Multiple Covers with Balls II: Weighted Averages

Voronoi diagrams and Delaunay triangulations have been extensively used to represent and compute geometric features of point configurations. We introduce a generalization to poset diagrams and poset complexes, which contain order-k and degree-k Voronoi diagrams and their duals as special cases. Exte...

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Bibliographic Details
Published in:Electronic notes in discrete mathematics 2016-10, Vol.54, p.169-174
Main Authors: Edelsbrunner, Herbert, Iglesias-Ham, Mabel
Format: Article
Language:English
Subjects:
Poset diagrams
Voronoi diagrams
Weighted points
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Summary:Voronoi diagrams and Delaunay triangulations have been extensively used to represent and compute geometric features of point configurations. We introduce a generalization to poset diagrams and poset complexes, which contain order-k and degree-k Voronoi diagrams and their duals as special cases. Extending a result of Aurenhammer from 1990, we show how to construct poset diagrams as weighted Voronoi diagrams of average balls.
ISSN:1571-0653
1571-0653
DOI:10.1016/j.endm.2016.09.030