Physics-Based Animation

Tianchen Hao, Jinxian Pan, Yangcheng Xiang, Xiangda Shen, Xinsheng Li, Yanci Zhang

A Mesoscale Convective System (MCS) is a collection of thunderstorms operating as a unified system, showcasing nature’s untamed power. They represent a phenomenon widely referenced in both the natural sciences and the visual effects (VFX) industries. However, in computer graphics, visually accurate simulation of MCS dynamics remains a significant challenge due to the inherent complexity of atmospheric microphysical processes. To achieve a high level of visual quality while ensuring practical performance, we introduce Thunderscapes, the first physically based simulation framework for visually realistic MCS tailored to graphical applications. Our model integrates mesoscale cloud microphysics with hydrometeor electrification processes to simulate thunderstorm development and lightning flashes. By capturing various thunderstorm types and their associated lightning activities, Thunderscapes demonstrates the versatility and physical accuracy of the proposed approach.

Thunderscapes: Simulating the Dynamics of Mesoscale Convective System

Huanbo Zhou, Zhenyu Xu, Xijun Liu, Xinyu Zhang

Simulating multi-object collisions in real-time environments remains a significant challenge, particularly when handling simultaneous collisions in a physically accurate manner. Traditional Gauss-Seidel solvers, widely employed in physics engines, often fail to preserve the symmetry and consistency of multi-object interactions that are often observed in physics. In this paper, we present a generalized and robust Gauss-Seidel solver to overcome the difficulties in simultaneous collisions. Using spatial and temporal collision states to classify and resolve constraints, our algorithm ensures correct collision propagation and symmetry, addressing the limitations commonly found in existing solvers. Moreover, our algorithm can mitigate jitters caused by floating-point errors, ensuring smooth and stable collision responses. Our approach demonstrates fast convergence and improved accuracy in scenarios involving complex multi-object collisions.

A Robust and Generalized Gauss-Seidel Solver for Physically-Correct Simultaneous Collisions

Shiguang Liu, Maolin Wu, Chenfanfu Jiang, Yisheng Zhang

This paper proposes a novel method to simulate the dynamic fracture effect of elastoplastic objects. Our method is based on the continuum damage mechanics (CDM) theory and uses the material point method (MPM) to discretize the governing equations. Our proposed approach distinguishes itself from previous works by incorporating a novel method for modeling decohesion, which preserves the incompressibility of the cracks. In contrast to existing methods that rely on material stiffness degradation, our approach leverages carefully crafted constitutive models for both fully and partially damaged materials. We further introduce a novel granular material model that effectively captures the physical behavior of fully damaged debris. This is augmented by a volume-aware deformation gradient tensor designed to evaluate and stabilize material expansion. We conduct a comprehensive evaluation of our proposed method on multiple dynamic fracturing scenarios and demonstrate its effectiveness in producing visually richer and more realistic behaviors compared to previous state-of-the-art MPM approaches.

An Incompressible Crack Model for Volume Preserving MPM Fracture

Jiong Chen, Florian T. Schäfer, Mathieu Desbrun

Boundary element methods (BEM) for solving linear elliptic partial differential equations have gained traction in a wide range of graphics applications: they eliminate the need for volumetric meshing by solving for variables exclusively on the domain boundary through a linear boundary integral equation (BIE). However, BEM often generate dense and ill-conditioned linear systems that lead to poor computational scalability and substantial memory demands for large-scale problems, limiting their applicability and efficiency in practice. In this paper, we address these limitations by generalizing the Kaporin-based approach to asymmetric preconditioning: we construct a sparse approximation of the inverse-LU factorization of arbitrary BIE matrices in a massively parallel manner. Our sparse inverse-LU factorization, when employed as a preconditioner for the generalized minimal residual (GMRES) method, significantly enhances the efficiency of BIE solves, often yielding orders-of-magnitude speedups in solving times.

