We present a comprehensive methodology for realistically animating liquid phenomena. Our approach unifies existing computer graphics techniques for simulating fluids and extends them by incorporating more complex behavior. It is based on the Navier-Stokes equations which couple momentum and mass conservation to completely describe fluid motion. Our starting point is an environment containing an arbitrary distribution of fluid, and submerged or semi-submerged obstacles. Velocity and pressure are defined everywhere within this environment, and updated using a set of finite difference expressions. The resulting vector and scalar fields are used to drive a height field equation representing the liquid surface. The nature of the coupling between obstacles in the environment and free variables allows for the simulation of a wide range of effects that were not possible with previous computer-graphics fluid models. Wave effects such as reflection, refraction and diffraction, as well as rotational effects such as eddies, vorticity, and splashing are a natural consequence of solving the system. In addition, the Lagrange equations of motion are used to place buoyant dynamic objects into a scene, and track the position of spray and foam during the animation process. Typical disadvantages to dynamic simulations such as poor scalability and lack of control are addressed by assuming that stationary obstacles align with grid cells during the finite difference discretization, and by appending terms to the Navier-Stokes equations to include forcing functions. Free surfaces in our system are represented as either a collection of massless particles in 2D, or a height field which is suitable for many of the water rendering algorithms presented by researchers in recent years.

This paper describes a new animation technique for modeling the turbulent rotational motion that occurs when a hot gas interacts with solid objects and the surrounding medium. The method is especially useful for scenes involving swirling steam, rolling or billowing smoke, and gusting wind. It can also model gas motion due to fans and heat convection. The method combines specialized forms of the equations of motion of a hot gas with an efficient method for solving volumetric differential equations at low resolutions. Particular emphasis is given to issues of computational efficiency and ease-of-use of the method by an animator. We present the details of our model, together with examples illustrating its use.

Abstract. In this paper we introduce a new framework for image registration. Our formulation is based on consistent discretization of the optimization problem coupled with a multigrid solution of the linear system which evolves in a Gauss–Newton iteration. We show that our discretization is h-elliptic independent of parameter choice, and therefore a simple multigrid implementation can be used. To overcome potential large nonlinearities and to further speed up computation, we use a multilevel continuation technique. We demonstrate the efficiency of our method on a realistic highly nonlinear registration problem.

Since the subject of traffic dynamics has captured the interest of physicists, many surprising effects have been revealed and explained. Some of the questions now understood are the following: Why are vehicles sometimes stopped by ‘‘phantom traffic jams’ ’ even though drivers all like to drive fast? What are the mechanisms behind stop-and-go traffic? Why are there several different kinds of congestion, and how are they related? Why do most traffic jams occur considerably before the road capacity is reached? Can a temporary reduction in the volume of traffic cause a lasting traffic jam? Under which conditions can speed limits speed up traffic? Why do pedestrians moving in opposite directions normally organize into lanes, while similar systems ‘‘freeze by heating’’? All of these questions have been answered by applying and extending methods from statistical physics and nonlinear dynamics to self-driven many-particle systems. This article considers the empirical data and then reviews the main approaches to modeling pedestrian and vehicle traffic. These include microscopic (particle-based), mesoscopic (gas-kinetic), and macroscopic (fluid-dynamic) models. Attention is also paid to the formulation of a micro-macro link, to aspects of universality, and to other unifying concepts, such as a general modeling framework for self-driven many-particle systems, including spin systems. While the primary focus is upon vehicle and pedestrian traffic, applications to biological or socio-economic systems such as bacterial colonies, flocks of birds, panics, and stock market dynamics are touched upon as well.

