ELSEVIER Automation in Construction 6 (1997) 31 l-322 Logic based design modeling with shape algebras Scott C. Chase * zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQ National Institute of Standards and Technology, Manufacturing Engineering Laboratory, Gaithersburg, MD 20899, USA zyxwvutsrqponm Abstract A new method of describing designs by combining the paradigms of shape algebras and predicate logic representations is presented. Representing shapes and spatial relations in logic provides a natural, intuitive method of developing complete computer systems for reasoning about designs. The advantages of shape algebra formalisms over more traditional representations of geometric objects are discussed. The method employed involves the definition of a large set of high level design relations from a small set of simple structures and spatial relations. Examples in architecture and geographic information systems are illustrated. 0 1997 Published by Elsevier Science B.V. 1. Background 1.1. Reductionist us. holistic approaches to design Evolutionary models supporting dynamic schema modification are a necessary requirement in the de- velopment of future CAD systems [ll. Current sys- tems development does not appear to support such models, in that they are constructed using a bottom-up ‘kit-of-parts’ approach, beginning with the design of low level data structures and operations. While this method is generally -used to facilitate efficient object manipulation, it also forces the designer or user into a specific manner of representing and manipulating those objects. What this does is fix the model’s structure at the beginning of design. This can be viewed as a reductionist philosophy of design, in which the design is perceived as a composition of * Corresponding author. As of January 1998, Key Centre of Design Computing, Uniwrsity of Sydney, Sydney, NSW 2006, Australia, E-mail: scott@arch.usyd.edu.au separate parts which, in various combinations, make up the whole: It is a natural human tendency to separate a whole into its parts, to categorize and classify, to draw boundaries between parts, and to define classes on the basis of rigidly defined boundaries. Boundaries so defined may be useful for some purposes, but they may badly confuse the accomplishment of other purposes [2]. By fixing the structure of a data model at the beginning of the modeling process, the possibility of other desirable forms in the future may be precluded. It is extremely difficult, if not impossible, to antici- pate all possible ways in which one might wish to view or classify parts of a model, due to the gener- ally unmanageable amount of information required. This can be seen as one of the causes for the failure of early CAD systems for buildings in the 1970’s and early ’80s which generally required the prede- termination of all types of information of interest, and for this information to be stored in a single model [3]. 0926-5805/97/$17.00 0 1997 Published by Elsevier Science B.V. All rights reserved. PII SO926-5805(97)00048-4