The goal of this project is the full incorporation of a larger class of swept surfaces for machining, robot motion, and other applications. The full incorporation of swept surfaces into solid models requires concentration on surface intersection and Boolean operations on solids involving swept surfaces. The development of a powerful tool for the analysis of swept surfaces for machining and other applications demands related work on interference detection, volume, representational issues, and sweep generation. One of the fundamental primitives in solid modeling is the swept surface. A swept surface is characterized by the type of sweep (i.e., the way the position and orientation of the cross-section changes), the cross-section that is being swept, and the ability of this cross-section to change shape. The literature and solid modeling systems are dominated by the consideration of sweep surfaces generated by translational or revolute sweeps, and rigid sweeps (the cross-section does not change shape). This project will investigate arbitrary sweeping of nonrigid objects, about which there is less literature and little algorithmic development. In order to make the problem tractable, the study will be restricted to simple cross-sections. Thus, the project will concentrate on the sweeping of lines and circles, although much of the theory applies to other simple cross-sections as well. The superellipse cross-section will also be studied.
