Physics-Based Animation

Steffen Weiwel, Byungsoo Kim, Vinicius C. Azevedo, Barbara Solenthaler, Nils Thuerey

We propose an end-to-end trained neural network architecture to robustly predict the complex dynamics of fluid flows with high temporal stability. We focus on single-phase smoke simulations in 2D and 3D based on the incompressible Navier-Stokes (NS) equations, which are relevant for a wide range of practical problems. To achieve stable predictions for long-term flow sequences, a convolutional neural network (CNN) is trained for spatial compression in combination with a temporal prediction network that consists of stacked Long Short-Term Memory (LSTM) layers. Our core contribution is a novel latent space subdivision (LSS) to separate the respective input quantities into individual parts of the encoded latent space domain. This allows to distinctively alter the encoded quantities without interfering with the remaining latent space values and hence maximizes external control. By selectively overwriting parts of the predicted latent space points, our proposed method is capable to robustly predict long-term sequences of complex physics problems. In addition, we highlight the benefits of a recurrent training on the latent space creation, which is performed by the spatial compression network.

Latent Space Subdivision: Stable and Controllable Time Predictions for Fluid Flow

All the SCA papers , physics-related and otherwise, along with their presentation videos, are on the SCA conference site. (Below I try to link to author pages, as usual.)

• Distant Collision Response in Rigid Body Simulations
• A Bending Model for Nodal Discretizations of Yarn-Level Cloth
• A Hybrid Lagrangian/Eulerian Collocated Velocity Advection and Projection Method for Fluid Simulation
• Linear Time Stable PD Controllers for Physics-based Character Animation
• A Finite Element Formulation of Baraff-Witkin Cloth
• Efficient 2D Simulation on Moving 3D Surfaces
• Particle-based Liquid Control using Animation Templates
• Primal/Dual Descent Methods for Dynamics
• Detailed Rigid Body Simulation with Extended Position Based Dynamics
• Higher-Order Time Integration for Deformable Solids
• Fully Convolutional Graph Neural Networks for Parametric Virtual Try-On
• Latent Space Subdivision: Stable and Controllable Time Predictions for Fluid Flow
• Making Procedural Water Waves Boundary-aware
• A Pixel-Based Framework for Data-Driven Clothing
• Cloth and Skin Deformation with a Triangle Mesh Based CNN
• Effective time step restrictions for explicit MPM simulation
• A Divergence Free Mixture Model for Multiphase Fluids

Invited presentations (Journal papers):

• The Matchstick Model for Anisotropic Friction Cones (CGF)
• Implicit Density Projection for Volume Conserving Liquids (TVCG)
• Turbulent Details Simulation for SPH Fluids via Vorticity Refinement (CGF)

Eulalie Coevoet, Sheldon Andrews, Denali Relles, Paul G. Kry

We use a finite element model to predict the vibration response of objects in a rigid body simulation, such that rigid objects are augmented to provide a plausible elastic collision response between distant objects due to vibration. We start with a generalized eigenvalue decomposition of the elastic model to precompute a response to an impact at any point on an elastic object with fixed boundary conditions. Then, given a collision between objects, we generate an approximate response impulse to distribute to other objects already in contact with the colliding bodies. This can lead to distant impacts causing an object to slip, or a delicate stack of objects to fall. We also use a geodesic distance based spatial attenuation approximation for travelling waves in objects to respond to an impact at one contact with an impulse at other locations. This response ultimately allows a long distance relationship between contacts, both across a single object being struck, but also traversing the contact graph of a larger collection of objects. We qualitatively validate our approach with a ground truth simulation, and demonstrate a number of scenarios where a long distance relationship between contacts is valuable.

Distant Collision Response in Rigid Body Simulations

José M. Pizana, Alejandro Rodríguez, Gabriel Cirio, Miguel A. Otaduy

To deploy yarn-level cloth simulations in production environments, it is paramount to design very efficient implementations,which mitigate the cost of the extremely high resolution. To this end, nodal discretizations aligned with the regularity of the fabric structure provide an optimal setting for efficient GPU implementations. However, nodal discretizations complicate the design of robust and controllable bending. In this paper, we address this challenge, and propose a model of bending that isboth robust and controllable, and employs only nodal degrees of freedom. We extract information of yarn and fabric orientation implicitly from the nodal degrees of freedom, with no need to augment the model explicitly. But most importantly, and unlike previous formulations that use implicit orientations, the computation of bending forces bears no overhead with respect to other nodal forces such as stretch. This is possible by tracking optimal orientations efficiently. We demonstrate the impact of our bending model in examples with controllable anisotropy, as well as ironing, wrinkling, and plasticity.

A Bending Model for Nodal Discretizations of Yarn-Level Cloth

Steven Gagniere, David Hyde, Alan Marquez-Razon, Chenfanfu Jiang, Ziheng Ge, Xuchen Han, Qi Guo, Joseph Teran

We present a hybrid particle/grid approach for simulating incompressible fluids on collocated velocity grids. Our approach supports both particle-based Lagrangian advection in very detailed regions of the flow and efficient Eulerian grid-based advection in other regions of the flow. A novel Backward Semi-Lagrangian method is derived to improve accuracy of grid based advection. Our approach utilizes the implicit formula associated with solutions of the inviscid Burgers’ equation. We solve this equation using Newton’s method enabled by C1continuous grid interpolation. We enforce incompressibility over collocated,rather than staggered grids. Our projection technique is variational and designed for B-spline interpolation over regular grids where multiquadratic interpolation is used for velocity and multilinear interpolation for pressure. Despite our use of regular grids, we extend the variational technique to allow for cut-cell definition of irregular flow domains for both Dirichlet and free surface boundary conditions.

