The goal of this research is the investigation of a scheme that allows for the representation of 2D and 3D shapes via compact and versatile geometric models which can model a large class of shapes and are amenable to stable and efficient numerical implementations. The models are to be capable of representing shapes whose topology is not known a priori. Geometric models are traditionally well suited for representing global shapes but not the local details. In this work, a powerful geometric shape meodeling scheme is investigated which allows for the representation of global shapes with local detail and permits model shaping via physics-based control as well as topological changes. These models are a blend of geometric and physics-based models, and are in spirit "similar" to the now popular deformable superquadrics, but differ from them considerably in their expressiveness and numerical stability, thereby promising greater applicability.
