Physics-Based Animation

Oscar Argudo, Eric Galin, Adrien Peytavie, Axel Paris, Eric Guerin

Glaciers are some of the most visually arresting and scenic elements of cold regions and high mountain landscapes. Although snow-covered terrains have previously received attention in computer graphics, simulating the temporal evolution of glaciers as well as modeling their wide range of features has never been addressed. In this paper, we combine a Shallow Ice Approximation simulation with a procedural amplification process to author high-resolution realistic glaciers. Our multiresolution method allows the interactive simulation of the formation and the evolution of glaciers over hundreds of years. The user can easily modify the environment variables, such as the average temperature or precipitation rate, to control the glacier growth, or directly use brushes to sculpt the ice or bedrock with interactive feedback. Mesoscale and smallscale landforms that are not captured by the glacier simulation, such as crevasses, moraines, seracs, ogives, or icefalls are synthesized using procedural rules inspired by observations in glaciology and according to the physical parameters derived from the simulation. Our method lends itself to seamless integration into production pipelines to decorate reliefs with glaciers and realistic ice features.

Simulation, Modeling and Authoring of Glaciers

Rafael Nakanishi, Filipe Nascimento, Rafael Campos, Paulo Pagliosa, Afonso Paiva

We introduce a novel liquid simulation approach that combines a spatially adaptive pressure projection solver with the Particle-in-Cell (PIC) method. The solver relies on a generalized version of the Finite Difference (FD) method to approximate the pressure field and its gradients in tree-based grid discretizations, possibly non-graded. In our approach, FD stencils are computed by using meshfree interpolations provided by a variant of Radial Basis Function (RBF), known as RBF-Finite-Difference (RBF-FD). This meshfree version of the FD produces differentiation weights on scattered nodes with high-order accuracy. Our method adapts a quadtree/octree dynamically in a narrow-band around the liquid interface, providing an adaptive particle sampling for the PIC advection step. Furthermore, RBF affords an accurate scheme for velocity transfer between the grid and particles, keeping the system’s stability and avoiding numerical dissipation. We also present a data structure that connects the spatial subdivision of a quadtree/octree with the topology of its corresponding dual-graph. Our data structure makes the setup of stencils straightforward, allowing its updating without the need to rebuild it from scratch at each time-step. We show the effectiveness and accuracy of our solver by simulating incompressible inviscid fluids and comparing results with regular PIC-based solvers available in the literature.

RBF Liquids: An Adaptive Pic Solver Using RBF-FD

Tao Du, Kui Wu, Andrew Spielberg, Wojciech Matusik, Bo Zhu, Eftychios Sifakis

We present a method for performance-driven optimization of fluidic devices. In our approach, engineers provide a high-level specification of a device using parametric surfaces for the fluid-solid boundaries. They also specify desired flow properties for inlets and outlets of the device. Our computational approach optimizes the boundary of the fluidic device such that its steady-state flow matches desired flow at outlets. In order to deal with computational challenges of this task, we propose an efficient, differentiable Stokes flow solver. Our solver provides explicit access to gradients of performance metrics with respect to the parametric boundary representation. This key feature allows us to couple the solver with efficient gradient-based optimization methods. We demonstrate the efficacy of this approach on designs of five complex 3D fluidic systems. Our approach makes an important step towards practical computational design tools for high-performance fluidic devices.

Functional Optimization of Fluidic Devices with Differentiable Stokes Flow

Jiayi Eris Zhang, Seungbae Bang, David IW Levin, Alec Jacobson

We present a novel approach to enrich arbitrary rig animations with elastodynamic secondary effects. Unlike previous methods which pit rig displacements and physical forces as adversaries against each other, we advocate that physics should complement artists’ intentions. We propose optimizing for elastodynamic displacements in the subspace orthogonal to displacements that can be created by the rig. This ensures that the additional dynamic motions do not undo the rig animation. The complementary space is high dimensional, algebraically constructed without manual oversight, and capable of rich high-frequency dynamics. Unlike prior tracking methods, we do not require extra painted weights, segmentation into fixed and free regions or tracking clusters. Our method is agnostic to the physical model and plugs into non-linear FEM simulations, geometric as-rigid-as-possible energies, or mass-spring models. Our method does not require a particular type of rig and adds secondary effects to skeletal animations, cage-based deformations, wire deformers, motion capture data, and rigid-body simulations.

