Variational tetrahedral meshing

ACM Transactions on Graphics

Volumn 24, Issue 3, 2005, Pages 617-625

  Alliez, Pierre ^a   Cohen Steiner, David ^a   Yvinec, Mariette ^a   Desbrun, Mathieu ^b  

^a INRIA   (France)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Delaunay mesh; Isotropic meshing; Sizing field; Slivers

Indexed keywords

DELAUNAY MESH; ISOTROPIC MESHING; MESH DESIGN; SIZING FIELD;

FUNCTION EVALUATION; INTERPOLATION; OPTIMIZATION; TOPOLOGY;

COMPUTER GRAPHICS;

EID: 33646046216     PISSN: 07300301     EISSN: 07300301     Source Type: Conference Proceeding    
DOI: 10.1145/1073204.1073238     Document Type: Conference Paper

References (40)

1. th Symp. on Computational Geometry (SCG'98), 39-48.
2. AMENTA, N., CHOI, S., DEY, T., AND LEEKHAU, N. 200. A Simple Algorithm for Homeomorphic Surface Reconstruction. In Proceedings of the Symposium on Computational geometry, 213-222.
3. BOISSONNAT, J.-D., AND OUDOT, S. 2005. Provably Good Sampling and Meshing of Surfaces. Graphical Models (special issue on Solid Modeling). To appear.
4. BOROUCHAKI, H., GEORGE, P., HECHT, F., LAUG, P., AND SALTEL, E. 1997. Delaunay mesh generation governed by metric specifications. Part 1 : Algorithms. Finite Elements in Analysis and Design 25, 61-83.
5. BOROUCHAKI, H., GEORGE, P., AND MOHAMMADI, B. 1997. Delaunay mesh generation governed by metric specifications. Part 2 : Application examples. Finite Elements in Analysis and Design 25, 85-109.
6. CAREY, G. F. 1997. Computational Grids: Generation, Adaptation, and Solution Strategies. Taylor & Francis eds.
7. CHEN, L., AND XU, J. 2004. "Optimal Delaunay triangulations". Journal of Computational Mathematics 22, 2, 299-308.
8. CHEN, L. 2004. Mesh smoothing schemes based on optimal Delaunay triangulations. In Proceedings of 13th International Meshing Roundtable, 109-120.
9. th ACM-SIAM Sympos. Discrete Algorithms, 137-146.
10. th ACM-SIAM Symposium on Discrete algorithms (SODA), 295-304.
11. CHENG, S.-W., DEY. T. K., EDELSBRUNNER, H., FACELLO, M. A., AND TENG, S.-H. 1999. Sliver Exudation. In Proc. 15th ACM Symp. Comput. Geom., 1-13.
12. CHENG, S.-W., DEY, T. K., RAMOS, E., AND RAY, T. 2004. Quality Meshing for Polyhedra with Small Angles. In Proc. of ACM Symp. on Comp. Geom., 290-299.
13. COHEN-STEINER, D., DE VERDIERE, E. C., AND YVINEC, M. 2002. Conforming Delaunay triangulations in 3D. In Proc. of Symp. on Comp. Geom., 237-246.
14. COHEN-STEINER, D., ALLIEZ, P., AND DESBRUN, M. 2004. Variational Shape Approximation. ACM Trans. on Graphics (SIGGRAPH), 905-914.
15. CUTLER, B., DORSEY, J., AND MCMILLAN, L. 2004. Simplification and Improvement of Tetrahedral Models for Simulation. In Proceedings of the 2004 Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, 95-104.
16. DU, Q., AND WANG, D. 2003. Tetrahedral mesh generation and optimization based on centroidal Voronoi tessellations. International Journal on Numerical Methods in Engineering 56(9), 1355-1373.
