Real-time nonlinear shape interpolation

ACM Transactions on Graphics

Volumn 34, Issue 3, 2015, Pages

  Von Tycowicz, Christoph ^a   Schulz, Christian ^b   Seidel, Hans Peter ^b   Hildebrandt, Klaus ^b,c  

^a ZUSE INSTITUTE BERLIN   (Germany)

^b MAX PLANCK INSTITUTE FOR INFORMATICS   (Germany)

^c DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Geometric modeling; Geometric optimization; Geometry processing; Interactive tools; Model reduction; Shape averaging; Shape interpolation

Indexed keywords

GEOMETRY; INTERPOLATION;

GEOMETRIC MODELING; GEOMETRIC OPTIMIZATION; GEOMETRY PROCESSING; INTERACTIVE TOOL; MODEL REDUCTION; SHAPE AVERAGING; SHAPE INTERPOLATION;

SHAPE OPTIMIZATION;

EID: 84930155622     PISSN: 07300301     EISSN: 15577368     Source Type: Journal    
DOI: 10.1145/2729972     Document Type: Article

References (44)

1. S. S. An, T. Kim, and D. L. James. 2008. Optimizing cubature for efficient integration of subspace deformations. ACM Trans. Graph. 27, 5, 1-10.
2. I. Baran, D. Vlasic, E. Grinspun, and J. Popović. 2009. Semantic deformation transfer. ACM Trans. Graph. 28, 3, 36:1-36:6.
3. J. Barbič, M. Da Silva, and J. Popović. 2009. Deformable object animation using reduced optimal control. ACM Trans. Graph. 28, 3, 53:1-53:9.
4. J. Barbič and D. L. James. 2005. Real-time subspace integration for St. Venant-Kirchhoff deformable models. ACM Trans. Graph. 24, 3, 982-990.
5. J. Barbič, F. Sin, and E. Grinspun. 2012. Interactive editing of deformable simulations. ACM Trans. Graph. 31, 4.
6. J. Bonet and R. D. Wood. 2008. Nonlinear Continuum Mechanics for Finite Element Analysis. Cambridge University Press.
7. M. Botsch and O. Sorkine. 2008. On linear variational surface deformation methods. IEEE Trans. Visualiz. Comput. Graph. 14, 1, 213-230.
8. M. Botsch, R. Sumner, M. Pauly, and M. Gross. 2006. Deformation transfer for detail-preserving surface editing. In Proceedings of the International Workshop on Vision, Modeling and Visualization (VMV'06). 357-364.
9. I. Chao, U. Pinkall, P. Sanan, and P. Schröder. 2010. A simple geometric model for elastic deformations. ACM Trans. Graph. 29, 38:1-38:6.
10. R. Chen, O. Weber, D. Keren, and M. Ben-Chen. 2013. Planar shape interpolation with bounded distortion. ACM Trans. Graph. 32, 4, 108:1-108:12.
11. H.-K. Chu and T.-Y. Lee. 2009. Multiresolution mean shift clustering algorithm for shape interpolation. IEEE Trans. Visual. Comput. Graph. 15, 5, 853-866.
12. P. G. Ciarlet. 2005. An Introduction to Differential Geometry with Applications to Elasticity. Springer.
13. S. Fröhlich and M. Botsch. 2011. Example-driven deformations based on discrete shells. Comput. Graph. Forum 30, 8, 2246-2257.
14. R. Gal, O. Sorkine, N. Mitra, and D. Cohen-Or. 2009. iWires: An analyzeand-edit approach to shape manipulation. ACM Trans. Graph. 28, 3.
15. E. Grinspun, A. N. Hirani, M. Desbrun, and P. Schröder. 2003. Discrete shells. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA'03). 62-67.
16. 1-close group actions. Mathematische Zeitschrift 132, 11-20.
17. B. Heeren, M. Rumpf, M. Wardetzky, and B. Wirth. 2012. Time-discrete geodesics in the space of shells. Comput. Graph. Forum 31, 5, 1755-1764.
18. th International Conference on Advances in Geometric Modeling and Processing (GMP'10). 296-314.
