Constructing the Boundaries of Swept Volumes for Screw Motions

Abstract

Screw motion primitives considerably extend the commonly used rotations and translations, but retain their representational conciseness and specific geometric properties. Each piecewise-screw motion is specified in terms of a sequence of key poses of the object that it interpolates at user controlled time values. The resulting piecewise-screw motion is unique and coordinate system independent. Also, the motion is independent of the manner in which the key-poses were specified. Although any two arbitrary poses may be interpolated by an infinite of motions we advocate screw motions for their simplicity, uniqueness and computational advantages. We present a new and efficient algorithm for constructing the boundaries of swept volumes created by moving polyhedra in screw motions. The algorithm takes a generate-and-test approach by computing the candidate surfaces of boundaries and trimming them after applying the point-in-sweep test. Examples are provided to show the efficacy of the algorithm.