Triangulation of p-order parametric surfaces

Journal of Scientific Computing

Volumn 34, Issue 3, 2008, Pages 308-335

  Nordsletten, D ^a,b   Smith, N P ^a,b  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b UNIVERSITY OF AUCKLAND   (New Zealand)

Author keywords

Delaunay triangulation; Function bounds; Multidomain meshes; Taylor series; Voronoi tessellation

Indexed keywords

DELAUNAY TRIANGULATION; FUNCTION BOUNDS; MULTIDOMAIN MESHES; VORONOI TESSELLATION;

APPROXIMATION THEORY; COMPUTATIONAL METHODS; NUMERICAL METHODS; PROBLEM SOLVING; TAYLOR SERIES;

TRIANGULATION;

EID: 39149101481     PISSN: 08857474     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10915-007-9167-3     Document Type: Article

References (54)

1. Anglada, M., Garcia, N., Crosa, P.: Directional adaptive surface triangulation. Comput. Aided Geom. Des. 16, 107-126 (1999)
2. Babuska, I., Aziz, A.: On the angle condition in the finite element method. SIAM J. Numer. Anal. 13(2), 214-226 (1976)
3. Babuska, I., Rheinboldt, W.: Error estimates for adaptive finite element computations. SIAM J. Numer. Anal. 15(4), 736-754 (1978)
4. Baker, T.: Adaptive modification of time evolving meshes. Comput. Methods Appl. Mech. Eng. 194, 4977-5001 (2005)
5. Bernardini, F., Mittleman, J., Rushmeier, H.: The ball-pivoting algorithm for surface reconstruction. IEEE Trans. Vis. Comput. Graph. 5(4), 349-359 (1999)
6. Boender, E.: Reliable Delaunay-based mesh generation and mesh improvement. Commun. Numer. Meth. Eng. 10, 773-783 (1994)
7. Boivin, C., Gooch, C.: Guaranteed-quality triangular mesh generation for domains with curved boundaries. Int. J. Numer. Methods Eng. 55, 1185-1213 (2002)
8. Borouchaki, H., Frey, P.: Simplification of surface mesh using Hausdorff envelope. Comput. Methods Appl. Mech. Eng. 194, 4864-4884 (2005)
9. Borouchaki, H., George, P.: Aspects of 2d Delaunay mesh generation. Int. J. Numer. Methods Eng. 40, 1957-1975 (1997)
10. Borouchaki, H., George, P., Hecht, F., Laug, P., Saltel, E.: Delaunay mesh generation governed by metric specifications, Part I. Algorithms. Finite Elem. Anal. Des. 25, 61-83 (1997)
11. Borouchaki, H., George, P., Mohammadi, B.: Delaunay mesh generation governed by metric specifications, Part II. Applications. Finite Elem. Anal. Des. 25, 85-109 (1997)
12. Borouchaki, H., Laug, P., George, P.: Parametric surface meshing using a combined advancing-front generalized Delaunay approach. Int. J. Numer. Methods Eng. 49, 233-259 (2000)
13. Bowyer, A.: Computing Dirichlet tessellations. Comput. J. 24(2), 162-166 (1981)
14. Chase, H.: Alternative convergence criteria for iterative methods of solving nonlinear equations. J. Franklin 317(2), 89-103 (1984)
15. Cherfils, C., Hermeline, F.: Diagonal swap procedures and characterizations of 2d-Delaunay triangulations. Math. Model. Numer. Anal. 24(5), 613-625 (1990)
16. Cuilliere, J.: An adaptive method for the automatic triangulation of 3d parametric surfaces. Comput. Aided Des. 30(2), 139-149 (1996)
17. Dennis, J., Schnabel, R.: Numerical Methods for Unconstrained Optimization and Nonlinear Equations. SIAM, Philadelphia (1996)
18. Du, Q., Wang, D.: Anisotropic centroidal Voronoi tessellations and their applications. SIAM J. Sci. Comput. 26(3), 737-761 (2005)
19. Eisenstat, S., Walker, H.: Globally convergent inexact Newton methods. SIAM J. Optim. 4(2), 393-422 (1994)
20. Ekaterinaris, J.A.: High-order accurate, low numerical diffusion methods for aerodynamics. Prog. Aerospace Sci. 41, 192-300 (2005)
21. Farhat, C., Lesoinne, M., Maman, N.: Mixed explicit/implicit time integration of coupled aeroelastic problems: Three-field formulation, geometric conservation and distributed solution. Int. J. Numer. Methods Fluids 21, 807-835 (1995)
22. Filip, D., Magedson, R., Markot, R.: Surface algorithms using bounds on derivatives. Comput. Aided Geom. Des. 3, 295-311 (1986)
23. Frey, P., Alauzet, F.: Anisotropic mesh adaption for cfd computations. Comput. Methods Appl. Mech. Eng. 194, 5068-5082 (2005)
24. Fuchs, A.: Automatic grid generation with almost regular Delaunay tetrahedra (1998)
25. Gudmundsson, J., Haverkort, H., Kreveld, M.: Constrained higher order Delaunay triangulations. Comput. Geom. 30, 271-277 (2005)
