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Title: Polyline-sourced geodesic voronoi diagrams on triangle meshes
Authors: Xu, Chunxu
Liu, Yong-Jin
Sun, Qian
Li, Jinyan
He, Ying
Keywords: Curve
Issue Date: 2014
Source: Xu, C., Liu, Y.-J., Sun, Q., Li, J., & He, Y. (2014). Polyline-sourced geodesic voronoi diagrams on triangle meshes. Computer Graphics Forum, 33(7), 161-170.
Series/Report no.: Computer Graphics Forum
Abstract: This paper studies the Voronoi diagrams on 2‐manifold meshes based on geodesic metric (a.k.a. geodesic Voronoi diagrams or GVDs), which have polyline generators. We show that our general setting leads to situations more complicated than conventional 2D Euclidean Voronoi diagrams as well as point‐source based GVDs, since a typical bisector contains line segments, hyperbolic segments and parabolic segments. To tackle this challenge, we introduce a new concept, called local Voronoi diagram (LVD), which is a combination of additively weighted Voronoi diagram and line‐segment Voronoi diagram on a mesh triangle. We show that when restricting on a single mesh triangle, the GVD is a subset of the LVD and only two types of mesh triangles can contain GVD edges. Based on these results, we propose an efficient algorithm for constructing the GVD with polyline generators. Our algorithm runs in O(nNlogN) time and takes O(nN) space on an n‐face mesh with m generators, where N=max{m, n}. Computational results on real‐world models demonstrate the efficiency of our algorithm.
ISSN: 0167-7055
DOI: 10.1111/cgf.12484
Rights: © 2014 The Author(s) (©The Eurographics Association and John Wiley & Sons Ltd). This is the author created version of a work that has been peer reviewed and accepted for publication by Computer Graphics Forum, The Author(s) (©The Eurographics Association and John Wiley & Sons Ltd). 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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