Physics-Based Animation

• Two-Pass Shock Propagation for Stable Stacking with Gauss-Seidel
• Singularity-free Twist Limit Constraints for the Ball Joint
• Rig My Ride: Automatic Rigging of Physics-based Vehicles for Games
• Real-Time Triangle-SDF Continuous Collision Detection
• FLAMEFORGE: Combustion Simulation of Wooden Structures
• Fast reconstruction of implicit surfaces using convolutional neural networks
• Representing Flow Fields with Divergence-Free Kernels for Reconstruction

Proceedings (all papers freely available): https://dl.acm.org/toc/pacmcgit/2025/8/4

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

Abhishek Madan, Nicholas Sharp, Francis Williams, Ken Museth, David I.W. Levin

We present a novel stochastic version of the Barnes-Hut approximation. Regarding the level-of-detail (LOD) family of approximations as control variates, we construct an unbiased estimator of the kernel sum being approximated. Through several examples in graphics applications such as winding number computation and smooth distance evaluation, we demonstrate that our method is well-suited for GPU computation, capable of outperforming a GPU-optimized implementation of the deterministic Barnes-Hut approximation by achieving equal median error in up to 9.4x less time.

Stochastic Barnes-Hut Approximation for Fast Summation on the GPU

Alvin Shi, Haomiao Wu, Theodore Kim

We present a method for simulating deformable bodies in four spatial dimensions. To accomplish this, we generalize several pieces of the traditional simulation pipeline. Starting from the meshing stage, we propose a simple method for generating a pentachoral mesh, the 4D analog of a tetrahedral mesh. Next, we show how to generalize the deformation invariants, allowing us to construct 4D hyperelastic energies that lead directly to hyper-dimensional deformation forces. Finally, we formulate collision detection and response in 4D. Our eigenanalyses of the resulting deformation and collision energies generalize to arbitrarily higher dimensions. The resulting simulations display a variety of previously unseen visual phenomena.

Hyper-Dimensional Deformation Simulation

Tao Huang, Haoyang Shi, Mengdi Wang*, Yuxing Qiu, Yin Yang, Kui Wu

The knit structure consists of interlocked yarns, with each yarn comprising multiple plies comprising tens to hundreds of twisted fibers. This intricate geometry and the large number of geometric primitives present substantial challenges for achieving high-fidelity simulation and rendering in real-time applications. In this work, we introduce the first real-time framework that takes an animated stitch mesh as input and enhances it with yarn-level simulation and fiber-level rendering. Our approach relies on a knot-based representation to model interlocked yarn contacts. The knot positions are interpolated from the underlying mesh, and associated yarn control points are optimized using a physically inspired energy formulation, which is solved through a GPU-based Gauss-Newton scheme for real-time performance. The optimized control points are sent to the GPU rasterization pipeline and rendered as yarns with fiber-level details. In real-time rendering, we introduce several decomposition strategies to enable realistic lighting effects on complex knit structures, even under environmental lighting, while maintaining computational and memory efficiency. Our simulation faithfully reproduces yarn-level structures under deformations, e.g., stretching and shearing, capturing interlocked yarn behaviors. The rendering pipeline achieves near-ground-truth visual quality while being 120,000x faster than path tracing reference with fiber-level geometries. The whole system provides real-time performance and has been evaluated through various application scenarios, including knit simulation for small patches and full garments and yarn-level relaxation in the design pipeline.

Real-Time Knit Deformation and Rendering

Jiahao Wen, Jernej Barbič, Danny M. Kaufman

We propose a coupled mesh-adaptation model and physical simulation algorithm to jointly generate, per timestep, optimal adaptive remeshings and implicit solutions for the simulation of frictionally contacting elastodynamics. To do so, we begin with Ferguson et al.’s [2023] recently developed in-timestep remeshing (ITR) framework, which proposes an Incremental Potential based objective for mesh refinement, and a corresponding, locally greedy remeshing algorithm to minimize it. While this initial ITR framework demonstrates significant improvements, its greedy remeshing does not generate optimal meshes, and so does not converge to improving physical solutions with increasing mesh resolution. In practice, due to lack of optimality, the original ITR framework can and will find mesh and state solutions with unnecessarily low-quality geometries and corresponding physical solution artifacts. At the same time, we also identify additional fundamental challenges to adaptive simulation in terms of both ITR’s original remeshing objective and its corresponding optimization problem formulation. In order to extend the ITR framework to high-quality, optimal in-timestep remeshing, we first construct a new remeshing objective function built from simple, yet critical, updates to the Incremental Potential energy, and a corresponding constrained model problem, whose minimizers provide locally optimal remeshings for physical problems. We then propose a new in-timestep remeshing optimization that jointly solves, per-timestep, for a new locally optimal remeshing and the next physical state defined upon it. To evaluate and demonstrate our extension of the ITR framework, we apply it to the optimal r-adaptive ITR simulation of frictionally contacting elasto-dynamics and statics. To enable r-adaptivity we additionally propose a new numerical method to robustly compute derivatives of the L2-projection operator necessary for optimal mesh-to-mesh state mappings within solves, a constraint model to enable on-boundary node adaptivity, and an efficient Newton-type optimization method for practically solving each per-timestep r-adaptive ITR solution. We extensively evaluate our method on challenging large-deformation and frictionally contacting scenarios. Here we observe optimal r-adaptivity captures comparable and better accuracy than unadapted meshes orders-of-magnitude larger, with corresponding significant advantages in both computation speedup and decrease in memory usage.

Optimal r-Adaptive In-Timestep Remeshing for Elastodynamics

Siyuan Shen, Tianjia Shao, Kun Zhou, Chenfanfu Jiang, Sheldon Andrews, Victor Zordan, Yin Yang

We present a framework of elastic locomotion, which allows users to enliven an elastic body to produce interesting locomotion by prescribing its high-level kinematics. We formulate this problem as an inverse simulation problem and seek the optimal muscle activations to drive the body to complete the desired actions. We employ the interior-point method to model wide-area contacts between the body and the environment with logarithmic barrier penalties. The core of our framework is a mixed second-order differentiation algorithm. By combining both analytic differentiation and numerical differentiation modalities, a general-purpose second-order differentiation scheme is made possible. Specifically, we augment complex-step finite difference (CSFD) with reverse automatic differentiation (AD). We treat AD as a generic function, mapping a computing procedure to its derivative w.r.t. output loss, and promote CSFD along the AD computation. To this end, we carefully implement all the arithmetics used in elastic locomotion, from elementary functions to linear algebra and matrix operation for CSFD promotion. With this novel differentiation tool, elastic locomotion can directly exploit Newton’s method and use its strong second-order convergence to find the needed activations at muscle fibers. This is not possible with existing first-order inverse or differentiable simulation techniques. We showcase a wide range of interesting locomotions of soft bodies and creatures to validate our method.

Elastic Locomotion with Mixed Second-order Differentiation