Irregular Subdivision and Multiresolution for Surfaces

Wavelets on irregularly sampled surfaces provide a useful framework for efficient mesh processing algorithms. The generalization of subdivision schemes in the non-uniform setting is a key component for such wavelet constructions. The analysis of irregular subdivision schemes is the focus of this talk. We shall overview available techniques and known results for the smoothness and convergence analysis of irregular subdivision schemes both on the real line and in the two-dimensional and surface setting. Some alternative approaches will also be discussed. Several example applications and open problems will be presented.