Physics-Based Animation

Tianyu Wang, Jiong Chen, Dongping Li, Xiaowei Liu, Huamin Wang, Kun Zhou

Step-and-project is a popular method to simulate non-penetrating deformable bodies in physically-based animation. The strategy is to first integrate the system in time without considering contacts and then resolve potential intersections, striking a good balance between plausibility and efficiency. However, existing methods can be defective and unsafe when using large time steps, taking risks of failure or demanding repetitive collision testing and resolving that severely degrade performance. In this paper, we propose a novel two-way method for fast and reliable continuous collision handling. Our method launches an optimization from both ends of the intermediate time-integrated state and the previous intersection-free state. It progressively generates a piecewise linear path and eventually obtains a feasible solution for the next time step. The algorithm efficiently alternates between a forward step and a backward step until the result is conditionally converged. Thanks to a set of unified volume-based contact constraints, our method offers flexible and reliable handling of various codimensional deformable bodies, including volumetric bodies, cloth, hair and sand. Experimental results demonstrate the safety, robustness, physical fidelity and numerical efficiency of our method, making it particularly suitable for scenarios involving large deformations or large time steps.

Fast GPU-Based Two-Way Continuous Collision Handling

Zachary Ferguson, Pranav Jain, Denis Zorin, Teseo Schneider, Daniele Panozzo

High-order bases provide major advantages over linear ones in terms of efficiency, as they provide (for the same physical model) higher accuracy for the same running time, and reliability, as they are less affected by locking artifacts and mesh quality. Thus, we introduce a high-order FE formulation (high-order bases) for elastodynamic simulation on high-order (curved) meshes with contact handling based on the recently proposed Incremental Potential Contact (IPC) model. Our approach is based on the observation that each IPC optimization step used to minimize the elasticity, contact, and friction potentials leads to linear trajectories even in the presence of nonlinear meshes or nonlinear FE bases. It is thus possible to retain the strong non-penetration guarantees and large time steps of the original formulation while benefiting from the high-order bases and high-order geometry. We accomplish this by mapping displacements and resulting contact forces between a linear collision proxy and the underlying high-order representation. We demonstrate the effectiveness of our approach in a selection of problems from graphics, computational fabrication, and scientific computing.

High-Order Incremental Potential Contact for Elastodynamic Simulation on Curved Meshes

Zachary Ferguson, Teseo Schneider, Danny M. Kaufman^† Daniele Panozzo^† (^†Joint last authors)

We propose a fully coupled, adaptive meshing algorithm for contacting elastodynamics where remeshing steps are tightly integrated, implicitly, within the time-step solve. Our algorithm refines and coarsens the domain automatically by measuring physical energy changes within each ongoing time-step solve. This provides consistent, efficient, and productive remeshing that, by construction, is physics-aware and so avoids the errors, over-refinements, artifacts, per-example hand-tuning, and instabilities commonly encountered when remeshing in time-stepping methods. Our in-time-step computation then ensures that each simulation step’s output is both a converged, stable solution on the updated mesh, and a temporally consistent trajectory with respect to the model and solution of the last time step. At the same time, the output is guaranteed safe (intersection- and inversion-free) across all operations. We demonstrate applications across a wide range of extreme stress tests with challenging contacts, sharp geometries, extreme compressions, large time steps, and wide material stiffness ranges – all scenarios well-appreciated to challenge existing remeshing methods.

In-Timestep Remeshing for Contacting Elastodynamics

• Two-Way Coupling of Skinning Transformations and Position Based Dynamics
• Physical Cyclic Animations
• Micropolar Elasticity in Physically-Based Animation
• A Linear and Angular Momentum Conserving Hybrid Particle/Grid Iteration for Volumetric Elastic Contact
• Towards Realtime: A Hybrid Physics-based Method for Hair Animation on GPU
• Lifted Curls: A Model for Tightly Coiled Hair Simulation
• An Eigenanalysis of Angle-Based Deformation Energies
• Adaptive Rigidification of Discrete Shells
• A Unified Analysis of Penalty-Based Collision Energies
• A Generalized Constitutive Model for Versatile MPM Simulation and Inverse Learning with Differentiable Physics
• A comparison of linear consistent correction methods for first-order SPH derivatives
• A Multilevel Active-Set Preconditioner for Box-Constrained Pressure Poisson Solvers
• DiffXPBD : Differentiable Position-Based Simulation of Compliant Constraint Dynamics

Yunuo Chen, Tianyi Xie, Cem Yuksel, Danny Kaufman,Yin Yang, Chenfanfu Jiang, Minchen Li

We present a novel mesh-based method for simulating the intricate dynamics of (potentially multi-layered) continuum thick shells. In order to accurately represent the constitutive behavior of structural responses in the thickness direction, we develop a dual-quadrature prism finite element formulation that is free from shear locking and naturally incorporates three-dimensional elastoplastic and viscoelastic constitutive models. Additionally, we introduce a simple and effective technique for embedding a high resolution membrane layer on top of the thick shell to enable independent high-frequency deformation modes that generate realistic wrinkles. With our novelly designed sparse basis vectors for the high-frequency deformations, the constrained Lagrangian mechanics problem is expressed as an unconstrained optimization and then efficiently solved by a custom alternating minimization technique. Our method opens up a new possibility for fast, high-quality, and thickness-aware simulations of leather garments, pillows, mats, metal boards, and potentially a variety of other thick structures.

