George E. Brown
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We propose a method for accurately simulating dissipative forces in deformable bodies when using optimization-based integrators. We represent such forces using dissipation functions which may be nonlinear in both positions and velocities, enabling us to model a range of dissipative effects including Coulomb friction, Rayleigh damping, and power-law dissipation. We propose a general method for incorporating dissipative forces into optimization-based time integration schemes, which hitherto have been applied almost exclusively to systems with only conservative forces. To improve accuracy and minimize artificial damping, we provide an optimization-based version of the second-order accurate TR-BDF2 integrator. Finally, we present a method for modifying arbitrary dissipation functions to conserve linear and angular momentum, allowing us to eliminate the artificial angular momentum loss caused by Rayleigh damping.
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- R. E. Bank, W. M. Coughran, W. Fichtner, E. H. Grosse, D. J. Rose, and R. K. Smith. 1985. Transient Simulation of Silicon Devices and Circuits. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 4, 4 (October 1985), 436--451. Google Scholar
Digital Library
- David Baraff. 1991. Coping with Friction for Non-penetrating Rigid Body Simulation. In Proceedings of the 18th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH '91). ACM, New York, NY, USA, 31--41. Google ScholarDigital Library
- David Baraff and Andrew Witkin. 1998. Large Steps in Cloth Simulation. In Proceedings of the 25th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH '98). ACM, New York, NY, USA, 43--54. Google ScholarDigital Library
- Jernej Barbič and Doug L. James. 2005. Real-Time Subspace Integration for St. Venant-Kirchhoff Deformable Models. ACM Trans. Graph. 24, 3 (July 2005), 982--990. Google ScholarDigital Library
- Klaus-Jürgen Bathe. 2007. Conserving Energy and Momentum in Nonlinear Dynamics: A Simple Implicit Time Integration Scheme. Comput. Struct. 85, 7--8 (April 2007), 437--445. Google ScholarDigital Library
- Klaus-Jürgen Bathe and Mirza M. Irfan Baig. 2005. On a Composite Implicit Time Integration Procedure for Nonlinear Dynamics. Comput. Struct. 83, 31--32 (Dec. 2005), 2513--2524. Google ScholarDigital Library
- Jan Bender, Matthias Müller, and Miles Macklin. 2015. Position-Based Simulation Methods in Computer Graphics. In EUROGRAPHICS 2015 Tutorials. Eurographics Association.Google Scholar
- Miklos Bergou, Max Wardetzky, David Harmon, Denis Zorin, and Eitan Grinspun. 2006. A Quadratic Bending Model for Inextensible Surfaces. In Proceedings of the Fourth Eurographics Symposium on Geometry Processing (SGP '06). Eurographics Association, Aire-la-Ville, Switzerland, Switzerland, 227--230. Google ScholarDigital Library
- Kiran S. Bhat, Christopher D. Twigg, Jessica K. Hodgins, Pradeep K. Khosla, Zoran Popović, and Steven M. Seitz. 2003. Estimating Cloth Simulation Parameters from Video. In Proceedings of the 2003 ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA '03). Eurographics Association, Aire-la-Ville, Switzerland, Switzerland, 37--51. Google ScholarDigital Library
- Sofien Bouaziz, Sebastian Martin, Tiantian Liu, Ladislav Kavan, and Mark Pauly. 2014. Projective Dynamics: Fusing Constraint Projections for Fast Simulation. ACM Trans. Graph. 33, 4, Article 154 (July 2014), 11 pages. Google ScholarDigital Library
- Stephen Boyd, Neal Parikh, Eric Chu, Borja Peleato, and Jonathan Eckstein. 2011. Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers. Found. Trends Mach. Learn. 3, 1 (Jan. 2011), 1--122. Google ScholarDigital Library
- Christopher Brandt, Elmar Eisemann, and Klaus Hildebrandt. 2018. Hyper-Reduced Projective Dynamics. 37, 4 (2018). To appear. Google ScholarDigital Library
