Incrementally constructing and updating constrained Delaunay tetrahedralizations with finite-precision coordinates

Engineering with Computers

Volumn 30, Issue 2, 2014, Pages 253-269

  Si, Hang ^a   Shewchuk, Jonathan Richard ^b  

^a WEIERSTRASS INSTITUTE FOR APPLIED ANALYSIS AND STOCHASTICS   (Germany)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Constrained Delaunay triangulation; Geometric robustness; Tetrahedral mesh generation

Indexed keywords

MESH GENERATION;

BISTELLAR FLIPS; CONSTRAINED DELAUNAY; CONSTRAINED DELAUNAY TRIANGULATION; DELAU-NAY TRIANGULATIONS; DELAUNAY TETRAHEDRALIZATION; FINITE PRECISION; TETRAHEDRAL MESH GENERATION; THREE-DIMENSIONAL DOMAIN;

TRIANGULATION;

EID: 84899643621     PISSN: 01770667     EISSN: 14355663     Source Type: Journal    
DOI: 10.1007/s00366-013-0331-0     Document Type: Conference Paper

References (31)

1. Bowyer A (1981) Computing Dirichlet tessellations. Comput J 24(2):62-166
2. Chazelle B (1984) Convex partition of a polyhedra: a lower bound and worst-case optimal algorithm. SIAM J Comput 13(3):488-507 (Pubitemid 15514408)
3. Cheng SW, Dey TK, Edelsbrunner H, Facello MA, Teng SH (2000) Sliver exudation. J Assoc Comput Mach 47(5):883-904
4. Cheng SW, Dey TK, Shewchuk JR (2012) Delaunay mesh generation. CRC Press, Boca Raton
5. Chew LP (1990) Building Voronoi diagrams for convex polygons in linear expected time. Tech Rep PCS-TR90-147. Department of Mathematics and Computer Science, Dartmouth College
6. Chew PL (1989) Guaranteed-quality triangular meshes. Tech Rep TR 89-983. Department of Computer Science, Cornell University
7. Clarkson KL, Shor PW (1989) Applications of random sampling in computational geometry, II. Discret Computat Geom 4(1):387-421
8. Devillers O, Pion S, Teillaud M (2001) Walking in a triangulation. In: Proceedings of the 17th Annual Symposium on Computational Geometry. Medford, Massachusetts, pp 106-114
9. Edelsbrunner H, Mücke EP (1990) Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms. ACM Trans Graph 9(1):66-104 (Pubitemid 20686102)
10. Fortune S, Van Wyk CJ (1996) Static analysis yields efficient exact integer arithmetic for computational geometry. ACM Trans Graph 15(3):223-248 (Pubitemid 126418645)
11. Guigue P, Devillers O (2003) Fast and robust triangle-triangle overlap test using orientation predicates. J Graph Tool 8(1):25-32
12. Hermeline F (1980) Une Methode Automatique de Maillage en Dimension n. Ph.D. thesis, Université Pierre et Marie Curie, Paris
13. Hermeline F (1982) Triangulation Automatique d'un Polyèdre en Dimension N. RAIRO Analyse Numérique 16(3):211-242
14. Lee DT, Lin AK (1986) Generalized Delaunay triangulations for planar graphs. Discret Comput Geom 1:201-217
15. Miller GL, Talmor D, Teng SH, Walkington NJ, Wang H (1996) Control volume meshes using sphere packing: generation, refinement and coarsening. In: Proceedings of the 5th International Meshing Roundtable. Pittsburgh, Pennsylvania, pp 47-61
16. Ruppert J (1995) A Delaunay refinement algorithm for quality 2-dimensional mesh generation. J Algorithms 18(3):548-585
17. Schönhardt E (1928) Über die Zerlegung von Dreieckspolyedern in Tetraeder. Mathematische Annalen 98:309-312
18. Schroeder WJ, Shephard MS (1988) Geometry-based fully automatical mesh generation and the Delaunay triangulation. Int J Numer Methods Eng 26(11):2503-2515 (Pubitemid 18664626)
19. Seidel R (1982) Voronoi diagrams in higher dimensions (1982). Diplomarbeit, Institut für Informationsverarbeitung, Technische Universität Graz
20. Shewchuk JR (1997) Adaptive precision floating-point arithmetic and fast robust geometric predicates. Discret Comput Geom 18(3):305-363
21. Shewchuk JR (1998) A condition guaranteeing the existence of higher-dimensional constrained Delaunay triangulations. In: Proceedings of the 14th Annual Symposium on Computational Geometry, pp 76-85
22. Shewchuk JR (1998) Tetrahedral mesh generation by Delaunay refinement. In: Proceedings of the 14th Annual Symposium on Computational Geometry. Minneapolis, Minnesota, pp 86-95
23. Shewchuk JR (2000) Mesh generation for domains with small angles. In: Proceedings of the 16th Annual Symposium on Computational Geometry. Hong Kong, pp 1-10
24. Shewchuk JR (2000) Sweep algorithms for constructing higher-dimensional constrained Delaunay triangulations. In: Proceedings of the 16th Annual Symposium on Computational Geometry. Hong Kong, pp 350-359
25. Shewchuk JR (2002) Constrained Delaunay tetrahedralizations and provably good boundary recovery. In: Proceedings of the 11th International Meshing Roundtable. Ithaca, New York, pp 193-204
26. Shewchuk JR (2003) Updating and constructing constrained Delaunay and constrained regular triangulations by flips. In: Proceedings of the 19th Annual Symposium on Computational Geometry, pp 181-190
27. Shewchuk JR (2008) General-dimensional constrained Delaunay triangulations and constrained regular triangulations I: combinatorial properties. Discret Comput Geom 39(1-3):580-637
28. Si H (2008) Adaptive tetrahedral mesh generation by constrained Delaunay refinement. Int J Numer Methods Eng 75(7):856-880
29. Si H, Gärtner K (2005) Meshing piecewise linear complexes by constrained Delaunay tetrahedralizations. In: Hanks BW (ed) Proceedings of the 14th International Meshing Roundtable, pp 147-163
30. Si H, Gärtner K (2011) 3D boundary recovery by constrained Delaunay tetrahedralization. Int J Numer Methods Eng 85(11):1341-1364
31. Watson DF (1981) Computing the n-dimensional Delaunay tessellation with application to Voronoi polytopes. Comput J 24(2):167-172 (Pubitemid 12503887)