Physics-Based Animation

Xingyu Ni*, Ruicheng Wang* (joint 1st authors), Bin Wang, Baoquan Chen

This paper introduces a novel Induce-on-Boundary (IoB) solver designed to address the magnetostatic governing equations of ferrofluids. The IoB solver is based on a single-layer potential and utilizes only the surface point cloud of the object, offering a lightweight, fast, and accurate solution for calculating magnetic fields. Compared to existing methods, it eliminates the need for complex linear system solvers and maintains minimal computational complexities. Moreover, it can be seamlessly integrated into conventional fluid simulators without compromising boundary conditions. Through extensive theoretical analysis and experiments, we validate both the convergence and scalability of the IoB solver, achieving state-of-the-art performance. Additionally, a straightforward coupling approach is proposed and executed to showcase the solver’s effectiveness when integrated into a grid-based fluid simulation pipeline, allowing for realistic simulations of representative ferrofluid instabilities.

An Induce-on-Boundary Magnetostatic Solver for Grid-Based Ferrofluids

Aryamaan Jain, Bedrich Benes, Guillaume Cordonnier

Erosion simulation is a common approach used for generating and authoring mountainous terrains. While water is considered the primary erosion factor, its simulation fails to capture steep slopes near the ridges. In these low-drainage areas, erosion is often approximated with slope-reducing erosion, which yields unrealistically uniform slopes. However, geomorphology observed that another process dominates the low-drainage areas: erosion by debris flow, which is a mixture of mud and rocks triggered by strong climatic events. We propose a new method to capture the interactions between debris flow and fluvial erosion thanks to a new mathematical formulation for debris flow erosion derived from geomorphology and a unified GPU algorithm for erosion and deposition. In particular, we observe that sediment and debris deposition tend to intersect river paths, which motivates the design of a new, approximate flow routing algorithm on the GPU to estimate the water path out of these newly formed depressions. We demonstrate that debris flow carves distinct patterns in the form of erosive scars on steep slopes and cones of deposited debris competing with fluvial erosion downstream.

Efficient Debris-flow Simulation for Steep Terrain Erosion

Logan Numerow, Yue Li, Stelian Coros, Bernhard Thomaszewski

Navigating topological transitions in cellular mechanical systems is a significant challenge for existing simulation methods. While abstract models lack predictive capabilities at the cellular level, explicit network representations struggle with topology changes, and per-cell representations are computationally too demanding for large-scale simulations. To address these challenges, we propose a novel cell-centered approach based on differentiable Voronoi diagrams. Representing each cell with a Voronoi site, our method defines shape and topology of the interface network implicitly. In this way, we substantially reduce the number of problem variables, eliminate the need for explicit contact handling, and ensure continuous geometry changes during topological transitions. Closed-form derivatives of network positions facilitate simulation with Newton-type methods for a wide range of per-cell energies. Finally, we extend our differentiable Voronoi diagrams to enable coupling with arbitrary rigid and deformable boundaries. We apply our approach to a diverse set of examples, highlighting splitting and merging of cells as well as neighborhood changes. We illustrate applications to inverse problems by matching soap foam simulations to real-world images. Comparative analysis with explicit cell models reveals that our method achieves qualitatively comparable results at significantly faster computation times.

Differentiable Voronoi Diagrams for Simulation of Cell-Based Mechanical Systems

Peter Heiss-Synak*, Aleksei Kalinov*, Malina Strugaru, Arian Etemadi, Huidong Yang, Chris Wojtan (*joint first authors)

We introduce a multi-material non-manifold mesh-based surface tracking algorithm that converts self-intersections into topological changes. Our algorithm generalizes prior work on manifold surface tracking with topological changes: it preserves surface features like mesh-based methods, and it robustly handles topological changes like level set methods. Our method also offers improved efficiency and robustness over the state of the art. We demonstrate the effectiveness of the approach on a range of examples, including complex soap film simulations with thousands of interacting bubbles, and Boolean unions of non-manifold meshes consisting of millions of triangles.

Multi-Material Mesh-Based Surface Tracking with Implicit Topology Changes

Yi-Lu Chen, Mickaël Ly, Chris Wojtan

Current numerical algorithms for simulating friction fall in one of two camps: smooth solvers sacrifice the stable treatment of static friction in exchange for fast convergence, and non-smooth solvers accurately compute friction at convergence rates that are often prohibitive for large graphics applications. We introduce a novel bridge between these two ideas that computes static and dynamic friction stably and efficiently. Our key idea is to convert the highly constrained non-smooth problem into an unconstrained smooth problem using logarithmic barriers that converges to the exact solution as accuracy increases. We phrase the problem as an interior point primal-dual problem that can be solved efficiently with Newton iteration. We observe quadratic convergence despite the non-smooth nature of the original problem, and our method is well-suited for large systems of tightly packed objects with many contact points. We demonstrate the efficacy of our method with stable piles of grains and stacks of objects, complex granular flows, and robust interlocking assemblies of rigid bodies.

Primal-Dual Non-Smooth Friction for Rigid Body Animation

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