منابع مشابه
Face-Guarding Polyhedra
We study the Art Gallery Problem for face guards in polyhedral environments. The problem can be informally stated as: how many (not necessarily convex) windows should we place on the external walls of a dark building, in order to completely illuminate it? We consider both closed and open face guards (i.e., faces with or without their boundary), and we give some upper and lower bounds on the min...
متن کاملEdge-guarding Orthogonal Polyhedra
We address the question: How many edge guards are needed to guard an orthogonal polyhedron of e edges, r of which are reflex? It was previously established [3] that e/12 are sometimes necessary and e/6 always suffice. In contrast to the closed edge guards used for these bounds, we introduce a new model, open edge guards (excluding the endpoints of the edge), which we argue are in some sense mor...
متن کاملGuarding and Searching Polyhedra
Guarding and searching problems have been of fundamental interest since the early years of Computational Geometry. Both are well-developed areas of research and have been thoroughly studied in planar polygonal settings. In this thesis we tackle the Art Gallery Problem and the Searchlight Scheduling Problem in 3-dimensional polyhedral environments, putting special emphasis on edge guards and ort...
متن کاملLists of Face-Regular Polyhedra
We introduce a new notion that connects the combinatorial concept of regularity with the geometrical notion of face transitivity. This new notion implies finiteness results in the case of bounded maximal face size. We give lists of structures for some classes and investigate polyhedra with constant vertex degrees and faces of only two sizes.
متن کاملOptimally Guarding 2-Reflex Orthogonal Polyhedra by Reflex Edge Guards
We study the problem of guarding an orthogonal polyhedron having reflex edges in just two directions (as opposed to three) by placing guards on reflex edges only. We show that ⌊ r − g 2 ⌋
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 2015
ISSN: 0925-7721
DOI: 10.1016/j.comgeo.2015.01.003