An optimal algorithm for detecting weak visibility of a polygon

Notation and a theorem are presented which, using a result of B. Chazelle and L.J. Guibas (1985), enable the authors to design an O(n log n) algorithm for reporting all visibility edges of a given n-vertex polygon. Improving on this bound to O(n) is presently focused upon. This problem is solved for polygons with at least one given visibility edge. It is assumed that both endpoints of this edge are convex vertices. Subsequently, it is shown how to drop this restriction. The general case of detecting weak edge visibility of an arbitrary simple polygon is dealt with.<
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