On the area bisectors of a polygon

K. F. Böhringer*, B. R. Donald, D. Halperin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


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 (n2) 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.

Original languageEnglish
Pages (from-to)269-285
Number of pages17
JournalDiscrete and Computational Geometry
Issue number2
StatePublished - Sep 1999


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