A cascadic geometric filtering approach to subdivision

Computer Aided Geometric Design

Volumn 19, Issue 9, 2002, Pages 675-694

  Diewald, U ^a   Morigi, S ^b   Rumpf, M ^a  

^a UNIVERSITY OF DUISBURG ESSEN   (Germany)

^b UNIVERSITY OF BOLOGNA   (Italy)

Author keywords

Curves and surfaces; Geometric modeling; Image processing; Surface fairing; Variational subdivision

Indexed keywords

COMPUTATIONAL GEOMETRY; COMPUTER SIMULATION; FINITE ELEMENT METHOD; IMAGE PROCESSING; ITERATIVE METHODS;

GEOMETRIC FILTERING;

COMPUTER GRAPHICS;

EID: 0036894002     PISSN: 01678396     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-8396(02)00150-4     Document Type: Article

References (33)

1. Bornemann F.A., Deuflhard P. The cascadic multigrid method for elliptic problems. Numer. Math. 75:(2):1996;135-152.
2. Catmull E., Clark J. Recursively generated b-spline surfaces on arbitrary topological meshes. Computer-Aided Design. 10:1978;350-355.
3. Chavel I. Eigenvalues in Riemannian Geometry. 1984;Academic Press.
4. Ciarlet P., Lions J. Handbook of Numerical Analysis, Vol. V: Techniques of Scientific Computing. 1997;Elsevier, Amsterdam.
5. Deckelnick K., Dziuk G. Discrete anisotropic curvature flow of graphs. Math. Modelling Numer. Anal. 33:(6):1999;1203-1222.
6. Desbrun M., Meyer M., Schroeder P., Barr A. Implicit fairing of irregular meshes using diffusion and curvature flow. Computer Graphics (SIGGRAPH '99 Proceedings). 1999;317-324.
7. Diewald U., Clarenz U., Rumpf M. Nonlinear anisotropic diffusion in surface processing. Proceedings of IEEE Visualization 2000. 2000.
8. do Carmo M.P. Riemannian Geometry. 1993;Birkhäuser, Boston.
9. Doo D., Sabin M. Analysis of the behaviour of recursive division surfaces near extraordinary points. Computer-Aided Design. 10:(4):1978;356-360.
10. Dyn N., Levin D., Gregory J. A 4-point interpolatory subdivision scheme for curve design. Computer Aided Geometric Design. 4:1987;257-268.
11. Dyn N., Levin D., Gregory J. A butterfly subdivision scheme for surface interpolation with tension control. ACM Trans. on Graphics. 9:1990;160-169.
12. Dziuk G. An algorithm for evolutionary surfaces. Numer. Math. 58:1991;603-611.
13. Giaquinta M. Introduction to Regularity Theory for Nonlinear Elliptic Systems. 1993;Birkhäuser-Verlag, Basel.
14. Gilbarg D., Trudinger N.S. Elliptic Partial Differential Equations of Second Order. 1983;Springer, Berlin.
15. Hackbusch W. Multi-grid Methods and Applications. 1985;Springer, Berlin/Heidelberg.
16. Hoppe H., DeRose T., Duchamp T., Halstead M., Jin H., McDonald J., Schweitzer J., Stuetzle W. Piecewise smooth surface reconstruction. Computer Graphics (SIGGRAPH 1994 Proceedings). 1994;295-302.
17. Huisken G. The volume preserving mean curvature flow. J. Reine Angew. Math. 382:1987;35-48.
18. Kobbelt L. Interpolatory subdivision on open quadrilateral nets with arbitrary topology. Proceedings of Eurographics 96, Computer Graphics Forum. 1996;409-420.
19. Kobbelt L. A variational approach to subdivision. Computer Aided Geometric Design. 13:1996;743-761.
20. Kobbelt L. Discrete fairing. Proceedings of the 7th IMA Conference on the Mathematics of Surfaces. 1997;101-131.
21. Kobbelt L. Discrete fairing and variational subdivision for free-form surface design. The Visual Computer. 16:(3/4):2000;142-158.
22. Kobbelt L., Schröder P. A multiresolution framework for variational subdivision. ACM Trans. on Graphics. 17:(4):1998;209-237.
23. Loop, C., 1987. Smooth subdivision surfaces based on triangles. Master Thesis, University of Utah.
24. Pinkall U., Polthier K. Computing discrete minimal surfaces and their conjugates. Exp. Math. 2:(1):1993;15-36.
25. Reif U. A unified approach to subdivision algorithms near extraordinary points. Computer Aided Geometric Design. 12:1995;153-174.
26. Schneider R., Kobbelt L. Geometric fairing of irregular meshes for free-form surface design. Computer Aided Geometric Design. 18:2001;359-379.
27. Taubin G. A signal processing approach to fair surface design. Computer Graphics (SIGGRAPH '95 Proceedings). 1995;351-358.
28. Thomée V. Galerkin - Finite Element Methods for Parabolic Problems. 1984;Springer.
29. Velho L., Zorin D. 4-8 subdivision. Computer Aided Geometric Design. 18:2001;397-427.
30. Welch W., Witkin A. Variational surface modeling. Computer Graphics (SIGGRAPH '92 Proceedings). 1992;157-166.
31. Zorin, D., 1997. Subdivision and multiresolution surface representations. PhD Thesis, Caltech, Pasadena.
32. 1 -continuity of subdivision surfaces. SIAM J. Numer. Anal. 37:(4):2000.
33. Zorin D., Schröder P., Sweldens W. Interpolating subdivision for meshes with arbitrary topology. Computer Graphics (SIGGRAPH '96 Proceedings). 1996;189-192.