Leif Kobbelt, University of Aachen, Germany

**Freeform Shape Representations for Efficient Geometry Processing**

Parametric and volumetric representations for freeform shapes both have their specific advantages and drawbacks. While the algebraic complexity of volumetric representations is usually independent from the shape, the structure of parametric representations has to be updated when the surface is modified significantly. On the other hand, the topology of parametric surfaces can be controlled explicitly while in a volumetric representation, the surface topology can change accidentally during deformation. Volumetric representations reduce distance queries to mere function evaluations but geodesic neighborhood relations between surface points are difficult to resolve.

I will show examples where the combination of both approaches leads to efficient and numerically stable algorithms for the solution of various geometry processing tasks. Applications include global error control for mesh decimation and smoothing, topology control for levelset surfaces, and multiresolution editing without local self-intersections.