Lightning-fast Boundary Element Method

• Lightning-Fast Boundary Element Method
• CK-MPM: A Compact-Kernel Material Point Method
• A Neural Particle Level Set Method for Dynamic Interface Tracking
• ANIME-Rod: Adjustable Nonlinear Isotropic Materials for Elastic Rods
• Stable Cosserat Rods
• Fast But Accurate: A Real-Time Hyperelastic Simulator with Robust Frictional Contact
• Unified Pressure, Surface Tension and Friction for SPH Fluids
• Digital Animation of Powder-Snow Avalanches
• Stressful Tree Modeling: Breaking Branches with Strands
• Neurally Integrated Finite Elements for Differentiable Elasticity on Evolving Domains
• Fast Physics-Based Modeling of Knots and Ties using Templates
• Physics-inspired Estimation of Optimal Cloth Mesh Resolution
• Automated Task Scheduling for Cloth and Deformable Body Simulations in Heterogeneous Computing Environments
• Painless Differentiable Rotation Dynamics
• Putting Rigid Bodies to Rest
• A Versatile Quaternion-Based Constrained Rigid Body Dynamics
• Arenite: A Physics-based Sandstone Simulator
• Controllable Complex Freezing Dynamics Simulation on Thin Films
• Quadtree Tall Cells for Eulerian Liquid Simulation
• Gaussian Fluids: A Grid-Free Fluid Solver based on Gaussian Spatial Representation
• Fast Subspace Fluid Simulation with a Temporally-Aware Basis
• Dress-1-to-3: Single Image to Simulation-Ready 3D Outfit with Diffusion Prior and Differentiable Physics
• Offset Geometric Contact
• Geometric Contact Potential
• Elastic Locomotion with Mixed Second-order Differentiation
• Real-Time Knit Deformation and Rendering
• Adaptive Algebraic Reuse of Reordering in Cholesky Factorizations with Dynamic Sparsity Patterns
• Progressive Dynamics++: A Framework for Stable, Continuous, and Consistent Animation Across Resolution and Time
• Optimal r-Adaptive In-Timestep Remeshing for Elastodynamics
• Adaptive Phase-Field-FLIP for Very Large Scale Two-Phase Fluid Simulation
• StiffGIPC: Advancing GPU IPC for Stiff Affine-Deformable Simulation
• Hyper-Dimensional Deformation Simulation
• Variational Elastodynamic Simulation
• Fluid Simulation on Vortex Particle Flow Maps
• Clebsch Gauge Fluid on Particle Flow Maps
• Cirrus: Adaptive Hybrid Particle-Grid Flow Maps on GPU
• Leapfrog Flow Maps for Real-Time Fluid Simulation
• Fluid Simulation on Compressible Flow Maps
• EDGE: Epsilon-Difference Gradient Evolution for Buffer-Free Flow Maps
• MiSo: A DSL for robust and efficient MINIMIZE and SOLVE problems
• Stochastic Barnes-Hut Approximation for Fast Summation on the GPU
• Elastic Locomotion with Mixed Second-order Differentiation
• JGS2: Near Second-order Converging Jacobi/Gauss-Seidel for GPU Elastodynamics
• High-performance CPU Cloth Simulation Using Domain-decomposed Projective Dynamics
• C5D: Sequential Continuous Convex Collision Detection Using Cone Casting
• MGPBD: A Multigrid Accelerated Global XPBD Solver
• Creating Fluid-Interactive Virtual Agents by an Efficient Simulator with Local-domain Control
• Lifting the Winding Number: Precise Discontinuities in Neural Fields for Physics Simulation
• A Hybrid Near-wall Model for Kinetic Simulation of Turbulent Boundary Layer Flows

Bosheng Li, Nikolas A. Schwarz, Wojtek Pałubicki, Sören Pirk, Dominik L. Michels, Bedrich Benes

We propose a novel approach for the computational modeling of lignified tissues, such as those found in tree branches and timber. We leverage a state-of-the-art strand-based representation for tree form, which we extend to describe biophysical processes at short and long time scales. Simulations at short time scales enable us to model different breaking patterns due to branch bending, twisting, and breaking. On long timescales, our method enables the simulation of realistic branch shapes under the influence of plausible biophysical processes, such as the development of compression and tension wood. We specifically focus on computationally fast simulations of woody material, enabling the interactive exploration of branches and wood breaking. By leveraging Cosserat rod physics, our method enables the generation of a wide variety of breaking patterns. We showcase the capabilities of our method by performing and visualizing numerous experiments.

Stressful Tree Modeling: Breaking Branches with Strands

Filipe Nascimento, Fabricio S. Sousa, Afonso Paiva

Powder-snow avalanches are natural phenomena that result from an instability in the snow cover on a mountain relief. It begins with a dense avalanche core moving fast down the mountain. During its evolution, the snow particles in the avalanche front mix with the air, forming a suspended turbulent cloud of snow dust surrounding the dense snow avalanche. This paper introduces a physically-based framework using the Finite Volume Method to simulate powder-snow avalanches under complex terrains. Specifically, the primary goal is to simulate the turbulent snow cloud dynamics within the avalanche in a visually realistic manner. Our approach relies on a multi-layer model that splits the avalanche into two main layers: dense and powder-snow. The dense-snow layer flow is simulated by solving a type of Shallow Water Equations suited for intricate basal surfaces, known as the Savage-Hutter model. The powder-snow layer flow is modeled as a two-phase mixture of miscible fluids and simulated using Navier-Stokes equations. Moreover, we propose a novel model for the transition layer, which is responsible for coupling the avalanche main layers, including the snow mass injected into the powder-snow cloud from the snow entrainment processes and its injection velocity. In brief, our framework comprehensively simulates powder-snow avalanches, allowing us to render convincing animations of one of the most complex gravity-driven flows.

Digital Animation of Powder-Snow Avalanches

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