In 1981, Avis and Toussaint gave a linear-time algorithm for the following problem. Given a simple n-Vertex polygon P and an edge of P, determine whether each point in P can be seen by some (not necessarily the same) point on the edge. They posed the more general problem of finding a subquadratic algorithm for determining whether such an edge exists. In this paper, we present a linear-time algorithm for determining all (if any) such edges of a given simple polygon.

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Keywords Algorithms, computational complexity, computational geometry, visibility
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Journal IEEE Transactions on Computers
Sack, J.-R, & Suri, S. (Subhash). (1990). An Optimal Algorithm for Detecting Weak Visibility of a Polygon. IEEE Transactions on Computers, 39(10), 1213–1219. doi:10.1109/12.59852