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

TL;DR

The paper introduces Augmented Mass-Spring (AMS), a real-time dense hair simulation framework that augments traditional mass-spring systems with a ghost rest-shape and a biphasic, one-way coupling to stabilize global hair structure while preserving local dynamics. A two-stage hybrid Eulerian/Lagrangian integration scheme handles hair interactions, enabling robust hair–hair and hair–solid collisions with reduced computational cost. AMS achieves high-fidelity, real-time performance for thousands of strands (e.g., up to $14{,}718$ strands at $67$ FPS, $7{,}528$ at $156$ FPS, and $10{,}298$ at $114$ FPS) on consumer GPUs and supports interactive grooming and facial-tracking integration. Compared to DER-based or neural approaches, AMS offers improved stability, global feature preservation, and non-Hookean behavior modeling, making high-quality dense hair simulation feasible for games and interactive media.

Abstract

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/.

Figures (15)

• Figure 1: Integrating video-based facial tracking deng2019retinaface with our real-time hair simulation enables the control of digital avatars with dynamic and coherent hair motion.
• Figure 1: Schematic representation of the tetrahedra formed between consecutive real particles (left), and the additional real-ghost interaction in our formulation (right). The angular one-way force enhances stability by preventing tetrahedron collapse when particles deviate from their original dihedral angles.
• Figure 2: Schematic of a hair strand: initially discretized with particles (left); built as MS (middle) with edge (green), bending (blue), torsion (red), ghost (blue/purple), and altitude (yellow) springs; and as our AMS (right), using a ghost rest-shape (dotted circles) and one-way biphasic springs (purple outline). MS requires $2N{-}1$ coupled particles; AMS only uses $N$. Right: deviations from rest-shape are handled via integrity springs ($\kappa_I$) based on point distance, and angular springs ($\kappa_\alpha$) based on angle distance $d\theta$, forming biphasic links to the ghost.
• Figure 2: Parametrization plot for incorporating non-Hookean responses in the $T_{I}$ term of the biphasic coupling.
• Figure 3: Simulated rest-shape of a single strand using our model and MS. Starting from a given configuration, our method preserves the global features by setting $\kappa_{L} = 10^{7}$ N${\text{m}^{-1}}$, $\kappa_{\alpha} = 0$ N${\text{rad}^{-1}}$, and $\kappa_{I} = 10^{2}$ N${\text{m}^{-1}}$, while in MS, the shape is not maintained even as $\kappa_{L}$ increases, eventually leading to instability.