[Gmsh] Error : Self intersecting surface mesh, computing intersections (this could take a while)

Steffen Becker steffenbecker87 at yahoo.de
Tue Mar 18 21:47:28 CET 2014


What I just think about:
I just deleted all the lines in my elements-list where area is <= 
0.000000001. Doesn't that mean that I have small holes in my surface 
mesh now? How is Gmsh able to work with this? I just don't understand 
why this makes a difference compared to just check if area is = 0

Steffen

Am 18.03.2014 21:41, schrieb Steffen Becker:
> Hi,
> puh, that's weird:
> First I checked my triangles if their area is > 0 (to get the ones 
> which are aligned). This didn't helped as I said in my last mail. Now 
> I (just for fun) checked if the area > 0.000000001 and now it works - 
> but I don't know why this is such a difference?!
>
> Anyway, thanks for your help!
> Steffen
>
> Am 18.03.2014 10:57, schrieb Zenker, Dr. Matthias:
>>
>> Hi Steffen,
>>
>> there are still ill-defined triangles, e.g. 2319, 2320, 2321. You can 
>> find that out by yourself by inspecting your mesh with gmsh in the 
>> way I described in my last mail.
>>
>> Remark: checking "surface faces" can help to examine the surface.
>>
>> HTH,
>>
>> Matthias
>>
>> *Von:*Steffen Becker [mailto:steffenbecker87 at yahoo.de]
>> *Gesendet:* Montag, 17. März 2014 22:39
>> *An:* Zenker, Dr. Matthias
>> *Cc:* Roman Fratczak; gmsh at geuz.org
>> *Betreff:* Re: [Gmsh] Error : Self intersecting surface mesh, 
>> computing intersections (this could take a while)
>>
>> Hi Matthias,
>>
>> thank you for your help!
>> I think I successfully deleted all the triangles with zero surface. 
>> Unfortunately the same error still appears (but at least with much 
>> less intersections). You find my new .msh file in the appendix. Do 
>> you have more ideas?
>>
>> Regards,
>> Steffen
>>
>> Am 17.03.2014 11:37, schrieb Zenker, Dr. Matthias:
>>
>>     Hi Steffen,
>>
>>     I think you have ill-defined triangles in your mesh. For example,
>>     there is a triangle 15328 which contains the nodes 7358, 7359,
>>     and 7360. But these nodes are aligned, so the triangle has zero
>>     surface. I would suspect this kind of problem to be the cause for
>>     the failure. I discovered that by examining your mesh after
>>     merging the intersect.pos, and by displaying node labels and
>>     surface labels in gmsh. I saw that this triangle was not visible,
>>     just its label, and searched for "15328" in your msh file to see
>>     what nodes it contains.
>>
>>     You should make sure that this kind of thing cannot happen when
>>     you define the surface mesh.
>>
>>     HTH,
>>
>>     Matthias
>>
>>     *Von:*Steffen Becker [mailto:steffenbecker87 at yahoo.de]
>>     *Gesendet:* Montag, 17. März 2014 11:20
>>     *An:* Zenker, Dr. Matthias
>>     *Cc:* Roman Fratczak; gmsh at geuz.org <mailto:gmsh at geuz.org>
>>     *Betreff:* Re: [Gmsh] Error : Self intersecting surface mesh,
>>     computing intersections (this could take a while)
>>
>>     Here it is.
>>
>>     Am 17.03.2014 11:14, schrieb Zenker, Dr. Matthias:
>>
>>         Hi Steffen,
>>
>>         I found out: Outlook is wrong.
>>
>>         I just discovered a small info saying that Outlook thinks
>>         that my_file.msh is insecure and that it has deleted the
>>         attachment (Grrrr). So the fault was on my side, sorry. Could
>>         you try to send it again with a changed extension, e.g.
>>         rename it to my_file.msh.txt?
>>
>>         Matthias
>>
>>         *Von:*Steffen Becker [mailto:steffenbecker87 at yahoo.de]
>>         *Gesendet:* Montag, 17. März 2014 10:55
>>         *An:* Zenker, Dr. Matthias
>>         *Cc:* Roman Fratczak; gmsh at geuz.org <mailto:gmsh at geuz.org>
>>         *Betreff:* Re: [Gmsh] Error : Self intersecting surface mesh,
>>         computing intersections (this could take a while)
>>
>>         Hi Matthias,
>>
>>         I don't know what's wrong here.
