A compact piecewise-linear Voronoi diagram for convex sites in the plane

Authors:
M. McAllister;D. Kirkpatrick;J. Snoeyink
Affiliations:
Dept. of Comput. Sci., British Columbia Univ., Vancouver, BC, Canada;Dept. of Comput. Sci., British Columbia Univ., Vancouver, BC, Canada;Dept. of Comput. Sci., British Columbia Univ., Vancouver, BC, Canada
Venue:
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Year:
1993

Citing 0
Cited 2

Efficient proximity search for 3-D cuboids

ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartIII
Tentative Prune-And-Search For Computing Fixed-Points With Applications To Geometric Computation

Fundamenta Informaticae

Quantified Score

Hi-index	0.00

Visualization

Abstract

In the plane, the post-office problem, which asks for the closest site to a query site, and retraction motion planning, which asks for a one-dimensional retract of the free space of a robot, are both classically solved by computing a Voronoi diagram. When the sites are k disjoint convex sets, we give a compact representation of the Voronoi diagram, using O(k) line segments, that is sufficient for logarithmic time post-office location queries and motion planning. If these sets are polygons with n total vertices, we compute this diagram optimally in O(klog n) deterministic time for the Euclidean metric and in O(klog nlog m) deterministic time for the convex distance function defined by a convex m-gon.