[vtkusers] Proving a surface mesh of closeness

[Dominik Szczerba]

I think for a simple (non-self-intersecting etc.) mesh it is enough for 
closedness if there are no boundary edges. No non-manifold edges proves 
topological correctness or 'simplicity', but is not required for closedness.

Dominik

On Thursday 09 October 2008 08:19:32 pm Marie-Gabrielle Vallet wrote:
> For a surface mesh, in the vtkFeatureEdges terminology :
>  - a boundary edge belongs to exactly one cell
>  - a manifold edge belongs to two cells
>  - a non-manifold edge belongs to 3 or more cells.
> A simple close surface has only manifold edges.
> BoundaryEdgesOn<http://www.vtk.org/doc/nightly/html/classvtkFeatureEdges.ht
>ml#d1db4f83238d8c67e1947d49b9cde809>()
> NonManifoldEdgesOn<http://www.vtk.org/doc/nightly/html/classvtkFeatureEdges
>.html#f500d450d2858feff66bf6d8ea445789>()
> ManifoldEdgesOff<http://www.vtk.org/doc/nightly/html/classvtkFeatureEdges.h
>tml#39683205bb877df465d166029307cbb8>()
> FeatureEdgesOff<http://www.vtk.org/doc/nightly/html/classvtkFeatureEdges.ht
>ml#bbe4158f8c4a8a29131e7e32637f563d>() should return an empty set.
>
> A simple open surface has boundary edges and may has manifold too.
> Having non-manifold edges means the surface intersects itself. It could
> still be close, but I guess you don't want to deal with...
>
>
> 2008/10/9 Dominik Szczerba <dominik at itis.ethz.ch>
>
> > Hmmm. Is a boundary edge of an open surface a non-manifold edge? It does
> > not
> > seem so, at least with the default settings.
> >
> > Dominik
> >
> > On Friday 03 October 2008 07:14:51 pm Marie-Gabrielle Vallet wrote:
> > > I think there is a easier way of checking the surface closeness. I mean
> > > using vtk facilities, instead of writing a (yet another) new algorithm.
> > >
> > > VTK library has algorithms to extract a mesh boundary, i.e. the set of
> > > faces (in 3D) or edges (in 2D) that are not shared by two cells. See
> > > vtkFeatureEdges. The mesh is close if and only if this set is empty. If
> >
> > it
> >
> > > not, you can visualize the holes that must still be closed.
> > >
> > > Pamela is trying to do the same thing today. Have a look at the thread
> >
> > "get
> >
> > > boundary triangles from a mesh" on this mailing list.
> > >
> > > By the way, Charles, are you sure you are not re-inventing the wheel ?
> > >
> > > Marie-Gabrielle
> > >
> > > >  Date: Fri, 3 Oct 2008 08:17:31 +0200
> > > >  From: Dominik Szczerba <dominik at itis.ethz.ch>
> > > >  Subject: Re: [vtkusers] Proving a surface mesh of closeness
> > > >  To: vtkusers at vtk.org
> > > >  Message-ID: <200810030817.31796.dominik at itis.ethz.ch>
> > > >  Content-Type: text/plain;  charset="utf-8"
> > > >
> > > >  If it is manifold then pick the 1st element and make sure each one
> > > > it has
> > >
> > > the
> > >
> > > >  proper number of neighbors (for triangles: 3). Mark the element as
> > >
> > > 'visited'
> > >
> > > >  and visit all his neighbors, repeating the procedure. At the end, if
> > >
> > > number
> > >
> > > >  of visited elements equals to number of elements in the mesh and all
> > > > have their expected neighbors the mesh is closed.
> > > >
> > > >  DS
> > > >
> > > >  On Friday 03 October 2008 02:48:59 am Charles Monty Burns wrote:
> > > >  > Hello,
> > > >  >
> > > >  > I repaired a surface mesh and want to prove whether the mesh is
> > > >  > totally closed or not. Save is save ...
> > > >  >
> > > >  > How can I do this?
> > > >  >
> > > >  > Greetings
> > > >
> > > >  --
> > > >  Dominik Szczerba, Ph.D.
> > > >  Computational Physics Group
> > > >  Foundation for Research on Information Technologies in Society
> > > >  http://www.itis.ethz.ch <http://www.itis.ethz.ch/>
> >
> > --
> > Dominik Szczerba, Ph.D.
> > Computational Physics Group
> > Foundation for Research on Information Technologies in Society
> > http://www.itis.ethz.ch



-- 
Dominik Szczerba, Ph.D.
Computational Physics Group
Foundation for Research on Information Technologies in Society
http://www.itis.ethz.ch