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Mathematicians Making Strides Toward Lifelike Animations

September 25, 2017
An animated head of hair in motion. The realistic motion of the hair is based on new computational methods developed by Tokman and her collaborators.

Imagine going to see the latest Pixar movie. You’re sitting in the theater enjoying the film, when you begin to notice the astounding level of detail in the animation. On screen, water is rippling and leaves are flittering with an almost uncanny realism. It’s art imitating life with incredible verisimilitude, and it makes you wonder how the animators are able to pull off such lifelike effects.

The answer, at least in part, lies in mathematics. With support from the National Science Foundation, UC Merced Professor Mayya Tokman and her collaborators — Professor Dominik Michels of King Abdullah University of Science & Technology and Stanford University, and Professor Vu Thai Luan of Southern Methodist University — are developing the computational tools that will allow animators to produce the next generation of true-to-life simulations.

Tokman recently returned from SIGGRAPH 2017, the world’s largest annual conference on computer graphics and interactive techniques, where a paper she coauthored with Michels and Luan was publicly debuted. Though the paper’s title — “A stiffly accurate integrator for elastodynamic problems” — may not immediately conjure images of lifelike animation, the new computer simulation methods described within are particularly relevant to the field.

“Elastodynamic systems are systems of bendable things,” Tokman explained. “In computer graphics, the best example is hair.”

When earlier generations of animators wanted to depict hair tousling or clothes wrinkling as a character moved about, they’d have to produce frame-by-frame drawings of the action. A realistic portrayal of hair, for example, would require repeatedly redrawing each individual strand in motion. The process was prohibitively time-consuming, which is why older animation tends to lack the lifelike flair of more recent work.

“For complicated effects, there was a need for easier methods than frame-by-frame redrawing,” Tokman said. “In computer graphics, for many effects people moved away from animation towards simulation. They developed mathematical equations that described the behavior and dynamics of a system, a system like hair shaking.”

New computational methods developed by Tokman and her collaborators can be used to produce more realistic renderings of waving flags and moving bacteria, among other applications.

To simulate a moving head of hair, each individual strand is defined by an equation. Since every hair on a shaking head can affect the movement of its neighbors, all the equations are interconnected. If one hair moves and hits another, the equations capture that.

The equations, however, are very complex and extremely difficult to solve. They’re impossible to solve by hand and even computers can take a long time to arrive at a solution. This inspired Tokman and her coauthors to develop new algorithms that can solve these equations more rapidly.

“We developed a new computational technique that allows us to simulate elastodynamic systems up to 20 times faster than previous methods,” Tokman said.

This means that computer-assisted animations that once required overnight processing can now be completed within the hour. But Tokman’s technique is useful for more than just animation.

“Our method is very general,” Tokman said. “The method is applicable to capturing the evolution of many complex systems. It can be used to simulate climate or weather patterns, to capture the process of combustion in a car’s engine or to model flaring in the Sun’s atmosphere. This means it’s useful for scientists and engineers as well as animators.”

In light of what she saw at SIGGRAPH, Tokman is convinced that students interested in a career in animation or video game design may want to pursue math and engineering as an alternative to the conventional arts-focused route.

“Animation studios used to not go to math and engineering schools to recruit. Now they do,” Tokman said. “Most major studios and companies have research departments. Some of the papers presented at SIGGRAPH were from Disney, Pixar, Google and Microsoft.”

Plus, animation isn’t the only field where computers are helping artists. At SIGGRAPH, Tokman met researchers who are working on simulating sound, portending a future where the majority of sound effects may one day be produced completely outside of the recording studio.

“It’s all simulation now,” she said. “It’s looking at systems in the physical world, designing equations that describe them, and running algorithms.”