Month: July 2009

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

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


Fast and Robust Tracking of Fluid Surfaces

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

Real-Time Deformation and Fracture in a Game Environment

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


A Point-based Method for Animating Elastoplastic Solids

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

A Point-based Method for Animating Incompressible Flow

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

Simple, yet accurate tensile stiffness

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