A ROAD MAP TO SOLID MODELING

The objective of solid modeling is to represent, manipulate, and reaso n about, the three-dimensional shape of solid physical objects, by com puter. Such representations should be unambiguous. Solid modeling is a n application-oriented field that began in earnest in the early 1970s. [46]. Major application areas include design, manufacturing, computer vision, graphics, and virtual reality. Technically, the field draws o n diverse sources including numerical analysis, symbolic algebraic com putation, approximation theory, applied mathematics, point set topolog y, algebraic geometry, computational geometry, and data bases. Monogra phs and major surveys of solid modeling include [13], [19], [27], [37] , [44], [45], [46]. In this road map article, we begin with some mathe matical foundations of the field. We review next the major representat ion schemata of solids. Then, major layers of abstraction in a typical solid modeling system are characterized: The lowest level of abstract ion comprises a substratum of basic service algorithms. At an intermed iate level of abstraction there are algorithms for larger, more concep tual operations. Finally, a yet higher level of abstraction presents t o the user a functional view that is typically targeted towards solid design. Here, we will look at some applications and at user interactio n concepts. The classical design paradigms of Solid Modeling concentra ted on obtaining one specific final shape. Those paradigms are becomin g supplanted by feature-based, constraint-based design paradigms that are oriented more toward the design process and define classes of shap e instances. These new paradigms venture into territory that has yet t o be explored systematically. Concurrent with this paradigm shift, the re is also a shift in the system architecture towards modularized conf ederations of plug-compatible functional components. We explore these trends lightly in the last section.