With help from the cosmetics field, animators figure out the math of highly coiled hair
There are all types of hair—long, short, straight, curly—and today’s computer animators have a good handle on many of them. But one type, highly coiled hair, continues to vex animators. With help from a mathematical tool borrowed from the cosmetics industry, Professor Theodore Kim and Ph.D. student Alvin Shi are changing that. They present their results this month at the prestigious SIGGRAPH North America conference.
Although the field of animation has spent a considerable amount of attention on animating hair, most of the advances have been for the straight or wavy hair most common to white characters. For a long time, the general thinking within the animation field was that once straight hair had been figured out, other types of hair would simply require modifications to the basic model. As a result, very little research has been conducted on highly coiled hair common to Black people. But the properties of hair composed of tight helices, or coils, are distinct enough from smooth hair to require significantly different methods.
Kim and his research team aim to fill this gap. “We've been working on CGI for highly coiled hair for a few years now, and everything about it is hard,” said Kim, who teaches computer science and has won two Academy Awards for his animation work.
This month, they will present the methods they developed for editing the depiction of highly coiled hair in animation at the 2026 SIGGRAPH North America conference in Los Angeles. Considered the premier conference in the field of computer animation, it is attended by leaders in both academia and industry.
Kim and his collaborators aren’t new to the issue of highly coiled hair. A few years ago, they published a study on the movement of coiled hair in animation. A later study explored the geometry of coiled hair. When Kim and Shi presented this paper at the Asia edition of the conference in 2024, SIGGRAPH Asia, it was the first time the topic of Afro-textured hair had been addressed there. And when they present their new paper this month, it will be the first time the topic has appeared as a full-length technical paper at the SIGGRAPH North America conference.
His work is proving influential. Netflix Animation has adapted Kim’s research and created its own version of his approach. Animators from the streaming giant will also be presenting their work at SIGGRAPH North America.
In their latest study, Kim and his collaborators have developed editing tools that allow animators to modify highly coiled hair in all sorts of ways—expand it, shrink it, ruffle it, and generally guide it in a natural way.
“How you edit highly coiled hair is something that nobody has really looked at. Once you have something in hand, how do you edit it so that it actually does the artistic thing that you want it to?
Theodore Kim
Professor of Computer Science
“How you edit highly coiled hair is something that nobody has really looked at,” said Kim. “Once you have something in hand, how do you edit it so that it actually does the artistic thing that you want it to?”
Typically, animators use XYZ spatial coordinates to animate hair, a system of numbers to know exactly where an object belongs. But Ph.D. student Alvin Shi, the lead author on the paper, noted that when animators do that for highly coiled hair, results can often be blurry or even something that doesn’t look like hair at all. Their new method instead uses curvature (how much a strand of hair curves from a straight line) as the primary mathematical variable. It adopts a sophisticated math formula called the super-helix model.
The super-helix model was developed by one of their collaborators, Florence Bertails-Descoubes, a computer graphics expert at Université Grenoble-Alpes in France, who had also used it when she worked with the cosmetics company L’Oreal. It hasn’t been used as much in the animation industry, Kim said, partly because the math is “a little daunting.”
“So we went straight to the source and said ‘Help us understand it so that we can see if it applies to this,’” Kim said. “And then once Alvin slugged through the math with Florence, it became clear that this is the way to go.”
By knowing exactly how curvy everything is, animators can “comb” the hair, muss it up, or make other modifications, while still respecting the underlying characteristics of the original version of the hair. A.M. Darke, a professor and artist at the University of California, Santa Cruz, collaborated with the rest of the team to apply the technique on various examples of Afro-textured hair.
Shi used the mathematical model to develop a tool they call a “ruffle operator” to make realistic-looking modifications to the hair.
“You can use it to sort of muss up the hair, but always respect the original curvature of the hair. When you're successful, it looks like someone messed up their hair. Just like in real life.”
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Published Date
Jul 15, 2026
