Physics-Based Animation

Xingyu Ni, Jingrui Xing, Xingqiao Li, Bin Wang, Baoquan Chen

Accurately reconstructing continuous flow fields from sparse or indirect measurements remains an open challenge, as existing techniques often suffer from oversmoothing artifacts, reliance on heterogeneous architectures, and the computational burden of enforcing physics-informed losses in implicit neural representations (INRs). In this paper, we introduce a novel flow field reconstruction framework based on divergence-free kernels (DFKs), which inherently enforce incompressibility while capturing fine structures without relying on hierarchical or heterogeneous representations. Through qualitative analysis and quantitative ablation studies, we identify the matrix-valued radial basis functions derived from Wendland’s polynomial (DFKs-Wen4) as the optimal form of analytically divergence-free approximation for velocity fields, owing to their favorable numerical properties, including compact support, positive definiteness, and second-order differentiability. Experiments across various reconstruction tasks, spanning data compression, inpainting, super-resolution, and time-continuous flow inference, have demonstrated that DFKs-Wen4 outperform INRs and other divergence-free representations in both reconstruction accuracy and computational efficiency, while requiring the fewest trainable parameters.

Representing Flow Fields with Divergence-Free Kernels for Reconstruction

Joël Pelletier-Guénette, Alexandre Mercier-Aubin, Sheldon Andrews

We introduce an efficient solution to the problem of continuous collision detection (CCD) between triangle geometry and signed distance fields (SDFs). We formulate the triangle-SDF collision problem as a novel spatio-temporal local optimization that solves for the first time of impact between a triangle and an SDF isosurface. Our method offers improved robustness over point sampling methods, and outperforms recent triangle-SDF discrete collision detection (DCD) algorithms. Furthermore, a novel method for adaptively refining the potential collision points on large triangles is proposed for robust triangle-SDF collision detection with coarse meshes. This enables the use of reduced geometry for efficient simulations. We demonstrate the benefits of our approach by comparing to state-of-the-art algorithms for triangle-SDF collision detection, and showcase its effectiveness through simulations involving complex collision scenarios.

Real-Time Triangle-SDF Continuous Collision Detection

Melissa Katz, Paul G. Kry, Sheldon Andrews

We extend the concept of traditional rigging, which links polygonal meshes to an underlying skeleton for 3D characters, to the creation of physics-based wheeled vehicle models directly from surface geometry. Unlike character rigging, physics-based rigging involves assigning joints and collision proxies to animate the surface geometry. We present an automated pipeline that transforms a polygon soup into a physics-based, multi-wheeled vehicle model. The pipeline begins by using text-driven 2D image segmentation to identify vehicle components, which are then mapped onto the 3D mesh. A rough estimate of collision geometries and joint parameters is then used to initialize a rigid body simulation of the vehicle. Then, a numerical optimization refines these parameters in order to produce more realistic vehicle behaviour. The final result is a functioning physics-based vehicle for real-time simulations, which is demonstrated across a variety of vehicles, including cars, tricycles, lunar rovers, and even a semi-truck with 10 wheels.

Rig My Ride: Automatic Rigging of Physics-based Vehicles for Games

• 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