Stephan Bischoff
Mario Botsch
Leif Kobbelt


The most important data structures for handling and storage of free
form shapes in geometry processing applications and computer graphics
can be classified according to the dimensionality of their basic
structural elements: point-sets, polygon meshes, as well as volumetric
representations are well established concepts to describe the shape of
arbitrarily complex objects. On the other hand, algorithms to process
a given geometric object can be classified according to the dominant
access operation which can be of the type evaluation (sampling), query
(e.g. inside/outside tests), or modification (of the geometry or the
topology). On a more abstract level, we can in principle distinguish
between unstructured geometry representations which do not imply any
global regularity and uniformly structured representations or even
hierarchically structured representations.

All these different types of shape representations will be presented
in this tutorial and the respective strengths and disadvantages will
be discussed in detail. For a given application we can analyze which
types of access operations are the most critial ones and then design
a custom data structure accoring to the usage profile. In some cases
it turns out that a proper combination of two different representations
provides the optimal performance or robustness. We will present a
couple of important geometry processing problems such as topology
control for deforming implicit surfaces, mesh decimation and smoothing
with global error control, and mesh restoration where this combination
of geometry data representations leads to superior algorithms compared
to the standard approaches. 

Short (incomplete) list of topics:
  * introduction
  * point-based representations
    (generation, storage, high-quality rendering, deformation)
  * polygon meshes
    (data structures, hierarchies)
  * volumetric representations
    (data structures, level sets)
  * geometry processing tasks
      remeshing            : (points and polygons)
      topology control     : (points and volumes)
      smoothing/decimation : (polygons and volumes)
      multiresolution      : (polygons and volumes)
      ... and others