The area bisectors of a polygon and force equilibria in programmable vector fields
K. F. Böhringer, Bruce Randall Donald, Dan Halperin · 1997
We consider the family of 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 show that there are simple polygons with n vertices that have fl(nz ) combinatorially distinct area bisectors (matching the obvious upper bound), and we present an output-sensitive algorithm for computing an explicit representation of all the bisectors of a given polygon.Our study is motivated by the development of novel, flexible feeding devices for parts positioning and orienting.The question of determining all the bisectors of polygonal parts arises in connection with the development of efficient part positioning strategies when using these devices.