CGAL users discussion list

[Mariette Yvinec <>]

If I understand well,
Bruce would like to mesh a polyhedral domain
while getting in the resulting mesh the original vertices
of the input polyhedron and an accurate representation
of the input polyhedron edges.

Therefore, the Polyhedral_mesh_domain_with_features_3 oracle
would do.
Simply, once the mesh is generated, Bruce should not
access it through the triangulation but through the C3T3
and he should use the API of this class to sort out the
tetrahedra  of the triangulation that belong to the meshed domain.

I hope this helps,
Mariette


Le 10/05/11 13:53, Bruce Duncan a écrit :

Hi Laurent,

On Friday 06 May 2011 17:09:46 Laurent Rineau (GeometryFactory) wrote:

On jeudi 05 mai 2011 19:06:47 Bruce Duncan wrote:

Let me know if images or code would help clarify what I'm trying to do.

Yes, sure! Your message is rather imprecise.

I'm not very good at getting my point across clearly. Please bear with me!

I've attached a NEF file (and a PNG of one view of it) which may help me to 
describe what I mean.

Hi all,

I am writing a mesh generator with quite specific requirements. As a
result, I need to output a polyhedron in CGNS format.

I can do the CGNS output very easily if I have a set of tetrahedra. In
fact I have already implemented this to output a Triangulation_3.

At first I tried to use Triangulation_3 and it's siblings directly.
However, they don't take into account edges and my concave polyhedra are
destroyed in the process of triangulation. Is there a way around this?

What have you tried exactly? How did you "use Triangulation_3"?

std::vector<Nef_polyhedron::Point_3> points;
for (Nef_polyhedron::Vertex_const_iterator it = N_[x][y][z].vertices_begin(); 
it != N_[x][y][z].vertices_end(); ++it)
    points.push_back(it->point());
Delaunay_triangulation T(points.begin(), points.end());

and then I have a loop over finite cells of the triangulation and vertices of 
those cells which outputs the CGNS data.

Obviously, the concave polyhedra are made convex and the resulting mesh is 
wrong.

Is there a triangulation class which preserves concavity?

Is there a method to cut a concave 3D polyhedron into multiple 3D convex 
polyhedra?

Next, I turned to the Mesh_triangulation_3 class. This accepts a
Polyhedron and gives access to a Triangulation_3. Excellent! The problem
is that it does not respect the vertices and edges of the input
Polyhedron. My application really depends on having the vertices remain
in the same place. Other vertices and edges may be added, however. Is
there a way to achieve this?

The class Mesh_triangulation_3<Polyhedron>::type in itself is just a
regular triangulation with speciall vertex and cell types.

Let's assume you have used the function CGAL::make_mesh_3 or
CGAL::refine_mesh_3 to construct a 3D mesh from your polyhedron.

I have tried to use the Polyhedral_mesh_domain_with_features_3 class but
without much success... I may post a test case about that next week.

The 3D mesh generator, in CGAL, with features or not, will remesh the
polyhedral domain. If there are features, for examples sharp edges to
respect, then those features will remeshed. You cannot use the CGAL 3D
mesh generator in a way to respect the full set of vertices, edges, and
facets of the input polyhedron.

OK thanks. I think the Mesh generator is unusable for my case.

If you explain better what you want to achieve, maybe we could suggest you
other ways to do. What is that mesh generator you want to write? What are
its requirements?

I am writing a cartesian cut cell grid generator. Given an arbitrary 
polyhedron (the "solid"), the generator must produce a grid which is mostly 
cartesian (the "fluid" region) with "cut" cells where the solid intersects a 
cartesian cell. A cut cell is a tetrahedral 3D mesh with facets which match 
those of the adjacent solid or fluid cells, but they don't have to map one-to-
one.

If it might help, and if you have the time, there is a paper describing the 
method: Developments in Cartesian cut cell methods, D.M.Ingram, Mathematics 
and Computers in Simulation 61 (2003) [1].

Thanks for your help!
Bruce

[1] 
http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V0T-460DH92-
B&_user=809099&_coverDate=01%2F30%2F2003&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1746953179&_rerunOrigin=scholar.google&_acct=C000043939&_version=1&_urlVersion=0&_userid=809099&md5=5f20a5f5b14d167766d7b4ad21f23a82&searchtype=a

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-- 
Mariette Yvinec
Geometrica project team
INRIA  Sophia-Antipolis