A progressive subdivision paradigm (PSP)

The increasing rate of growth in size of currently available datasets is a well known issue. The possibility of developing fast and easy to implement frameworks able to visualize at least part of a tera-sized volume is a challenging task. Several techniques have been proposed in recent years ranging from simplification to wavelet analysis. Subdivision methods have been one of the most successful techniques applied to the multi-resolution representation and visualization of surface meshes. Extensions of these techniques to the volumetric case presents positive effects and major challenges mainly concerning the generalization of the combinatorial structure of the refinement procedure and the analysis of the smoothness of the limit mesh. In this paper we address mainly the first part of the problem, presenting a framework that exploits a subdivision scheme suitable for extension to 3D and higher dimensional meshes. We introduce a technique that combines the flexibility of a progressive multi-resolution representation with the advantage of a recursive subdivision scheme. The main contributions of the paper are: (a) a progressive algorithm that builds a multi-resolution surface by successive refinements so that a consistent representation of the output is always available (b) a multi-resolution representation where any adaptively selected level of detail is guaranteed to be consistently embedded in 3D space (no self-intersections).