![]() To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. INTRODUCTION The visibility graph is a fundamental geometric structure useful in many applications, including illumination and ren- Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Categories and Subject Descriptors: F.2.2 : Nonnumerical Algorithms and Problems-geometrical problems and computations General Terms: Algorithms, Theory Keywords: Visibility graphs, polygons, illumination, guarding, fatness, output-sensitive algorithms 1. Other results include an algorithm to detect if there are any visible pairs among P, and algorithms for output-sensitive computation of visibility graphs with distance restrictions, invisibility graphs, and rectangle visibility graphs. We introduce a notion of “fat” or “robust” visibility, and give a nearly optimal algorithm for computing visibility graphs according to it, in polygons Q that may have holes. We give an output-sensitive algorithm, which is nearly optimal, when Q is a simple polygon. We examine the general case in which P is an arbitrary set of points, interior or on the boundary of Q and study a variety of algorithmic questions. ![]() ![]() Efficient output-sensitive algorithms are known for the case in which P is the set of all vertices of Q. Computing the Visibility Graph of Points Within a Polygon ABSTRACT Boaz Ben-Moshe Computer Science Ben-Gurion University Beer-Sheva 84105, Israel We study the problem of computing the visibility graph defined by a set P of n points inside a polygon Q: two points p, q ∈ P are joined by an edge if the segment pq ⊂ Q.
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