Advances in studies and applications of Centroidal Voronoi tessellations

Numerical Mathematics

Volumn 3, Issue 2, 2010, Pages 119-142

  Du, Qiang ^a   Gunzburger, Max ^b   Ju, Lili ^c  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

^b FLORIDA STATE UNIVERSITY   (United States)

^c UNIVERSITY OF SOUTH CAROLINA   (United States)

Author keywords

Centroids; Clustering; Image processing; Mesh generation and optimization; Model reduction; Point sampling; Voronoi tessellations

Indexed keywords

EID: 79957493465     PISSN: 10048979     EISSN: 20797338     Source Type: Journal    
DOI: 10.4208/nmtma.2010.32s.1     Document Type: Review

References (123)

1. P. ALLIEZ, D. COHEN-STEINER, M. YVINEC, AND M. DESBRUN, Variational tetrahedral meshing, in Proceedings of SIGGRAPH, 2005, pp. 617-625.
2. L. ANTANI, C. DELAGE, AND P. ALLIEZ, Mesh sizing with additively weighted Voronoi diagrams, in Proceedings of Meshing Roundtable Conference, 2007, pp. 335-346.
3. S. ARYA AND D. MOUNT, Approximate nearest neighbor searching, Proceedings of the Fourth Ann. ACM-SIAM Symposium on Discrete Algorithms (SODA), 1993, pp. 271-280.
4. M. AINSWORTH AND J. ODEN, A Posteriori Error estimation in Finite Element Analysis, Wiley & Sons, 2002.
5. P. ALLIEZ, T. DE VERDIERE, O. DEVILLERS, AND M. ISENGURG, Centroidal Voronol diagrams for isotropic surface remeshing, Graphic Models, 67(2005), pp. 204-231. (Pubitemid 40429234)
6. E. ABAYA AND G. WISE, Convergence of vector quantizers with application to optimal quantization, SIAM J. Appl. Math., 44(1984), pp. 183-189.
7. T. BAKER, Automatic mesh generation for complex three-dimensional regions using a constrained Delaunay triangulation, Engrg. Comput., 5(1989), pp. 161-175. (Pubitemid 20636635)
8. G. BARLOW, Hexagonal territories, Animal Behav., 22(1974), pp. 876-878.
9. P. BAJCSY AND N. AHUJA, Location-and density-based hierarchical clustering using similarity analysis, IEEE Trans. Pattern Anal. Mach. Intel., 20(1980), pp. 1011-1015.
10. F. BULLO AND J. CORTES, Adaptive and distributed coordination algorithms for mobile sensing networks, Lecture Notes in Control and Information Sciences 309 (2005) pp. 43-62. (Pubitemid 39436811)
11. J. BURKARDT, M. GUNZBURGER, AND H.-C. LEE, Centroidal Voronoi tessellation-based reducedorder modeling of complex systems, SIAM J. Sci. Comput., 28(2006), pp. 459-484. (Pubitemid 46422101)
12. J. BURKARDT, M. GUNZBURGER, AND H.-C. LEE, POD and CVT-based reduced-order modeling of Navier-Stokes flows, Comp. Methods Appl. Mech. Engrg., 196(2006), pp. 337-355. (Pubitemid 46158189)
13. J. BURKARDT, M. GUNZBURGER, J. PETERSON, AND R. BRANNON, Centroidal Voronoi point placement and associated zeroth, first, and second moment determination, Sandia National Laboratories Report, SAND2002-0099, 2002.
14. G. BERKOOZ, P. HOLMES, AND J. LUMLEY, The proper orthogonal decomposition in the analysis of turbulent flows, Ann. Rev. Fluid. Mech., 25(1993), pp. 539-575.
15. T. BELYTSCHKO, Y. KRONGAUZ, D. ORGAN, M. FLEMING, AND P. KRYSL, Meshless methods: an overview and recent developments, Comput. Methods Appl. Mech. Engrg., 139(1996), pp. 3-47. (Pubitemid 126382692)
16. H. BOROUCHAKI AND S. LO, Fast Delaunay triangulation in three dimensions, Comp. Methods Appl. Mech. Engrg., 128(1995), pp. 153-167. (Pubitemid 26442387)
17. I. BOIER-MARTIN, H. RUSHMEIER, AND J. JIN, Parameterization of triangle Meshes over quadrilateral domains, Proceedings of the Eurographics/ACM SIGGRAPH Symp., 2004, pp. 193-203.
