Konrad Polthier, Technische Universität Berlin, Germany
Efficient Optimization of Polyhedral Shapes
The development of a discrete differential geometry has provided an effective new source for the analysis and optimization of geometric shapes in recent years. Discrete differential operators on meshes offer a parametrization independent approach at the intersection of geometry, partial differential equations and computer graphics.
In this talk we will give an overview of geometric properties of polyhedral shapes and show recent applications and developments such as anisotropic shape operators and surface features, the topology of discrete tensor fields and differential forms, and the stability analysis of optimization problems. We will conclude with an outlook on geometric properties of other discrete shapes such as non-conforming simplicial meshes and statistical manifolds.