||Advances in scanning and sensing technologies within the last decade have enabled the creation of complex digital models from real-world objects. The field of geometry processing concerns the representation, analysis, manipulation, and optimization of the resulting geometric data. The findings in this field are of importance for many industrial applications, for example in the automotive industry and architecture.
Fundamental to geometry processing is an understanding of geometric properties of the shapes to be processed. Since these are discrete and not smooth manifolds, they lie out of the realm of classical differential geometry. Discrete differential geometry develops notions and concepts that describe geometric properties of discrete manifolds in analogy to the smooth theory. Concepts developed in this field form a basis for many algorithms in geometry processing.
One line of our research focuses on the construction of discrete differential operators and discrete curvatures on polyhedral surfaces and the study of their convergence properties. A second line aims at developing computational models and efficient algorithms for problems in geometry processing and other areas of visual computing, including surface modeling, fairing and denoising, shape analysis, feature detection, real-time simulation of deformable objects, and control of physical trajectories.
Since April 2015 Klaus Hildebrandt holds a faculty position in the Computer Graphics and Visualization department at the University of Delft, Netherlands.