Anisotropic centroidal voronoi tessellations and their applications

Anisotropic centroidal voronoi tessellations and their applications

In this paper, we introduce a novel definition of the anisotropic centroidal Voronoi tessellation (ACVT) corresponding to a given Riemann metric tensor. A directional distance function is used in the definition to simplify the computation. We provide algorithms to approximate the ACVT using the Lloy...

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Bibliographic Details
Main Authors: Wang, Desheng, Du, Qiang
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2009
Subjects:
DRNTU::Science::Mathematics::Applied mathematics::Numerical analysis
Online Access:https://hdl.handle.net/10356/98741
http://hdl.handle.net/10220/6047
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Institution: Nanyang Technological University
Language: English
Description
Summary:In this paper, we introduce a novel definition of the anisotropic centroidal Voronoi tessellation (ACVT) corresponding to a given Riemann metric tensor. A directional distance function is used in the definition to simplify the computation. We provide algorithms to approximate the ACVT using the Lloyd iteration and the construction of anisotropic Delaunay triangulation under the given Riemannian metric. The ACVT is applied to the optimization of two-dimensional anisotropic Delaunay triangulation, to the generation of surface CVT, and high-quality triangular mesh on general surfaces. Various numerical examples demonstrating the effectiveness of the proposed method are presented.

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