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Title: Discrete geodesic graph (DGG) for computing geodesic distances on polyhedral surfaces
Authors: Wang, Xiaoning
Fang, Zheng
Wu, Jiajun
Xin, Shi-Qing
He, Ying
Keywords: Geodesic Distances
Polyhedral Surfaces
Issue Date: 2017
Source: Wang, 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.
Series/Report no.: Computer Aided Geometric Design
Abstract: We 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.
ISSN: 0167-8396
DOI: 10.1016/j.cagd.2017.03.010
Schools: School of Computer Science and Engineering 
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: [].
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SCSE Journal Articles

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