Multi-layer Thick Shells

Wei Li, Mathieu Desbrun

Real-life flows exhibit complex and visually appealing behaviors such as bubbling, splashing, glugging and wetting that simulation techniques in graphics have attempted to capture for years. While early approaches were not capable of reproducing multiphase flow phenomena due to their ex- cessive numerical viscosity and low accuracy, kinetic solvers based on the lattice Boltzmann method have recently demonstrated the ability to simulate water-air interaction at high Reynolds numbers in a massively-parallel fashion. However, robust and accurate handling of fluid-solid coupling has remained elusive: be it for CG or CFD solvers, as soon as the motion of immersed objects is too fast or too sudden, pressures near boundaries and interfacial forces exhibit spurious oscillations leading to blowups. Built upon a phase-field and velocity-distribution based lattice-Boltzmann solver for multiphase flows, this paper spells out a series of numerical improvements in momentum exchange, interfacial forces, and two-way coupling to drastically reduce these typical artifacts, thus significantly expanding the types of fluid-solid coupling that we can efficiently simulate. We highlight the numerical benefits of our solver through various challenging simulation results, including comparisons to previous work and real footage.

Fluid-Solid Coupling in Kinetic Two-Phase Flow Simulation

Chaoyang Lyu, Kai Bai, Yiheng Wu, Mathieu Desbrun, Changxi Zheng, Xiaopei Liu

Virtual wind tunnel testing is a key ingredient in the engineering design process for the automotive and aeronautical industries as well as for urban planning: through visualization and analysis of the simulation data, it helps optimize lift and drag coefficients, increase peak speed, detect high pressure zones, and reduce wind noise at low cost prior to manufacturing. In this paper, we develop an efficient and accurate virtual wind tunnel system based on recent contributions from both computer graphics and computational fluid dynamics in high-performance kinetic solvers. Running on one or multiple GPUs, our massively-parallel lattice Boltzmann model meets industry standards for accuracy and consistency while exceeding current mainstream industrial solutions in terms of efficiency Ð especially for unsteady turbulent flow simulation at very high Reynolds number (on the order of 10^7) — due to key contributions in improved collision modeling and boundary treatment, automatic construction of multiresolution grids for complex models, as well as performance optimization. We demonstrate the efficacy and reliability of our virtual wind tunnel testing facility through comparisons of our results to multiple benchmark tests, showing an increase in both accuracy and efficiency compared to state-of-the-art industrial solutions. We also illustrate the fine turbulence structures that our system can capture, indicating the relevance of our solver for both VFX and industrial product design.

Building a Virtual Weakly-Compressible Wind Tunnel Testing Facility

Kangrui Xue, Ryan M. Aronson, Jui-Hsien Wang, Timothy R. Langlois, Doug L. James

We introduce a practical framework for synthesizing bubble-based water sounds that captures the rich inter-bubble coupling effects responsible for low-frequency acoustic emissions from bubble clouds. We propose coupled bubble oscillator models with regularized singularities, and techniques to reduce the computational cost of time stepping with dense, time-varying mass matrices. Airborne acoustic emissions are estimated using finite-difference time-domain (FDTD) methods. We propose a simple, analytical surface acceleration model, and a sample-and-hold GPU wavesolver that is simple and faster than prior CPU wavesolvers. Sound synthesis results are demonstrated using bubbly flows from incompressible, two-phase simulations, as well as procedurally generated examples using single-phase FLIP fluid animations. Our results demonstrate sound simulations with hundreds of thousands of bubbles, and perceptually significant frequency transformations with fuller low-frequency content.

Improved Water Sound Synthesis using Coupled Bubbles

Simon Duenser, Bernhard Thomaszewski, Roi Poranne, Stelian Coros

Many flexible structures are characterized by a small number of compliant modes, i.e., large deformation paths that can be traversed with little mechanical effort, whereas resistance to other deformations is much stiffer. Predicting the compliant modes for a given flexible structure, however, is challenging. While linear eigenmodes capture the small-deformation behavior, they quickly divert into states of unrealistically high energy for larger displacements. Moreover, they are inherently unable to predict nonlinear phenomena such as buckling, stiffening, multistability, and contact. To address this limitation, we propose Nonlinear Compliant Modes—a physically-principled extension of linear eigenmodes for large-deformation analysis. Instead of constraining the entire structure to deform along a given eigenmode, our method only prescribes the projection of the system’s state onto the linear mode while all other degrees of freedom follow through energy minimization. We evaluate the potential of our method on a diverse set of flexible structures, ranging from compliant mechanisms to topology-optimized joints and structured materials. As validated through experiments on physical prototypes, our method correctly predicts a broad range of nonlinear effects that linear eigenanalysis fails to capture.

Nonlinear Compliant Modes for Large-Deformation Analysis of Flexible Structures

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

We consider motion effected by shape change. Such motions are ubiquitous in nature and the human made environment, ranging from single cells to platform divers and jellyfish. The shapes may be immersed in various media ranging from the very viscous to air and nearly inviscid fluids. In the absence of external forces these settings are characterized by constant momentum. We exploit this in an algorithm which takes a sequence of changing shapes, say, as modeled by an animator, as input and produces corresponding motion in world coordinates. Our method is based on the geometry of shape change and an appropriate variational principle. The corresponding Euler-Lagrange equations are first order ODEs in the unknown rotations and translations and the resulting time stepping algorithm applies to all these settings without modification as we demonstrate with a broad set of examples.

Motion From Shape Change