Art Gallery Problem

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How many omnidirectional cameras are needed to fully observe every part of a polygonal art gallery? Move the cameras by dragging the colored locators ("guards") to try to cover the polygon with the fewest guards.

Contributed by: Shreyas Poyrekar, Arifa Sultana and Aaron T. Becker (September 2019)
Open content licensed under CC BY-NC-SA


This Demonstration calculates the visible region for each guard. Up to eight guards can be used, and all are moveable.

Three different environments are provided. The "movable obstacles" environment contains a movable square and triangle.


[1] D.-T. Lee, "Proximity and Reachability in the Plane," Ph.D. dissertation, University of Illinois at Urbana-Champaign, Illinois, ProQuest Dissertations Publishing, 1978 7913526.

[2] Wikipedia. "Isovist." (Aug 22, 2019)

[3] Wikipedia. "Visibility Polygon." (Aug 22, 2019)

[4] Wikipedia. "Visibility Graph." (Aug 22, 2019)

[5] Wikipedia. "Art Gallery Problem." (Aug 22, 2019)


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