Lifted Curls: A Model for Tightly Coiled Hair Simulation
Proceedings of Symposium on Computer Animation (SCA) 2023

Alvin Shi*
Haomiao Wu*
Jarred Parr
A.M. Darke
Theodore Kim
Yale University
Yale University
Yale University
University of California, Santa Cruz
Yale University
*joint first authors

Left: 200K hairs generated from 2K simulated wisps, each containing 100 vertices, naturally form a "clumped" look.
Right: 200K hairs across 8K simulated wisps produces a more "picked out" look.


We present an isotropic, hyperelastic model specifically designed for the efficient simulation of tightly coiled hairs whose curl radii approach 5 mm. Our model is robust to large bends and torsions, even when they appear at the scale of the strand discretization. The terms of our model are consistently quadratic with respect to their primary variables, do not require per-edge frames or any parallel transport operators, and can efficiently take large timesteps on the order of 1/30 of a second. Additionally, we show that it is possible to obtain fast, closed-form eigensystems for all the terms in the energy. Our eigenanalysis is sufficiently generic that it generalizes to other models. Our entirely vertex-based formulation integrates naturally with existing finite element codes, and we demonstrate its efficiency and robustness in a variety of scenarios.

    Paper [PDF, 35.7 MB]     Video [MOV, 786 MB]
     (Scroll down for YouTube)


    2K, Newton = 3
2K, Newton = 3, Slower
2K, Newton = 6
2K, Newton = 12
      4K, Newton = 3
4K, Newton = 3, Slower
4K, Newton = 6
4K, Newton = 12
      8K, Newton = 3
8K, Newton = 3, Slower
8K, Newton = 6
8K, Newton = 12
Compression Test
    DVT, 30% Compression, Unfiltered
DVT, 30% Compression, Filtered
DVT, 30% Compression, Gauss-Newton
DVT, 30% Compression, Gauss-Newton + Stretch
Lifted Curls, 30% Compression

        DVT, 40% Compression, Unfiltered
DVT, 40% Compression, Filtered
DVT, 40% Compression, Gauss-Newton
DVT, 40% Compression, Gauss-Newton + Stretch
Lifted Curls, 40% Compression
    DVT, 60% Compression, Unfiltered
DVT, 60% Compression, Filtered
DVT, 60% Compression, Gauss-Newton
DVT, 60% Compression, Gauss-Newton + Stretch
Lifted Curls, 60% Compression

        DVT, 99.999% Compression, Filtered
Lifted Curls, 99.999% Compression
Jitter Test
    DVT, 1mm jitter, Unfiltered
DVT, 1mm jitter, Filtered
DVT, 1mm jitter, Gauss-Newton
DVT, 1mm jitter, Gauss-Newton + Stretch
Lifted Curls, 1mm jitter

        DVT, 2mm jitter, Unfiltered
DVT, 2mm jitter, Filtered
DVT, 2mm jitter, Gauss-Newton
DVT, 2mm jitter, Gauss-Newton + Stretch
Lifted Curls, 2mm jitter
Lifted Curls, 5mm jitter

Straighten Test
    DVT, Unfiltered
DVT, Filtered
DVT, Gauss-Newton
DVT, Gauss-Newton + Stretch
Lifted Curls

Volumes Test
    With Bowl
Without Bowl

This work was supported by the Bungie Foundation, Adobe, the Teng and Han Family Fund, and the National Science Foundation (IIS-2132280). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.