Physics-Based Animation

We describe a method for replacing certain stages of rigid body simulation with a statistically-based approximation. We begin by collecting statistical data regarding changes in linear and angular momentum for collisions of a given object. From this data we extract a statistical “signature” for the object, giving a compact representation of the object’s response to collision events. During object simulation, both the collision detection and the collision response calculations are replaced by simpler calculations based on the statistical signature. Using this approach, we are able to achieve significant improvement in the performance of rigid body simulation. The statistical behavior of the simulation is maintained, including achieving valid resting positions. We present results from a variety of simulations that demonstrate the method and its performance improvement. The method is appropriate for rigid body simulation situations requiring significant performance improvement, and allowing for some loss in fidelity

Statistical Simulation of Rigid Bodies

We present an algorithm for creating realistic animations of characters that are swimming through fluids. Our approach combines dynamic simulation with data-driven kinematic motions (motion capture data) to produce realistic animation in a fluid. The interaction of the articulated body with the fluid is performed by incorporating joint constraints with rigid animation and by extending a solid/fluid coupling method to handle articulated chains. Our solver takes as input the current state of the simulation and calculates the angular and linear accelerations of the connected bodies needed to match a particular motion sequence for the articulated body. These accelerations are used to estimate the forces and torques that are then applied to each joint. Based on this approach, we demonstrate simulated swimming results for a variety of different strokes, including crawl, backstroke, breaststroke and butterfly. The ability to have articulated bodies interact with fluids also allows us to generate simulations of simple water creatures that are driven by simple controllers.

Fluid Simulation with Articulated Bodies

This paper presents a method for simulating anisotropic friction for deforming surfaces and solids. Frictional contact is a complex phenomenon that fuels research in mechanical engineering, computational contact mechanics, composite material design and rigid body dynamics, to name just a few. Many real-world materials have anisotropic surface properties. As an example, most textile materials exhibit direction-dependent frictional behavior, but despite its tremendous impact on visual appearance, only simple isotropic models have been considered for cloth and solid simulation so far.
In this work, we propose a simple, application-oriented but physically sound model that extends existing methods to account for anisotropic friction.
The sliding properties of surfaces are encoded in friction tensors, which allows us to model frictional resistance freely along arbitrary directions. We also consider heterogeneous and asymmetric surface roughness and demonstrate the increased simulation quality on a number of two- and three-dimensional examples. Our method is computationally efficient and can easily be integrated into existing systems.

Anisotropic Friction for Deformable Surfaces and Solids

We propose a novel method for obtaining more accurate tangential velocities for solid fluid coupling. Our method works for both rigid and deformable objects as well as both volumetric objects and thin shells. The fluid can be either one phase such as smoke or two phase such as water with a free surface. The coupling between the solid and the fluid can either be one-way with kinematic solids or fully two-way coupled. The only previous scheme that was general enough to handle both two-way coupling and thin shells required a mass lumping strategy that did not allow for freely flowing tangential velocities. Similar to that previous work, our method prevents leaking of fluid across a thin shell, however unlike that work our method does not couple the tangential velocities in any fashion, allowing for the proper slip independently on each side of the body. Moreover, since it accurately and directly treats the tangential velocity, it does not rely on grid refinement to obtain a reasonable solution. Therefore, it gives a highly improved result on coarse meshes.

Accurate Tangential Velocities for Solid-Fluid Coupling

We propose a novel approach to guiding of Eulerian-based smoke animations through coupling of simulations at different grid resolutions. Specifically we present a variational formulation that allows smoke animations to adopt the low-frequency features from a lower resolution simulation (or non-physical synthesis), while simultaneously developing higher frequencies. The overall motivation for this work is to address the fact that art-direction of smoke animations is notoriously tedious. Particularly a change in grid resolution can result in dramatic changes in the behavior of smoke animations, and existing methods for guiding either significantly lack high frequency detail or may result in undesired features developing over time. Provided that the bulk movement can be represented satisfactorily at low resolution, our technique effectively allows artists to prototype simulations at low resolution (where computations are fast) and subsequently add extra details without altering the overall “look and feel”. Our implementation is based on a customized multi-grid solver with memory-efficient data structures.

