CGAL 5.1 - 2D Triangulation
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 CDT::Point Point;
typedef CGAL::Polygon_2<K> Polygon_2;
typedef CDT::Face_handle Face_handle;
void
mark_domains(CDT& ct,
Face_handle start,
int index,
std::list<CDT::Edge>& border )
{
if(start->info().nesting_level != -1){
return;
}
std::list<Face_handle> queue;
queue.push_back(start);
while(! queue.empty()){
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);
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::Face_handle f : cdt.all_face_handles()){
f->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();
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 (Face_handle f : cdt.finite_face_handles())
{
if ( f->info().in_domain() ) ++count;
}
std::cout << "There are " << count << " facets in the domain." << std::endl;
return 0;
}