>>         When I check my mails, there is a .msh file in the mail from
>>         12.03.2014 18:21 and also one in the mail from 14.03.2014 12:33.
>>         Finally, I sent you again a .msh file in this mail. Do you
>>         receive it?
>>
>>         Steffen
>>
>>
>>         Am 17.03.2014 09:52, schrieb Zenker, Dr. Matthias:
>>
>>             Hi Steffen,
>>
>>             in the mail you mention there is only a geo file...
>>
>>             Matthias
>>
>>             *Von:*Steffen Becker [mailto:steffenbecker87 at yahoo.de]
>>             *Gesendet:* Freitag, 14. März 2014 21:09
>>             *An:* Zenker, Dr. Matthias
>>             *Cc:* Roman Fratczak; gmsh at geuz.org <mailto:gmsh at geuz.org>
>>             *Betreff:* Re: [Gmsh] Error : Self intersecting surface
>>             mesh, computing intersections (this could take a while)
>>
>>             Hi Matthias,
>>
>>             hm, I sent it on 12.03.2014 18:21, don't know what went
>>             wrong.
>>             As you see, I created a ASCII .msh file as explained in
>>             the documentation, so I hope it's correct.
>>             What can I do now?
>>
>>             Steffen
>>
>>             Am 14.03.2014 13:05, schrieb Zenker, Dr. Matthias:
>>
>>                 Hi Steffen,
>>
>>                 there was no msh file in any of your mails.
>>
>>                 Depending on what is in the msh file, your steps seem
>>                 correct to me.
>>
>>                 Matthias
>>
>>                 *Von:*Steffen Becker [mailto:steffenbecker87 at yahoo.de]
>>                 *Gesendet:* Freitag, 14. März 2014 12:33
>>                 *An:* Zenker, Dr. Matthias
>>                 *Cc:* Roman Fratczak; gmsh at geuz.org
>>                 <mailto:gmsh at geuz.org>
>>                 *Betreff:* Re: [Gmsh] Error : Self intersecting
>>                 surface mesh, computing intersections (this could
>>                 take a while)
>>
>>                 Hi Matthias,
>>
>>                 I think you are talking about your mail from
>>                 12.03.2014 09:59 ?
>>                 In one of my last mails I already sent you a
>>                 selfcreated .msh file - but the 3D mesh still failes.
>>                 The intersect.pos shows me some
>>
>>                 intersections, but when I check my nodes for
>>                 duplicates I can't find any.
>>                 Hope my steps are correct:
>>                 - create "my_file.msh" with my python script and
>>                 check it for nodes duplications -> none found
>>                 - open "my_file.geo" in Gmsh
>>                 - do "Modules" -> "Mesh" -> "3D"
>>                 - receive error message
>>                 - merge "intersect.pos" and see some intersections
>>                 but I don't know why because the are no duplicated nodes
>>
>>                 Steffen
>>
>>
>>                 Am 14.03.2014 09:50, schrieb Zenker, Dr. Matthias:
>>
>>                     Hi Steffen,
>>
>>                     you should be able to generate a filled volume
>>                     mesh if you follow my suggestion from the other mail:
>>
>>                     Write  the 2D mesh in gmsh format (e.g. as
>>                     outerface.msh, gmsh documentation for more info
>>                     on the msh format) and merge that one instead of
>>                     the myfile.ply2 file, leaving the other command
>>                     lines in your .geo file as they are. If you then
>>                     do a 3D mesh, gmsh will take the 2D mesh as
>>                     defined in your file. You can then refine the
>>                     mesh if you wish.
>>
>>                     HTH,
>>
>>                     Matthias
>>
>>                     *Von:*Steffen Becker
>>                     [mailto:steffenbecker87 at yahoo.de]
>>                     *Gesendet:* Mittwoch, 12. März 2014 20:00
>>                     *An:* Roman Fratczak
>>                     *Cc:* Zenker, Dr. Matthias; gmsh at geuz.org
>>                     <mailto:gmsh at geuz.org>
>>                     *Betreff:* Re: [Gmsh] Error : Self intersecting
>>                     surface mesh, computing intersections (this could
>>                     take a while)
>>
>>                     Hi,
>>
>>                     I'm so sorry for all time you spent with my
>>                     problem, but now I see: We talk at cross. It's my
>>                     fault, I didn't explained correctly what I need.
