Isotropic Remeshing with Fast and Exact Computation of Restricted Voronoi Diagram

We propose a new isotropic remeshing method, based on Centroidal Voronoi Tessellation (CVT). Constructing CVT requires to repeatedly compute Restricted Voronoi Diagram (RVD), defined as the intersection between a 3D Voronoi diagram and an input mesh surface. Existing methods use some approximations...

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Vydané v:Computer graphics forum Ročník 28; číslo 5; s. 1445 - 1454
Hlavní autori: Yan, Dong-Ming, Lévy, Bruno, Liu, Yang, Sun, Feng, Wang, Wenping
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Oxford, UK Blackwell Publishing Ltd 01.07.2009
Wiley
Predmet:
Approximation
Computer graphics
Computer programming
Computer Science
Graphics
I.3.3 [Computer Graphics]: Picture/Image Generation-Line and curve generation
Image processing systems
Quality
Studies
ISSN:0167-7055, 1467-8659
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Popis
Shrnutí:We propose a new isotropic remeshing method, based on Centroidal Voronoi Tessellation (CVT). Constructing CVT requires to repeatedly compute Restricted Voronoi Diagram (RVD), defined as the intersection between a 3D Voronoi diagram and an input mesh surface. Existing methods use some approximations of RVD. In this paper, we introduce an efficient algorithm that computes RVD exactly and robustly. As a consequence, we achieve better remeshing quality than approximation‐based approaches, without sacrificing efficiency. Our method for RVD computation uses a simple procedure and a kd‐tree to quickly identify and compute the intersection of each triangle face with its incident Voronoi cells. Its time complexity is O(mlog n), where n is the number of seed points and m is the number of triangles of the input mesh. Fast convergence of CVT is achieved using a quasi‐Newton method, which proved much faster than Lloyd's iteration. Examples are presented to demonstrate the better quality of remeshing results with our method than with the state‐of‐art approaches.
Bibliografia:istex:421B82DD357C88F6F7D1907D8501ADA805A7AECE
ark:/67375/WNG-3Q2QG58M-T
ArticleID:CGF1521
SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ObjectType-Article-2
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ISSN:0167-7055
1467-8659
DOI:10.1111/j.1467-8659.2009.01521.x