Physics-Based Animation

Ondrej Jamriska, Jakub Fiser, Paul Asente, Jingwan Lu, Eli Shechtman, Daniel Sykora

In this paper we present a novel approach to appearance transfer for fluid animations based on flow-guided texture synthesis. In contrast to common practice where pre-captured sets of fluid elements are combined in order to achieve desired motion and look, we bring the possibility of fine-tuning motion properties in advance using CG techniques, and then transferring the desired look from a selected appearance exemplar. We demonstrate that such a practical workflow cannot be simply implemented using current state-of-the-art techniques, analyze what the main obstacles are, and propose a solution to resolve them. In addition, we extend the algorithm to allow for synthesis with rich boundary effects and video exemplars. Finally, we present numerous results that demonstrate the versatility of the proposed approach.

LazyFluids: Appearance Transfer for Fluid Animations

Hongyi Xu, Funshing Sin, Yufeng Zhu, Jernej Barbic

The Finite Element Method is widely used for solid deformable object simulation in film, computer games, virtual reality and medicine. Previous applications of nonlinear solid elasticity employed materials from a few standard families such as linear corotational, nonlinear St.Venant-Kirchhoff, Neo-Hookean, Ogden or Mooney-Rivlin materials. However, the spaces of all nonlinear isotropic and anisotropic materials are infinite-dimensional and much broader than these standard materials. In this paper, we demonstrate how to intuitively explore the space of isotropic and anisotropic nonlinear materials, for design of animations in computer graphics and related fields. In order to do so, we first formulate the internal elastic forces and tangent stiffness matrices in the space of the principal stretches of the material. We then demonstrate how to design new isotropic materials by editing a single stress-strain curve, using a spline interface. Similarly, anisotropic (orthotropic) materials can be designed by editing three curves, one for each material direction. We demonstrate that modifying these curves using our proposed interface has an intuitive, visual, effect on the simulation. Our materials accelerate simulation design and enable visual effects that are difficult or impossible to achieve with standard nonlinear materials.

Nonlinear Material Design Using Principal Stretches

Andreas Peer, Markus Ihmsen, Jens Cornelis, Matthias Teschner

We present a novel implicit formulation for highly viscous fluids simulated with Smoothed Particle Hydrodynamics SPH. Compared to explicit methods, our formulation is significantly more efficient and handles a larger range of viscosities. Differing from existing implicit formulations, our approach reconstructs the velocity field from a target velocity gradient. This gradient encodes a desired shear-rate damping and preserves the velocity divergence that is introduced by the SPH pressure solver to counteract density deviations. The target gradient ensures that pressure and viscosity computation do not interfere. Therefore, only one pressure projection step is required, which is in contrast to state-of-the-art implicit Eulerian formulations. While our model differs from true viscosity in that vorticity diffusion is not encoded in the target gradient, it nevertheless captures many of the qualitative behaviors of viscous liquids. Our formulation can easily be incorporated into complex scenarios with one- and two-way coupled solids and multiple fluid phases with different densities and viscosities.

An Implicit Viscosity Formulation for SPH Fluids

Makoto Okabe, Yoshinori Dobashi, Ken Anjyo, Rikio Onai

We propose a method of three-dimensional (3D) modeling of volumetric fluid phenomena from sparse multi-view images (e.g., only a single-view input or a pair of front- and side-view inputs). The volume determined from such sparse inputs using previous methods appears blurry and unnatural with novel views; however, our method preserves the appearance of novel viewing angles by transferring the appearance information from input images to novel viewing angles. For appearance information, we use histograms of image intensities and steerable coefficients. We formulate the volume modeling as an energy minimization problem with statistical hard constraints, which is solved using an expectation maximization (EM)-like iterative algorithm. Our algorithm begins with a rough estimate of the initial volume modeled from the input images, followed by an iterative process whereby we first render the images of the current volume with novel viewing angles. Then, we modify the rendered images by transferring the appearance information from the input images, and we thereafter model the improved volume based on the modified images. We iterate these operations until the volume converges. We demonstrate our method successfully provides natural-looking volume sequences of fluids (i.e., fire, smoke, explosions, and a water splash) from sparse multi-view videos. To create production-ready fluid animations, we further propose a method of rendering and editing fluids using a commercially available fluid simulator.
Fluid Volume Modeling from Sparse Multi-view Images by Appearance Transfer

Maxime Tournier, Matthieu Nesme, Benjamin Gilles, Francois Faure

We present a unification of the two main approaches to simulate deformable solids, namely elasticity and constraints. Elasticity accurately handles soft to moderately stiff objects, but becomes numerically hard as stiffness increases. Constraints efficiently handle high stiffness, but when integrated in time they can suffer from instabilities in the nullspace directions, generating spurious transverse vibrations when pulling hard on thin inextensible objects or articulated rigid bodies. We show that geometric stiffness, the tensor encoding the change of force directions (as opposed to intensities) in response to a change of positions, is the missing piece between the two approaches. This previously neglected stiffness term is easy to implement and dramatically improves the stability of inextensible objects and articulated chains, without adding artificial bending forces. This allows time step increases up to several orders of magnitude using standard linear solvers.

