Representations for Rigid Solids: Theory, Methods, and Systems

Computer-based systems for modelling the geometry of rigid solid objects are becoming increasingly important in mechanical and civil engineering, architecture, computer graphics, computer vision, and other fields that deal with spatial phenomena. At the heart of such systems are symbol structures (representations) designating'abstract solids'(subsets of Euclidean space) that model physical solids. Representations are the sources of data for procedures which compute useful properties of objects. The variety and uses of systems embodying representations of solids are growing rapidly, but so are the difficulties in assessing current designs, specifying the characteristics that future systems should exhibit, and designing systems to meet such specifications. This paper resolves many of these difficulties by providing a coherent view, based on sound theoretical principles, of what is presently known about the representation of solids. The paper is divided into three parts. The first introduces a simple mathematical framework for characterizing certain important aspects of representations, for example, their semantic (geometric) integrity. The second part uses the framework to describe and compare all of the major known schemes for representing solids. The third part briefly surveys extant geometric modelling systems and then applies the concepts developed in the paper to the high-level design of a multiple- representation geometric modelling system which exhibits a level of reliability and versatility superior to that of systems currently used in industrial computer-aided design and manufacturin