ISSN:
1432-0444
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract. Let Ω be a set of pairwise-disjoint polyhedral obstacles in R 3 with a total of n vertices, and let B be a ball in R 3. We show that the combinatorial complexity of the free configuration space F of B amid Ω:, i.e., (the closure of) the set of all placements of B at which B does not intersect any obstacle, is O(n 2+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 . The special case in which Ω is a set of lines is studied separately. We also present a few extensions of this result, including a randomized algorithm for computing the boundary of F whose expected running time is O(n 2+ε ).
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s004540010064
