# Computing the minimum visible vertex distance between two polygons

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## Abstract

Given two non-intersecting simple polygons *P* and *Q* with *n* and *m* vertices, respectively, a vertex of *P* is said to be visible from a vertex of *Q* if the segment joining these vertices does not properly intersect any edge of these polygons. The problem of finding a closest visible pair of vertices requires finding two vertices, *p*∈*P* and *q*∈*Q*, that are visible to each other and that are closest to each other among all such pairs. In this paper, we present an *O*((*n*+*m*) log log(*n*+*m*)) time algorithm; this improves upon an earlier result of Wang and Chan by an *O*(log(*n*+*m*)/ log log(*n*+*m*)) factor.

## Key Words

Closest pair visible polygons totally-monotone window-trees link-distance## Preview

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## Copyright information

© Springer-Verlag Berlin Heidelberg 1989