“Water surface wavelets” by Jeschke, Skrivan, Müller-Fischer, Chentanez, Macklin, et al. …

  • ©Stefan Jeschke, Tomas Skrivan, Matthias Müller-Fischer, Nuttapong Chentanez, Miles Macklin, and Chris Wojtan

  • ©Stefan Jeschke, Tomas Skrivan, Matthias Müller-Fischer, Nuttapong Chentanez, Miles Macklin, and Chris Wojtan



Entry Number: 94


    Water surface wavelets

Session/Category Title:   Fluids 2: Vortex Boogaloo




    The current state of the art in real-time two-dimensional water wave simulation requires developers to choose between efficient Fourier-based methods, which lack interactions with moving obstacles, and finite-difference or finite element methods, which handle environmental interactions but are significantly more expensive. This paper attempts to bridge this long-standing gap between complexity and performance, by proposing a new wave simulation method that can faithfully simulate wave interactions with moving obstacles in real time while simultaneously preserving minute details and accommodating very large simulation domains.Previous methods for simulating 2D water waves directly compute the change in height of the water surface, a strategy which imposes limitations based on the CFL condition (fast moving waves require small time steps) and Nyquist’s limit (small wave details require closely-spaced simulation variables). This paper proposes a novel wavelet transformation that discretizes the liquid motion in terms of amplitude-like functions that vary over space, frequency, and direction, effectively generalizing Fourier-based methods to handle local interactions. Because these new variables change much more slowly over space than the original water height function, our change of variables drastically reduces the limitations of the CFL condition and Nyquist limit, allowing us to simulate highly detailed water waves at very large visual resolutions. Our discretization is amenable to fast summation and easy to parallelize. We also present basic extensions like pre-computed wave paths and two-way solid fluid coupling. Finally, we argue that our discretization provides a convenient set of variables for artistic manipulation, which we illustrate with a novel wave-painting interface.


