The shape of material objects plays an important role in a variety of research and application areas. Shapes can be constructed or computed, e.g., in engineering and architecture, or they can be empirically given, e.g., in medicine, materials science and archaeology. Shape is a key factor in understanding complex phenomena, gaining knowledge and optimizing industrial processes. For computerized processing, shapes generally need to be discretized.
A major challenge in the digital age is to deal with the increasing amount of data, for example in large-scale clinical studies. This requires the development of robust, efficient, and automatic analysis and processing tools. Such tools must be based on flexible and geometrically consistent descriptions of complex and realistic geometries.
EF2 deals with the mathematics behind this: What are smooth discrete shapes, how can shapes be reconstructed, interpolated, compared and characterized? Specific questions we are concerned with are the definition and theory of smooth discrete surfaces, the theories and algorithms for generating particularly regular volume triangulations, for characterizing cellular microstructures topologically and geometrically, and for reconstructing and analyzing parameter-dependent shapes.
Scientists in Charge: Alexander Bobenko, Hans-Christian Hege