“Wave particles” by Yuksel, House and Keyser

We present a new method for the real-time simulation of fluid surface waves and their interactions with floating objects. The method is based on the new concept of wave particles, which offers a simple, fast, and unconditionally stable approach to wave simulation. We show how graphics hardware can be used to convert wave particles to a height field surface, which is warped horizontally to account for local wave-induced flow. The method is appropriate for most fluid simulation situations that do not involve significant global flow. It is demonstrated to work well in constrained areas, including wave reflections off of boundaries, and in unconstrained areas, such as an ocean surface. Interactions with floating objects are easily integrated by including wave forces on the objects and wave generation due to object motion. Theoretical foundations and implementation details are provided, and experiments demonstrate that we achieve plausible realism. Timing studies show that the method is scalable to allow simulation of wave interaction with several hundreds of objects at real-time rates.

1. Angelidis, A., and Neyret, F. 2005. Simulation of smoke based on vortex filament primitives. In ACM-SIGGRAPH/EG Symposium on Computer Animation. Google ScholarDigital Library
2. Bascom, W. 1980. Waves and Beaches. Anchor Books, Garden City, NY.Google Scholar
3. Baxter, W., Wendt, J., and Lin, M. C. 2004. Impasto: a realistic, interactive model for paint. In NPAR ’04, 45–148. Google ScholarDigital Library
4. Carlson, M., Mucha, P. J., and Turk, G. 2004. Rigid fluid: animating the interplay between rigid bodies and fluid. ACM Trans. Graph. 23, 3, 377–384. Google ScholarDigital Library
5. Chen, J. X., and da Vitoria Lobo, N. 1995. Toward interactive-rate simulation of fluids with moving obstacles using navier-stokes equations. Graph. Models Image Process. 57, 2, 107–116. Google ScholarDigital Library
6. Enright, D., Marschner, S., and Fedkiw, R. 2002. Animation and rendering of complex water surfaces. In Proc. of SIGGRAPH ’02, 736–744. Google ScholarDigital Library
7. Fedkiw, R., Stam, J., and Jensen, H. W. 2001. Visual simulation of smoke. In Proc. of SIGGRAPH ’01, 15–22. Google ScholarDigital Library
8. Fedkiw, R. P. 2002. Coupling an eulerian fluid calculation to a lagrangian solid calculation with the ghost fluid method. J. Comput. Phys. 175, 1, 200–224. Google ScholarDigital Library
9. Feldman, B. E., O’Brien, J. F., and Klingner, B. M. 2005. Animating gases with hybrid meshes. In Proc. of SIGGRAPH ’05, 904–909. Google ScholarDigital Library
10. Foster, N., and Fedkiw, R. 2001. Practical animation of liquids. In Proc. of SIGGRAPH ’01, 23–30. Google ScholarDigital Library
11. Foster, N., and Metaxas, D. 1996. Realistic animation of liquids. Graph. Models Image Process. 58, 5, 471–483. Google ScholarDigital Library
12. Foster, N., and Metaxas, D. 1997. Controlling fluid animation. In CGI ’97: Proc. of the 1997 Conference on Computer Graphics International, 178. Google ScholarDigital Library
13. Foster, N., and Metaxas, D. 1997. Modeling the motion of a hot, turbulent gas. In Proc. of SIGGRAPH ’97, 181–188. Google ScholarDigital Library
14. Fournier, A., and Reeves, W. T. 1986. A simple model of ocean waves. In Proc. of SIGGRAPH ’86, 75–84. Google ScholarDigital Library
15. Genevaux, O., Habibi, A., and Dischler, J. M. 2003. Simulating fluid-solid interaction. In Graphics Interface, 31–38.Google Scholar
16. Gerstner, F. V. 1802. Theory of waves. Abhandlungen der Koenigl, boehmischen Gesellschaft der Wissenschaften zu Prag.Google Scholar
17. Guendelman, E., Bridson, R., and Fedkiw, R. 2003. Non-convex rigid bodies with stacking. ACM Trans. Graph. 22, 3, 871–878. Google ScholarDigital Library
18. Guendelman, E., Selle, A., Losasso, F., and Fedkiw, R. 2005. Coupling water and smoke to thin deformable and rigid shells. In Proc. of SIGGRAPH ’05, 973–981. Google ScholarDigital Library
19. Houston, B., Nielsen, M. B., Batty, C., Nilsson, O., and Museth, K. 2006. Hierarchical rle level set: A compact and versatile deformable surface representation. ACM Trans. Graph. 25, 1, 151–175. Google ScholarDigital Library
20. Irving, G., Guendelman, E., Losasso, F., and Fedkiw, R. 2006. Efficient simulation of large bodies of water by coupling two and three dimensional techniques. In Proc. ’06 SIGGRAPH ’06, 805–811. Google ScholarDigital Library
21. Jensen, L. S., and Goliáš, R. 2001. Deep-water animation and rendering. In Proc. Game Developer’s Conference.Google Scholar
22. Johanson, C. 2004. Real-time Water Rendering. Ms thesis, Lund University.Google Scholar