- Robert Bridson, Ronald Fedkiw, and John Anderson. 2002. Robust Treatment of Collisions, Contact and Friction for Cloth Animation. ACM Trans. Graph. 21, 3 (July 2002), 594--603. Google ScholarDigital Library
- Kwang-Jin Choi and Hyeong-Seok Ko. 2002. Stable but Responsive Cloth. ACM Trans. Graph. 21, 3 (July 2002), 604--611. Google ScholarDigital Library
- S. Claici, M. Bessmeltsev, S. Schaefer, and J. Solomon. 2017. Isometry-Aware Preconditioning for Mesh Parameterization. Comput. Graph. Forum 36, 5 (Aug. 2017), 37--47. Google ScholarDigital Library
- Gilles Daviet and Florence Bertails-Descoubes. 2016. A Semi-implicit Material Point Method for the Continuum Simulation of Granular Materials. ACM Trans. Graph. 35, 4, Article 102 (July 2016), 13 pages. Google ScholarDigital Library
- Gilles Daviet, Florence Bertails-Descoubes, and Laurence Boissieux. 2011. A Hybrid Iterative Solver for Robustly Capturing Coulomb Friction in Hair Dynamics. In Proceedings of the 2011 SIGGRAPH Asia Conference (SA '11). ACM, New York, NY, USA, Article 139, 12 pages. Google ScholarDigital Library
- Gilles Debunne, Mathieu Desbrun, Marie-Paule Cani, and Alan H. Barr. 2001. Dynamic Real-time Deformations Using Space & Time Adaptive Sampling. In Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH '01). ACM, New York, NY, USA, 31--36. Google ScholarDigital Library
- Dimitar Dinev, Tiantian Liu, and Ladislav Kavan. 2018a. Stabilizing Integrators for Real-Time Physics. ACM Transactions on Graphics 37, 1 (2018), to appear. Google ScholarDigital Library
- Dimitar Dinev, Tiantian Liu, Jing Li, Bernhard Thomaszewski, and Ladislav Kavan. 2018b. FEPR: Fast Energy Projection for Real-Time Simulation of Deformable Objects. 37, 4 (2018). To appear. Google ScholarDigital Library
- Christian Duriez, Frederic Dubois, Abderrahmane Kheddar, and Claude Andriot. 2006. Realistic Haptic Rendering of Interacting Deformable Objects in Virtual Environments. IEEE Transactions on Visualization and Computer Graphics 12, 1 (Jan. 2006), 36--47. Google ScholarDigital Library
- Elliot English and Robert Bridson. 2008. Animating Developable Surfaces Using Non-conforming Elements. ACM Trans. Graph. 27, 3, Article 66 (Aug. 2008), 5 pages. Google ScholarDigital Library
- Marco Fratarcangeli, Valentina Tibaldo, and Fabio Pellacini. 2016. Vivace: A Practical Gauss-seidel Method for Stable Soft Body Dynamics. ACM Trans. Graph. 35, 6, Article 214 (Nov. 2016), 9 pages. Google ScholarDigital Library
- Theodore F. Gast, Craig Schroeder, Alexey Stomakhin, Chenfanfu Jiang, and Joseph M. Teran. 2015. Optimization Integrator for Large Time Steps. IEEE Transactions on Visualization and Computer Graphics 21, 10 (Oct. 2015), 1103--1115. Google ScholarDigital Library
- Herbert Goldstein, Charles P. Poole, and John L. Safko. 2002. Classical Mechanics (3rd ed.). Addison-Wesley.Google Scholar
- M.E. Hosea and L.F. Shampine. 1996. Analysis and implementation of TR-BDF2. Applied Numerical Mathematics 20, 1 (1996), 21 -- 37. Method of Lines for Time-Dependent Problems. Google ScholarDigital Library
- Chenfanfu Jiang, Theodore Gast, and Joseph Teran. 2017. Anisotropic Elastoplasticity for Cloth, Knit and Hair Frictional Contact. ACM Trans. Graph. 36, 4, Article 152 (July 2017), 14 pages. Google ScholarDigital Library
- Ioannis Karamouzas, Nick Sohre, Rahul Narain, and Stephen J. Guy. 2017. Implicit Crowds: Optimization Integrator for Robust Crowd Simulation. ACM Trans. Graph. 36, 4, Article 136 (July 2017), 13 pages. Google ScholarDigital Library
- Danny M. Kaufman, Shinjiro Sueda, Doug L. James, and Dinesh K. Pai. 2008. Staggered Projections for Frictional Contact in Multibody Systems. ACM Trans. Graph. 27, 5, Article 164 (Dec. 2008), 11 pages. Google ScholarDigital Library
