Mesh quality improvement: radial basis functions approach

References

• Amenta , N. , Bern , M. and Eppstein , D. 1999 . Optimal point placement for mesh smoothing . J. Algorithms , 30 ( 2 ) : 302 – 322 .
   Google Scholar
• Babuska , I. , Zienkiewicz , O. C. , Gago , J. and de A. Oliviera , E. R. 1986 . Accuracy Estimates and Adaptive Refinements in Finite Element Computations , 281 – 297 . Chichester : John Wiley & Sons .
   Google Scholar
• Balendran , B. A direct smoothing method for surface meshing . Proceedings of the 8th International Meshing Roundtable . South Lake Tahoe, CA, USA. pp. 189 – 193 .
   Google Scholar
• Bookstein , F. L. Two shapes metrics for biomedical outline data: bending energy, procrustes distance, and the biometrical modeling of shape phenomena . International Conference on Shape Modeling and Applications . March 3–6 , Aizu, Japan. pp. 110 – 120 .
   Google Scholar
• Bossen , F. J. and Heckbert , P. S. A pliant method for anisotropic mesh generation . Proceedings of the 5th International Meshing Roundtable . Pittsburgh, PA. pp. 63 – 74 .
   Google Scholar
• Buhmann , M. D. 2003 . Radial Basis Functions: Theory and Implementation , Cambridge University Press .
   Google Scholar
• Calvo , N. A. and Idelsohn , S. R. 2001 . All-hexahedral mesh smoothing with a node-based measure of quality . Int. J. Numer. Methods Eng. , 50 : 1957 – 1967 .
   Google Scholar
• Canann , S. A. , Stephenson , M. B. and Blacker , T. D. 1993 . Optismoothing: an optimization-driven approach to mesh smoothing . J. Finite Elemen. Anal. Design , 13 : 185 – 190 .
   Google Scholar
• Canann , S. A. , Tristano , J. R. and Staten , M. L. An approach to combined laplacian and optimization-based smoothing for triangular, quadrilateral, and quad-dominant meshes . Proceedings of the 7th International Meshing Roundtable . pp. 479 – 494 .
   Google Scholar
• Carr , J. C. , Mitchell , T. J. , Beatson , R. K. , Cherrie , J. B. , Fright , W. R. , McCallumn , B. C. and Evans , T. R. Reconstruction and representation of 3D objects with radial basis functions . Proceedings of SIGGRAPH’01 . pp. 67 – 76 .
   Google Scholar
• Diacchin , L. F. , Knupp , P. , Munson , T. and Shontz , S. 2004 . A comparison of two optimization methods for mesh quality improvement . 13th Mesh Roundtable Conference . Sept 19–24 2004 . pp. 243 – 254 .
   Google Scholar
• Djidjev , H. N. Force-directed methods for smoothing unstructured triangular and tetrahedral meshes . Proceedings of the 9th International Meshing Roundtable . pp. 395 – 406 . Sandia National Laboratories .
   Google Scholar
• Dompierre , J. , Labbe , P. , Guibault , F. and Camarero , R. Proposals of benchmarks for 3D unstructured tetrahedral mesh optimization . Proceedings of the 7th International Roundtable Conference . pp. 459 – 478 . Sandia Lab .
   Google Scholar
• Egorova , O. Tokyo, , Japan : Tokyo Institute of Technology . Doctor Thesis
   Google Scholar
• Field , D. A. 1998 . Laplacian smoothing and delaunay triangulations . J. Commun. Appl. Numer. Methods , 4 : 709 – 712 .
   Google Scholar
• Freitag , L. A. 1997 . “ On combining laplacian and optimization-based mesh smoothing techniques, AMD – vol. 220 ” . 37 – 43 . Trends in Unstructured Mesh Generation .
   Google Scholar
• Freitag , L. A. and Olliver-Gooch , C. A comparison of tetrahedral mesh improvement techniques . Proceedings of the 5th International Roundtable . pp. 87 – 106 . Albuquerque, NM : Sandia National Lab .
   Google Scholar
• Freitag , L. , Knupp , P. , Munson , T. and Shontz , S. Comparison of optimization software for mesh shape-qualiy improvement problems . Proceedings of the 11th International Meshing Roundtable . pp. 29 – 40 . Sandia National Lab .
