(Editor's note: This story was originally published on Sept. 3, 2010 on the Columbia News website and on Sept. 2 in The Record.)

Honey dribbling over toast, an artist’s brush sweeping across a canvas or a dress swaying as a model sashays down a runway. All of these fluid movements can be reduced to mathematical formulas.

Above: still from Disney’s animated movie Tangled. The swaying movement of the heroine’s dress was based on Grinspun’s research. Below: Simulations conducted by Professor Grinspun’s team reproduce honey poured onto a moving belt. On the left is real honey; on the right is a computer simulation. © Disney Enterprises, Inc. All Rights Reserved

Eitan Grinspun, an associate professor of computer science, studies the basic rules of motion and turns them into computer programs that are animating Hollywood movies and creating new tools for graphic designers. The programs also might be used for medical training, crash-test simulation and industrial packaging, determining, for example, how to minimize air bubbles while bottling shampoo.

Soon, Grinspun’s work will be viewed by millions. Walt Disney Animation Studios is using his technology as part of its system to animate clothing worn by the characters in Tangled, its November 2010 feature film based on the Rapunzel story. The scientist is now collaborating with Weta Digital, the visual effects studio behind Avatar and The Lord of the Rings, on technology for some of its projects currently in production. (Weta is working on Steven Spielberg’s 2011 film, The Adventures of Tintin.) Last spring, Adobe Systems Inc. included a new paintbrush tool based on Grinspun’s work as part of its most recent editions of Adobe Photoshop and Adobe Illustrator.

“We are interested in computing how materials move,” said Grinspun, 34, who was born in Israel to Chilean parents but grew up in Ann Arbor, Mich., and Toronto.

Take, for example, a rubber mat. Like all elastic materials, rubber resists changes to its shape. If you could measure the energy required to roll up a rubber mat, you could predict how quickly and completely that mat could unfurl. Grinspun uses geometry to take into account the “bendiness” of an object by measuring how much the material curves under different pressures.

Rubber mats, Grinspun explained, share the same properties as syrups, textiles and plastics. “With elastic materials, the more you bend them, the more they want to unbend,” he said. “If you bend a sheet of rubber, the more it’s bent, the more it will fight to return to a straight shape. But with honey, it doesn’t matter how much you’ve bent it—it matters how fast.”

Grinspun partners with physicists and mathematicians to determine the best formulas to use as a starting point for his work. From there, his research team refines and customizes the formulas they use in their programs.

In the case of viscous liquids, Grinspun assembled a team consisting of a theoretical physicist, Basile Audoly of the University of Paris, geometry professor Max Wardetzky of Göttingen University and graduate student Miklós Bergou (SEAS’10). The team sought a mathematical explanation for the patterns that honey forms as it drips. They were inspired by a YouTube video of honey pouring onto a moving conveyor belt. The more quickly the belt moved, the more the honey stretched out as it fell, creating a progressively straighter line. As the belt slowed, the honey formed waves, loops, figure eights and other geometric shapes on the belt’s surface.

Grinspun’s team identified formulas that would help predict those patterns on a computer. “The formula for the honey is beautiful and, most importantly, simple,” said Grinspun. “All of the behaviors we observed were due to the interaction between bending, twisting and stretching.”

Those same measurements have led to simulation software that can predict how a steerable needle, a device similar to a catheter, will move inside a patient’s body and how a paintbrush responds to pressure. Other types of movements, such as the swaying of the heroine’s dress in Tangled, are based on a similar set of algorithms.

“In life and in physics, the unexpected interaction between a small number of simple rules can lead to huge arrays of complex behavior,” said Grinspun. “And that’s the beauty of this work.”

—by Anna Kuchment