Freeform structures play a prominent role in contemporary architecture. In order to stay within reasonable cost limits, computational shape design has to incorporate aspects of structural analysis and fabrication constraints. The talk discusses solutions to important problems in this area. They concern the design of polyhedral surfaces with nearly rectangular faces, polyhedral surfaces in static equilibrium, the smoothest visual appearance of polyhedral surfaces, and the closely related problem of finding material-minimizing forms and structures. From a methodology perspective, there is an interplay of geometry, mechanics and optimization. Classical subjects such as isotropic geometry, and a simple Cayley-Klein geometry, play a role as well as most recent developments in discrete differential geometry. We also show how practical requirements have led to new results and open problems in geometry
Helmut Pottmann is a professor of AMCS and CS at KAUST and founding director of the Visual Computing Center (formerly Geometric Modeling and Scientific Visualization Center). He has had faculty positions in the US and in Germany and has been a Professor of Applied geometry at TU Vienna since 1992. His research interests are in Applied Geometry, Visual Computing, and most recently Geometric Computing for Architecture and Manufacturing. He is a Fellow of SIAM and received a number of awards including the Eurographics Outstanding Technical Contributions Award, the Bezier Award of the Solid Modeling Association, and the John Gregory Award for fundamental contributions to geometric modeling.