CGAL users discussion list

[Sean McDuffee <>]

But wait isn't a 3D Delaunay triangulation of an input surface mesh (set of points) a tet mesh that covers the convex hull of the original surface? 

 It's ok that the connectivity changes on the input mesh.  That is in fact exactly what I want.  I'm remeshing to get a better (close to isotropic) triangulation and Chen and Xu showed that for a given vertex set the 3D Delaunay triangulation optimizes the triangulation from this regard.

Thanks and regards,
Sean

On Wed, Apr 1, 2009 at 1:37 PM, Sean McDuffee <> wrote:

k will try

On Wed, Apr 1, 2009 at 8:34 AM, Mariette Yvinec <> wrote:

Sean McDuffee wrote:

Ok - I'll try once more.

This is for remeshing of an input mesh.  I need to be able to compute a 3D Delaunay Triangulation on a set of vertices, then access the cells around each vertex.  Would it be best to read in the vertex positions of my original mesh by using insert from a vector<Point_3>'s I built into a Triangulation_hiearchy_3 to get the Delaunay triangulation?  Is there a good way for marking my original points in the triangulation?

OK - I try an answer.

If you compute a Delaunay triangulation with the vertices of your input mesh,
you will get a triangulation with those vertices only,
so there is no use to mark them .... However this won't solve your meshing problem: there is no guarantee
that you find the faces of your input mesh in the Delaunay triangulation of the vertices.

If I understand well, what you need is a remesh of a polyhedral surface.
Although the remeshing of polyhedral surface is not yet in cgal,
you can find this functionality in an undocumented feature available in the
Polyhedron demo  (see CGAL documnetation chapter 39, section 5).
The volume mesher is not yet available, will most probably appear in the next release.
If you wish to have your input vertices appear as vertices
in the ouput mesh, you have to input them into the initial
3D Delaunay triangulation pointed to by the c2t3 argument of
the make_surface_mesh function.

I would like to then iterate through those points and possibly output an iterator over neighboring cells finite_incident_cells?  Does this sound reasonable?  Is there a more efficient way to do any of this?

Thanks,
Sean

On Tue, Mar 31, 2009 at 12:21 PM, Sean McDuffee <> wrote:

Anybody?

On Mon, Mar 30, 2009 at 1:01 PM, Sean McDuffee <> wrote:

Yes, I'm trying to remesh an input surface mesh.  I'm following Pierre Alliez's paper for variational tet meshing.  I want to compute the Delaunay triangulation for a given inputted vertex set and then for that given connectivity move the vertices.  I was hoping to use CGAL to compute the triangulation and also to use 1-ring circulators to get the info I need to move the vertices.  I don't need the entire tet mesh though.  Only a well triangulated surface is what I desire in the end.

Thanks for all the help,

Sean

On Mon, Mar 30, 2009 at 12:15 PM, Mariette Yvinec <> wrote:

Most probably what is wanted here
is a remesh of the input surface mesh

Laurent Rineau (GeometryFactory) wrote:

On Monday 30 March 2009 16:45:02 Sean McDuffee wrote:
  

Hi,

I'd like to input a surface mesh and compute it's Delaunay triangulation.
It seems I should use Polyhedron_incremental_builder_3 for reading in the
.obj file.  This will fill out a Polyhedron_3.  For a triangulation I guess
I need to somehow insert this Poly data structure into a
Delaunay_Triangulation_3 with the original Polyhedron_3 as a
SurfaceMeshComplex_2InTriangulation_3 and then use the make_surface_mesh
function to get a mesh I can output back to a .obj.  Can someone tell me if
this is the right track?  I don't seem to know how to exactly put this
together.
    

You can compute the Delaunay triangulation of *a set of points*, and not from 
a surface mesh. Maybe your surface mesh is included in the triangulation, as a 
subset of facets, but that is not the general case. If you are sure that all 
the faces of your surface are a union of facets of the Delaunay triangulation 
of its vertices, then you can compute the Delaunay triangulation of the 
vertices of the surface, and then manually mark the surface in a c2t3. I do 
not see the interest. I think I have misunderstood your goal.

  

-- 
Mariette Yvinec
Geometrica project team
INRIA  Sophia-Antipolis  


        

-- 
Mariette Yvinec
Geometrica project team
INRIA  Sophia-Antipolis