“High-resolution interaction with corotational coarsening models” by Torres, Rodríguez, Espadero and Otaduy
Conference:
Type(s):
Title:
- High-resolution interaction with corotational coarsening models
Session/Category Title: Fantastic Elastics
Presenter(s)/Author(s):
Abstract:
This paper presents a numerical coarsening method for corotational elasticity, which enables interactive large deformation of high-resolution heterogeneous objects. Our method derives a coarse elastic model from a high-resolution discretization of corotational elasticity with high-resolution boundary conditions. This is in contrast to previous coarsening methods, which derive a coarse elastic model from an unconstrained high-resolution discretization of regular linear elasticity, and then apply corotational computations directly on the coarse setting. We show that previous approaches fail to handle high-resolution boundary conditions correctly, suffering accuracy and robustness problems. Our method, on the other hand, supports efficiently accurate high-resolution boundary conditions, which are fundamental for rich interaction with high-resolution heterogeneous models. We demonstrate the potential of our method for interactive deformation of complex medical imaging data sets.
References:
1. Allard, J., Faure, F., Courtecuisse, H., Falipou, F., Duriez, C., and Kry, P. G. 2010. Volume contact constraints at arbitrary resolution. ACM Trans. Graph. 29, 4, 82:1–82:10.
2. Barbič, J., and James, D. L. 2005. Real-time subspace integration for st. venant-kirchhoff deformable models. ACM Trans. Graph. 24, 3, 982–990.
3. Barbič, J., and Zhao, Y. 2011. Real-time large-deformation substructuring. ACM Trans. Graph. 30, 4, 91:1–91:8.
4. Barbič, J. 2012. Exact corotational linear FEM sitffness matrix. Tech. rep., University of Southern California.
5. Bro-Nielsen, M., and Cotin, S. 1996. Real-time volumetric deformable models for surgery simulation using finite elements and condensation. Computer Graphics Forum 15, 3, 57–66. Cross Ref
6. Capell, S., Green, S., Curless, B., Duchamp, T., and Popović, Z. 2002. A multiresolution framework for dynamic deformations. In Proceedings of the 2002 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, 41–47.
7. Chao, I., Pinkall, U., Sanan, P., and Schröder, P. 2010. A simple geometric model for elastic deformations. ACM Trans. Graph. 29, 4, 38:1–38:6.
8. Chen, D., Levin, D. I. W., Sueda, S., and Matusik, W. 2015. Data-driven finite elements for geometry and material design. ACM Trans. Graph. 34, 4, 74:1–74:10.
9. Cioranescu, D., and Donato, P. 2000. An Introduction to Homogenization. Oxford University Press.
10. Debunne, G., Desbrun, M., Cani, M.-P., and Barr, A. H. 2001. Dynamic real-time deformations using space & time adaptive sampling. In Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques, 31–36.
11. Faure, F., Gilles, B., Bousquet, G., and Pai, D. K. 2011. Sparse Meshless Models of Complex Deformable Solids. ACM Transactions on Graphics 30, 4, Article No. 73.
12. Filonova, V., Liu, Y., Bailakanavar, M., Fish, J., and Yuan, Z. 2013. Corotational formulation of reduced order homogenization. Computers, Materials & Continua 34, 3, 177–198.
13. Gascon, J., Espadero, J. M., Perez, A. G., Torres, R., and Otaduy, M. A. 2013. Fast deformation of volume data using tetrahedral mesh rasterization. In Proc. of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation, 181–185.
14. Georgii, J., and Westermann, R. 2006. A generic and scalable pipeline for gpu tetrahedral grid rendering. Visualization and Computer Graphics, IEEE Transactions on 12, 5, 1345–1352.
15. Goldstein, H., Poole, C. P., and Safko, J. L. 2001. Classical Mechanics (3rd Edition), 3 ed. Addison-Wesley.
16. Golub, G. H., and Van Loan, C. F. 1996. Matrix Computations (3rd Ed.). Johns Hopkins University Press, Baltimore, MD, USA.
17. Grinspun, E., Krysl, P., and Schröder, P. 2002. Charms: A simple framework for adaptive simulation. ACM Trans. Graph. 21, 3, 281–290.
