CGAL users discussion list

["Laurent Rineau (CGAL/GeometryFactory)" <>]

On Saturday, January 5, 2019 1:53:50 PM CET Marc Alexa wrote:
> Dear all,
> 
> I am generating a tetrahedral mesh using the suite of algorithms in Mesh_3.
> I want to use the resulting mesh in my code, which is based on
> Triangulation_3. The vertex and cell base classes are incompatible. My
> preferred way for doing this would be writing the mesh to a file.
> Unfortunately, the formats of the stream operators are different. Is there
> an easy way to “reduce” what is being written by Mesh_3 to what is being
> expected by Triangulation_3?
> 
> On a side note: I understand that if I am not using sliver exudation, the
> triangulation generated by Mesh_3 will be Delaunay. This means I could
> export the points only (and then reconstruct the tetrahedra). Then I only
> need information on which tetrahedra are in the interior of the meshed
> surface.

Hi Marc,

Note that the trianguation is not a Delaunay triangulation, but a *weighted* 
Delaunay triangulation (call a regular triangulation). If your mesh domain 
does not have 1D featured curves, then all the weights will be 0, and then 
only the triangulation is equivalent to a Delaunay triangulation. (And as 
soon 
as you use the sliver exuder, then the non-zero weights reappear.)

> I tried to circumvent this by using a simple convex surface,
> namely a sphere. Yet even for the sphere some tetrahedra are excluded,
> despite clearly lying in the interior. I do understand that the excluded
> tetrahedra are slivers, but wouldn’t it make sense that a tetrahedral mesh
> with the boundary vertices on the sphere contained everything inside the
> sphere?

I agree that could be surprising, but that is not the definition of the 
Delaunay triangulation restricted to the mesh domain.

-- 
Laurent Rineau, PhD
R&D Engineer at GeometryFactory           http://www.geometryfactory.com/
Release Manager of the CGAL Project       http://www.cgal.org/