Physics-Based Animation

In this paper, we present an adaptive model for dynamically deforming hyper-elastic rods. In contrast to existing approaches, adaptively introduced control points are not governed by geometric subdivision rules. Instead, their states are determined by employing a non-linear energy-minimization approach. Since valid control points are computed instantaneously, post-stabilization schemes are avoided and the stability of the dynamic simulation is improved.  Due to inherently complex contact configurations, the simulation of knot tying using rods is a challenging task. In order to address this problem, we combine our adaptive model with a robust and accurate collision handling method for elastic rods. By employing our scheme, complex knot configurations can be simulated in a physically plausible way.

An Adaptive Contact Model for the Robust Simulation of Knots

Two methods have been used extensively to model resting contact for rigid body simulation. The first approach, the penalty method, applies virtual springs to surfaces in contact to minimize interpenetration. This method, as typically implemented, results in oscillatory behavior and considerable penetration. The second approach, based on formulating resting contact as a linear complementarity problem, determines the resting contact forces analytically to prevent interpenetration. The analytical method exhibits expected-case polynomial complexity in the number of contact points, and may fail to find a solution in polynomial time when friction is modeled. We present a fast penalty method that minimizes oscillatory behavior and leads to little penetration during resting contact; our method compares favorably to the analytical method with regard to these two measures, while exhibiting much faster performance both asymptotically and empirically.

A Fast and Stable Penalty Method for Rigid Body Simulation

Grid-based methods have difficulty resolving features on or below the scale of the underlying grid. Although adaptive methods (e.g. RLE, octrees) can alleviate this to some degree, separate techniques are still required for simulating small-scale phenomena such as spray and foam, especially since these more diffuse materials typically behave quite differently than their denser counterparts. In this paper, we propose a two-way coupled simulation framework that uses the particle level set method to efficiently model dense liquid volumes and a smoothed particle hydrodynamics (SPH) method to simulate diffuse regions such as sprays. Our novel SPH method allows us to simulate both dense and diffuse water volumes, fully incorporates the particles that are automatically generated by the particle level set method in under-resolved regions, and allows for two way mixing between dense SPH volumes and grid-based liquid representations.

Two-Way Coupled SPH and Particle Level Set Fluid Simulation

In 2D, incompressible flows, the Stokes equations that represent the dynamics of very viscous flows and vorticity formulation of hydrodynamic equations both reduce to a scalar stream-function representation in terms of elliptic equations. By making use of this simplification and the properties of Fourier space representation of elliptic equations, we use a common spectral method to solve both of these equations. Based on this system of equations, we propose a level set based input description which provides a flexible environment for the user to model a wide range of flows and artistic effects in 2D. This input type allows the modeling of vortex sheet patterns and other complex flows with a very practical approach and chaotic, dynamic flows, even with viscous Stokes equations. A user interface is developed for the level set input which allows the user to draw the strokes or edit the level set data by applying transformation functions or perturbations. To sum up, this model can be used for the simulation of very viscous flows, vorticity dynamics, vortex sheet patterns, turbulent and chaotic flows as well as other artistic effects such as the traditional marbling patterns, with a simple, fast and stable system at high resolutions.

Level Set Driven Flows

Claude Lacoursiere’s thesis on variational techniques for rigid bodies:
Ghosts and Machines: regularized variational methods for interactive simulations of multibodies with dry frictional contacts

Frank Losasso’s PhD thesis on fluid simulation, which contains previously unpublished work on coupling together SPH and level set based fluid simulations:

Algorithms for Increasing the Efficiency and Fidelity of Fluid Simulation

Eftychios Sifakis’ PhD thesis on face, muscle, speech, and surgery simulation:

Algorithmic Aspects of the Simulation and Control of Computer Generated Human Anatomy Models

Geoffrey Irving’s PhD thesis on a variety of physics simulation topics:

Methods for the Physically-Based Simulation of Solids and Fluids

Update: While I’m doing the thesis thing, here’s a couple slightly older ones that are probably worth a look.

Adam Bargteil’s PhD thesis on liquid surface tracking.

Surface Tracking and Texturing

Bart Adams PhD thesis on point-based graphics:

Point-Based Modeling, Animation and Rendering of Dynamic Objects

We propose a novel method of controlling a multi-phase fluid so that it flows into a target shape in a natural way. To preserve the sharp detail of the target shape, we represent it as an implicit function and construct the level-set of that function. Previous approaches add the target-driven control force as an external term, which then becomes attenuated during the velocity projection step, making the convergence process unstable and causing sharp detail to be lost from the target shape. But we calculate the force on the fluid from the pressure discontinuity at the interface between phases, and integrate the control force into the projection step so as to preserve its effect. The control force is calculated using an enhanced version of the ghost fluid method (GFM), which guarantees that the fluid flows from the source shape and converges into the target shape, while achieving a more natural animation than other approaches. Our control force is merged during the projection step avoiding the need for a post-optimization process to eliminate divergence at the liquid interface. This makes our method easy to implement using existing fluid engines and it incurs little computational overhead. Experimental results show the accuracy and robustness of this technique.

Target-driven liquid animation with interfacial discontinuities

This paper describes a motion blur technique which can be applied to rendering fluid simulations that are carried out in the Eulerian framework. Existing motion blur techniques can be applied to rigid bodies, deformable solids, clothes, and several other kinds of objects, and produce satisfactory results. As there is no specific reason to discriminate fluids from the above objects, one may consider applying an existing motion blur technique to render fluids. However, here we show that existing motion blur techniques are intended for simulations carried out in the Lagrangian framework, and are not suited to Eulerian simulations. Then, we propose a new motion blur technique that is suitable for rendering Eulerian simulations.

Eulerian Motion Blur

GPU Gems 3 is out, and it contains a chapter on real-time 3D simulation & rendering of fluids (smoke and liquids) on the GPU, and is available as a free sample chapter online. You may have seen some of these results before on Keenan Crane’s website.

GPU Gems 3

In this paper, we present a simple method for animating natural phenomena such as erosion, sedimentation, and acidic corrosion. We discretize the appropriate physical or chemical equations using finite differences, and we use the results to modify the shape of a solid body. We remove mass from an object by treating its surface as a level set and advecting it inward, and we deposit the chemical and physical byproducts into simulated fluid. Similarly, our technique deposits sediment onto a surface by advecting the level set outward. Our idea can be used for off-line high quality animations as well as interactive applications such as games, and we demonstrate both in this paper.

Animating Corrosion and Erosion