18. Gunderson, L. L., Willett, C. G., Calvo, F. A., and Harrison, L. B. 2011. Intraoperative irradiation: techniques and results. Springer Science & Business Media.
19. Guyan, R. J. 1965. Reduction of stiffness and mass matrices. AIAA journal 3, 2, 380–380. Cross Ref
20. Harmon, D., and Zorin, D. 2013. Subspace integration with local deformations. ACM Trans. Graph. 32, 4, 107:1–107:10.
21. Hoberock, J., and Bell, N., 2010. Thrust: A parallel template library. Version 1.7.0.
22. James, D. L., and Pai, D. K. 1999. Artdefo: Accurate real time deformable objects. In Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques, 65–72.
23. Kharevych, L., Mullen, P., Owhadi, H., and Desbrun, M. 2009. Numerical coarsening of inhomogeneous elastic materials. ACM Trans. on Graphics 28, 3, 51:1–51:8.
24. Kim, T., and James, D. L. 2011. Physics-based character skinning using multi-domain subspace deformations. In Proceedings of the 2011 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, 63–72.
25. Malgat, R., Gilles, B., Levin, D. I. W., Nesme, M., and Faure, F. 2015. Multifarious hierarchies of mechanical models for artist assigned levels-of-detail. In Proceedings of the 14th ACM SIGGRAPH / Eurographics Symposium on Computer Animation, 27–36.
26. McAdams, A., Zhu, Y., Selle, A., Empey, M., Tamstorf, R., Teran, J., and Sifakis, E. 2011. Efficient elasticity for character skinning with contact and collisions. ACM Trans. Graph. 30, 4, 37:1–37:12.
27. Michel, J., Moulinec, H., and Suquet, P. 1999. Effective properties of composite materials with periodic microstructure: a computational approach. Computer Methods in Applied Mechanics and Engineering 172, 14, 109 — 143. Cross Ref
28. Müller, M., and Gross, M. 2004. Interactive virtual materials. Proc. of Graphics Interface.
29. Nesme, M., Kry, P. G., Jerábková, L., and Faure, F. 2009. Preserving topology and elasticity for embedded deformable models. ACM Trans. on Graphics 28, 3, 52:1–52:9.
30. Owhadi, H., and Zhang, L. 2007. Metric-based upscaling. Communications on Pure and Applied Mathematics 60, 5, 675–723. Cross Ref
31. Owhadi, Houman, Zhang, Lei, and Berlyand, Leonid. 2014. Polyharmonic homogenization, rough polyharmonic splines and sparse super-localization. ESAIM: M2AN 48, 2, 517–552.
32. Panetta, J., Zhou, Q., Malomo, L., Pietroni, N., Cignoni, P., and Zorin, D. 2015. Elastic textures for additive fabrication. ACM Trans. Graph. 34, 4, 135:1–135:12.
33. Pentland, A., and Williams, J. 1989. Good vibrations: Modal dynamics for graphics and animation. SIGGRAPH Comput. Graph. 23, 3, 207–214.
34. Schroeder, W., Martin, K., and Lorensen, B. 2004. The Visualization Toolkit: An object-oriented approach to 3D graphics, 3rd edition. Tech. rep., Kitware Inc.
35. Schumacher, C., Bickel, B., Rys, J., Marschner, S., Daraio, C., and Gross, M. 2015. Microstructures to control elasticity in 3d printing. ACM Trans. Graph. 34, 4, 136:1–136:13.
36. Sifakis, E., and Barbic, J. 2012. Fem simulation of 3d deformable solids: A practitioner’s guide to theory, discretization and model reduction. In ACM SIGGRAPH 2012 Courses, 20:1–20:50.
37. Teng, Y., Otaduy, M. A., and Kim, T. 2014. Simulating articulated subspace self-contact. ACM Trans. Graph. 33, 4, 106:1–106:9.
38. Teng, Y., Meyer, M., DeRose, T., and Kim, T. 2015. Subspace condensation: Full space adaptivity for subspace deformations. ACM Trans. Graph. 34, 4, 76:1–76:9.
39. Torres, R., Espadero, J. M., Calvo, F. A., and Otaduy, M. A. 2014. Interactive deformation of heterogeneous volume data. In Proc. of ISBMS.
