On the Area Bisectors of a Polygon* R --i
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چکیده
We consider the family of lines that are area bisectors of a polygon (possibly with holes) in the plane. We say that two bisectors of a polygon P are combinatorially distinct if they induce different partitionings of the vertices of P. We derive an algebraic characterization of area bisectors. We then show that there are simple polygons with II vertices that have R (n*) combinatorially distinct area bisectors (matching the obvious upper bound), and present an output-sensitive algorithm for computing an explicit representation of all the bisectors of a given polygon. * Work on this paper by Karl-Friedrich Bohringer and Bruce Randall Donald has been supported in part by the National Science Foundation under Grant Nos. IRI-8802390, IRI-9000532, IRI-9201699, IRI-9530785, IRI-9896020, by a Presidential Young Investigator award to Bruce Donald, by an NSF/ARPA Small Grant for Exploratory Research No. IRI-9403903, by an NSF CISE Postdoctoral Associateship to Karl Bohringer No. CDA-9705022, and in part by the Air Force Office of Sponsored Research, the Mathematical Sciences Institute, Intel Corporation, and AT&T Bell laboratories. Work on this paper by Dan Halperin has been supported in part by an Alon Fellowship, by ESPRIT IV LTR Project No. 21957 (CGAL), by the USA-Israel Binational Science Foundation, by the Israel Science Foundation founded by the Israel Academy of Sciences and Humanities, and by the Hermann Minkowski Minerva Center for Geometry at Tel Aviv University. A preliminary and abridged version of the paper appeared in Proc. 13thACMSymp. on Compurarional Geometry, Nice, 1997, pp. 457-459. Part of the work on this paper was carried out while Dan Halperin was at the Robotics Laboratory, Department of Computer Science, Stanford University.
منابع مشابه
On the Area Bisectors of a Polygon
We consider the family of lines that are area bisectors of a polygon (possibly with holes) in the plane. We say that two bisectors of a polygon P are combinatorially distinct if they induce di erent partitionings of the vertices of P . We derive an algebraic characterization of area bisectors. We then show that there are simple polygons with n vertices that have (n) combinatorially distinct are...
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تاریخ انتشار 1999