On Boundaries of Highly Visible Spaces and Applications

13 years 9 months ago

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The purpose of this paper is to investigate the properties of a certain class of highly visible spaces. For a given geometric space C containing obstacles speciﬁed by disjoint subsets of C, the free space F is deﬁned to be the portion of C not occupied by these obstacles. The space is said to be highly visible if at each point in F a viewer can see at least an fraction of the entire F. This assumption has been used for robotic motion planning in the analysis of random sampling of points in the robot’s conﬁguration space, as well as the upper bound of the minimum number of guards needed for art gallery problems. However, there is no prior result on the implication of this assumption to the geometry of the space under study. For the two-dimensional case, with the additional assumptions that C is bounded within a rectangle of constant aspect ratio and that the volume ratio between F and C is a constant, we use the proof technique of “charging” each obstacle boundary segment b...

John H. Reif, Zheng Sun

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