Physics-Based Animation

Jerry Hsu, Tongtong Wang, Zherong Pan, Xifeng Gao, Cem Yuksel, Kui Wu

Lagrangian/Eulerian hybrid strand-based hair simulation techniques have quickly become a popular approach in VFX and real-time graphics applications. With Lagrangian hair dynamics, the inter-hair contacts are resolved in the Eulerian grid using the continuum method, i.e., the MPM scheme with the granular Drucker–Prager rheology, to avoid expensive collision detection and handling. This fuzzy collision handling makes the authoring process significantly easier. However, although current hair grooming tools provide a wide range of strand-based modeling tools for this simulation approach, the crucial sag-free initialization functionality remains often ignored. Thus, when the simulation starts, gravity would cause any artistic hairstyle to sag and deform into unintended and undesirable shapes. This paper proposes a novel four-stage sag-free initialization framework to solve stable quasistatic configurations for hybrid strand-based hair dynamic systems. These four stages are split into two global-local pairs. The first one ensures static equilibrium at every Eulerian grid node with additional inequality constraints to prevent stress from exiting the yielding surface. We then derive several associated closed-form solutions in the local stage to compute segment rest lengths, orientations, and particle deformation gradients in parallel. The second global-local step solves along each hair strand to ensure all the bend and twist constraints produce zero net torque on every hair segment, followed by a local step to adjust the rest Darboux vectors to a unit quaternion. We also introduce an essential modification for the Darboux vector to eliminate the ambiguity of the Cosserat rod rest pose in both initialization and simulation. We evaluate our method on a wide range of hairstyles, and our approach can only take a few seconds to minutes to get the rest quasistatic configurations for hundreds of hair strands. Our results show that our method successfully prevents sagging and has minimal impact on the hair motion during simulation.

Sag-Free Initialization for Strand-based Hybrid Hair Simulation

Pengbin Tang, Stelian Coros, Bernhard Thomaszewski

We present a method for computational modeling, mechanical characterization, and macro-scale simulation of discrete interlocking materials (DIM)—3D-printed chainmail fabrics made of quasi-rigid interlocking elements. Unlike conventional elastic materials for which deformation and restoring force are directly coupled, the mechanics of DIM are governed by contacts between individual elements that give rise to anisotropic deformation constraints. To model the mechanical behavior of these materials, we propose a computational approach that builds on three key components. (a): we explore the space of feasible deformations using native-scale simulations at the per-element level. (b): based on this simulation data, we introduce the concept of strain-space boundaries to represent deformation limits for in- and out-of-plane deformations, and (c): we use the strain-space boundaries to drive an efficient macro-scale simulation model based on homogenized deformation constraints. We evaluate our method on a set of representative discrete interlocking materials and validate our findings against measurements on physical prototypes.

Beyond Chainmail: Computational Modeling of
Discrete Interlocking Materials

Zhen Chen, Danny M. Kaufman, Mélina Skouras, Etienne Vouga

We propose a new approach for representing wrinkles, designed to capture complex and detailed wrinkle behavior on coarse triangle meshes, called Complex Wrinkle Fields. Complex Wrinkle Fields consist of an almost-everywhere-unit complex-valued phase function over the surface; a frequency one-form; and an amplitude scalar, with a soft compatibility condition coupling the frequency and phase. We develop algorithms for interpolating between two such wrinkle fields, for visualizing them as displacements of a Loop-subdivided refinement of the base mesh, and for making smooth local edits to the wrinkle amplitude, frequency, and/or orientation. These algorithms make it possible, for the first time, to create and edit animations of wrinkles on triangle meshes that are smooth in space, evolve smoothly through time, include singularities along with their complex interactions, and that represent frequencies far finer than the surface resolution.

Complex Wrinkle Field Evolution

Stefan Jeschke, Chris Wojtan

This paper introduces a novel method for simulating large bodies of water as a height field. At the start of each time step,we partition the waves into a bulk flow (which approximately satisfies the assumptions of the shallow water equations) and surface waves (which approximately satisfy the assumptions of Airy wave theory). We then solve the two wave regimes separately using appropriate state-of-the-art techniques, and re-combine the resulting wave velocities at the end of each step. This strategy leads to the first heightfield wave model capable of simulating complex interactions between both deep and shallow water effects, like the waves from a boat wake sloshing up onto a beach, or a dam break producing wave interference patterns and eddies.We also analyze the numerical dispersion created by our method and derive an exact correction factor for waves at a constant water depth, giving us a numerically perfect re-creation of theoretical water wave dispersion patterns.

Generalizing Shallow Water Simulations with Dispersive Surface Waves

Nicholas Sharp, Cristian Romero, Alec Jacobson, Etienne Vouga, Paul G. Kry, David I.W. Levin, Justin Solomon

Physical systems ranging from elastic bodies to kinematic linkages are defined on high-dimensional configuration spaces, yet their typical low-energy configurations are concentrated on much lower-dimensional subspaces. This work addresses the challenge of identifying such subspaces automatically: given as input an energy function for a high-dimensional system, we produce a low-dimensional map whose image parameterizes a diverse yet low-energy submanifold of configurations. The only additional input needed is a single seed configuration for the system to initialize our procedure; no dataset of trajectories is required. We represent subspaces as neural networks that map a low-dimensional latent vector to the full configuration space, and propose a training scheme to fit network parameters to any system of interest. This formulation is effective across a very general range of physical systems; our experiments demonstrate not only nonlinear and very low-dimensional elastic body and cloth subspaces, but also more general systems like colliding rigid bodies and linkages. We briefly explore applications built on this formulation, including manipulation, latent interpolation, and sampling.

