Physics-Based Animation

Zizhou Huang, Davi Colli Tozoni, Arvi Gjoka, Zachary Ferguson, Teseo Schneider, Daniele Panozzo, Denis Zorin

We introduce a general differentiable solver for time-dependent deformation problems with contact and friction. Our approach uses a finite element discretization with a high-order time integrator coupled with the recently proposed incremental potential contact method for handling contact and friction forces to solve PDE- and ODE-constrained optimization problems on scenes with a complex geometry. It support static and dynamic problems and differentiation with respect to all physical parameters involved in the physical problem description, which include shape, material parameters, friction parameters, and initial conditions. Our analytically derived adjoint formulation is efficient, with a small overhead (typically less than 10% for nonlinear problems) over the forward simulation, and shares many similarities with the forward problem, allowing the reuse of large parts of existing forward simulator code. We implement our approach on top of the open-source PolyFEM library, and demonstrate the applicability of our solver to shape design, initial condition optimization, and material estimation on both simulated results and in physical validations.

Differentiable solver for time-dependent deformation problems with contact

Ying Jiang, Chang Yu, Tianyi Xie, Xuan Li, Yutao Feng, Huamin Wang, Minchen Li, Henry Lau, Feng Gao, Yin Yang, Chenfanfu Jiang

As consumer Virtual Reality (VR) and Mixed Reality (MR) technologies gain momentum, there’s a growing focus on the development of engagements with 3D virtual content. Unfortunately, traditional techniques for content creation, editing, and interaction within these virtual spaces are fraught with difficulties. They tend to be not only engineering-intensive but also require extensive expertise, which adds to the frustration and inefficiency in virtual object manipulation. Our proposed VR-GS system represents a leap forward in human-centered 3D content interaction, offering a seamless and intuitive user experience. By developing a physical dynamics-aware interactive Gaussian Splatting in a Virtual Reality setting, and constructing a highly efficient two-level embedding strategy alongside deformable body simulations, VR-GS ensures real-time execution with highly realistic dynamic responses. The components of our Virtual Reality system are designed for high efficiency and effectiveness, starting from detailed scene reconstruction and object segmentation, advancing through multi-view image in-painting, and extending to interactive physics-based editing. The system also incorporates real-time deformation embedding and dynamic shadow casting, ensuring a comprehensive and engaging virtual experience.

VR-GS: A Physical Dynamics-Aware Interactive Gaussian Splatting System in Virtual Reality

Yousuf Soliman, Marcel Padilla, Oliver Gross, Felix Knöppel, Ulrich Pinkall, Peter Schröder

Given a sequence of poses of a body we study the motion resulting when the body is immersed in a (possibly) moving, incompressible medium. With the poses given, say, by an animator, the governing second-order ordinary differential equations are those of a rigid body with time-dependent inertia acted upon by various forces. Some of these forces, like lift and drag, depend on the motion of the body in the surrounding medium. Additionally, the inertia must encode the effect of the medium through its added mass. We derive the corresponding dynamics equations which generalize the standard rigid body dynamics equations. All forces are based on local computations using only physical parameters such as mass density. Notably, we approximate the effect of the medium on the body through local computations avoiding any global simulation of the medium. Consequently, the system of equations we must integrate in time is only 6 dimensional (rotation and translation). Our proposed algorithm displays linear complexity and captures intricate natural phenomena that depend on body-fluid interactions.

Going with the Flow

Pranav Jain, Peter Yichen Chen, Ziyin Qu, Oded Stein

The idea of using a neural network to represent continuous vector fields (i.e., neural fields) has become popular for solving PDEs arising from physics simulations. Here, the classical spatial discretization (e.g., finite difference) of PDE solvers is replaced with a neural network that models a differentiable function, so the spatial gradients of the PDEs can be readily computed via autodifferentiation. When used in fluid simulation, however, neural fields fail to capture many important phenomena, such as the vortex shedding experienced in the von Kármán vortex street experiment. We present a novel neural network representation for fluid simulation that augments neural fields with explicitly enforced boundary conditions as well as a Monte Carlo pressure solver to get rid of all weakly enforced boundary conditions. Our method, the Neural Monte Carlo method (NMC), is completely mesh-free, i.e., it doesn’t depend on any grid-based discretization. While NMC does not achieve the state-of-the-art accuracy of the well-established gridbased methods, it significantly outperforms previous mesh-free neural fluid methods on fluid flows involving intricate boundaries and turbulence regimes.

