A Formal Approach to Multiresolution Hypersurface Modeling

Abstract

Multiresolution geometrie models support the representation and processing of geometric entities at different levels of detail, and are useful in several application fields, such as geographic information systems, CAD systems and scientific visualization. The aim of this paper is to provide a framework for multiresolution geometric modeling, independent both of the dimension of spatial objects under consideration, and of the specific application. This paper introduces a formal model, called the Multiresolution Simplicial Model (MSM), capable of capturing the characteristics of most multiresolution models proposed in the literature. The paper provides an analysis of the relationships between the intrinsic structures of different multiresolution models, as well as a definition of relevant application-independent operations on them. Major data structures used to encode multiresolution models are reviewed, as well as algorithms which implement the operations on each data structure.