18. E. BARNES AND N. SLOANE, The optimal lattice quantizer in three dimensions, SIAM J. Algebraic Discrete Methods, 4(1983), pp. 31-40.
19. D. COHEN-STEINER, P. ALLIEZ, AND M. DESBRUN, Variational shape approximation, ACM Transactions on graphics, 23(2004), pp. 905-914.
20. M. CAPPELLARI AND Y. COPIN, Adaptive spatial binning of integral-field spectroscopic data using Voronoi tessellations, Monthly Notices of the Royal Astronomical Society, 342(2003), pp. 345-354. (Pubitemid 37268730)
21. Y. CHOI AND S. KIM, Node generation scheme for meshfree method by Voronoi diagram and weighted bubble packing, Proceedings of the Fifth U. S. National Congress on Computational Mechanics, Boulder, 1999.
22. J. CORTES, S. MARTINEZ, T. KARATAS, AND F. BULLO, Coverage control for mobile sensing networks, IEEE Trans. Robotics and Automation, 20(2004), pp. 243-255.
23. T. CHAN, J. SHEN, AND L. VESE, Variational PDE models in image processing, Notices of AMS, American Mathematical Society, 50(2003), pp. 14-26.
24. Y. CHEN, Z. WANG, AND J. LIANG, Optimal dynamic actuator location in distributed feedback control of a diffusion process, Inter. J. Sensor Networks, 2(2007), pp. 169-178.
25. L. CHEN AND J. XU, Optimal Delaunay triangulation, J. Comp. Math., 22(2004), pp. 299-308.
26. S. DIEHL AND T. STATLER, Adaptive binning of X-Ray data with weighted Voronoi tesselations, MNRAS, 368(2006), pp. 497-510. (Pubitemid 43659695)
27. Q. DU AND M. EMELIANENKO, Acceleration schemes for computing the centroidal Voronoi tessellations, Numer. Linear Alg. Appl., 13(2006), pp. 173-192. (Pubitemid 43479877)
28. Q. DU AND M. EMELIANENKO, Uniform convergence of a nonlinear energy-based multilevel quantization scheme via centroidal Voronoi tessellations, SIAM J. Numer. Anal., 46(2008), pp. 1483-1502.
29. Q. DU, M. EMELIANENKO AND L. JU, Convergence of the Lloyd algorithm for computing centroidal Voronoi tessellations, SIAM J. Numer. Anal., 44(2006), pp. 102-119. (Pubitemid 46352064)
30. Q. DU, M. EMELIANENKO, H. LEE AND X. WANG, Ideal point distributions, best mode selections and optimal spatial partitions via centroidal Voronoi tessellations, Proceedings of the Second Inter. Symp. Voronoi Diagrams Sci. Engrg., Seoul, Korea, 2005, pp. 325-333.
31. Q. DU, V. FABER, AND M. GUNZBURGER, Centroidal Voronoi tessellations: Applications and algorithms, SIAM Review, 41(1999), pp. 637-676. (Pubitemid 30536738)
32. Q. DU AND M. GUNZBURGER, Grid generation and optimization based on centroidal Voronoi tessellations, Applied Math. Comptut., 133(2002), pp. 591-607. (Pubitemid 34991495)
33. Q. DU AND M. GUNZBURGER, Model reduction by proper orthogonal decomposition coupled with centroidal Voronoi tessellation, Proceedings of the Fluids Engineering Division Summer Meeting, FEDSM2002-31051, ASME, 2002.
34. Q. DU AND M. GUNZBURGER, Centroidal Voronoi tessellation based proper orthogonal decomposition analysis, Control and Estimation of Distributed Parameter Systems, Birkhauser, Basel, 2003, pp. 137-150.
35. Q. DU, M. GUNZBURGER, AND L. JU, Meshfree, probabilistic determination of points, sets and support regions for meshless computing, Comput. Methods Appl. Mech. Engrg., 191(2002), pp. 1349-1366. (Pubitemid 34135049)
36. Q. DU, M. GUNZBURGER, AND L. JU, Constrained centroidal Voronoi tessellations for surfaces, SIAM J. Sci. Comput., 24(2003), pp. 1488-1506.
37. Q. DU, M. GUNZBURGER, AND L. JU, Voronoi-based finite volume methods, optimal Voronoi meshes and PDEs on the sphere, Comput. Methods Appl. Mech. Engrg., 192(2003), pp. 3933-3957. (Pubitemid 37042315)