    1. Roland Angst, Nils Thuerey, Mario Botsch, and Markus Gross. 2008. Robust and efficient wave simulations on deforming meshes. In Computer Graphics Forum, Vol. 27. Wiley Online Library, 1895–1900.Google Scholar
    2. Robert Bridson. 2015. Fluid simulation for computer graphics. CRC Press. Google ScholarDigital Library
    3. José A. Canabal, David Miraut, Nils Thuerey, 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
    4. Stephen Chenney. 2004. Flow tiles. In Proceedings of the 2004 ACM SIGGRAPH/Eurographics symposium on Computer animation. Eurographics Association, 233–242. Google ScholarDigital Library
    5. Robert L. Cook. 1986. Stochastic Sampling in Computer Graphics. ACM Trans. Graph. 5, 1 (Jan. 1986), 51–72. Google ScholarDigital Library
    6. Ronald Fedkiw, Jos Stam, and Henrik Wann Jensen. 2001. Visual Simulation of Smoke. In Proceedings of SIGGRAPH 2001 (Computer Graphics Proceedings, Annual Conference Series), Eugene Fiume (Ed.). ACM, 15–22. Google ScholarDigital Library
    7. Dennis Gabor. 1946. Theory of communication. Part 1: The analysis of information. Journal of the Institution of Electrical Engineers-Part III: Radio and Communication Engineering 93, 26 (1946), 429–441.Google ScholarCross Ref
    8. Robert Geist, Christopher Corsi, Jerry Tessendorf, and James Westall. 2010. Lattice-boltzmann water waves. In Advances in visual Computing. Springer, 74–85. Google ScholarDigital Library
    9. Damien Hinsinger, Fabrice Neyret, and Marie-Paule Cani. 2002. Interactive animation of ocean waves. In Proc. ACM SIGGRAPH/Eurographics Symp. on Comput. Anim. 161–166. Google ScholarDigital Library
    10. Christopher J Horvath. 2015. Empirical directional wave spectra for computer graphics. In Proceedings of the 2015 Symposium on Digital Production. ACM, 29–39. Google ScholarDigital Library
    11. Stefan Jeschke and Chris Wojtan. 2015. Water Wave Animation via Wavefront Parameter Interpolation. ACM Trans. Graph. 34, 3, Article 27 (May 2015), 14 pages. Google ScholarDigital Library
    12. Stefan Jeschke and Chris Wojtan. 2017. Water Wave Packets. ACM Trans. Graph. 36, 4, Article 103 (2017), 12 pages. Google ScholarDigital Library
    13. R.S. Johnson. 1997. A modern introduction to the mathematical theory of-water waves. Vol. 19. Cambridge university press.Google Scholar
    14. M. Kass and G. Miller. 1990. Rapid, stable fluid dynamics for computer graphics. In Computer Graphics, Vol. 24. 49–57. Google ScholarDigital Library
    15. Theodore Kim, Jerry Tessendorf, and Nils Thuerey. 2013. Closest Point Turbulence for Liquid Surfaces. ACM Trans. Graph. 32, 2, Article 15 (April 2013), 13 pages. Google ScholarDigital Library
    16. Jörn Loviscach. 2002. A convolution-based algorithm for animated water waves. In Eurographics, Vol. 2. 381–389.Google Scholar
    17. Pierre-Luc Manteaux, Ulysse Vimont, Chris Wojtan, Damien Rohmer, and Marie-Paule Cani. 2016. Space-time sculpting of liquid animation. In Proceedings of the 9th International Conference on Motion in Games. ACM, 61–71. Google ScholarDigital Library
    18. Gary A Mastin, Peter A Watterberg, and John F Mareda. 1987. Fourier synthesis of ocean scenes. Computer Graphics and Applications, IEEE 7, 3 (1987), 16–23. Google ScholarDigital Library
    19. A. McNamara, A. Treuille, Z. Popović, and J. Stam. 2004. Fluid control using the adjoint method. In ACM Trans. Graph., Vol. 23. ACM, 449–456. Google ScholarDigital Library
    20. Michael B Nielsen, Andreas Söderström, and Robert Bridson. 2013. Synthesizing waves from animated height fields. ACM Trans. Graph. 32, 1 (2013), 2. Google ScholarDigital Library
    21. M. Nießner, B. Keinert, M. Fisher, M. Stamminger, C. Loop, and H. Schäfer. 2016. Real-Time Rendering Techniques with Hardware Tessellation. Computer Graphics Forum 35, 1 (2016), 113–137. Google ScholarDigital Library
    22. Björn Ottosson. 2011. Real-time Interactive Water Waves. Master’s thesis. KTH, Sweden.Google Scholar
    23. Zherong Pan, Jin Huang, Yiying Tong, Changxi Zheng, and Hujun Bao. 2013. Interactive localized liquid motion editing. ACM Transactions on Graphics (TOG) 32, 6 (2013), 184. Google ScholarDigital Library
    24. K. Raveendran, N. Thuerey, C. Wojtan, and G. Turk. 2012. Controlling Liquids Using Meshes. In Eurographics/ACM SIGGRAPH Symposium on Computer Animation. 255–264. Google ScholarDigital Library
    25. Karthik Raveendran, Chris Wojtan, Nils Thuerey, and Greg Turk. 2014. Blending liquids. ACM Transactions on Graphics (TOG) 33, 4 (2014), 137. Google ScholarDigital Library
    26. Bruce Schachter. 1980. Long crested wave models. Computer Graphics and Image Processing 12, 2 (1980), 187–201.Google ScholarCross Ref
    27. Claude Elwood Shannon. 1949. Communication in the presence of noise. Proceedings of the IRE 37, 1 (1949), 10–21.Google ScholarCross Ref
    28. Lin Shi and Yizhou Yu. 2005. Taming liquids for rapidly changing targets. In Proceedings of the 2005 ACM SIGGRAPH/Eurographics symposium on Computer animation. ACM, 229–236. Google ScholarDigital Library
    29. Jerry Tessendorf. 2004a. Interactive water surfaces. Game Programming Gems 4 (2004), 265–274.Google Scholar
    30. Jerry Tessendorf. 2004b. Simulating ocean water. ACM SIGGRAPH Courses (2004).Google Scholar
    31. Jerry Tessendorf. 2014. eWave: Using an Exponential Solver on the iWave Problem. . Technical Note.Google Scholar
    32. William “Lord Kelvin” Thomson. 1891. Popular lectures and addresses. Vol. 3. Macmillan London. 481–8 pages.Google Scholar
    33. Nils Thuerey. 2016. Interpolations of Smoke and Liquid Simulations. ACM Transactions on Graphics (TOG) 36, 1 (2016), 3. Google ScholarDigital Library
    34. N. Thuerey, R. Keiser, M. Pauly, and U. Rüde. 2009. Detail-preserving fluid control. Graphical Models 71, 6 (2009), 221–228. Google ScholarDigital Library
    35. N. Thuerey, C. Wojtan, M. Gross, and G. Turk. 2010. A multiscale approach to mesh-based surface tension flows. ACM Trans. Graph. 29, 4 (2010), 48. Google ScholarDigital Library
    36. 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. Eurographics Association, 29–36. Google ScholarDigital Library
    37. Jihun Yu, Chris Wojtan, Greg Turk, and Chee Yap. 2012. Explicit Mesh Surfaces for Particle Based Fluids. EUROGRAPHICS 2012 30 (2012), 41–48.Google Scholar
    38. Cem Yuksel, Donald H. House, and John Keyser. 2007. Wave particles. In Proc. SIGGRAPH. 99. Google ScholarDigital Library

ACM Digital Library Publication:

Overview Page: