Pi Mu Epsilon Lecture: How math improves movies

Michael Dorff (fifth from right) and new members of the Nebraska Alpha Chapter of Pi Mu Epsilon. COURTESY PHOTO

On Sept. 25, the Department of Mathematics was honored to host Michael Dorff as the 2015 Pi Mu Epsilon (PME) Lecturer.

Michael Dorff is a professor of mathematics at Brigham Young University in Utah. His areas of expertise include geometric function theory, complex analysis and minimal surfaces. He is a renowned mathematics expository speaker and well-known for his work in undergraduate research. Dorff is the founder and director of the $2.6 million NSF-funded Center for Undergraduate Research in Mathematics. He has received several university and national teaching awards and is a Fellow of the American Mathematical Society.

In his address, “How Mathematics is Making Hollywood Movies Better,” Dorff discussed mathematical methods at the frontier of the motion picture industry. He surveyed many techniques used to bring virtual worlds to life, for instance, how to speed up the animation of digital characters, whose polygonal 3D models include thousands or even millions of vertices, by tying their complex geometry to simpler “encasing skeletons.”

Next, he described how differential equations were employed by Pixar (Disney) in “Brave” to create the feisty heroine’s realistic hair as a network of tiny springs.

The lecture also featured simulated solutions to the Navier-Stokes equations of fluid dynamics used for realistic water effects, ranging from splashing waves to massive whirlpools. Though likewise water-based, a rather different class of models is employed to accurately depict snow.

Dorff discussed the representation of snow crystals as fractals, and showed how the models built for Pixar’s movie “Frozen” incorporated parameters controlling various physical properties of the simulated snow, making it possible to render everything from mushy snowballs to specs dancing in a blizzard on a winter night.

The Pi Mu Epsilon lecture series each year brings a prominent mathematician and educator to give a public talk at UNL for undergraduate math and science majors. It is organized by the Nebraska Alpha Chapter of the Pi Mu Epsilon honor society, with the support of the Department of Mathematics and the Nebraska Math Scholars program.

– Daniel Toundykov