Physics-Based Animation

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

Xingyu Ye, Xiaokun Wang, Yanrui Xu, Jirí Kosinka, Alexandru C. Telea, Lihua You, Jian Jun Zhang, Jian Chang

For vortex particle methods relying on SPH-based simulations, the direct approach of iterating all fluid particles to capture velocity from vorticity can lead to a significant computational overhead during the Biot-Savart summation process. To address this challenge, we present a Monte Carlo vortical smoothed particle hydrodynamics (MCVSPH) method for efficiently simulating turbulent flows within an SPH framework. Our approach harnesses a Monte Carlo estimator and operates exclusively within a pre-sampled particle subset, thus eliminating the need for costly global iterations over all fluid particles. Our algorithm is decoupled from various projection loops which enforce incompressibility, independently handles the recovery of turbulent details, and seamlessly integrates with state-of-the-art SPH-based incompressibility solvers. Our approach rectifies the velocity of all fluid particles based on vorticity loss to respect the evolution of vorticity, effectively enforcing vortex motions. We demonstrate, by several experiments, that our MCVSPH method effectively preserves vorticity and creates visually prominent vortical motions.

Monte Carlo Vortical Smoothed Particle Hydrodynamics for Simulating Turbulent Flows

Sergio Sancho, Jingwei Tang, Christopher Batty, Vinicius Azevedo

An ongoing challenge in fluid animation is the faithful preservation of vortical details, which impacts the visual depiction of flows. We propose the Impulse Particle-In-Cell (IPIC) method, a novel extension of the popular Affine Particle-In-Cell (APIC) method that makes use of the impulse gauge formulation of the fluid equations. Our approach performs a coupled advection-stretching during particle-based advection to better preserve circulation and vortical details. The associated algorithmic changes are simple and straightforward to implement, and our results demonstrate that the proposed method is able to achieve more energetic and visually appealing smoke and liquid flows than APIC.

The Impulse Particle-In-Cell Method

Ryan S. Zesch, Vismay Modi, Shinjiro Sueda, David I.W. Levin

We present neural collision fields as an alternative to contact point sampling in physics simulations. Our approach is built on top of a novel smoothed integral formulation for the contact surface patches between two triangle meshes. By reformulating collisions as an integral, we avoid issues of sampling common to many collision-handling algorithms. Because the resulting integral is difficult to evaluate numerically, we store its solution in an integrated neural collision field — a 6D neural field in the space of triangle pair vertex coordinates. Our network generalizes well to new triangle meshes without retraining. We demonstrate the effectiveness of our method by implementing it as a constraint in a position-based dynamics framework and show that our neural formulation successfully handles collisions in practical simulations involving both volumetric and thin-shell geometries.

Neural Collision Fields for Triangle Primitives

Mitsuki Hamamichi, Kentaro Nagasawa, Masato Okada, Ryohei Seto, Yonghao Yue

We estimate the three Herschel–Bulkley parameters (yield stress, power-law index, and consistency parameter) for shear-dependent fluid-like materials possibly with large-scale inclusions, for which rheometers may fail to provide a useful measurement. We perform experiments using the unknown material for dam-break (or column collapse) setups and capture video footage. We then use simulations to optimize for the material parameters. For better match up with the simple shear flow encountered in a rheometer, we modify the flow rule for the elasto-viscoplastic Herschel-Bulkley model. Analyzing the loss landscape for optimization, we realize a similarity relation; material parameters far away within this relation would result in matched simulations, making it hard to distinguish the parameters. We found that by exploiting the setup dependency of the similarity relation, we can improve on the estimation using multiple setups, which we propose by analyzing the Hessian of the similarity relation. We validate the efficacy of our method by comparing the estimations to the measurements from a rheometer (for materials without large-scale inclusions) and show applications to materials with large-scale inclusions, including various salad or pasta sauces, and congee.

Non-Newtonian ViRheometry via Similarity Analysis

Otman Benchekroun, Ty Trusty, Eitan Grinspun, Danny M. Kaufman, David I.W. Levin

Real-time elastodynamic solvers are well-suited for the rapid simulation of homogeneous elastic materials, with high-rates generally enabled by aggressive early termination of timestep solves. Unfortunately, the introduction of strong domain heterogeneities can make these solvers slow to converge. Stopping the solve short creates visible damping artifacts and rotational errors. To address these challenges we develop a reduced mixed finite element solver that pre serves rich rotational motion, even at low-iteration regimes. Specifically, this solver augments time-step solve optimizations with auxiliary stretch degrees of freedom at mesh elements, and maintains consistency with the primary positional degrees of freedoms at mesh nodes via explicit constraints. We make use of a Skinning Eigenmode subspace for our positional degrees of freedom. We accelerate integration of non-linear elastic energies with a cubature approximation, placing stretch degrees of freedom at cubature points. Across a wide range of examples we demonstrate that this subspace is particularly well suited for heterogeneous material simulation. Our resulting method is a subspace mixed finite element method completely decoupled from the resolution of the mesh that is well-suited for real-time simulation of heterogeneous domains.

Subspace Mixed Finite Elements for Real-Time Heterogeneous Elastodynamics

Doug L. James, David I.W. Levin

Motion control of large-scale, multibody physics animations with contact is difficult. Existing approaches, such as those based on optimization, are computationally daunting, and, as the number of interacting objects increases, can fail to find satisfactory solutions. We present a new, complementary method for the visual control of multibody animations that exploits object motion and visibility, and has overall cost comparable to a single simulation. Our method is highly practical, and is demonstrated on numerous large-scale, contact-rich examples involving both rigid and deformable bodies.

ViCMA: Visual Control of Multibody Animations