38. Q. DU, M. GUNZBURGER, L. JU, AND X.-Q. WANG, Centroidal Voronoi tessellation algorithms for image compression, segmentation and multichannel restoration, J. Math. Imaging Vision, 24(2006), pp. 177-194.
39. O. DEUSSEN, S. HILLER, C. VAN OVERVELD, AND T. STROHTHOTTE, Floating points: A method for computing stipple drawings, Comput. Graph. Forum, 19(2000), pp. 41-50.
40. Q. DU, Z.-H. HUANG, AND D. WANG, Mesh and solver coadaptation in finite element methods for anisotropic problems, Numer. Meth. for PDEs, 21(2005), pp. 859-874. (Pubitemid 41085345)
41. Q. DU AND L. JU, Numerical simulations of the quantized vortices in a thin superconducting hollow sphere, J. Comput. Phys., 201(2004), pp. 511-530. (Pubitemid 39525417)
42. Q. DU AND L. JU, Approximations of a Ginzburg-Landau model for superconducting hollow spheres based on spherical centroidal Voronoi tessellations, Math. Comp., 74(2005), pp. 1257-1280. (Pubitemid 40937963)
43. Q. DU AND L. JU, Finite volume methods on spheres and spherical centroidal Voronoi meshes, SIAMJ. Numer. Anal, 43(2005), pp. 1673-1692. (Pubitemid 44231212)
44. Q. DU AND D. WANG, Tetrahedral mesh generation and optimization based on centroidal Voronoi tessellations, Int. J. Numer. Methods Engrg., 56(2003), pp. 1355-1373. (Pubitemid 36339786)
45. Q. DU AND D. WANG, Constrained boundary recovery for 3D Delaunay triangulations, Int. J. Num. Method. In. Eng., 61(2004), pp. 1471-1500. (Pubitemid 39483561)
46. Q. DU AND D. WANG, Anisotropic centroidal Voronoi tessellations and their applications, SIAM. J. Sci. Comput, 26(2005), pp. 737-761. (Pubitemid 40738105)
47. Q. DU AND D. WANG, On the optimal centroidal Voronoi tessellations and the Gersho's conjecture in the three dimensional space, Comput. Math. Appl, 49(2005), pp. 1355-1373. (Pubitemid 41101290)
48. Q. DU AND D. WANG, Mesh optimization based on centroidal Voronoi tessellations, Inter. J. Numer. Anal. Model, 2(2005), pp. 100-114.
49. Q. DU AND D. WANG, Recent progress in robust and quality Delaunay mesh generation, J. Comput. Appl. Math., 195(2006), pp. 8-23. (Pubitemid 43929180)
50. Q. DU AND X. WANG, Tessellation and clustering by mixture models and their parallel implementations, Proceedings of the Fourth SIAM Inter. Conf. Data Mining, Orlando, FL, 2004, SIAM, 2004, pp. 257-268.
51. Q. DU AND X. WANG, Centroidal Voronoi tessellation based algorithms for vector fields visualization and segmentation, Proceedings of the IEEE Visualization, Austin, Texas, 2004, pp. 43-50. (Pubitemid 40497906)
52. Q. DU AND T. WONG, Numerical studies of the k-means algorithm, Comput. Math. Appl, 44(2002), pp. 511-523.
53. d, SIAMJ. Numer. Anal, 46(2008), pp. 1423-1441.
54. P. FLEISCHER, Sufficient conditions for achieving minimum distortion in a quantizer, IEEE Int. Convention Record I (1964), pp. 104-111.
55. A. GERSHO, Asymptotically optimal block quantization, IEEE Trans. Inform. Theory, 25(1979), pp. 373-380.
56. P. GRUBER, Optimum quantization and its applications, Adv. Math., 186(2004), pp. 456-497. (Pubitemid 38881866)
57. P. GUIO AND N. ACHILLEOS, The VOISE algorithm: a versatile tool for automatic segmentation of astronomical images, Mon. Not. R. Astron. Soc, 2009, doi:10.1111/j.1365-2966.2009.15218.x.
58. A. GERSHO AND R. GRAY, Vector Quantization and Signal Compression, Kluwer, Boston, 1992.
59. R. GRAY, J. KIEFFER, AND Y. LINDE, Locally optimal block quantizer design, Inform. Control, 45(1980), pp. 178-198.
