Physics-Based Animation

Huanyu Chen, Jiahao Wen, Jernej Barbič

We give a method to simulate large deformations of 3D elastic rods under arbitrary nonlinear isotropic 3D solid materials. Rod elastic energies in existing graphics literature are derived from volumetric models under the small-strain linearization assumptions. While the resulting equations can and are commonly applied to large deformations, the material modeling has been limited to a single material, namely linear Hooke law. Starting from any 3D solid nonlinear isotropic elastic energy density function psi, we derive our rod elastic energy by subjecting the 3D solid volumetric material to the limit process whereby rod thickness is decreased to zero. This enables us to explain rod stretching, bending and twisting in a unified model. Care must be taken to adequately model cross-sectional in-plane and out-of-plane deformations. Our key insight is to compute the three cross-sectional deformation modes corresponding to bending (in the two directions) and twisting, using linear theory. Then, given any psi we use these modes to derive an analytical formula for a 5D “macroscopic” large-deformation rod elastic energy function of the local longitudinal stretch, radial scaling, the two bending curvatures and torsion. Our model matches linear theory for small deformations, including cross-sectional shrinkage due to Poisson’s effect, and produces correct bending and torsional constants. Our experiments demonstrate that our energy closely matches volumetric FEM even under large stretches and curvatures, whereas commonly used methods in graphics deviate from it. We also compare to closely related work from mechanics literature; we give an explicit expansion of all energy terms in terms of the rod cross-section diameter, allowing independent adjustment of stretching, bending and twisting. Finally, we observe an inherent limitation in the ability of rod models to control nonlinear bendability and twistability. We propose to “relax” rod physics to more easily control nonlinear bending and twisting in computer graphics applications.

ANIME-Rod: Adjustable Nonlinear Isotropic Materials for Elastic Rods

Chengzhu He, Zhendong Wang, Zhaorui Meng, Junfeng Yao, Shihui Guo

The concept of the Internet of Things (IoT) has driven the development of system-on-a-chip (SoC) technology for embedded and mobile systems, which may define the future of next-generation computation. In SoC devices, efficient cloth and deformable body simulations require parallelized, heterogeneous computation across multiple processing units. The key challenge in heterogeneous computation lies in task distribution, which must account for varying inter-task dependencies and communication costs. This paper proposes a novel framework for automated task scheduling to optimize simulation performance by minimizing communication overhead and aligning tasks with the specific strengths of each device. To achieve this, we introduce an efficient scheduling method based on the Heterogeneous Earliest Finish Time (HEFT) algorithm, adapted for hybrid systems. We model simulation tasks—such as those in iterative methods like Jacobi and Gauss-Seidel—as a Directed Acyclic Graph (DAG). To maximize the parallelism of nonlinear Gauss-Seidel simulation tasks, we present an innovative asynchronous Gauss-Seidel method with specialized data synchronization across units. Additionally, we employ task merging and tailored task-sorting strategies for Gauss-Seidel tasks to achieve an optimal balance between convergence and efficiency. We validate the effectiveness of our framework across various simulations, including XPBD, vertex block descent, and second-order stencil descent, using Apple M-series processors with both CPU and GPU cores. By maximizing computational efficiency and reducing processing times, our method achieves superior simulation frame rates compared to approaches that rely on individual devices in isolation. The source code with hybrid Metal/C++ implementation is available at https://github.com/ChengzhuUwU/libAtsSim.

Automated Task Scheduling for Cloth and Deformable Body Simulations in Heterogeneous Computing Environments

