Polyline-sourced Geodesic Voronoi Diagrams on Triangle Meshes

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‐sou...

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Vydáno v:	Computer graphics forum Ročník 33; číslo 7; s. 161 - 170
Hlavní autoři:	Xu, Chunxu, Liu, Yong-Jin, Sun, Qian, Li, Jinyan, He, Ying
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Oxford Blackwell Publishing Ltd 01.10.2014
Témata:	Algorithms Analysis and object representations Categories and Subject Descriptors (according to ACM CCS) Computer graphics I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling-Curve I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Curve, surface, solid, and object representations solid Studies surface Topological manifolds
ISSN:	0167-7055, 1467-8659
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Popis
Shrnutí:	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.
Bibliografie:	ark:/67375/WNG-18X0SHKM-S Supporting Information istex:BC38B30276BFD61D83AA16B93EF388F68E6C6B41 ArticleID:CGF12484 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14
ISSN:	0167-7055 1467-8659
DOI:	10.1111/cgf.12484