60. R. GRAY AND D. NEUHOFF, Quantization, IEEE Trans. Inform. Theory, 44(1998), pp. 2325-2383.
61. A. GUESSAB AND E. CHMEISSERR, Construction of positive definite cubature formulae and approximation of functions via Voronoi tessellations, Adv Comput Math, 32(2010), pp. 25-41.
62. A. HAUSNER, Simulating decorative mosaics, Proceedings of SIGGRAPH, 2001, pp. 573-578.
63. W HUANG, Metric tensors for anisotropic mesh generation, J. Comput. Phys., 204(2005), pp. 633-665. (Pubitemid 40435825)
64. H. HELLWIG, R. ENGELMANN, AND O. DEUSSEN, Contact pressure models for spiral phyllotaxis and their computer simulation, J. Theo. Biol, 240(2005), pp. 489-500.
65. H. HELLWIG, M. JESCHKE, AND O. DEUSSEN, A contact pressure model based on centroidal Voronoi diagrams for surfaces of revolution, Proceedings of the Fifth Annual Inter. Symp. Voronoi Diagrams Sci. Engr., 2008.
66. S. HILLER, H. HELLWIG, AND O. DEUSSEN, Beyond stippling - methods for distributing objects on the plane, Computer Graphics Forum, 22(2003), pp. 515-522.
67. Y. HUANG, H. QIN, AND D. WANG, Centroidal Voronoi tessellation-based finite element superconvergence, Inter. J. Numer. Meths. Engrg., 76(2008), pp. 1819-1839.
68. Y. HUANG, H. QIN, D. WANG, AND Q. DU, Convergent adaptive finite element method based on centroidal Voronoi tessellations and superconvergence, preprint, 2009.
69. L. JU, Conforming centroidal Voronoi Delaunay triangulation for quality mesh generation, Inter. J. Numer. Anal. Model., 4(2007), pp. 531-547.
70. L. JU, Q. DU, AND M. GUNZBURGER, Probabilistic methods for centroidal Voronoi tessellations and their parallel implementations, Parallel Comput., 28(2002), pp. 1477-1500.
71. L. JU, M. GUNZBURGER, AND W.-D. ZHAO, Adaptive finite element methods for elliptic PDEs based on conforming centroidal Voronoi Delaunay triangulations, SIAM J. Sci. Comput., 28(2006), pp. 2023-2053. (Pubitemid 350150402)
72. L. JU, H.-C. LEE, AND L. TIAN, Numerical simulations of the steady Navier-Stokes equations using adaptive meshing schemes, Int. J. Numer. Meth. Fluids, 56(2008), pp. 703-721. (Pubitemid 351279361)
73. L. JU, W. WU, AND W.-D. ZHAO, Adaptive finite volume methods for steady convection-diffusion equations with mesh optimization, Dis. Cont. Dyn. Sys. B, 11(2009), pp. 669-690.
74. J. KIEFFER, Uniqueness of locally optimal quantizer for log-concave density and convex error function, IEEE Trans. Infor. Theory, 29(1983), pp. 42-47.
75. T. KANUNGO, D. MOUNT, N. NETANYAHU, C. PIATKO, R. SILVERMAN, AND A. WU, An efficient kmeans clustering algorithm: Analysis and implementation, IEEE Trans. Pattern Anal. Mach. Intel., 24(2002), pp. 881-892. (Pubitemid 34835464)
76. K. KUNISCH AND S. VOLKWEIN, Galerkin proper orthogonal decomposition methods for parabolic problems, Numer. Math., 90(2001), pp. 117-148.
77. F. LABELLE AND J. SHEWCHUK, Anisotropic voronoi diagrams and guaranteed-quality anisotropic mesh generation. In Proc. 19th Symposium on Computational Geometry (SoCG), pages 191-200, New York, NY, USA, 2003. ACM Press.
78. H.-C. LEE, S.-W. LEE AND G.-R. PIAO, Reduced-order modeling of Burger equations based on centroidal Voronoi Tessellation Int. J. Numer. Anal. Model., 4(2007), pp. 559-583.
79. D. LIBERZON, Hybrid feedback stabilization of systems with quantized signals, Automatica, 39(2003), pp. 1543-1554.
80. W. LIPSCOMB AND T. RINGLER, An incremental remapping transport scheme on a spherical geodesic grid, Monthly Weather Reiview, 133(2005), pp. 2335-2350. (Pubitemid 41320026)
