CGAL users discussion list

["Sebastien Loriot (GeometryFactory)" <>]

 wrote:
> Thanks for the answer.
>
> But if I have to do this check manually, what's the purpose of the
> Polyhedron::is_closed() function? I thought this function is capable of
> doing this.
> And if I'm going to check this manually, why should I use the incremental
> builder? one then can create triangles from points, which is a lot simpler
> to implement (like my first example I wrote in this e-mail), and then do
> this check manually (while the check Polyhedron::is_closed() fails to give
> the right answer).
>
> Could you please explain what is_closed() function does? 
I am not an export of Polyhedron, I was not aware this function exists. 
I had a look at the code for the is_closed, and it is checking that no 
halfedge is on the boundary.
> and why I'm
> supposed to use the incremental builder for my task if I'm to do this
> check manually?
>
> Is there a shorter way to create my polyhedra than I'm taking?
>
> Thank you,
> Best regards,
> Samer Afach
>
> >  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
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