Neural Monte Carlo Fluid Simulation

Ryusuke Sugimoto, Christopher Batty, Toshiya Hachisuka

We present a velocity-based Monte Carlo fluid solver that overcomes the limitations of its existing vorticity-based counterpart. Because the velocity-based formulation is more commonly used in graphics, our Monte Carlo solver can be readily extended with various techniques from the fluid simulation literature. We derive our method by solving the Navier-Stokes equations via operator splitting and designing a pointwise Monte Carlo estimator for each substep. We reformulate the projection and diffusion steps as integration problems based on the recently introduced walk-on-boundary technique [Sugimoto et al. 2023]. We transform the volume integral arising from the source term of the pressure Poisson equation into a form more amenable to practical numerical evaluation. Our resulting velocity-based formulation allows for the proper simulation of scenes that the prior vorticity-based Monte Carlo method [Rioux-Lavoie and Sugimoto et al. 2022] either simulates incorrectly or cannot support. We demonstrate that our method can easily incorporate advancements drawn from conventional non-Monte Carlo methods by showing how one can straightforwardly add buoyancy effects, divergence control capabilities, and numerical dissipation reduction methods, such as advection-reflection and PIC/FLIP methods.

Velocity-Based Monte Carlo Fluids

Wei Li, Kui Wu, Mathieu Desbrun

Despite its visual appeal, the simulation of separated multiphase flows (i.e., streams of fluids separated by interfaces) faces numerous challenges in accurately reproducing complex behaviors such as guggling, wetting, or bubbling. These difficulties are especially pronounced for high Reynolds numbers and large density variations between fluids, most likely explaining why they have received comparatively little attention in Computer Graphics compared to single- or two-phase flows. In this paper, we present a full LBM solver for multifluid simulation. We derive a conservative phase field model with which the spatial presence of each fluid or phase is encoded to allow for the simulation of miscible, immiscible and even partially-miscible fluids, while the temporal evolution of the phases is performed using a D3Q7 lattice-Boltzmann discretization. The velocity field, handled through the recent high-order moment-encoded LBM (HOME-LBM) framework to minimize its memory footprint, is simulated via a velocity-based distribution stored on a D3Q27 or D3Q19 discretization to offer accuracy and stability to large density ratios even in turbulent scenarios, while coupling with the phases through pressure, viscosity, and interfacial forces is achieved by leveraging the diffuse encoding of interfaces. The resulting solver addresses a number of limitations of kinetic methods in both computational fluid dynamics and computer graphics: it offers a fast, accurate, and low-memory fluid solver enabling efficient turbulent multiphase simulations free of the typical oscillatory pressure behavior near boundaries. We present several numerical benchmarks, examples and comparisons of multiphase flows to demonstrate our solver’s visual complexity, accuracy, and realism.

Kinetic Simulation of Turbulent Multifluid Flows

Jiong Chen, Florian Schäfer, Mathieu Desbrun

The method of fundamental solutions (MFS) and its associated boundary element method (BEM) have gained popularity in computer graphics due to the reduced dimensionality they offer: for three-dimensional linear problems, they only require variables on the domain boundary to solve and evaluate the solution throughout space, making them a valuable tool in a wide variety of applications. However, MFS and BEM have poor computational scalability and huge memory requirements for large-scale problems, limiting their applicability and efficiency in practice. By leveraging connections with Gaussian Processes and exploiting the sparse structure of the inverses of boundary integral matrices, we introduce a variational preconditioner that can be computed via a sparse inverse-Cholesky factorization in a massively parallel manner. We show that applying our preconditioner to the Preconditioned Conjugate Gradient algorithm greatly improves the efficiency of MFS or BEM solves, up to four orders of magnitude in our series of tests.

