Curly Hair Simulation using Curly Finite Elements

2026-07-24

AI Summary

This work addresses the significant challenge of simulating realistic curly hair, where macroscopic deformations are tightly coupled with high-frequency geometric details such as waves and spirals. The authors propose a coiled finite element representation that models each hair strand as a rod-like base augmented with analytically defined high-frequency wrinkles, whose deformation is governed primarily by bending or twisting. To enhance numerical stability, they introduce a curvature energy splitting strategy that decouples stretching, buckling, and bending energies. Combined with a hybrid collision handling scheme and guide-hair-based interpolation, the method efficiently generates dense, structurally intricate curls. The approach achieves stable, visually plausible simulations across diverse scenarios while balancing computational efficiency and geometric fidelity.

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.

Problem

• curly hair
• hair simulation
• geometric details
• macroscopic deformation
• high-frequency wrinkles

Innovation

• curly finite elements
• curvature-energy splitting
• hybrid collision handling
• analytical high-frequency details
• guide-strand interpolation