A Hybrid Iterative Solver for Robustly Capturing Coulomb Friction in Hair Dynamics

Gilles Daviet, Florence Bertails-Descoubes, Laurence Boissieux
ACM Transactions on Graphics (Proceedings of the ACM SIGGRAPH Asia 2011 Conference)


Dry friction between hair fibers plays a major role in the collective hair dynamic behavior as it accounts for typical nonsmooth features such as stick-slip instabilities. However, due the challenges posed by the modeling of nonsmooth friction, previous mechanical models for hair either neglect friction or use an approximate smooth friction model, thus losing important visual features. In this paper we present a new generic robust solver for capturing Coulomb friction in large assemblies of tightly packed fibers such as hair. Our method is based on an iterative algorithm where each single contact problem is efficiently and robustly solved by introducing a hybrid strategy that combines a new zero-finding formulation of (exact) Coulomb friction together with an analytical solver as a fail-safe. Our global solver turns out to be very robust and highly scalable as it can handle up to a few thousand densely packed fibers subject to tens of thousands frictional contacts at a reasonable computational cost. It can be conveniently combined to any fiber model with various rest shapes, from smooth to curly. Our results, visually validated against real hair motions, depict typical hair collective effects and greatly enhance the realism of standard hair simulators.


Erratum : The original publication contained a typo in Appendix A.1, which led to an incorrect formulation of the Jacobian. This error has been fixed in the PDF available above.

Cover image

Our paper is making the front cover image of the ACM Transactions on Graphics (vol 30, issue 6) !
Corresponding images at high resolution can be downloaded below.


We are grateful to Sylvain Paris and Tilke Judd for sharing with us their video captures of hair that we have been using as reference data.