In a paper published this month in the journal Transactions on Graphics, Desbrun and his team describe the approach they take to model swirling fluids around and within solid objects such as a snow globe. The traditional approach would approximate the velocity of the liquid at various points in space and time and use this to approximate its motion along a circular path. But Desbrun's equations model the actual circulation of the liquid, as if it were a property as fundamental as velocity.

To simulate the circulation of liquid, the researchers must capture the fundamental property of that circulation, called flux. Flux, or the amount of liquid that moves through a space at any given time, is captured by breaking the whirlpool into tiny pieces and determining the flow at each piece. These values are folded into the motion equation, allowing the liquid to flow more accurately.

So far, says Desbrun, the results are promising. This approach "has been shown to provide good statistical predictability ... ensuring high visual quality."

The research could be significant for the computer-graphics community, says Eva Kanso, professor of aerospace and mechanical engineering at the University of Southern California, in Los Angeles, who models fluids computationally. "Traditionally," she says, "the trend was to use fast computation that is similar to reality but not based on real physics. It's a big step for the computer-graphics community to look at physical laws and try to simulate them, especially now with a big demand on more-realistic animation."

James O'Brien, professor of computer science at the University of California, Berkeley, says that if the traditional computational method and Desbrun's method were to go head-to-head, there wouldn't be much difference in the amount of time it takes to render an animation. However, he says, "the real point is getting better-looking results for the same amount of effort."

Right now, says Desbrun, his new computation approach isn't ready for prime time in the software found at animation studios, but colleagues at Columbia University are exploring the option. "We haven't pushed our research to the point where we could help movie companies to add more control over the way fluid flows," he says. But, he adds, if the equations are used in software, artists could, with the click of a button, easily modify special effects and animation far more accurately than they can today.