A comparison of sampling strategies for computing general sweeps

Sweeping moving objects has become one of the basic geometric operations used in engineering design, analysis and physical simulation. Despite their relevance, computing the boundary of the set swept by a non-polyhedral moving object is largely an open problem due to well known theoretical and computational difficulties of the envelopes. We have recently introduced a generic point membership classification (PMC) test for general solid sweeping. Importantly, this PMC test provides complete geometric information about the set swept by the moving object, including the ability to compute the self-intersections of the sweep itself. In this paper, we compare two recursive strategies for sampling points of the space in which the object moves, and show that the sampling based on a fast marching cubes algorithm possesses the best combination of features in terms of performance and accuracy for the boundary evaluation of general sweeps. Furthermore, we show that the PMC test can be used as the foundation of a generic sweep boundary evaluator in conjunction with efficient space sampling strategies for solids of arbitrary complexity undergoing affine motions.