Physics-Based Animation

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

Jing Li, Tiantian Liu, Ladislav Kavan

We propose a fast and robust solver to simulate continuum-based deformable models with constraints, in particular, rigid-body and joint constraints useful for soft articulated characters. Our method embeds degrees of freedom of both articulated rigid bodies and deformable bodies in one unified optimization problem, thus coupling the deformable and rigid bodies. Our method can efficiently simulate character models, with rigid-body parts (bones) being correctly coupled with deformable parts (flesh). Our method is stable because backward Euler time integration is applied to rigid as well as deformable degrees of freedom. Our method is rigorously derived from constrained Newtonian mechanics. In an example simulation with rigid bodies only, we demonstrate that our method converges to the same motion as classical explicitly integrated rigid body simulator

Fast Simulation of Deformable Characters with Articulated Skeletons in Projective Dynamics

Daniel Holden, Bang Chi Duong, Sayantan Datta, Derek Nowrouzezahrai

Data-driven methods for physical simulation are an attractive option for interactive applications due to their ability to trade precomputation and memory footprint in exchange for improved runtime performance. Yet, existing data-driven methods fall short of the extreme memory and performance constraints imposed by modern interactive applications like AAA games and virtual reality. Here, performance budgets for physics simulation range from tens to hundreds of micro-seconds per frame, per object. We present a data-driven physical simulation method that meets these constraints. Our method combines subspace simulation techniques with machine learning which, when coupled, enables a very efficient subspace-only physics simulation that supports interactions with external objects – a longstanding challenge for existing sub-space techniques. We also present an interpretation of our method as a special case of subspace Verlet integration, where we apply machine learning to efficiently approximate the physical forces of the system directly in the subspace. We propose several practical solutions required to make effective use of such a model, including a novel training methodology required for prediction stability, and a GPU-friendly subspace decompression algorithm to accelerate rendering.

Subspace Neural Physics: Fast Data-Driven Interactive Simulation

Peter Kadlecek, Ladislav Kavan

The human face is an anatomical system exhibiting heterogenous and anisotropic mechanical behavior. This leads to complex deformations even in a neutral facial expression due to external forces such as gravity. We start by building a volumetric model from magnetic resonance images of a neutral facial expression. To obtain data on facial deformations we capture and register 3D scans of the face with different gravity directions and with various facial expressions. Our main contribution consists in solving an inverse physics problem where we learn mechanical properties of the face from our training data (3D scans). Specifically, we learn heterogenous stiffness and prestrain (which introduces anisotropy). The generalization capability of our resulting physics-based model is tested on 3D scans. We demonstrate that our model generates predictions of facial deformations more accurately than recent related physics-based techniques.

Building Accurate Physics-Based Face Models From Data

Yu Ju (Edwin) Chen, David I.W. Levin, Danny Kaufman, Uri Ascher, Dinesh K. Pai

Elastodynamic system simulation is a key procedure in computer graphics and robotics applications. To enable these simulations, the governing differential system is discretized in space (employing FEM) and then in time. For many simulation-based applications keeping the spatial resolution of the computational mesh effectively coarse is crucial for securing acceptable computational efficiency.However, this can introduce numerical stiffening effects that impede visual accuracy. We propose and demonstrate, for both linear and nonlinear force models, a new method called EigenFit that improves the consistency and accuracy of the lower energy, primary deformation modes, as the spatial mesh resolution is coarsened. EigenFit applies a partial spectral decomposition, solving a generalized eigenvalue problem in the leading mode subspace and then replacing the first several eigenvalues of the coarse mesh by those of the fine one at rest. EigenFit’s performance relies on a novel subspace model reduction technique which restricts the spectral decomposition to finding just a few of the leading eigenmodes. We demonstrate its efficacy on a number of objects with both homogeneous and heterogeneous material distributions.

EigenFit for Consistent Elastodynamic Simulation Across Mesh Resolution