“Fundamental solutions for water wave animation” by Schreck, Hafner and Wojtan

  • ©Camille Schreck, Christian Hafner, and Chris Wojtan

Conference:


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Title:

    Fundamental solutions for water wave animation

Session/Category Title: Fluids II


Presenter(s)/Author(s):



Abstract:


    This paper investigates the use of fundamental solutions for animating detailed linear water surface waves. We first propose an analytical solution for efficiently animating circular ripples in closed form. We then show how to adapt the method of fundamental solutions (MFS) to create ambient waves interacting with complex obstacles. Subsequently, we present a novel wavelet-based discretization which outperforms the state of the art MFS approach for simulating time-varying water surface waves with moving obstacles. Our results feature high-resolution spatial details, interactions with complex boundaries, and large open ocean domains. Our method compares favorably with previous work as well as known analytical solutions. We also present comparisons between our method and real world examples.

References:


    1. Stefano Alliney. 1981. Water waves diffraction around cylindrical obstacles. Applied Mathematical Modelling 5, 4 (1981), 237–240.Google ScholarCross Ref
    2. Jernej Barbič, Funshing Sin, and Eitan Grinspun. 2012. Interactive editing of deformable simulations. ACM Transactions on Graphics (TOG) 31, 4 (2012), 70. Google ScholarDigital Library
    3. Morten Bojsen-Hansen, Hao Li, and Chris Wojtan. 2012. Tracking surfaces with evolving topology. ACM Trans. Graph. 31, 4 (2012), 53–1. Google ScholarDigital Library
    4. Morten Bojsen-Hansen and Chris Wojtan. 2013. Liquid surface tracking with error compensation. ACM Transactions on Graphics (TOG) 32, 4 (2013), 68. Google ScholarDigital Library
    5. Tyson Brochu, Todd Keeler, and Robert Bridson. 2012. Linear-time smoke animation with vortex sheet meshes. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation. Eurographics Association, 87–95. Google ScholarDigital Library
    6. José A. Canabal, David Miraut, Nils Thüerey, Theodore Kim, Javier Portilla, and Miguel A. Otaduy. 2016. Dispersion Kernels for Water Wave Simulation. ACM Trans. Graph. 35, 6, Article 202 (Nov. 2016), 10 pages. Google ScholarDigital Library
    7. Ronald Coifman, Vladimir Rokhlin, and Stephen Wandzura. 1993. The fast multipole method for the wave equation: A pedestrian prescription. IEEE Antennas and Propagation Magazine 35, 3 (1993), 7–12.Google ScholarCross Ref
    8. Georges-Henri Cottet, Petros D Koumoutsakos, D Petros, et al. 2000. Vortex methods: theory and practice. Cambridge university press.Google Scholar
    9. Fang Da, Christopher Batty, Chris Wojtan, and Eitan Grinspun. 2015. Double bubbles sans toil and trouble: discrete circulation-preserving vortex sheets for soap films and foams. ACM Transactions on Graphics (TOG) 34, 4 (2015), 149. Google ScholarDigital Library
    10. Fang Da, David Hahn, Christopher Batty, Chris Wojtan, and Eitan Grinspun. 2016. Surface-only liquids. ACM Transactions on Graphics (TOG) 35, 4 (2016), 78. Google ScholarDigital Library
    11. Fernando De Goes and Doug L James. 2017. Regularized kelvinlets: sculpting brushes based on fundamental solutions of elasticity. ACM Transactions on Graphics (TOG) 36, 4 (2017), 40. Google ScholarDigital Library
    12. Fernando De Goes and Doug L James. 2018. Dynamic kelvinlets: secondary motions based on fundamental solutions of elastodynamics. ACM Transactions on Graphics (TOG) 37, 4 (2018), 81. Google ScholarDigital Library