>>                     I want to receive a *filled* volume mesh.
>>                     I created 2 files (steffen.stl and steffen2.stl)
>>                     with my python script.
>>                     With steffen.stl I successfully could create such
>>                     a filled volume mesh as seen in steffen.msh.
>>                     When I try exactly the same with steffen2.stl
>>                     then I get the error message in the subject (and
>>                     the surface mesh doesn't get filled).
>>                     So that's why the .iges file you sent me isn't
>>                     what I need.
>>
>>                     Sorry for all this confusion,
>>                     Steffen
>>
>>
>>                     Am 12.03.2014 18:53, schrieb Roman Fratczak:
>>
>>                         Steffen,
>>
>>                         I did a volume based on your surface mesh -
>>                         see attached IGES (compressed with 7-zip).
>>                         After reading it into GMSH, you can create
>>                         the 1D, then 2D and finally 3D mesh with no
>>                         errors.
>>
>>                         You can do the same using GMSH volume
>>                         definition (as already wrote)-> it will work,
>>                         as the fundamental faces are plane triangles.
>>
>>                         Regards
>>                         Roman
>>
>>
>>                         W dniu 12.03.2014 18:27, Steffen Becker pisze:
>>
>>                             Wrong .geo file, sorry!
>>
>>                             Am 12.03.2014 18:21, schrieb Steffen Becker:
>>
>>                                 Thank you so far,
>>
>>                                 I create both files: .msh and .geo,
>>                                 but I still get the same error.
>>                                 What's my mistake?
>>
>>                                 Steffen
>>
>>                                 Am 12.03.2014 11:48, schrieb Roman
>>                                 Fratczak:
>>
>>                                     Hi,
>>
>>                                     FYI - you can remove double
>>                                     vertices/edges (or repair) in
>>                                     mesh in FreeCad (for exampe).
>>
>>                                     regards
>>                                     Roman
>>
>>
>>
>>                                     W dniu 12.03.2014 10:17, Steffen
>>                                     Becker pisze:
>>
>>                                         Hi Matthias & Roman,
>>
>>                                         I create a nodes- and
>>                                         elements-list like this:
>>                                         # nodes:
>>                                         N1 0,0,0
>>                                         N2 0,1,0
>>                                         N3 1,0,0
>>                                         N4 0,0,1
>>                                         # elements, which describe
>>                                         triangles:
>>                                         E1 1,2,3
>>                                         E2 2,3,4
>>
>>                                         So I do have double edges
>>                                         (here: between node 2+3).
>>                                         Didn't now that this is a
>>                                         problem for gmsh, sorry.
>>
>>                                         I will try Romans solution
>>                                         asap and give you a feedback.
>>                                         Thank you both!
>>
>>                                         Steffen
>>
>>
>>                                         Am 12.03.2014 09:59, schrieb
>>                                         Zenker, Dr. Matthias:
>>
>>                                             Hi Steffen,
>>
>>                                             I am not totally sure
>>                                             from what you wrote that
>>                                             there are really no
>>                                             duplicated nodes. In
>>                                             gmsh, you need to define
>>                                             the surfaces in a way
>>                                             that neighbouring
>>                                             surfaces/facets with a
>>                                             common border use the
>>                                             _/same/_ nodes to define
>>                                             the border. I could not
>>                                             see from your file if
>>                                             there are duplicated
>>                                             nodes, and would propose
>>                                             that you make sure that
>>                                             there are really no such
>>                                             duplications.
>>
>>                                             If the meshing still
>>                                             fails, then this is a
>>                                             question for the real
>>                                             gurus (Christophe?).
>>
>>                                             HTH,
>>
>>                                             Matthias
>>
>>                                             *Von:*Roman Fratczak
>>                                             [mailto:fratczakroman at o2.pl]
>>                                             *Gesendet:*Mittwoch, 12.
>>                                             März 2014 09:51
>>                                             *An:* Steffen Becker
>>                                             *Cc:* gmsh at geuz.org
>>                                             <mailto:gmsh at geuz.org>
>>                                             *Betreff:* Re: [Gmsh]
>>                                             Error : Self intersecting
>>                                             surface mesh, computing
>>                                             intersections (this could
>>                                             take a while)
>>
>>                                             Hi Steffen,
>>
>>                                             No it is more clear. If
>>                                             you are working with
>>                                             cloud of point, then you
>>                                             may use Meshlab for
>>                                             surface regeneration.
