Let Ω be a set of pairwise-disjoint polyhedral obstacles in R3 with a total of n vertices, and let B be a ball. We show that the combinatorial complexity of the free configuration space F of B amid Ω, i.e., the set of all placements of B at which B does not intersect any obstacle, is O(n2+ε), for any ε>0; the constant of proportionality depends on ε. This upper bound almost matches the known quadratic lower bound on the maximum possible complexity of F. We also present a randomized algorithm to compute the boundary of F whose expected running time is O(n2+ε), for any ε>0.
|Number of pages
|Published - 1999
|Proceedings of the 1999 15th Annual Symposium on Computational Geometry - Miami Beach, FL, USA
Duration: 13 Jun 1999 → 16 Jun 1999
|Proceedings of the 1999 15th Annual Symposium on Computational Geometry
|Miami Beach, FL, USA
|13/06/99 → 16/06/99