Physics-Based Animation

Mengdi Wang, Yitong Deng, Xiangxin Kong, Aditya H. Prasad, Shiying Xiong, Bo Zhu

We propose a particle-based method to simulate thin-film fluid that jointly facilitates aggressive surface deformation and vigorous tangential flows. We build our dynamics model from the surface tension driven Navier-Stokes equation with the dimensionality reduced using the asymptotic lubrication theory and customize a set of differential operators based on the weakly compressible Smoothed Particle Hydrodynamics (SPH) for evolving pointset surfaces. The key insight is that the compressible nature of SPH, which is unfavorable in its typical usage, is helpful in our application to co-evolve the thickness, calculate the surface tension, and enforce the fluid incompressibility on a thin film. In this way, we are able to two-way couple the surface deformation with the in-plane flows in a physically based manner. We can simulate complex vortical swirls, fingering effects due to Rayleigh-Taylor instability, capillary waves, Newton’s interference fringes, and the Marangoni effect on liberally deforming surfaces by presenting both realistic visual results and numerical validations. The particle-based nature of our system also enables it to conveniently handle topology changes and codimension transitions, allowing us to marry the thin-film simulation with a wide gamut of 3D phenomena, such as pinch-off of unstable catenoids, dripping under gravity, merging of droplets, as well as bubble rupture.

Thin-Film Smoothed Particle Hydrodynamics Fluid

Liangwang Ruan, Jinyuan Liu, Bo Zhu, Shinjiro Sueda, Bin Wang, Baoquan Chen

We propose a novel three-way coupling method to model the contact interaction between solid and fluid driven by strong surface tension. At the heart of our physical model is a thin liquid membrane that simultaneously couples to both the liquid volume and the rigid objects, facilitating accurate momentum transfer, collision processing, and surface tension calculation. This model is implemented numerically under a hybrid Eulerian-Lagrangian framework where the membrane is modelled as a simplicial mesh and the liquid volume is simulated on a background Cartesian grid. We devise a monolithic solver to solve the interactions among the three systems of liquid, solid, and membrane. We demonstrate the efficacy of our method through an array of rigid-fluid contact simulations dominated by strong surface tension, which enables the faithful modeling of a host of new surface-tension-dominant phenomena including: objects with higher density than water can keep afloat on top of it; ‘Cheerios effect’ about floating objects that do not normally float attract one another; surface tension weakening effect caused by surface-active constituents.

Solid-Fluid Interaction with Surface-Tension-Dominant Contact

Jingyu Chen, Victoria Kala, Ala Marquez-Razon, Elias Gueidon, David A. B. Hyde, Joseph Teran

We present a novel Material Point Method (MPM) discretization of surface tension forces that arise from spatially varying surface energies. These variations typically arise from surface energy dependence on temperature and/or concentration. Furthermore, since the surface energy is an interfacial property depending on the types of materials on either side of an interface, spatial variation is required for modeling the contact angle at the triple junction between a liquid, solid and surrounding air. Our discretization is based onthe surface energy itself, rather than on the associated traction condition most commonly used for discretization with particle methods. Our energy based approach automatically captures surface gradients without the explicit need to resolve them as in traction condition based approaches. We include an implicit discretization of thermomechanical material coupling with anovel particle-based enforcement of Robin boundary conditions associated with convective heating. Lastly, we design a particle resampling approach needed to achieve perfect conservation of linear and angular momentum with Affine-Particle-In-Cell (APIC) [Jiang et al.2015]. We show that our approach enables implicit time stepping for complex behaviors like the Marangoni effect and hydrophobicity/hydrophilicity. We demonstrate the robustness and utility of our method by simulating materials that exhibit highly diverse degrees of surface tension and thermomechanical effects,such as water, wine and wax.

