Constrained boundary recovery for three dimensional Delaunay triangulations

International Journal for Numerical Methods in Engineering

Volumn 61, Issue 9, 2004, Pages 1471-1500

  Du, Qiang ^a,c   Wang, Desheng ^b,c  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

^b SWANSEA UNIVERSITY   (United Kingdom)

^c INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

Author keywords

Guaranteed constrained boundary recovery; Mesh generation and optimization; Steiner point insertion and placement; Three dimensional Delaunay triangulation

Indexed keywords

BOUNDARY CONDITIONS; CONSTRAINT THEORY; GEOMETRY; NUMERICAL METHODS;

BOUNDARY RECOVERY; MESH GENERATION; STEINER POINTS;

FLUID MECHANICS;

MATHEMATICAL METHOD; OPTIMIZATION;

EID: 8344280878     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.1120     Document Type: Article

References (22)

1. Watson D. Computing the n-dimensional Delaunay tessellation with applications to Voronoi polytopes. Computer Journal 1981; 24:167-172.
2. Bowyer A. Computing Dirichlet tessellations. Computer Journal 1981; 24(2):162-166.
3. Borouchaki H, George P. Aspects of 2-D Delaunay mesh generation. International Journal for Numerical Methods in Engineering 1997; 40:1957-1975.
4. Weatherill N. The integrity of geometrical boundaries in the two-dimensional Delaunay triangulation. Computer Applications in Numerical Methods 1990; 6:101-109.
5. Borouchaki H, George P, Lo S. Optimal Delaunay point insertion. International Journal for Numerical Methods in Engineering 1996; 39:3407-3437.
6. Borouchaki H, Lo S. Fast Delaunay triangulation in three dimensions. Computer Methods in Applied Mechanics and Engineering 1995; 128:153-167.
7. Rassineux A. Generation and optimization of tetrahedral meshes by advancing front technique, International Journal for Numerical Methods in Engineering 1998; 41:651-674.
8. Shephard M, Georges M. Automatic three-dimensional mesh generation by the finite octree technique. International Journal for Numerical Methods in Engineering 1991; 32:709-749.
9. Lohner R, Parikh P. Generation of three-dimensional unstructured grids by the advancing-front method. International Journal for Numerical Methods in Engineering 1988; 8:1135-1149.
10. Frey PJ, Borouchaki H, George PL. 3D Delaunay mesh generation coupled with an advancing-front approach. Computer Methods in Applied Mechanics and Engineering 1998; 157:115-131.
11. Liu A, Baida M. How far flipping can go towards 3D conforming /constrained triangulation. 9th International Meshing Roundtable 2000; 295-306.
12. George P, Hecht F, Saltel E. Automatic mesh generation with specified boundary. Computer Methods in Applied Mechanics and Engineering 1991; 92:169-188.
13. Weatherill N, Hassan O. Efficient three dimensional Delaunay triangulation with automatic point creation and imposed boundary constraints. International Journal for Numerical Methods in Engineering 1994; 37: 2005-2039.
14. Shewchuk J. Delaunay refinement mesh generation. Ph.D. Thesis, Computer Science Department, Carnegie Mellon University 1997.
15. Karamete B, Beall M, Shephard M. Triangulation of arbitrary polyhedra to support automatic mesh generators. International Journal for Numerical Methods in Engineering 2000; 49:167-191.
16. Wright J, Jack A. Aspects of three-dimensional constrained Delaunay meshing. International Journal for Numerical Methods in Engineering 1994; 37:1841-1846.
17. George P, Borouchaki H. Delaunay Triangulation and Meshing: Application to Finite Elements. Hermes: Paris, 1998.
18. Du Q, Wang D. Boundary recovery for 3D conforming Delaunay triangulation. Computer Methods in Applied Mechanics and Engineering 2003; 193:2547-2563.
19. Schewchuk J. Constrained Delaunay tetrahedralization and provably good boundary recovery. Proceedings of the 11th International Meshing Roundtable 2002; 193-204.
20. Du Q, Wang D. Tetrahedral mesh generation and optimization based on centroidal Voronoi tessellation. International Journal for Numerical Methods in Engineering 2003; 56(9):1355-1373.
21. Laug P, Borouchaki H. Molecular surface modelling and meshing. Engineering with Computers 2002; 18:199-210.
22. Hassan O. Private communication, 2003.