An optimal algorithm for constructing the weighted Voronoi diagram in the plane
Aurenhammer,Franz
Herbert Edelsbrunner
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.
Springer
1984
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doc-type:article
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https://research-explorer.app.ist.ac.at/record/4125
Aurenhammer F, Edelsbrunner H. An optimal algorithm for constructing the weighted Voronoi diagram in the plane. <i>Pattern Recognition</i>. 1984;17(2):251-257. doi:<a href="https://doi.org/10.1016/0031-3203(84)90064-5">10.1016/0031-3203(84)90064-5</a>
info:eu-repo/semantics/altIdentifier/doi/10.1016/0031-3203(84)90064-5
info:eu-repo/semantics/closedAccess