A Momentum-Conserving Implicit Material Point Method for Surface Tension with Contact Angles and Spatial Gradients

Jiong Chen, Florian Schäfer, Jin Huang, Mathieu Desbrun

Many computer graphics applications boil down to solving sparse systems of linear equations. While the current arsenal of numerical solvers available in various specialized libraries and for different computer architectures often allow efficient and scalable solutions to image processing, modeling and simulation applications, an increasing number of graphics problems face large-scale and ill-conditioned sparse linear systems — a numerical challenge which typically chokes both direct factorizations (due to high memory requirements) and iterative solvers (because of slow convergence). We propose a novel approach to the efficient preconditioning of such problems which often emerge from the discretization over unstructured meshes of partial differential equations with heterogeneous and anisotropic coefficients. Our numerical approach consists in simply performing a fine-to-coarse ordering and a multiscale sparsity pattern of the degrees of freedom, using which we apply an incomplete Cholesky factorization. By further leveraging supernodes for cache coherence, graph coloring to improve parallelism and partial diagonal shifting to remedy negative pivots, we obtain a preconditioner which, combined with a conjugate gradient solver, far exceeds the performance of existing carefully-engineered libraries for graphics problems involving bad mesh elements and/or high contrast of coefficients. We also back the core concepts behind our simple solver with theoretical foundations linking the recent method of operator-adapted wavelets used in numerical homogenization to the traditional Cholesky factorization of a matrix, providing us with a clear bridge between incomplete Cholesky factorization and multiscale analysis that we leverage numerically.

Multiscale Cholesky Preconditioning for Ill-conditioned Problems

Siyuan Shen, Yang Yin, Tianjia Shao, He Wang, Chenfanfu Jiang, Lei Lan, Kun Zhou

This paper provides a new avenue for exploiting deep neural networks to improve physics-based simulation. Specifically, we integrate the classic Lagrangian mechanics with a deep autoencoder to accelerate elastic simulation of deformable solids. Due to the inertia effect, the dynamic equilibrium cannot be established without evaluating the second-order derivatives of the deep autoencoder network. This is beyond the capability of off-the-shelf automatic differentiation packages and algorithms, which mainly focus on the gradient evaluation. Solving the nonlinear force equilibrium is even more challenging if the standard Newton’s method is to be used. This is because we need to compute a third-order derivative of the network to obtain the variational Hessian. We attack those difficulties by exploiting complex-step finite difference, coupled with reverse automatic differentiation. This strategy allows us to enjoy the convenience and accuracy of complex-step finite difference and in the meantime, to deploy complex-value perturbations as collectively as possible to save excessive network passes.With a GPU-based implementation, we are able to wield deep autoencoders(e.g.,10+layers) with a relatively high-dimension latent space in real-time.Along this pipeline, we also design a sampling network and a weighting net-work to enable weight-varying Cubature integration in order to incorporate nonlinearity in the model reduction. We believe this work will inspire and benefit future research efforts in nonlinearly reduced physical simulation problems.

High-order Differentiable Autoencoder for Nonlinear Model Reduction

Huamin Wang

In this paper, we study physics-based cloth simulation in a very high reso-lution setting, presumably at submillimeter levels with millions of vertices,to meet perceptual precision of our human eyes. State-of-the-art simulation techniques, mostly developed for unstructured triangular meshes, can hardly meet this demand due to their large computational costs and memory footprints. We argue that in a very high resolution, it is more plausible touse regular meshes with an underlying grid structure, which can be highly compatible with GPU acceleration like high-resolution images. Based on this idea, we formulate and solve the nonlinear optimization problem for simulating high-resolution wrinkles, by a fast block-based descent method with reduced memory accesses. We also investigate the development of the collision handling component in our system, whose performance benefits greatly from the grid structure. Finally, we explore various issues related tothe applications of our system, including initialization for fast convergence and temporal coherence, gathering effects, inflation and stuffing models,and mesh simplification. We can treat our system as a quasistatic wrinkle synthesis tool, run it as a standalone dynamic simulator, or integrate it into a multi-resolution solver as an additional component. The experiment demonstrates the capability, efficiency and flexibility of our system in producing avariety of high-resolution wrinkles effects.