Data-Free Learning of Reduced-Order Kinematics

Yuxing Qiu, Samuel T. Reeve, Minchen Li, Yin Yang, Stuart R. Slattery, Chenfanfu Jiang

In this article, we present a four-layer distributed simulation system and its adaptation to the Material Point Method (MPM). The system is built upon a performance portable C++ programming model targeting major High-Performance-Computing (HPC) platforms. A key ingredient of our system is a hierarchical block-tile-cell sparse grid data structure that is distributable to an arbitrary number of Message Passing Interface (MPI) ranks. We additionally propose strategies for efficient dynamic load balance optimization to maximize the efficiency of MPI tasks. Our simulation pipeline can easily switch among backend programming models, including OpenMP and CUDA, and can be effortlessly dispatched onto supercomputers and the cloud. Finally, we construct benchmark experiments and ablation studies on supercomputers and consumer workstations in a local network to evaluate the scalability and load balancing criteria. We demonstrate massively parallel, highly scalable, and gigascale resolution MPM simulations of up to 1.01 billion particles for less than 323.25 seconds per frame with 8 OpenSSH-connected workstations.

A Sparse Distributed Gigascale Resolution Material Point Method

Lei Lan, Minchen Li, Chenfanfu Jiang, Huamin Wang, Yin Yang

In this paper, we present a GPU algorithm for finite element hyperelastic simulation. We show that the interior-point method, known to be effective for robust collision resolution, can be coupled with non-Newton procedures and be massively sped up on the GPU. Newton’s method has been widely chosen for the interior-point family, which fully solves a linear system at each step. After that, the active set associated with collision/contact constraints is updated. Mimicking this routine using a non-Newton optimization (like gradient descent or ADMM) unfortunately does not deliver expected accelerations. This is because the barrier functions employed in an interior-point method need to be updated at every iteration to strictly confine the search to the feasible region. The associated cost (e.g., per-iteration CCD) quickly overweights the benefit brought by the GPU, and a new parallelism modality is needed. Our algorithm is inspired by the domain decomposition method and designed to move interior-point-related computations to local domains as much as possible. We minimize the size of each domain (i.e., a stencil) by restricting it to a single element, so as to fully exploit the capacity of modern GPUs. The stencil-level results are integrated into a global update using a novel hybrid sweep scheme. Our algorithm is locally second-order offering better convergence. It enables simulation acceleration of up to two orders over its CPU counterpart. We demonstrate the scalability, robustness, efficiency, and quality of our algorithm in a variety of simulation scenarios with complex and detailed collision geometries.

Second-order Stencil Descent for Interior-point Hyperelasticity

Jingwei Tang, Byungsoo Kim, Vinicius Azevedo, Barbara Solenthaler

Controlling fluid simulations is notoriously difficult due to its high computational cost and the fact that user control inputs can cause unphysical motion. We present an interactive method for deformation-based fluid control. Our method aims at balancing the direct deformations of fluid fields and the preservation of physical characteristics. We train convolutional neural networks with physics-inspired loss functions together with a differentiable fluid simulator, and provide an efficient workflow for flow manipulations at test time. We demonstrate diverse test cases to analyze our carefully designed objectives and show them leading that they lead to physical and eventually visually appealing modifications on edited fluid data.

Physics-Informed Neural Corrector for Deformation-based Fluid Control

Timo Probst, Matthias Teschner,

We propose a novel monolithic pure SPH formulation to simulate fluids strongly coupled with rigid bodies. This includes fluid incompressibility, fluid-rigid interface handling and rigid-rigid contact handling with a viable implicit particle-based dry friction formulation. The resulting global system is solved using a new accelerated solver implementation that outperforms existing fluid and coupled rigid-fluid simulation approaches. We compare results of our simulation method to analytical solutions, show performance evaluations of our solver and present a variety of new and challenging simulation scenarios.

Monolithic Friction and Contact Handling for Rigid Bodies and Fluids using SPH

He Chen, Elie Diaz, Cem Yuksel

We introduce a method for efficiently computing the exact shortest path to the boundary of a mesh from a given internal point in the presence of self-intersections. We provide a formal definition of shortest boundary paths for self-intersecting objects and present a robust algorithm for computing the actual shortest boundary path. The resulting method offers an effective solution for collision and self-collision handling while simulating deformable volumetric objects, using fast simulation techniques that provide no guarantees on collision resolution. Our evaluation includes complex self-collision scenarios with a large number of active contacts, showing that our method can successfully handle them by introducing a relatively minor computational overhead.

Shortest Path to Boundary for Self-Intersecting Meshes