Physics-Based Animation

Mohammad Sina Nabizadeh, Ravi Ramamoorthi, Albert Chern

Solving partial differential equations (PDEs) on infinite domains has been a challenging task in physical simulations and geometry processing. We introduce a general technique to transform a PDE problem on an unbounded domain to a PDE problem on a bounded domain. Our method uses the Kelvin Transform, which essentially inverts the distance from the origin. However, naive application of this coordinate mapping can still result in a singularity at the origin in the transformed domain. We show that by factoring the desired solution into the product of an analytically known (asymptotic) component and another function to solve for, the problem can be made continuous and compact, with solutions significantly more efficient and well-conditioned than traditional finite element and Monte Carlo numerical PDE methods on stretched coordinates. Specifically, we show that every Poisson or Laplace equation on an infinite domain is transformed to another Poisson (Laplace) equation on a compact region. In other words, any existing Poisson solver on a bounded domain is readily an infinite domain Poisson solver after being wrapped by our transformation. We demonstrate the integration of our method with finite difference and Monte Carlo PDE solvers, with applications in the fluid pressure solve and simulating electromagnetism, including visualizations of the solar magnetic field. Our transformation technique also applies to the Helmholtz equation whose solutions oscillate out to infinity. After the transformation, the Helmholtz equation becomes a tractable equation on a bounded domain without infinite oscillation. To our knowledge, this is the first time that the Helmholtz equation on an infinite domain is solved on a bounded grid without requiring an artificial absorbing boundary condition.

Kelvin Transformations for Simulations on Infinite Domains

Mihail Francu, Árni Gunnar Ásgeirsson, Erleben, Kenny, Mads J. L. Rønnow

The simulation of incompressible materials suffers from locking when us-ing the standard finite element method (FEM) and coarse linear tetrahedral meshes. Locking increases as the Poisson ratio𝜈gets close to0.5and often lower Poisson ratio values are used to reduce locking, affecting volume preservation. We propose a novel mixed FEM approach to simulating in-compressible solids that alleviates the locking problem for tetrahedra. Our method uses linear shape functions for both displacements and pressure and adds one scalar per node. It can accommodate nonlinear isotropic materials described by a Young’s modulus and any Poisson ratio value by enforcing a volumetric constitutive law. The most realistic such material is Neo-Hookean and we focus on adapting it to our method. For𝜈=0.5we can obtain full volume preservation up to any desired numerical accuracy. We show that standard Neo-Hookean simulations using tetrahedra are often locking which in turn affects accuracy. We show that our method gives better results and that our Newton solver is more robust. As an alternative, we propose a dual ascent solver that is simple and has a good convergence rate. We validate these results using numerical experiments and quantitative analysis

Locking-Proof Tetrahedra

• Revisiting Integration in the Material Point Method: A Scheme for Easier Separation and Less Dissipation
• Mechanics-Aware Deformation of Yarn Pattern Geometry
• Kelvin Transformations for Simulations on Infinite Domains
• QuanTaichi: A Compiler for Quantized Simulations
• A Unified Second-Order Accurate in Time MPM Formulation for Simulating Viscoelastic Liquids with Phase Change
• Bijective and Coarse High-Order Tetrahedral Meshes
• Physical validation of simulators in Computer Graphics: A new framework dedicated to slender elastic structures and frictional contact
• Stream-Guided Smoke Simulations
• Solid-Fluid Interaction with Surface-Tension-Dominant Contact
• Fire in Paradise: Mesoscale Simulation of Wildfires
• Systematically Differentiating Parametric Discontinuities
• Thin-Film Smoothed Particle Hydrodynamics Fluid
• Clebsch Gauge Fluid
• Incompressible Flow Simulation on Vortex Segment Clouds
• Codimensional Incremental Potential Contact
• Intersection-free Rigid Body Dynamics
• Medial IPC: Accelerated Incremental Potential Contact With Medial Elastics
• High-order Differentiable Autoencoder for Nonlinear Model Reduction
• Fast Linking Numbers for Topology Verification
• of Loopy Structures
• Learning Contact Corrections for Handle-Based Subspace Dynamics
• The Shape Matching Element Method: Direct Animation of Curved Surface Models
• GPU-Based Simulation of Cloth Wrinkles at Submillimeter Levels
• Multiscale Cholesky Preconditioning for Ill-conditioned Problems
• A Momentum-Conserving Implicit Material Point Method for Surface Tension with Contact Angles and Spatial Gradients
• SANM: A Symbolic Asymptotic Numerical Solver with Applications in Mesh Deformation
• Learning Meaningful Controls for Fluids
• Unified Particle System for Multiple-fluid Flow and Porous Material
• Constrained Projective Dynamics: Real-time Simulation of Deformable Objects With Energy-momentum Conservation

