Physics-Based Animation

Lixin Ren, Xiaowei He, Shusen Liu, Yuzhong Guo, Enhua Wu

Prior research has demonstrated the efficacy of balanced trees as spatially adaptive grids for large-scale simulations. However, state-of-the-art methods for balanced tree construction are restricted by the iterative nature of the ripple effect, thus failing to fully leverage the massive parallelism offered by modern GPU architectures. We propose to reframe the construction of balanced trees as a process to merge N -balanced Minimum Spanning Trees (N -balanced MSTs) generated from a collection of seed points. To ensure optimal performance, we propose a stack-free parallel strategy for constructing all internal nodes of a specified N -balanced MST. This approach leverages two 32-bit integer registers as buffers rather than relying on an integer array as a stack during construction, which helps maintain balanced workloads across different GPU threads. We then propose a dynamic update algorithm utilizing refinement counters for all internal nodes to enable parallel insertion and deletion operations of N -balanced MSTs. This design achieves significant efficiency improvements compared to full reconstruction from scratch, thereby facilitating fluid simulations in handling dynamic moving boundaries. Our approach is fully compatible with GPU implementation and demonstrates up to an order-of-magnitude speedup compared to the state-of-the-art method [Wang et al. 2024]. The source code for the paper is publicly available at https://github.com/peridyno/peridyno.

A Stack-Free Parallel ℎ-Adaptation Algorithm for Dynamically Balanced Trees on GPUs

Cuncheng Zhu, Hang Yin, Albert Chern

We present a vorticity method for simulating incompressible viscous flows on curved surfaces governed by the Navier–Stokes equations. Unlike previous approaches, our formulation incorporates the often-overlooked Gaussian-curvature-dependent term in the viscous force, which influences both the vorticity equation and the evolution of harmonic components. We show that these curvature-related terms are crucial for reproducing physically correct fluid behavior. We introduce an implicit–explicit (IMEX) scheme for solving the resulting system on triangle meshes and demonstrate its effectiveness on surfaces with arbitrary topology, including non-orientable surfaces, and under a variety of boundary conditions. Our theoretical contributions include several explicit formulas: a vorticity jump condition across curvature sheets, a geometric correspondence between friction coefficients and boundary curvature adjustments, and the influence of boundary curvature on harmonic modes. These results not only simplify the algorithmic design but also offer geometric insight into curvature-driven fluid phenomena, such as the emergence of the Kutta condition under free-slip boundaries.

Viscous Vortex Dynamics on Surfaces

Daoming Liu, Jonathan Klein, Florian Rist, Wojtek Pałubicki, Sören Pirk, Dominik L. Michels

We propose a unified volumetric combustion simulator that supports general wooden structures capturing the multi-phase combustion of charring materials. Complex geometric structures can conveniently be represented in a voxel grid for the effective evaluation of volumetric effects. In addition, a signed distance field is introduced to efficiently query the surface information required to compute the insulating effect caused by the char layer. Non-charring materials such as acrylic glass or non-combustible materials such as stone can also be modeled in the simulator. Adaptive data structures are utilized to enable memory-efficient computations within our multiresolution approach. The simulator is qualitatively validated by showcasing the numerical simulation of a variety of scenes covering different kinds of structural configurations and materials. Two-way coupling of our combustion simulator and position-based dynamics is demonstrated capturing characteristic mechanical deformations caused by the combustion process. The volumetric combustion process of wooden structures is further quantitatively assessed by comparing our simulated results to sub-surface measurements of a real-world combustion experiment.

FLAMEFORGE: Combustion Simulation of Wooden Structures

Ziyan Xiong, Andrew Leach, Griffith Thomas, Shinjiro Sueda

Rigid body simulators using the Gauss–Seidel method have been widely adopted for their simplicity, efficiency, and robustness. However, these methods struggle when simulating stable stacking with frictional contact because, unlike global methods, local methods, such as Gauss–Seidel, resolve constraints individually, leading to slow information propagation between bodies. To address this limitation, we introduce two-pass shock propagation, a technique that preserves the advantages of local methods while achieving stable and efficient simulation of frictional stacking without the need to rely on global approaches. The core idea behind two-pass shock propagation is that the upward pass leaves unused impulses on the bottom body, which can be stored and effectively applied during the downward pass. Through extensive experiments, we demonstrate that two-pass shock propagation significantly improves both performance and accuracy.

