An interactive, visual approach to developing and applying parametric three-dimensional spatial grammars

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. Since the introduction of the underlying formalism, they have been successfully applied to different domains including visual arts, architecture, and engineering. Although many spatial grammars exist on paper, only a few, limited spatial grammar systems have been computationally implemented to date; this is especially true for three-dimensional (3-D) systems. Most spatial grammars are hard-coded, that is, once implemented, the vocabulary and rules cannot be changed without reprogramming. This article presents a new approach and prototype implementation for a 3-D spatial grammar interpreter that enables interactive, visual development and application of grammar rules. The method is based on a set grammar that uses a set of parameterized primitives and includes the definition of nonparametric and parametric rules, as well as their automatic application. A method for the automatic matching of the left hand side of a rule in a current working shape, including defining parametric relations, is outlined. A prototype implementation is presented and used to illustrate the approach through three examples: the “kindergarten grammar,” vehicle wheel rims, and cylinder cooling fins. This approach puts the creation and use of 3-D spatial grammars on a more general level and supports designers with facilitated definition and application of their own rules in a familiar computer-aided design environment without requiring programming.