Practical animation of liquids

ABSTRACT

We present a general method for modeling and animating liquids. The system is specifically designed for computer animation and handles viscous liquids as they move in a 3D environment and interact with graphics primitives such as parametric curves and moving polygons. We combine an appropriately modified semi-Lagrangian method with a new approach to calculating fluid flow around objects. This allows us to efficiently solve the equations of motion for a liquid while retaining enough detail to obtain realistic looking behavior. The object interaction mechanism is extended to provide control over the liquid s 3D motion. A high quality surface is obtained from the resulting velocity field using a novel adaptive technique for evolving an implicit surface.

REFERENCES

• 1: Abbot, M. and Basco, D., "Computational Fluid Dynamics - An Introduction for Engineers", Longman, 1989.
• 2: Barrett, R., Berry, M., Chan, T., Demmel, J., Donato, J., Dongarra, J., Eijkhout, V., Pozo, R., Romine, C. and van der Vorst, H., "Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods", Society for Industrial and Applied Mathematics, 1993.
• 3: Jules Bloomenthal , Brian Wyvill, Introduction to Implicit Surfaces, Morgan Kaufmann Publishers Inc., San Francisco, CA, 1997
• 4: 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]
• 5: Chen, S., Johnson, D., Raad, P. and Fadda, D., "The Surface Marker and Micro Cell Method", Int. J. Numer. Methods in Fluids 25, 749-778 (1997).
• 6: Courant, R., Issacson, E. and Rees, M., "On the Solution of Nonlinear Hyperbolic Differential Equations by Finite Differences", Comm. Pure and Applied Math 5, 243-255 (1952).
• 7: Desbrun, M. and Cani-Gascuel, M.P., "Active Implicit Surface for Animation", Graphics Interface 98, 143-150 (1998).
• 8: Ronald P. Fedkiw , Tariq Aslam , Barry Merriman , Stanley Osher, A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method), Journal of Computational Physics, v.152 n.2, p.457-492, July 1, 1999 [doi>10.1006/jcph.1999.6236]
• 9: Nick Foster , Dimitris Metaxas, Controlling Fluid Animation, Proceedings of the 1997 Conference on Computer Graphics International, p.178, June 23-27, 1997
• 10: Nick Foster , Dimitris Metaxas, Modeling the motion of a hot, turbulent gas, Proceedings of the 24th annual conference on Computer graphics and interactive techniques, p.181-188, August 1997 [doi>10.1145/258734.258838]
• 11: 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]
• 12: 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
• 13: Gates, W.F., "Interactive Flow Field Modeling for the Design and Control of Fluid Motion in Computer Animation", UBC CS Master's Thesis, 1994.
• 14: Golub, G.H. and Van Loan, C.F., "Matrix Computations", The John Hopkins University Press, 1996.
• 15: Harlow, F.H. and Welch, J.E., "Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid with a Free Surface", The Physics of Fluids 8, 2182-2189 (1965).
• 16: Myungjoo Kang , Ronald P. Fedkiw , Xu-Dong Liu, A Boundary Condition Capturing Method for Multiphase Incompressible Flow, Journal of Scientific Computing, v.15 n.3, p.323-360, Sept. 2000 [doi>10.1023/A:1011178417620]
• 17: 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
• 18: William E. Lorensen , Harvey E. Cline, Marching cubes: A high resolution 3D surface construction algorithm, ACM SIGGRAPH Computer Graphics, v.21 n.4, p.163-169, July 1987
• 19: Miller, G. and Pearce, A., "Globular Dynamics: A Connected Particle System for Animating Viscous Fluids", Computers and Graphics 13, 305-309 (1989).
• 20: J. F. O'Brien , J. K. Hodgins, Dynamic simulation of splashing fluids, Proceedings of the Computer Animation, p.198, April 19-21, 1995
• 21: 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]
• 22: Darwyn R. Peachey, Modeling waves and surf, Proceedings of the 13th annual conference on Computer graphics and interactive techniques, p.65-74, August 1986
• 23: Schachter, B., "Long Crested Wave Models", Computer Graphics and Image Processing 12, 187-201 (1980).
• 24: Sethian, J.A. "Level Set Methods and Fast Marching Methods", Cambridge University Press, Cambridge 1999.
• 25: 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]
• 26: Staniforth, A. and Cote, J., "Semi-Lagrangian Integration Schemes for Atmospheric Models - A Review", Monthly Weather Review 119, 2206-2223 (1991).
• 27: Terzopoulos, D., Platt, J. and Fleischer, K., "Heating and Melting Deformable Models (From Goop to Glop)", Graphics Interface 89, 219-226 (1995).
• 28: Gary D. Yngve , James F. O'Brien , Jessica K. Hodgins, Animating explosions, Proceedings of the 27th annual conference on Computer graphics and interactive techniques, p.29-36, July 2000 [doi>10.1145/344779.344801]

INDEX TERMS

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

Additional Classification:
  I. Computing Methodologies
  I.6 SIMULATION AND MODELING
      I.6.4 Model Validation and Analysis
      I.6.8 Types of Simulation
          Subjects: Animation

General Terms:
Experimentation, Performance

Keywords:
Navier-Stokes, animation, computational fluid dynamics, implicit surface, level set, liquids, natural phenomena, particles, semi-Lagrangian