Physics-Based Animation

Tassilo Kugelstadt, Jan Bender, José Antonio Fernández-Fernández, Stefan Rhys Jeske, Fabian Löschner and Andreas Longva

We develop a new operator splitting formulation for the simulation of corotated linearly elastic solids with Smoothed Particle Hydrodynamics (SPH). Based on the technique of Kugelstadt et al. [2018] originally devel-
oped for the Finite Element Method (FEM), we split the elastic energy into two separate terms corresponding to stretching and volume conservation, and based on this principle, we design a splitting scheme compatible with
SPH. The operator splitting scheme enables us to treat the two terms separately, and because the stretching forces lead to a stiffness matrix that is constant in time, we are able to prefactor the system matrix for the
implicit integration step. Solid-solid contact and fluid-solid interaction is achieved through a unified pressure solve. We demonstrate more than an order of magnitude improvement in computation time compared to a
state-of-the-art SPH simulator for elastic solids. We further improve the stability and reliability of the simulation through several additional contributions. We introduce a new implicit penalty mechanism that suppresses zero-energy modes inherent in the SPH formulation for elastic solids, and present a new, physics-inspired sampling algorithm for generating high-quality particle distributions for the rest shape of an elastic solid. We finally also devise an efficient method for interpolating vertex positions of a high-resolution surface mesh based on the SPH particle positions for use in high-fidelity visualization.

Fast Corotated Elastic SPH Solids with Implicit Zero-Energy Mode Control

Tao Du, Kui Wu, Pingchuan Ma, Sebastien Wah, Andrew Spielberg, Daniela Rus, Wojciech Matusik

We present a novel, fast differentiable simulator for soft-body learning and control applications. Existing differentiable soft-body simulators can be classified into two categories based on their time integration methods: Simulators using explicit time-stepping scheme require tiny time steps to avoid numerical instabilities in gradient computation, and simulators using implicit time integration typically compute gradients by employing the adjoint method and solving the expensive linearized dynamics. Inspired by Projective Dynamics (PD), we present Differentiable Projective Dynamics (DiffPD), an efficient differentiable soft-body simulator based on PD with implicit time integration. The key idea in DiffPD is to speed up backpropagation by exploiting the prefactorized Cholesky decomposition in forward PD simulation. In terms of contact handling, DiffPD supports two types of contacts: a penalty-based model describing contact and friction forces and a complementarity-based model enforcing non-penetration conditions and static friction. We evaluate the performance of DiffPD and observe it is 4-19 times faster compared to the standard Newton’s method in various applications including system identification, inverse design problems, trajectory optimization, and closed-loop control. We also apply DiffPD in a real-to-sim example with contact and collisions and show its capability of reconstructing a digital twin of real-world scenes.

DiffPD: Differentiable Projective Dynamics

Libo Huang, Ziyin Qu, Xun Tan, Xinxin Zhang, Dominik L. Michels, Chenfanfu Jiang

The simulation of large open water surface is challenging for a uniform volumetric discretization of the Navier-Stokes equation. The water splashes near moving objects, which height field methods for water waves cannot capture, necessitates high resolution simulation such as the Fluid-Implicit-Particle (FLIP) method. On the other hand, FLIP is not efficient for the long-lasting water waves that propagates to long distances, which requires sufficient depth for correct dispersion relationship. This paper presents a new method to tackle this dilemma through an efficient hybridization of volumetric and surface-based advection-projection discretizations. We design a hybrid time-stepping algorithm that combines a FLIP domain and an adaptively remeshed Boundary Element Method (BEM) domain for the incompressible Euler equations. The resulting framework captures the detailed water splashes near moving objects with FLIP, and produces convincing water waves with correct dispersion relationship at modest additional cost.

Ships, Splashes, and Waves on a Vast Ocean

• Honey I Shrunk the Domain: Reduced Domain Decomposition for Efficient Optimization of Fluids
• Two-step Temporal Interpolation Network using Forward-advection for Efficient Smoke Simulation
• Patch Erosion for Deformable Lapped Textures on 3D Fluids
• Physically-based Book Simulation with Freeform Developable Surfaces
• EMU: Efficient Muscle Simulation in Deformation Space
• Realistic Buoyancy Model for Real-Time Applications
• Physically Based Simulation and Rendering of Urban Thermography
• Simulating the Evolution of Ancient Fortified Cities
• Broadmark: A Testing Framework for Broad-Phase Collision Detection Algorithms
• Data Assimilation for Full 4D PC-MRI Measurements: Physics-Based Denoising and Interpolation

Mengyu Chu,  Nils Thuerey, Hans-Peter Seidel, Christian Theobalt, Rhaleb Zayer

While modern fluid simulation methods achieve high-quality simulation results, it is still a big challenge to interpret and control motion from visual quantities, such as the advected marker density. These visual quantities play an important role in user interactions: Being familiar and meaningful to humans, these quantities have a strong correlation with the underlying motion. We propose a novel data-driven conditional adversarial model that solves the challenging, and theoretically ill-posed problem of deriving plausible velocity fields from a single frame of a density field. Besides density modifications, our generative model is the first to enable the control of the results using all of the following control modalities: obstacles, physical parameters, kinetic energy, and vorticity. Our method is based on a new conditional generative adversarial neural network that explicitly embeds physical quantities into the learned latent space, and a new cyclic adversarial network design for control disentanglement. We show the high quality and versatile controllability of our results for density-based inference, realistic obstacle interaction, and sensitive responses to modifications of physical parameters, kinetic energy, and vorticity.