Complementary Dynamics

• Monolith: A Monolithic Pressure-Viscosity-Contact Solver for Strong Two-Way Rigid-Rigid Rigid-Fluid Coupling
• A Novel Discretization and Numerical Solver for Non-Fourier Diffusion
• Complementary Dynamics
• Functional Optimization of Fluid Devices with Differentiable Stokes Flow
• Surface-Only Ferrofluids
• RBF Liquids: An Adaptive PIC Solve Using RBF-FD
• Simulation, Modeling and Authoring of Glaciers
• Stormscapes: Simulating Cloud Dynamics in the Now
• P-Cloth: Interactive Complex Cloth Simulation on Multi-GPU Systems using Dynamic Matrix Assembly and Pipelined Implicit Integrators
• An Extended Cut-cell method for Sub-Grid Liquids Tracking with Surface Tension
• An Adaptive Staggered-Tilted Grid for Incompressible Flow Simulation
• ADD: Analytically Differentiable Dynamics for Multi-Body Systems with Frictional Contact
• A Moving Least Square Reproducing Kernel Particle Method for Unified Multiphase Continuum Simulation
• Interactive Liquid Splash Modeling by User Sketches
• Frequency-Domain Smoke Guiding
• Semi-Analytic Boundary Handling Below Particle Resolution for Smoothed Particle Hydrodynamics
• An Implicit Updated Lagrangian Formulation for Liquids with Large Surface Energy
• Higher-Order Finite Elements for Embedded Simulation
• Learning to Manipulate Amorphous Materials
• A Harmonic Balance Approach for Designing Compliant Mechanical Systems with Nonlinear Periodic Motions

Tao Xue, Haozhe Su, Chengguizi Han, Chenfanfu Jiang, Mridul Aanjaneya

We introduce the C-F diffusion model [Anderson and Tamma 2006; Xue et al.2018] to computer graphics for diffusion-driven problems that has several attractive properties: (a) it fundamentally explains diffusion from the perspective of the non-equilibrium statistical mechanical Boltzmann TransportE quation, (b) it allows for a finite propagation speed for diffusion, in contrast to the widely employed Fick’s/Fourier’s law, and (c) it can capture some of the most characteristic visual aspects of diffusion-driven physics, such as hydrogel swelling, limited diffusive domain for smoke flow, snowflake and dendrite formation, that span from Fourier-type to non-Fourier-type diffusive phenomena. We propose a unified convection-diffusion formulationusing this model that treats both the diffusive quantity and its associated flux as the primary unknowns, and that recovers the traditional Fourier-type diffusion as a limiting case. We design a novel semi-implicit discretization for this formulation on staggered MAC grids and a geometric Multigrid-preconditioned Conjugate Gradients solver for efficient numerical solution.To highlight the efficacy of our method, we demonstrate end-to-end examples of elastic porous media simulated with the Material Point Method (MPM), and diffusion-driven Eulerian incompressible fluids.

A Novel Discretization and Numerical Solver for Non-Fourier Diffusion

Yu Fang*, Ziyin Qu*, Minchen Li, Xinxin Zhang, Yixin Zhu, Mridul Aanjaneya, Chenfanfu Jiang

We propose a novel scheme for simulating two-way coupled interactions between nonlinear elastic solids and incompressible fluids. The key ingredient of this approach is a ghost matrix operator-splitting scheme for strongly coupled nonlinear elastica and incompressible fluids through the weak form of their governing equations. This leads to a stable and efficient method handling large time steps under the CFL limit while using a single monolithic solve for the coupled pressure fields, even in the case with highly nonlinear elastic solids. The use of the Material Point Method (MPM) is essential in the designing of the scheme, it not only preserves discretization consistency with the hybrid Lagrangian-Eulerian fluid solver, but also works naturally with our novel interface quadrature (IQ) discretization for free-slip boundary conditions. While traditional MPM suffers from sticky numerical artifacts, our framework naturally supports discontinuous tangential velocities at the solid-fluid interface. Our IQ discretization results in an easy-to-implement, fully particle-based treatment of the interfacial boundary, avoiding the additional complexities associated with intermediate level set or explicit mesh representations. The efficacy of the proposed scheme is verified by various challenging simulations with fluid-elastica interactions.