17. DU, Q., GUNZBURGER, M., AND JU, L. 2003. Constrained Centroidal Voronoi Tessellations for Surfaces. SIAM J. Sci. Comput. 24, 5, 1488-1506.
18. th Int. Meshing Roundtable, Newport Beach.
19. FABRI, A., GIEZEMAN, G.-J., KETTNER, L., SCHIRRA, S., AND SCHÖNHERR, S. 2000. On the Design of COAL, a Computational Geometry Algorithms Library. Softw. - Pract. Exp. 30, 11, 1167-1202. www.cgal.org.
20. FREITAG, L., AND OLLIVIER-GOOCH, C. 1996. A comparison of Tetrahedral Mesh Improvement Techniques. In Proc. of 6th Int. Meshing Roundtable, 87-1000.
21. FREY, J. L., AND GEORGE, P. L. 2000. Mesh Generation: Applications to Finite Elements. Hermès, Paris.
22. HARDIN, D. P., AND SAFF, E. B. 2004. Discretizing Manifolds via Minimum Energy Points. Notices of the AMS 51(10), 1186-1194.
23. HOPPE, H., DEROSE, T., DUCHAMP, T., MCDONALD, J., AND STUETZLE, W. 1993. "Mesh Optimization". ACM Trans. on Graphics (SIGGRAPH), 19-26.
24. KRYSL, P., AND ORTIZ, M. 2001. Variational Delaunay Approach to the Generation of Finite Element Meshes. Int. J. for Num. Meth. in Eng. 50(7), 1681-1700.
25. th ACM-SIAM Sympos. Discrete Algorithms.
26. LI, X.-Y., TENG, S.-H., AND UNGOR, A. 2000. "Biting: Advancing Front Meets Sphere Packing". Int. J. on Num. Methods in Eng. 49, 1, 61-81.
27. LLOYD, S. P. 1957. Least Squares Quantization in PCM's. Tech. rep., Bell Telephone Laboratories, Murray Hill, NJ.
28. MITCHELL, S., AND VAVASIS, S. 2000. Quality Mesh Generation in Higher Dimensions. SIAM J. Sci. Comput. 29, 1334-1370.
29. MOLINO, N., BRIDSON, R., TERAN, J., AND FEDKIW, R. 2003. A Crystalline, Red Green Strategy for Meshing Highly Deformable Objects with Tetrahedra. In Proceedings of the 12th International Meshing Roundtable, 103-114.
30. OSTROMOUKHOV, V. 2001. A simple and efficient error-diffusion algorithm. In Proceedings of ACM SIGGRAPH, 567-572.
31. OWEN, S. J. 1998. A Survey of Unstructured Mesh Generation Technology. In Proceedings of the 7th International Meshing Roundtable, 239-267.
32. QUADROS, W. R., SHIMADA, K., AND OWEN, S. J., 2004. 3D Discrete Skeleton Generation by Wave Propagation on PR-Octree for Finite Element Mesh Sizing. Poster, Solid Modeling Conference.
33. th ACM/SIAM Symp. on Disc. Algo. (SODA), 83-92.
34. th Annu. ACM Sympos. Comput. Geom., 76-85.
35. SHEWCHUK, J. R. 1998. Tetrahedral mesh generation by Delaunay refinement. In Proc. I4th Annu. ACM Sympos. Comput. Geom., 86-95.
36. th Int. Meshing Roundtable, 115-126.
37. SHEWCHUK, J. R. 2002. Delaunay Refinement Algorithms for Triangular Mesh Generation. Computational Geometry: Theory and Applications 22, 21-74.
38. th Int. Meshing Roundtable.
39. TENG, S.-H., WONG, C. W., AND LEE, D. T. 2000. Unstructured Mesh Generation: Theory, Practice, and Perspectives. International Journal Computational Geometry and Applications 10, 3 (June), 227-266.
40. WARREN, J., SCHAEFER, S., HIRANI, A., AND DESBRUN, M., 2004. Barycentric Coordinates for Convex Sets. Preprint.