10.1016/0031-3203(84)90064-5
Aurenhammer,Franz
Franz
Aurenhammer
Herbert Edelsbrunner
Herbert
Edelsbrunner0000-0002-9823-6833
An optimal algorithm for constructing the weighted Voronoi diagram in the plane
Springer
1984
2018-12-11T12:07:05Z
2019-04-26T07:22:41Z
journal_article
https://research-explorer.app.ist.ac.at/record/4125
https://research-explorer.app.ist.ac.at/record/4125.json
Let S denote a set of n points in the plane such that each point p has assigned a positive weight w(p) which expresses its capability to influence its neighbourhood. In this sense, the weighted distance of an arbitrary point x from p is given by de(x,p)/w(p) where de denotes the Euclidean distance function. The weighted Voronoi diagram for S is a subdivision of the plane such that each point p in S is associated with a region consisting of all points x in the plane for which p is a weighted nearest point of S.
An algorithm which constructs the weighted Voronoi diagram for S in O(n2) time is outlined in this paper. The method is optimal as the diagram can consist of Θ(n2) faces, edges and vertices.