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YSM Issue 96.3

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FOCUS<br />

Computer Science<br />

REPRESENTATION<br />

IN ANIMATION<br />

Computer Science<br />

Captures The Physics<br />

of Afro-Textured Hair<br />

BY ABIGAIL JOLTEUS<br />

PHOTOGRAPH COURTESY OF FAREED SALMON<br />

In the past, in computer animation, many Black characters would<br />

have poorly animated braids, or more frequently, just have<br />

straight hair. For years, computer animations would use these<br />

inaccurate representations of tightly coiled hair, also known as afrotextured<br />

hair. Recently, as more people of color have been hired and<br />

cast for animation roles, the animation industry has moved towards<br />

becoming more diverse and inclusive than ever before.<br />

However, this increase in diversity did not translate into more<br />

accurate animation of afro-textured hair. “The way that hair<br />

has been simulated, at least since the ‘90s, has been many line<br />

segments chained together, and making them small enough gives<br />

a smooth appearance,” said Theodore Kim, an associate professor<br />

of computer science at Yale. Animating hair is achieved through<br />

various mathematical equations where the twists of each strand<br />

must be carefully simulated for accurate hair motion. “Therefore,<br />

when a character shakes their head, you can see realistic movement,”<br />

Kim said. However, this process only works for the overwhelming<br />

majority of animated characters who are white and have straight<br />

hair. “The trouble appears with the physics equations selected for<br />

simulation,” he said.<br />

A team of computer scientists at Yale have created a novel<br />

physical model that allows for more accurate animation of tightly<br />

coiled hair, more realistically capturing the way it looks and moves.<br />

“We were concerned with three different types of elastic energy<br />

for hair: stretching, bending, and twisting energies,” said Haomiao<br />

Wu, one of the lead researchers on the project. “These energies<br />

constrain how the strands behave in an elastic way. We proposed<br />

a different set of those three energies for a model so that it is more<br />

stable.” In other words, they wanted to capture the true essence of<br />

afro-textured hair using sophisticated mathematical modeling.<br />

Their isotropic, hyperelastic model was specifically designed for<br />

better simulation of tightly coiled hair. “Isotropic means that no<br />

matter the direction, the restorative force is the same,” said Alvin<br />

Shi, another one of the lead researchers on the study. Restorative<br />

force is the force needed for an object to return to its initial size<br />

and shape. In this case, it enables a hair strand to return to its initial<br />

coiled state, which better captures afro-textured hair. This model is<br />

also faster, simpler, and more robust than previous models.<br />

The researchers devised this model by discarding the previous<br />

assumption for mathematical equations to simulate the curling<br />

pattern of each strand and instead consider large bends and<br />

torsions, as well as assuming, to a certain extent, that the hair is<br />

non-straight. While this model was designed for kinky, curly, or<br />

coily hair, the researchers discovered that it is also effective for<br />

straight hair.<br />

As with all simulations, there are flaws. Some of these limitations<br />

include the scaling behavior of tight, coily hair and lack of variation<br />

in how the hair can look. Currently, the model can account for only<br />

two different appearances of afro-textured hair: a clumped look,<br />

well-defined curls, and a more picked-out look, or fluffed-out<br />

afro-textured hair. By decreasing the radius of a wisp—a clump of<br />

hair strands common in afro-textured hair—but keeping the same<br />

total number of hair strands, a more picked-out look is obtained.<br />

However, these looks are not incredibly realistic compared to reallife<br />

individuals with the same hair type. “We are looking to improve<br />

on the realistic aspect of our model,” Shi said.<br />

For the next steps, the researchers plan to conduct further<br />

experiments with the realism of the simulated hair and possibly test<br />

an anisotropic model, meaning the pattern is different in various<br />

directions, which could lead to better animations of different<br />

hairstyles with afro-textured hair.<br />

While no animated content or games are perfect, it is important<br />

that Black individuals see themselves adequately represented in<br />

the media that they consume. As the creators of one of the first<br />

models specifically for tight, coily hair, the team also hopes that<br />

other researchers will be inspired to conduct similar research. “We<br />

are looking forward to seeing more and more research in this field,<br />

not just from us but other researchers as well,” Wu said. Ultimately,<br />

they want their model to lead to greater and better racial and ethnic<br />

representation in animated games and movies. “It might take<br />

longer than we wish for these techniques to be implemented, but<br />

we are hoping as soon as possible,” Wu said. ■<br />

10 Yale Scientific Magazine September 2023 www.yalescientific.org

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