Delaunay meshing of piecewise smooth complexes without expensive predicates

Algorithms

Volumn 2, Issue 4, 2009, Pages 1327-1349

  Dey, Tamal K ^a   Levine, Joshua A ^a  

^a Ohio State University   (United States)

Author keywords

Delaunay refinement; Mesh generation; Non manifoldness; Non smoothness; Piecewise smooth complexes

Indexed keywords

EID: 77956375993     PISSN: None     EISSN: 19994893     Source Type: Journal    
DOI: 10.3390/a2041327     Document Type: Article

References (22)

1. Chew, L.P. Guaranteed-quality triangular meshes. Technical Report TR-89-983, Comp. Science Department, Cornell University, Ithaca, NY, USA, 1989.
2. Chew, L.P. Guaranteed-quality mesh generation for curved surfaces. In Proceedings of the 9th Symposium on Computational Geometry. San Diego, CA, USA, May 19-21, 1993; pp. 274-280.
3. Boissonnat, J.D.; Oudot, S. Provably good sampling and meshing of surfaces. Graph. Models 2005, 67, 405-451.
4. Cheng, S.W.; Dey, T.K.; Ramos, E.A.; Ray, T. Sampling and meshing a surface with guaranteed topology and geometry. SIAM J. Comput. 2007, 37, 1199-1227.
5. Shewchuk, J.R. Mesh generation for domains with small angles. In Proceedings of the 16th Symposium on Computational Geometry. Hong Kong, China, June 12-14, 2000; pp. 1-10.
6. Boissonnat, J.D.; Oudot, S. Provably good sampling and meshing of Lipschitz surfaces. In Proceedings of the 22nd Symposium on Computational geometry. Sedona, AZ, USA, June 5-7, 2006; pp. 337-346.
7. Rineau, L.; Yvinec, M. Meshing 3D Domains Bounded by Piecewise Smooth Surfaces. In Proceedings of the 16th International Meshing Roundtable. Seattle, WA, USA, October 14-17, 2007; pp. 443-460.
8. Cheng, S.W.; Dey, T.K.; Ramos, E.A. Delaunay refinement for piecewise smooth complexes. In Proceedings of the 18th ACM-SIAM Symposium on Discrete Algorithms. New Orleans, LA, USA, January 7-9, 2007; pp. 1096-1105.
9. Cheng, S.W.; Poon, S.H. Three-Dimensional Delaunay Mesh Generation. Disc. Comput. Geom. 2006, 36, 419-456.
10. Cohen-Steiner, D.; de Verdière, É.C.; Yvinec, M. Conforming Delaunay triangulations in 3D. Comput. Geom. 2004, 28, 217-233
11. Murphy, M.; Mount, D.M.; Gable, C.W. A Point-Placement Strategy for Conforming Delaunay Tetrahedralization. Int. J. Comput. Geom. Appl. 2001, 11, 669-682.
12. Aurenhammer, F. Power Diagrams: Properties, Algorithms and Applications. SIAM J. Comput. 1987, 16, 78-96.
13. Edelsbrunner, H. Geometry and Topology for Mesh Generation; Cambridge University: Cambridge, UK, 2001.
14. Ruppert, J. A Delaunay Refinement Algorithm for Quality 2-Dimensional Mesh Generation. J. Algorithms 1995, 18, 548-585.
15. Cheng, S.W.; Dey, T.K.; Levine, J.A. A practical Delaunay meshing algorithm for a large class of domains. In Proceedings of the 16th International Meshing Roundtable. Seattle, Washington, USA, October 14-17, 2007; pp. 477-494.
16. Dey, T.K.; Levine, J.A. DelPSC: a Delaunay mesher for piecewise smooth complexes (multimedia submission). In Proceedings of the 24th ACM Symposium on Computational Geometry. College Park, MD, USA, June 9-11, 2008; pp. 220-221.
17. Edelsbrunner, H.; Shah, N.R. Triangulating Topological Spaces. Int. J. Comput. Geometry Appl. 1997, 7, 365-378.
18. CGAL. Computational Geometry Algorithms Library. Available online: http://www.cgal.org (accessed September 25, 2009).
19. Oudot, S.; Rineau, L.; Yvinec, M. Meshing volumes bounded by smooth surfaces. In Proceedings of the 14th International Meshing Roundtable. San Diego, CA, USA, September 11-14, 2005; pp. 203-219.
20. Amenta, N.; Bern, M. Surface reconstruction by Voronoi filtering. Disc. Comput. Geom. 1999, 22, 481-504.
21. Dey, T.K. Curve and Surface Reconstruction: Algorithms with Mathematical Analysis. Cambridge University: New York, NY, USA, 2007.
22. Amenta, N.; Dey, T. Normal variation with adaptive feature size. Available online: http://www.cse.ohio-state.edu/tamaldey/paper/norvar/norvar.pdf (accessed September 25, 2009).