The sweep-envelope differential equation algorithm for general deformed swept volumes

The Sweep-Envelope Differential Equation (SEDE) and some aspects of the Sweep Differential Equation (SDE) approaches for characterizing swept volume boundaries are extended to include objects experiencing deformation in this paper. For deformed swept volume, it is found that the structure and algorithm of the SEDE is surprisingly similar to those for rigid swept volumes. The property of autonomous SDE for deforming swept volumes is completely described. Finally, the effectiveness of the algorithm for deformed cases is verified by applying it to some examples using the commercial geometric modeling software Gems 5.0 developed by the CAD Center of Tsinghua University.