Three-dimensional labels: A unified approach to labels for a general spatial grammar interpreter

Spatial grammars are rule-based, generative systems for the specification of formal languages. Set and shape grammar formulations of spatial grammars enable the definition of spatial design languages and the creation of alternative designs. The original formalism includes labels that provide the possibility to restrict the application of rules or to incorporate additional, nongeometric information in grammar rules. Labels have been used in various ways. This paper investigates the different uses of labels in existing spatial grammars, both paper based and computational, and introduces a new concept of threedimensional (3-D) labels for spatial grammars. The approach consolidates the different label types in one integrated concept. The main use of 3-D labels is that they can simplify the matching of the left-hand side of rules in parametric grammars. A prototype implementation is used to illustrate the approach through a mechanical engineering example of generating robot arm concepts. This approach more readily enables the use of complex solid geometry in the definition and application of parametric rules. Thus, the flexible generation of complex, meaningful design solutions for mechanical engineering applications can be achieved using parametric spatial grammars combined with 3-D labels.