Abstract
Simulation of soft tissue behavior for surgical training systems is a particularly demanding application of deformable modeling. Explicit integration methods on single mesh require small time step to maintain stability, but this produces slow convergence spatially through the object. In this paper, we propose a multigrid integration scheme to improve the stability and convergence of explicit integration. Our multigrid method uses multiple unstructured independent meshes on the same object. It is shown that, with the proposed multigrid integration, both stability and convergence can be improved significantly over single level explicit integration.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Fung, Y.: Biomechanics: Mechanical Properties of Living Tissues. Springer, New York (1993)
Alterovitz, R., Pouliot, J., Taschereau, R., Hsu, I.C., Goldberg, K.: Simulating needle insertion and radioactive seed implantation for prostate brachytherapy. In: Westwood, J., et al. (eds.) Medicine Meets Virtual Reality 11, pp. 19–25. IOS Press, Amsterdam (2003)
Bro-Nielsen, M.: Finite element modeling in surgery simulation. Proc. IEEE 86, 490–502 (1998)
Cotin, S., Delingette, H., Bro-Nielsen, M., Ayache, N., et al.: Geometric and physical representations for a simulator of hepatic surgery. In: Weghorst, S., et al. (eds.) Medicine Meets Virtual Reality: 4, pp. 139–151. IOS Press, Amsterdam (1996)
James, D., Pai, D.: ARTDEFO: Accurate real time deformable objects. In: Proceedings of SIGGRAPH 1999. Computer Graphics Proceedings, Annual Conference Series, Lecture Notes in Computer Science, vol. 13, pp. 65–72. ACM, ACM Press/ACM SIGGRAPH (1999)
Cotin, S., Delingette, H., Ayache, N.: Real-time elastic deformations of soft tissues for surgery simulation. IEEE Transactions on Visualization and Computer Graphics 5, 62–73 (1999)
Picinbono, G., Delingette, H., Ayache, N.: Non-linear and anisotropic elastic soft tissue models for medical simulation. In: Proc. IEEE Intl. Conf. Robotics and Automation, Seoul, Korea, pp. 1371–1376 (2001)
Müller, M., Dorsey, J., McMillan, L., Jagnow, R., Cutler, B.: Stable real time deformations. In: Proc. ACM SIGGRAPH symposium on Computer Animation, San Antonio, TX, pp. 49–54 (2002)
Székely, G., Brechbühler, C., Hutter, R., Rhomberg, A., Ironmonger, N., Schmid, P.: Modelling of soft tissue deformation for laparoscopic surgery simulation. Medical Image Analysis 4, 57–66 (2000)
Zhuang, Y., Canny, J.: Real-time simulation of physically realistic global deformation. In: SIGGRAPH 1999 Sketches and Applications. SIGGRAPH, Los Angeles, California (1999)
Wu, X., Downes, M., Goktekin, T., Tendick, F.: Adaptive nonlinear.nite elements for deformable body simulation using dynamic progressive meshes. In: Chalmers, A., Rhyne, T.M. (eds.) Eurographics 2001, Manchester, UK, September 2001. Appearing in Computer Graphics Forum, vol. 20(3), pp. 349–358 (2001)
Bara., D., Witkin, A.: Large steps in cloth simulation. In: Proceedings of SIGGRAPH 1998. Computer Graphics Proceedings, Annual Conference Series, pp. 43–54. ACM, ACM Press/ACM SIGGRAPH (1998)
Capell, S., Green, S., Curless, B., Duchamp, T., Popovic, Z.: A multiresolution framework for dynamic deformations. In: Proc. ACM SIGGRAPH symposium on Computer Animation, San Antonio, TX, pp. 41–47 (2002)
Zienkiewicz, O., Taylor, R.: The Finite Element Method. McGraw-Hill, London (1994)
Debunne, G., Desbrun, M., Cani, M.P., Barr, A.: Dynamic real-time deformations using space and time adaptive sampling. In: Proceedings of SIGGRAPH 2001. Computer Graphics Proceedings, Annual Conference Series, pp. 31–36. ACM, ACM Press/ACM SIGGRAPH (2001)
Grinspun, E., Krysl, P., Schröder, P.: CHARMS: a simple framework for adaptive simulation. In: Proceedings of SIGGRAPH 2002. Computer Graphics Proceedings, Annual Conference Series, pp. 281–290. ACM, ACM Press/ACM SIGGRAPH (2002)
Wesseling, P.: An Introduction to Multigrid Methods. John Wiley, New York (1992)
Demmel, J.: Applied Numerical Linear Algebra. SIAM, Philadelphia (1997)
Wu, X.: Design of an Interactive Nonlinear Finite Element Based Deformable Object Simulator. PhD thesis, Department of Mechanical Engineering, University of California, Berkeley (2002)
Shewchuk, J.: Triangle: Engineering a 2D quality mesh generator and Delaunay triangulator. In: Lin, M., Manocha, D. (eds.) Applied Computational Geometry: Towards Geometric Engineering, pp. 203–222. Springer, Heidelberg (1996)
Geuzaine, C., Remacle, J.F.: Gmsh: a three-dimensional .nite element mesh generator with pre- and post-processing facilities (2002), http://www.geuz.org/gmsh/
Bathe, K.: Finite Element Procedures. Prentice Hall, Englewood Cliffs (1996)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wu, X., Tendick, F. (2004). Multigrid Integration for Interactive Deformable Body Simulation. In: Cotin, S., Metaxas, D. (eds) Medical Simulation. ISMS 2004. Lecture Notes in Computer Science, vol 3078. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25968-8_11
Download citation
DOI: https://doi.org/10.1007/978-3-540-25968-8_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22186-9
Online ISBN: 978-3-540-25968-8
eBook Packages: Springer Book Archive