Algorithm of Mesh Generation of Feature Constraint-based Tetrahedralization

  • Key Laboratory of Virtual Geographical Environment, Nanjing Normal University, Nanjing 210046,China

Received date: 2012-06-27

  Revised date: 2012-09-19

  Online published: 2012-10-25


In the modeling process of Virtual Geographic Environment (VGE), as the geological objects generally have characteristics such as complex boundary, many spatial feature constraints including point, line, face and inside hole type, and meanwhile geosciences analysis and calculation require meshes with high quality, it is hard to construct three-dimensional meshes which regard for complex spatial feature constraints of geological objects exactly and have high quality for geosciences analysis and calculation. Aiming at this problem, a constrained Delaunay discrete algorithm of tetrahedral mesh is put forward in this paper. This algorithm first expresses constrained features of complex geological objects as a series of constraint points, constraint segments and constraint faces in Piecewise Linear Complexes (PLC), and then implements the initial Delaunay tetrahedral subdivision from the initial point set of the geological objects Piecewise Linear Complexes by using the Bowyer-Watson algorithm. Following the upper steps, the algorithm recovers the lost constraint lines and the lost constraint faces in sequence through adding some extra vertices during the mesh discrete process and it should guarantee the adding vertices do not encroach other constraint lines or constraint faces. The constraint face recovery is after the constraint line recovery and it is more difficult and complex than the constraint line recovery. In this step, some local meshes are demanded to reconstruct and must conform to the Delaunay empty circumsphere criterion. And then, the object model external tetrahedron elements should be deleted by adopting a marking method. After this step, it performs the mesh quality control process by restricting the maximum radius-distance ratio or the volume of tetrahedron element in the mesh. In this step, some extra vertices are also added in the tetrahedron elements which can not satisfy the user restricting quality. It is proved that the algorithm can produce meshes not only satisfying different constrained criteria but also with high quality for geosciences analysis and calculation.

Cite this article

GUO Fei, TU Chu-Juan, LI Xiang, ZHOU Liang-Chen . Algorithm of Mesh Generation of Feature Constraint-based Tetrahedralization[J]. Journal of Geo-information Science, 2012 , 14(5) : 555 -561 . DOI: 10.3724/SP.J.1047.2012.00555


[1] 闾国年. 地理分析导向的虚拟地理环境:框架、结构与功能[J].中国科学,2011,41(4):549-561.

[2] 韦玉春,陈锁忠,等. 地理建模原理与方法[M].北京:科学出版社,2005,306-311.

[3] 李爽,姚静. 虚拟地理环境的多维数据模型与地理过程表达[J].地理与地理信息科学,2005,21(4):1-5.

[4] 王彦兵,吴立新,史文中. GTP模型中四面体的引入及其空间模型扩展[J].地理与地理信息科学,2003,19 (5):16-19.

[5] Rajan V T. Optimality of the Delaunay triangulation in R4[J]. Discrete & Computational Geometry, 1994,12:189-202.

[6] 赵建军,王启付. 边界一致的Delaunay四面体网格稳定生成算法[J].机械工程学报,2004,40(6):100-105.

[7] Preparata E P, Shamos M I. Computational geometry: An introduction . New York/Berlin: Springer-Verlag, 1985.

[8] Si H. On refinement of constrained Delaunay tetrahedralizations . In: Proc. of the 15th International Meshing Roundtable, 2006,509-528.

[9] Shewchuk J R. Tetrahedral mesh generation by Delaunay refinement . In: Proceedings of the 14th ACM Symposium on Computational Geometry. New York: ACM, 1998,86-95.

[10] Edelsbrunner H. Geometry and topology for mesh generation[M]. Cambridge: Cambridge University Press, 2001.

[11] Si H. Three dimensional boundary conforming Delaunay mesh generation . Institute of Mathematics, Technische Universität Berlin, 2008.

[12] Si H, Gärtner K. Meshing piecewise linear complexes by constrained Delaunay tetrahedralizations . Proceedings of 14th International Meshing Roundtable, Sandia National Laboratories, San Diego, CA, USA 2005, 147-163.

[13] Cheng S W, Dey T K, Ramos E A, Ray T. Quality meshing for polyhedra with small angles[J]. International Journal on Computational Geometry and Applications, 2005,15:421-461.

[14] Si H. Constrained Delaunay tetrahedral mesh generation and refinement[J]. Finite Elem. Anal. Des. 2010, 46(1-2),33-46.

[15] Lewis R W, Yao Z, Gethin D T. Three dimensional unstructured mesh generation[J]: Part 3. Volume meshes. Comput. Methods Appl. Mech. Engrg., 1996,134:285-310.

[16] 宋超,关振群,顾元宪.三维约束Delaunay 三角化的边界恢复和薄元消除方法[J].计算力学学报,2004,21(2):169-176.

[17] Joe B. Construction of three-dimensional improved-quality triangulation using local transforms[J]. SLAM J. of Sci. Compt, 1995,6:1292-1307.

[18] Scott C, Joseph T, Matthew S. An approach to combined Laplacian and optimization-based smoothing for triangular, quadrilateral, and quad-dominant meshes . In: Proceedings of 7th International Meshing Roundtable, Michigan, 1998,421-436.