The Area Bisectors of a Polygon and Force Equilibria in Programmable Vector Fields

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 di erent partitionings of the vertices of P. We show that there are simple polygons with n vertices that have n2 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, exible feeding devices for parts positioning and orienting. The question of determining all the bisectors of polygonal parts arises in connection with the development of e cient part positioning strategies when using these devices.

• Type: Conference
• Year: 1997
• Where: COMPGEOM
• Authors: Karl-Friedrich Böhringer, Bruce Randall Donald, Dan Halperin
• Keywords: Area Bisectors, COMPGEOM 1997, Discrete Geometry, Distinct Area Bisectors, Polygons