Curly Hair Simulation using Curly Finite Elements

Curly hair remains one of the nastier problems in character simulation because the visible shape depends on both large-scale strand motion and tiny repeating structure. Curly Finite Elements tackles that by representing each strand as a base rod plus analytically defined wrinkles: planar waves for wavy hair and volumetric helices for spiral hair. In practice, that means the solver can treat bending and twisting differently depending on the curl type instead of trying to brute-force every loop in the strand.

The method also introduces a curvature-energy splitting scheme that separates stretching, buckling, and bending, along with cheaper energy approximations to improve robustness and cut compute cost. That combination is aimed at the usual pain points in hair simulation: instability, expensive solves, and detail loss when you simplify too aggressively. For teams shipping real-time or near-real-time character work, the appeal is obvious: better-looking curls without turning the groom into a simulation budget sink.

Collision handling is another practical piece. The system uses coarse collision proxies for the base configuration while handling the high-frequency detail analytically, which is a sensible way to keep curls from exploding without paying full geometric collision costs everywhere. It also adapts guide-strand interpolation to the curly finite-element representation so dense hair can be generated while keeping the fine structure intact.

The work was submitted to arXiv on July 24, 2026 by Xinming Pei, Zhendong Wang, Lei Lan, Weiwei Xu, Yin Yang, and Huamin Wang....