Modal shape analysis beyond Laplacian

Computer Aided Geometric Design

Volumn 29, Issue 5, 2012, Pages 204-218

  Hildebrandt, Klaus ^a   Schulz, Christian ^a   Von Tycowicz, Christoph ^a   Polthier, Konrad ^a  

^a FREIE UNIVERSITÄT BERLIN   (Germany)

Author keywords

Laplace Beltrami operator; Modal shape analysis; Shape signatures; Spectral mesh processing

Indexed keywords

CLOSED FORM; CURVED SURFACES; DEFORMATION ENERGY; DIFFERENTIAL OPERATORS; EIGEN MODES; EIGENVIBRATIONS; EUCLIDEAN PLANES; FUNCTION SPACES; GENERAL CLASS; LAPLACE OPERATOR; LAPLACE-BELTRAMI OPERATOR; LAPLACIANS; MESH PROCESSING; MODAL SHAPE; SHAPE ANALYSIS; SHAPE SIGNATURES; SHAPE SPACE;

DEFORMATION; EIGENVALUES AND EIGENFUNCTIONS; MATHEMATICAL OPERATORS;

LAPLACE TRANSFORMS;

EID: 84860464740     PISSN: 01678396     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cagd.2012.01.001     Document Type: Conference Paper

References (36)

