Multiresolution Representation of Shapes Based on Cell Complexes

. This paper introduces a dimension-independent multiresolution model of a shape, called the Multi-Complex (MC), which is based on decomposition into cells. An MC describes a shape as an initial cell complex approximating it, plus a collection of generic modification patterns to such complex arranged according to a partial order. The partial order is essential to extract variable-resolution shape descriptions in real time. We show how existing multiresolution models reduce to special cases of MCs characterized by specific modification patterns. The MC acts as a unifying framework that is also useful for comparing and evaluating the expressive power of different approaches. 1 Introduction Multiresolution geometric models support representation and processing of spatial entities at different levels of detail. Such representations have gained recently much of attention in the literature because of their potential impact on applications, such as terrain modeling in geographic information ..