26. Holmes, D., Snyder, D.: The Generation of Unstructured Triangular Meshes Using Delaunay Triangulations. Pineridge, Swansed (1988)
27. Reynolds, H., Smith, N., Hunter, P.: Construction of an anatomically accurate geometric model of the forearm and hand musculo-skeletal system. In: Annual Meeting Proceedings, 26th IEEE EMBS Annual International Conference, San Francisco, Sept. 1-5, 2004, pp. 265-269
28. Hunter, P., Pullan, A., Smaill, B.: Modelling total heart function. Ann. Rev. Biomed. Eng. 5, 147-177 (2003)
29. Joe, B.: Delaunay triangular meshes in convex polygons. SIAM J. Sci. Comput. 7(2), 514-539 (1986)
30. Joe, B.: Delaunay versus max-min solid angle triangulations for three-dimensional mesh generation. Int. J. Numer. Methods Eng. 31, 987-997 (1991)
31. Joe, B.: Construction of three-dimensional improved-quality triangulations using local transformations. SIAM J. Sci. Comput. 16(6), 1292-1307 (1995)
32. Kuo, C., Yau, H.: A Delaunay-based region growing approach to surface reconstruction from unorganized points. Comput. Aided Des. 37, 825-835 (2005)
33. Labelle, F., Shewchuk, J.: Anisotropic Voronoi diagrams and guaranteed-quality anisotropic mesh generation. SoGC, pp. 191-200 (2003)
34. Lee, C.: Automatic metric advancing front triangulation over curved surfaces. Eng. Comput. 17(1), 48-74 (2000)
35. Lee, C.: On curvature element-size control in metric surface mesh generation. Int. J. Numer. Methods Eng. 50, 787-807 (2001)
36. LeGrice, I., Hunter, P., Young, A., Smaill, B.: The architecture of the heart: A data-based model. Phil. Trans. R. Soc. Lond. 359, 1217-1232 (2001)
37. Liu, A., Joe, B.: Relationship between tetrahedron shape measures. BIT 34, 268-287 (1994)
38. Lo, S.: Automatic mesh generation and adaption by using contours. Int. J. Numer. Methods Eng. 31, 689-707 (1991)
39. Lohner, R.: Regridding surface triangulations. J. Comput. Phys. 126, 1-10 (1996)
40. Lohner, R.: Automatic unstructured grid generators. Finite Elem. Anal. Des. 25, 111-134 (1997)
41. Mavriplis, D.: An advancing front Delaunay triangulation algorithm designed for robustness. J. Comput. Phys. 117, 90-101 (1995)
42. Nash, M., Hunter, P.: Computational mechanics of the heart. J. Elast. 61, 113-141 (2000)
43. Nickerson, D., Niederer, S., Stevens, C., Nash, M., Hunter, P.: A computational model of cardiac electromechanics. In: 28th Annual International Conference of the IEEE Engineering in Medicine and Biology Society. New York, September 2006
44. Okabe, A., Boots, B., Sugihara, K., Chiu, S.: Spatial Tessellations: Concepts and Applications of Voronoi Diagrams, 2 edn. Wiley, New York (2000)
45. Pang, M., Pan, Z., Zhang, M., Zhang, F.: An adaptive and efficient algorithm for polygonization of implicit surfaces, pp. 245-255 (2005)
46. Parthasarathy, V., Graichen, C., Hathaway, A.: A comparison of tetrahedron quality measures. Finite Elem. Anal. Des. 15, 255-261 (1993)
47. Rebay, S.: Efficient unstructured mesh generation by means of Delaunay triangulation and Bowyer-Watson algorithm. J. Comput. Phys. 106, 125-138 (1991)
48. Stevens, C., Remme, E., LeGrice, I., Hunter, P.: Ventricular mechanics in diastole: Material parameter sensitivity. J. Biomech. 36, 737-748 (2003)
49. Tremel, U., Deister, F., Hassan, O., Weatherill, N.: Automatic unstructured surface mesh generation for complex configurations. Int. J. Numer. Methods Fluids 45, 341-364 (2004)
50. Tremel, U., Deister, F., Hassan, O., Weatherill, N.: Parallel generation of unstructured surface grids. Eng. Comput. 21, 36-46 (2005)
51. van Essen, N., Anderson, I., Hunter, P., Carman, J., Clarke, R., Pullan, A.: Anatomically based model of the human skull and jaw. Cells Tissues Organs 180, 44-53 (2005)
52. Wang, Z.: Spectral (finite) volume method for conservation laws on unstructured grids. J. Comput. Phys. 178, 210-251 (2002)
53. Wang, Z., Liu, Y.: Spectral (finite) volume method for conservation laws on unstructured grids. J. Comput. Phys. 179, 665-697 (2002)
54. Watson, D.: Computing the n-dimensional Delaunay tessellation with application to Voronoi polytopes. Comput. J. 24(2), 167-172 (1981)