>>                                             There are many software
>>                                             that are able to handle
>>                                             in a resonable way the
>>                                             cloud of points (like
>>                                             rhino3D + resurf, other).
>>                                             But these are rather
>>                                             commercial.
>>
>>                                             From the other side - try
>>                                             to do the simplest thing:
>>
>>                                             Adjust your python script
>>                                             for surface creation in
>>                                             order to save not as PLY
>>                                             but as GMSH "geo" file
>>                                             using points and lines
>>
>>                                             Point(1)={0,0,0} ;
>>                                             Point(2)={0,1,0} ;
>>                                             ...
>>
>>                                             Line(1) = {1,2};
>>                                             ..
>>                                             and.. Line Loop & Surface
>>                                             -> Volume ..
>>
>>                                             Then you will get a
>>                                             volume defined by
>>                                             geometric entities. In
>>                                             this case is shoul be
>>                                             easier to create a better
>>                                             mesh on surface and then
>>                                             on whole volume.
>>
>>                                             Regards
>>                                             Roman
>>
>>
>>
>>                                             W dniu 11.03.2014 17:59,
>>                                             Steffen Becker pisze:
>>
>>                                                 Hi,
>>
>>                                                 @ Roman:
>>                                                 some more details:
>>                                                 I have a point cloud
>>                                                 given and generate
>>                                                 the surface mesh by
>>                                                 myself (with python).
>>                                                 I don't know a good
>>                                                 algorithm to create a
>>                                                 volume mesh out of
>>                                                 this surface mesh -
>>                                                 that's why I use gmsh
>>                                                 for this task.
>>                                                 I also checked my
>>                                                 surface mesh for
>>                                                 double vertexes but I
>>                                                 didn't find any. What
>>                                                 do you mean with
>>                                                 "double egdes"? Isn't
>>                                                 there always a
>>                                                 "double edge",
>>                                                 because two neighbour
>>                                                 facets always have
>>                                                 one same edge?!
>>
>>                                                 I will send you a
>>                                                 .step or .iges file
>>                                                 as soon as I figured
>>                                                 out how to handle the
>>                                                 "No OpenCASCADE model
>>                                                 found" error.
>>
>>                                                 I'm appending the
>>                                                 other mailing history
>>                                                 (with Matthias) to
>>                                                 this mail - sorry for
>>                                                 that "double
>>                                                 mailing", I just
>>                                                 forgot one time to
>>                                                 "reply to all" -.-
>>                                                 Anyone else has an
>>                                                 idea why the meshing
>>                                                 fails?
>>
>>                                                 Regards and thank you
>>                                                 a lot,
>>                                                 Steffen
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>                                                 Hi Steffen,
>>
>>                                                   
>>
>>                                                 I don't see either why the meshing fails, sorry.
>>
>>                                                   
>>
>>                                                 Matthias
>>
>>                                                   
>>
>>                                                 -----Ursprüngliche Nachricht-----
>>
>>                                                 Von: Steffen Becker [mailto:steffenbecker87 at yahoo.de]
>>
>>                                                 Gesendet: Dienstag, 11. März 2014 14:42
>>
>>                                                 An: Zenker, Dr. Matthias
>>
>>                                                 Cc:gmsh at geuz.org  <mailto:gmsh at geuz.org>
>>
>>                                                 Betreff: Re: [Gmsh] Error : Self intersecting surface mesh, computing
>>
>>                                                 intersections (this could take a while)
>>
>>                                                   
>>
>>                                                 Oh I'm really sorry, here is the file.
>>
>>                                                 In addition I sent you also the intersect.pos. I don't understand why exactly
>>
>>                                                 these surfaces are problematic and the "neighbour surfaces"
>>
>>                                                 aren't - although they have the same geometry =/
>>
>>                                                   
>>
>>                                                 Am 11.03.2014 12:07, schrieb Zenker, Dr. Matthias:
>>
>>                                                 Hi Steffen,
>>
>>                                                   
>>
>>                                                 if you don't provide the myfile.ply2, we cannot see your geometry...
>>
>>                                                   You can visualize intersect.pos by merging it to your geometry.
