Abstract
Given simple polygons P and Q, their separation, denoted by σ(P,Q), is defined to be the minimum distance between their boundaries. We present an optimal Θ(N) algorithm for determining the separation of two simple polygons P and Q, where |P|+|Q|=|N|. The best previous algorithm for this problem is due to Kirkpatrick and has complexity O(N log N). In addition, a parallel version of our algorithm can be implemented in O(log N) time using O(N) processors on a CREW PRAM. Our results are obtained by providing a unified treatment of the separation and the closest visible vertex problems for simple polygons.
Cite
CITATION STYLE
Amato, N. M. (1993). An optimal algorithm for finding the separation of simple polygons. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 709 LNCS, pp. 48–59). Springer Verlag. https://doi.org/10.1007/3-540-57155-8_235
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