Physics-Based Animation

Mohammad Sina Nabizadeh, Ritoban Roy-Chowdhury, Hang Yin, Ravi Ramamoorthi, Albert Chern

We propose Coadjoint Orbit FLIP (CO-FLIP), a high order accurate, structure preserving fluid simulation method in the hybrid Eulerian-Lagrangian framework. We start with a Hamiltonian formulation of the incompressible Euler Equations, and then, using a local, explicit, and high order divergence free interpolation, construct a modified Hamiltonian system that governs our discrete Euler flow. The resulting discretization, when paired with a geometric time integration scheme, is energy and circulation preserving (formally the flow evolves on a coadjoint orbit) and is similar to the Fluid Implicit Particle (FLIP) method. CO-FLIP enjoys multiple additional properties including that the pressure projection is exact in the weak sense, and the particle-to-grid transfer is an exact inverse of the grid-to-particle interpolation. The method is demonstrated numerically with outstanding stability, energy, and Casimir preservation. We show that the method produces benchmarks and turbulent visual effects even at low grid resolutions.

Fluid Implicit Particles on Coadjoint Orbits

Jiayi Eris Zhang, Doug L. James, Danny M. Kaufman

We propose Progressive Dynamics, a coarse-to-fine, level-of-detail simulation method for the physics-based animation of complex frictionally contacting thin shell and cloth dynamics. Progressive Dynamics provides tight-matching consistency and progressive improvement across levels, with comparable quality and realism to high-fidelity, IPC-based shell simulations [Li et al. 2021] at finest resolutions. Together these features enable an efficient animation-design pipeline with predictive coarse-resolution previews providing rapid design iterations for a final, to-be-generated, high-resolution animation. In contrast, previously, to design such scenes with comparable dynamics would require prohibitively slow design iterations via repeated direct simulations on high-resolution meshes. We evaluate and demonstrate Progressive Dynamics’s features over a wide range of challenging stress-tests, benchmarks, and animation design tasks. Here Progressive Dynamics efficiently computes consistent previews at costs comparable to coarsest-level direct simulations. Its matching progressive refinements across levels then generate rich, high-resolution animations with high-speed dynamics, impacts, and the complex detailing of the dynamic wrinkling, folding, and sliding of frictionally contacting thin shells and fabrics.

Progressive Dynamics for Cloth and Shell Animation

C. Zhao, Tamar Shinar, Craig Schroeder

In this paper, we present a novel network-based approach for reconstructing signed distance functions from fluid particles. The method uses a weighting kernel to transfer particles to a regular grid, which forms the input to a convolutional neural network. We propose a regression-based regularization to reduce surface noise without penalizing high-curvature features. The reconstruction exhibits improved spatial surface smoothness and temporal coherence compared with existing state of the art surface reconstruction methods. The method is insensitive to particle sampling density and robustly handles thin features, isolated particles, and sharp edges.

Reconstruction of implicit surfaces from fluid particles using convolutional neural networks

• Fluid Implicit Particles on Coadjoint Orbits
• Particle-Laden Fluid on Flow Maps
• An Eulerian Vortex Method on Flow Maps
• Solid-Fluid Interaction on Particle Flow Maps
• Volumetric Homogenization for Knitwear Simulation
• Efficient Cloth Simulation Using Non-distance Barriers and Subspace Reuse
• Barrier-Augmented Lagrangian for GPU-based Elastodynamic Contact
• XPBI: Position-Based Dynamics with Smoothing Kernels Handles Continuum Inelasticity
• Computational Biomimetics of Winged Seeds
• Optimized shock-protecting microstructures
• Tencers: Tension-Constrained Elastic Rods
• Polar Interpolants for Thin-Shell Microstructure Homogenization
• A Time-Dependent Inclusion-Based Method for Continuous Collision Detection between Parametric Surfaces
• gDist: Efficient Distance Computation between 3D Meshes on GPU
• Trading Spaces: Adaptive Subspace Time Integration for Contacting Elastodynamics
• Accelerate Neural Subspace-Based Reduced-Order Solver of Deformable Simulation by Lipschitz Optimization
• Trust-Region Eigenvalue Filtering for Projected Newton
• A Cubic Barrier with Elasticity-Inclusive Dynamic Stiffness
• An Impulse Ghost Fluid Method for Simulating Two-Phase Flows
• MiNNIE: a Mixed Multigrid Method for Real-time Simulation of Nonlinear Near-Incompressible Elastics
• Analytic rotation-invariant modelling of anisotropic finite elements
• Neural Implicit Reduced Fluid Simulation
• Neural Garment Dynamic Super-Resolution
• Q3T Prisms: A Linear-Quadratic Solid Shell Element for Elastoplastic Surfaces
• A Mesh-based Simulation Framework using Automatic Code Generation

Egor Larionov, Andreas Longva, Uri M. Ascher, Jan Bender, Dinesh K. Pai

Dynamics simulation with frictional contacts is important for a wide range of applications, from cloth simulation to object manipulation. Recent methods using smoothed lagged friction forces have enabled robust and differentiable simulation of elastodynamics with friction. However, the resulting frictional behavior can be inaccurate and may not converge to analytic solutions. Here we evaluate the accuracy of lagged friction models in comparison with implicit frictional contact systems. We show that major inaccuracies near the stick-slip threshold in such systems are caused by lagging of friction forces rather than by smoothing the Coulomb friction curve. Furthermore, we demonstrate how systems involving implicit or lagged friction can be correctly used with higher-order time integration and highlight limitations in earlier attempts. We demonstrate how to exploit forward-mode automatic differentiation to simplify and, in some cases, improve the performance of the inexact Newton method. Finally, we show that other complex phenomena can also be simulated effectively while maintaining smoothness of the entire system. We extend our method to exhibit stick-slip frictional behavior and preserve volume on compressible and nearly-incompressible media using soft constraints.

