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res:
bibo_abstract:
- |-
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.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Franz
foaf_name: Aurenhammer,Franz
foaf_surname: Aurenhammer
- foaf_Person:
foaf_givenName: Herbert
foaf_name: Herbert Edelsbrunner
foaf_surname: Edelsbrunner
foaf_workInfoHomepage: http://www.librecat.org/personId=3FB178DA-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0002-9823-6833
bibo_doi: 10.1016/0031-3203(84)90064-5
bibo_issue: '2'
bibo_volume: 17
dct_date: 1984^xs_gYear
dct_publisher: Springer@
dct_title: An optimal algorithm for constructing the weighted Voronoi diagram in
the plane@
...