Cut Locus Construction using Deformable Simplicial Complexes

Marek Krzysztof Misztal, Jakob Andreas Bærentzen, François Anton, Steen Markvorsen

    Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

    Abstract

    In this paper we present a method for appproximating cut loci for a given point p on Riemannian 2D manifolds, closely related to the notion of Voronoi diagrams. Our method finds the cut locus by advecting a front of points equally distant from p along the geodesics originating at p and finding the lines of self-intersections of the front in the parametric space. This becomes possible by using the deformable simplicial complexes (DSC, [1]) method for deformable interface tracking. DSC provide a simple collision detection mechanism, allows for interface topology control, and does not require the domain to have disk topology. We test our method for tori of revolution and compare our results to the benchmark ones from [2]. The method, however, is generic and can be easily adapted to construct cut loci for other manifolds of genera other than 1.
    Original languageEnglish
    Title of host publication2011 Eighth International Symposium on Voronoi Diagrams in Science and Engineering (ISVD)
    PublisherIEEE
    Publication date2011
    Pages134-141
    ISBN (Print)978-1-4577-1026-1
    DOIs
    Publication statusPublished - 2011
    Event8th International Symposium on Voronoi Diagrams in Science and Engineering - Qingdao, China
    Duration: 28 Jun 201130 Jun 2011
    Conference number: 8
    http://informatik.uni-trier.de/~ley/db/conf/isvd/isvd2011.html

    Conference

    Conference8th International Symposium on Voronoi Diagrams in Science and Engineering
    Number8
    CountryChina
    CityQingdao
    Period28/06/201130/06/2011
    Internet address

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