Meshing is the task of partitioning a spatial domain into simple
geometric elements such as triangles (in 2D) or tetrahedrons (in
3D). Meshes typically have to conform to boundaries. Furthermore,
for many applications there are quality criteria that need to
be met, such as ensuring that angles are not too small. Meshing
is a huge industry, with dozens of companies selling meshing software,
hundreds of companies using software, and a diverse set of applications,
including graphics, geographic information systems, computer vision,
and air flow and structural simulations.
In the past decade there have been many important theoretical
advances in algorithm design for meshing related problems, but
only some of these have made it into meshing software. The goal
of this PROBE is to build a stronger link between the theory and
practice of meshing. The hope is both for the algorithms community
to better understand the needs of applications and for applications
community to more rapidly integrate algorithmic ideas into their
software.
Towards this end it is important to develop a shared infrastructure
that the algorithms community can use to make it easier to prototype
code for their ideas. It is also important to involve application
users in the problem definitions. The infrastructure should include
shared code, shared problem instances, and documented file formats
for representing various geometric structures. Interesting research
issues arise in deciding what some of the shared interfaces should
be. For examples, how should curves surfaces be represented. Also,
it is exactly in these definitions where it is important to involve
the application developers.
The
Meshing Infrastructure Workshop, Ithaca, New York, September 18,
2002