::flush;
p.first=m_map.template beta<0, 2>(p.first);
p.second=m_map.template beta<0>(p.second);
//std::cout<<" -> "<<m_map.darts().index(p.first)<<", "
// <<m_map.darts().index(p.second)<<std::endl;
}
// 3) We remove all the old edges.
for (typename CMap_for_homotopy_tester::Dart_range::iterator
it=m_map.darts().begin(), itend=m_map.darts().end(); it!=itend;
++it)
{
if (m_map.is_dart_used(it) && m_map.is_marked(it, oldedges))
{ m_map.template remove_cell<1>(it); }
}
m_map.free_mark(oldedges);
}
/// Update all length two paths, before edge removal. Edges that will be
/// removed are marked with toremove mark.
void update_length_two_paths_before_edge_removals
(typename Map::size_type toremove,
const boost::unordered_map<Dart_handle,
typename Map::Dart_const_handle>& copy_to_origin)
{
// std::cout<<"************************************************"<<std::endl;
for (auto it=m_original_map.darts().begin();
it!=m_original_map.darts().end(); ++it)
{
if (!m_original_map.is_marked(it, m_mark_T) &&
!m_original_map.is_marked(it, m_mark_L) &&
typename Map::Dart_const_handle(it)<m_original_map.template beta<2>(it))
{ // Surviving dart => belongs to the border of the face
std::pair<Dart_const_handle, Dart_const_handle>& p=paths[it];
Dart_handle initdart=m_map.darts().iterator_to
(const_cast<typename CMap_for_homotopy_tester::Dart &>
(*(p.first)));
Dart_handle initdart2=m_map.template beta<2>(initdart);
CGAL_assertion(initdart2==p.second);
CGAL_assertion(!m_map.is_marked(initdart, toremove));
CGAL_assertion(!m_map.is_marked(initdart2, toremove));
// 1) We update the dart associated with p.second
p.second=m_map.template beta<1>(initdart);
while (m_map.is_marked(p.second, toremove))
{ p.second=m_map.template beta<2, 1>(p.second); }
// 2) We do the same loop, linking all the inner darts with p.second
initdart=m_map.template beta<1>(initdart);
while (m_map.is_marked(initdart, toremove))
{
CGAL_assertion(copy_to_origin.count(initdart)==1);
typename Map::Dart_const_handle
d1=copy_to_origin.find(initdart)->second;
typename Map::Dart_const_handle
d2=m_original_map.template beta<2>(d1);
if (d1<d2) { paths[d1].first=p.second; }
else { paths[d2].second=p.second; }
initdart=m_map.template beta<2, 1>(initdart);
}
// 3) We do the same loop but starting from initdart2
initdart2=m_map.template beta<1>(initdart2);
Dart_handle enddart2=initdart2;
while (m_map.is_marked(enddart2, toremove))
{ enddart2=m_map.template beta<2, 1>(enddart2); }
while (m_map.is_marked(initdart2, toremove))
{
CGAL_assertion(copy_to_origin.count(initdart2)==1);
typename Map::Dart_const_handle
d1=copy_to_origin.find(initdart2)->second;
typename Map::Dart_const_handle
d2=m_original_map.template beta<2>(d1);
if (d1<d2) {
CGAL_assertion(paths.count(d1)==1);
paths[d1].first=enddart2;
}
else {
CGAL_assertion(paths.count(d2)==1);
paths[d2].second=enddart2;
}
initdart2=m_map.template beta<2, 1>(initdart2);
}
}
}
}
/// @return true iff the edge containing adart is associated with a path.
/// (used for debug purpose because we are suppose to be able to
/// test this by using directly the mark m_mark_T).
bool is_edge_has_path(typename Map::Dart_const_handle adart) const
{
typename Map::Dart_const_handle
opposite=m_original_map.template beta<2>(adart);
if (adart<opposite)
{
return paths.find(adart)!=paths.end();
}
return paths.find(opposite)!=paths.end();
}
/// @return the pair of darts associated with the edge containing adart
/// in m_original_map.
/// @pre the edge containing adart must not belong to T.
std::pair<Dart_const_handle, Dart_const_handle>& get_pair_of_darts
(typename Map::Dart_const_handle adart)
{
CGAL_assertion(!m_original_map.is_marked(adart, m_mark_T));
CGAL_assertion(is_edge_has_path(adart));
typename Map::Dart_const_handle
opposite=m_original_map.template beta<2>(adart);
if (adart<opposite)
{ return paths.find(adart)->second; }
return paths.find(opposite)->second;
}
Dart_const_handle get_first_dart_of_the_path
(typename Map::Dart_const_handle adart, bool withopposite=true) const
{
CGAL_assertion(!m_original_map.is_marked(adart, m_mark_T));
CGAL_assertion(is_edge_has_path(adart));
typename Map::Dart_const_handle
opposite=m_original_map.template beta<2>(adart);
if (adart<opposite)
{
const std::pair<Dart_const_handle, Dart_const_handle>&
p=paths.find(adart)->second;
return p.first;
}
const std::pair<Dart_const_handle, Dart_const_handle>&
p=paths.find(opposite)->second;
return (withopposite?m_map.template beta<2>(p.second):p.second);
}
Dart_const_handle get_second_dart_of_the_path
(typename Map::Dart_const_handle adart, bool withopposite=true) const
{
CGAL_assertion(!m_original_map.is_marked(adart, m_mark_T));
CGAL_assertion(is_edge_has_path(adart));
typename Map::Dart_const_handle
opposite=m_original_map.template beta<2>(adart);
if (adart<opposite)
{
const std::pair<Dart_const_handle, Dart_const_handle>&
p=paths.find(adart)->second;
return p.second;
}
const std::pair<Dart_const_handle, Dart_const_handle>&
p=paths.find(opposite)->second;
return (withopposite?m_map.template beta<2>(p.first):p.first);
}
/// Test if paths are valid, i.e.:
/// 1) all the darts of m_original_map that do not belong to T are
/// associated with a pair of darts;
/// 2) all the darts of the paths belong to m_map;
/// 3) the origin of the second dart of the pair is the extremity of the
/// first dart.