   Google Scholar
• Frey , W. H. and Field , D. 1991 . Mesh relaxation: a new technique for improving triangulations . Int. J. Numer. Methods Eng. , 31 ( 6 ) : 1121 – 1133 .
   Google Scholar
• Garimella , R. V. and Shashkov , M. J. 2004 . Polygonal surface mesh optimization . Eng. Comput. , 20 : 265 – 272 .
   Google Scholar
• Holder , M. and Richardson , J. Genetic algorithms, another tool for quad mesh optimization? . Proceedings of the 7th International Meshing Roundtable . pp. 497 – 504 . Sandia National Lab .
   Google Scholar
• Hoppe , H. , DeRose , T. , Duchamp , T. , McDonald , J. and Stuetzle , W. Surface reconstruction from unorganized points . Proceedings of SIGGRAPH’92 . pp. 71 – 78 .
   Google Scholar
• Jacquotte , O. P. and Coussement , G. 1992 . Structured mesh adaptation: space accuracy and interpolation methods . Comput. Methods Appl. Mech. Eng. , 101 : 397 – 432 .
   Web of Science ®Google Scholar
• Joe , B. 1995 . Construction of three-dimensional improved-quality triangulations using local transformations . Math. Comput. , 16 : 1292 – 1307 .
   Google Scholar
• Kovalev , K. , Delanaye , M. and Hirsch , Ch. Untangling and optimization of unstructured hexahedral meshes . Proceedings of Workshop Communication on Applied Mathematics Grid Generations: Theory and Applications . Moscow.
   Google Scholar
• Lable , P. , Dompierre , J. , Guibault , F. and Camarero , R. On element shape measures for mesh optimazation . 2nd Symposium on Trends in Unstructured Mesh Generation . August . Boulder : University of Colorado .
   Google Scholar
• Lohner , R. , Morgan , K. and Zienkiewicz , O. C. Adaptive grid refinement for the euler and compressible navier stokes equation . Proceedings of the International Conference on Accuracy Estimates and Adaptive Refinement in Finite Element Computations . Lisbon.
   Google Scholar
• MS. PATRAN, 2003 FEA Help Files
   Google Scholar
• Nelder , J. A. and Mead , R. 1965 . Comput. J. , 7 : 308 – 313 .
   Web of Science ®Google Scholar
• Parthasarathy , V. and Kodiyalam , S. 1991 . A constrained optimization approach to finite element mesh smoothing . J. Finite Elemen. Anal. Design , 9 : 309 – 320 .
   Google Scholar
• Reymond , M. and Miller , M. 1996 . MSC.Nastran Quick Reference Guide Version 68 , The Macneal- Schwendler Corporation .
   Google Scholar
• Savchenko , V. and Schmitt , L. Reconstructing occlusal surfaces of teeth using a genetic algorithm with simulated annealing type selection . 6th ACM Symposium on Solid Modeling and Applications . June 4–8 . pp. 39 – 41 . Ann Arbor, Michigan : Sheraton Inn .
   Google Scholar
• Shewchuk , J. R. What is a good linear element? . Interpolation, Conditioning, and Quality Measures, Proceedings of the 11th International Meshing Roundtable . pp. 115 – 126 . Sandia National Laboratories .
   Google Scholar
• Schreder , W. , Martin , K. and Lorensen , B. 1998 . The Visualization Toolkit , 2 , Prentice Hall, Inc. .
   Google Scholar
• Shimada , K. Anisotropic triangular meshing of parametric surfaces via close packing of ellipsoidal bubbles . Proceedings of the 6th International Meshing Roundtable, Sandia National Laboratories . pp. 375 – 390 .
   Google Scholar
• Shimada , K. and Gossard , D. C. Bubble mesh: automated triangular meshing of non-manifold geometry by sphere packing . Proceedings of the ACM Third Symposium on Solid Modeling and Applications . pp. 409 – 419 .
   Google Scholar
• Zhou , T. and Shimada , K. An angle-based approach to two-dimensional mesh smoothing . Proceedings of the 9th International Meshing Roundtable . pp. 373 – 384 .
   Google Scholar