Linear time algorithms for computing reachability regions from polygonal figures

Abstract

Let δ(x, y) denote the Euclidean distance between points x and y in the plane. We define the distance l reachability region R(l, S) from set S $\subseteq$ R ² as being the set R (l, S)={q∈R ² | ∃ p∈S such that δ(q, p)=l }. We also define a solid figure F in the plane as being the compact set bounded by a Jordan curve. A nonsolid figure in the plane is defined as being a compact set containing holes. A figure is simply a solid figure or a nonsolid figure. In this paper, we study some properties of reachability regions from figures. We also present linear time algorithms for computing reachability regions (1) from solid figures bounded by convex polygons or by simple polygons with convex pockets, (2) from nonsolid figures bounded (outside) by convex polygons or by simple polygons with convex pockets, having holes bounded by convex polygons.

Partially supported by NSERC grant A0368 and funds from McRCIM (McGill Research Center for Intelligent Machines).