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 -