    13. Robert Geist, Christopher Corsi, Jerry Tessendorf, and James Westall. 2010. Lattice-boltzmann water waves. In International Symposium on Visual Computing. Springer. Google ScholarDigital Library
    14. Christian Hafner and Chris Wojtan. 2019. Supplementary Material: Closed Form Integration of Gravity-Capillary Rings. (2019).Google Scholar
    15. David Hahn and Chris Wojtan. 2015. High-resolution brittle fracture simulation with boundary elements. ACM Transactions on Graphics (TOG) 34, 4 (2015), 151. Google ScholarDigital Library
    16. David Hahn and Chris Wojtan. 2016. Fast approximations for boundary element based brittle fracture simulation. ACM Transactions on Graphics (TOG) 35, 4 (2016), 104. Google ScholarDigital Library
    17. Damien Hinsinger, Fabrice Neyret, and Marie-Paule Cani. 2002. Interactive Animation of Ocean Waves. In ACM-SIGGRAPH/EG Symposium on Computer Animation (SCA’02), Stephen N. Spencer (Ed.). ACM SIGGRAPH, San Antonio, United States, 161 — 166. Google ScholarDigital Library
    18. Christopher J. Horvath. 2015. Empirical Directional Wave Spectra for Computer Graphics. In Proceedings of the 2015 Symposium on Digital Production (DigiPro ’15). ACM. Google ScholarDigital Library
    19. Geoffrey Irving, Eran Guendelman, Frank Losasso, and Ronald Fedkiw. 2006. Efficient Simulation of Large Bodies of Water by Coupling Two and Three Dimensional Techniques. ACM Trans. Graph. 25, 3 (July 2006), 805–811. Google ScholarDigital Library
    20. Doug L. James, Jernej Barbič, and Dinesh K. Pai. 2006. Precomputed Acoustic Transfer: Output-sensitive, Accurate Sound Generation for Geometrically Complex Vibration Sources. ACM Trans. Graph. 25, 3 (July 2006), 987–995. Google ScholarDigital Library
    21. Doug L James and Dinesh K Pai. 1999. ArtDefo: accurate real time deformable objects. In Proceedings of the 26th annual conference on Computer graphics and interactive techniques. ACM Press/Addison-Wesley Publishing Co., 65–72. Google ScholarDigital Library
    22. Harold Jeffreys and Bertha Swirles Jeffreys. 1966. Methods of mathematical physics (3rd ed ed.). London: Cambridge University Press.Google Scholar
    23. Stefan Jeschke, Tomáš Skřivan, Matthias Müller-Fischer, Nuttapong Chentanez, Miles Macklin, and Chris Wojtan. 2018. Water surface wavelets. ACM Transactions on Graphics (TOG) 37, 4 (2018), 94. Google ScholarDigital Library
    24. Stefan Jeschke and Chris Wojtan. 2015. Water Wave Animation via Wavefront Parameter Interpolation. ACM Transactions on Graphics 34, 3 (2015), 1–14. Google ScholarDigital Library
    25. Stefan Jeschke and Chris Wojtan. 2017. Water Wave Packets. ACM Transactions on Graphics (SIGGRAPH 2017) 36, 4 (2017). Google ScholarDigital Library
    26. Michael Kass and Gavin Miller. 1990. Rapid, stable fluid dynamics for computer graphics. In ACM Siggraph Computer Graphics, Vol. 24. ACM, 49–57. Google ScholarDigital Library
    27. T. Keeler and R. Bridson. 2014. Ocean Waves Animation Using Boundary Integral Equations and Explicit Mesh Tracking. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA ’14). Eurographics Association, Aire-la-Ville, Switzerland, Switzerland, 11–19. Google ScholarDigital Library
    28. Theodore Kim, Jerry Tessendorf, and Nils Thürey. 2013. Closest Point Turbulence for Liquid Surfaces. ACM Trans. Graph. 32, 2, Article 15 (April 2013), 13 pages. Google ScholarDigital Library
    29. Stefan Kurz, Oliver Rain, and Sergej Rjasanow. 2002. The adaptive cross-approximation technique for the 3D boundary-element method. IEEE transactions on Magnetics 38, 2 (2002), 421–424.Google ScholarCross Ref
    30. Bernard Le Méhauté. 1988. Gravity-capillary rings generated by water drops. Journal of Fluid Mechanics 197 (1988), 415–427.Google ScholarCross Ref
