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Thank you for the fast answer.

This is actually mentioned in the manual, and this is why I'm surprised!
how could the program say they are halfedges while they're connected from
2 sides?

Anyone please, could you please tell me how to convert 2 halfedges to an
edge? I guess this would solve the problem and make my polyhedron closed!

Thank you,
Samer Afach

> 
>  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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>>>>>
>>>>
>>>>
>>>
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>>>
>>
>>
>>
>
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