Physics-Based Animation

Christopher Brandt, Leonardo Scandolo, Elmar Eisemann, Klaus Hildebrandt

We introduce the Reduced Immersed Method (RIM) for the real-time simu-lation of two-way coupled incompressible fluids and elastic solids and theinteraction of multiple deformables with (self-)collisions. Our framework isbased on a novel discretization of theimmersed boundary equations of motion,which model fluid and deformables as a single incompressible medium andtheir interaction as a unified system on a fixed domain combining Eulerianand Lagrangian terms. One advantage for real-time simulations resultingfrom this modeling is that two-way coupling phenomena can be faithfullysimulated while avoiding costly calculations such as tracking the deform-ing fluid-solid interfaces and the associated fluid boundary conditions. Ourdiscretization enables the combination of a PIC/FLIP fluid solver with areduced-order Lagrangian elasticity solver. Crucial for the performance ofRIM is the efficient transfer of information between the elasticity and thefluid solver and the synchronization of the Lagrangian and Eulerian set-tings. We introduce the concept oftwin subspacesthat enables an efficientreduced-order modeling of the transfer. Our experiments demonstrate thatRIM handles complex meshes and highly resolved fluids for large time stepsat high framerates on off-the-shelf hardware, even in the presence of highvelocities and rapid user interaction. Furthermore, it extends reduced-orderelasticity solvers such as Hyper-Reduced Projective Dynamics with naturalcollision handling.

The Reduced Immersed Method for Real-Time Fluid-Elastic Solid Interaction and Contact Simulation

Marie-Lena Eckert, Kiwon Um, Nils Thuerey

In this paper, we present ScalarFlow, a first large-scale data set of reconstructions of real-world smoke plumes. In addition, we propose a framework for accurate physics-based reconstructions from a small number of video streams. Central components of our framework are a novel estimation of unseen inflow regions and an efficient optimization scheme constrained by a simulation to capture real-world fluids. Our data set includes a large number of complex natural buoyancy-driven flows. The flows transition to turbulence and contain observable scalar transport processes. As such, the ScalarFlow data set is tailored towards computer graphics, vision, and learning applications. The published data set will contain volumetric reconstructions of velocity and density as well as the corresponding input image sequences with calibration data, code, and instructions how to reproduce the commodity hardware capture setup. We further demonstrate one of the many potential applications: a first perceptual evaluation study, which reveals that the complexity of the reconstructed flows would require large simulation resolutions for regular solvers in order to recreate at least parts of the natural complexity contained in the captured data.

ScalarFlow: A Large-Scale Volumetric Data Set of Real-world Scalar Transport Flows for Computer Animation and Machine Learning

Byungsoo Kim, Vinicius C. Azevedo, Markus Gross, Barbara Solenthaler

Artistically controlling fluids has always been a challenging task. Optimization techniques rely on approximating simulation states towards target velocity or density field configurations, which are often handcrafted by artists to indirectly control smoke dynamics. Patch synthesis techniques transfer image textures or simulation features to a target flow field. However, these are either limited to adding structural patterns or augmenting coarse flows with turbulent structures, and hence cannot capture the full spectrum of different styles and semantically complex structures. In this paper, we propose the first Transport-based Neural Style Transfer (TNST) algorithm for volumetric smoke data. Our method is able to transfer features from natural images to smoke simulations, enabling general content-aware manipulations ranging from simple patterns to intricate motifs. The proposed algorithm is physically inspired, since it computes the density transport from a source input smoke to a desired target configuration. Our transport-based approach allows direct control over the divergence of the stylization velocity field by optimizing incompressible and irrotational potentials that transport smoke towards stylization. Temporal consistency is ensured by transporting and aligning subsequent stylized velocities, and 3D reconstructions are computed by seamlessly merging stylizations from different camera viewpoints.

