[Gmsh] Zero volume elements in Delaunay 2d triangulation

[Jose Paulo Moitinho de Almeida]

On Tuesday 01 April 2008, Jean-François Remacle wrote:
> Jose Paulo Moitinho de Almeida a écrit :
> > On Monday 31 March 2008, you wrote:
> >> Jose Paulo Moitinho de Almeida a écrit :
> >>> Hello
> >>>
> ....
> >
> > With the -rand 1e-11 parameter and del2d I got fewer, but still some zero
> > volume elements.
>
> This is strange, because I do not have that pb here with the files you gave
> us.
>
> I tryed
>
> gmsh ref.geo -algo del2d -2 -bgm ref.bgm -rand 1.e-11 -statreport ref.stat
>
> and the worst element has an aspect ratio of 0.61
>
> I then tryed
>
> gmsh ref.geo -algo del2d -2 -bgm ref.bgm -rand 1.e-9 -append_statreport
> ref.stat
>
> and the worst element has an aspect ratio of 0. (sliver)
>

I tried now and it worked. But doing so many tests I may have lost one 
background mesh. I will be alert to see if it appears again.


> > 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
>
> No problem here, the stats look very much the same.

Sorry. I explained it too fast. It broke on the following step, for a 
background mesh which I did not send (attached now), with dimensions that are 
a bit exaggerated.

>
> > 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
>
> Yes, you cannot generate a mesh with gmsh with such a ratio of
> characteristic lengths.
> In the files you gave us, the ratio was about 10-6.
>
> > (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.
>
> The warnings are ther, in the message console window of gmsh

You are right. I was expecting that the console would pop up, but posted 
without checking that. 

(It pops up for an error, but not for a warning, correct?)

>
> > 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.
>
> I cannot observe that here.
>

I got the attached screenshot with the following command
gmsh ref.geo -algo frontal -bgm ref.xxx2 -rand 1.e-11
which produces "wrong elements" and was just wondering what is the cause of 
the "missing edges".

Regards and thanks again

ZP
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