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Journal of Zhejiang University SCIENCE A 2006 Vol.7 No.12 P.2031-2042

http://doi.org/10.1631/jzus.2006.A2031


Redesign of a conformal boundary recovery algorithm for 3D Delaunay triangulation


Author(s):  CHEN Jian-jun, ZHENG Yao

Affiliation(s):  Center for Engineering and Scientific Computation, School of Computer Science, Zhejiang University, Hangzhou 310027, China

Corresponding email(s):   zdchenjj@yahoo.com.cn, yao.zheng@zju.edu.cn

Key Words:  Boundary recovery, Delaunay triangulation, Mesh generation, Data structure


CHEN Jian-jun, ZHENG Yao. Redesign of a conformal boundary recovery algorithm for 3D Delaunay triangulation[J]. Journal of Zhejiang University Science A, 2006, 7(12): 2031-2042.

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author="CHEN Jian-jun, ZHENG Yao",
journal="Journal of Zhejiang University Science A",
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number="12",
pages="2031-2042",
year="2006",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2006.A2031"
}

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%A ZHENG Yao
%J Journal of Zhejiang University SCIENCE A
%V 7
%N 12
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%DOI 10.1631/jzus.2006.A2031

TY - JOUR
T1 - Redesign of a conformal boundary recovery algorithm for 3D Delaunay triangulation
A1 - CHEN Jian-jun
A1 - ZHENG Yao
J0 - Journal of Zhejiang University Science A
VL - 7
IS - 12
SP - 2031
EP - 2042
%@ 1673-565X
Y1 - 2006
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2006.A2031


Abstract: 
boundary recovery is one of the main obstacles in applying the Delaunay criterion to mesh generation. A standard resolution is to add Steiner points directly at the intersection positions between missing boundaries and triangulations. We redesign the algorithm with the aid of some new concepts, data structures and operations, which make its implementation routine. Furthermore, all possible intersection cases and their solutions are presented, some of which are seldom discussed in the literature. Finally, numerical results are presented to evaluate the performance of the new algorithm.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1] Chen, J.J., 2006. Unstructured Mesh Generation and Its Parallelization. Ph.D Thesis, College of Computer Science, Zhejiang University (in Chinese).

[2] Du, Q., Wang, D.S., 2004. Constrained boundary recovery for three dimensional Delaunay triangulations. International Journal for Numerical Methods in Engineering, 61(9):1471-1500.

[3] George, P.L., Hecht, F., Saltel, E., 1991. Automatic mesh generator with specified boundary. Computer Methods in Applied Mechanics and Engineering, 92(3):269-288.

[4] George, P.L., Borouchaki, H., Saltel, E., 2003. ‘Ultimate’ robustness in meshing an arbitrary polyhedron. International Journal for Numerical Methods in Engineering, 58(7):1061-1089.

[5] Lewis, R.W., Zheng, Y., Gethin, D.T., 1996. Three-dimensional unstructured mesh generation: part 3. volume meshes. Computer Methods in Applied Mechanics and Engineering, 134(3-4):285-310.

[6] Liu, A., Baida, M., 2000. How Far Flipping Can Go towards 3D Conforming/Constrained Triangulations. Proceedings of the 11th International Meshing Roundtable, New Orleans, Louisiana, USA, p.307-315.

[7] Ruppert, J., Seidel, R., 1992. On the difficulty of triangulating three-dimensional non-convex polyhedra. Discrete and Computational Geometry, 7(3):227-254.

[8] Song, C., Guan, Z.Q., Gu, Y.X., 2004. Boundary restore algorithm and sliver elimination of 3D constrained Delaunay triangulation. Chinese Journal of Computational Mechanics, 21(2):169-176 (in Chinese).

[9] Weatherill, N.P., Hassan, O., 1994. Efficient three-dimensional Delaunay triangulation with automatic point creation and imposed boundary constraints. International Journal for Numerical Methods in Engineering, 37(12):2005-2039.

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