Untangling the problem of animating tightly curled hair

Computer animators still struggle with issues like tightly curled hair, wrinkling in cloth, and how objects collide. Theodore Kim, an associate professor of computer science, and his research team have created new mathematical techniques that allow faster, stronger, and more accurate representations of these and other natural events. They will be discussed in three papers presented this week at the ACM SIGGRAPH / Eurographics Symposium on Computer Animation (SCA) by Kim and his doctoral students, Haomiao Wu and Alvin Shi.

Researchers presented a new physical model for animating curled hair, afro-textured, kinky, or Type 4 tightly. This includes its hair movement when it is stretched or bent. This study aims to keep hair types in animation studios, as there is a growing demand for a broader range of ethnic and racial representations in their stories.

Theodore Kim, who earned his second Academy Award for computer animations, said, “The closest previous work to this is the curly hair system developed for Merida in Brave, referring to the white main character of the 2012 Pixar movie, who has loosely curled hair. But we are looking at curls that are much tighter than that.” This is a coincidence since Kim and his colleagues also presented the Brave technique at the same conference ten years ago.

Advanced mathematical formulae are used to obtain the math for highly curly hair. Kim and his colleagues discovered that the math for very curly hair can actually be much simpler than that for straight hair.  They closely analyzed natural hair by purchasing wigs with curls with a radius of less than 5 millimeters and taking measurements of the curl’s tightness and the space between successive curls.

They also discussed with Professor A.M. Darke of the University of California, Santa Cruz, who is a specialist in the digital representation of tightly coiled hair. Professor Darke, a co-author of the paper, provided specific insights into the shapes and movements of the hair.

Researchers discovered that some of the math they had developed for tightly coiled hair could be applied to other phenomena, such as soda cans buckling or colliding objects.

The researcher said, “Usually, the people computing these things just see a sea of numbers, and it was hard to know what’s happening. But with our analysis methods, we can start seeing the geometric structure of what’s happening. We can gain a much better understanding of what’s going on inside all these collisions.”

Graduate student Haomiao Wu applied hair analysis to elastic rod and shell simulations, resulting in realistic collapse and buckled fencing. Alvin Shi used hair techniques to analyze collision energies, demonstrating that two bundles of ropes tensely stretch against each other correctly. Wu’s results differed from popular simulation techniques, which only contracted unconvincingly. Both papers demonstrate the potential of hair analysis in predicting real-world collisions.

He said, “If you look at the math of previous models, they’re kind of tailored for straight hair, so you can get wavy hair like on Moana, referring to the title character of the 2016 Disney film. “But if you put her side-by-side with a photo of somebody with actual afro-textured hair, it’s not close.” 

According to the researcher, It would be wonderful if their work could find its way to film studios and result in more excellent representation in the upcoming wave of animated films. Ten different curly-haired models would be fantastic to behold.

The Bungie Foundation and the National Science Foundation funded the study.

Journal Reference:

Alvin Shi, Haomiao Wu, et al. Lifted Curls: A Model for Tightly Coiled Hair Simulation. Proceedings of ACM Computer. DOI: 10.1145/3606920

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