We have reduced the problem of a swept solid description to a global extremum search by a parameter of movement. It allows the user to apply arbitrary variable-shape and CSG solids as generators, arbitrary parametrized movement and self-intersections. An example of sweeping by falling cup and spoon is shown below.

Simulation of NC machining uses time-dependent set-theoretic operations with a part and a cutter in relative motion:

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More sweeps

Details can be found in the paper:

Sourin A.I., Pasko A.A. “Function representation for sweeping by a moving solid”, IEEE Transactions on Visualization and Computer Graphics, vol.2, No.1, March 1996, Special issue on solid modeling, pp.11-18.
Electronic version: PostScript (294K) and PostScript + gzip (64K)