Physics-Based Animation

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

Xuan Li, Chang Yu, Wenxin Du, Ying Jiang, Tianyi Xie, Yunuo Chen, Yin Yang, Chenfanfu Jiang

Recent advances in large models have significantly advanced image-to-3D reconstruction. However, the generated models are often fused into a single piece, limiting their applicability in downstream tasks. This paper focuses on 3D garment generation, a key area for applications like virtual try-on with dynamic garment animations, which require garments to be separable and simulation-ready. We introduce Dress-1-to-3, a novel pipeline that reconstructs physics-plausible, simulation-ready separated garments with sewing patterns and humans from an in-the-wild image. Starting with the image, our approach combines a pre-trained image-to-sewing pattern generation model for creating coarse sewing patterns with a pre-trained multi-view diffusion model to produce multi-view images. The sewing pattern is further refined using a differentiable garment simulator based on the generated multi-view images. Versatile experiments demonstrate that our optimization approach substantially enhances the geometric alignment of the reconstructed 3D garments and humans with the input image. Furthermore, by integrating a texture generation module and a human motion generation module, we produce customized physics-plausible and realistic dynamic garment demonstrations.

Dress-1-to-3: Single Image to Simulation-Ready 3D Outfit with
Diffusion Prior and Differentiable Physics

Fumiya Narita, Nimiko Ochiai, Takashi Kanai, Ryoichi Ando

This paper introduces a novel grid structure that extends tall cell methods for efficient deep water simulation. Unlike previous tall cell methods, which are designed to capture all the fine details around liquid surfaces, our approach subdivides tall cells horizontally, allowing for more aggressive adaptivity and a significant reduction in the number of cells. The foundation of our method lies in a new variational formulation of Poisson’s equations for pressure solve tailored for tall-cell grids, which naturally handles the transition of variable-sized cells. This variational view not only permits the use of the efficacy-proven conjugate gradient method but also facilitates monolithic two-way coupled rigid bodies. The key distinction between our method and previous general adaptive approaches, such as tetrahedral or octree grids, is the simplification of adaptive grid construction. Our method performs grid subdivision in a quadtree fashion, rather than an octree. These 2D cells are then simply extended vertically to complete the tall cell population. We demonstrate that this novel form of adaptivity, which we refer to as quadtree tall cells, delivers superior performance compared to traditional uniform tall cells.

Quadtree Tall Cells for Eulerian Liquid Simulation

Zhanyu Yang, Aryamaan Jain, Guillaume Cordonnier, Marie-Paule Cani, Zhaopeng Wang, Bedrich Benes

We introduce Arenite, a novel physics-based approach for modeling sandstone structures. The key insight of our work is that simulating a combination of stress and multi-factor erosion enables the generation of a wide variety of sandstone structures observed in nature. We isolate the key shape-forming phenomena: multi-physics fabric interlocking, wind and fluvial erosion, and particle-based deposition processes. Complex 3D structures such as arches, alcoves, hoodoos, or buttes can be achieved by creating simple 3D structures with user-painted erodable areas and vegetation and running the simulation. We demonstrate the algorithm on a wide variety of structures, and our GPU-based implementation achieves the simulation in less than 5 minutes on a desktop computer for our most complex example.

Arenite: A Physics-based Sandstone Simulator

Behrooz Zarebavani, Danny Kaufman, David I W Levin, Maryam Mehri Dehnavi

We introduce Parth, a fill-reducing ordering method for sparse Cholesky solvers with dynamic sparsity patterns (e.g., in physics simulations with contact or geometry processing with local remeshing). Parth facilitates the selective reuse of fill-reducing orderings when sparsity patterns exhibit temporal coherence, avoiding full symbolic analysis by localizing the effect of dynamic sparsity changes on the ordering vector. We evaluated Parth on over 175,000 linear systems collected from both physics simulations and geometry processing applications, and show that for some of the most challenging physics simulations, it achieves up to 14x reordering runtime speedup, resulting in a 2x speedup in Cholesky solve time—even on top of well-optimized solvers such as Apple Accelerate and Intel MKL.

Adaptive Algebraic Reuse of Reordering in Cholesky Factorizations with Dynamic Sparsity Patterns

Anka Chen, Jerry Hsu, Ziheng Liu, Miles Macklin, Yin Yang, Cem Yuksel

We present a novel contact model, termed Offset Geometric Contact (OGC), for guaranteed penetration-free simulation of codimensional objects with minimal computational overhead. Our method is based on constructing a volumetric shape by offsetting each face along its normal direction, ensuring orthogonal contact forces, thus allows large contact radius without artifacts. We compute vertex-specific displacement bounds to guarantee penetration-free simulation, which improves convergence and avoids the need for expensive continuous collision detection. Our method relies solely on massively parallel local operations, avoiding global synchronization and enabling efficient GPU implementation. Experiments demonstrate real-time, large-scale simulations with performance more than two orders of magnitude faster than prior methods while maintaining consistent computational budgets.

Offset Geometric Contact

Jingrui Xing, Bin Wang, Mengyu Chu, Baoquan Chen

We present a grid-free fluid solver featuring a novel Gaussian representation. Drawing inspiration from the expressive capabilities of 3D Gaussian Splatting in multi-view image reconstruction, we model the continuous flow velocity as a weighted sum of multiple Gaussian functions. This representation is continuously differentiable, which enables us to derive spatial differentials directly and solve the time-dependent PDE via a custom first‑order optimization tailored to fluid dynamics. Compared to traditional discretizations, which typically adopt Eulerian, Lagrangian, or hybrid perspectives, our approach is inherently memory-efficient and spatially adaptive, enabling it to preserve fine-scale structures and vortices with high fidelity. While these advantages are also sought by implicit neural representations, GSR offers enhanced robustness, accuracy, and generality across diverse fluid phenomena, with improved computational efficiency during temporal evolution. Though our first‑order solver does not yet match the speed of fluid solvers using explicit representations, its continuous nature substantially reduces spatial discretization error and opens a new avenue for high‑fidelity simulation. We evaluate the proposed solver across a broad range of 2D and 3D fluid phenomena, demonstrating its ability to preserve intricate vortex dynamics, accurately capture boundary-induced effects such as Kármán vortex streets, and remain robust across long time horizons—all without additional parameter tuning. Our results suggest that GSR offers a compelling direction for future research in fluid simulation.

Gaussian Fluids: A Grid-Free Fluid Solver based on Gaussian Spatial Representation

Yijie Liu, Taiyuan Zhang, Xiaoxiao Yan, Han Yan, Nuoming Liu, Bo Ren

The freezing of thin films is a mesmerizing natural phenomenon, inspiring photographers to capture its beauty through their lenses and digital artists to recreate its allure using effects tools. In this paper, we present a novel method for physically simulating the intricate freezing dynamics on thin films. By accounting for the influence of phase and temperature changes on surface tension, our method reproduces Marangoni freezing and the “Snow-Globe Effect”, characterized by swirling ice dendrites on the film. We introduce a novel Phase Map method on top of the state-of-the-art Moving Eulerian-Lagrangian Particles (MELP) meshless framework, enabling dendritic crystal simulation on mobile particles and offering precise control over freezing patterns. We demonstrate that our method is able to capture a wide range of dynamic freezing processes of soap bubbles and is stable for complex boundaries in our experiments.

Controllable Complex Freezing Dynamics Simulation on Thin Films