Shaping geometric objects by cumulative translational sweeps

This paper introduces the cumulative translational sweep (CTS) as a tool for shaping geometric objects. It describes how it may be applied, in combination with Boolean operations, to stimulate growth and shrinking over the boundary regions of polyhedral models, and how, by creating additional facets, it may be used to achieve global rounding effects along model edges and around their vertices. CTSs are examined in terms of a conceptual framework that describes their effects as Minkowski sums—of the polyhedra to be swept, with convex polyhedra from the class of mathematical objects known as zonotopes. Included is a discussion of applications in the OYSTER program, a CAD system for the simulation of semiconductor wafer fabrication.