A methodology for controlling fluid animations is developed using the concept of an embedded controller. A controller acts as an interface between the animator and a general tool for calculating three dimensional fluid flow. The major contribution of this paper is that for the first time, it is possible for computer graphics animators, to specify and control a three dimensional fluid animation, without knowledge of the underlying equations, or the method used to solve them. In addition, the technique is stable, physically accurate, and can be integrated with other animation tools that deal with dynamic objects. To illustrate the method, animations of moving objects, fountains, and explosions, together with the straightforward control functions that are used to create them, are presented. 1. Introduction Computer animators want to create and control the flow of events in an animation. Their goal is to do this quickly and precisely, making use of tools that provide high-level constructs...

mesh generation, mesh coarsening, multigrid Abstract A numerical method for the solution of a partial differential equation (PDE) requires the following steps: (1) discretizing the domain (mesh generation); (2) using an approximation method and the mesh to transform the problem into a linear system; (3) solving the linear system. The approximation error and convergence of the numerical method depend on the geometric quality of the mesh, which in turn depends on the size and shape of its elements. For example, the shape quality of a triangular mesh is measured by its element's aspect ratio. In this work, we shift the focus to the geometric properties of the nodes, rather than the elements, of well shaped meshes. We introduce the concept of well-spaced points and their spacing functions, and show that these enable the development of simple and efficient algorithms for the different stages of the numerical solution of PDEs. We first apply well-spaced point sets and their accompanying technology to mesh coarsening, a crucial step in the multigrid solution of a PDE. A good aspect-ratio coarsening sequence of an unstructured mesh M0 is a sequence of good aspect-ratio meshes M1; : : : ; Mk such that Mi is an approximation of Mi\Gamma 1 containing fewer nodes and elements. We present a new approach to coarsening that guarantees the sequence is also of optimal size and width up to a constant factor-- the first coarsening method that provides these guarantees. We also present experimental results, based on an implementation of our approach, that substantiate the theoretical claims.

Two versions of flux corrected transport and two versions of total variation diminishing schemes are tested for several one- and two-dimensional hydrodynamic and magnetohydrodynamic problems. Two of the schemes, YDFCT and TVDLF are tested extensively for the first time. The results give an insight into the limitations of the methods, their relative strengths and weaknesses. Some subtle points of the algorithms and the effects of selecting different options for certain methods are emphasised. 1 INTRODUCTION Many interesting and important problems arise in astrophysical, solar, magnetospheric and thermonuclear research which can be described by the system of magnetohydrodynamic (MHD) equations. The complexity of these problems often prohibits an analytical investigation and/or only some of the variables can be observed or measured experimentally, thus the researcher has to rely on numerical simulations. In many situations, MHD flows develop steep gradients, shock waves, contact disconti...

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Image registration techniques are used routinely in a variety of today’s medical imaging diagnosis. Since the problem is ill-posed, one may like to add additional information about distortions. This applies, for example, to the registration of contrast enhanced images, where variations of substructures are not related to patient motion but to contrast uptake. Here, one may only be interested in registrations which do not alter the volume of any substructure. In this paper we discuss image registration techniques with a focus on volume preserving constraints. These constraints can reduce the non-uniqueness of the registration problem significantly. Our implementation is based on a constrained optimization formulation. Upon discretization, we obtain a large, discrete, highly nonlinear optimization problem and the necessary conditions for the solution form a discretize nonlinear partial differential equation. To solve the problem we use a variant of Sequential Quadratic Programming method. Moreover, we present results on synthetic as well as on real life data. 1

ix Acknowledgements x Acknowledgements : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : x Publication History : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : x 1. Introduction 1 1.1 Introduction to Direct Volume Rendering : : : : : : : : : : : : : : : : : : : 2 1.1.1 Volumetric Grids : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 3 1.1.2 Image-space Rendering Algorithms : : : : : : : : : : : : : : : : : : : 4 1.1.3 Object-space Rendering Algorithms : : : : : : : : : : : : : : : : : : 5 1.1.4 Shear Transformations : : : : : : : : : : : : : : : : : : : : : : : : : : 7 1.1.5 Complexity : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 7 1.2 Motivation for Parallel Direct Volume Rendering : : : : : : : : : : : : : : : 8 1.2.1 Scalability Is Important : : : : : : : : : : : : : : : : : : : : : : : : : 8 1.3 Context for Use : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 9 1.3.1 Distributed Graphical Us...