Finding minimal convex nested polygons

Authors:
Alok Aggarwal;Heather Booth;Joseph O'Rourke;Subhash Suri;Chee K. Yap
Affiliations:
Mathematical Science Department, IBM Research Center, Yorktown Heights, New York;Department of Rlectrical Engineering and Computer Science, The Johns Hopkins University, Baltimore MD;Department of Rlectrical Engineering and Computer Science, The Johns Hopkins University, Baltimore MD;Department of Rlectrical Engineering and Computer Science, The Johns Hopkins University, Baltimore MD;Courant Institute of Mathematical Sciences, 251 Mcrce Street, New York, NY
Venue:
SCG '85 Proceedings of the first annual symposium on Computational geometry
Year:
1985

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Abstract

We consider the problem of finding a polygon nested between two given convex polygons that has a minimal number of vertices. Our main result is an &Ogr;(nlog&kgr;) algorithm for solving the problem, where n is the total number of vertices of the given polygons, and &kgr; is the number of vertices of a minimal nested polygon. We also present an &Ogr;(n) sub-optimal algorithm, and a simple &Ogr;(nk) optimal algorithm.