Animation and control of breaking waves

ABSTRACT

Controlling fluids is still an open and challenging problem in fluid animation. In this paper we develop a novel fluid animation control approach and we present its application to controlling breaking waves. In our <i>Slice Method</i> framework an animator defines the shape of a breaking wave at a desired moment in its evolution based on a library of breaking waves. Our system computes then the subsequent dynamics with the aid of a 3D Navier-Stokes solver. The wave dynamics previous to the moment the animator exerts control can also be generated based on the wave library. The animator is thus enabled to obtain a full animation of a breaking wave while controlling the shape and the timing of the breaking. An additional advantage of the method is that it provides a significantly faster method for obtaining the full 3D breaking wave evolution compared to starting the simulation at an early stage and using solely the 3D Navier-Stokes equations. We present a series of 2D and 3D breaking wave animations to demonstrate the power of the method.

REFERENCES

• 1: {BCG87} Bell J. B., Colella P., Glaz H. M.: A second-order projection method for the incompressible Navier-Stokes equations. Journal of Computational Physics 85 (1987), 257--283.
• 2: {CKZL99} Chen G., Kharif C., Zaleski S., Li J.: Two-dimensional Navier-Stokes simulation of breaking waves. Physics of Fluids 11, 1 (1999), 121--133.
• 3: Jim X. Chen , Niels da Vitoria Lobo, Toward interactive-rate simulation of fluids with moving obstacles using Navier-Stokes equations, Graphical Models and Image Processing, v.57 n.2, p.107-116, March 1995 [doi>10.1006/gmip.1995.1012]
• 4: {Vue4} www.e-onsoftware.com.
• 5: Douglas Enright , Ronald Fedkiw , Joel Ferziger , Ian Mitchell, A hybrid particle level set method for improved interface capturing, Journal of Computational Physics, v.183 n.1, p.83-116, November 20, 2002 [doi>10.1006/jcph.2002.7166]
• 6: Douglas Enright , Stephen Marschner , Ronald Fedkiw, Animation and rendering of complex water surfaces, ACM Transactions on Graphics (TOG), v.21 n.3, July 2002
• 7: Nick Foster , Ronald Fedkiw, Practical animation of liquids, Proceedings of the 28th annual conference on Computer graphics and interactive techniques, p.23-30, August 2001 [doi>10.1145/383259.383261]
• 8: Nick Foster , Dimitri Metaxas, Realistic animation of liquids, Graphical Models and Image Processing, v.58 n.5, p.471-483, Sept. 1996 [doi>10.1006/gmip.1996.0039]
• 9: Nick Foster , Dimitris Metaxas, Controlling Fluid Animation, Proceedings of the 1997 Conference on Computer Graphics International, p.178, June 23-27, 1997
• 10: Alain Fournier , William T. Reeves, A simple model of ocean waves, Proceedings of the 13th annual conference on Computer graphics and interactive techniques, p.75-84, August 1986
• 11: {HW65} Harlow F. H., Welch J. E.: Numerical calculation of time-dependent viscous incompressible flow of fluid with a free surface. Physics of Fluids 8 (1965), 212--218.
• 12: Michael Kass , Gavin Miller, Rapid, stable fluid dynamics for computer graphics, Proceedings of the 17th annual conference on Computer graphics and interactive techniques, p.49-57, September 1990, Dallas, TX, USA
• 13: {MP89} Miller G., Pearce A.: Globular dynamics: a connected particle system for animating viscous fluids. Computers and Graphics 13, 3 (1989), 305--309.
• 14: Antoine McNamara , Adrien Treuille , Zoran Popović , Jos Stam, Fluid control using the adjoint method, ACM Transactions on Graphics (TOG), v.23 n.3, August 2004
• 15: Gary A. Mastin , Peter A. Watterberg , John F. Mareda, Fourier synthesis of ocean scenes, IEEE Computer Graphics and Applications, v.7 n.3, p.16-23, March 1987 [doi>10.1109/MCG.1987.276961]
• 16: J. F. O'Brien , J. K. Hodgins, Dynamic simulation of splashing fluids, Proceedings of the Computer Animation, p.198, April 19-21, 1995
• 17: Stanley Osher , James A. Sethian, Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics, v.79 n.1, p.12-49, Nov. 1988 [doi>10.1016/0021-9991(88)90002-2]
• 18: Darwyn R. Peachey, Modeling waves and surf, ACM SIGGRAPH Computer Graphics, v.20 n.4, p.65-74, Aug. 1986
• 19: Ken Perlin, An image synthesizer, ACM SIGGRAPH Computer Graphics, v.19 n.3, p.287-296, Jul. 1985
• 20: Nick Rasmussen , Duc Quang Nguyen , Willi Geiger , Ronald Fedkiw, Smoke simulation for large scale phenomena, ACM Transactions on Graphics (TOG), v.22 n.3, July 2003
• 21: {Sch80} Schachter B.: Long crested wave models. Computer Graphics and Imagage Processing 12 (1980), 187--201.
• 22: Mark Sussman , Elbridge Gerry Puckett, A coupled level set and volume-of-fluid method for computing 3D and axisymmetric incompressible two-phase flows, Journal of Computational Physics, v.162 n.2, p.301-337, Aug 2000 [doi>10.1006/jcph.2000.6537]
• 23: Jos Stam, Stable fluids, Proceedings of the 26th annual conference on Computer graphics and interactive techniques, p.121-128, July 1999 [doi>10.1145/311535.311548]
• 24: Mark Sussman, A second order coupled level set and volume-of-fluid method for computing growth and collapse of vapor bubbles, Journal of Computational Physics, v.187 n.1, p.110-136, May 2003 [doi>10.1016/S0021-9991(03)00087-1]
• 25: Pauline Y. Ts'o , Brian A. Barsky, Modeling and rendering waves: wave-tracing using beta-splines and reflective and refractive texture mapping., ACM Transactions on Graphics (TOG), v.6 n.3, p.191-214, July 1987 [doi>10.1145/35068.35070]
• 26: Sebastien Thon , Jean-Michel Dischler , Djamchid Ghazanfarpour, Ocean Waves Synthesis Using a Spectrum-Based Turbulence Function, Proceedings of the International Conference on Computer Graphics, p.65, June 19-24, 2000
• 27: {Tes99} Tessendorf J.: Simulating ocean water. Siggraph Course Notes (1999).
• 28: {TFK*03} Takahashi T., Fujii H., Kunimatsu A., Hiwada K., Saito T., Tanaka K., Ueki H.: Realistic animation of fluid with splash and foam. Eurographics (2003).
• 29: Adrien Treuille , Antoine McNamara , Zoran Popović , Jos Stam, Keyframe control of smoke simulations, ACM Transactions on Graphics (TOG), v.22 n.3, July 2003
• 30: {TPF95} Terzopoulos D., Platt J., Fleische K.: Heating and melting deformable models (from goop to glop). Graphics Interface 89 (1995), 219--226.
• 31: {Yab97} Yabe T.: Universal solver CIP for solid, liquid and gas. CFD Review (1997).

INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.7 Three-Dimensional Graphics and Realism