Geometric modeling is the construction or application of geometric models. Geometric models are employed in computer graphics, computer-aided design and manufacturing, as well as many applied fields such as medical image processing to model shapes, growth processes or pathologies. Furthermore, robust tools to process or interact with geometric structures are required (such as intersection, union, continuous attachment ...). Important sub-fields of geometric modeling are curves and (subdivision) surfaces (B-Splines, NURBS, ...). These representations not only allow modeling of shapes, but can also be used for analytic purposes (e.g. the solution of multinomial systems, see [1]). Another of our research directions deals with the medial axis (a skeletal shape representation) and its usability for shape parametrization. This work allows to efficiently combine design, meshing, FEM analysis and possible automatic design optimization in a single loop - a process that otherwise can take up to days [2-3].

[1] Solving Nonlinear Polynomial Systems in the Barycentric Bernstein Basis (JTVC 2007)
[2] Geometric Modeling for Engineering Applications (Book Chapter 2007)
[3] Shape Optimization and efficient FEM Comp. employing the Medial Axis (Patent Appl. 2007)
[4] Geometric Modeling of Complex Shapes and Engineering Artifacts (Book Chapter 2004)