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by Thomas Shermer, Godfried Toussaint
School of Computer Science, McGill Univ
http://www-cgrl.cs.mcgill.ca/~godfried/publications/constar.ps.gz
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Abstract:
A chord of a simple polygon P is a line segment [x,y] that intersects the boundary of P only at both endpoints x and y. A chord of P is called an interior chord provided the interior of [x,y] lies in the interior of P. P is said to be weakly visible from [x,y] if for every point v in P there exists a point w in [x,y] such that [v,w] lies in P. In this paper we characterize star-shaped and convex polygons in terms of weak visibility properties of their internal chords. We also provide a new Krasnoselskii-type characterization of isothetic star-shaped polygons 1.
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