Diyang Zhang, Zhendong Wang, Zegao Liu, Xinming Pei, Weiwei Xu

In this paper, we tackle an important yet often overlooked question: What is the optimal mesh resolution for cloth simulation, without relying on preliminary simulations? The optimal resolution should be sufficient to capture fine details of all potential wrinkles, while avoiding an unnecessarily high resolution that wastes computational time and memory on excessive vertices. This challenge stems from the complex nature of wrinkle distribution, which varies spatially, temporally, and anisotropically across different orientations. To address this, we propose a method to estimate the optimal cloth mesh resolution, based on two key factors: material stiffness and boundary conditions. To determine the influence of material stiffness on wrinkle wavelength and amplitude, we apply the experimental theory presented by Cerda and Mahadevan [2003] to calculate the optimal mesh resolution for cloth fabrics. Similarly, for boundary conditions influencing local wrinkle formation, we use the same scaling law to determine the source resolution for stationary boundary conditions introduced by garment-making techniques such as shirring, folding, stitching, and down-filling, as well as predicted areas accounting for dynamic wrinkles introduced by collision compression caused by human motions. To ensure a smooth transition between different source resolutions, we apply another experimental theory from [Vandeparre et al. 2011] to compute the transition distance. A mesh sizing map is introduced to facilitate smooth transitions, ensuring precision in critical areas while maintaining efficiency in less important regions. Based on these sizing maps, triangular meshes with optimal resolution distribution are generated using Poisson sampling and Delaunay triangulation. The resulting method can not only enhance the realism and precision of cloth simulations but also support diverse application scenarios, making it a versatile solution for complex garment design.

Physics-inspired Estimation of Optimal Cloth Mesh Resolution

Kemeng Huang, Xinyu Lu, Huancheng Lin, Taku Komura, Minchen Li

Incremental Potential Contact (IPC) is a widely used, robust, and accurate method for simulating complex frictional contact behaviors. However, achieving high efficiency remains a major challenge, particularly as material stiffness increases, which leads to slower Preconditioned Conjugate Gradient (PCG) convergence, even with the state-of-the-art preconditioners. In this paper, we propose a fully GPU-optimized IPC simulation framework capable of handling materials across a wide range of stiffnesses, delivering consistent high performance and scalability with up to 10 × speedup over state-of-the-art GPU IPC methods. Our framework introduces three key innovations: 1) A novel connectivity-enhanced Multilevel Additive Schwarz (MAS) preconditioner on the GPU, designed to efficiently capture both stiff and soft elastodynamics and improve PCG convergence at a reduced preconditioning cost. 2) A C²-continuous cubic energy with an analytic eigensystem for inexact strain limiting, enabling more parallel-friendly simulations of stiff membranes, such as cloth, without membrane locking. 3) For extremely stiff behaviors where elastic waves are barely visible, we employ affine body dynamics (ABD) with a hash-based two-level reduction strategy for fast Hessian assembly and efficient affine-deformable coupling. We conduct extensive performance analyses and benchmark studies to compare our framework against state-of-the-art methods and alternative design choices. Our system consistently delivers the fastest performance across soft, stiff, and hybrid simulation scenarios, even in cases with high resolution, large deformations, and high-speed impacts.

StiffGIPC: Advancing GPU IPC for Stiff Affine-Deformable Simulation

Duowen Chen, Junwei Zhou, Bo Zhu

We propose a neural particle level set (Neural PLS) method to accommodate tracking and evolving dynamic neural representations. At the heart of our approach is a set of oriented particles serving dual roles of interface trackers and sampling seeders. These dynamic particles are used to evolve the interface and construct neural representations on a multi-resolution grid-hash structure to hybridize coarse sparse distance fields and multi-scale feature encoding. Based on these parallel implementations and neural-network-friendly architectures, our neural particle level set method combines the computational merits on both ends of the traditional particle level sets and the modern implicit neural representations, in terms of feature representation and dynamic tracking. We demonstrate the efficacy of our approach by showcasing its performance surpassing traditional level-set methods in both benchmark tests and physical simulations.

A Neural Particle Level Set Method for Dynamic Interface Tracking

Qixin Liang

We present six thin plate/shell models, derived from three distinct types of curvature operators formulated within the corotational frame, for simulating both rest-flat and rest-curved triangular meshes. Each curvature operator derives a curvature expression corresponding to both a plate model and a shell model. The corotational edge-based hinge model uses an edge-based stencil to compute directional curvature, while the corotational FVM hinge model utilizes a triangle-centered stencil, applying the finite volume method (FVM) to superposition directional curvatures across edges, yielding a generalized curvature. The corotational smoothed hinge model also employs a triangle-centered stencil but transforms directional curvatures into a generalized curvature based on a quadratic surface fit. All models assume small strain and small curvature, leading to constant bending energy Hessians, which benefit implicit integrators. Through quantitative benchmarks and qualitative elastodynamic simulations with large time steps, we demonstrate the accuracy, efficiency, and stability of these models. Our contributions enhance the thin plate/shell library for use in both computer graphics and engineering applications.