Guiding of Smoke Animations Through Variational Coupling of Simulations at Different Resolutions

Surface tracking is an important problem with applications in many research fields. Among the most famous examples in computer graphics is the simulation and rendering of liquids with free surfaces. A surface that is advected by a general velocity field constantly changes its topology. This is the main reason why moving surfaces are typically defined implicitly as the zero set of a scalar field rather than by an explicit representation such as a mesh for instance.
In this paper we present a method for tracking fluid surfaces using triangle meshes. This is done in two steps. First, the vertices are advected by the velocity field of the fluid. Second, self-penetrations are fixed using marching cubes triangle templates. The technique is efficient in terms of computation and memory consumption, it is simple to implement and allows for direct control of volume and feature preservation.

Fast and Robust Tracking of Fluid Surfaces

This paper describes a simulation system that has been developed to model the deformation and fracture of solid objects in a real-time gaming context. Based around a corotational tetrahedral finite element method, this system has been constructed from components published in the graphics and computational physics literatures. The goal of this paper is to describe how these components can be combined to produce an engine that is robust to unpredictable user interactions, fast enough to model reasonable scenarios at real-time speeds, suitable for use in the design of a game level, and with appropriate controls allowing content creators to match artistic direction. Details concerning parallel implementation, solver design, rendering method, and other aspects of the simulation are elucidated with the intent of providing a guide to others wishing to implement similar systems. Examples from in-game scenes captured on the Xbox 360, PS3, and PC platforms are included.

Real-Time Deformation and Fracture in a Game Environment

In this paper we describe a point-based approach for animating elastoplastic materials. Our primary contribution is a simple method for computing the deformation gradient for each particle in the simulation. The deformation gradient is computed for each particle by finding the affine transformation that best approximates the motion of neighboring particles over a single timestep. These transformations are then composed to compute the total deformation gradient that describes the deformation around a particle over the course of the simulation. Given the deformation gradient we can apply arbitrary constitutive models and compute the resulting elastic forces. Our method has two primary advantages: we do not store or compare to an initial rest configuration and we work directly with the deformation gradient. The first advantage avoids poor numerical conditioning and the second naturally leads to a multiplicative model of deformation appropriate for finite deformations. We demonstrate our approach on a number of examples that exhibit a wide range of material behaviors.

A Point-based Method for Animating Elastoplastic Solids

In this paper, we present a point-based method for animating incompressible flow. The advection term is handled by moving the sample points through the flow in a Lagrangian fashion. However, unlike most previous approaches, the pressure term is handled by performing a projection onto a divergence-free field. To perform the pressure projection, we compute a Voronoi diagram with the sample points as input. Borrowing from Finite Volume Methods, we then invoke the divergence theorem and ensure that each Voronoi cell is divergence free. To handle complex boundary conditions, Voronoi cells are clipped against obstacle boundaries and free surfaces. The method is stable, flexible and combines many of the desirable features of point-based and grid-based methods. We demonstrate our approach on several examples of splashing and streaming liquid and swirling smoke.

A Point-based method for Animating Incompressible Flow

Recent Particle System models have evolved toward accurate representation of elastic stiffness based on continuum mechanics, converging to formulations that make them quite analogous to fast Finite Element methods. These formulations usually involve the linearization of tensors that help their formulation in the context of linear elasticity. Toward our objective of simulating the nonlinear properties of cloth accurately, we show through this work that this linearization can indeed be suppressed and replaced by adapted strain-stress laws relating precisely the nonlinear behavior of the material. This leads to very streamlined computations that are particularly efficient for simulating the nonlinear anisotropic tensile elasticity of deformable surfaces. Through a simple and efficient implementation using the Particle System formalism, we demonstrate the efficiency of this method with examples related to garment simulation.

Simple, yet accurate tensile stiffness