Visible Points in a Polygon

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Imagine a guard in a polygonal gallery at night. Only using her flashlight, there are walls she cannot point to from one spot. In this Demonstration, the guard is depicted by a red disk and the gallery by a blue polygon, which can even be self-intersecting. The yellow polygon is the set of all visible points. To vary the figure, drag the red point or the vertices of the gallery. When the guard is not inside the polygon, the set of visible points is sometimes unbounded.

Contributed by: Jaime Rangel-Mondragon (August 2014)
Open content licensed under CC BY-NC-SA




[1] S. K. Ghosh, Visibility Algorithms in the Plane, Cambridge: Cambridge University Press, 2007.

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