1. P.R. Amestoy, I.S. Duff, J. Koster, and J.Y. L'Excellent A fully asynchronous multifrontal solver using distributed dynamic scheduling SIAM Journal on Matrix Analysis and Applications 23 2001 15 41
2. Baraff, D., Witkin, A., 1998. Large steps in cloth simulation. In: Proceedings of ACM SIGGRAPH, pp. 43-54.
3. J. Barbič, and D.L. James Real-time subspace integration for St. Venant-Kirchhoff deformable models ACM Transactions on Graphics 24 2005 982 990
4. Bridson, R., Marino, S., Fedkiw, R., 2003. Simulation of clothing with folds and wrinkles. In: Proceedings of ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp. 28-36.
5. M.G. Choi, and H.S. Ko Modal warping: Real-time simulation of large rotational deformation and manipulation IEEE Transactions on Visualization and Computer Graphics 11 2005 91 101 (Pubitemid 40168685)
6. U. Clarenz, U. Diewald, G. Dziuk, M. Rumpf, and R. Rusu A finite element method for surface restoration with smooth boundary conditions Computer Aided Geometric Design 21 2004 427 445
7. T.K. Dey, K. Li, C. Luo, P. Ranjan, I. Safa, and Y. Wang Persistent heat signature for pose-oblivious matching of incomplete models Computer Graphics Forum 29 2010 1545 1554
8. S. Dong, P.T. Bremer, M. Garland, V. Pascucci, and J.C. Hart Spectral surface quadrangulation ACM Transactions on Graphics 25 2006 1057 1066 (Pubitemid 44481068)
9. G. Dziuk Finite elements for the Beltrami operator on arbitrary surfaces Partial Differential Equations and Calculus of Variations Lecture Notes in Mathematics vol. 1357 1988 Springer 142 155
10. G. Dziuk An algorithm for evolutionary surfaces Numerical Mathematics 58 1991 603 611
11. Eckstein, I., Pons, J.P., Tong, Y., Kuo, C.C.J., Desbrun, M., 2007. Generalized surface flows for mesh processing. In: Symposium on Geometry Processing, Eurographics Association, pp. 183-192.
12. Garg, A., Grinspun, E., Wardetzky, M., Zorin, D., 2007. Cubic shells. In: Proceedings of ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp. 91-98.
13. K. Gebal, J.A. Bærentzen, H. Aanæs, and R. Larsen Shape analysis using the auto diffusion function Computer Graphics Forum 28 2009 1405 1413
14. Grinspun, E., Hirani, A.N., Desbrun, M., Schröder, P., 2003. Discrete shells. In: Proceedings of ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp. 62-67.
15. Hauser, K.K., Shen, C., O'Brien, J.F., 2003. Interactive deformation using modal analysis with constraints. In: Graphics Interface, pp. 247-256.
16. K. Hildebrandt, K. Polthier, and M. Wardetzky On the convergence of metric and geometric properties of polyhedral surfaces Geometricae Dedicata 123 2006 89 112
17. K. Hildebrandt, C. Schulz, C. von Tycowicz, and K. Polthier Interactive surface modeling using modal analysis ACM Transactions on Graphics 30 119 2011 1 11
18. J. Huang, M. Zhang, J. Ma, X. Liu, L. Kobbelt, and H. Bao Spectral quadrangulation with orientation and alignment control ACM Transactions on Graphics 27 2008 1 9
19. Q. Huang, M. Wicke, B. Adams, and L. Guibas Shape decomposition using modal analysis Computer Graphics Forum 28 2009 407 416
20. J. Jost Riemannian Geometry and Geometric Analysis 2008 Springer-Verlag
21. R.B. Lehoucq, D.C. Sorensen, and C. Yang ARPACK Users' Guide - Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods. Software, Environments, Tools 1998 SIAM
22. Lévy, B., Zhang, H., 2009. Spectral mesh processing. In: ACM, SIGGRAPH ASIA Courses, pp. 1-47.
23. M. Ovsjanikov, Q. Mérigot, F. Mémoli, and L. Guibas One point isometric matching with the heat kernel Computer Graphics Forum 29 2010 1555 1564
24. M. Ovsjanikov, J. Sun, and L. Guibas Global intrinsic symmetries of shapes Computer Graphics Forum 27 2008 1341 1348
25. Pentland, A., Williams, J., 1989. Good vibrations: modal dynamics for graphics and animation. In: Proceedings of ACM SIGGRAPH, pp. 215-222.
26. U. Pinkall, and K. Polthier Computing discrete minimal surfaces and their conjugates Experimental Mathematics 2 1993 15 36
27. K. Polthier Computational aspects of discrete minimal surfaces J. Hass, D. Hoffman, A. Jaffe, H. Rosenberg, R. Schoen, M. Wolf, Global Theory of Minimal Surfaces 2005 Clay Foundation
28. Reuter, M., Wolter, F.E., Peinecke, N., 2005. Laplace-spectra as fingerprints for shape matching. In: Proceedings of the ACM Symposium on Solid and Physical Modeling, pp. 101-106. (Pubitemid 43111280)
29. M. Reuter, F.E. Wolter, and N. Peinecke Laplace-Beltrami spectra as "Shape-DNA" of surfaces and solids Computer-Aided Design 38 2006 342 366
30. Rustamov, R.M., 2007. Laplace-Beltrami eigenfunctions for deformation invariant shape representation. In: Proceedings of Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, pp. 225-233.
31. Y. Saad Numerical Methods for Large Eigenvalue Problems 1992 Manchester University Press
32. Sorkine, O., Alexa, M., 2007. As-rigid-as-possible surface modeling. In: Proceedings of Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, pp. 109-116.
33. J. Sun, M. Ovsjanikov, and L.J. Guibas A concise and provably informative multi-scale signature based on heat diffusion Computer Graphics Forum 28 2009 1383 1392
34. B. Vallet, and B. Lévy Spectral geometry processing with manifold harmonics Computer Graphics Forum 27 2 2008 251 260 (Pubitemid 351612842)
35. M. Wardetzky, M. Bergou, D. Harmon, D. Zorin, and E. Grinspun Discrete quadratic curvature energies Computer Aided Geometric Design 24 2007 499 518 (Pubitemid 47562134)
36. H. Zhang, O. van Kaick, and R. Dyer Spectral mesh processing Computer Graphics Forum 29 6 2010 1865 1894 10.1111/j.1467-8659.2010.01655.x