CGAL users discussion list

[Mariette Yvinec <>]

 wrote:
> I am interested in knowing how general the Triangulation_3 class is.  It 
> requires that the triangulation be a triangulation of a 4-sphere;  the basic 
> idea is that the triangulation is a finite triangulation of some convex body 
> together with a point at infinity.
>
> In some cases it would be possible to extend a tetrahedral mesh of a 
> nonconvex body to a mesh of the convex hull of the mesh vertices, but I 
> believe it is not always possible to do this without adding new vertices.  
> For example, consider a tetrahedral mesh with a hole in the shape of a 
> Schonhardt polyhedron.
>   
right
> Is there a known way to use Triangulation_3 to represent arbitrary conformal 
> tetrahedral meshes by ignoring validity checks or adding tetrahedra and 
> vertices to the mesh?
>   
No
> I noticed that "3D Triangulations and Meshes" is a work in progress.  Should 
> I wait for that item to be completed?  What is the current status of that development 
> item?
>   
The 3D Triangulations and Meshes will hopefully appear in a few months
with the next public release of CGAL.
It will provide mesh generation tools for 3D domains whose boundary surfaces
are defined in various way :
implicit surfaces,
polyhedral surfaces,
grey level or segmented 3D images.
Unless you are willing to remesh the domain you are interested in,
(you could  consider its bounding surface as a polyhedral
surface)
I don't think it will solve your problem ...

> Thanks much,
> Evan VanderZee
> Mathematics/CSE Graduate Student
> University of Illinois at Urbana-Champaign
>   

--
Mariette Yvinec
Geometrica project team
INRIA  Sophia-Antipolis