dc.contributor.authorWang, Xiaoning
dc.contributor.authorFang, Zheng
dc.contributor.authorWu, Jiajun
dc.contributor.authorXin, Shi-Qing
dc.contributor.authorHe, Ying
dc.identifier.citationWang, X., Fang, Z., Wu, J., Xin, S.-Q., & He, Y. (2017). Discrete geodesic graph (DGG) for computing geodesic distances on polyhedral surfaces. Computer Aided Geometric Design, 52-53, 262-284.en_US
dc.description.abstractWe present a new graph-based method, called discrete geodesic graph (DGG), to compute discrete geodesics in a divide-and-conquer manner. Let M be a manifold triangle mesh with n vertices and ε>0 the given accuracy parameter. Assume the vertices are uniformly distributed on the input mesh. We show that the DGG associated to M has O(n/sqrt(ε)) edges and the shortest path distances on the graph approximate geodesic distances on M with relative error O(ε). Computational results show that the actual error is less than 0.6ε on common models. Taking advantage of DGG's unique features, we develop a DGG-tailored label-correcting algorithm that computes geodesic distances in empirically linear time. With DGG, we can guarantee the computed distances are true distance metrics, which is highly desired in many applications. We observe that DGG significantly outperforms saddle vertex graph (SVG) – another graph based method for discrete geodesics – in terms of graph size, accuracy control and runtime performance.en_US
dc.description.sponsorshipMOE (Min. of Education, S’pore)en_US
dc.format.extent19 p.en_US
dc.relation.ispartofseriesComputer Aided Geometric Designen_US
dc.rights© 2017 Elsevier. This is the author created version of a work that has been peer reviewed and accepted for publication by Computer Aided Geometric Design, Elsevier. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [http://dx.doi.org/10.1016/j.cagd.2017.03.010].en_US
dc.subjectGeodesic Distancesen_US
dc.subjectPolyhedral Surfacesen_US
dc.titleDiscrete geodesic graph (DGG) for computing geodesic distances on polyhedral surfacesen_US
dc.typeJournal Article
dc.contributor.schoolSchool of Computer Science and Engineeringen_US
dc.description.versionAccepted versionen_US

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