GPU-Based Simulation of Cloth Wrinkles at Submillimeter Levels

Longhua Wu, Botao Wu, Yin Yang, Huamin Wang

Cloth dynamics and collision handling are the two most challenging topics in cloth simulation. While researchers have substantially improved the performance of cloth dynamics solvers recently, their success in fast collision detection and handling is rather limited. In this paper, we focus our research on the safety, efficiency and realism of the repulsion-based collision handling approach, which has demonstrated its potential in existing GPU-based simulators. Our first discovery is the necessary vertex distance conditions for cloth to enter self intersections, the negations of which can be viewed as vertex distance constraints continuous in time for sufficiently avoiding self collisions. Continuous constraints, however, cannot be enforced with ease.Our solution is to convert continuous constraints into three types of constraints: discrete edge length constraints, discrete vertex distance constraints and vertex displacement constraints. Based on this solution, we develop a fast and safe collision handling process for enforcing constraints, a novel splitting method for integrating collision handling with dynamics solvers,and static and adaptive remeshing schemes to further improve the runtime performance. In summary, our cloth simulator is efficient, safe, robust and parallelizable on a GPU. The experiment shows that it runs at least one order of magnitude faster than existing simulators.

A Safe and Fast Repulsion Method for GPU-based Cloth Self Collisions

Syuhei Sato, Yoshinori Dobashi, Theodore Kim

High-resolution fluid simulations are computationally expensive, so many post-processing methods have been proposed to add turbulent details to low-resolution flows. Guiding methods are one promising approach for adding naturalistic, detailed motions as a post-process, but can be inefficient. Thus, we propose a novel, efficient method that formulates fluid guidance as a minimization problem in stream function space. Input flows are first converted into stream functions, and a high resolution flow is then computed via optimization. The resulting problem sizes are much smaller than previous approaches, resulting in faster computation times. Additionally, our method does not require an expensive pressure projection, but still preserves mass. The method is both easy to implement and easy to control, as the user can control the degree of guiding with a single, intuitive parameter. We demonstrate the effectiveness of our method across various examples.

Stream-Guided Smoke Simulations

Ty Trusty, Honglin Chen, David I.W. Levin

We introduce a new method for direct physics-based animation of volumetric curved models, represented using NURBS surfaces. Our technical contribution is the Shape Matching Element Method (SEM). SEM is a completely meshless algorithm, the first to simultaneously be robust to gaps and overlaps in geometry, be compatible with standard constitutive models and time integration schemes, support contact and frictional interactions and to preserve feature correspondence during simulation which enables editable simulated output. We demonstrate the efficacy of our algorithm by producing compelling physics-based animations from a variety of curved input models.

The Shape Matching Element Method: Direct Animation of Curved Surface Models

Lei Lan*, Yin Yang*, Danny M. Kaufman, Junfeng Yao, Minchen Li, Chenfanfu Jiang (*equal contribution)

We propose a framework of efficient nonlinear deformable simulation with both fast continuous collision detection and robust collision resolution. We name this new framework Medial IPC as it integrates the merits from medial elastics, for an efficient and versatile reduced simulation, as well as incremental potential contact, for a robust collision and contact resolution. We leverage medial axis transform to construct a kinematic subspace. Instead of resorting to projective dynamics, we use classic hyperelastics to embrace real-world nonlinear materials. A novel reduced continuous collision detection algorithm is presented based on the medial mesh. Thanks to unique geometric properties of medial axis and medial primitives, we derive closed-form formulations for identifying between-primitive collision within the reduced medial space. In the meantime, the implicit barrier energy that generates necessary repulsion forces for collision resolution is also formulated with the medial coordinate. In other words, Medial IPC exploits a universal reduced coordinate for simulation, continuous self-/collision detection, and IPC-based collision resolution. Continuous collision detection also allows more aggressive time stepping. In addition, we carefully implement our system with a heterogeneous CPU-GPU deployment such that massively parallelizable computations are carried out on the GPU while few sequential computations are on the CPU. Such implementation also frees us from generating training poses for selecting Cubature points and precomputing their weights. We have tested our method on complicated deformable models and collision-rich simulation scenarios. Due to the reduced nature of our system,the computation is faster than fullspace IPC or other fullspace methods using continuous collision detection by at least one order. The simulation remains high-quality as the medial subspace captures intriguing and local deformations with sufficient realism.

Medial IPC: Accelerated Incremental Potential Contact with Medial Elastics