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Linear time algorithms for computing reachability regions from polygonal figures

  • Rongyao Zhao
Conference paper
  • 656 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 382)

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\( \subseteq \)R2 as being the set R (l, S)={qR2 | ∃ pS 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.

Keywords

Outer Boundary Convex Polygon Jordan Curve Open Disc Linear Time Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Rongyao Zhao
    • 1
  1. 1.School of Computer ScienceMcGill UniversityMontrealCanada

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