Category: Uncategorized

Theodore Kim

The Baraff-Witkin model has been a popular formulation for cloth for 20 years. However, its relationship to the finite element method (FEM) has always been unclear, because the model resists being written as an isotropic, hyperelastic strain energy. In this paper, we show that this is because the Baraff-Witkin model is actually a coupled anisotropic strain energy. We show that its stretching term approximates the isotropic As-Rigid-As-Possible (ARAP) energy, and its shearing term is a cross-fiber coupling energy common in biomechanics. While it has been known empirically for some time that the model can produce indefinite force Jacobians, the conditions under which they occur has never been clear. Our formulation enables a complete eigenanalysis that precisely characterizes exactly when indefiniteness occurs, and leads to fast, analytic, semi-positive-definite projection methods. Finally, our analysis suggests a generalized Baraff-Witkin energy with non-orthogonal warp and weft directions.

A Finite Element Formulation of Baraff-Witkin Cloth

Cheng Li, Min Tang, Ruofeng Tong, Ming Cai, Jieyi Zhao, Dinesh Manocha

We present a novel parallel algorithm for cloth simulation that exploits multiple GPUs for fast computation and the handling of very high resolution meshes. To accelerate implicit integration, we describe new parallel algorithms for sparse matrix-vector multiplication (SpMV) and for dynamic matrix assembly on a multi-GPU workstation. Our algorithms use a novel work queue generation scheme for a fat-tree GPU interconnect topology. Furthermore, we present a novel collision handling scheme that uses spatial hashing for discrete and continuous collision detection along with a non-linear impact zone solver. Our parallel schemes can distribute the computation and storage overhead among multiple GPUs and enable us to perform almost interactive simulation on complex cloth meshes, which can hardly be handled on a single GPU due to memory limitations. We have evaluated the performance with two multi-GPU workstations (with 4 and 8 GPUs, respectively) on cloth meshes with 0.5-1.65M triangles. Our approach can reliably handle the collisions and generate vivid wrinkles and folds at 2-5 fps, which is significantly faster than prior cloth simulation systems. We observe almost linear speedups with respect to the number of GPUs.

P-Cloth: Interactive Complex Cloth Simulation on Multi-GPU Systems using Dynamic Matrix Assembly and Pipelined Implicit Integrators

Torsten Hädrich, Miłosz Makowski, Wojtek Pałubicki, Daniel T. Banuti, Soren Pirk, Dominik L. Michels

The complex interplay of a number of physical and meteorological phenomena makes simulating clouds a challenging and open research problem. We explore a physically accurate model for simulating clouds and the dynamics of their transitions. We propose first-principle formulations for computing buoyancy and air pressure that allow us to simulate the variations of atmospheric density and varying temperature gradients. Our simulation allows us to model various cloud types, such as cumulus, stratus, and stratoscumulus, and their realistic formations caused by changes in the atmosphere. Moreover, we are able to simulate large-scale cloud super cells – clusters of cumulonimbus formations – that are commonly present during thunderstorms. To enable the efficient exploration of these stormscapes, we propose a lightweight set of high-level parameters that allow us to intuitively explore cloud formations and dynamics. Our method allows us to simulate cloud formations of up to about 20km×20km extents at interactive rates. We explore the capabilities of physically accurate and yet interactive cloud simulations by showing numerous examples and by coupling our model with atmosphere measurements of real-time weather services to simulate cloud formations in the now. Finally, we quantitatively assess our model with cloud fraction profiles, a common measure for comparing cloud types.

Stormscapes: Simulating Cloud Dynamics in the Now

Libo Huang, Dominik L. Michels.

We devise a novel surface-only approach for simulating the three dimensional free-surface flow of incompressible, inviscid, and linearly magnetizable ferrofluids. A Lagrangian velocity field is stored on a triangle mesh capturing the fluid’s surface. The two key problems associated with the dynamic simulation of the fluid’s interesting geometry are the magnetization process transitioning the fluid from a non-magnetic into a magnetic material, and the evaluation of magnetic forces. In this regard, our key observation is that for linearly incompressible ferrofluids, their magnetization and application of magnetic forces only require knowledge about the position of the fluids’ boundary. Consequently, our approach employs a boundary element method solving the magnetization problem and evaluating the so-called magnetic pressure required for the force evaluation. The magnetic pressure is added to the Dirichlet boundary condition of a surface-only liquids solver carrying out the dynamical simulation. By only considering the fluid’s surface in contrast to its whole volume, we end up with an efficient approach enabling more complex and realistic ferrofluids to be explored in the digital domain without compromising efficiency. Our approach allows for the use of physical parameters leading to accurate simulations as demonstrated in qualitative and quantitative evaluations.

Surface-Only Ferrofluids

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