Month: May 2025

Timo Probst, Matthias Teschner,

Fluid droplets behave significantly different from larger fluid bodies. At smaller scales, surface tension and friction between fluids and the boundary play an essential role and are even able to counteract gravitational forces. There are quite a few existing approaches that model surface tension forces within an SPH environment. However, as often as not, physical correctness and simulation stability are still major concerns with many surface tension formulations. We propose a new approach to compute surface tension that is both robust and produces the right amount of surface tension. Conversely, less attention was given to friction forces at the fluid-boundary interface. Recent experimental research indicates that Coulomb friction can be used to describe the behavior of droplets resting on a slope. Motivated by this, we develop a novel friction force formulation at the fluid-boundary interface following the Coulomb model, which allows us to replicate a new range of well known fluid behavior such as the motion of rain droplets on a window pane. Both forces are combined with an IISPH variant into one unified solver that is able to simultaneously compute strongly coupled surface tension, friction and pressure forces.

Unified Pressure, Surface Tension and Friction for SPH Fluids

Ziqiu Zeng, Siyuan Luo, Fan Shi, Zhongkai Zhang

We present a GPU-friendly framework for real-time implicit simulation of elastic material in the presence of frictional contacts. The integration of hyperelasticity, non-interpenetration contact, and friction in real-time simulations presents formidable nonlinear and non-smooth problems, which are highly challenging to solve. By incorporating nonlinear complementarity conditions within the local-global framework, we achieve rapid convergence in addressing these challenges. While the structure of local-global methods is not fully GPU-friendly, our proposal of a simple yet efficient solver with sparse presentation of the system inverse enables highly parallel computing while maintaining a fast convergence rate. Moreover, our novel splitting strategy for non-smooth indicators not only amplifies overall performance but also refines the complementarity preconditioner, enhancing the accuracy of frictional behavior modeling. Through extensive experimentation, the robustness of our framework in managing real-time contact scenarios, ranging from large-scale systems and extreme deformations to non-smooth contacts and precise friction interactions, has been validated. Compatible with a wide range of hyperelastic models, our approach maintains efficiency across both low and high stiffness materials. Despite its remarkable efficiency, robustness, and generality, our method is elegantly simple, with its core contributions grounded solely on standard matrix operations.

Fast But Accurate: A Real-Time Hyperelastic Simulator with Robust Frictional Contact

Jerry Hsu, Tongtong Wang, Kui Wu, Cem Yuksel

Cosserat rods have become an increasingly popular framework for simulating complex bending and twisting in thin elastic rods, used for hair, tree, and yarn-level cloth models. However, traditional approaches often encounter significant challenges in robustly and efficiently solving for valid quaternion orientations, even when employing small time steps or computationally expensive global solvers. We introduce stable Cosserat rods, a new solver that can achieve high accuracy with high stiffness levels and maintain stability under large time steps. It is also inherently suitable for parallelization. Our key contribution is a split position and rotation optimization scheme with a closed-form Gauss-Seidel quasi-static orientation update. This solver significantly improves the numerical stability with Cosserat rods, allowing faster computation and larger time steps. We validate our method across a wide range of applications, including simulations of hair, trees, yarn-level cloth, slingshots, and bridges, demonstrating its ability to handle diverse material behaviors and complex geometries. Furthermore, we show that our method is orders of magnitude faster and more stable than alternative rod solvers, such as extended position-based dynamics and discrete elastic rods.

Stable Cosserat Rods

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