Stable Constrained Dynamics

David Hahn, Chris Wojtan

We present a method for simulating brittle fracture under the assumptions of quasi-static linear elastic fracture mechanics (LEFM). Using the boundary element method (BEM) and Lagrangian crack-fronts, we produce highly detailed fracture surfaces. The computational cost of the BEM is alleviated by using a low-resolution mesh and interpolating the resulting stress intensity factors when propagating the high-resolution crack-front. Our system produces physics-based fracture surfaces with high spatial and temporal resolution, taking spatial variation of material toughness and/or strength into account. It also allows for crack initiation to be handled separately from crack propagation, which is not only more reasonable from a physics perspective, but can also be used to control the simulation. Separating the resolution of the crack-front from the resolution of the computational mesh increases the efficiency and therefore the amount of visual detail on the resulting fracture surfaces. The BEM also allows us to re-use previously computed blocks of the system matrix.

High-Resolution Brittle Fracture Simulation with Boundary Elements

Nathan Mitchell, Court Cutting, Eftychios Sifakis

We present an interactive simulation framework for authoring surgical procedures of soft tissue manipulation using physics-based simulation to animate the flesh. This interactive authoring tool can be used by clinical educators to craft three-dimensional illustrations of the intricate maneuvers involved in craniofacial repairs, in contrast to two-dimensional sketches and still photographs which are the medium used to describe these procedures in the traditional surgical curriculum. Our virtual environment also allows surgeons-intraining to develop cognitive skills for craniofacial surgery by experimenting with different approaches to reconstructive challenges, adapting stock techniques to flesh regions with nonstandard shape, and reach preliminary predictions about the feasibility of a given repair plan. We use a Cartesian grid-based embedded discretization of nonlinear elasticity to maximize regularity, and expose opportunities for aggressive multithreading and SIMD accelerations. Using a grid-based approach facilitates performance and scalability, but constrains our ability to capture the topology of thin surgical incisions. We circumvent this restriction by hybridizing the grid-based discretization with an explicit hexahedral mesh representation in regions where the embedding mesh necessitates overlap or nonmanifold connectivity. Finally, we detail how the front-end of our system can run on lightweight clients, while the core simulation capability can be hosted on a dedicated server and delivered as a network service.

GRIDiron: An interactive authoring and cognitive training foundation for reconstructive plastic surgery procedures

Yonghao Yue, Breannan Smith, Christopher Batty, Changxi Zheng, Eitan Grinspun

We consider the simulation of dense foams composed of microscopic bubbles, such as shaving cream and whipped cream. We represent foam not as a collection of discrete bubbles, but instead as a continuum. We employ the Material Point Method (MPM) to discretize a hyperelastic constitutive relation augmented with the Herschel-Bulkley model of non-Newtonian plastic flow, which is known to closely approximate foam behavior. Since large shearing flows in foam can produce poor distributions of material points, a typical MPM implementation can produce non-physical internal holes in the continuum. To address these artifacts, we introduce a particle resampling method for MPM. In addition, we introduce an explicit tearing model to prevent regions from shearing into artificially-thin, honey-like threads. We evaluate our method’s efficacy by simulating a number of dense foams, and we validate our method by comparing to real-world footage of foam.

Continuum Foam: A Material Point Method for Shear-Dependent Flows

Yufeng Zhu, Robert Bridson, Chen Greif

We present a new brittle fracture simulation method based on a boundary integral formulation of elasticity and recent explicit surface mesh evolution algorithms. Unlike prior physically-based simulations in graphics, this avoids the need for volumetric sampling and calculations, which aren’t reflected in the rendered output. We represent each quasi-rigid body by a closed triangle mesh of its boundary, on which we solve quasi-static linear elasticity via boundary integrals in response to boundary conditions and loads such as impact forces and gravity. A fracture condition based on maximum tensile stress is subsequently evaluated at mesh vertices, while crack initiation and propagation are formulated as an interface tracking procedure in material space. Existing explicit mesh tracking methods are modified to support evolving cracks directly in the triangle mesh representation, giving highly detailed fractures with sharp features, independent of any volumetric sampling (unlike tetrahedral mesh or level set approaches); the triangle mesh representation also allows simple integration into rigid body engines. We also give details on our well-conditioned integral equation treatment solved with a kernel-independent Fast Multipole Method for linear time summation. Various brittle fracture scenarios demonstrate the efficacy and robustness of our new method.

Simulating Rigid Body Fracture with Surface Meshes

Chenfanfu Jiang, Craig Schroeder, Andrew Selle, Joseph Teran, Alexey Stomakhin

Hybrid Lagrangian/Eulerian simulation is commonplace in computer graphics for fluids and other materials undergoing large deformation. In these methods, particles are used to resolve transport and topological change, while a background Eulerian grid is used for computing mechanical forces and collision responses. Particle- in-Cell (PIC) techniques, particularly the Fluid Implicit Particle (FLIP) variants have become the norm in computer graphics calculations. While these approaches have proven very powerful, they do suffer from some well known limitations. The original PIC is stable, but highly dissipative, while FLIP, designed to remove this dissipation, is more noisy and at times, unstable. We present a novel technique designed to retain the stability of the original PIC, with- out suffering from the noise and instability of FLIP. Our primary observation is that the dissipation in the original PIC results from a loss of information when transferring between grid and particle representations. We prevent this loss of information by augmenting each particle with a locally affine, rather than locally constant, description of the velocity. We show that this not only stably removes the dissipation of PIC, but that it also allows for exact conservation of angular momentum across the transfers between particles and grid.

The Affine Particle-In-Cell Method