Physics-Based Animation

David Hahn, Pol Banzet, James M. Bern, Stelian Coros

This paper presents a method for optimizing visco-elastic material parameters of a finite element simulation to best approximate the dynamic motion of real-world soft objects. We compute the gradient with respect to the material parameters of a least-squares error objective function using either direct sensitivity analysis or an adjoint state method. We then optimize the material parameters such that the simulated motion matches real-world observations as closely as possible. In this way, we can directly build a useful simulation model that captures the visco-elastic behaviour of the specimen of interest. We demonstrate the effectiveness of our method on various examples such as numerical coarsening, custom-designed objective functions,and of course real-world flexible elastic objects made of foam or 3D printed lattice structures, including a demo application in soft robotics

Real2Sim: Visco-elastic parameter estimation from dynamic motion

Juyong Zhang, Yue Peng, Wenqing Ouyang, Bailin Deng

The alternating direction method of multipliers (ADMM) is a popular approach for solving optimization problems that are potentially non-smooth and with hard constraints. It has been applied to various computer graphics applications, including physical simulation, geometry processing, and image processing. However, ADMM can take a long time to converge to a solution of high accuracy. Moreover, many computer graphics tasks involve non-convex optimization, and there is often no convergence guarantee for ADMM on such problems since it was originally designed for convex optimization. In this paper, we propose a method to speed up ADMM using Anderson acceleration, an established technique for accelerating fixed-point iterations. We show that in the general case, ADMM is a fixed-point iteration of the second primal variable and the dual variable, and Anderson acceleration can be directly applied. Additionally, when the problem has a separable target function and satisfies certain conditions, ADMM becomes a fixed-point iteration of only one variable, which further reduces the computational overhead of Anderson acceleration. Moreover, we analyze a particular non-convex problem structure that is common in computer graphics, and prove the convergence of ADMM on such problems under mild assumptions. We apply our acceleration technique on a variety of optimization problems in computer graphics, with notable improvement on their convergence speed.

Accelerating ADMM for Simulation and Optimization

Jiong Chen, Max Budninskiy, Houman Owhadi, Hujun Bao, Jin Huang, Mathieu Desbrun

In this paper, we introduce a hierarchical construction of material-adapted refinable basis functions and associated wavelets to offer efficient coarse-graining of linear elastic objects. While spectral methods rely on global basis functions to restrict the number of degrees of freedom, our basis functions are locally supported; yet, unlike typical polynomial basis functions, they are adapted to the material inhomogeneity of the elastic object to better capture its physical properties and behavior. In particular, they share spectral approximation properties with eigenfunctions, offering a good compromise between computational complexity and accuracy. Their construction involves only linear algebra and follows a fine-to-coarse approach, leading to a block-diagonalization of the stiffness matrix where each block corresponds to an intermediate scale space of the elastic object. Once this hierarchy has been precomputed, we can simulate an object at runtime on very coarse resolution grids and still capture the correct physical behavior, with orders of magnitude speedup compared to a fine simulation. We show on a variety of heterogeneous materials that our approach outperforms all previous coarse-graining methods for elasticity.

Material-adapted Refinable Basis Functions for Elasticity Simulation

Sehee Min, Jungdam Won, Seunghwan Lee, Jungnam Park, Jehee Lee

We present a novel and general framework for the design and control of underwater soft-bodied animals. The whole body of an animal consisting of soft tissues is modeled by tetrahedral and triangular FEM meshes. The contraction of muscles embedded in the soft tissues actuates the body and limbs to move. We present a novel muscle excitation model that mimics the anatomy of muscular hydrostats and their muscle excitation patterns. Our deep reinforcement learning algorithm equipped with the muscle excitation model successfully learned the control policy of soft-bodied animals, which can be physically simulated in real-time, controlled interactively, and resilient to external perturbations. We demonstrate the effectiveness of our approach with various simulated animals including octopuses, lampreys, starfishes, stingrays and cuttlefishes. They learn diverse behaviors such as swimming, grasping, and escaping from a bottle. We also implemented a simple user interface system that allows the user to easily create their creatures.

SoftCon: Simulation and Control of Soft-Bodied Animals with Biomimetic Actuators

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