[Gmsh] surface reparametrization

Pierre JUILLARD pierre.juillard at gmail.com
Fri Sep 17 07:15:52 CEST 2010

```Dear Mrs Marchandise,

Following our previous mail discussion, and after reading of the paper "High
Quality Surface Remeshing Using Harmonic Maps", I have some additionnal
questions and I would greatly appreciate any help for a better understanding
of confusing subjects to me.

1) As you have been saying in a previous mail about the outputs of the
surface remeshing process:
>>  No the parametrization is not a kind of B-spline surface but a planar
surface (the surface has been flattened during the parametrization process)
If you remesh with the option -saveall, you will see a bunch of files that
show you the mapping u(x))
see for example UVX-idSurf.pos that shows the X coordinates of the initial
surface on the parametric plane UV.

I would like to know what kind of surface is actually shown on the right of
the pictures "1_surface1.png" & "2_plane1.png" enclosed here, and extracted
from the paper "High Quality Surface Remeshing Using Harmonic Maps" (shapes
displaying no mesh)? Are they in this case very fine meshes obtained after
the surface division step into surfaces of genus = 0?

2) I have also a question on the surface division step. The surface shown on
picture "1_surface1.png" presents if I understand correctly a genus g=0.
However, the subdivision returns finally 3 surfaces.
I guess that the subdivision step also split the surface into smaller ones
according sharp edges identification, am I wrong?
Then, the outer surface of the shape displayed on picture 1 has a genus 1
and should be split. Is that right?
However, I seem to miss something because as highlighted on picture
"3_plane2.png", the parametrization appears to be able to handle surfaces
with holes.
If till now, my understanding is correct, why couldn't it handle the outer
surfaces of "1_surface1.png" as a single one instead of 2?

3) If there does be a sharp edge identification step, I am curious about its
logic. Is there a reference toward a paper maybe presenting it?

4) In the paper, a benchmark is presented between different remeshing
methods.
The 2 first results present the performances of the surface remeshing based
on the harmonic mapping algorithm implemented in GMSH, but using two
different meshing algorithms: "meshadapt" and "del2d": is it possible to the
user to chose which one to use with the current implementation?
Currently which one is used?

5) Finally, I tried on a test case enclosed in teh 7zip archive: starting
from "testUnconnectedTria.stl", and I would have liked to obtain a quad mesh
Using GMSH 2.4.2, and the script "surfaceRemeshing.geo", I however obtain
the error message below.
Do you know what is wrong?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Info    : Running '/opt/aster/outils/gmsh surfaceRemeshing.geo -2'
Info    : Started on Thu Sep 16 22:10:08 2010
Info    : 29092 facets in solid 0
Error   : 'surfaceRemeshing.geo', line 4 : syntax error (;)
Info    : Meshing 1D...
Info    : Mesh 1D complete (0 s)
Info    : Meshing 2D...
Info    : Mesh 2D complete (0 s)
Info    : 15320 vertices 35204 elements
Info    : Writing 'surfaceRemeshing.msh'
Info    : Wrote 'surfaceRemeshing.msh'
Info    : Stopped on Thu Sep 16 22:11:33 2010
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

6) Also, do you know how I could ensure a quad mesh similar to the mesh:

appreciated.

Best regards,

Pierre

2010/8/17 Marchandise Emilie <emilie.marchandise at uclouvain.be>

> Hi,
>
> As I said in a previous post, I encounter problem with surface remeshing
> considering the following *.geo and *.msh files.
> Could someone help me on this topic?
> I tried with a quad mesh saved in a *.msh format, and the message console
> tells me there is a syntax error at line 6 of my *.geo file containing the
> remeshing commands.
> The *.geo file is actually very similar to the one given as exemple in the
> wiki.
>
>
> >> I didn't find the .geo file in the mailing list (only the msh files). I
> can try to see what's wrong if you send it by e-mail.
> The reparametrization has been written for trinagular meshes. So, if you
> have a quad mesh, you should first transform it into a triangular mesh.
>
> Also, would someone give us an advice about the difference between Harmonic
> or Conformal mapping in terms maybe of quality and speed? Or in which kind
> of cases one is better suited than the other.
>
> >> Harmonic map parametrize the surface onto a unit disk while conformal
> map is an open boundray  parametrization (which improves the quality of the
> mesh near the boundary). It is however a bit slower and requires gmsh
> compiled with petsc and slepc.
>
> I tried with a quad mesh saved in a *.msh format, and the message console
> tells me there is a syntax error at line 6 of my *.geo file containing the
> remeshing commands.
>
> >> You should try with triangle mesh
>
> Finally, I have a last question: if I understand well, the logic for
> remeshing is to reparametrize a surface before recreating a mesh. Does it
> mean that the 'new' mesh is realized on a kind of 'B-spline surfaces'
> (which
> would be the reparametrized surface)?
> If yes, is it possible to save this re-created surface in brep or step?
>
> >>  No the parametrization is not a kind of B-spline surface but a planar
> surface (the surface has been flattened during the parametrization process)
> If you remesh with the option -saveall, you will see a bunch of files that
> show you the mapping u(x))
> see for example UVX-idSurf.pos that shows the X coordinates of the initial
> surface on the parametric plane UV.
>
>
> Bests,
>
> Pierre
>
>
>
> ---------------------------------------------------
> Prof. Emilie Marchandise
> Université catholique de Louvain (UCL)
> Institute of Mechanics, Materials and Civil Engineering (iMMC)
> Center for Systems Engineering and Applied Mechanics (CESAME)
> Euler building, 4 avenue G. Lemaitre,
> B-1348 Louvain-la-neuve, BELGIUM
> Tel: 010/47.23.53
> e-mail: emilie.marchandise at uclouvain.be
>
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