    31. Seongkyu Lee. 2017. Review: The Use of Equivalent Source Method in Computational Acoustics. Journal of Computational Acoustics 25, 01 (2017).Google ScholarCross Ref
    32. Seongkyu Lee, Kenneth Steven Brentner, and Philip John Morris. 2010. Acoustic scattering in the time domain using an equivalent source method. AIAA Journal 48, 12 (1 12 2010), 2772–2780.Google ScholarCross Ref
    33. Jörn Loviscach. 2002. A Convolution-Based Algorithm for Animated Water Waves. In Eurographics 2002 – Short Presentations. Eurographics Association.Google Scholar
    34. G. A. Mastin, P. A. Watterberg, and J. F. Mareda. 1987. Fourier Synthesis of Ocean Scenes. IEEE Computer Graphics and Applications 7, 3 (March 1987), 16–23. Google ScholarDigital Library
    35. R. Mehra and D. Manocha. 2014. Wave-based sound propagation for VR applications. In 2014 IEEE VR Workshop: Sonic Interaction in Virtual Environments (SIVE). 41–46.Google Scholar
    36. Ravish Mehra, Nikunj Raghuvanshi, Lakulish Antani, Anish Chandak, Sean Curtis, and Dinesh Manocha. 2013. Wave-based Sound Propagation in Large Open Scenes Using an Equivalent Source Formulation. ACM Trans. Graph. 32, 2, Article 19 (2013). Google ScholarDigital Library
    37. Olivier Mercier, Cynthia Beauchemin, Nils Thuerey, Theodore Kim, and Derek Nowrouzezahrai. 2015. Surface Turbulence for Particle-based Liquid Simulations. ACM Trans. Graph. 34, 6, Article 202 (Oct. 2015), 10 pages. Google ScholarDigital Library
    38. Tobias Pfaff, Nils Thüerey, and Markus Gross. 2012. Lagrangian vortex sheets for animating fluids. ACM Transactions on Graphics (TOG) 31, 4 (2012), 112. Google ScholarDigital Library
    39. Stefan A Sauter and Christoph Schwab. 2010. Boundary element methods. In Boundary Element Methods. Springer, 183–287.Google Scholar
    40. Jerry Tessendorf. 2004a. Interactive water surfaces. Game Programming Gems 4 (2004).Google Scholar
    41. Jerry Tessendorf. 2004b. Simulating Ocean Water. (2004).Google Scholar
    42. Jerry Tessendorf. 2014. eWave: Using an Exponential Solver on the iWave Problem. Technical Note (2014).Google Scholar
    43. William “Lord Kelvin” Thomson. 1891. Popular lectures and addresses. Vol. 3. Macmillan London. 481–8 pages.Google Scholar
    44. Nils Thürey, Ulrich Rüde, and Marc Stamminger. 2006. Animation of Open Water Phenomena with coupled Shallow Water and Free Surface Simulations. 157–164. Google ScholarDigital Library
    45. Nils Thürey, Chris Wojtan, Markus Gross, and Greg Turk. 2010. A multiscale approach to mesh-based surface tension flows. ACM Transactions on Graphics (TOG) 29, 4 (2010), 48. Google ScholarDigital Library
    46. Steffen Weißmann and Ulrich Pinkall. 2010. Filament-based smoke with vortex shedding and variational reconnection. In ACM Transactions on Graphics (TOG), Vol. 29. ACM. Google ScholarDigital Library
    47. Sheng Yang, Xiaowei He, Huamin Wang, Sheng Li, Guoping Wang, Enhua Wu, and Kun Zhou. 2016. Enriching SPH Simulation by Approximate Capillary Waves. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA ’16). Eurographics Association, Goslar Germany, Germany, 29–36. Google ScholarDigital Library
    48. Jihun Yu, Chris Wojtan, Greg Turk, and Chee Yap. 2012. Explicit mesh surfaces for particle based fluids. In Computer Graphics Forum, Vol. 31. Wiley Online Library. Google ScholarDigital Library
    49. Cem Yuksel, Donald H House, and John Keyser. 2007. Wave particles. In ACM Transactions on Graphics (TOG), Vol. 26. ACM, 99. Google ScholarDigital Library
    50. Yufeng Zhu, Robert Bridson, and Chen Greif. 2015. Simulating rigid body fracture with surface meshes. ACM Transactions on Graphics (TOG) 34, 4 (2015), 150. Google ScholarDigital Library


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