This paper describes a technology for modelling and rendering of heterogeneous objects containing entities of various dimensionality 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. First, we describe a formal framework for such a hybrid representation and propose a general structure for implicit complexes. Then, we consider in detail how an implicit complex can be described geometrically and topologically along with its associated attributes. The attachment operation which is the main mechanism allowing the construction of implicit complexes is described in detail. Two types of rendering algorithms for implicit complexes using polygonization and ray-tracing are also described. Finally, we present some examples illustrating the proposed methods and algorithms.
Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Curve, Solid, and Object Representations; I.3.7 [Three-Dimensional Graphics and Realism]: Ray-tracing