- L. Kharevych, Weiwei Yang, Y. Tong, E. Kanso, J. E. Marsden, P. Schröder, and M. Desbrun. 2006. Geometric, Variational Integrators for Computer Animation. In Proceedings of the 2006 ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA '06). Eurographics Association, Aire-la-Ville, Switzerland, Switzerland, 43--51. Google ScholarDigital Library
- Gergely Klár, Theodore Gast, Andre Pradhana, Chuyuan Fu, Craig Schroeder, Chenfanfu Jiang, and Joseph Teran. 2016. Drucker-prager Elastoplasticity for Sand Animation. ACM Trans. Graph. 35, 4, Article 103 (July 2016), 12 pages. Google ScholarDigital Library
- Martin Komaritzan and Mario Botsch. 2018. Projective Skinning. In Proc. ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games.Google Scholar
- Shahar Z. Kovalsky, Meirav Galun, and Yaron Lipman. 2016. Accelerated Quadratic Proxy for Geometric Optimization. ACM Trans. Graph. 35, 4, Article 134 (July 2016), 11 pages. Google ScholarDigital Library
- Tiantian Liu, Adam W. Bargteil, James F. O'Brien, and Ladislav Kavan. 2013. Fast Simulation of Mass-spring Systems. ACM Trans. Graph. 32, 6, Article 214 (Nov. 2013), 7 pages. Google ScholarDigital Library
- Tiantian Liu, Sofien Bouaziz, and Ladislav Kavan. 2016. Towards Real-time Simulation of Hyperelastic Materials. arXiv preprint arXiv:1604.07378 (2016).Google Scholar
- Miles Macklin, Matthias Müller, and Nuttapong Chentanez. 2016. XPBD: Position-based Simulation of Compliant Constrained Dynamics. In Proceedings of the 9th International Conference on Motion in Games (MIG '16). ACM, New York, NY, USA, 49--54. Google ScholarDigital Library
- Jerrold E. Marsden and Tudor Ratiu. 1999. Introduction to Mechanics and Symmetry. Springer.Google Scholar
- Sebastian Martin, Bernhard Thomaszewski, Eitan Grinspun, and Markus Gross. 2011. Example-based Elastic Materials. ACM Trans. Graph. 30, 4, Article 72 (July 2011), 8 pages. Google ScholarDigital Library
- Eder Miguel, Rasmus Tamstorf, Derek Bradley, Sara C. Schvartzman, Bernhard Thomaszewski, Bernd Bickel, Wojciech Matusik, Steve Marschner, and Miguel A. Otaduy. 2013. Modeling and Estimation of Internal Friction in Cloth. ACM Trans. Graph. 32, 6, Article 212 (Nov. 2013), 10 pages. Google ScholarDigital Library
- David Minor. 2018. Making Space for Cloth Simulations Using Energy Minimization. In ACM SIGGRAPH 2018 Talks (SIGGRAPH '18). ACM, New York, NY, USA, Article 41, 2 pages. Google ScholarDigital Library
- Matthias Müller, Bruno Heidelberger, Marcus Hennix, and John Ratcliff. 2007. Position Based Dynamics. J. Vis. Comun. Image Represent. 18, 2 (April 2007), 109--118.Google ScholarDigital Library
- Rahul Narain, Abhinav Golas, and Ming C. Lin. 2010. Free-flowing Granular Materials with Two-way Solid Coupling. ACM Trans. Graph. 29, 6, Article 173 (Dec. 2010), 10 pages. Google ScholarDigital Library
- James F. O'Brien and Jessica K. Hodgins. 1999. Graphical Modeling and Animation of Brittle Fracture. In Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH '99). ACM Press/Addison-Wesley Publishing Co., New York, NY, USA, 137--146. Google ScholarDigital Library
- Miguel A. Otaduy, Takeo Igarashi, and Joseph J. LaViola, Jr. 2009. Interaction: Interfaces, Algorithms, and Applications. In ACM SIGGRAPH 2009 Courses (SIGGRAPH '09). ACM, New York, NY, USA, Article 14, 66 pages. Google ScholarDigital Library
- Matthew Overby, George E. Brown, Jie Li, and Rahul Narain. 2017. ADMM ⊇ Projective Dynamics: Fast Simulation of Hyperelastic Models with Dynamic Constraints. IEEE Trans. Vis. Comput. Graph. 23, 10 (2017), 2222--2234.Google ScholarDigital Library
- Simon Pabst, Bernhard Thomaszewski, and Wolfgang Straßer. 2009. Anisotropic Friction for Deformable Surfaces and Solids. In Proceedings of the 2009 ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA '09). ACM, New York, NY, USA, 149--154. Google ScholarDigital Library
