Hybrid simulation of deformable solids

ABSTRACT

Although mesh-based methods are efficient for simulating simple hyperelasticity, maintaining and adapting a mesh-based representation is less appealing in more complex scenarios, e.g. collision, plasticity and fracture. Thus, meshless or point-based methods have enjoyed recent popularity due to their added flexibility in dealing with these situations. Our approach begins with an initial mesh that is either conforming (as generated by one's favorite meshing algorithm) or non-conforming (e.g. a BCC background lattice). We then propose a framework for embedding arbitrary sample points into this initial mesh allowing for the straightforward handling of collisions, plasticity and fracture without the need for complex remeshing. A straightforward consequence of this new framework is the ability to naturally handle T-junctions alleviating the requirement for a manifold initial mesh. The arbitrarily added embedded points are endowed with full simulation capability allowing them to collide, interact with each other, and interact with the parent geometry in the fashion of a particle-centric simulation system. We demonstrate how this formulation facilitates tasks such as arbitrary refinement or resampling for collision processing, the handling of multiple and possibly conflicting constraints (e.g. when cloth is nonphysically pinched between two objects), the straightforward treatment of fracture, and sub-element resolution of elasticity and plasticity.

REFERENCES

• 1: Pierre Alliez , David Cohen-Steiner , Mariette Yvinec , Mathieu Desbrun, Variational tetrahedral meshing, ACM SIGGRAPH 2005 Papers, July 31-August 04, 2005, Los Angeles, California
• 2: {BW97} Baraff D., Witkin A.: Partitioned Dynamics. Tech. rep., Carnegie Mellon University, 1997.
• 3: David Baraff , Andrew Witkin, Large steps in cloth simulation, Proceedings of the 25th annual conference on Computer graphics and interactive techniques, p.43-54, July 1998 [doi>10.1145/280814.280821]
• 4: David Baraff , Andrew Witkin , Michael Kass, Untangling cloth, ACM SIGGRAPH 2003 Papers, July 27-31, 2003, San Diego, California
• 5: Steve Capell , Seth Green , Brian Curless , Tom Duchamp , Zoran Popović, Interactive skeleton-driven dynamic deformations, Proceedings of the 29th annual conference on Computer graphics and interactive techniques, July 23-26, 2002, San Antonio, Texas
• 6: Steve Capell , Seth Green , Brian Curless , Tom Duchamp , Zoran Popović, A multiresolution framework for dynamic deformations, Proceedings of the 2002 ACM SIGGRAPH/Eurographics symposium on Computer animation, July 21-22, 2002, San Antonio, Texas [doi>10.1145/545261.545268]
• 7: Gilles Debunne , Mathieu Desbrun , Marie-Paule Cani , Alan H. Barr, Dynamic real-time deformations using space & time adaptive sampling, Proceedings of the 28th annual conference on Computer graphics and interactive techniques, p.31-36, August 2001 [doi>10.1145/383259.383262]
• 8: J. Dequidt , D. Marchal , L. Grisoni, Time-critical animation of deformable solids: Collision Detection and Deformable Objects, Computer Animation and Virtual Worlds, v.16 n.3-4, p.177-187, July 2005 [doi>10.1002/cav.v16:3/4]
• 9: Eran Guendelman , Robert Bridson , Ronald Fedkiw, Nonconvex rigid bodies with stacking, ACM SIGGRAPH 2003 Papers, July 27-31, 2003, San Diego, California
• 10: {GBT06} Gissler M., Becker M., Teschner M.: Local constraint methods for deformable objects. In Proc. of the 3rd Workshop in VR Interactions and Physical Simulation (VRIPHYS) (2006), pp. 1--8.
• 11: {GD04} Guy S., Debunne G.: Monte-Carlo collision detection. Tech. Rep. RR-5136, INRIA, March 2004.
• 12: Eitan Grinspun , Petr Krysl , Peter Schröder, CHARMS: a simple framework for adaptive simulation, Proceedings of the 29th annual conference on Computer graphics and interactive techniques, July 23-26, 2002, San Antonio, Texas
• 13: G. Irving , J. Teran , R. Fedkiw, Invertible finite elements for robust simulation of large deformation, Proceedings of the 2004 ACM SIGGRAPH/Eurographics symposium on Computer animation, August 27-29, 2004, Grenoble, France [doi>10.1145/1028523.1028541]
• 14: {JV03} Jansson J., Vergeest J.: Combining deformable and rigid body mechanics simulation. The Vis. Comput. J. (2003).
• 15: R. Loubère , E. J. Caramana, The force/work differencing of exceptional points in the discrete, compatible formulation of Lagrangian hydrodynamics, Journal of Computational Physics, v.216 n.1, p.1-18, 20 July 2006 [doi>10.1016/j.jcp.2005.11.022]
