Kim’s research is working to change that. The paper, published at the Symposium on Computer Animation, delves into the physics of three types of energy needed to simulate a strand: stretching, bending, and torsion. For the character of Blaze, Pixar borrowed Kim’s mathematical model specifically for bending.
“If you want to take two ends of a piece of wire and bend it into a circle, this is the part of the material that will resist you,” said Kim. “It's called the bending energy, and we derived its eigenvalues, which is a key quantity that is needed to simulate it.”
Alvin Shi and Haomiao Wu, Ph.D. students in Kim’s lab, were the co-lead authors of the paper.
The Toy Story 5 creators also drew inspiration from the research to depict a twisting, or torsion, movement.
“You can think of it as the force that resists you when you grab two ends of a piece of string and try twirling one end so that the whole thing spins into a corkscrew,” he said. “We came up with a way of doing this that was very different from the way that others had been doing it for over a decade.”
Back when Kim was a research scientist at Pixar before coming to Yale, he worked with David Eberle, a Pixar senior software engineer who made use of this research for Toy Story 5.