/// 4) all the darts of m_map are not free (both for beta 1 and 2)
/// 5) The two darts in a pair are different
bool are_paths_valid() const
{
if (paths.empty()) { return true; }
bool res=true;
for (auto it=m_original_map.darts().begin(),
itend=m_original_map.darts().end(); it!=itend; ++it)
{
if (!m_original_map.is_marked(it, m_mark_T))
{
if (!is_edge_has_path(it))
{
std::cout<<"ERROR: an edge that does not belong to the spanning "
<<"tree T has no associated path."<<std::endl;
res=false;
}
}
else
{
if (is_edge_has_path(it))
{
std::cout<<"ERROR: an edge that belongs to the spanning tree"
<<" T has an associated path."<<std::endl;
res=false;
}
}
}
for (auto it=m_map.darts().begin(),
itend=m_map.darts().end(); it!=itend; ++it)
{
if (m_map.is_free(it, 1))
{
std::cout<<"ERROR: a dart of the quandrangulated map is 1-free"
<<std::endl;
res=false;
}
if (m_map.is_free(it, 2))
{
std::cout<<"ERROR: a dart of the quandrangulated map is 2-free"
<<std::endl;
res=false;
}
}
for (auto it=paths.begin(); it!=paths.end(); ++it)
{
if (!m_map.is_dart_used(it->second.first))
{
std::cout<<"ERROR: first dart in paths does not exist anymore in m_map."
<<std::endl;
res=false;
}
else if (!m_map.darts().owns(it->second.first))
{
std::cout<<"ERROR: first dart in paths does not belong to m_map."
<<std::endl;
res=false;
}
if (!m_map.is_dart_used(it->second.second))
{
std::cout<<"ERROR: second dart in paths does not exist anymore in m_map."
<<std::endl;
res=false;
}
else if (!m_map.darts().owns(it->second.second))
{
std::cout<<"ERROR: second dart in paths does not belong to m_map."
<<std::endl;
res=false;
}
if (it->second.first==it->second.second)
{
std::cout<<"ERROR: two darts in the same pair are equal."
<<std::endl;
res=false;
}
}
for (auto it=m_original_map.darts().begin(),
itend=m_original_map.darts().end(); it!=itend; ++it)
{
if (!m_original_map.is_marked(it, m_mark_T))
{
Dart_const_handle d1=get_first_dart_of_the_path(it);
Dart_const_handle d2=get_second_dart_of_the_path(it);
if (d1==NULL || d2==NULL)
{
std::cout<<"ERROR: an edge is associated with a null dart in paths."
<<std::endl;
res=false;
}
else
{
Dart_const_handle dd1=m_map.other_extremity(d1);
CGAL_assertion(dd1!=NULL);
if (!CGAL::belong_to_same_cell<CMap_for_homotopy_tester,0>(m_map, dd1, d2))
{
std::cout<<"ERROR: the two darts in a path are not consecutive."
<<std::endl;
res=false;
}
}
}
}
return res;
}
protected:
const typename Get_map<Mesh, Mesh>::storage_type m_original_map; // The original map
CMap_for_homotopy_tester m_map; /// the transformed map
TPaths paths; /// Pair of edges associated with each edge of m_original_map
/// (except the edges that belong to the spanning tree T).
std::size_t m_mark_T; /// mark each edge of m_original_map that belong to the spanning tree T
std::size_t m_mark_L; /// mark each edge of m_original_map that belong to the dual spanning tree L
#ifdef CGAL_PWRLE_TURN_V2
TDartIds m_dart_ids; /// Ids of each dart of the transformed map, between 0 and n-1 (n being the number of darts)
/// so that darts between 0...(n/2)-1 belong to the same vertex and
/// d1=beta<1, 2>(d0), d2=beta<1, 2>(d1)...
/// The same for darts between n/2...n-1 for the second vertex
/// Thanks to these ids, we can compute in constant time the positive and
/// negative turns between two consecutive darts
#endif // CGAL_PWRLE_TURN_V2
};
} // namespace Surface_mesh_topology
} // namespace CGAL
#endif // CGAL_CURVES_ON_SURFACE_TOPOLOGY_H //
// EOF //
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