Obtuse triangle suppression in anisotropic meshes

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

Obtuse triangle suppression in anisotropic meshes

Type

Article

Authors

Sun, Feng
Choi, Yi King
Wang, Wen Ping
Yan, Dongming

Liu, Yang
Lévy, Bruno L.

KAUST Department

Visual Computing Center (VCC)

Date

2011-12

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.

Citation

Sun, F., Choi, Y.-K., Wang, W., Yan, D.-M., Liu, Y., & Lévy, B. (2011). Obtuse triangle suppression in anisotropic meshes. Computer Aided Geometric Design, 28(9), 537–548. doi:10.1016/j.cagd.2011.09.007

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).