Yale computer scientists discover new visualization methods for Afro-textured hair on the screen

Courtesy of Haomiao Wu, Alvin Shi, A.M. Darke, and Theodore Kim

When Theodore Kim was in high school, he watched “Jurassic Park” and “Toy Story,” which motivated him to work at the intersection of art and technology. 

Recently, he has led Yale researchers towards discovering new visualization methods for Afro-textured hair, which deepened his commitment to innovating computational methods for rendering diverse characters. 

Kim co-authored “Curly-Cue: Geometric Methods for Highly Coiled Hair” with Haomiao Wu GRD ’27 and Alvin Shi GRD ’27, fourth-year doctoral students in his laboratory, alongside A.M. Darke, assistant professor of Digital Arts and New Media at the University of Santa Cruz, California. The manuscript is set to be presented on Dec. 3-6 at SIGGRAPH Asia, a computer graphics conference held annually, this year in Tokyo, Japan. 

Wu and Shi introduced new mathematical solutions for visualizing Afro-textured hair on the screen –– solving long-standing difficulties with the heavy computational load that rendering so many complex helices has posed in the past, which has been an obstacle to proper animation of characters of color on the big screen. “Curly-Cue” specifically focuses on hair geometry, solving physical simulation problems of interactions between hundreds of thousands of helices. 

While many computer graphics researchers consider hair texture a solved problem, Kim gestures to this as a symptom of a larger tendency in science to ignore underrepresented populations in favor of proclaiming rapid progress in scientific research. 

“Social assumptions become baked into, and hidden, in the math of our everyday algorithms,” Kim said. “Prior to our work, others in the field considered the problem of hair to be ‘solved,’ when in fact there had only been progress on the topic of straight hair.” 

Translating these low-frequency parabola models used for straight hair to a high-frequency helix, needed to render curly hair, has been a computational issue dominantly ignored by researchers, Kim said. 

Type 4 curls, which “Curly-Cue” focuses on, contain hundreds of thousands of helices that bounce and glide against the air, skin and other strands –– a problem that can cause inadequate visualization programs to crash, causing animators to rely on less realistic rendering methods.

Kim, whose previous work has been seen in “Harry Potter and the Sorcerer’s Stone” and “Coco,” noted the difficulty of translating academic work into industry. Over the years, research geared toward visualizing Afro-textured hair has specifically not received much attention.

“It’s this computationally intensive method of figuring out twist forces associated with highly twisted and coily hairs,” Shi said. “Trying to scale that up to a full head makes it really slow. We’re interested in [making] a simulator that can handle this in a reasonable timescale.” 

Not only do animations move more slowly, but there may be simply inadequate memory to hold the amount of data underlying previous models. 

As a result, animations of Black characters may look less realistic. A straight-haired boy running around in animation would be rendered with dynamic and complex hair motion, Shi noted, but a boy with an afro may not be. 

Since 2023, Wu and Shi have repeatedly developed and tested new mathematical models for representing these helices; Shi said some of these simulations required over 17 computationally intensive iterations, each taking days to render. 

This new paper’s model involves three components: phase-locking, in which wave-based signals are condensed into discrete steps; switchbacks, in which perversions are generated in a helix; and period skipping, in which a single strand of hair can break away from its parent curl, all based on high-resolution physics simulation. 

Kim’s two Academy Awards in science and technology arrived in 2023 and 2012 –– the first for his work on Fizt2, an elastic simulation system he helped design as a senior research scientist at Pixar, and the second for his work on Wavelet Turbulence, which increased the realism of fires and explosions. Much of Kim’s work now focuses on counteracting racial biases in the computer graphics industry. 

Wu and Shi previously published a precursor paper to “Curly-Cue” called “Lifted Curls: A Model for Tightly Coiled Hair Simulation” in 2023 — a computational method for simulating individual Type 4 curls arising from a spherical head, but without considering the geometry of interactions between strands with as much nuance as the present paper. 

Having now simulated between-strand interactions, the team may now investigate the simulation of hairstyles next — informed by their collaborations with other artists, like Professor Darke, who runs the Open Source Afro Hair Library, a three-dimensional model database for Black hair textures and styles. 

“Artists care more about the look,” Wu said. Darke’s guidance pointed to when things “just look[ed] wrong,” Kim noted. 

Kim said that the film industry is fickle with its demands, but there are moments in which novel methods will be incorporated into the big screen. He expressed hope that the laboratory’s work will combat claims about the universality of who modern technology serves. 

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