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

Steffen Becker steffenbecker87 at yahoo.de
Thu Mar 20 21:42:11 CET 2014


Thank you a lot!
I couldn't yet find out why/where I create those ill-defined triangles, 
but that's not you problem ;-P

I have one last question:
Can you tell me in a short, easy way the algorithm how Gmsh creates new 
nodes inside the given surface-mesh?

Regards,
Steffen

Am 19.03.2014 09:15, schrieb Zenker, Dr. Matthias:
>
> Hi Steffen,
>
> the difference between 0 and 0.0000000001 might be a rounding error.
>
> Now if you have holes in your surface if you just delete all 
> ill-defined triangles, I don't know. It depends on how you made your 
> triangulation. IMO it would be better to make sure that such triangles 
> are not even be created.
>
> Matthias
>
> *Von:*Steffen Becker [mailto:steffenbecker87 at yahoo.de]
> *Gesendet:* Dienstag, 18. März 2014 21:47
> *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)
>
> 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 <mailto: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
>
>
>
>
>
>
>
>
>
>
>
>                                                                                 _______________________________________________
>
>                                                                                 gmsh mailing list
>
>                                                                                 gmsh at geuz.org  <mailto:gmsh at geuz.org>
>
>                                                                                 http://www.geuz.org/mailman/listinfo/gmsh
>
>
>
>
>
>
>
>
>
>
>
>
>                                                                             _______________________________________________
>
>                                                                             gmsh mailing list
>
>                                                                             gmsh at geuz.org  <mailto:gmsh at geuz.org>
>
>                                                                             http://www.geuz.org/mailman/listinfo/gmsh
>
>
>
>
>
>
>
>
>
>
>
>
>                                                                         _______________________________________________
>
>                                                                         gmsh mailing list
>
>                                                                         gmsh at geuz.org  <mailto:gmsh at geuz.org>
>
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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
>
>
>
>             _____________________________________________________________________
>             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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