Implicit Frictional Dynamics with Soft Constraints

Yinwei Du, Yue Li, Stelian Coros, Bernhard Thomaszewski,

Modeling contact between deformable solids is a fundamental problem in computer animation, mechanical design, and robotics. Existing methods based on C0-discretizations—piece-wise linear or polynomial surfaces—suffer from discontinuities and irregularities in tangential contact forces, which can significantly affect simulation outcomes and even prevent convergence. In this work, we show that these limitations can be overcome with a smooth surface representation based on Implicit Moving Least Squares (IMLS). In particular, we propose a self collision detection scheme tailored to IMLS surfaces that enables robust and efficient handling of challenging self contacts. Through a series of test cases, we show that our approach offers advantages over existing methods in terms of accuracy and robustness for both forward and inverse problems.

Robust and Artefact-Free Deformable Contact with Smooth Surface Representations

Alexandre Mercier-Aubin, Paul G. Kry

We present a novel multi-layer method for extended position-based dynamics that exploits a sequence of reduced models consisting of rigid and elastic parts to speed up convergence. Taking inspiration from concepts like adaptive rigidification and long-range constraints, we automatically generate different rigid bodies at each layer based on the current strain rate. During the solve, the rigid bodies provide coupling between progressively less distant vertices during layer iterations, and therefore the fully elastic iterations at the final layer start from a lower residual error. Our layered approach likewise helps with the treatment of contact, where the mixed solves of both rigid and elastic in the layers permit fast propagation of impacts. We show several experiments that guide the selection of parameters of the solver, including the number of layers, the iterations per layers, as well as the choice of rigid patterns. Overall, our results show lower compute times for achieving a desired residual reduction across a variety of simulation models and scenarios.

A Multi-Layer Solver for XPBD

Lukas Westhofen, José Antonio Fernández-Fernández, Stefan Rhys Jeske, Jan Bender

We present a strongly coupled method for the robust simulation of linear magnetic rigid bodies. Our approach describes the magnetic effects as part of an incremental potential function. This potential is inserted into the reformulation of the equations of motion for rigid bodies as an optimization problem. For handling collision and friction, we lean on the Incremental Potential Contact (IPC) method. Furthermore, we provide a novel, hybrid explicit / implicit time integration scheme for the magnetic potential based on a distance criterion. This reduces the fill-in of the energy Hessian in cases where the change in magnetic potential energy is small, leading to a simulation speedup without compromising the stability of the system. The resulting system yields a strongly coupled method for the robust simulation of magnetic effects. We showcase the robustness in theory by analyzing the behavior of the magnetic attraction against the contact resolution. Furthermore, we display stability in practice by simulating exceedingly strong and arbitrarily shaped magnets. The results are free of artifacts like bouncing for time step sizes larger than with the equivalent weakly coupled approach. Finally, we showcase the utility of our method in different scenarios with complex joints and numerous magnets.

Strongly Coupled Simulation of Magnetic Rigid Bodies

Quoc-Minh Ton-That, Paul G. Kry, Sheldon Andrews

Traditional mesh-based methods for cutting deformable bodies rely on modifying the simulation mesh by deleting, duplicating, deforming or subdividing its elements. Unfortunately, such topological changes eventually lead to instability, reduced accuracy, or computational efficiency challenges. Hence, state of the art algorithms favor the extended finite element method (XFEM), which decouples the cut geometry from the simulation mesh, allowing for stable and accurate cuts at an additional computational cost that is local to the cut region. However, in the 3-dimensional setting, current XFEM frameworks are limited by the cutting configurations that they support. In particular, intersecting cuts are either prohibited or require sophisticated special treatment. Our work presents a general XFEM formulation that is applicable to the 1-, 2-, and 3-dimensional setting without sacrificing the desirable properties of the method. In particular, we propose a generalized enrichment which supports multiple intersecting cuts of various degrees of non-linearity by leveraging recent advances in robust mesh-Boolean technology. This novel strategy additionally enables analytic discontinuous integration schemes required to compute mass, force and elastic energy. We highlight the simplicity, expressivity and accuracy of our XFEM implementation across various scenarios in which intersecting cutting patterns are featured.

Generalized eXtended Finite Element Method for Deformable Cutting via Boolean Operations

Yalan Zhang, Long Shen, Yanrui Xu, and Xiaokun Wang, Chao Yao, Jiri Kosinka, Alexandru Telea, Steffen Frey, Xiaojuan Ban

We propose a method for simulating viscoelastic non-Newtonian fluids within a multiphase framework. For this, we use mixture models to handle component transport and conformation tensor methods to handle the fluid’s viscoelastic stresses. In addition, we consider a bonding effects network to handle the impact of microscopic chemical bonds on phase transport. Our method supports the simulation of both steady-state viscoelastic fluids and discontinuous shear behavior. Compared to previous work on single-phase viscous non-Newtonian fluids, our method can capture more complex behavior, including material mixing processes that generate non-Newtonian fluids. We adopt a uniform set of variables to describe shear thinning, shear thickening, and ordinary Newtonian fluids while automatically calculating local rheology in inhomogeneous solutions. In addition, our method can simulate large viscosity ranges under explicit integration schemes, which typically requires implicit viscosity solvers under earlier single-phase frameworks.

Multiphase Viscoelastic Non-Newtonian Fluid Simulation