IQ-MPM: An Interface Quadrature Material Point Method for Non-sticky Strongly Two-Way Coupled Nonlinear Solids and Fluids

Doug L. James

Physics-based simulations of deforming tetrahedral meshes are widely used to animate detailed embedded geometry. Unfortunately most practitioners still use linear interpolation (or other low-order schemes) on tetrahedra, which can produce undesirable visual artifacts, e.g., faceting and shading artifacts, that necessitate increasing the simulation’s spatial resolution and, unfortunately, cost. In this paper, we propose Phong Deformation, a simple, robust and practical vertex-based quadratic interpolation scheme that, while still only C0 continuous like linear interpolation, greatly reduces visual artifacts for embedded geometry. The method first averages element-based linear deformation models to vertices, then barycentrically interpolates the vertex models while also averaging with the traditional linear interpolation model. The method is a fast, robust, and easily implemented replacement for linear interpolation that produces visually better results for embedded deformation with irregular tetrahedral meshes.

Phong Deformation: A better C0 interpolant for embedded deformation

Joshuah Wolper, Yunuo Chen, Minchen Li, Yu Fang, Ziyin Qu, Jiecong Lu, Meggie Cheng, Chenfanfu Jiang

Dynamic fracture surrounds us in our day-to-day lives, but animating this phenomenon is notoriously difficult and only further complicated by anisotropic materials—those with underlying structures that dictate preferred fracture directions. Thus, we present AnisoMPM: a robust and general approach for animating the dynamic fracture of isotropic, transversely isotropic, and orthotropic materials. AnisoMPM has three core components: a technique for anisotropic damage evolution, methods for anisotropic elastic response, and a coupling approach. For anisotropic damage, we adopt a non-local continuum damage mechanics (CDM) geometric approach to crack modeling and augment this with structural tensors to encode material anisotropy. Furthermore, we discretize our damage evolution with explicit and implicit integration, giving a high degree of computational efficiency and flexibility. We also utilize a QR-decomposition based anisotropic constitutive model that is inversion safe, more efficient than SVD models, easy to implement, robust to extreme deformations, and that captures all aforementioned modes of anisotropy. Our elasto-damage coupling is enforced through an additive decomposition of our hyperelasticity into a tensile and compressive component in which damage is used to degrade the tensile contribution to allow for material separation. For extremely stiff fibered materials, we further introduce a novel Galerkin weak form discretization that enables embedded directional inextensibility. We present this as a hard-constrained grid velocity solve that poses an alternative to our anisotropic elasticity that is locking-free and can model very stiff materials.

AnisoMPM: Animating Anisotropic Damage Mechanics

Jan Bender, Tassilo Kugelstadt, Marcel Weiler, Dan Koschier

In this paper, we present a novel method for the robust handling of static and dynamic rigid boundaries in Smoothed Particle Hydrodynamics (SPH) simulations. We build upon the ideas of the density maps approach which has been introduced recently by Koschier and Bender. They precompute the density contributions of solid boundaries and store them on a spatial grid which can be efficiently queried during runtime. This alleviates the problems of commonly used boundary particles, like bumpy surfaces and inaccurate pressure forces near boundaries. Our method is based on a similar concept but we precompute the volume contribution of the boundary geometry. This maintains all benefits of density maps but offers a variety of advantages which are demonstrated in several experiments. Firstly, in contrast to the density maps method we can compute derivatives in the standard SPH manner by differentiating the kernel function. This results in smooth pressure forces, even for lower map resolutions, such that precomputation times and memory requirements are reduced by more than two orders of magnitude compared to density maps. Furthermore, this directly fits into the SPH concept so that volume maps can be seamlessly combined with existing SPH methods. Finally, the kernel function is not baked into the map such that the same volume map can be used with different kernels. This is especially useful when we want to incorporate common surface tension or viscosity methods that use different kernels than the fluid simulation.

Implicit Frictional Boundary Handling for SPH