Lightning-fast Method of Fundamental Solutions

• Lightning-Fast Method of Fundamental Solutions
• Kinetic Simulation of Turbulent Multifluid Flows
• Velocity-based Monte Carlo Fluids
• Neural Monte Carlo Fluid Simulation
• Going with the Flow
• VR-GS: A Physical Dynamics-Aware Interactive Gaussian Splatting System in Virtual Reality
• Differentiable solver for time-dependent deformation problems with contact
• Real-time Wing Deformation Simulation for Flying Insects
• Cyclogenesis: Simulating Hurricanes and Tornadoes
• Scintilla: Simulating Combustible Vegetation for Wildfires
• GIPC: Fast and stable Gauss-Newton optimization of IPC barrier energy
• Vertex Block Descent
• Primal-Dual Non-Smooth Friction for Rigid Body Animation
• Multi-Material Mesh-Based Surface Tracking with Implicit Topology Changes
• Modelling a Feather as a Strongly Anisotropic Elastic Shell
• Differentiable Voronoi Diagrams for Simulation of Cell-based Mechanical Systems
• Efficient Debris-flow Simulation for Steep Terrain Erosion
• An Induce-on-Boundary Magnetostatic Solver for Grid-based Ferrofluids
• A Vortex Particle-on-mesh Method for Soap Film Simulation
• Real-time Physically Guided Hair Interpolation
• Proxy Asset Generation for Cloth Simulation in Games
• A Dynamic Duo of Finite Elements and Material Points
• Lagrangian Covector Fluid With Free Surface
• Fluid Control With Laplacian Eigenfunctions
• Implicit Surface Tension for SPH Fluid Simulation
• A Dual-Particle Approach for Incompressible SPH Fluids
• Eulerian-Lagrangian Fluid Simulation on Particle Flow Maps
• A Framework for Solving Parabolic Partial Differential Equations on Discrete Domains
• MERCI: Mixed curvature-based elements for computing equilibria of thin elastic ribbons
• Neural-assisted Homogenization of Yarn-level Cloth
• ContourCraft: Learning to Resolve Intersections in Neural Multi-garment Simulations
• Progressive Dynamics for Cloth and Shell Animation
• Super-resolution Cloth Animation With Spatial and Temporal Coherence
• Position-based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity
• Stabler Neo-Hookean Simulation: Absolute Eigenvalue Filtering for Projected Newton
• Simplicits: Mesh-free, Geometry-agnostic Elastic Simulation
• Efficient Position-based Deformable Colon Modeling for Endoscopic Procedures Simulation
• A Neural Network Model for Efficient Musculoskeletal-driven Skin Deformation
• Preconditioned Nonlinear Conjugate Gradient Method for Real-time Interior-point Hyperelasticity
• Contact Detection Between Curved Fibres: High Order Makes a Difference

Petros Tzathas, Boris Gailleton, Philippe Steer, Guillaume Cordonnier

Terrain generation methods have long been divided between procedural and physically-based. Procedural methods build upon the fast evaluation of a mathematical function but suffer from a lack of geological consistency, while physically-based simulation enforces this consistency at the cost of thousands of iterations unraveling the history of the landscape. In particular, the simulation of the competition between tectonic uplift and fluvial erosion expressed by the stream power law raised recent interest in computer graphics as this allows the generation and control of consistent large-scale mountain ranges, albeit at the cost of a lengthy simulation. In this paper, we explore the analytical solutions of the stream power law and propose a method that is both physically-based and procedural, allowing fast and consistent large-scale terrain generation. In our approach, time is no longer the stopping criterion of an iterative process but acts as the parameter of a mathematical function, a slider that controls the aging of the input terrain from a subtle erosion to the complete replacement by a fully formed mountain range. While analytical solutions have been proposed by the geomorphology community for the 1D case, extending them to a 2D heightmap proves challenging. We propose an efficient implementation of the analytical solutions with a multigrid accelerated iterative process and solutions to incorporate landslides and hillslope processes – two erosion factors that complement the stream power law.

Physically-based analytical erosion for fast terrain generation

Peizhuo Li, Tuanfeng Y. Wang, Timur Levent Kesdogan, Duygu Ceylan, Olga Sorkine-Hornung

Data driven and learning based solutions for modeling dynamic garments have significantly advanced, especially in the context of digital humans. However, existing approaches often focus on modeling garments with respect to a fixed parametric human body model and are limited to garment geometries that were seen during training. In this work, we take a different approach and model the dynamics of a garment by exploiting its local interactions with the underlying human body. Specifically, as the body moves, we detect local garment-body collisions, which drive the deformation of the garment. At the core of our approach is a mesh-agnostic garment representation and a manifold-aware transformer network design, which together enable our method to generalize to unseen garment and body geometries. We evaluate our approach on a wide variety of garment types and motion sequences and provide competitive qualitative and quantitative results with respect to the state of the art.

Neural Garment Dynamics via Manifold-Aware Transformers