Optimally computing a shortest weakly visible line segment inside a simple polygon

A simple polygon is said to be weakly internally visible from a line segment lying inside it if every point on the boundary of the polygon is visible from some point on the line segment. In this paper, we present an optimal linear-time algorithm for the following problem: Given a simple polygon, either compute a shortest line segment from which the polygon is weakly internally visible, or report that the polygon is not weakly internally visible.The algorithm presented is conceptually simple. This paper also incorporates a significant improvement over the linear-time algorithm for the same problem, presented in a preliminary version [12], in the sense that it eliminates the need for using two complicated preprocessing tools: Chazelle's linear-time triangulation algorithm [7], and the algorithm for computing single-source-shortest-paths from a specified vertex in a triangulated polygon [16], thus making the algorithm practical.

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