A road map to solid modeling

The objective of solid modeling is to represent, manipulate and reason about the 3D shape of solid physical objects by computer. Such representations should be unambiguous. Solid modeling's major application areas include design, manufacturing, computer vision, graphics and virtual reality. The field draws on diverse sources, including numerical analysis, symbolic algebraic computation, approximation theory, applied mathematics, point set topology, algebraic geometry, computational geometry and databases. In this article, we begin with some mathematical foundations of the field. We next review the major representation schemata of solids. Then, major layers of abstraction in a typical solid modeling system are characterized. The lowest level of abstraction comprises a substratum of basic service algorithms. At an intermediate level of abstraction there are algorithms for larger, more conceptual operations. Finally, a yet higher level of abstraction presents to the user a functional view that is typically targeted towards solid design. We look at some applications and at user interaction concepts. The classical design paradigms of solid modeling concentrated on obtaining one specific final shape. Those paradigms are becoming supplanted by feature-based, constraint-based design paradigms that are oriented more toward the design process and define classes of shape instances. These new paradigms venture into territory that has yet to be explored systematically. Concurrent with this paradigm shift, there is also a shift in the system architecture towards modularized confederations of plug-compatible functional components.