Multiple covers with balls I: Inclusion–exclusion

Inclusion–exclusion is an effective method for computing the volume of a union of measurable sets. We extend it to multiple coverings, proving short inclusion–exclusion formulas for the subset of Rn covered by at least k balls in a finite set. We implement two of the formulas in dimension n=3 and re...

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Bibliographic Details
Published in:Computational geometry : theory and applications 2018-03, Vol.68, p.119-133
Main Authors: Edelsbrunner, Herbert, Iglesias-Ham, Mabel
Format: Article
Language:English
Subjects:
Exact computation
Hyperplane arrangements
Inclusion–exclusion
Multiple cover with balls
Voronoi diagrams
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Summary:Inclusion–exclusion is an effective method for computing the volume of a union of measurable sets. We extend it to multiple coverings, proving short inclusion–exclusion formulas for the subset of Rn covered by at least k balls in a finite set. We implement two of the formulas in dimension n=3 and report on results obtained with our software.
ISSN:0925-7721
DOI:10.1016/j.comgeo.2017.06.014