A continuum theory for unstructured mesh generation in two dimensions

Computer Aided Geometric Design

Volumn 25, Issue 1, 2008, Pages 14-40

  Bunin, Guy ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Differential geometry; Unstructured mesh generation

Indexed keywords

CONTINUUM MECHANICS; INVERSE PROBLEMS; POISSON EQUATION;

DIFFERENTIAL GEOMETRY; IRREGULAR VERTICES;

MESH GENERATION;

EID: 36649015809     PISSN: 01678396     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cagd.2007.05.002     Document Type: Article

References (27)

1. Alliez P., Cohen-Steiner D., Devillers O., Levy B., and Desbrun M. Anisotropic polygonal remeshing. ACM Trans. Graph. 22 3 (2003) 485-493
2. Alliez P., Ucelli G., Gotsman C., and Attene M. Recent advances in remeshing of surfaces. http://www.cs.technion.ac.il/~gotsman/AmendedPubl/Pierre/remeshing_survey.pdf
3. Aubin T. Some Nonlinear Problems in Riemannian Geometry (1998), Springer
4. Chang S.A. Non-Linear Elliptic Equations in Conformal Geometry (2004), European Mathematical Society
5. El-Badia A., and Ha-Duong T. An inverse source problem in potential analysis. Inverse Problems 16 (2000) 651-663
6. Floater M.S., and Hormann K. Surface parameterization: A tutorial and survey. In: Dodgson M.S.F.N., and Sabin M. (Eds). Advances on Multiresolution in Geometric Modelling (2004), Springer, New York
7. Garabedian P.R. Partial Differential Equations (1964), John Wiley & Sons
8. Gu, X., Yau, S., 2003. Global conformal surface parameterization. In: Eurographics Symposium on Geometry Processing
9. Hämäläinen M., Hari R., Ilmoniemi R.J., Knuutila J., and Lounasmaa O.V. Magnetoencephalography-theory, instrumentation, and applications to noninvasive studies of the working human brain. Rev. Modern Phys. 65 2 (1993) 413-497
10. Hansen G., Zardecki A., Greening D., and Bos R. A finite element method for three dimensional unstructured grid smoothing. J. Comp. Phys. 202 (2005) 281-297
11. Hatcher A. Algebraic Topology (2001), Cambridge University Press. http://www.math.cornell.edu/~hatcher/ Available at:
12. Ioannides A.A., et al. Continuous probabilistic solutions to the biomagnetic inverse problem. Inverse Problems 6 (1990) 523-542
13. Jin, M., Kim, J., Luo, F., Lee, S., Gu, X., 2006. Conformal surface parameterization using Euclidean Ricci flow. Technical Report
14. In: Johnston P. (Ed). Computational Inverse Problems in Electrocardiography (2001), WIT Press, Southampton
15. Kharevych L., Springborn B., and Schröder P. Discrete conformal mappings via circle patterns. ACM Trans. Graph. 25 2 (2006)
16. Laugwitz D. Differential and Riemannian Geometry (1965), Academic Press
17. Liseikin V.D. A Computational Differential Geometry Approach to Grid Generation (2004), Springer
18. Millman R.S., and Parker G.D. Elements of Differential Geometry (1977), Prentice Hall
19. Owen, S.J., 1998. A survey of unstructured mesh generation technology. In: Proceedings of the 7th International Meshing Roundtable
20. Ray N., Li W.C., Levy B., Sheffer A., and Alliez P. Periodic global parameterization. ACM Trans. Graph. 25 4 (2006)
21. Shimada, K., Liao, J., Itoh, T., 1998. Quadrilateral meshing with directionality control through the packing of square cells. In: 7th Int. Meshing Roundtable, pp. 61-76
22. Thompson J.F., Soni B., and Weatherrill N.P. Handbook of Grid Generation (1999), CRC Press
23. Tong, Y., Alliez, P., Cohen-Steiner, D., Desbrun, M., 2006. Designing quadrangulations with discrete harmonic forms. In: Eurographics Symposium on Geometry Processing
24. Tyn M. Partial Differential Equations of Mathematical Physics (1973), Elsevier, Amsterdam
25. Volterra V. Sur l'équilibre des corps élastiques multiplement connexes. Ann. Ec. Norm. Sup. 24 (1907) 401-517
26. In: Yamaguti M., et al. (Ed). Inverse Problems in Engineering Sciences (1991), Springer, Tokyo
27. Zidarov D. Inverse Gravimetric Problem in Geoprospecting and Geodesy (1990), Elsevier, Amsterdam