- Yue Peng, Bailin Deng, Juyong Zhang, Fanyu Geng, Wenjie Qin, and Ligang liu. 2018. Anderson Acceleration for Geometry Optimization and Physics Simulation. 37, 4 (2018). To appear. Google ScholarDigital Library
- John C. Platt and Alan H. Barr. 1988. Constraints Methods for Flexible Models. SIGGRAPH Comput. Graph. 22, 4 (June 1988), 279--288. Google ScholarDigital Library
- Xavier Provot. 1997. Collision and self-collision handling in cloth model dedicated to design garments. In Computer Animation and Simulation (Eurographics 1997). Springer, Vienna, 177--189.Google ScholarCross Ref
- Michael Rabinovich, Roi Poranne, Daniele Panozzo, and Olga Sorkine-Hornung. 2017. Scalable Locally Injective Mappings. ACM Trans. Graph. 36, 2, Article 37a (April 2017). Google ScholarDigital Library
- Zhimin Ren, Hengchin Yeh, and Ming C. Lin. 2013. Example-guided Physically Based Modal Sound Synthesis. ACM Trans. Graph. 32, 1, Article 1 (Feb. 2013), 16 pages. Google ScholarDigital Library
- R. Tyrrell Rockafellar. 1970. Convex Analysis. Princeton University Press.Google Scholar
- Jun Saito and Simon Yuen. 2017. Efficient and Robust Skin Slide Simulation. In Proceedings of the ACM SIGGRAPH Digital Production Symposium (DigiPro '17). ACM, New York, NY, USA, Article 10, 6 pages. Google ScholarDigital Library
- Rosa M. Sánchez-Banderas and Miguel A. Otaduy. 2017. Dissipation Potentials for Yarn-Level Cloth. (2017).Google Scholar
- Ruediger Schmedding, Marc Gissler, and Matthias Teschner. 2009. Optimized Damping for Dynamic Simulations. In Proceedings of the 25th Spring Conference on Computer Graphics (SCCG '09). ACM, New York, NY, USA, 189--196. Google ScholarDigital Library
- Anna Shtengel, Roi Poranne, Olga Sorkine-Hornung, Shahar Z. Kovalsky, and Yaron Lipman. 2017. Geometric Optimization via Composite Majorization. ACM Trans. Graph. 36, 4, Article 38 (July 2017), 11 pages. Google ScholarDigital Library
- Eftychios Sifakis and Jernej Barbic. 2012. FEM Simulation of 3D Deformable Solids: A Practitioner's Guide to Theory, Discretization and Model Reduction. In ACM SIGGRAPH 2012 Courses (SIGGRAPH '12). ACM, New York, NY, USA, Article 20, 50 pages. Google ScholarDigital Library
- Demetri Terzopoulos, John Platt, Alan Barr, and Kurt Fleischer. 1987. Elastically Deformable Models. In Proceedings of the 14th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH '87). ACM, New York, NY, USA, 205--214. Google ScholarDigital Library
- Demetri Terzopoulos and Andrew Witkin. 1988. Physically Based Models with Rigid and Deformable Components. IEEE Comput. Graph. Appl. 8, 6 (Nov. 1988), 41--51. Google ScholarDigital Library
- Bin Wang, Longhua Wu, KangKang Yin, Uri Ascher, Libin Liu, and Hui Huang. 2015. Deformation Capture and Modeling of Soft Objects. ACM Trans. Graph. 34, 4, Article 94 (July 2015), 12 pages. Google ScholarDigital Library
- Marcel Weiler, Dan Koschier, and Jan Bender. 2016. Projective Fluids. In Proceedings of the 9th International Conference on Motion in Games (MIG '16). ACM, New York, NY, USA, 79--84. Google ScholarDigital Library
- Hongyi Xu and Jernej Barbič. 2017. Example-based Damping Design. ACM Trans. Graph. 36, 4, Article 53 (July 2017), 14 pages. Google ScholarDigital Library
- Hongyi Xu, Funshing Sin, Yufeng Zhu, and Jernej Barbič. 2015. Nonlinear Material Design Using Principal Stretches. ACM Trans. Graph. 34, 4, Article 75 (July 2015), 11 pages. Google ScholarDigital Library
- Yufeng Zhu, Robert Bridson, and Danny M. Kaufman. 2018. Blended Cured Quasi-newton for Distortion Optimization. ACM Trans. Graph. 37, 4, Article 40 (July 2018), 14 pages. Google ScholarDigital Library
Index Terms
- Accurate dissipative forces in optimization integrators
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