Transport-Based Neural Style Transfer for Smoke Simulations

Yun (Raymond) Fei, Christopher Batty, Eitan Grinspun, Changxi Zheng

We propose a framework for simulating the complex dynamics of strands interacting with compressible, shear-dependent liquids, such as oil paint, mud, cream, melted chocolate, and pasta sauce. Our framework contains three main components: the strands modeled as discrete rods, the bulk liquid represented as a continuum (material point method), and a reduced-dimensional flow of liquid on the surface of the strands with detailed elastoviscoplastic behavior. These three components are tightly coupled together. To enable discrete strands interacting with continuum-based liquid, we develop models that account for the volume change of the liquid as it passes through strands and the momentum exchange between the strands and the liquid. We also develop an extended constraint-based collision handling method that supports cohesion between strands. Furthermore, we present a principled method to preserve the total momentum of a strand and its surface flow, as well as an analytic plastic flow approach for Herschel-Bulkley fluid that enables stable semi-implicit integration at larger time steps. We explore a series of challenging scenarios, involving splashing, shaking, and agitating the liquid which causes the strands to stick together and become entangled.

A Multi-Scale Model for Coupling Strands with Shear-Dependent Liquid

Zangyueyang Xian, Xin Tong, Tiantian Liu

We propose a simple yet efficient multigrid scheme to simulate high-resolution deformable objects in their full spaces at interactive frame rates. The point of departure of our method is the Galerkin projection which is simple to construct. However, a naive Galerkin multigrid does not scale well for large and irregular grids because it trades-off matrix sparsity for smaller sized linear systems which eventually stops improving the performance. Given that observation, we design our special projection criterion which is based on skinning space coordinates with piecewise constant weights, to make our Galerkin multigrid method scale for high-resolution meshes without suffering from dense linear solves. The usage of skinning space coordinates enables us to reduce the resolution of grids more aggressively, and our piecewise constant weights further ensure us to always deal with reasonably-sparse linear solves. Our projection matrices also help us to manage multi-level linear systems efficiently. Therefore, our method can be applied to different optimization schemes such as Newton’s method and Projective Dynamics, pushing the resolution of a real-time simulation to orders of magnitudes higher. Our final GPU implementation outperforms the other state-of-the-art GPU deformable body simulators, enabling us to simulate large deformable objects with hundred thousands of degrees of freedom in real-time.

A Scalable Galerkin Multigrid Method for Real-time Simulation of Deformable Objects

• Mandoline: Robust Cut-Cell Generation for Arbitrary Triangle Meshes
• A Scalable Galerkin Multigrid Method for Real-time Simulation of Deformable Objects
• A Multi-Scale Model for Coupling Strands with Shear-Dependent Liquid
• Video-Guided Real-to-Virtual Parameter Transfer for Viscous Fluids
• A Thermomechanical Material Point Method for Baking and Cooking
• Transport-Based Neural Style Transfer for Smoke Simulations
• Taichi: A Language for High-Performance Computation on Spatially Sparse Data Structures
• Accelerating ADMM for Efficient Simulation and Optimization
• Accelerated Complex Step Finite Difference for Expedient Deformable Simulation
• Material-adapted Refinable Basis Functions for Elasticity Simulation
• ScalarFlow: A Large-Scale Volumetric Data Set of Real-world Scalar Transport Flows for Computer Animation and Machine Learning
• The Reduced Immersed Method for Real-Time Fluid-Elastic Solid Interaction and Contact Simulation
• SoftCon: Simulation and Control of Soft-Bodied Animals with Biomimetic Actuators
• Consistent Shepard Interpolation for SPH-Based Fluid Animation
• Learning an Intrinsic Garment Space for Interactive Authoring of Garment Animation
• Real2Sim: Visco-elastic parameter estimation from dynamic motion
• Fluid Carving: Intelligent Resizing for Fluid Simulation Data
• Schur Complement-based Substructuring of Stiff Multibody Systems with Contact (TOG)
• X-CAD: Optimizing CAD Models with Extended Finite Elements
• SoftCon: Simulation and Control of Soft-Bodied Animals with Biomimetic Actuators

