Mathematical methods in mesh-based modelling

Mesh-based geometric modelling refers to the modelling of surfaces of 3D geometric objects using polygonal meshes, typically triangular meshes. We are currently seeing a growing trend to model geometry using triangular meshes, and this is especially so in computer animation and medical imaging, where objects often have complex topologies and the potential advantage of the topological flexibility of triangular meshes is most apparent. What this kind of geometric modelling frequently suffers from, however, is a lack of really robust and reliable methods and algorithms, due, we believe, to an insufficient supporting mathematical foundation. In contrast to spline-based geometric modelling, which is based on the well-developed mathematical theory behind mesh-b ased modelling is still in its infancy. The research will focus on a fruitful interplay between the steady development of relevant methematical theory and the parallel development of fast robust numerical methods.