Two-Pass Shock Propagation for Stable Stacking with Gauss-Seidel

• Viscous Vortex Dynamics on Surfaces
• Fast Galerkin Multigrid Method for Unstructured Meshes
• A Stack-Free Parallel h-Adaptation Algorithm for Dynamically Balanced Trees on GPUs
• Implicit Position-Based Fluids
• Reliable Iterative Dynamics: A Versatile Method for Fast and Robust Simulation
• Implicit Bonded Discrete Element Method with Manifold Optimization
• Precise Gradient Discontinuities in Neural Fields for Subspace Physics
• Neural Kinematic Bases for Fluids
• A Highly-Efficient Hybrid Simulation System for Flight Controller Design and Evaluation of Unmanned Aerial Vehicles
• CFC: Simulating Character-Fluid Coupling using a Two-Level World Model
• Fast & Stable Control of Coupled Solid-Fluid Dynamic Systems
• Force-Dual Modes: Subspace Design from Stochastic Forces
• Numerical Homogenization of Sand from Grain-level Simulations
• Improving Curl Noise
• Neighbor-Aware Data-Driven Relaxation of Stitch Mesh Models for Knits
• A Nonconforming Formulation of Cloth
• PhysiOpt: Physics-Driven Shape Optimization for 3D Generative Models
• An Adjoint Method for Differentiable Fluid Simulation on Flow Maps
• The Granule-In-Cell Method for Simulating Sand-Water Mixtures
• Kinetic Free-Surface Flows and Foams with Sharp Interfaces
• Implicit Incompressible Porous Flow using SPH
• Fire-X: Extinguishing Fire with Stoichiometric Heat Release
• Multiphase Particle-Based Simulation of Poro-Elasto-Capillary Effects
• Wavelet Fluids

Chen Zhao, Tamar Shinar, Craig Schroeder

Recently, Zhao et al . [2024] proposed a new method for constructing signed distance functions from fluid simulation particles. This method was able to achieve superior surface smoothness, noise reduction, and temporal coherence compared with previous methods. One of the main limitations of the method was its relatively slow construction times, even though it utilized both the CPU and GPU. In this paper, we consider two modifications to this scheme that make the algorithm easier to optimize without introducing any perceptible changes in reconstruction quality, as illustrated in Figure 1. With these improvements, a surface can be reconstructed from a single fluid simulation with 2M particles in 2.21 seconds, compared with 72.3 seconds for the original method, resulting in a single-frame reconstruction speedup of about 33×, making the surface reconstruction fast enough for use within a simulation framework. When reconstructing surface for multiple simulation frames together, we achieve a speedup of about 5× compared with the original. The optimized implementation will be released with the publication.

Fast Reconstruction of Implicit Surfaces Using Convolutional Neural Networks

Yue Chang, Mengfei Liu, Zhecheng Wang, Peter Yichen Chen, Eitan Grinspun

Cutting thin-walled deformable structures is common in daily life, but poses significant challenges for simulation due to the introduced spatial discontinuities. Traditional methods rely on mesh-based domain representations, which require frequent remeshing and refinement to accurately capture evolving discontinuities. These challenges are further compounded in reduced-space simulations, where the basis functions are inherently geometry- and mesh-dependent, making it difficult or even impossible for the basis to represent the diverse family of discontinuities introduced by cuts. Recent advances in representing basis functions with neural fields offer a promising alternative, leveraging their discretization-agnostic nature to represent deformations across varying geometries. However, the inherent continuity of neural fields is an obstruction to generalization, particularly if discontinuities are encoded in neural network weights. We present Wind Lifter, a novel neural representation designed to ac-
curately model complex cuts in thin-walled deformable structures. Our approach constructs neural fields that reproduce discontinuities precisely at specified locations, without “baking in” the position of the cut line. To achieve this, we augment the input coordinates of the neural field with the generalized winding number of any given cut line, effectively lifting the input from two to three dimensions. Lifting allows the network to focus on the easier problem of learning a 3D everywhere-continuous volumetric field, while a corresponding restriction operator enables the final output field to precisely resolve strict discontinuities. Crucially, our approach does not embed the discontinuity in the neural network’s weights, opening avenues to generalization of cut placement. Our method achieves real-time simulation speeds and supports dynamic updates to cut line geometry during the simulation. Moreover, the explicit representation of discontinuities makes our neural field intuitive to control and edit, offering a significant advantage over traditional neural fields, where discontinuities are embedded within the network’s weights, and enabling new applications that rely on general cut placement.

Lifting the Winding Number: Precise Discontinuities in Neural Fields for Physics Simulation

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