Physics-Based Animation

Georg Sperl, Rahul Narain, Chris Wojtan

We present a method for animating yarn-level cloth effects using a thin-shell solver. We accomplish this through numerical homogenization: we first use a large number of yarn-level simulations to build a model of the potential energy density of the cloth and then use this energy density function to compute forces in a thin shell simulator. We model several yarn-based materials, including both woven and knitted fabrics. Our model faithfully reproduces expected effects like the stiffness of woven fabrics, and the highly deformable nature and anisotropy of knitted fabrics. Our approach does not require any real-world experiments nor measurements; because the method is based entirely on simulations, it can generate entirely new material models quickly, without the need for testing apparatuses or human intervention. We provide data-driven models of several woven and knitted fabrics, which can be used for efficient simulation with an off-the-shelf cloth solver.

Homogenized Yarn-Level Cloth

Sadashige Ishida*, Peter Synak*, Fumiya Narita, Toshiya Hachisuka, Chris Wojtan

Previous research on animations of soap bubbles, films, and foams largely focuses on the motion and geometric shape of the bubble surface. These works neglect the evolution of the bubble’s thickness, which is normally responsible for visual phenomena like surface vortices, Newton’s interference patterns, capillary waves, and deformation-dependent rupturing of films in a foam. In this paper, we model these natural phenomena by introducing the film thickness as a reduced degree of freedom in the Navier-Stokes equations and deriving their equations of motion. We discretize the equations on a non-manifold triangle mesh surface and couple it to an existing bubble solver. In doing so, we also introduce an incompressible fluid solver for 2.5D films and a novel advection algorithm for convecting fields across non-manifold surface junctions. Our simulations enhance state-of-the-art bubble solvers with additional effects caused by convection, rippling, draining, and evaporation of the thin film.

A Model for Soap Film Dynamics with Evolving Thickness

Wei Li, Yixin Chen, Mathieu Desbrun, Changxi Zheng, Xiaopei Liu

Despite their cinematic appeal, turbulent flows involving fluid-solid coupling remain a computational challenge in animation. At the root of the current limitation is the numerical dispersion from which most accurateNavier-Stokes solvers suffer: proper coupling between fluid and solid often generates artificial dispersion in the form of local, parasitic trains of velocity oscillations, eventually leading to numerical instability. While successive improvements over the years have led to conservative and detail-preserving fluid integrators, the dispersive nature of these solvers is rarely discussed despite its dramatic impact on fluid-structure interaction. In this paper, we introduce a novel low-dissipation and low-dispersion fluid solver that can simulate two-way coupling in an efficient and scalable manner, even for turbulent flows. In sharp contrast with most current CG approaches, we construct our solver from a kinetic formulation of the flow derived from statistical mechanics. Unlike existing lattice Boltzmann solvers, our approach leverages high-order moment relaxations as a key to controlling both dissipation and dispersion of the resulting scheme. Moreover, we combine our new fluid solver with the immersed boundary method to easily handle fluid-solid coupling through time adaptive simulations. Our kinetic solver is highly parallelizable by nature, making it ideally suited for implementation on single- or multi-GPU computing platforms. Extensive comparisons with existing solvers on synthetic tests and real-life experiments are used to highlight the multiple advantages of our work over traditional and more recent approaches, in terms of accuracy, scalability, and efficiency.

Fast and Scalable Turbulent Flow Simulation with Two-Way Coupling

Xinlei Wang*, Minchen Li*, Yu Fang, Xinxin Zhang, Ming Gao, Min Tang, Danny M. Kaufman, Chenfanfu Jiang

We propose Hierarchical Optimization Time Integration (HOT) for efficient implicit time-stepping of the Material Point Method (MPM) irrespective of simulated materials and conditions. HOT is an MPM-specialized hierarchical optimization algorithm that solves nonlinear time step problems for large-scale MPM systems near the CFL-limit. HOT provides convergent simulations “out-of-the-box” across widely varying materials and computational resolutions without parameter tuning. As an implicit MPM time stepper accelerated by a custom-designed Galerkin multigrid wrapped in a quasi-Newton solver, HOT is both highly parallelizable and robustly convergent. As we show in our analysis, HOT maintains consistent and efficient performance even as we grow stiffness, increase deformation, and vary materials over a wide range of finite strain, elastodynamic and plastic examples. Through careful benchmark ablation studies, we compare the effectiveness of HOT against seemingly plausible alternative combinations of MPM with standard multigrid and other Newton-Krylov models. We show how these alternative designs result in severe issues and poor performance. In contrast, HOT outperforms the existing state-of-the-art, heavily optimized implicit MPM codes with an up to 10x performance speedup across a wide range of challenging benchmark test simulations.

Hierarchical Optimization Time Integration for CFL-rate MPM Stepping

Ryan Goldade, Mridul Aanjaneya, Christopher Batty

We propose to enhance the capability of standard free-surface flow simulators with efficient support for immersed bubbles through two new models: constraint-based bubbles and affine fluid regions. Unlike its predecessors, our constraint-based model entirely dispenses with the need for advection or projection inside zero-density bubbles, with extremely modest additional computational overhead that is proportional to the surface area of all bubbles. This surface-only approach is easy to implement, realistically captures many familiar bubble behaviors, and even allows two or more distinct liquid bodies to correctly interact across completely unsimulated air. We augment this model with a per-bubble volume-tracking and correction framework to minimize the cumulative effects of gradual volume drift. To support bubbles with non-zero densities, we propose a novel reduced model for an irregular fluid region with a single pointwise incompressible affine vector field. This model requires only 11 interior velocity degrees of freedom per affine fluid region in 3D, and correctly reproduces buoyant, stationary, and sinking behaviors of a secondary fluid phase with non-zero density immersed in water. Since the pressure projection step in both the above schemes is a slightly modified Poisson-style system, we propose novel Multigrid-based preconditioners for Conjugate Gradients for fast numerical solutions of our new discretizations. Furthermore, we observe that by enforcing an incompressible affine vector field over a coalesced set of grid cells, our reduced model is effectively an irregular coarse super-cell. This offers a convenient and flexible adaptive coarsening strategy that integrates readily with the standard staggered grid approach for fluid simulation, yet supports coarsened regions that are arbitrary voxelized shapes, and provides an analytically divergence-free interior. We demonstrate its effectiveness with a new adaptive liquid simulator whose interior regions are coarsened into a mix of tiles with regular and irregular shapes.