Baptiste Angles, Daniel Rebain, Miles Macklin, Brian Wyvill, Loic Barthe, JP Lewis, Javier von der Pahlen, Shahram Izadi, Julien Valentin, Sofien Bouaziz, Andrea Tagliasacchi

We extend the formulation of position-based rods to include elastic volumetric deformations. We achieve this by introducing an additional degree of freedom per vertex — isotropic scale (and its velocity). Including scale enriches the space of possible deformations, allowing the simulation of volumetric effects, such as a reduction in cross-sectional area when a rod is stretched. We rigorously derive the continuous formulation of its elastic energy potentials, and hence its associated position-based dynamics (PBD) updates to realize this model, enabling the simulation of up to 26000 DOFs at 140 Hz in our GPU implementation. We further show how rods can provide a compact alternative to tetrahedral meshes for the representation of complex muscle deformations, as well as providing a convenient representation for collision detection. This is achieved by modeling a muscle as a bundle of rods, for which we also introduce a technique to automatically convert a muscle surface mesh into a rods-bundle. Finally, we show how rods and/or bundles can be skinned to a surface mesh to drive its deformation, resulting in an alternative to cages for real-time volumetric deformation.

VIPER: Volume Invariant Position-based Elastic Rods

Xuchen Han, Theodore Gast, Qi Guo, Stephanie Wang, Chenfanfu Jiang, Joseph Teran

We present a new hybrid Lagrangian Material Point Method for simulating elastic objects like hair, rubber,and soft tissues that utilizes a Lagrangian mesh for internal force computation and an Eulerian mesh for self collision as well as coupling with external materials. While recent Material Point Method (MPM) techniques allow for natural simulation of hyperelastic materials represented with Lagrangian meshes, they utilize an updated Lagrangian discretization where the Eulerian grid degrees of freedom are used to take variations of the potential energy. This often coarsens the degrees of freedom of the Lagrangian mesh and can lead to artifacts.We develop a hybrid approach that retains Lagrangian degrees of freedom while still allowing for natural coupling with other materials simulated with traditional MPM, e.g. sand, snow, etc. Furthermore, while recent MPM advances allow for resolution of frictional contact with codimensional simulation of hyperelasticity, they do not generalize to the case of volumetric materials. We show that our hybrid approach resolves these issues.We demonstrate the efficacy of our technique with examples that involve elastic soft tissues coupled with kinematic skeletons, extreme deformation, and coupling with multiple elastoplastic materials. Our approach also naturally allows for two-way rigid body coupling.

A Hybrid Material Point Method for Frictional Contact with Diverse Materials

Miles Macklin, Kier Storey, Michelle Lu, Pierre Terdiman, Nuttapong Chentanez, Stefan Jeschke, Matthias Müller

In this paper we re-examine the idea that implicit integrators with large time steps offer the best stability/performance trade-off for stiff systems. We make the surprising observation that performing a single large time step with n constraint solver iterations is less effective than computing n smaller time steps, each with a single constraint solver iteration. Based on this observation, our approach is to split every visual time step into n substeps of length ∆t/n and to perform a single iteration of extended position-based dynamics (XPBD) in each such substep. When compared to a traditional implicit integrator with large time steps we find constraint error and damping are significantly reduced. When compared to an explicit integrator we find that our method is more stable and robust for a wider range of stiffness parameters. This result holds even when compared against more sophisticated implicit solvers based on Krylov methods. Our method is straightforward to implement, and is not sensitive to matrix conditioning nor is it to overconstrained problems

Small Steps in Physics Simulation

Rahul Narain, Jonas Zehnder, Bernhard Thomaszewski

Zehnder et al. [2018] recently introduced an advection-reflection method for fluid simulation that dramatically reduces artificial dissipation. We establish a connection between their method and the implicit midpoint time integration scheme, and present a simple modification to obtain an advection-reflection scheme with second-order accuracy in time. We compare with existing alternatives, including a second-order semi-Lagrangian method based on BDF2, and demonstrate the improved energy-preservation properties.

A Second-Order Advection-Reflection Solver