81. D. LIU AND J. NOCEDAL, On the limited memory BFGS method for large scale optimization, Mathematical Programming: A and B, 45(1989), pp. 503-528. (Pubitemid 20660315)
82. Y. LIU, W. WANG, B. LEVY, F. SUNG, AND D-M. YAN, On centroidal Voronoi tessellation - Energy smoothness and fast computation, ACM Trans. Graphics, 28(2009), pp. 1-17.
83. S. LLOYD, Least squares quantization in PCM, IEEE Trans. Inform. Theory, 28(1982), pp. 129-137.
84. R. LOHNER AND P. PARIKH, Generation of three-dimensional unstructured grids by the advancing-front method, Int. J. Num. Meth. Fluid, 8(1988), pp. 1135-1149. (Pubitemid 18664788)
85. L. LU, B. LEVY AND W.-B. WANG, Centroidal Voronoi tesselation of line segments and graphs, INRIA-ALICE Technical report, 2009.
86. D. LUENBERGER, Linear and Nonlinear Programming, Addison-Wesley, Reading, MA, 1984.
87. J. MACQUEEN, Some methods for classification and analysis of multivariate observations, Proceedings of the Fifth Berkeley Symp. Math. Stat. and Prob., Vol I, Ed. by L. Le Cam and J. Neyman, University of California, 1967, pp. 281-297.
88. Y. MADAY, A. PATERA, AND G. TURINICI, A priori convergence theory for reduced-basis approximations of single-parameter elliptic partial differential equations, J. Sci. Comput., 17 (2002) pp. 437-446.
89. M. MURPHY, D. MOUNT, AND C. GABLE, A point-placement strategy for Conforming Delaunay tetrahedralization, Inter. J. Comput. Geom. Appl., 11(2001), pp. 669-682. (Pubitemid 33677175)
90. P. MORIN, R. NOCHETTO, AND K. SIEBERT, Data oscillation and convergence of adaptive finite element methods, SIAM J. Numer. Anal., 38(2000), pp. 466-488. (Pubitemid 33779242)
91. M. MORIGUCHI AND K. SUGIHARA, Constructing centroidal Voronoi tessellations on surface meshes, Studies in Computational Intelligence, 158(2009), pp. 235-245.
92. D. NEWMAN, The hexagon theorem, IEEE Trans. Inform. Theory, 28(1982), pp. 137-139.
93. F. NIELSON, J. BOISSONNAT AND R. NOCK, Bregman Voronoi Diagrams: Properties, Algorithms and Application, preprint, 2007.
94. H. NGUYEN, J. BURKARDT, M. GUNZBURGER, L. JU, AND Y. SAKA, Constrained CVT meshes and a comparison of triangular mesh generators, Comput. Geom.: Theory Appl., 42(2009), pp. 1-19.
95. H. NGUYEN, M. GUNZBURGER, L. JU, AND J. BURKARDT, Adaptive anisotropic meshing for steady convection-dominated problems, Comput. Methods Appl. Mech. Engrg., 198(2009), pp. 2964-2981.
96. A. NOOR, Recent advances in reduction methods for nonlinear problems, Comput. & Struc., 13(1981), pp. 31-44.
97. A. OKABE, B. BOOTS, K. SUGIHARA, AND S. CHIU, Spatial Tessellations: Concepts and Applications of Voronoi Diagrams, 2nd edition, Wiley, Chichester, 2000.
98. V. OSTROMOUKHOV, C. DONOHUE, AND P. JODOIN, Fast hierarchical importance sampling with blue noise properties, ACM Trans. Graphics, 23(2004), pp. 488-495. (Pubitemid 41557008)
99. Y. OUYANG, Design of vehicle routing zones for large-scale distribution systems, Transportation Research B: Methodological, 41(2007), pp. 1079-1093. (Pubitemid 47520483)
100. Y. OUYANG AND C. DAGANZO, Discretization and validation of the continuum approximation scheme for terminal system design, Transportation Science, 40(2006), pp. 89-98.
101. S. OSHER AND N. PARAGIOS, Geometric Level Set Methods in Imaging, Vision and Graphics, Springer, 2002.
102. J. PETERSON, The reduced basis method for incompressible flow calculations, SIAM J. Sci. Stat. Comput., 10(1989), pp. 777-786.
