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Sweeping is a powerful and versatile method of designing objects. Boundary ofvolumes (henceforth envelope) obtained by sweeping solids have been extensivelyinvestigated in the past, though, obtaining an accurate parametrization of theenvelope remained computationally hard. The present work reports our approachto this problem as well as the important problem of identifyingself-intersections within the envelope. Parametrization of the envelope is, ofcourse, necessary for its use in most current CAD systems. We take the moreinteresting case when the solid is composed of several faces meeting smoothly.We show that the face structure of the envelope mimics locally that of thesolid. We adopt the procedural approach at defining the geometry in this workwhich has the advantage of being accurate as well as computationally efficient.The problem of detecting local self-intersections is central to a robustimplementation of the solid sweep. This has been addressed by computing asubtle mathematical invariant which detects self-intersections, and which iscomputationally benign and requires only point queries.

A procedural framework and mathematical analysis for solid sweeps