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.
|Number of pages||17|
|Journal||Discrete and Computational Geometry|
|State||Published - Sep 1999|