Point based animation of elastic, plastic and melting objects

ABSTRACT

We present a method for modeling and animating a wide spectrum of volumetric objects, with material properties anywhere in the range from stiff elastic to highly plastic. Both the volume and the surface representation are point based, which allows arbitrarily large deviations form the original shape. In contrast to previous point based elasticity in computer graphics, our physical model is derived from continuum mechanics, which allows the specification of common material properties such as Young's Modulus and Poisson's Ratio.

In each step, we compute the spatial derivatives of the discrete displacement field using a Moving Least Squares (MLS) procedure. From these derivatives we obtain strains, stresses and elastic forces at each simulated point. We demonstrate how to solve the equations of motion based on these forces, with both explicit and implicit integration schemes. In addition, we propose techniques for modeling and animating a point-sampled surface that dynamically adapts to deformations of the underlying volumetric model.

REFERENCES

• 1: Anders Adamson , Marc Alexa, Approximating and intersecting surfaces from points, Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing, June 23-25, 2003, Aachen, Germany
• 2: Marc Alexa , Johannes Behr , Daniel Cohen-Or , Shachar Fleishman , David Levin , Claudio T. Silva, Computing and Rendering Point Set Surfaces, IEEE Transactions on Visualization and Computer Graphics, v.9 n.1, p.3-15, January 2003 [doi>10.1109/TVCG.2003.1175093]
• 3: {Ask97} Askes H.: Everything you always wanted to know about the Element-Free Galerkin method, and more. Tech. rep., TU Delft nr. 03.21.1.31.29, 1997.
• 4: {BKO*96} Belytschko T., Krongauz Y., Organ D., Fleming M., Krysl P.: Meshless methods: An overview and recent developments. Computer Methods in Applied Mechanics and Engineering 139, 3 (1996), 3--47.
• 5: James F. Blinn, A Generalization of Algebraic Surface Drawing, ACM Transactions on Graphics (TOG), v.1 n.3, p.235-256, July 1982 [doi>10.1145/357306.357310]
• 6: {BS95} Blac C., Schlick C.: Extended field functions for soft objects. In Implicit Surfaces '95 (1995), pp. 21--32.
• 7: 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]
• 8: {Chu96} Chung T. J.: Applied Continuum Mechanics. Cambridge Univ. Press, NY, 1996.
• 9: Robert Davis Cook, Finite Element Modeling for Stress Analysis, John Wiley & Sons, Inc., New York, NY, 1994
• 10: Mathieu Desbrun , Marie-Paule Gascuel, Animating soft substances with implicit surfaces, Proceedings of the 22nd annual conference on Computer graphics and interactive techniques, p.287-290, September 1995 [doi>10.1145/218380.218456]
• 11: Mathieu Desbrun , Marie-Paule Gascuel, Smoothed particles: a new paradigm for animating highly deformable bodies, Proceedings of the Eurographics workshop on Computer animation and simulation '96, p.61-76, December 1996, Poitiers, France
• 12: {DC99} Desbrun M., Cani M.-P.: Space-Time Adaptive Simulation of Highly Deformable Substances. Tech. rep., INRIA Nr. 3829, 1999.
• 13: 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]
• 14: Mathieu Desbrun , Peter Schröder , Alan Barr, Interactive animation of structured deformable objects, Proceedings of the 1999 conference on Graphics interface '99, p.1-8, September 1999, Kingston, Ontario, Canada
• 15: {FM03} Fries T.-P., Matthies H. G.: Classification and Overview of Meshfree Methods. Tech. rep., TU Brunswick, Germany Nr. 2003-03, 2003.
• 16: 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
• 17: {GM97} Gibson S. F., Mirtich B.: A survey of deformable models in computer graphics. Technical Report TR-97-19, MERL, Cambridge, MA, 1997.
