Complementary Dynamics SIGGRAPH ASIA 2020

Jiayi Eris Zhang, Seungbae Bang, David I.W. Levin, Alec Jacobson

University of Toronto
Animation artists use low-dimensional rigs to control the primary motion of their characters. Our displacement filtering optimization adds elastodynamic secondary effects orthogonal to the rig’s subspace, ensuring that interesting effects emerge but do not compete with or undo the artist’s original animation.


We present a novel approach to enrich arbitrary rig animations with elastodynamic secondary effects. Unlike previous methods which pit rig displacements and physical forces as adversaries against each other, we advocate that physics should complement artists’ intentions. We propose optimizing for elastodynamic displacements in the subspace orthogonal to displacements that can be created by the rig. This ensures that the additional dynamic motions do not undo the rig animation. The complementary space is high dimensional, algebraically constructed without manual oversight, and capable of rich high-frequency dynamics. Unlike prior tracking methods, we do not require extra painted weights, segmentation into fixed and free regions or tracking clusters. Our method is agnostic to the physical model and plugs into non-linear FEM simulations, geometric as-rigid-as-possible energies, or mass-spring models. Our method does not require a particular type of rig and adds secondary effects to skeletal animations, cage-based deformations, wire deformers, motion capture data, and rigid-body simulations.




  title = {Complementary Dynamics},
  author = {Jiayi Eris Zhang and Seungbae Bang and David I.W. Levin and Alec Jacobson},
  year = {2020},
  journal = {ACM Transactions on Graphics},


This work is funded in part by NSERC Discovery (RGPIN–2017–05524, RGPIN-2017–05235, RGPAS–2017–507938, RGPAS–2017–507909), Connaught Fund (503114), CFI-JELF Fund, New Frontiers of Research Fund (NFRFE–201), the Ontario Early Research Award program, the Canada Research Chairs Program, the Fields Centre for Quantitative Analysis and Modelling and gifts by Adobe Systems, Autodesk and MESH Inc. We especially thank Paul Kry for hosting the 2018 Bellairs workshop on Computer Animation and the attendees for inspiring initial project ideas. We thank Otman Benchekroun, Rinat Abdrashitov and Josh Holinaty for proofreading; John Hancock for the IT support; anonymous reviewers for their helpful comments and suggestions.