Papers
Topics
Authors
Recent
Search
2000 character limit reached

Implicit-Explicit simulation of Mass-Spring-Charge Systems

Published 5 Mar 2024 in cs.GR | (2403.03005v2)

Abstract: Point masses connected by springs, or mass-spring systems, are widely used in computer animation to approximate the behavior of deformable objects. One of the restrictions imposed by these models is that points that are not topologically constrained (linked by a spring) are unable to interact with each other explicitly. Such interactions would introduce a new dimension for artistic control and animation within the computer graphics community. Beyond graphics, such a model could be an effective proxy to use for model-based learning of complex physical systems such as molecular biology. We propose to imbue masses in a mass-spring system with electrostatic charge leading a system with internal forces between all pairs of charged points -- regardless of whether they are linked by a spring. We provide a practical and stable algorithm to simulate charged mass-spring systems over long time horizons. We demonstrate how these systems may be controlled via parameters such as guidance electric fields or external charges, thus presenting fresh opportunities for artistic authoring. Our method is especially appropriate for computer graphics applications due to its robustness at larger simulation time steps.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (51)
  1. 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). Association for Computing Machinery, New York, NY, USA, 43–54. https://doi.org/10.1145/280814.280821
  2. Adam W. Bargteil and Tamar Shinar. 2019. An introduction to physics-based animation. In ACM SIGGRAPH 2019 Courses (Los Angeles, California) (SIGGRAPH ’19). Association for Computing Machinery, New York, NY, USA, Article 2, 57 pages. https://doi.org/10.1145/3305366.3328050
  3. Josh Barnes and Piet Hut. 1986. A hierarchical O (N log N) force-calculation algorithm. nature 324, 6096 (1986), 446–449.
  4. James V. Beck and Kenneth J. Arnold. 1977. Parameter estimation in engineering and science. Wiley, New York.
  5. A survey on position based dynamics, 2017. Proceedings of the European Association for Computer Graphics: Tutorials (2017), 1–31.
  6. Projective dynamics: fusing constraint projections for fast simulation. ACM Trans. Graph. 33, 4, Article 154 (jul 2014), 11 pages. https://doi.org/10.1145/2601097.2601116
  7. Robust treatment of collisions, contact and friction for cloth animation. In Proceedings of the 29th annual conference on Computer graphics and interactive techniques. 594–603.
  8. Gabriel S. Cabrera. 2021. nBody: GPU-accelerated N-Body particle simulator. https://github.com/GabrielSCabrera/nBody.
  9. Di Cao and Rick Parent. 2010. Electrostatic Dynamics Interaction for Cloth. In ACM SIGGRAPH ASIA 2010 Sketches (Seoul, Republic of Korea) (SA ’10). Association for Computing Machinery, New York, NY, USA, Article 24, 2 pages. https://doi.org/10.1145/1899950.1899974
  10. Kwang-Jin Choi and Hyeong-Seok Ko. 2005. Stable but Responsive Cloth. In ACM SIGGRAPH 2005 Courses (Los Angeles, California) (SIGGRAPH ’05). Association for Computing Machinery, New York, NY, USA, 1–es. https://doi.org/10.1145/1198555.1198571
  11. Tao Du. 2023. Deep Learning for Physics Simulation. In ACM SIGGRAPH 2023 Courses (Los Angeles, California) (SIGGRAPH ’23). Association for Computing Machinery, New York, NY, USA, Article 6, 25 pages. https://doi.org/10.1145/3587423.3595518
  12. DiffPD: Differentiable Projective Dynamics. ACM Trans. Graph. 41, 2, Article 13 (nov 2021), 21 pages. https://doi.org/10.1145/3490168
  13. Jeff Erickson. 2001. Nice point sets can have nasty Delaunay triangulations. In Proceedings of the Seventeenth Annual Symposium on Computational Geometry (Medford, Massachusetts, USA) (SCG ’01). Association for Computing Machinery, New York, NY, USA, 96–105. https://doi.org/10.1145/378583.378636
  14. Donald L Ermak. 1975. A computer simulation of charged particles in solution. I. Technique and equilibrium properties. The Journal of Chemical Physics 62, 10 (1975), 4189–4196.
  15. Leonhard Euler. 1769. Institutionum calculi integralis volumen primum… (English translation). Vol. 2. http://www.17centurymaths.com/contents/ English translation accessed online at 17th Century Mathematics, translated by Dr. Ian Bruce..
  16. P. P. Ewald. 1921. Die berechnung optischer und elektrostatischer gitterpotentiale. Annalen der Physik 369, 3 (1921), 253–287. https://doi.org/10.1002/andp.19213690304
  17. Christopher J Fennell and J Daniel Gezelter. 2006. Is the Ewald summation still necessary? Pairwise alternatives to the accepted standard for long-range electrostatics. The Journal of chemical physics 124, 23 (2006).
  18. Simplifying hamiltonian and lagrangian neural networks via explicit constraints. Advances in neural information processing systems 33 (2020), 13880–13889.
  19. Hamiltonian neural networks. Advances in neural information processing systems 32 (2019).
  20. NeuroAnimator: fast neural network emulation and control of physics-based models. In Proceedings of the 25th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH ’98). Association for Computing Machinery, New York, NY, USA, 9–20. https://doi.org/10.1145/280814.280816
