Shortest path solves edge-to-edge visibility in a polygon

Abstract Given a simple polygon P = ( p 1 , p 2 , …, p n ) consisting of n edges e i = [ p i p i +1 ], i = 1,2, …, n , two edges e i and e j are said to be visible if there exists a point χϵe i and a point yϵe j such that the line segment [ χ y ] lies in P . An edge-to-edge visibility query asks for whether a specified pair of edges of P is visible. It is shown that with O( n log n ) preprocessing of P , an edge-to-edge visibility query can be answered in O( n ) time. The algorithm also reports a line-of-sight if the answer is in the affirmative.

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