Month: May 2024

Anka He Chen, Ziheng Liu, Yin Yang, Cem Yuksel

We introduce vertex block descent, a block coordinate descent solution for the variational form of implicit Euler through vertex-level Gauss-Seidel iterations. It operates with local vertex position updates that achieve reductions in global variational energy with maximized parallelism. This forms a physics solver that can achieve numerical convergence with unconditional stability and exceptional computation performance. It can also fit in a given computation budget by simply limiting the iteration count while maintaining its stability and superior convergence rate. We present and evaluate our method in the context of elastic body dynamics, providing details of all essential components and showing that it outperforms alternative techniques. In addition, we discuss and show examples of how our method can be used for other simulation systems, including particle-based simulations and rigid bodies.

Vertex Block Descent

Kemeng Huang, Floyd Chitalu, Huancheng Lin, Taku Komura

Barrier functions are crucial for maintaining an intersection and inversion free simulation trajectory but existing methods which directly use distance can restrict implementation design and performance. We present an approach to rewriting the barrier function for arriving at an efficient and robust approximation of its Hessian. The key idea is to formulate a simplicial geometric measure of contact using mesh boundary elements, from which analytic eigensystems are derived and enhanced with filtering and stiffening terms that ensure robustness with respect to the convergence of a Project-Newton solver. A further advantage of our rewriting of the barrier function is that it naturally caters to the notorious case of nearly-parallel edge-edge contacts for which we also present a novel analytic eigensystem. Our approach is thus well suited for standard second order unconstrained optimization strategies for resolving contacts, minimizing nonlinear nonconvex functions where the Hessian may be indefinite. The efficiency of our eigensystems alone yields a 3x speedup over the standard IPC barrier formulation. We further apply our analytic proxy eigensystems to produce an entirely GPU-based implementation of IPC with significant further acceleration.

GIPC: Fast and stable Gauss-Newton optimization of IPC barrier energy

Andrzej Kokosza, Helge Wrede, Daniel Gonzalez Esparza, Milosz Makowski, Daoming Liu, Dominik L. Michels, Sören Pirk, Wojtek Pałubicki

Wildfires are a complex physical phenomenon that involves the combustion of a variety of flammable materials ranging from fallen leaves and dried twigs to decomposing organic material and living flora. All these materials can potentially act as fuel with different properties that determine the progress and severity of a wildfire. In this paper, we propose a novel approach for simulating the dynamic interaction between the varying components of a wildfire, including processes of convection, combustion and heat transfer between vegetation, soil and atmosphere. We propose a novel representation of vegetation that includes detailed branch geometry, fuel moisture, and distribution of grass, fine fuel, and duff. Furthermore, we model the ignition, generation, and transport of fire by firebrands and embers. This allows simulating and rendering virtual 3D wildfires that realistically capture key aspects of the process, such as progressions from ground to crown fires, the impact of embers carried by wind, and the effects of fire barriers and other human intervention methods. We evaluate our approach through numerous experiments and based on comparisons to real-world wildfire data.

Scintilla: Simulating Combustible Vegetation for Wildfires

J. A. Amador Herrera, J. Klein, D. Liu, W. Pałubicki, S. Pirk, D. L. Michels

Cyclones are large-scale phenomena that result from complex heat and water transfer processes in the atmosphere, as well as from the interaction of multiple hydrometeors, i.e., water and ice particles. When cyclones make landfall, they are considered natural disasters and spawn dread and awe alike. We propose a physically-based approach to describe the 3D development of cyclones in a visually convincing and physically plausible manner. Our approach allows us to capture large-scale heat and water continuity, turbulent microphysical dynamics of hydrometeors, and mesoscale cyclonic processes within the planetary boundary layer. Modeling these processes enables us to simulate multiple hurricane and tornado phenomena. We evaluate our simulations quantitatively by comparing to real data from storm soundings and observations of hurricane landfall from climatology research. Additionally, qualitative comparisons to previous methods are performed to validate the different parts of our scheme. In summary, our model simulates cyclogenesis in a comprehensive way that allows us to interactively render animations of some of the most complex weather events.

Cyclogenesis: Simulating Hurricanes and Tornadoes

Qiang Chen, Zhigang Deng, Feng Li, Yuming Fang, Tingsong Lu, Yang Tong, Yifan Zuo

Realistic simulation of the intricate wing deformations seen in flying insects not only deepens our comprehension of insect flight mechanics but also opens up numerous applications in fields such as computer animation and virtual reality. Despite its importance, this research area has been relatively underexplored due to the complex and diverse wing structures and the intricate patterns of deformation. This paper presents an efficient skeleton-driven model specifically designed to real-time simulate realistic wing deformations across a wide range of flying insects. Our approach begins with the construction of a virtual skeleton that accurately reflects the distinct morphological characteristics of individual insect species. This skeleton serves as the foundation for the simulation of the intricate deformation wave propagation often observed in wing deformations. To faithfully reproduce the bending effect seen in these deformations, we introduce both internal and external forces that act on the wing joints, drawing on periodic wing-beat motion and a simplified aerodynamics model. Additionally, we utilize mass-spring algorithms to simulate the inherent elasticity of the wings, helping to prevent excessive twisting. Through various simulation experiments, comparisons, and user studies, we demonstrate the effectiveness, robustness, and adaptability of our model.

Real-time Wing Deformation Simulations for Flying Insects

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