#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);
    }
  }
}

void insert_polygon(CDT& cdt,const Polygon_2& polygon){
  if ( polygon.is_empty() ) return;
  CDT::Vertex_handle v_prev=cdt.insert(*CGAL::cpp11::prev(polygon.vertices_end()));
  for (Polygon_2::Vertex_iterator vit=polygon.vertices_begin();
       vit!=polygon.vertices_end();++vit)
  {
    CDT::Vertex_handle vh=cdt.insert(*vit);
    cdt.insert_constraint(vh,v_prev);
    v_prev=vh;
  }  
}

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 polyons into a constrained triangulation
  CDT cdt;
  insert_polygon(cdt,polygon1);
  insert_polygon(cdt,polygon2);
  
  //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;
}
