[Gmsh] Zero volume elements in Delaunay 2d triangulation

[Jose Paulo Moitinho de Almeida]

On Monday 31 March 2008, you wrote:
> Jose Paulo Moitinho de Almeida a écrit :
> > Hello
> >
> > I know that the Delaunay triangulation is "experimental", but I was
> > solving the problem of face orientation when post-processing the mesh.
> >
> > Now, when refining the mesh around a singularity I came to an example
> > where I get
> >
> > $ gmsh ref.geo -algo del2d -2 -bgm ref.bgm
> > ....
> > Warning : Colinear points in circum circle computation
> > ....
> >
> > and the resulting mesh has triangles with colinear nodes.
>
> gmsh ref.geo -algo del2d -2 -bgm ref.bgm -rand 1.e-11
>
> gives a better result. Indeed your mesh has sizes that varies a lot, so it
> is better to perturbate less the points of the initial mesh. BTW, if you
> use nightly snapshots, try the "very very experimental"
>
>
> gmsh ref.geo -algo frontal -2 -bgm ref.bgm -rand 1.e-11
>
> that produce more regular meshes.
>
> JFR
>

Merci

With the -rand 1e-11 parameter and del2d I got fewer, but still some zero 
volume elements.

With the frontal algorithm it worked fine, but broke again on the next step, 
with zero volume elements and the message
Warning : Colinear points in circum circle computation

I know that I am reaching the limit for the precision of my numbers (the 
minimum characteristic length is 2.85e-9 in this case) and reducing the 
perturbation parameter results in 
Error   : 3 identical points in Qtest

(Two details)
While playing around I found that by doing the mesh from the command line
gmsh ref.geo -algo frontal -2 -rand 1.e-11 -bgm ref.xxx2
I get the warnings mentioned above, but if I use the gui
gmsh ref.geo -algo frontal -rand 1.e-11 -bgm ref.xxx2
I don't, though the zero volume elements are there.

When zoooooooooming in for these small elements it seems that some edges 
have "dissapeared" near the singular vertices. I could not understand if this 
has to do with the failure of the mesher or some (understandable) tolerance 
failure in the render process.

Regards

ZP