1. A method for using a computer to model interactions between a first body experiencing a first translation concurrent with a first rotation and a second body experiencing a second translation concurrent with a second rotation, comprising: a) receiving into the computer representations of said first body, said first translation concurrent with said first rotation, said second body, and said second translation concurrent with said second rotation; b) using the computer to transform the representation of said first body and the representation of said first translation concurrent with said first rotation into a first swept representation comprising a hierarchical bounding volume representation whose leaves each contain an approximate representation of the region swept by a section of said first body during said first translation concurrent with said first rotation, wherein the union of said volumes is approximately a superset of the region swept by the surface of said first body during said first translation concurrent with said first rotation; c) using the computer to transform the representation of said second body and the representation of said second translation concurrent with said second rotation into a second swept representation comprising a hierarchical bounding volume representation whose leaves each contain an approximate representation of the region swept by a section of said second body during said second translation concurrent with said second rotation, wherein the union of said volumes is approximately a superset of the region swept by the surface of said second body during said second translation concurrent with said second rotation; d) using the computer to determine an interaction between said first swept representation and said second swept representation; and e) communicating the interaction.