On measuring the visual complexity of 3D solid objects John GERO, Vladimir KAZAKOV ** Abstract: A computational model of the visual complexity of solids is presented. It is based on using a qualitative representation for 3-dimensional objects as semantic graphs. Then information-theoretic measures are constructed for these graphs. This measure of visual complexity allows for the comparison of different architectural forms. An example of the application of this model is presented. Keywords: visual reasoning; complexity; 3D modelling 1 Introduction Drawings are the most common form of design representation. They are used in a variety of ways including memory aids and external representations that can be re- interpreted [PG 97]. Drawings are the most evident of design outcomes both during and at the completion of the process of designing. In research into computer support for designing, the focus on drawings has been primarily as the end result although there has recently been interest in drawings as a medium for the representation of ideas. If computer support for designing is to extend beyond the mere increase in the efficiency of the production of drawings then we need to be able to derive and “measure” attributes and qualities of the content of drawings. Earlier work focussed on deriving design semantics from drawings [GRO 96; JG 98]. Computer support during the process of designing will have to be involved with the design drawings before they are finalised. If we are going to use measures of designs based on their drawings we need to be able to use a measure that can differentiate them based on their drawings How do we measure the difference between two designs visually? Commonly we measure some aspect of their behaviours such as cost, environmental efficiency or structural sufficiency. However, all of these assume that a detailed design is available. What is needed is a means of measuring the difference between designs at a visual level that does not depend on a knowledge of the detailed design itself so that such measures could be utilised at any stage during the design, including at the very early stages when only the form is known. This implies that what is being measured cannot depend directly on quantitative descriptions but rather on qualitative representations. Qualitative symbolic modeling represents objects as classes rather than as instances. As a consequence they can be used at the early stages of designing when objects do not yet have a fixed geometry, only fixed topology and restrictions on geometry, based on their topology. The framework of qualitative representations allows ** Key Centre of Design Computing and Cognition, University of Sydney, Australia. john@arch.usyd.edu.au