\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - 2D Triangulation

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Triangulation_2/polygon_triangulation.cpp
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Constrained_Delaunay_triangulation_2.h>
#include <CGAL/Triangulation_face_base_with_info_2.h>
#include <CGAL/Polygon_2.h>
#include <iostream>
struct FaceInfo2
{
FaceInfo2(){}
int nesting_level;
bool in_domain(){
return nesting_level%2 == 1;
}
};
typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
typedef CGAL::Triangulation_vertex_base_2<K> Vb;
typedef CGAL::Triangulation_face_base_with_info_2<FaceInfo2,K> Fbb;
typedef CGAL::Constrained_triangulation_face_base_2<K,Fbb> Fb;
typedef CGAL::Triangulation_data_structure_2<Vb,Fb> TDS;
typedef CGAL::Exact_predicates_tag Itag;
typedef CGAL::Constrained_Delaunay_triangulation_2<K, TDS, Itag> CDT;
typedef CDT::Point Point;
typedef CGAL::Polygon_2<K> Polygon_2;
void
mark_domains(CDT& ct,
CDT::Face_handle start,
int index,
std::list<CDT::Edge>& border )
{
if(start->info().nesting_level != -1){
return;
}
std::list<CDT::Face_handle> queue;
queue.push_back(start);
while(! queue.empty()){
CDT::Face_handle fh = queue.front();
queue.pop_front();
if(fh->info().nesting_level == -1){
fh->info().nesting_level = index;
for(int i = 0; i < 3; i++){
CDT::Edge e(fh,i);
CDT::Face_handle n = fh->neighbor(i);
if(n->info().nesting_level == -1){
if(ct.is_constrained(e)) border.push_back(e);
else queue.push_back(n);
}
}
}
}
}
//explore set of facets connected with non constrained edges,
//and attribute to each such set a nesting level.
//We start from facets incident to the infinite vertex, with a nesting
//level of 0. Then we recursively consider the non-explored facets incident
//to constrained edges bounding the former set and increase the nesting level by 1.
//Facets in the domain are those with an odd nesting level.
void
mark_domains(CDT& cdt)
{
for(CDT::All_faces_iterator it = cdt.all_faces_begin(); it != cdt.all_faces_end(); ++it){
it->info().nesting_level = -1;
}
std::list<CDT::Edge> border;
mark_domains(cdt, cdt.infinite_face(), 0, border);
while(! border.empty()){
CDT::Edge e = border.front();
border.pop_front();
CDT::Face_handle n = e.first->neighbor(e.second);
if(n->info().nesting_level == -1){
mark_domains(cdt, n, e.first->info().nesting_level+1, border);
}
}
}
int main( )
{
//construct two non-intersecting nested polygons
Polygon_2 polygon1;
polygon1.push_back(Point(0,0));
polygon1.push_back(Point(2,0));
polygon1.push_back(Point(2,2));
polygon1.push_back(Point(0,2));
Polygon_2 polygon2;
polygon2.push_back(Point(0.5,0.5));
polygon2.push_back(Point(1.5,0.5));
polygon2.push_back(Point(1.5,1.5));
polygon2.push_back(Point(0.5,1.5));
//Insert the polygons into a constrained triangulation
CDT cdt;
cdt.insert_constraint(polygon1.vertices_begin(), polygon1.vertices_end(), true);
cdt.insert_constraint(polygon2.vertices_begin(), polygon2.vertices_end(), true);
//Mark facets that are inside the domain bounded by the polygon
mark_domains(cdt);
int count=0;
for (CDT::Finite_faces_iterator fit=cdt.finite_faces_begin();
fit!=cdt.finite_faces_end();++fit)
{
if ( fit->info().in_domain() ) ++count;
}
std::cout << "There are " << count << " facets in the domain." << std::endl;
return 0;
}