Friday, April 29, 2011

face guards by Andrew Winslow, Diane Souvaine and me


A classic problem in computational geometry is the art gallery problem: given an enclosure, how should guards be placed to ensure every location in the enclosure is seen by some guard. In this paper we consider guarding the interior of a simple polyhedron using face guards: guards that roam over an entire interior face of the polyhedron.
Bounds for the number of face guards g that are necessary and sufficient to guard any polyhedron with f faces are given.
We show that for orthogonal polyhedra,

while for general polyhedra

Example of the orthogonal polyhedron:

PDF version of the submitted paper.

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