This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Digital Marbling: A Multiscale Fluid Model
July/August 2006 (vol. 12 no. 4)
pp. 600-614

Abstract—This paper presents a multiscale fluid model based on mesoscale dynamics and viscous fluid equations as a generic tool for digital marbling purposes. The model uses an averaging technique on the adaptation of a stochastic mesoscale model to obtain the effect of fluctuations at different levels. It allows various user controls to simulate complex flow behaviors as in traditional marbling techniques, as well as laminar and turbulent flows. Material transport is based on an improved advection solution to be able to match the highly detailed, sharp fluid interfaces in marbling patterns. In the transport model, two reaction models are introduced to create different effects and to simulate density fluctuations.

[1] D. Maurer-Mathison, The Ultimate Marbling Handbook: A Guide to Basic and Advanced Techniques for Marbling Paper and Fabric. New York: Watson-Guptill Publishing, 1999.
[2] N. Cressie, Statistics for Spatial Data. John Wiley and Sons, 1991.
[3] D. Weiskopf, “Dye Advection without the Blur: A Level-Set Approach for Texture,” Computer Graphics Forum, Proc. Eurographics 2004, vol. 23, no. 3, pp. 479-488, 2004.
[4] J. Chen and N. Lobo, “Toward Interactive-Rate Simulation of Fluids with Moving Obstacles Using Navier-Stokes Equations,” Graphical Models and Image Processing, vol. 57, no. 2, pp. 107-116, 1995.
[5] N. Foster and D. Metaxas, “Realistic Animation of Liquids,” Graphical Models and Image Processing, vol. 58, no. 5, pp. 471-483, 1996.
[6] M. Kass and G. Miller, “Rapid, Stable Fluid Dynamics for Computer Graphics,” Computer Graphics, Proc. SIGGRAPH '90, vol. 24, no. 3, pp. 49-57, 1990.
[7] N. Foster and D. Metaxas, “Controlling Fluid Animation,” Proc. Computer Graphics Int'l Conf. (CGI '97), 1997.
[8] J. Stam, “Stable Fluids,” Proc. SIGGRAPH '99, pp. 121-128, Aug. 1999.
[9] R. Fedkiw, J. Stam, and H.W. Jensen, “Visual Simulation of Smoke,” Proc. SIGGRAPH 2001 Conf., pp. 23-30, 2001.
[10] J. Stam, “Flows on Surfaces of Arbitrary Topology,” Proc. ACM SIGGRAPH 2003 Conf., pp. 724-731, Aug. 2003.
[11] D. Nguyen, R. Fedkiw, and H. Jensen, “Physically Based Modeling and Animation of Fire,” ACM Trans. Graphics, vol. 21, pp. 721-728, 2002.
[12] J. Stam and E. Fiume, “Turbulent Wind Fields for Gaseous Phenomena,” Proc. SIGGRAPH '93 Conf., pp. 369-376, 1993.
[13] N. Rasmussen, D.Q. Nguyen, D.W. Geiger, and R. Fedkiw, “Smoke Simulation for Large Scale Phenomena,” ACM Trans. Graphics, vol. 22, no. 3, pp. 703-707, 2003.
[14] N. Foster and D. Metaxas, “Modeling the Motion of a Hot, Turbulent Gas,” ACM Trans. Graphics, vol. 22, Aug. 1997.
[15] J. Steinhoff and D. Underhill, “Modification of the Euler Equations for Vorticity Confinement: Application to the Computation of Interacting Vortex Rings,” Physics of Fluids, vol. 6, pp. 2738-2744, 1994.
[16] B.E. Feldman, J.F. O'Brien, and O. Arikan, “Animating Suspended Particle Explosions,” ACM Trans. Graphics, vol. 22, no. 3, pp. 708-715, 2003.
[17] J. Stam and E. Fiume, “Depicting Fire and Other Gaseous Phenomena Using Diffusion Processes,” ACM Computer Graphics, pp. 129-136, Aug. 1995.
[18] R. Fattal and D. Lischinksi, “Target-Driven Smoke Animation,” ACM Trans. Graphics, vol. 23, no. 3, 2004.
