Computing a Shortest Weakly Externally Visible Line Segment for a Simple Polygon

A simple polygon P is said to be weakly extrenally visible from a line segment L if it lies outside P and for every point p on the boundary of P there is a point q on L such that no point in the interior of $\overline{pq}$ lies inside P. In this paper, a linear time algorithm is proposed for computing a shortest line segment from which P is weakly externally visible. This is done by a suitable generalization of a linear time algorithm which solves the same problem for a convex polygon.

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