19. K. Hildebrandt, C. Schulz, C. Von Tycowicz, and K. Polthier. 2011. Interactive surface modeling using modal analysis. ACM Trans. Graph. 30, 5, 119:1-119:11.
20. K. Hildebrandt, C. Schulz, C. Von Tycowicz, and K. Polthier. 2012. Interactive spacetime control of deformable objects. ACM Trans. Graph. 31, 4, 71:1-71:8.
21. A. Jacobson, I. Baran, L. Kavan, J. Popović, and O. Sorkine. 2012. Fast automatic skinning transformations. ACM Trans. Graph. 31, 4, 77:1-77:10.
22. M. Kilian, N. J. Mitra, and H. Pottmann. 2007. Geometric modeling in shape space. ACM Trans. Graph. 26, 3, 64:1-64:8.
23. S. Kircher and M. Garland. 2008. Free-form motion processing. ACM Trans. Graph. 27, 2, 12:1-12:13.
24. S. Li, J. Huang, F. De Goes, X. Jin, H. Bao, and M. Desbrun. 2014. Spacetime editingofelastic motion through material optimization and reduction. ACM Trans. Graph. 33, 4, 108:1-108:10.
25. Y. Lipman, O. Sorkine, D. Levin, and D. Cohen-Or. 2005. Linear rotationinvariant coordinates for meshes. ACM Trans. Graph. 24, 3, 479-487.
26. F. A. Lülf, D.-M. Tran, and R. Ohayon. 2013. Reduced bases for nonlinear structural dynamic systems: A comparative study. J. Sound Vibrat. 332, 15, 3897-3921.
27. J. E. Marsden and T. J. R. Hughes. 1994. Mathematical Foundations of Elasticity. Dover Publications.
28. S. Martin, B. Thomaszewski, E. Grinspun, and M. Gross. 2011. Examplebased elastic materials. ACM Trans. Graph. 30, 4, 72:1-72:8.
29. nd Ed. Springer.
30. M. Rumpf and B. Wirth. 2009. A nonlinear elastic shape averaging approach. SIAM J. Imag. Sci. 2, 3, 800-833.
31. Y. Saad. 1992. Numerical Methods for Large Eigenvalue Problems. Manchester University Press.
32. C. Schulz, C. Von Tycowicz, H.-P. Seidel, and K. Hildebrandt. 2014. Animating deformable objects using sparse spacetime constraints. ACM Trans. Graph. 33, 4, 109:1-109:10.
33. nd International Symposium on 3D Data Processing, Visualization, and Transmission (3DPVT'04). 68-75.
34. F. S. Sin, D. Schroeder, and J. Barbič. 2013. Vega: Non-linear FEM deformable object simulator. Comput. Graph. Forum 32, 1, 36-48.
35. th Eurographics/ACM SIGGRAPH Symposium on Geometry Processing (SGP'07). 109-116.
36. R. W. Sumner and J. Popović. 2004. Deformation transfer for triangle meshes. ACM Trans. Graph. 23, 3, 399-405.
37. R. W. Sumner, M. Zwicker, C. Gotsman, and J. Popović. 2005. Mesh-based inverse kinematics. ACM Trans. Graph. 24, 3, 488-495.
38. C. Von Tycowicz, C. Schulz, H.-P. Seidel, and K. Hildebrandt. 2013. An efficient construction of reduced deformable objects. ACM Trans. Graph. 32, 6, 213:1-213:10.
39. E. L. Wilson, M.-W. Yuan, and J. M. Dickens. 1982. Dynamic analysis by direct superposition of Ritz vectors. Earthquake Engin. Struct. Dynamics 10, 6, 813-821.
40. T. Winkler, J. Drieseberg, M. Alexa, and K. Hormann. 2010. Multi-scale geometry interpolation. Comput. Graph. Forum 29, 2, 309-318.
41. B. Wirth, L. Bar, M. Rumpf, and G. Sapiro. 2011. A continuum mechanical approach to geodesics in shape space. Int. J. Comput. Vis. 93, 3, 293-318.
42. A. Witkin and M. Kass. 1988. Spacetime constraints. ACM SIGGRAPH Comput. Graph. 22, 159-168.
43. X. Wu, M. Wand, K. Hildebrandt, P. Kohli, and H.-P. Seidel. 2014. Realtime symmetry-preserving deformation. Comput. Graph. Forum 33, 7, 229-238.
44. D. Xu, H. Zhang, Q. Wang, and H. Bao. 2005. Poisson shape interpolation. In Proceedings of the ACM Symposium on Solid and Physical Modeling (SPM'05). 267-274.