Month: July 2025

Jiayi Eris Zhang, Doug L. James, Danny M. Kaufman

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.

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

Federico Sichetti, Enrico Puppo, Zizhou Huang, Marco Attene, Denis Zorin, Daniele Panozzo

Many problems in computer graphics can be formulated as finding the
global minimum of a function subject to a set of non-linear constraints
(Minimize), or finding all solutions of a system of non-linear constraints
(Solve). We introduce MiSo, a domain-specific language and compiler for
generating efficient C++ code for low-dimensional Minimize and Solve
problems, that uses interval methods to guarantee conservative results while
using floating point arithmetic. We demonstrate that MiSo-generated code
shows competitive performance compared to hand-optimized codes for
several computer graphics problems, including high-order collision detection
with non-linear trajectories, surface-surface intersection, and geometrical
validity checks for finite element simulation.

MiSo: A DSL for Robust and Efficient SOLVE and MINIMIZE Problems

Siyuan Chen, Yixin Chen, Jonathan Panuelos, Otman Benchekroun, Yue Chang, Eitan Grinspun, Zhecheng Wang

We present a novel reduced-order fluid simulation technique leveraging Dynamic Mode Decomposition (DMD) to achieve fast, memory-efficient, and user-controllable subspace simulation. We demonstrate that our approach combines the strengths of both spatial reduced order models (ROMs) as well as spectral decompositions. By optimizing for the operator that evolves a system state from one timestep to the next, rather than the system state itself, we gain both the compressive power of spatial ROMs as well as the intuitive physical dynamics of spectral methods. The latter property is of particular interest in graphics applications, where user control of fluid phenomena is of high demand. We demonstrate this in various applications including spatial and temporal modulation tools and fluid upscaling with added turbulence. We adapt DMD for graphics applications by reducing computational overhead, incorporating user-defined force inputs, and optimizing memory usage with randomized SVD. The integration of OptDMD and DMD with Control (DMDc) facilitates noise-robust reconstruction and real-time user interaction. We demonstrate the technique’s robustness across diverse simulation scenarios, including artistic editing, time-reversal, and super-resolution. Through experimental validation on challenging scenarios, such as colliding vortex rings and boundary-interacting plumes, our method also exhibits superior performance and fidelity with significantly fewer basis functions compared to existing spatial ROMs. Leveraging the inherent linearity of the DMD formulation, we demonstrate a range of diverse applications. This work establishes another avenue for developing real-time, high-quality fluid simulations, enriching the space of fluid simulation techniques in interactive graphics and animation.

Fast Subspace Fluid Simulation With A Temporally-Aware Basis

Guirec Maloisel, Ruben Grandia, Christian Schumacher, Espen Knoop, Moritz Bächer

We present a constrained Rigid Body Dynamics (RBD) that guarantees satisfaction of kinematic constraints, enabling direct simulation of complex mechanical systems with arbitrary kinematic structures. We present a constrained Rigid Body Dynamics (RBD) that guarantees satisfaction of kinematic constraints, enabling direct simulation of complex mechanical systems with arbitrary kinematic structures. To ensure constraint satisfaction, we use an implicit integration scheme. For this purpose, we derive compatible dynamic equations expressed through the quaternion time derivative, adopting an additive approach to quaternion updates instead of a multiplicative one, while enforcing quaternion unit-length as a constraint. We support all joints between rigid bodies that restrict subsets of the three translational or three rotational degrees of freedom, including position- and force-based actuation. Their constraints are formulated such that Lagrange multipliers are interpretable as joint forces and torques. We discuss a unified solution strategy for systems with redundant constraints, overactuation, and passive degrees of freedom, by eliminating redundant constraints and navigating the subspaces spanned by multipliers. As our method uses a standard additive update, we can interface with unconditionally-stable implicit integrators. Moreover, the simulation can readily be made differentiable as we show with examples.

A Versatile Quaternion-based Constrained Rigid Body Dynamics