TOG papers to be presented:

• Dynamic Upsampling of Smoke through Dictionary-based Learning
• Frictional Contact on Smooth Elastic Solids
• A Safe and Fast Repulsion Method for GPU-based Cloth Self Collisions
• Optimized Refinement for Spatially Adaptive SPH
• SIERE: A Hybrid Semi-implicit Exponential Integrator for Efficiently Simulating Stiff Deformable Objects

Jingwei Tang, Vinicius C. Azevedo, Guillaume Cordonnier, Barbara Solenthaler

Fluid control often uses optimization of control forces that are added to a simulation at each time step, such that the final animation matches a single or multiple target density keyframes provided by an artist. The optimization problem is strongly under-constrained with a high-dimensional parameter space, and finding optimal solutions is challenging, especially for higher resolution simulations. In this paper, we propose two novel ideas that jointly tackle the lack of constraints and high dimensionality of the parameter space. We first consider the fact that optimized forces are allowed to have divergent modes during the optimization process. These divergent modes are not entirely projected out by the pressure solver step, manifesting as unphysical smoke sources that are explored by the optimizer to match a desired target. Thus, we reduce the space of the possible forces to the family of strictly divergence-free velocity fields, by optimizing directly for a vector potential. We synergistically combine this with a smoothness regularization based on a spectral decomposition of control force fields. Our method enforces lower frequencies of the force fields to be optimized first by filtering force frequencies in the Fourier domain. The mask-growing strategy is inspired by Kolmogorov’s theory about scales of turbulence. We demonstrate improved results for 2D and 3D fluid mcontrol especially in higher-resolution settings, while eliminating the need for manual parameter tuning. We showcase various applications of our method, where the user effectively creates or edits smoke simulations.

Honey, I Shrunk the Domain: Frequency-aware Force FieldReduction for Efficient Fluids Optimization

Kai Bai, Wei Li, Mathieu Desbrun, Xiaopei Liu

Simulating turbulent smoke flows with fine details is computationally intensive. For iterative editing or simply faster generation, efficiently upsampling a low-resolution numerical simulation is an attractive alternative. We propose a novel learning approach to the dynamic upsampling of smoke flows based on a training set of flows at coarse and fine resolutions.Our multiscale neural network turns an input coarse animation into a sparse linear combination of small velocity patches present in a precomputed over-complete dictionary. These sparse coefficients are then used to generate a high-resolution smoke animation sequence by blending the fine counterparts of the coarse patches. Our network is initially trained from a sequence of example simulations to both construct the dictionary of corresponding coarse and fine patches and allow for the fast evaluation of a sparse patch encoding of any coarse input. The resulting network provides an accurate upsampling when the coarse input simulation is well approximated by patches present in the training set (e.g., for re-simulation), or simply visually-plausible upsampling when input and training set differ significantly. We show a variety of examples to ascertain the strengths and limitations of our approach, and offer comparisons to existing approaches to demonstrate its quality and effectiveness.

Dynamic Upsampling of Smoke through Dictionary-based Learning

Yun (Raymond) Fei, Qi Guo, Rundong Wu, Li Huang, Ming Gao

The material point method recently demonstrated its efficacy at simulating many materials and the coupling between them on a massive scale. However, in scenarios containing debris, MPM manifests more dissipation and numerical viscosity than traditional Lagrangian methods. We have two observations from carefully revisiting existing integration methods used in MPM. First, nearby particles would end up with smoothed velocities without recovering momentum for each particle during the particle-grid-particle transfers. Second, most existing integrators assume continuity in the entire domain and advect particles by directly interpolating the positions from deformed nodal positions, which would trap the particles and make them harder to separate. We propose an integration scheme that corrects particle positions at each time step. We demonstrate our method’s effectiveness with several large-scale simulations involving brittle materials. Our approach effectively reduces diffusion and unphysical viscosity compared to traditional integrators.

