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 II vertices that have R (n*) combinatorially distinct...

Details of algorithms to construct the Voronoi diagrams and medial axes of planars domain bounded by free-form (polynomial or rational) curve segments are presented, based on theoretical foundations given in the rst installment Ramamurthy and Farouki, J. Comput. Appl. Math. (1999) 102 119–141 of this two-part paper. In particular, we focus on key topological and computational issues that arise ...

In this paper we initiate the study of tropical Voronoi diagrams. We start out with investigating bisectors finitely many points respect to arbitrary polyhedral norms. For more general scenario show that three are homeomorphic a non-empty open subset Euclidean space, provided certain degenerate cases excluded. Specializing our results then yields structural and algorithms for

We investigate the structure of the bisector of point sites under arbitrary convex distance functions in three dimensions. Our results show that it is advantageous for analyzing bisectors to consider their central projection on the unit sphere, thereby reducing by one the dimension of the problem. From the concept of “silhouettes” and their intersections we obtain simple characterizations of im...

In the present paper some geometric inequalities concerning the angle bisectors and the medians of a triangle are established. Mathematics subject classification (2010): Primary 26D15.