Curly Hair Simulation using Curly Finite Elements

Abstract

Realistic simulation of curly hair is challenging due to the tight coupling between macroscopic strand deformation and high-frequency geometric details such as waves and helices. In this paper, we propose a curly hair model that decomposes each strand into curly elements, consisting of a rod-base configuration and an analytically defined high-frequency wrinkles represented by planar waves or volumetric helices, with deformation governed primarily by bending for wavy hair and twisting for spiral hair. A curvature-energy splitting scheme separates stretching, buckling, and bending contributions, and efficient energy approximations improve numerical robustness and reduce computational cost without degrading visual fidelity. We further introduce a hybrid collision handling strategy that combines coarse collision proxies for the base configuration with analytical treatment of high-frequency details, and adapt guide-strand interpolation to our curly finite-element representation to generate dense hair while preserving fine structure. Experiments demonstrate stable, efficient, and visually faithful simulation of curly hair across diverse scenarios.