103. G. PEYRE AND L. COHEN, Surface segmentation using geodesic centroidal tesselation, Proceedings of the Second Inter. Symp. 3D Data Processing, Visualization and Transmission, 2004, pp. 995-1002. (Pubitemid 40456399)
104. G. PIAO, H.-C. LEE AND Q. DU, Adaptive CVT-based reduced-order modeling of Burgers equation, J. Korean SIAM, 13(2009), pp. 141-159.
105. P.-O. PERSSON AND G. STRANG, A simple mesh generator in Matlab, SIAM Review, 46(2004), pp. 329-345.
106. R. RENKA, ALGORITHM 772. STRIPACK: Delaunay triangulation and Voronoi diagrams on the surface of a sphere, ACM Trans. Math. Soft., 23(1997), pp. 416-434. (Pubitemid 127448484)
107. T. RINGLER, Comparing truncation error to PDE solution error on spherical Voronoi Tessellations, Tech report, Dept. Atmospheric Sci., Colorado State Univ., 2003.
108. V. ROMERO, J. BOURKARDT, M. GUNZBURGER AND J. PETERSON, Comparison of pure and "Latinized" centroidal Voronoi tessellation against various other statistical sampling methods, Reliab. Engrg. Sys. Safe., 91(2006), pp. 1266-1280.
109. T. RINGLER, L. JU, AND M. GUNZBURGER, A multi-resolution method for climate system modeling, Ocean Dynamics, 58(2008), pp. 475-498.
110. M. RATHINAM AND L. PETZOLD, A new look at proper orthogonal decomposition, SIAM J. Numer. Anal., 41(2003), pp. 1893-1925.
111. A. SECORD, Weighted Voronoi stippling, Proceedings of the Second International Symposium on Non-Photorealistic Animation and Rendering, NPAR, 2002.
112. J. SHEWCHUK, Triangle: Engeering a 2D quality mesh generator and Delaunay triangulator, Lecture Notes in Comput. Sci., 1148(1996), Springer-Verlag, New York, pp. 203-222. (Pubitemid 126140158)
113. M. SAMOZINO, M. ALEXA, P. ALLIEZ, AND M. YVINEC, Reconstruction with Voronoi centered radial basis functions, Proceedings of Sympos. Geom. Processing, 2006, pp. 51-60.
114. M. SHEPHARD AND M. GEORGES, Automatic three-dimensional mesh generation technique by the finite element octree technique, Inter. J. Numer. Meths. Engrg., 32(1991), pp. 709-749. (Pubitemid 21713596)
115. J. SABIN AND R. GRAY, Global convergence and empirical consistency of the generalized Lloyd algorithm, IEEE Trans. Inform. Theory, 32 (1986) pp. 148-155. (Pubitemid 16613622)
116. Y. SAKA, M. GUNZBURGER, AND J. BURKARDT, Latinized, improved LHS, and CVT point sets in hypercubes, Int. J. Numer. Anal. Model, 4(2007), pp. 729-743.
117. S. VALETTE AND J. CHASSERY, Approximated centroidal Voronoi diagrams for uniform polygonal mesh coarsening, Computer Graphics forum, 23(2004), pp. 381-389.
118. S. VALETTE, J. CHASSERY, AND R. PROST, Generic remeshing of 3D triangular meshes with metric-Dependent discrete Voronoi diagrams, IEEE Trans. Visual. Comput. Graphics, 14(2008), pp. 369-381. (Pubitemid 351169663)
119. D. WANG, A new method for efficient generation of high quality surface triangular meshes, Comms. Comput. Phys., 1(2006), pp. 716-735.
120. X. WU, On Convergence of Lloyd's Method I, IEEE Trans. Inform. Theory, 38(1992), pp. 171-174.
121. D. WANG, O. HASSAN, K. MORGAN, AND N. WEATHERILL, EQSM: An efficient high quality surface grid generation method based on remeshing, Comput. Methods Appl. Mech. Engrg., 195(2006), pp. 5621-5633. (Pubitemid 43942194)
122. J. WANG, L. JU, AND X. WANG, An edge-weighted centroidal Voronoi tessellation model for image segmentation, IEEE Trans. Image Processing, 18(2009), pp. 1844-1858.
123. D. WILLIAMSON, J. DRAKE, J. HACK, R. JAKOB, AND P. SWARZTRAUBER, A standard test set for numerical approximations to the shallow water equations in spherical geometry, J. Comput. Phys., 102(2001), pp. 211-224.