Revisiting Integration in the Material Point Method: A Scheme for Easier Separation and Less Dissipation

George Sperl, Rahul Narain, Chris Wojtan

Triangle mesh-based simulations are able to produce satisfying animations of knitted and woven cloth; however, they lack the rich geometric detail of yarn-level simulations. Naive texturing approaches do not consider yarn-level physics, while full yarn-level simulations may become prohibitively expensive for large garments. We propose a method to animate yarn-level cloth geometry on top of an underlying deforming mesh in a mechanics-aware fashion. Using triangle strains to interpolate precomputed yarn geometry, we are able to reproduce effects such as knit loops tightening under stretching. In combination with precomputed mesh animation or real-time mesh simulation, our method is able to animate yarn-level cloth in real-time at large scales.

Mechanics-Aware Deformation of Yarn Pattern Geometry

Vismay Modi, Lawson Fulton, Shinjiro Sueda, Alec Jacobson, David I.W. Levin

EMU is an efficient and scalable model to simulate bulk musculoskeletal motion with heterogenous materials. First, EMU requires no model reductions, or geometric coarsening, thereby producing results visually accurate when compared to an FEM simulation. Second, EMU is efficient and scales much better than state-of-the-art FEM with the number of elements in the mesh, and is more easily parallelizable. Third, EMU can handle heterogeneously stiff meshes with an arbitrary constitutive model, thus allowing it to simulate soft muscles, stiff tendons and even stiffer bones all within one unified system. These three key characteristics of EMU enable us to efficiently orchestrate muscle activated skeletal movements. We demonstrate the efficacy of our approach via a number of examples with tendons, muscles, bones and joints.

EMU: Efficient Muscle Simulation in Deformation Space

Kuixin Zhu, Xiaowei He, Sheng Li, Hongan Wang, Guoping Wang

Granular media is the second-most-manipulated substance on Earth, second only to water. However, simulation of granularmedia is still challenging due to the complexity of granular materials and the large number of discrete solid particles. As we know, drygranular materials could form a hybrid state between a fluid and a solid, therefore we propose a two-layer model and divide thesimulation domain into a dilute layer, where granules can move freely as a fluid, and a dense layer, where granules act more like asolid. Motivated by the shallow water equations, we derive a set of shallow sand equations for modeling dry granular flows bydepth-integrating three-dimensional governing equations along its vertical direction. Unlike previous methods for simulating a 2Dgranular media, our model does not restrict the depth of the granular media to be shallow anymore. To allow efficient fluid-solidinteractions, we also present a ray casting algorithm for one-way solid-fluid coupling. Finally, we introduce a particle-tracking method toimprove the visual representation. Our method can be efficiently implemented based on a height field and is fully compatible withmodern GPUs, therefore allows us to simulate large-scale dry granular flows in real time.

Shallow Sand Equations: Real-Time Height Field Simulation of Dry Granular Flows

Bohan Wang, Jernej Barbič

Real-time deformable object simulation is important in interactive applications such as games and virtual reality. One common approach to achieve speed is to employ model reduction, a technique whereby the equations of motion of a deformable object are projected to a suitable low-dimensional space. Improving the real-time performance of model-reduced systems has been the subject of much research. While modern GPUs play an important role in real-time simulation and parallel computing, existing model reduction systems typically utilize CPUs and seldom employ GPUs. We give a method to efficiently employ GPUs for vertex position computation in model-reduced simulations. Our CUDA-based algorithm gives a substantial speedup compared to a CPU implementation, thanks to our system architecture that employs a memory layout friendly to GPU memory, reduces the communication between the CPU and GPU, and enables the CPU and GPU to work in parallel.

CUDA Deformers for Model Reduction