The differential equation algorithm for general deformed swept volumes (Q1592641)

Sweeping of 3-dimensional objects is a standard technique for constructing surfaces or volumes in geometric modelling. The differential equations approach has turned out to be fruitful for analyzing swept volumes. In particular, the sweep-envelope differential equation (SEDE) algorithm is a powerful tool for computing 3-dimensional smooth objects in rigid smooth motion. Here this method is extended to smooth objects experiencing deformation during the motion. The authors show that the structure of the SEDE (and hence, the corresponding algorithm) remains essentially unchanged in this more general situation.