[vtkusers] Volumetric Method for Mesh Generation

[Matthieu Ferrant]

Hi,

> BTW, do one of you know any pointers to papers describing a way to robustly
> fill (approximate) the space (volume) between two surfaces with
> tetrahedrons ? For example, given two 3D reconstruction corresponding to
> two anatomic tissues, approximate the volume between both tissues with
> tetrahedrons ? FEM purposes for example.
If you just have the two surfaces, you need to look into Delaunay-based
algorithms. There's plenty of that kind of algorithms out there, but
only few of them do ok on complicated structures (e.g. anatomical
structures). I ran into this problem 3 years ago. At that time, all
publicly available software I tried would either fail or generate far
too many elements (e.g. millions of tets !). The only one that works
really well is the one by P.L.George (INRIA rocquencourt), who really
seems to be a meshing champion. His software is sold by a spin-off and a
single research license costs 150k French Francs ! If it is a one-time
shot, you can send them your surface meshes, they'll mesh them for free.
But if you have very regular, quite convex surfaces, you can look for
software at :
http://www.andrew.cmu.edu/user/sowen/mesh.html. If I remember well, the
GRUMMP works quite well, and it has tools for improving the quality of
your meshes if the ultimate goal is to do FE analysis.

If you have the image data the surfaces were generated from, there is a
paper by Nielson for tetrahedrizing volumes. It was published at the
IEEE conf on Visualization '97 pp 221-228 : "Interval volume
Tetrahedrization". It is a volumetric generalization of the marching
tetrahedra.

I have implemented a version of this algorithm myself, with a
possibility to refine regions in the initial tetrahedral mesh depending
on the underlying image content up to a given level. The clipping to cut
the mesh along the boundary surfaces is done using a volumetric marching
tetrahedra approach with a case table. It is not a 
VTK class, but the algorithm spits out a vtk unstructured grid. There's
a rather complete description of my implementation in the paper at 
http://www.tele.ucl.ac.be/PEOPLE/mat/Papers/DGCI00/Paper.pdf.

I'd be happy to share the code (it is c code, easy to compile) if you
feel like giving it a try. You would not be the first one to use it,
other people have been  using it at the surgical planning lab in boston
(BWH, harvard), and at the medical imaging lab in leuven.

best,

matt

-- 
M.Ferrant - Ph.D. Student
UCL/TELE Room A-157 Place du Levant, 2 B-1348LLN - Belgium
Tel. +32-10-478073 Fax. : +32-10-472089
http://www.tele.ucl.ac.be/MEMBERS/Ferrant_Matthieu_e.html