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[N2a <>]

Hello, 
I was making tests on the mesh 2D generation and I have 2 things I do not
understand.
I run a constrained triangulation on a non convex hull. The boundary is
constrained.

Problem 1: I iterate over FINITE faces and when I print the vertex index for
each one I get three faces (over more than 1000) with the infinite vertex 0.
Problem 2: Each triangle have a positive signed area. I want to isolate the
mesh from the triangulated part. Do I miss something in the boundary
orientation?  

Thank You in advance,
Benjamin

Here is the a piece of code:
Declaration are the ones of the mesh_global.cpp example.

  std::map<Vertex_handle,int> vertex_index;
  int idx = 0;
  int nn=cdt.number_of_vertices();
  std::vector<Vertex_handle> TV(nn);
  int ii=0;
  for(CDT::Vertex_iterator vit=cdt.vertices_begin(); vit !=
cdt.vertices_end(); ++vit)  
   {
           vertex_index[vit]=idx++;
                TV[ii++]=vit;
   }

   for (i=1; i<= nn-1; ++i) 
   { 
             output << TV[i]->point() << std::endl;          
   }

   for(CDT::Finite_faces_iterator fit=cdt.finite_faces_begin(); fit !=
cdt.finite_faces_end(); ++fit)  
   {
        int i0 = vertex_index[fit->vertex(0)];
        int i1 = vertex_index[fit->vertex(1)];
        int i2 = vertex_index[fit->vertex(2)];
        output << i0 << " "<< i1 << " " << i2 << " " ;
        
         Triangle_2 Tri_2(TV[i0]->point(),TV[i1]->point(),TV[i2]->point());
         output2 << Tri_2.area() << std::endl;
   }
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