[19] I. Celik, “Introductory Turbulence Modeling,” technical report, Mechanical and Aerospace Eng. Dept., West Virginia Univ., Aug. 1999.
[20] Y. Zhou, W.D. McComb, and G. Vahala, “Renormalization Group (RG) in Turbulence: Historical and Comparative Perspective,” Technical Report 97-36, NASA Langley Research Center, Hampton, Aug. 1997.
[21] Statistical Physics, Course of Theoretical Physics, vol. 5, L.D. Landau and E.M. Lifshitz, eds. Oxford: Pergamon, 1980.
[22] R.D. Groot and P.B. Warren, “Dissipative Particle Dynamics: Bridging the Gap between Atomistic and Mesoscale Simulation,” Europhysics Letters, vol. 42, no. 4, pp. 377-382, 1998.
[23] M. Serrano and P. Espanol, “Thermodynamically Consistent Mesoscopic Fluid Particle Model,” Physical Rev. E, vol. 64, no. 4, pp. 46-115, 2001.
[24] E.G. Flekkoy, P.V. Coveney, and G.D. Fabritiis, “Foundations of Dissipative Particle Dynamics,” Physical Rev. E, vol. 62, no. 2, pp. 2140-2158, 2000.
[25] C.W. Gardiner, Handbook of Stochastic Methods. Springer, 1985.
[26] A.J. Chorin, “Numerical Simulation of the Navier-Stokes Equations,” Mathematics of Computation, vol. 22, no. 104, pp. 745-762, 1968.
[27] J.B. Bell, P. Colella, and H.M. Glaz, “A Second Order Projection Method for the Incompressible Navier-Stokes Equations,” J. Computational Physics, vol. 85, pp. 257-283, 1989.
[28] M. Unser, “Splines: A Perfect Fit for Signal and Image Processing,” IEEE Signal Processing Magazine, vol. 16, no. 6, pp. 22-38, 1999.
[29] M. Unser, A. Aldroubi, and M. Eden, “B-Spline Signal Processing: Part I-Theory,” IEEE Trans. Signal Processing, vol. 41, no. 2, pp. 821-832, 1993.
[30] M. Unser, A. Aldroubi, and M. Eden, “B-Spline Signal Processing: Part II-Efficient Design and Applications,” IEEE Trans. Signal Processing, vol. 41, no. 2, pp. 834-848, 1993.
[31] T. Yabe and F. Xiao, “Description of Complex and Sharp Interface During Shock Wave Interaction with Liquid Drop,” J. Physics Soc. of Japan, vol. 62, no. 8, pp. 2537-2540, 1993.
[32] T. Kuroda, “Suminagashi: Exposition,” http://www5e.biglobe. ne.jp/~kurodamypagekaisetu-E.htm , 2005.
[33] A. Witkin and M. Kass, “Reaction-Diffusion Textures,” Proc. Computer Graphics Conf. (SIGGRAPH '91), vol. 25, pp. 299-308, 1991.
[34] Z. Neufeld, P. Haynes, and T. Tel, “Chaotic Mixing Induced Transitions in Reaction-Diffusion Systems,” Chaos, vol. 12, no. 2, pp. 426-438, 2002.
[35] A.J. Majda and P.R. Kramer, “Simplified Models for Turbulent Diffusion: Theory, Numerical Modeling and Physical Phenomena,” Physics Reports, vol. 314, pp. 237-574, 1999.
[36] Z. Neufeld, C. Lopez, and P.H. Haynes, “Smooth Filamental Transition of Active Tracer Fields Stirred by Chaotic Advection,” Physical Rev. Letters, vol. 82, no. 12, pp. 2606-2609, 1999.
[37] H. Aref, “Stirring by Chaotic Advection,” J. Fluid Mechanics, vol. 143, pp. 1-21, 1984.
[38] M. VanDyke, An Album of Fluid Motion. Stanford, Calif.: Parabolic Press, 1983.
[39] A. Chambers, Suminagashi: The Japanese Art of Marbling. John Wiley and Sons, 1991.

Index Terms:
Multiscale fluid modeling, stochastic mesoscopic fluid dynamics, turbulence modeling, turbulent diffusion, advection-reaction equations.
Citation:
R? Acar, Pierre Boulanger, "Digital Marbling: A Multiscale Fluid Model," IEEE Transactions on Visualization and Computer Graphics, vol. 12, no. 4, pp. 600-614, July-Aug. 2006, doi:10.1109/TVCG.2006.66
Usage of this product signifies your acceptance of the Terms of Use.