Implementation issues of parallel shape grammars

Abstract

Shape grammars come in a variety of forms. Algebras of shapes have been defined for spatial elements of different kinds, as well as for shapes augmented with varying attributes, allowing for grammar forms to be expressed in terms of a direct product of basic algebras. This algebraic approach is extended here to the algebraic derivation of combinations of basic shape algebras with attribute algebras. This algebraic abstraction at the same time serves as a procedural abstraction, giving insights into the modular implementation of a general shape grammar interpreter for different grammar forms. In addition, we consider practical limitations on algebraic compositions of basic shape algebras with attribute algebras and identify a complication with respect to solving the matching problem for parallel and compound shape grammars, suggesting a way to address this complication.