During his visit, Martin has been working on the following projects:
- Connectivity Shapes
In this project we introduced a 3D shape representation that is based
solely on mesh connectivity -- the connectivity shape. Given a
connectivity, we defined its natural geometry as a smooth embedding in
space with uniform edge lengths and describe efficient techniques to
In the Figure above we see the well-known polygonal mesh of a cow (a).
Ignoring the geometry, we have mapped the cow's connectivity onto the
unit sphere (b), where the different densities hint to the features of
the cow. In (c) the corresponding connectivity shape is shown.
It is a smooth embedding with uniform edge lengths of the connectivity
graph of (a) and (b) in three dimensional space.
Imagine all edges of the cow being springs of the same equilibrium
length. In the embedding (b) we forced the spring system into
a high energy state. In (c) we released all vertices and the spring
system relaxed into a low energy state, with more or less uniform
edge lengths. This is the connectivity's natural shape. More poetically, the
sphere embedding in (b) has the body of a sphere, but the soul
of an animal. The natural embedding in (c) reveals the geometric soul
of the cow's connectivity.
Furthermore, we show how to generate connectivity shapes that
approximate given shapes. This is done by (re)meshing the given
shape with uniform edge lengths. For example, the connectivity
shape in (d) bears a striking resemblance to the original (a).
The only information in this mesh is its connectivity, in the
sense that it induces the mesh geometry.
Finally we describe applications of connectivity shapes to modeling, mesh
coding, graph drawing, and
. See also our project webpage at
The following publications summarize some of the results of the
research work that Martin has participated in during his stay:
- "Connectivity Shapes"
by Martin Isenburg, Stefan Gumhold, and Craig Gotsman
submitted for publication
Martin was sponsered by MINGLE to participate in the following conferences
and workshops, presenting recent research results:
- MINGLE workshop,
January 18-19, 2001,