23. Kass, M., and Miller, G. 1990. Rapid, stable fluid dynamics for computer graphics. In Proc. of SIGGRAPH ’90, 49–57. Google ScholarDigital Library
24. Kim, J., Kim, S., Ko, H., and Terzopoulos, D. 2006. Fast gpu computation of the mass properties of a general shape and its application to buoyancy simulation. The Visual Computer 22, 856–864. Google ScholarDigital Library
25. Klingner, B. M., Feldman, B. E., Chentanez, N., and O’Brien, J. F. 2006. Fluid animation with dynamic meshes. In Proc. of SIGGRAPH ’06, 820–825. Google ScholarDigital Library
26. Layton, A. T., and van De Panne, M. 2002. A numerically efficient and stable algorithm for animating water waves. The Visual Computer 18, 1, 41–53.Google ScholarCross Ref
27. Losasso, F., Gibou, F., and Fedkiw, R. 2004. Simulating water and smoke with an octree data structure. ACM Trans. Graph. 23, 3, 457–462. Google ScholarDigital Library
28. Losasso, F., Irving, G., and Guendelman, E. 2006. Melting and burning solids into liquids and gases. IEEE Trans. on Vis. and Comp. Graph. 12, 3, 343–352. Google ScholarDigital Library
29. Mastin, G. A., Watterberg, P. A., and Mareda, J. F. 1987. Fourier synthesis of ocean scenes. IEEE Comput. Graph. Appl. 7, 3, 16–23. Google ScholarDigital Library
30. Miller, G., and Pearce, A. 1989. Globular dynamics: A connected particle system for animating viscous fluids. Computers and Graphics 13, 3, 305–309.Google ScholarCross Ref
31. Müller, M., Charypar, D., and Gross, M. 2003. Particle-based fluid simulation for interactive applications. In SCA ’03: Proceedings of the 2003 ACM Siggraph/Eurographics symposium on Computer animation, 154–159. Google ScholarDigital Library
32. Munson, B. R., Young, D. F., and Okiishi, T. H. 2006. Fundamentals of fluid mechanics. Wiley, New York, NY.Google Scholar
33. O’Brien, J. F., and Hodgins, J. K. 1995. Dynamic simulation of splashing fluids. In CA ’95: Proc. of the Computer Animation, 198. Google ScholarDigital Library
34. Peachey, D. R. 1986. Modeling waves and surf. In Proc. of SIGGRAPH ’86, 65–74. Google ScholarDigital Library
35. Perlin, K., and Hoffert, E. M. 1989. Hypertexture. In Proc. of SIGGRAPH ’89, 253–262. Google ScholarDigital Library
36. Peskin, C. S. 2002. The immersed boundary method. Acta Numerical 11, 479–517.Google ScholarCross Ref
37. Premoze, S., Tasdizen, T., Bigler, J., Lefohn, A., and Whitaker, R. 2003. Particle-based simulation of fluids. In Comp. Graph. Forum (Eurographics Proc.), vol. 22, 401–410.Google ScholarCross Ref
38. Reeves, W. T. 1983. Particle systems a technique for modeling a class of fuzzy objects. ACM Trans. Graph. 2, 2, 91–108. Google ScholarDigital Library
39. Schachter, B. 1980. Long crested wave models. Computer Graphics and Image Processing 12, 187–201.Google ScholarCross Ref
40. Schneider, J., and Westermann, R. 2001. Towards real-time visual simulation of water surfaces. In VMV ’01: Proc. of the Vision Modeling and Visualization Conference 2001, 211–218. Google ScholarDigital Library
41. Selle, A., Rasmussen, N., and Fedkiw, R. 2005. A vortex particle method for smoke, water and explosions. In Proc. of SIGGRAPH ’05, 910–914. Google ScholarDigital Library
42. Shah, M. A., Konttinen, J., and Pattanaik, S. 2007. Caustics mapping: An image-space technique for real-time caustics. IEEE TVCG 13, 2, 272–280. Google ScholarDigital Library
43. Stam, J. 1999. Stable fluids. In Proc. of SIGGRAPH ’99, 121–128. Google ScholarDigital Library
44. Takashi, T., Heihachi, U., and Kunimatsu, A. 2002. The simulation of fluid-rigid body interaction. In SIGGRAPH ’02: Sketches & Applications, 226. Google ScholarDigital Library
45. Takashi, T., Fujii, H., Kunimatsu, A., Hiwada, K., Saito, T., Tanaka, K., and Ueki, H. 2003. Realistic animation of fluid with splash and foam. Computer Graphics Forum 22 3, 391–401.Google Scholar
46. Terzopoulos, D., Platt, J., and Fleischer, K. 1989. Heating and melting deformable models (from goop to glop). Graphics Interface 89, 219–226.Google Scholar
47. Tessendorf, J. 2001. Simulating ocean water. In Simulating Nature: Realistic and Interactive Techniques, ACM SIGGRAPH ’01 Course #47 Notes.Google Scholar
48. Tessendorf, J. 2004. Interactive water surfaces. Game Programming Gems 4.Google Scholar
49. Treuille, A., Lewis, A., and Popovic, Z. 2006. Model reduction for real-time fluids. ACM Trans. Graph. 25, 3, 826–834. Google ScholarDigital Library
50. Ts’O, P. Y, and Barsky, B. A. 1987. Modeling and rendering waves: wave-tracing using beta-splines and reflective and refractive texture mapping. ACM Trans. Graph. 6, 3, 191–214. Google ScholarDigital Library
51. Zhu, Y., and Bridson, R. 2005. Animating sand as a fluid. ACM Trans. Graph. 24, 3, 965–972. Google ScholarDigital Library