Covering points with orthogonally convex polygons
نویسندگان
چکیده
منابع مشابه
Covering the Plane with Convex Polygons
It is proved that for any centrally symmetric convex polygonal domain P and for any natural number r, there exists a constant k = k(P, r) such that any k-fold covering of the plane with translates of P can be split into r simple coverings.
متن کاملCovering convex bodies by cylinders and lattice points by flats ∗
In connection with an unsolved problem of Bang (1951) we give a lower bound for the sum of the base volumes of cylinders covering a d-dimensional convex body in terms of the relevant basic measures of the given convex body. As an application we establish lower bounds on the number of k-dimensional flats (i.e. translates of k-dimensional linear subspaces) needed to cover all the integer points o...
متن کاملCovering Orthogonal Polygons with Sliding k-Transmitters
In this paper we consider a new variant of covering in an orthogonal art gallery problem where each guard is a sliding k-transmitter. Such a guard can travel back and forth along an orthogonal line segment, say s, inside the polygon. A point p is covered by this guard if there exists a point q ∈ s such that pq is a line segment normal to s and has at most k intersections with the polygon’s boun...
متن کاملCovering oriented points in the plane with orthogonal polygons is NP-complete
We address the problem of covering points with orthogonal polygons. Specifically, given a set of n grid-points in the plane each designated in advance with either a horizontal or vertical reading, we investigate the existence of an orthogonal polygon covering these n points in such a way that each edge of the polygon covers exactly one point and each point is covered by exactly one edge with th...
متن کاملCovering space with convex bodies
1. A few years ago Rogers [1] showed that, if K is any convex body in n-dimensional Euclidian space, there is a covering of the whole space by translates of K with density less than nlogn+nloglogn+5n, provided n > 3. However the fact that the covering density is reasonably small does not imply that the maximum multiplicity is also small. In the natural covering of space by closed cubes, the den...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Computational Geometry
سال: 2011
ISSN: 0925-7721
DOI: 10.1016/j.comgeo.2010.12.001