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[Ianic <>]

Cells are oriented positively, see 

http://www.cgal.org/Manual/3.7-beta1/doc_html/cgal_manual/Triangulation_3/Chapter_main.html#Section_37.1

Facet is represented implicitly as a pair of 1) cell it belongs to and 2) an
opposite vertex number. So you can look at a facet from two adjacent cells
and therefore there is no orientation per se unless you enforce it somehow.
The way I did it is this. First, I make sure that I look at a facet from
within the domain of interest. Then I check the opposite vertex number i. If
it is even (i = 0 or 2), then the positive facet (i.e. with vertices
enumerated counterclockwise) will consist of cell vertices with numbers 

(i + 1) % 4, (i + 2) % 4, (i + 3) % 4.

Otherwise it should be

(i + 1) % 4, (i + 3) % 4, (i + 2) % 4.

If you output facets this way, you will have a consistent surface
orientation. Here is the portion of File_medit.h file that I edited to
output it this way:

  //-------------------------------------------------------
  // Facets
  //-------------------------------------------------------
  int number_of_triangles = c3t3.number_of_facets();
  if ( print_each_facet_twice )
    number_of_triangles += number_of_triangles;
  
  os << "Triangles" << std::endl
     << number_of_triangles << std::endl;

  for( Facet_iterator fit = c3t3.facets_begin();
       fit != c3t3.facets_end();
       ++fit)
  {
    const Facet f = ( c3t3.is_in_complex(fit->first) ) ? *fit :
c3t3.triangulation().mirror_facet(*fit);
    // facet vertices in CCW order
    const Vertex_handle& vh1 = f.first->vertex( (f.second + 1)%4 );

    const Vertex_handle& vh2 = (f.second % 2 != 1) ?
                               f.first->vertex( (f.second + 2)%4 ) :
                               f.first->vertex( (f.second + 3)%4 );
                               
    const Vertex_handle& vh3 = (f.second % 2 != 1) ?
                               f.first->vertex( (f.second + 3)%4 ) :
                               f.first->vertex( (f.second + 2)%4 );

    os << V[vh1] << " " << V[vh2] << " " << V[vh3] << " ";
    os << get(facet_pmap, f) << std::endl;
    
    // Print triangle again if needed
    if ( print_each_facet_twice )
    {
      os << V[vh1] << " " << V[vh2] << " " << V[vh3] << " ";
      os << get(facet_twice_pmap, f) << std::endl;
    }
  }

Hope this helps.


mparusinski wrote:
> 
> Actually how are the tetrahedra orientated and how are the facets
> orientated in CGAL?
> 

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