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COMPGEOM
2007
ACM

Guard placement for efficient point-in-polygon proofs

8 years 8 months ago
Guard placement for efficient point-in-polygon proofs
We consider the problem of placing a small number of angle guards inside a simple polygon P so as to provide efficient proofs that any given point is inside P. Each angle guard views an infinite wedge of the plane, and a point can prove membership in P if it is inside the wedges for a set of guards whose common intersection contains no points outside the polygon. This model leads to a broad class of new art gallery type problems, which we call "sculpture garden" problems and for which we provide upper and lower bounds. In particular, we show there is a polygon P such that a "natural" angle-guard vertex placement cannot fully distinguish between points on the inside and outside of P (even if we place a guard at every vertex of P), which implies that Steiner-point guards are sometimes necessary. More generally, we show that, for any polygon P, there is a set of n + 2(h - 1) angle guards that solve the sculpture garden problem for P, where h is the number of holes in ...
David Eppstein, Michael T. Goodrich, Nodari Sitchi
Added 14 Aug 2010
Updated 14 Aug 2010
Type Conference
Year 2007
Where COMPGEOM
Authors David Eppstein, Michael T. Goodrich, Nodari Sitchinava
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