• 18: Doug L. James , Dinesh K. Pai, ArtDefo: accurate real time deformable objects, Proceedings of the 26th annual conference on Computer graphics and interactive techniques, p.65-72, July 1999 [doi>10.1145/311535.311542]
• 19: David Levin, The approximation power of moving least-squares, Mathematics of Computation, v.67 n.224, p.1517-1531, Oct. 1998 [doi>10.1090/S0025-5718-98-00974-0]
• 20: {Lev01} Levin D.: Mesh-independent surface interpolation. In Advances in Computational Mathematics (2001).
• 21: {Liu02} Liu G. R.: Mesh-Free Methods. CRC Press, 2002.
• 22: {LS81} Lancaster P., Salkauskas K.: Surfaces generated by moving least squares methods. Mathematics of Computation 87 (1981), 141--158.
• 23: Matthias Müller , David Charypar , Markus Gross, Particle-based fluid simulation for interactive applications, Proceedings of the 2003 ACM SIGGRAPH/Eurographics symposium on Computer animation, July 26-27, 2003, San Diego, California
• 24: {Mon92} Monaghan J.: Smoothed particle hydrodynamics. Annu. Rev. Astron. and Astrophysics 30 (1992), 543.
• 25: {NTVR92} Nayroles B., Touzot G., Villon P., Ricard A.: Generalizing the finite element method: diffuse approximation and diffuse elements. Computational Mechanics 10, 5 (1992), 307--318.
• 26: James F. O'Brien , Adam W. Bargteil , Jessica K. Hodgins, Graphical modeling and animation of ductile fracture, Proceedings of the 29th annual conference on Computer graphics and interactive techniques, July 23-26, 2002, San Antonio, Texas
• 27: 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]
• 28: Mark Pauly , Markus Gross , Leif P. Kobbelt, Efficient simplification of point-sampled surfaces, Proceedings of the conference on Visualization '02, October 27-November 01, 2002, Boston, Massachusetts
• 29: Mark Pauly , Richard Keiser , Leif P. Kobbelt , Markus Gross, Shape modeling with point-sampled geometry, ACM Transactions on Graphics (TOG), v.22 n.3, July 2003
• 30: William H. Press , Saul A. Teukolsky , William T. Vetterling , Brian P. Flannery, Numerical recipes in C (2nd ed.): the art of scientific computing, Cambridge University Press, New York, NY, 1992
• 31: Richard Szeliski , David Tonnesen, Surface modeling with oriented particle systems, ACM SIGGRAPH Computer Graphics, v.26 n.2, p.185-194, July 1992
• 32: {Suk03} Sukumar N.: Meshless methods and partition of unity finite elements. In of the Sixth International ESAFORM Conference on Material Forming (2003), pp. 603--606.
• 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: {THM*03} Teschner M., Heidelberger B., Müller M., Pomeranerts D., Gross M.: Optimized spatial hashing for collision detection of deformable objects. In Proc. Vision, Modeling, Visualization VMV (2003), pp. 47--54.
• 35: David Love Tonnesen , Demetri Terzopoulos, Dynamically coupled particle systems for geometric modeling, reconstruction, and animation, 1998
• 36: 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
• 37: {TPF89} Terzopoulos D., Platt J., Fleischer K.: Heating and melting deformable models (from goop to glop). In Graphics Interface '89 (1989), pp. 219--226.
• 38: Demetri Terzopoulos , Andrew Witkin, Physically Based Models with Rigid and Deformable Components, IEEE Computer Graphics and Applications, v.8 n.6, p.41-51, November 1988 [doi>10.1109/38.20317]
• 39: Andrew P. Witkin , Paul S. Heckbert, Using particles to sample and control implicit surfaces, Proceedings of the 21st annual conference on Computer graphics and interactive techniques, p.269-277, July 1994 [doi>10.1145/192161.192227]
• 40: {WW89} Wyvill B., Wyvill G.: Field functions for implicit surfaces. In Visual Computer (1989).

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