||Solid modeling is rapidly emerging as a central area of research and de- velopment in such diverse applications as engineering and product design, computer-aided manufacturing, electronic prototyping, o -line robot pro- gramming, and motion planning. All these applications require represent- ing the shapes of solid physical objects, and such representations and basic operations on them can be provided by solid modeling. As a eld, solid modeling spans several disciplines, including mathemat- ics, computer science, and engineering. In consequence, it is a broad subject that must accommodate a diversity of viewpoints and has to meet a diversity of goals. Sometimes, this diversity of goals can lead to con icting demands. Current thinking on the subject views the proper resolution of these con- icts to be application-dependent. That is, it is no longer thought realistic to envision a comprehensive solid-modeling system that satis es the needs of all potential users. Rather, as it is argued, we should concentrate on con- structing a software environment in which many tools for geometric and solid computation are available and can be combined with ease as appropriate for the speci c application under consideration.