A Hybrid Lagrangian/Eulerian Collocated Velocity Advection and Projection Method for Fluid Simulation

Zhiqi Yin, KangKang Yin

In physics-based character animation, Proportional-Derivative (PD) controllers are commonly used for tracking reference motions in motor control tasks. Stable PD (SPD) controllers significantly improve the numerical stability of traditional PD controllers and support large gains and large integration time steps during simulation. For an articulated rigid body system with n degrees of freedom, all SPD implementations to date, however, use an O(n^3) dense matrix factorization based method. In this paper, we propose a linear time algorithm for SPD computation, which is based on Featherstone’s forward dynamics formulation for articulated rigid body systems in generalized coordinates. We demonstrate the performance advantage of our algorithm by comparing with both the conventional dense matrix factorization based method and an alternative sparse matrix factorization based method. We show that the proposed algorithm provides superior stability when controlling complex models at large time steps. We further demonstrate that our algorithm can improve the learning speed and quality of a Deep Reinforcement Learning (DRL) system for physics-based character animation.

Linear Time Stable PD Controllers for Physics-based Character Animation

Theodore Kim

The Baraff-Witkin model has been a popular formulation for cloth for 20 years. However, its relationship to the finite element method (FEM) has always been unclear, because the model resists being written as an isotropic, hyperelastic strain energy. In this paper, we show that this is because the Baraff-Witkin model is actually a coupled anisotropic strain energy. We show that its stretching term approximates the isotropic As-Rigid-As-Possible (ARAP) energy, and its shearing term is a cross-fiber coupling energy common in biomechanics. While it has been known empirically for some time that the model can produce indefinite force Jacobians, the conditions under which they occur has never been clear. Our formulation enables a complete eigenanalysis that precisely characterizes exactly when indefiniteness occurs, and leads to fast, analytic, semi-positive-definite projection methods. Finally, our analysis suggests a generalized Baraff-Witkin energy with non-orthogonal warp and weft directions.

A Finite Element Formulation of Baraff-Witkin Cloth

Cheng Li, Min Tang, Ruofeng Tong, Ming Cai, Jieyi Zhao, Dinesh Manocha

We present a novel parallel algorithm for cloth simulation that exploits multiple GPUs for fast computation and the handling of very high resolution meshes. To accelerate implicit integration, we describe new parallel algorithms for sparse matrix-vector multiplication (SpMV) and for dynamic matrix assembly on a multi-GPU workstation. Our algorithms use a novel work queue generation scheme for a fat-tree GPU interconnect topology. Furthermore, we present a novel collision handling scheme that uses spatial hashing for discrete and continuous collision detection along with a non-linear impact zone solver. Our parallel schemes can distribute the computation and storage overhead among multiple GPUs and enable us to perform almost interactive simulation on complex cloth meshes, which can hardly be handled on a single GPU due to memory limitations. We have evaluated the performance with two multi-GPU workstations (with 4 and 8 GPUs, respectively) on cloth meshes with 0.5-1.65M triangles. Our approach can reliably handle the collisions and generate vivid wrinkles and folds at 2-5 fps, which is significantly faster than prior cloth simulation systems. We observe almost linear speedups with respect to the number of GPUs.

P-Cloth: Interactive Complex Cloth Simulation on Multi-GPU Systems using Dynamic Matrix Assembly and Pipelined Implicit Integrators

Torsten Hädrich, Miłosz Makowski, Wojtek Pałubicki, Daniel T. Banuti, Soren Pirk, Dominik L. Michels

The complex interplay of a number of physical and meteorological phenomena makes simulating clouds a challenging and open research problem. We explore a physically accurate model for simulating clouds and the dynamics of their transitions. We propose first-principle formulations for computing buoyancy and air pressure that allow us to simulate the variations of atmospheric density and varying temperature gradients. Our simulation allows us to model various cloud types, such as cumulus, stratus, and stratoscumulus, and their realistic formations caused by changes in the atmosphere. Moreover, we are able to simulate large-scale cloud super cells – clusters of cumulonimbus formations – that are commonly present during thunderstorms. To enable the efficient exploration of these stormscapes, we propose a lightweight set of high-level parameters that allow us to intuitively explore cloud formations and dynamics. Our method allows us to simulate cloud formations of up to about 20km×20km extents at interactive rates. We explore the capabilities of physically accurate and yet interactive cloud simulations by showing numerous examples and by coupling our model with atmosphere measurements of real-time weather services to simulate cloud formations in the now. Finally, we quantitatively assess our model with cloud fraction profiles, a common measure for comparing cloud types.

Stormscapes: Simulating Cloud Dynamics in the Now

Libo Huang, Dominik L. Michels.

We devise a novel surface-only approach for simulating the three dimensional free-surface flow of incompressible, inviscid, and linearly magnetizable ferrofluids. A Lagrangian velocity field is stored on a triangle mesh capturing the fluid’s surface. The two key problems associated with the dynamic simulation of the fluid’s interesting geometry are the magnetization process transitioning the fluid from a non-magnetic into a magnetic material, and the evaluation of magnetic forces. In this regard, our key observation is that for linearly incompressible ferrofluids, their magnetization and application of magnetic forces only require knowledge about the position of the fluids’ boundary. Consequently, our approach employs a boundary element method solving the magnetization problem and evaluating the so-called magnetic pressure required for the force evaluation. The magnetic pressure is added to the Dirichlet boundary condition of a surface-only liquids solver carrying out the dynamical simulation. By only considering the fluid’s surface in contrast to its whole volume, we end up with an efficient approach enabling more complex and realistic ferrofluids to be explored in the digital domain without compromising efficiency. Our approach allows for the use of physical parameters leading to accurate simulations as demonstrated in qualitative and quantitative evaluations.

Surface-Only Ferrofluids