Deformation, Cutting, and Fracture

Denis Steinemann, Miguel Otaduy, Markus Gross

The simulation of elastic and plastic objects presents inherent computational challenges due to the large amount of degrees of freedom that must be simulated. We are evaluating different representations and simulation techniques, trying to identify those that are best suited for simulating various elastic, plastic, and topology-varying effects, under different interactivity constraints.

Mass-spring systems serve to represent deformable models very efficiently, as the dynamic behavior of the models can be computed by numerically integrating positions and velocities of mass points over time. We intend to investigate the aspects that are responsible for the performance of mass-spring systems. These include the type and strength of damping, force-deformation relationships between mass points, topological aspects, hierarchical model representations, and last but not least the numerical integration approach.

Tetrahedral meshes with finite element methods are another popular approach for simulating deformable models. We have devised fast and stable simulation methods, based on linear elasticity models, stiffness warping, and underlying tetrahedral meshes that drive the deformation and fracture of detailed triangulated surfaces.

Furthermore, we have exploited dynamic deformation textures for encoding and solving the 3D elastic deformations of layered deformable objects in 2D parametric atlases. Parallel solution algorithms enable fast simulation of geometrically rich objects under contact, accounting for dynamic effects and the coupling of local deformations and global motion.

Recently, particle-based Lagrangian methods have shown tremendous potential for simulating elasto-plastic and fracturing solids. The use of particles instead of a volumetric mesh has several advantages. First, point-sampling of the volume of a given object is very simple in comparison to the generation of a mesh. Second, a particle representation is better suited than a mesh with fixed connectivity for plastic deformations, where the object can deviate substantially from its original configuration and even change its topology. And third, using a particle-based Lagrangian approach enables the combination of deformable solids and fluids into one framework.

By integrating particle-based methods with algorithms for handling topological changes on the surface, we have a very flexible framework at hand with which we can simulate both highly detailed surfaces as well as large deformations and topological changes. We demonstrate fracturing both rigid and ductile materials, the simulation of thin shells that fracture, and melting and freezing of objects. The simulation of topological changes on elastic objects can be further accelerated by incorporating crack synthesis algorithms for triangle meshes and visibility graphs for fast local update of the particle-based discretization. This enables, for example, flexible cutting in virtual surgery applications.

Finally, we have also devised unconditionally stable animation methods for deformable objects using explicit integration. This is achieved by fitting the original configuration of points (the rest state) to the deformed configuration after an animation step using shape matching techniques. The fitted rest shape yields goal positions for all points. We show that by pulling the animated points towards the goal positions, the animation is unconditionally stable.

• M. Wicke, P. Hatt, M. Pauly, M. Müller, M. Gross, Versatile Virtual Materials using Implicit Connectivity, Proceedings of the IEEE/Eurographics Symposium on Point-Based Graphics (Boston, USA, July 29-30, 2006), pp. 73-82
  [Abstract] [PDF] [Video]
• D. Steinemann, M. A. Otaduy, M. Gross, Fast Arbitrary Splitting of Deforming Objects, Proceedings of the 2006 ACM SIGGRAPH/Eurographics Symposium on Computer Animation (Vienna, Austria, September 2-4, 2006), pp. 63-72
  [Abstract] [PDF] [Video]
• N. Galoppo, M. A. Otaduy, P. Mecklenburg, M. Gross, M. C. Lin, Fast Simulation of Deformable Models in Contact Using Dynamic Deformation Textures, Proceedings of the 2006 ACM SIGGRAPH/Eurographics Symposium on Computer Animation (Vienna, Austria, September 2-4, 2006), pp. 73-82
  [Abstract] [PDF] [Video]
• M. Wicke, D. Steinemann, M. Gross, Efficient Animation of Point-Sampled Thin Shells, Proceedings of Eurographics '05, pp. 667-676 (Dublin, Ireland, Aug 29th - Sep 2nd, 2005)
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• B. Adams, R. Keiser, M. Pauly, L. J. Guibas, M. Gross, P. Dutré, Efficient Raytracing of Deforming Point-Sampled Surfaces, Proceedings of Eurographics 2005, pp. 677-684 (Dublin, Ireland, August 29 - September 3, 2005)
  [Abstract] [PDF] [Video]
• R. Keiser, B. Adams, D. Gasser, P. Bazzi, P. Dutré, M. Gross, A Unified Lagrangian Approach to Solid-Fluid Animation, Proceedings of the Symposium on Point-Based Graphics 2005, pp. 125-133 (Stony Brook, USA, June 21-22)
  [Abstract] [PDF] [Video] [Video] [Video] [Video] [Video]
• M. Pauly, R. Keiser, B. Adams, P. Dutré, M. Gross, L. J. Guibas, Meshless Animation of Fracturing Solids, Proceedings of ACM SIGGRAPH 2005 (Los Angeles, USA, July 31 - August 4, 2005), pp. 957-964
  [Abstract] [PDF] [Video]
• M. Müller, B. Heidelberger, M. Teschner, M. Gross, Meshless Deformations Based on Shape Matching, Proceedings of ACM SIGGRAPH 2005 (Los Angeles, USA, July 31 - August 4, 2005), pp. 471-478
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• M. Pauly, D. K. Pai, L. J. Guibas, Quasi-Rigid Objects in Contact, ACM Siggraph/Eurographics Symposium on Computer Animation 2004
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• M. Müller, R. Keiser, A. Nealen, M. Pauly, M. Gross, M. Alexa, Point Based Animation of Elastic, Plastic and Melting Objects, Proceedings of ACM SIGGRAPH / Eurographics Symposium on Computer Animation 2004, p. 141-151 (ACM SIGGRAPH / Eurographics Symposium on Computer Animation (SCA 2004), Genoble, France, August 27-29, 2004)
  [Abstract] [PDF] [Video] [Video]
• M. Müller, M. Teschner, M. Gross, Physically-Based Simulation of Objects Represented by Surface Meshes, Proceedings of Computer Graphics International 2004 (CGI 2004), pp. 26-33 (CGI'04, Heraklion, Crete, Greece, June 16-19, 2004)
  [Abstract] [PDF]
• M. Müller, M. Gross, Interactive Virtual Materials, Proceedings of Graphics Interface 2004, pp. 239-246 (Graphics Interface 2004, London, Ontario, Canada, May 17-19, 2004)
  [Abstract] [PDF] [Video]
• M. Teschner, B. Heidelberger, M. Müller, M. Gross, A Versatile and Robust Model for Geometrically Complex Deformable Solids, Proceedings of Computer Graphics International 2004, pp. 312-319 (CGI'04, Heraklion, Crete, Greece, June 16-19, 2004)
  [Abstract] [PDF] [Video] [Video] [Video] [Video] [Video] [Video]