• 16: Julien Lenoir , Sylvere Fonteneau, Mixing Deformable and Rigid-Body Mechanics Simulation, Proceedings of the Computer Graphics International, p.327-334, June 16-19, 2004 [doi>10.1109/CGI.2004.65]
• 17: Neil Molino , Zhaosheng Bao , Ron Fedkiw, A virtual node algorithm for changing mesh topology during simulation, ACM SIGGRAPH 2004 Papers, August 08-12, 2004, Los Angeles, California
• 18: {MBTF03} Molino N., Bridson R., Teran J., Fedkiw R.: A crystalline, red green strategy for meshing highly deformable objects with tetrahedra. In 12th Int. Meshing Roundtable (2003), pp. 103--114.
• 19: Matthias Müller , Markus Gross, Interactive virtual materials, Proceedings of Graphics Interface 2004, p.239-246, May 17-19, 2004, London, Ontario, Canada
• 20: Matthias Müller , Bruno Heidelberger , Matthias Teschner , Markus Gross, Meshless deformations based on shape matching, ACM SIGGRAPH 2005 Papers, July 31-August 04, 2005, Los Angeles, California
• 21: M. Müller , R. Keiser , A. Nealen , M. Pauly , M. Gross , M. Alexa, Point based animation of elastic, plastic and melting objects, Proceedings of the 2004 ACM SIGGRAPH/Eurographics symposium on Computer animation, August 27-29, 2004, Grenoble, France [doi>10.1145/1028523.1028542]
• 22: {MTG04} Müller M., Teschner M., Gross M.: Physically-based simulation of objects represented by surface meshes. In Proc. Comput. Graph. Int. (June 2004), pp. 156--165.
• 23: James F. O'Brien , Jessica K. Hodgins, Graphical modeling and animation of brittle fracture, Proceedings of the 26th annual conference on Computer graphics and interactive techniques, p.137-146, July 1999 [doi>10.1145/311535.311550]
• 24: James F. O'Brien , Victor Brian Zordan , Jessica K. Hodgins, Combining Active and Passive Simulations for Secondary Motion, IEEE Computer Graphics and Applications, v.20 n.4, p.86-96, July 2000 [doi>10.1109/38.851756]
• 25: Mark Pauly , Richard Keiser , Bart Adams , Philip Dutré , Markus Gross , Leonidas J. Guibas, Meshless animation of fracturing solids, ACM SIGGRAPH 2005 Papers, July 31-August 04, 2005, Los Angeles, California
• 26: Eftychios Sifakis , Kevin G. Der , Ronald Fedkiw, Arbitrary cutting of deformable tetrahedralized objects, Proceedings of the 2007 ACM SIGGRAPH/Eurographics symposium on Computer animation, August 02-04, 2007, San Diego, California
• 27: Denis Steinemann , Matthias Harders , Markus Gross , Gabor Szekely, Hybrid Cutting of Deformable Solids, Proceedings of the IEEE conference on Virtual Reality, p.35-42, March 25-29, 2006 [doi>10.1109/VR.2006.74]
• 28: {Sif07} Sifakis E.: Algorithmic aspects of the simulation and control of computer generated human anatomy models. PhD thesis, Stanford University, June 2007.
• 29: Eftychios Sifakis , Igor Neverov , Ronald Fedkiw, Automatic determination of facial muscle activations from sparse motion capture marker data, ACM SIGGRAPH 2005 Papers, July 31-August 04, 2005, Los Angeles, California
• 30: Denis Steinemann , Miguel A. Otaduy , Markus Gross, Fast arbitrary splitting of deforming objects, Proceedings of the 2006 ACM SIGGRAPH/Eurographics symposium on Computer animation, September 02-04, 2006, Vienna, Austria
• 31: Eftychios Sifakis , Andrew Selle , Avram Robinson-Mosher , Ronald Fedkiw, Simulating speech with a physics-based facial muscle model, Proceedings of the 2006 ACM SIGGRAPH/Eurographics symposium on Computer animation, September 02-04, 2006, Vienna, Austria
• 32: {TF88a} Terzopoulos D., Fleischer K.: Deformable models. The Vis. Comput. 4, 6 (1988), 306--331.
• 33: Demetri Terzopoulos , Kurt Fleischer, Modeling inelastic deformation: viscolelasticity, plasticity, fracture, Proceedings of the 15th annual conference on Computer graphics and interactive techniques, p.269-278, June 1988
• 34: Demetri Terzopoulos , John Platt , Alan Barr , Kurt Fleischer, Elastically deformable models, Proceedings of the 14th annual conference on Computer graphics and interactive techniques, p.205-214, August 1987
• 35: Joseph Teran , Eftychios Sifakis , Silvia S. Blemker , Victor Ng-Thow-Hing , Cynthia Lau , Ronald Fedkiw, Creating and Simulating Skeletal Muscle from the Visible Human Data Set, IEEE Transactions on Visualization and Computer Graphics, v.11 n.3, p.317-328, May 2005 [doi>10.1109/TVCG.2005.42]
• 36: {WSG05} Wicke M., Steinemann D., Gross M.: Efficient animation of point-sampled thin shells. In Proc. of Eurographics (2005), vol. 24.

INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.5 Computational Geometry and Object Modeling

Additional Classification:
  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.7 Three-Dimensional Graphics and Realism