Abstract.
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 n vertices that have Ω(n 2 ) 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.
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Received September 11, 1997, and in revised form April 8, 1998.
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-F. Böhringer, K., Donald, B. & Halperin, D. On the Area Bisectors of a Polygon . Discrete Comput Geom 22, 269–285 (1999). https://doi.org/10.1007/PL00009460
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DOI: https://doi.org/10.1007/PL00009460