Average Vector Field Integration for St. Venant-Kirchhoff Deformable Models

Junior Rojas
University of Utah
Tiantian Liu
University of Pennsylvania
Ladislav Kavan
University of Utah

The Average Vector Field (AVF) method approximates ground truth motion trajectories with straight lines (left). We propose an implicit integration scheme based on AVF which exactly conserves energy for St. Venant-Kirchhoff materials. Compared to backward Euler, our method does not introduce numerical damping and corresponding loss of details (middle). Compared to implicit midpoint and Newmark methods, our method avoids explosions even with large time steps and long simulation runs (right).


We propose Average Vector Field (AVF) integration for simulation of deformable solids in physics-based animation. Our method achieves exact energy conservation for the St. Venant-Kirchhoff material without any correction steps or extra parameters. Exact energy conservation implies that our resulting animations 1) cannot explode and 2) do not suffer from numerical damping, which are two common problems with previous numerical integration techniques. Our method produces lively motion even with large time steps as typically used in physics-based animation. Our implicit update rules can be formulated as a minimization problem and solved in a similar way as optimization-based backward Euler, with only a mild computing overhead. Our approach also supports damping and collision response models, making it easy to deploy in practical computer animation pipelines.


Junior Rojas, Tiantian Liu, Ladislav Kavan. Average Vector Field Integration for St. Venant-Kirchhoff Deformable Models. IEEE Transactions on Visualization and Computer Graphics, 2018.  

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We would like to thank Bernhard Thomaszewski and Eftychios Sifakis for the valuable discussions, Petr Kadlecek for his help with rendering and Jing Li for her help generating our simulation examples. This material is based upon work supported by the National Science Foundation under Grant Numbers IIS-1617172 and IIS-1622360. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. We also gratefully acknowledge the support of Activision.