Planar Minimization Diagrams via Subdivision with Applications to Anisotropic Voronoi Diagrams

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dc.contributor.authorBennett, Hucken_US
dc.contributor.authorPapadopoulou, Evanthiaen_US
dc.contributor.authorYap, Cheeen_US
dc.contributor.editorMaks Ovsjanikov and Daniele Panozzoen_US
dc.date.accessioned2016-06-17T14:12:09Z
dc.date.available2016-06-17T14:12:09Z
dc.date.issued2016en_US
dc.description.abstractLet X = {f1, . . ., fn} be a set of scalar functions of the form fi : R2 →R which satisfy some natural properties. We describe a subdivision algorithm for computing a clustered e-isotopic approximation of the minimization diagram of X. By exploiting soft predicates and clustering of Voronoi vertices, our algorithm is the first that can handle arbitrary degeneracies in X, and allow scalar functions which are piecewise smooth, and not necessarily semi-algebraic. We apply these ideas to the computation of anisotropic Voronoi diagram of polygonal sets; this is a natural generalization of anisotropic Voronoi diagrams of point sites, which extends multiplicatively weighted Voronoi diagrams. We implement a prototype of our anisotropic algorithm and provide experimental results.en_US
dc.description.number5en_US
dc.description.sectionheadersVoronoi et al.en_US
dc.description.seriesinformationComputer Graphics Forumen_US
dc.description.volume35en_US
dc.identifier.doi10.1111/cgf.12979en_US
dc.identifier.issn1467-8659en_US
dc.identifier.pages229-247en_US
dc.identifier.urihttps://doi.org/10.1111/cgf.12979en_US
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.subjecten_US
dc.titlePlanar Minimization Diagrams via Subdivision with Applications to Anisotropic Voronoi Diagramsen_US
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35-Issue 5
SGP16: Eurographics Symposium on Geometry Processing (CGF 35-5)