Combining context provisions with graph grammar rewriting rules - the three-dimensional case

In this paper we consider the representation and generation of three-dimensional structures by means of formal descriptive methods. Graph and graph grammar theory present us with a powerful two-dimensional representational method, and we propose to use these concepts as basis for the three-dimensional case. Three dimensional structures however, often appear in other structures and within a certain context. This context may be defined or influenced by the overall structure, or other related structures. We therefore need to be cognisant of the role that these contexts play when we introduce the concepts of three-dimensional graph and graph grammar systems, with particular reference to contextual rewriting rules. It is the combination of context provisions with graph grammar rewriting rules that results in a formal descriptive method which represents three-dimensional structures. The generative abilities of the concepts we introduce and discuss, are illustrated by considering the generation of various chemical structural formulae