Construction of Implicit Complexes: A Case Study

Abstract

This paper presents a detailed description of a case-study demonstrating a novel method for modelling and rendering of heterogeneous objects containing entities of various dimensionalities within a cellular-functional framework based on the implicit complex notion. Implicit complexes make it possible to combine a cellular representation and a constructive function representation. We briefly describe a formal framework for such a hybrid representation as well as a general structure for implicit complexes. Then, using a representative example, we show how an implicit complex can be constructed geometrically and topologically. We also consider the main rendering issues specific to implicit complexes and describe some implementation problems.