Using logic to specify shapes and spatial relations in design grammars

Shape algebraic representations provide several advantages over more traditional geometric representations. The use of predicate logic formulations of shape and spatial relations provides a natural, intuitive way to extend shape representations of the shape grammar formalism to provide generalized, parametric grammars. Introduction Research in the use of grammars and similar production systems for design has been ongoing for several decades. Many different approaches to the problem of design generation have been attempted. All, however, must deal with the basic elements of any grammar or production system, neatly categorized in (Gips, Stiny, 1980) in terms of 1) the objects to which they apply; 2) the way they are defined; 3) the interpretive mechanism used to apply the productions, and 4) the objects they generate. The author’s primary interest is in the representation of objects in such a system, in the belief that the underlying object representation should be the major consideration in the development of a production system. The representations used in shape grammars (Stiny, Gips, 1972) bear this out by demonstrating significant advantages over more traditional representations. The problem of predetermination The ‘kit-of-parts’ approach to design, generally considered an efficient method of generating designs, tends to force the designer into a specific manner of representing and manipulating objects. Thus, the structure of a model must be decided at the start. This can be considered a reductionist philosophy, in which the universe is considered to be composed of separate parts which, in various combinations, make up the whole. However, it is extremely difficult, if not impossible, to anticipate all possible ways in which one might wish to view or classify parts of a model. This often requires an unmanageable amount of information. The problems with this approach were among the causes of the failure of early CAD building modeling systems in the 1970’s and early ’80s, which often required the predetermination of all types of information of interest, and for this information to be stored in a single model. On the other hand, a holistic philosophy considers the universe to be a whole rather than the sum of its parts. A system which forces no preconceived structure upon the user, but rather, allows one to find all sorts of emergent features and properties from within the whole, would be extremely desirable. Shape algebras and shape grammars in design The algebras of shape as defined by Stiny (1991) can support both holistic and reductionist views. By considering shapes as finite sets of elements which can carry fixed properties, a reductionist view is supported. The real power of such algebras, however, lies in the fact that the elements of a shape and their properties may be defined in such a manner as to enable the emergence of features which are not apparent in the initial formulation of a shape. In addition, the generality of their representations, their reliance upon a minimum of structure, and their use in combination can