Constraint Bubbles and Affine Regions: Reduced Fluid Models for Efficient Immersed Bubbles and Flexible Spatial Coarsening

Lei Lan, Ran Luo, Marco Fratarcangeli, Weiwei Xu, Huamin Wang, Xiaohu Guo, Junfeng Yao, Yin Yang

We propose a framework for the interactive simulation of nonlinear de-formable objects. The primary feature of our system is the seamless integration of deformable simulation and collision culling, which are often independently handled in existing animation systems. The bridge connect-ing them is the medial axis transform or MAT, a high-fidelity volumetric approximation of complex 3D shapes. From the physics simulation perspective, MAT leads to an expressive and compact reduced nonlinear model. We employ a semi-reduced projective dynamics formulation, which well captures high-frequency local deformations of high-resolution models while retaining a low computation cost. Our key observation is that the most compelling (nonlinear) deformable effects are enabled by the local constraint projection, which should not be aggressively reduced, and only apply model reduction at the global stage. From the collision detection/culling perspective, MAT is geometrically versatile using linear-interpolated spheres (i.e.the so-called medial primitives) to approximate the boundary of the input model. The intersection test between two medial primitives is formulated as a quadratically constrained quadratic program problem. We give an algorithm to solve this problem exactly, which returns the deepest penetration between a pair of intersecting medial primitives. When coupled with spatial hashing, collision (including self-collision) can be efficiently identified on the GPU within few milliseconds even for massive simulations. We have tested our system on a variety of geometrically complex and high-resolution deformable objects, and our system produces convincing animations with all the collisions/self-collisions well handled at an interactive rate.

Medial Elastics: Efficient and Collision-ready Deformation via Medial Axis Transform

Rosa M. Sánchez-Banderas, Alejandro Rodríguez, Héctor Barreiro, Miguel A. Otaduy

This paper introduces a method to simulate complex rod assemblies and stacked layers with implicit contact handling, through Eulerian-on-Lagrangian (EoL) discretizations. Previous EoL methods fail to handle such complex situations, due to ubiquitous and intrinsic degeneracies in the contact geometry, which prevent the use of remeshing and make simulations unstable. We propose a novel mixed Eulerian-Lagrangian discretization that supports accurate and efficient contact as in EoL methods, but is transparent to internal rod forces, and hence insensitive to degeneracies. By combining the standard and novel EoL discretizations as appropriate, we derive mixed statics-dynamics equations of motion that can be solved in a unified manner with standard solvers. Our solution is simple and elegant in practice and produces robust simulations on large-scale scenarios with complex rod arrangements and pervasive degeneracies. We demonstrate our method on multi-layer yarn-level cloth simulations, with implicit handling of both intra- and inter-layer contacts.

Robust Eulerian-on-Lagrangian Rods

José A. Canabal, Miguel A. Otaduy, Byungmoon Kim, Jose Echevarria

We present a new system for interactive dendritic painting. Dendritic painting is characterized by the unique and intricate branching patterns that grow from the interaction of inks, solvents and medium. Painting sessions thus become very dynamic and experimental. To achieve a compelling simulation of this painting technique we introduce a new Reaction-Diffusion model with carefully designed terms to allow natural interactions in a painting context. We include additional user control not possible in the real world to guide and constrain the growth of the patterns in expressive ways. Our multi-field model is able to capture and simulate all these complex phenomena efficiently in real-time, expanding the tools available to the digital artist, while producing compelling animations for motion graphics.

Simulation of Dendritic Painting

• Local Bases for Model-Reduced Smoke Simulation
• Displacement-Correlated XFEM for Simulating Brittle Fracture
• Mixing Yarns and Triangles in Cloth Simulation
• Binary Ostensibly-Implicit Trees for Fast Collision Detection
• A Practical Method for Animating Anisotropic Elastoplastic Materials
• Fast and Scalable Solvers for the Fluid Pressure Equations with Separating Solid Boundary Conditions
• Simulation of Dendritic Painting
• SoftSMPL: Data-driven Modeling of Nonlinear Soft-tissue Dynamics for Parametric Humans
• Modeling and Estimation of Nonlinear Skin Mechanics for Animated Avatars
• Interactive Meso-scale Simulation of Skyscapes
• Asynchronous Eulerian Liquid Simulation

Olivier Mercier, Derek Nowrouzezahrai

We present a flexible model reduction method for simulating incompressible fluids. We derive a novel vector field basis composed of localized basis flows that have simple analytic forms and can be tiled on regular lattices, avoiding the use of complicated data structures or neighborhood queries. Local basis flow interactions can be precomputed and reused to simulate fluid dynamics on any simulation domain without additional overhead. We introduce heuristic simulation dynamics tailored to our basis and derived from a projection of the Navier-Stokes equations to produce physically plausible motion, exposing intuitive parameters to control energy distribution across scales. Our basis can adapt to curved simulation boundaries, can be coupled with dynamic obstacles, and offers simple adjustable trade-offs between speed and visual resolution.

Local Bases for Model-reduced Smoke Simulations