Bisectors and Voronoi Diagrams for Convex Distance Functions
نویسنده
چکیده
Dissertation zur Erlangung des akademischen Grades eines Doktors der Naturwissenschaften
منابع مشابه
Dilation, smoothed distance, and minimization diagrams of convex functions
Clarkson recently introduced the o-smoothed distance do(p,q) = 2d(p,q)/(d(o, p)+d(o,q)+d(p,q)) (where d denotes the Euclidean distance in the plane) as a geometric analogue of the Jaccard distance; its Voronoi diagrams can be used to determine for a query point q the site p maximizing the dilation (d(p,o)+d(o,q))/d(p,q) of p and q in a star network centered at o. Although smoothed distance is n...
متن کاملAbstract Voronoi diagrams revisited
Voronoi Diagrams Revisited Rolf Klein∗ Elmar Langetepe∗ Zahra Nilforoushan† Abstract Abstract Voronoi diagrams [21] were designed as a unifying concept that should include as many concrete types of diagrams as possible. To ensure that abstract Voronoi diagrams, built from given sets of bisecting curves, are finite graphs, it was required that any two bisecting curves intersect only finitely oft...
متن کاملThe geometric stability of Voronoi diagrams in normed spaces which are not uniformly convex
The Voronoi diagram is a geometric object which is widely used in many areas. Recently it has been shown that under mild conditions Voronoi diagrams have a certain continuity property: small perturbations of the sites yield small perturbations in the shapes of the corresponding Voronoi cells. However, this result is based on the assumption that the ambient normed space is uniformly convex. Unfo...
متن کاملStraight Skeletons by Means of Voronoi Diagrams Under Polyhedral Distance Functions
We consider the question under which circumstances the straight skeleton and the Voronoi diagram of a given input shape coincide. More precisely, we investigate convex distance functions that stem from centrally symmetric convex polyhedra as unit balls and derive sufficient and necessary conditions for input shapes in order to obtain identical straight skeletons and Voronoi diagrams with respec...
متن کاملVoronoi Diagrams for Convex Polygon-Offset Distance Functions
In this paper we develop the concept of a convex polygon-offset distance function. Using offset as a notion of distance, we show how to compute the corresponding nearestand furthest-site Voronoi diagrams of point sites in the plane. We provide nearoptimal deterministic O(n(log n + log m) + m)-time algorithms, where n is the number of points and m is the complexity of the underlying polygon, for...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2000