Anisotropic centroidal Voronoi tessellations and their applications

被引：111

作者：

Du, Q ^{[1
]}

Wang, DS

机构：

[1] Penn State Univ, Dept Math, University Pk, PA 16802 USA

[2] Univ Coll Swansea, Sch Engn, Civil & Computat Engn Ctr, Swansea SA2 8PP, W Glam, Wales

[3] Acad Sinica, Lab Sci & Engn Comp, Beijing, Peoples R China

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2005年 / 26卷 / 03期

关键词：

Voronoi tessellations; anisotropy; Riemannian metric; anisotropic Delaunay triangulation; optimal tessellations; optimal mesh; surface mesh; surface triangulation;

D O I：

10.1137/S1064827503428527

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：737 / 761

页数：25

共 39 条

[31]

2-F

[32]

Leibon Greg., 2000, Symp. Comp. Geom, P341, DOI https://doi.org/10.1145/336154.336221

[33]

LI XY, 1999, P 8 INT MESH ROUNDT, P97

[34]

LLOYD SP, 1982, IEEE T INFORM THEORY, V28, P129, DOI 10.1109/TIT.1982.1056489

[35] Regridding surface triangulations [J].

Lohner, R .

JOURNAL OF COMPUTATIONAL PHYSICS, 1996, 126 (01) :1-10

[36]

Okabe A., 1992, SPATIAL TESSELLATION

[37] AUTOMATIC 3-DIMENSIONAL MESH GENERATION BY THE FINITE OCTREE TECHNIQUE [J].

SHEPHARD, MS ;

GEORGES, MK .

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 1991, 32 (04) :709-749

[38]

SHIMADA K, 1997, P 6 INT MESH ROUNDT, P63

[39]

Tristano J., 1998, P 7 INT MESHING ROUN, P429

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