MODELING DESIGNS WITH SHAPE ALGEBRAS AND FORMAL LOGIC. Scott C. Chase, University of California, Los Angeles, Dept. of Architecture and Urban Design, chases@nist.gov

 

Design modeling systems have traditionally used kit-of-parts representations which require the predetermination of how a design can be constructed and decomposed. Shape algebraic representations can release the designer from such restrictions, as they require only minimal predetermination of structure. Through direct manipulation of emergent features, they can thus support discovery of innovative forms. Although these representations have a strong mathematical basis, most previous work with them has consisted of describing designs by a combination of drawing and natural language. The use of a more symbolic representation of shape can facilitate shape computation and spatial reasoning. Here, a formal, hierarchical model of shape, spatial relations and non-spatial properties is presented, constructed from first principles of geometry, topology and logic. The model is developed by extending the formalisms of shape algebras with the use of logic to make more precise, generalized, parametric definitions of shape and spatial relations than has been previously possible with shape algebras. By developing the model in a layered approach, building from base primitive operations to high level relations and operations which are natural to design, one can examine formal properties of relations and identify issues which may affect implementation. The use of a symbolic logic formulation also allows one to focus on abstract knowledge, rather than the details of data structures. The value of such a model is demonstrated by the use of these generalized spatial relations for solving problems in the fields of geographic information systems and architectural design. The advantages of the representations used over more traditional ones are illustrated through the examples. The computational problems which arise from the use of these representations are discussed, along with potential solutions.