CGAL users discussion list

["Sebastien Loriot (GeometryFactory)" <>]

 wrote:
> Thank you so much for your answer.
>
> but I still have 1 unclear issue. I've seen that that example creates a
> triangle, meaning a surface. What if I want to create a closed polyhedron
> (like a cube or a tetrahedron)? as a general question I would like to ask,
> is CGAL able to form a "closed" polyhedron and know that it's closed in an
> automatic manner? because as I drew in my first problem, I created the
> surfaces, but the program wasn't able to detect that it's a closed
> polyhedron (while it's of course closed, since I followed the same simple
> point-structure of the example).
>
> How can I tell CGAL to confirm (not check) that my polyhedron is closed,
> so that if I use the check function Polyhedron::is_closed() I would get
> the right answer?
>
> Is the incremental builder the right tool for that task?
>
> Thank you again,
>
> Best Regards,
> Samer Afach

First note that Polyhedron can only be used to represent one or more 
surfaces.

In the example joint, I manually create a tetrahedron to show that the
incremental builder add faces in a clever way (halfedge are reused when
you add a facet). The number of halfedges is 12.

To know if your surface is closed, you can rely on the theorem of
classification of surface and the Euler characteristic
(http://en.wikipedia.org/wiki/Euler_characteristic).

The Euler characteristic is 2 for each closed surface encoded by the 
polyhedron (the for each is really important here).


S.




> > Hello,
> >
> >  From what I understand you probably need to use the
> > Polyhedron_incremental_builder_3.
> >
> > Have a look here for the documentation (there is an example at the end
> > of the page)
> > http://www.cgal.org/Manual/last/doc_html/cgal_manual/Polyhedron_ref/Class_Polyhedron_incremental_builder_3.html
> >
> > S.
> >
> >
> >
> >  wrote:
> > > Dear programmers,
> > >
> > > I've drawn this question but no one has given me an answer. I would
> > > really
> > > appreciate it so much if someone could even give me a hint to solve this
> > > problem. It's really very important for me.
> > >
> > > Thank you in advance,
> > >
> > > Sincerely,
> > > Samer
> > >
> > > ---------------------------- Original Message
> > > ----------------------------
> > > Subject: [cgal-discuss] Tetrahedron-Polyhedron problem
> > > From:    "Samer Afach" 
> > > <>
> > > Date:    Fri, March 12, 2010 5:15 pm
> > > To:      
> > >
> > > --------------------------------------------------------------------------
> > >
> > > Hello :),
> > >
> > > I'm starting to create some simple polyhedra in order to go to bigger
> > > applications, and so I'm trying to understand how this library works
> > > with it.
> > >
> > > I have a problem, the problem is that I'm failing to create 4 triangles
> > > and form a tetrahedron from them. I'm avoiding using the function
> > > Polyhedron::make_tetrahedron(...) because my aim in the future is
> > > creating random polyhedra by combining triangles and check whether they
> > > are closed and fulfill some conditions. Here's my program:
> > >
> > > #include <CGAL/Homogeneous.h>
> > > #include <CGAL/Polyhedron_traits_with_normals_3.h>
> > > #include <CGAL/Polyhedron_3.h>
> > > #include <iostream>
> > > #include <algorithm>
> > >
> > > using namespace std;
> > >
> > > struct Normal_vector
> > > {
> > >     template <class Facet>
> > >     typename Facet::Plane_3 operator()( Facet& f) {
> > >     typename Facet::Halfedge_handle h = f.halfedge();
> > >     // Facet::Plane_3 is the normal vector type. We assume the
> > >     // CGAL Kernel here and use its global functions.
> > >     return CGAL::cross_product(
> > >     h->next()->vertex()->point() - h->vertex()->point(),
> > >     h->next()->next()->vertex()->point() -
> > > h->next()->vertex()->point());
> > >     }
> > > };
> > >     typedef CGAL::Homogeneous<int> Kernel;
> > >     typedef Kernel::Point_3 Point_3;
> > >     typedef Kernel::Vector_3 Vector_3;
> > >     typedef CGAL::Polyhedron_traits_with_normals_3<Kernel> Traits;
> > >     typedef CGAL::Polyhedron_3<Traits> Polyhedron;
> > >     typedef Polyhedron::Halfedge_handle Halfedge_handle;
> > >     int main() {
> > >     Point_3 p( 1, 0, 0);
> > >     Point_3 q( 0, 1, 0);
> > >     Point_3 r( 0, 0, 1);
> > >     Point_3 s( 0, 0, 0);
> > >     Polyhedron P;
> > >     //P.make_tetrahedron( p, q, r, s);
> > >
> > >     P.make_triangle(p,q,r);
> > >     P.make_triangle(p,r,s);
> > >     P.make_triangle(p,s,q);
> > >     P.make_triangle(q,s,r);
> > >
> > >     if(P.is_closed())
> > >     {
> > >         cout<<"It's closed"<<endl;
> > >     }
> > >     if(P.is_pure_trivalent())
> > >     {
> > >         cout<<"Trivalent"<<endl;
> > >     }
> > >     std::transform( P.facets_begin(), P.facets_end(), P.planes_begin(),
> > >     Normal_vector());
> > >     CGAL::set_pretty_mode( std::cout);
> > >     std::copy( P.planes_begin(), P.planes_end(),
> > >     std::ostream_iterator<Vector_3>( std::cout, "\n"));
> > >     return 0;
> > > }
> > >
> > > I copied this program from a sample in the manual. What's confusing me
> > > is that when I create a tetrahedron using the make_tetrahedron function,
> > > the conditions work fine, but I can't get the same output when creating
> > > a tetrahedron by "connecting" 3 dimensional triangles. I was even
> > > careful having the same output as the example (same order for the norms)
> > >
> > > Could anyone please tell me why that's happening, and I would appreciate
> > > it so much if someone also could apply the function
> > > Polyhedron::is_tetrahedron(Polyhedron::Halfedge_handle) also, because I
> > > failed to do it because I didn't know how to get the right call for
> > > Halfedge_handle.
> > >
> > > Sincerest regards,
> > > Samer Afach
> > > Institute of computational physics, University of Stuttgart
> >
> > --
> > You are currently subscribed to cgal-discuss.
> > To unsubscribe or access the archives, go to
> > https://lists-sop.inria.fr/wws/info/cgal-discuss