  21. Ernst Hairer. 1997. Variable time step integration with symplectic methods. Applied Numerical Mathematics 25, 2-3 (1997), 219–227.
  22. Geometric numerical integration. Oberwolfach Reports 3, 1 (2006), 805–882.
  23. Simplistic Coulomb Forces in Molecular Dynamics: Comparing the Wolf and Shifted-Force Approximations. The Journal of Physical Chemistry B 116, 19 (2012), 5738–5743. https://doi.org/10.1021/jp300750g PMID: 22497264.
  24. Interactive deformation using modal analysis with constraints. In Proceedings of the Graphics Interface 2003 Conference (Halifax, Nova Scotia, Canada). Canadian Human-Computer Communications Society and A K Peters Ltd., 247–256. http://graphicsinterface.org/wp-content/uploads/gi2003-29.pdf
  25. Roger W Hockney and James W Eastwood. 1988. Computer simulation using particles (Ch. 8). CRC Press. https://doi.org/10.1201/9780367806934
  26. gradSim: Differentiable simulation for system identification and visuomotor control. arXiv preprint arXiv:2104.02646 (2021).
  27. John Lekner. 1991. Summation of Coulomb fields in computer-simulated disordered systems. Physica A: Statistical Mechanics and its Applications 176, 3 (1991), 485–498.
  28. Diffcloth: Differentiable cloth simulation with dry frictional contact. ACM Transactions on Graphics (TOG) 42, 1 (2022), 1–20.
  29. LibreTexts. n.d.. Physical Chemistry. https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)
  30. Fast simulation of mass-spring systems. ACM Transactions on Graphics (TOG) 32, 6 (2013), 1–7.
  31. Quasi-newton methods for real-time simulation of hyperelastic materials. Acm Transactions on Graphics (TOG) 36, 3 (2017), 1–16.
  32. Erwin Madelung. 1919. Das elektrische Feld in Systemen von regelmäßig angeordneten Punktladungen. Physikalische Zeitschrift 19 (1919), 524–533.
  33. Example-based elastic materials. In ACM SIGGRAPH 2011 papers. 1–8.
  34. Per-Gunnar Martinsson. 2015. Fast Multipole Methods. Springer Berlin Heidelberg, Berlin, Heidelberg, 498–508. https://doi.org/10.1007/978-3-540-70529-1_448
  35. Nelson Max and Tino Weinkauf. 2009. Critical Points of the Electric Field from a Collection of Point Charges. Springer Berlin Heidelberg, Berlin, Heidelberg, 101–114. https://doi.org/10.1007/978-3-540-88606-8_8
  36. Stable real-time deformations. In Proceedings of the 2002 ACM SIGGRAPH/Eurographics symposium on Computer animation. 49–54.
  37. Position based dynamics. Journal of Visual Communication and Image Representation 18, 2 (2007), 109–118.
  38. Topological phase transitions of non-Abelian charged nodal lines in spring-mass systems. Physical Review B 105, 21 (2022), 214108.
  39. Reinhardt M Rosenberg and WE Schmitendorf. 1978. Analytical dynamics of discrete systems. Journal of Applied Mechanics 45, 1 (1978), 233.
  40. Simulating the structure and dynamics of human hair: modelling, rendering and animation. The Journal of Visualization and Computer Animation 2, 4 (1991), 141–148.
  41. Samuel Schoenholz and Ekin Dogus Cubuk. 2020. Jax md: a framework for differentiable physics. Advances in Neural Information Processing Systems 33 (2020), 11428–11441.
  42. A mass spring model for hair simulation. ACM Trans. Graph. 27, 3 (aug 2008), 1–11. https://doi.org/10.1145/1360612.1360663
  43. Olga Sorkine and Marc Alexa. 2007. As-rigid-as-possible surface modeling. In Symposium on Geometry processing, Vol. 4. 109–116.
  44. Ari Stern and Mathieu Desbrun. 2006. Discrete geometric mechanics for variational time integrators. In ACM SIGGRAPH 2006 Courses. 75–80.
  45. A versatile and robust model for geometrically complex deformable solids. In Proceedings Computer Graphics International, 2004. IEEE, 312–319.
  46. LAMMPS - a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales. Comp. Phys. Comm. 271 (2022), 108171. https://doi.org/10.1016/j.cpc.2021.108171
  47. Mujoco: A physics engine for model-based control. In 2012 IEEE/RSJ international conference on intelligent robots and systems. IEEE, 5026–5033.
  48. Wilfred F Van Gunsteren and Herman JC Berendsen. 1990. Computer simulation of molecular dynamics: methodology, applications, and perspectives in chemistry. Angewandte Chemie International Edition in English 29, 9 (1990), 992–1023.
  49. A fixed multi-site interaction charge model for an accurate prediction of the QM/MM interactions. Physical Chemistry Chemical Physics 23, 37 (2021), 21001–21012.
  50. Exact method for the simulation of Coulombic systems by spherically truncated, pairwise r- 1 summation. The Journal of chemical physics 110, 17 (1999), 8254–8282.
  51. Preparing for the unknown: Learning a universal policy with online system identification. arXiv preprint arXiv:1702.02453 (2017).

Summary

No one has generated a summary of this paper yet.

Sign Up to Summarize

Paper to Video (Beta)

No one has generated a video about this paper yet.

Sign Up to Generate All Videos Subscribe on YouTube

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Sign Up to Generate

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Generate Now

Continue Learning

We haven't generated follow-up questions for this paper yet.

Generate Now