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�…