Simulating Bubbles Michael Running Wolf 4/1/05 Introduction In researching journal articles relating to simulating bubbles, two categories of work exist. In one body of work, the physical mechanics of fluid is simulated, essentially rendering life like liquid; bubbles in liquids make for an interesting fluid problem. Then, in another, the effects bubbles have on light is studied, characterized by soap bubble simulation. Bubbles in Liquid In this field, the complex physical properties of liquids are studied then approximated. Much of the research has been stimulated by the movie industry. Apparently simulating the sinking of a ship in the Atlantic, through CGI, is more efficient than actually sinking an early 20 th century luxury liner. Key to understanding, and subsequently replicating liquid systems, are the physical equations that describe fluid mechanics. Main concepts Navier Stokes formula This formula was developed by Claude Navier (1785-1836), a French physicist/engineer, and George Stokes((1819-1903), an Irish physicist in the 1800 s. This equation was initially an accidental discovery by Navier, who not entirely understanding the physics of liquids fused several equations together haphazardly. Stokes simultaneously developed the same equation.
This equation describes how liquid pressure, temperature, and density of moving fluid are related. At the time, it was a revolutionary discovery in fluid mechanics. Various integration methods, and other ugly calculus math, is required to solve the system; approximations are generally used in practice. Approximating and solving the Navier Stokes equation is the Computation Fluid Dynamics field of study. Surface Tension Liquid molecules have a strong attractive force between one another, this is called cohesion. Within the body of a liquid, a molecule will have a strong cohesive force with neighbors surrounding it. While a particle on the surface has no molecules above it to share its cohesive force. As a result surface molecules share a stronger bond with its nearest surface neighbors; surface cohesion is stronger than internal cohesion. This is surface tension.
Papers in this field One of the more prominent, and recent, CGI researchers in this field is Nick Foster. Starting in the mid-1990 s Foster began submitting a series of collaborative works to SIGGRAPH on simulating liquids. Engineering methods exist to create liquid models, however are tuned for accuracy not speed. Foster created real time rendering systems that approximated the Navier Stokes equation using finite grid systems. Much of Foster s work was based upon approximation algorithms developed Jos Stam. The liquid surface was created by creating a curve with from grid points.
Animation of Bubbles in Liquid This paper essentially gathered the work done in liquids by Stam and Foster and applied it to simulating bubbles in water. They used a 3D grid system like Foster and approximated the liquid dynamics with methods similar to those developed by Stam. A marching cubes algorithm made grid points solid. Soap Bubbles Glassner s stuff I Love soap bubbles. They re beautiful, delicate, and though they live on briefly, it s a glorious moment, Glassner. In two IEEE Computer Graphics and Applications articles entitled Soap Bubbles: Part 1 and Soap Bubbles: Part 2, Glassner provides and overview of the effects soap has upon water and the mechanics of soap bubbles. In part one of the papers, the trigonometry of soap films is explained. When three pegs are dipped into a solution of soap and water three 120-degree angles are created. It turns out that this configuration is the most efficient structure requiring a minimal amount of soap film length. In other words, when soap films intersect, a network of soap films with the least length of segments is created. When three soap film segments insect, vertex angles of 120 degrees is the efficient configuration. This property holds true when soap bubbles join. As two bubbles collide, the 120 angles are created, while this equation also holds true. Similarly with 3 bubbles:
Obeying the mathematics of bubbles realistic soap bubbles can be modeled. The rest of Glassner paper briefly describes simulating varying the thickness of bubbles and simulating light diffraction. All of his work was done using 3D Studio Max. Various other papers build off Glassner s work and focus upon creating fast light approximations for real time rendering; for example, ``Real-time Rendering of Soap Bubbles Taking into Account Light Interference by Wei et al. <movie> Of these other papers, Blowing in the Wind by Wei et al, is fairly interesting. This group created an accurate model of various objects being manipulated by air currents, including soap bubbles.
References A. Glassner, Soap Bubbles: Part1, IEEE Computer Graphics and Applications, Vol.20, No.5, pp.76-84, 2000. A. Glassner, Soap Bubbles: Part2, IEEE Computer Graphics and Applications, Vol.20, No.6, pp.99-109, 2000. J. Hong, C. Kim, Animation of Bubbles in Liquid. Computer Graphics Forum 22(3): 253-262 (2003) K. Iwasaki, K. Matsuzawa, T. Nishita, ``Real-time Rendering of Soap Bubbles Taking into Account Light Interference", Computer Graphics International 2004, pp.344-348. N. Foster and D. Metaxas, Realistic animation of liquids, Graphical Models and Image Processing, 58, 471 483 (1996). N. Foster and R. Fedkiw, Practical animation of liquids, In Proceedings of ACM SIGGRAPH 2001, 23 30 (2001). J. Stam, Stable fluids, In Proceedings of ACM SIGGRAPH 1999, 121-128 (1999). Websites: Nick Foster s Website http://www.cis.upenn.edu/~fostern/ A compilation of various liquid research animations http://graphics.stanford.edu/~fedkiw/ Website for Real-time Rendering of Soap Bubbles Taking into Account Light Interference http://nis-lab.is.s.u-tokyo.ac.jp/~kei-i/bubble/ Website for Animation of Bubbles in Liquid http://kucg.korea.ac.kr/research/research_group3/bubbles/index.shtml