>>
>>                                                   
>>
>>                                                 HTH,
>>
>>                                                   
>>
>>                                                 Matthias
>>
>>                                                   
>>
>>                                                   
>>
>>                                                 Am 11.03.2014 14:33,
>>                                                 schrieb Roman Fratczak:
>>
>>                                                     Hello,
>>
>>                                                     It is possible,
>>                                                     that you will get
>>                                                     your geometry in
>>                                                     other format?
>>                                                     In your "ply"
>>                                                     there is already
>>                                                     a surface mesh
>>                                                     given. Try maybe
>>                                                     use STEP,
>>                                                     IGES,...  as
>>                                                     input- then it is
>>                                                     easer to
>>                                                     recalculate the
>>                                                     surface mesh.
>>
>>                                                     In case of need
>>                                                     of usage of "a
>>                                                     dead mesh" -
>>                                                     maybe try first
>>                                                     to remesh it
>>                                                     (i.e. in blender
>>                                                     with modification
>>                                                     Remesh) and/or
>>                                                     clean it
>>                                                     (removing double
>>                                                     vertexes and edges).
>>
>>                                                     regards
>>                                                     Roman
>>
>>
>>
>>
>>                                                     W dniu 11.03.2014
>>                                                     12:13, Steffen
>>                                                     Becker pisze:
>>
>>                                                         Hi,
>>
>>                                                         in the
>>                                                         appendix you
>>                                                         find my model.
>>                                                         Thanks for help!!
>>
>>                                                         Regards,
>>                                                         Steffen
>>
>>                                                         Am 11.03.2014
>>                                                         11:47,
>>                                                         schrieb Roman
>>                                                         Fratczak:
>>
>>                                                             Hello
>>                                                             Steffen,
>>
>>                                                             Yes. You
>>                                                             can try
>>                                                             to the
>>                                                             first
>>                                                             Optimize
>>                                                             quality
>>                                                             of tetra,
>>                                                             or all of
>>                                                             them
>>                                                             (just try).
>>
>>                                                             I don't
>>                                                             know how
>>                                                             your
>>                                                             model
>>                                                             looks
>>                                                             like. If
>>                                                             the
>>                                                             elements
>>                                                             on the
>>                                                             surface
>>                                                             are too
>>                                                             big, then
>>                                                             the solid
>>                                                             elements
>>                                                             (probably
>>                                                             tetragonal)
>>                                                             may be
>>                                                             with
>>                                                             intersecting
>>                                                             edges or
>>                                                             faces.
>>                                                             Therefore
>>                                                             the
>>                                                             reducing
>>                                                             size of
>>                                                             element
>>                                                             may help
>>                                                             (especially
>>                                                             on the
>>                                                             surfaces).
>>
>>                                                             Or- just
>>                                                             share
>>                                                             your
>>                                                             model
>>                                                             (ply) -in
>>                                                             order to
>>                                                             be more
>>                                                             precise.
>>
>>                                                             regards
>>                                                             Roman
>>
>>
>>
>>                                                             W dniu
>>                                                             10.03.2014 18:06,
>>                                                             Steffen
>>                                                             Becker pisze:
>>
>>                                                                 Hi Roman,
>>                                                                 when
>>                                                                 you
>>                                                                 say
>>                                                                 "enable
>>                                                                 option:
>>                                                                 optimize",
>>                                                                 you
>>                                                                 mean"
>>                                                                 Tools
>>                                                                 ->
>>                                                                 Options
>>                                                                 ->
>>                                                                 Mesh
>>                                                                 ->
>>                                                                 Advanced
>>                                                                 ->
>>                                                                 Optimize
>>                                                                 quality
>>                                                                 of
>>                                                                 tetrahedra,
>>                                                                 Optimize
>>                                                                 quality
>>                                                                 of
>>                                                                 tetrahedra
>>                                                                 with
>>                                                                 Netgen,
>>                                                                 Optimize
>>                                                                 high
>>                                                                 order
>>                                                                 meshes (experimental)"
>>                                                                 ?
>>                                                                 And
>>                                                                 why
>>                                                                 is
>>                                                                 reducing
>>                                                                 element
>>                                                                 size
>>                                                                 important?
>>                                                                 In my
>>                                                                 case
>>                                                                 it is
>>                                                                 important
>>                                                                 that
>>                                                                 the
>>                                                                 object has
>>                                                                 such
>>                                                                 "90
>>                                                                 degree corners".
