Obtuse triangle suppression in anisotropic meshes

Feng Sun; Yi King Choi; Wen Ping Wang; Dongming Yan; Yang Liu; Bruno L. Lévy

doi:10.1016/j.cagd.2011.09.007

Obtuse triangle suppression in anisotropic meshes

Feng Sun, Yi King Choi, Wen Ping Wang, Dongming Yan, Yang Liu, Bruno L. Lévy

Computer, Electrical and Mathematical Sciences and Engineering

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

Abstract

Anisotropic triangle meshes are used for efficient approximation of surfaces and flow data in finite element analysis, and in these applications it is desirable to have as few obtuse triangles as possible to reduce the discretization error. We present a variational approach to suppressing obtuse triangles in anisotropic meshes. Specifically, we introduce a hexagonal Minkowski metric, which is sensitive to triangle orientation, to give a new formulation of the centroidal Voronoi tessellation (CVT) method. Furthermore, we prove several relevant properties of the CVT method with the newly introduced metric. Experiments show that our algorithm produces anisotropic meshes with much fewer obtuse triangles than using existing methods while maintaining mesh anisotropy. © 2011 Elsevier B.V. All rights reserved.

Original language	English (US)
Pages (from-to)	537-548
Number of pages	12
Journal	Computer Aided Geometric Design
Volume	28
Issue number	9
DOIs	https://doi.org/10.1016/j.cagd.2011.09.007
State	Published - Dec 2011

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: We thank the reviewers for constructive comments. This work is funded in part by the Research Grant Council of Hong Kong (718010 and 718209), the State Key Program of NSFC project of China (60933008) and the European Research Council (GOODSHAPE ERC-2tG-205693).

ASJC Scopus subject areas

Modeling and Simulation
Computer Graphics and Computer-Aided Design
Automotive Engineering
Aerospace Engineering

Access to Document

10.1016/j.cagd.2011.09.007

Cite this

@article{d6d8bc40c2a64b409d2976a4e5cf8dd5,

title = "Obtuse triangle suppression in anisotropic meshes",

abstract = "Anisotropic triangle meshes are used for efficient approximation of surfaces and flow data in finite element analysis, and in these applications it is desirable to have as few obtuse triangles as possible to reduce the discretization error. We present a variational approach to suppressing obtuse triangles in anisotropic meshes. Specifically, we introduce a hexagonal Minkowski metric, which is sensitive to triangle orientation, to give a new formulation of the centroidal Voronoi tessellation (CVT) method. Furthermore, we prove several relevant properties of the CVT method with the newly introduced metric. Experiments show that our algorithm produces anisotropic meshes with much fewer obtuse triangles than using existing methods while maintaining mesh anisotropy. {\textcopyright} 2011 Elsevier B.V. All rights reserved.",

author = "Feng Sun and Choi, {Yi King} and Wang, {Wen Ping} and Dongming Yan and Yang Liu and L{\'e}vy, {Bruno L.}",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: We thank the reviewers for constructive comments. This work is funded in part by the Research Grant Council of Hong Kong (718010 and 718209), the State Key Program of NSFC project of China (60933008) and the European Research Council (GOODSHAPE ERC-2tG-205693).",

year = "2011",

month = dec,

doi = "10.1016/j.cagd.2011.09.007",

language = "English (US)",

volume = "28",

pages = "537--548",

journal = "Computer Aided Geometric Design",

issn = "0167-8396",

publisher = "Elsevier B.V.",

number = "9",

}

TY - JOUR

T1 - Obtuse triangle suppression in anisotropic meshes

AU - Sun, Feng

AU - Choi, Yi King

AU - Wang, Wen Ping

AU - Yan, Dongming

AU - Liu, Yang

AU - Lévy, Bruno L.

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: We thank the reviewers for constructive comments. This work is funded in part by the Research Grant Council of Hong Kong (718010 and 718209), the State Key Program of NSFC project of China (60933008) and the European Research Council (GOODSHAPE ERC-2tG-205693).

PY - 2011/12

Y1 - 2011/12

N2 - Anisotropic triangle meshes are used for efficient approximation of surfaces and flow data in finite element analysis, and in these applications it is desirable to have as few obtuse triangles as possible to reduce the discretization error. We present a variational approach to suppressing obtuse triangles in anisotropic meshes. Specifically, we introduce a hexagonal Minkowski metric, which is sensitive to triangle orientation, to give a new formulation of the centroidal Voronoi tessellation (CVT) method. Furthermore, we prove several relevant properties of the CVT method with the newly introduced metric. Experiments show that our algorithm produces anisotropic meshes with much fewer obtuse triangles than using existing methods while maintaining mesh anisotropy. © 2011 Elsevier B.V. All rights reserved.

AB - Anisotropic triangle meshes are used for efficient approximation of surfaces and flow data in finite element analysis, and in these applications it is desirable to have as few obtuse triangles as possible to reduce the discretization error. We present a variational approach to suppressing obtuse triangles in anisotropic meshes. Specifically, we introduce a hexagonal Minkowski metric, which is sensitive to triangle orientation, to give a new formulation of the centroidal Voronoi tessellation (CVT) method. Furthermore, we prove several relevant properties of the CVT method with the newly introduced metric. Experiments show that our algorithm produces anisotropic meshes with much fewer obtuse triangles than using existing methods while maintaining mesh anisotropy. © 2011 Elsevier B.V. All rights reserved.

UR - http://hdl.handle.net/10754/561945

UR - https://linkinghub.elsevier.com/retrieve/pii/S0167839611001208

UR - http://www.scopus.com/inward/record.url?scp=81355146381&partnerID=8YFLogxK

U2 - 10.1016/j.cagd.2011.09.007

DO - 10.1016/j.cagd.2011.09.007

M3 - Article

SN - 0167-8396

VL - 28

SP - 537

EP - 548

JO - Computer Aided Geometric Design

JF - Computer Aided Geometric Design

IS - 9

ER -

Obtuse triangle suppression in anisotropic meshes

Abstract

Bibliographical note

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this