Category: Uncategorized

Fabian Löschner, Andreas Longva, Stefan Jeske, Tassilo Kugelstadt, Jan Bender

Visually appealing and vivid simulations of deformable solids represent an important aspect of physically based computer animation. For the temporal discretization, it is customary in computer animation to use first-order accurate integration methods, such as Backward Euler, due to their simplicity and robustness. Although there is notable research on second-order methods, their use is not widespread. Many of these well-known methods have significant drawbacks such as severe numerical damping or scene-dependent time step restrictions to ensure stability. In this paper, we discuss the most relevant requirements on such methods in computer animation and motivate the interest beyond first-order accuracy. Keeping these requirements in mind, we investigate several promising methods from the families of diagonally implicit Runge-Kutta (DIRK) and Rosenbrock methods which currently do not appear to have considerable popularity in this field. We show that the usage of such methods improves the visual quality of physical animations. In addition, we demonstrate that they allow distinctly more control over damping at lower computational cost than classical methods. As part of our theoretical contribution, we review aspects of simulations that are often considered more intricate with higher-order methods, such as contact handling. To this end, we derive an implicit linearized contact model based on a predictor-corrector approach that leads to consistent behavior with higher-order integrators as predictors. Our contact model is well suited for the simulation of stiff, nonlinear materials with the integration methods presented in this paper and more common methods such as Backward Euler alike.

Higher-Order Time Integration for Deformable Solids

Matthias Müller, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tae-Yong Kim

We present a rigid body simulation method that can resolve small temporal and spatial details by using a quasi explicit integration scheme that is unconditionally stable. Traditional rigid body simulators linearize constraints because they operate on the velocity level or solve the equations of motion implicitly thereby freezing the constraint directions for multiple iterations. Our method always works with the most recent constraint directions. This allows us to trace high speed motion of objects colliding against curved geometry, to reduce the number of constraints, to increase the robustness of the simulation, and to simplify the formulation of the solver. In this paper we provide all the details to implement a fully fledged rigid body solver that handles contacts, a variety of joint types and the interaction with soft object

Detailed Rigid Body Simulation with Extended Position Based Dynamics

Miles Macklin, Kenny Erleben, Matthias Müller-Fischer, Nuttapong Chentanez, Stefan Jeschke, Tae-Yong Kim

We examine the relationship between primal, or force-based, and dual, or constraint-based formulations of dynamics. Variational frameworks such as Projective Dynamics have proved popular for deformable simulation, however they have not been adopted for contact-rich scenarios such as rigid body simulation. We propose a new preconditioned frictional contact solver that is compatible with existing primal optimization methods, and competitive with complementarity-based approaches. Our relaxed primal model generates improved contact force distributions when compared to dual methods, and has the advantage of being differentiable, making it well-suited for trajectory optimization. We derive both primal and dual methods from a common variational point of view, and present a comprehensive numerical analysis of both methods with respect to conditioning. We demonstrate our method on scenarios including rigid body contact, deformable simulation, and robotic manipulation.

Primal/Dual Descent Methods for Dynamics

Stefan Jeschke, Christian Hafner, Nuttapong Chentanez, Miles Macklin, Matthias Muller-Fischer, Chris Wojtan

The “procedural” approach to animating ocean waves is the dominant algorithm for animating larger bodies of water in interactive applications as well as in off-line productions — it provides high visual quality with a low computational demand. In this paper, we widen the applicability of procedural water wave animation with an extension that guarantees the satisfaction of boundary conditions imposed by terrain while still approximating physical wave behavior. In combination with a particle system that models wave breaking, foam, and spray, this allows us to naturally model waves interacting with beaches and rocks. Our system is able to animate waves at large scales at interactive frame rates on a commodity PC.

Making Procedural Water Waves Boundary-aware

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