# Augmented Mass-Spring model for Real-Time Dense Hair Simulation

arXiv: https://arxiv.org/abs/2412.17144 · HTML: https://mlsanity.com/paper/2412.17144/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Dec 2024.

## Built on by (most cited first, 3 of 3)

- [HairFormer: Transformer-Based Dynamic Neural Hair Simulation](https://mlsanity.com/paper/2507.12600/) (2025)
- [Detangled: A Framework for Creating, Editing, and Inferencing Feature Rich Hair Strands](https://mlsanity.com/paper/2607.09811/) (2026)
- [Head Avatars with Dynamic Explicit Hair](https://mlsanity.com/paper/2607.23861/) (2026)

## Abstract (arXiv)

We propose a novel Augmented Mass-Spring (AMS) model for real-time simulation of dense hair at strand level. Our approach considers the traditional edge, bending, and torsional degrees of freedom in mass-spring systems, but incorporates an additional one-way biphasic coupling with a ghost rest-shape configuration. Trough multiple evaluation experiments with varied dynamical settings, we show that AMS improves the stability of the simulation in comparison to mass-spring discretizations, preserves global features, and enables the simulation of non-Hookean effects. Using an heptadiagonal decomposition of the resulting matrix, our approach provides the efficiency advantages of mass-spring systems over more complex constitutive hair models, while enabling a more robust simulation of multiple strand configurations. Finally, our results demonstrate that our framework enables the generation, complex interactivity, and editing of simulation-ready dense hair assets in real-time. More details can be found on our project page: https://agrosamad.github.io/AMS/.