Progressive Dynamics++: A Framework for Stable, Continuous, and Consistent Animation Across Resolution and Time

Jiayi Eris Zhang1,2, Doug L. James2, Danny M. Kaufman1

1Adobe Research, 2Stanford University

ACM Transactions on Graphics (SIGGRAPH 2025)
Designing a five-hat-trick animation with Progressive Dynamics: Tossing a floppy hat onto a coat rack is hard, but adjusting initial conditions to successfully throw five hats is nearly impossible when using slow-to-compute, direct, fine-level simulations, due to tricky dynamics, sensitive collisions, and frictional contact. However, using our new Progressive Dynamics++ framework we can quickly explore a large number of coarse preview simulations (Left) to rapidly find a sample that makes the toss work. Once we find this rare, needle-in-a-haystack scenario, with our coarse simulation (Level 0), where all the hats magically fit and delicately settle on the hooks and one another, Progressive Dynamics++ then progressively (Levels 1-3) synthesizes production-level animations with millions of fine-scale vertices, capturing intricate physical details and, most importantly, maintaining consistent five-hat-trick outcomes.

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Abstract

The recently developed Progressive Dynamics framework [Zhang et al. 2024] addresses the long-standing challenge in enabling rapid iterative design for high-fidelity cloth and shell animation. In this work, we identify fundamental limitations of the original method in terms of stability and temporal continuity. For robust progressive dynamics simulation we seek methods that provide: (1) stability across all levels of detail (LOD) and timesteps, (2) temporally continuous animations without jumps or jittering, and (3) user-controlled balancing between geometric consistency and enrichment at each timestep, thereby making it a practical previewing tool with high-quality results at the finest level to be used as the final output.
We propose a general framework, Progressive Dynamics++, for constructing a family of progressive dynamics integration methods that advance physical simulation states forward in both time and spatial resolution, which includes Zhang et al. [2024]'s method as one member. We analyze necessary stability conditions for Progressive Dynamics integrators and introduce a novel, stable method that significantly improves temporal continuity, supported by a new quantitative measure. Additionally, we present a quantitative analysis of the trade-off between geometric consistency and enrichment, along with strategies for balancing between these aspects in transitions across resolution and time.
Happy Face Balloons with Detailed Enrichment: In this high-speed collision scenario, two character balloons entangle and detangle under extreme deformation. Using a 4-level hierarchy, the VelPro integration method in the Progressive Dynamics++ framework captures increasingly intricate wrinkles across levels while preserving consistent deformation, timing, and trajectories.

BibTeX

@article{zhang2025progressive,
  title={Progressive Dynamics++: A Framework for Stable, Continuous, and
    Consistent Animation Across Resolution and Time},
  author={Zhang, Jiayi Eris and James, Doug L. and Kaufman, Danny M.},
  journal={ACM Transactions on Graphics (TOG)},
  volume={44},
  number={4},
  pages={1--20},
  year={2025},
  publisher={ACM New York, NY, USA}
}

Supplemental Video (5 mins)

Coming soon!

Acknowledgements

Jiayi Eris Zhang is supported by the Stanford Graduate Fellowship, the Roblox Graduate Fellowship, and the NVIDIA Graduate Fellowship. Doug James acknowledges support from Adobe, SideFX, NVIDIA, and the Department of Energy, National Nuclear Security Administration under Award Number DE-NA0003968; Houdini software courtesy of SideFX. We thank Zhenyuan Zhang for insightful discussions and for proofreading all the appendix proofs.