#include <CGAL/Simple_cartesian.h>
#include <CGAL/Polyhedron_incremental_builder_3.h>
#include <CGAL/Polyhedron_3.h>

// A modifier creating a triangle with the incremental builder.
template <class HDS>
class Build_triangle : public CGAL::Modifier_base<HDS> {
public:
    Build_triangle() {}
    void operator()( HDS& hds) {
        // Postcondition: `hds' is a valid polyhedral surface.
        CGAL::Polyhedron_incremental_builder_3<HDS> B( hds, true);
        B.begin_surface( 3, 1, 6);
        typedef typename HDS::Vertex   Vertex;
        typedef typename Vertex::Point Point;
        B.add_vertex( Point( 0, 0, 0));
        B.add_vertex( Point( 1, 0, 0));
        B.add_vertex( Point( 0, 1, 0));
        B.add_vertex( Point( 1, 1, 1));
        B.begin_facet();
        B.add_vertex_to_facet( 0);
        B.add_vertex_to_facet( 1);
        B.add_vertex_to_facet( 2);
        B.end_facet();
        B.begin_facet();
        B.add_vertex_to_facet( 1);
        B.add_vertex_to_facet( 3);
        B.add_vertex_to_facet( 2);
        B.end_facet();
      
        B.begin_facet();
        B.add_vertex_to_facet( 1);
        B.add_vertex_to_facet( 0);
        B.add_vertex_to_facet( 3);
        B.end_facet();

        B.begin_facet();
        B.add_vertex_to_facet( 0);
        B.add_vertex_to_facet( 2);
        B.add_vertex_to_facet( 3);
        B.end_facet();
      
        B.end_surface();
    }
};

typedef CGAL::Simple_cartesian<double>     Kernel;
typedef CGAL::Polyhedron_3<Kernel>         Polyhedron;
typedef Polyhedron::HalfedgeDS             HalfedgeDS;

int main() {
    Polyhedron P;
    Build_triangle<HalfedgeDS> triangle;
    P.delegate( triangle);
    //~ CGAL_assertion( P.is_triangle( P.halfedges_begin()));
    std::cout << P.size_of_halfedges () << std::endl;
  
    int v=P.size_of_vertices();
    int e=P.size_of_halfedges() / 2;
    int f=P.size_of_facets ();
    
 
    assert(v-e+f==2);
  
    return 0;
}