Learning Meaningful Controls for Fluids

Thomas Wolf, Victor Cornillere, Olga Sorkine-Hornung

Reading books or articles digitally has become accessible and widespread thanks to the large amount of affordable mobile devices and distribution platforms. However, little effort has been devoted to improving the digital book reading experience,despite studies showing disadvantages of digital text media consumption, such as diminished memory recall and enjoyment,compared to physical books. In addition, a vast amount of physical, printed books of interest exist, many of them rare andnot easily physically accessible, such as out-of-print art books, first editions, or historical tomes secured in museums. Digital replicas of such books are typically either purely text based, or consist of photographed pages, where much of the essenceof leafing through and experiencing the actual artifact is lost. In this work, we devise a method to recreate the experience of reading and interacting with a physical book in a digital 3D environment. Leveraging recent work on static modeling of freeform developable surfaces, which exhibit paper-like properties, we design a method for dynamic physical simulation of such surfaces, accounting for gravity and handling collisions to simulate pages in a book. We propose a mix of 2D and 3Dmodels, specifically tailored to represent books to achieve a computationally fast simulation, running in real time on mobile devices. Our system enables users to lift, bend and flip book pages by holding them at arbitrary locations and provides a holistic interactive experience of a virtual 3D book

Physically-based Book Simulation with Freeform Developable Surfaces

Shiying Xiong, Rui Tao, Yaorui Zhang, Fan Feng, Bo Zhu

We propose a novel Lagrangian geometric representation using segment clouds to simulate incompressible fluid exhibiting strong anisotropic vortical features. The central component of our approach is a cloud of discrete segments enhanced by a set of local segment reseeding operations to facilitate both the geometrical evolution and the topological updates of vortical flow. We build a vortex dynamics solver with the support for dynamic solid boundaries based on discret segment primitives. We demonstrate the efficacy of our approach by simulating a broad range of challenging flow phenomena, such as reconnection of non-closed vortex tubes and vortex shedding behind a rotating object.

Incompressible flow simulation on vortex segment clouds

Shuqi Yang, Shiying Xiong, Yaorui Zhang, Fan Feng, Jinyuan Liu, Bo Zhu

We propose a novel gauge fluid solver based on Clebsch wave functions to solve incompressible fluid equations. Our method combines the expressive power of Clebsch wave functions to represent coherent vortical structures and the generality of gauge methods to accommodate a broad array of fluid phenomena. By evolving a transformed wave function as the system’s gauge variable enhanced by an additional projection step to enforce pressure jumps on the free boundaries, our method can significantly improve the vorticity generation and preservation ability for a broad range of gaseous and liquid phenomena. Our approach can be easily implemented by modifying a standard grid-based fluid simulator. It can be used to solve various fluid dynamics, including complex vortex filament dynamics, fluids with different obstacles, and surface-tension flow.

Clebsch Gauge Fluid

Rene Winchenbach, Andreas Kolb

In this paper we propose an improved refinement process for the simulation of incompressible low-viscosity turbulent flows using Smoothed Particle Hydrodynamics, under adaptive volume ratios of up to 1 : 1,000,000. We derive a discretized objective function, which allows us to generate ideal refinement patterns for any kernel function and any number of particles a priori without requiring intuitive initial user-input. We also demonstrate how this objective function can be optimized online to further improve the refinement process during simulations by utilizing a gradient descent and a modified evolutionary optimization. Our investigation reveals an inherent residual refinement error term, which we smooth out using improved and novel methods. Our improved adaptive method is able to simulate adaptive volume ratios of1 : 1,000,000and higher, even under highly turbulent flows,only being limited by memory consumption. In general, we achieve more than an order of magnitude greater adaptive volume ratios than prior work.

Optimized Refinement for Spatially Adaptive SPH

Kai Jia

Solving nonlinear systems is an important problem. Numerical continuation methods efficiently solve certain nonlinear systems. The Asymptotic Numerical Method (ANM) is a powerful continuation method that usually converges faster than Newtonian methods. ANM explores the landscape of the function by following a parameterized solution curve approximated with a high-order power series. Although ANM has successfully solved a few graphics and engineering problems, prior to our work, applying ANM to new problems required significant effort because the standard ANM assumes quadratic functions, while manually deriving the power series expansion for nonquadratic systems is a tedious and challenging task. This paper presents a novel solver, SANM, that applies ANM to solve symbolically represented nonlinear systems. SANM solves such systems in a fully automated manner. SANM also extends ANM to support many nonquadratic operators, including intricate ones such as singular value decomposition. Furthermore, SANM generalizes ANM to support the implicit homotopy form. Moreover, SANM achieves high computing performance via optimized system design and implementation. We deploy SANM to solve forward and inverse elastic force equilibrium problems and controlled mesh deformation problems with a few constitutive models. Our results show that SANM converges faster than Newtonian solvers, requires little programming effort for new problems, and delivers comparable or better performance than a hand-coded, specialized ANM solver. While we demonstrate on mesh deformation problems, SANM is generic and potentially applicable to many tasks.

SANM: A Symbolic Asymptotic Numerical Solver with Applications in Mesh Deformation