>>
>>                                                                 Regards,
>>                                                                 Steffen
>>
>>                                                                 Am
>>                                                                 10.03.2014
>>                                                                 16:55, schrieb
>>                                                                 Roman
>>                                                                 Fratczak:
>>
>>                                                                     Hi Steffen,
>>
>>                                                                     If your
>>                                                                     volume
>>                                                                     is OK
>>                                                                     (is
>>                                                                     really
>>                                                                     a
>>                                                                     closed
>>                                                                     one)
>>                                                                     -
>>                                                                     try
>>                                                                     to:
>>
>>                                                                     1. Reduce
>>                                                                     element
>>                                                                     size
>>                                                                     (especially
>>                                                                     in a
>>                                                                     curved
>>                                                                     shapes)
>>                                                                     2. Enable
>>                                                                     option
>>                                                                     "Optimize"
>>                                                                     -
>>                                                                     in mesh
>>                                                                     options
>>
>>
>>                                                                     Regards
>>                                                                     Roman
>>
>>
>>
>>                                                                     W
>>                                                                     dniu
>>                                                                     10.03.2014
>>                                                                     16:41,
>>                                                                     Steffen
>>                                                                     Becker
>>                                                                     pisze:
>>
>>                                                                         Hello
>>                                                                         everyone,
>>
>>
>>                                                                         I'm
>>                                                                         a gmsh
>>                                                                         beginner
>>                                                                         and
>>                                                                         I want
>>                                                                         to
>>                                                                         create
>>                                                                         a 3D
>>                                                                         volume
>>                                                                         mesh
>>                                                                         out
>>                                                                         of
>>                                                                         a given
>>                                                                         surface-mesh
>>                                                                         but
>>                                                                         I got
>>                                                                         the
>>                                                                         error
>>                                                                         message
>>                                                                         as
>>                                                                         seen
>>                                                                         in
>>                                                                         the
>>                                                                         subject.
>>                                                                         You
>>                                                                         find
>>                                                                         my
>>                                                                         .geo
>>                                                                         file
>>                                                                         in
>>                                                                         the
>>                                                                         appendix.
>>
>>                                                                         Can
>>                                                                         anyone
>>                                                                         tell
>>                                                                         me
>>                                                                         what
>>                                                                         I have
>>                                                                         to
>>                                                                         do
>>                                                                         to
>>                                                                         create
>>                                                                         a 3D
>>                                                                         mesh?
>>                                                                         I even
>>                                                                         can't
>>                                                                         figure
>>                                                                         out
>>                                                                         where
>>                                                                         the
>>                                                                         intersection
>>                                                                         are
>>                                                                         located
>>                                                                         (don't
>>                                                                         know
>>                                                                         how
>>                                                                         to
>>                                                                         read
>>                                                                         the
>>                                                                         intersect.pos).
>>
>>                                                                         Sorry
>>                                                                         for
>>                                                                         my
>>                                                                         poor
>>                                                                         english.
>>
>>
>>                                                                         Regards,
>>
>>                                                                         Steffen
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
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>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
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>>
>>
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>>                 ERBE Elektromedizin GmbH
>>                 Firmensitz: 72072 Tuebingen
>>                 Geschaeftsfuehrer: Christian O. Erbe, Reiner Thede
>>                 Registergericht: Stuttgart HRB 380137
>>
>>
>>
>>             _____________________________________________________________________
>>             ERBE Elektromedizin GmbH
>>             Firmensitz: 72072 Tuebingen
>>             Geschaeftsfuehrer: Christian O. Erbe, Reiner Thede
>>             Registergericht: Stuttgart HRB 380137
>>
>>
>>
>>         _____________________________________________________________________
>>         ERBE Elektromedizin GmbH
>>         Firmensitz: 72072 Tuebingen
>>         Geschaeftsfuehrer: Christian O. Erbe, Reiner Thede
>>         Registergericht: Stuttgart HRB 380137
>>
>>
>>
>>     _____________________________________________________________________
>>     ERBE Elektromedizin GmbH
>>     Firmensitz: 72072 Tuebingen
>>     Geschaeftsfuehrer: Christian O. Erbe, Reiner Thede
>>     Registergericht: Stuttgart HRB 380137
>>
>>
>>
>> _____________________________________________________________________
>> ERBE Elektromedizin GmbH
>> Firmensitz: 72072 Tuebingen
>> Geschaeftsfuehrer: Christian O. Erbe, Reiner Thede
>> Registergericht: Stuttgart HRB 380137
>>
>

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