Corotational Hinge-based Thin Plates/Shells

Deshan Gong, Yin Yang, Tianjia Shao, He Wang

Persistent wrinkles are often observed on crumpled garments e.g., the wrinkles around the knees after sitting for a while. Such wrinkles can be easily recovered if not deformed for long, and otherwise be persistent. Since they are vital to the visual realism of cloth animation, we aim to simulate realistic looking persistent wrinkles. To this end, we present a physics-inspired fine-grained wrinkle model. Different from existing methods, we recognize the importance of the interplay between internal friction and plasticity during wrinkle formation. Furthermore, we model their time dependence for persistent wrinkles. Our model is capable of not only simulating realistic wrinkle patterns, but also their time-dependent changes according to how long the deformation is maintained. Through extensive experiments, we show that our model is effective in simulating realistic spatial and temporal varying wrinkles, versatile in simulating different materials, and capable of generating more fine-grained wrinkles than the state of the art.

Cloth Animation with Time-dependent Persistent Wrinkles

Tomoyo Kikuchi, Takashi Kanai

We present a unified, primitive-first framework with DCD for collision response in physics-based simulations. Previous methods do not provide sufficient solutions on a framework that resolves edge-triangle and edge-edge collisions when handling self-collisions and inter-object collisions in a unified manner. We define a scalar function and its gradient, representing the distance between two triangles and the movement direction for collision response, respectively. The resulting method offers an effective solution for collisions with minor computational overhead and robustness for any type of deformable object, such as solids or cloth. The algorithm is conceptually simple and easy to implement. When using PBD/XPBD, it is straightforward to incorporate our method into a collision constraint.

A Unified Discrete Collision Framework for Triangle Primitives

Yuhan Wu, Nobuyuki Umetani

We propose BlendSim, a novel framework for editable simulation, and its lightweight storage using spacetime optimization. Traditional spacetime control methods suffer from a high computational complexity, which limits their use in interactive animation. The proposed approach effectively reduces the dimensionality of the problem by representing the motion trajectories of each vertex using continuous parametric Bézier splines with variable keyframe times. Because this mesh animation representation is continuous and fully differentiable, it can be optimized such that it follows the laws of physics under various constraints. The proposed method also integrates constraints, such as collisions and cyclic motion, making it suitable for real-world applications where seamless looping and physical interactions are required. Leveraging projective dynamics, we further enhance the computational efficiency by decoupling the optimization into local parallelizable and global quadratic steps, enabling a fast and stable simulation.

BlendSim: Simulation on Parametric Blendshapes using Spacetime Projective Dynamics

Xiaowei He, Shusen Liu, Yuzhong Guo, Jian Shi, Ying Qiao

In simulating fluids using position-based dynamics, the accuracy and robustness depend on numerous numerical parameters, including the time step size, iteration count, and particle size, among others. This complexity can lead to unpredictable control of simulation behaviors. In this paper, we first reformulate the problem of enforcing fluid compressibility/incompressibility into an nonlinear optimization problem, and then introduce a semi-implicit successive substitution method (SISSM) to solve the nonlinear optimization problem by adjusting particle positions in parallel. In contrast to calculating an intermediate variable, such as pressure, to enforce fluid incompressibility within the position-based dynamics (PBD) framework, the proposed semi- implicit approach eliminates the necessity of such calculations. Instead, it directly employs successive substitution of particle positions to correct density errors. This method exhibits reduced dependency to numerical parameters, such as particle size and time step variations, and improves consistency and stability in simulating fluids that range from highly compressible to nearly incompressible. We validates the effectiveness of applying a variety of different techniques in accelerating the convergence rate.

A Semi-Implicit SPH Method for Compressible and Incompressible
Flows with Improved Convergence