SPECIAL POINTS OF WEIGHTED VORONOI TELES IN THE Lp METRIC

摘要

Voronoi diagrams have frequently been used to model competition in physical and biological systems [1] and optimal algorithms for their construction have been well studied [2]. These forms of tesselation do not model the effects due to the differing sizes of individuals; however, a deficiency which is addressed by Weighted Voronoi Diagrams (WVD) [3], where distances between objects are calculated in a weighted sense. An optimal algorithm for determining the WVD was developed by Aurenhammer and Edelsbrunner [3] and a method employing the clipping and shielding concepts of computer graphics was developed by Hoskins and Hoskins [4]. Lee [5] considered a more general form of Voronoi Diagram, where the distance measure was defined to be the Lp metric, but did not extend the Lp metric to an examination of WVD. In this paper, we consider WVD in the Lp metric.