Analysis and modelling of deformed swept volumes

Abstract The sweep differential equation approach and the boundary-flow method developed for the analysis and representation of swept volumes are extended to include objects experiencing deformation. It is found that the theoretical framework can be generalized quite naturally to deformed swept volumes by the enlargement of the Lie group structure of the sweeps. All the usual results, including the boundary-flow formula, are shown to have extensions for swept volumes with deformation. Several special classes of deformation are identified, and their particular properties are studied insofar as they pertain to swept volumes. A program for obtaining deformed swept volumes of planar polygons is described, and is then applied to several examples to demonstrate its effectiveness.

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