Master of Science

thesisIt is common to extract isosurfaces from simulation eld data to visualize and gain understanding of the underlying physical phenomenon being simulated. As the input parameters of the simulation change, the resulting isosurface varies, and there has been increased interest in quantifying and visualization of these variations as part of the larger interest in uncertainty quantification. In this thesis, we propose an analysis and visualization pipeline for examining the intrinsic variation in isosurfaces caused by simulation parameter perturbation. Drawing inspiration from the shape modeling community, we incorporate the use of heat-kernel signatures (HKS) with a simple nite-difference approach for quantifying the degree to which a region (or even a point) on an isosurface has undergone intrinsic change. Coupled with a clustering technique and the use of color maps, our pipeline allows the user to select the level of fidelity with which they wish to evaluate and visualize the amount of intrinsic change. The pipeline is described with a simple example to walk the reader through the different steps, and experimental validation of parameter choices in the pipeline is provided to justify our design. Then we present canonical and simulation examples to demonstrate the pipeline's use in different applications

Implicit surfaces for interactive animated characters

Thesis (S.M.)--Massachusetts Institute of Technology, Program in Media Arts & Sciences, 1999.Includes bibliographical references (leaves 64-68).Implicit surface modeling in computer graphics is a powerful technique for representing smooth and organic shapes. Skeletal elements of an implicit surface blend to create a smooth, seamless skin which exhibits desired properties for animation such as squash and stretch. Because of their high computational cost to render, implicit surfaces have not been used extensively in the real-time graphics domain. This thesis discusses the problems and some solutions in the application of implicit surfaces to the domain of interactive character animation. A design process for an implicit surface-based character is proposed, from the modeling and texturing stages to animation and rendering.by Kenneth Bradley Russell.S.M

Two algorithms for Lossy compression of 3D images

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1995.Includes bibliographical references (leaves 107-108).by Bernard Yiow-Min Chin.M.Eng

Visualization of two-phase flow dynamics : techniques for droplet interactions, interfaces, and material transport

Computational visualization allows scientists and engineers to better understand simulation data and gain insights into the studied natural processes. Particularly in the field of computational fluid dynamics, interactive visual presentation is essential in the investigation of physical phenomena related to gases and liquids. To ensure effective analysis, flow visualization techniques must adapt to the advancements in the field of fluid dynamics that benefits substantially from the growing computational power of both commodity desktops and supercomputers on the one hand, and steadily expanding knowledge about fluid physics on the other. A prominent example of these advances can be found in the research of two-phase flow with liquid droplets and jets, where high performance computation and sophisticated algorithms for phase tracking enable well resolved and physically accurate simulations of liquid dynamics. Yet, the field of two-phase flow has remained largely unexplored in visualization research so far, leaving the scientists and engineers with a number of challenges when analyzing the data. These include the difficulty in tracking and investigating topological events in large droplet groups, high complexity of droplet dynamics due to the involved interfaces, and a limited choice of high quality interactive methods for the analysis of related transport phenomena. It is therefore the aim of this thesis to address these challenges by providing a multi-scale approach for the visual investigation of two-phase flow, with the focus on the analysis of droplet interaction, fluid interfaces, and material transport. To address the problem of analyzing highly complex two-phase flow simulations with droplet groups and jets, a linked-view approach with three-dimensional and abstract space-time graph representation of droplet dynamics is proposed. The interactive brushing and linking allows for general exploration of topological events as well as detailed inspection of dynamics in terms of oscillations and rotations of droplets. Another approach further examines the separation of liquid phases by segmenting liquid volumes according to their topological changes in future time. For visualization, boundary surfaces of these volume segments are extracted that reveal intricate details of droplet topology dynamics. Additionally, within this framework, visualization of advected particles corresponding to arbitrarily selected segment provides useful insights into the spatio-temporal evolution of the segment. The analysis of interfaces is necessary to understand the interplay of interface dynamics and the dynamics of droplet interactions. A commonly used technique for interface tracking in the volume of fluid-based simulations is the piecewise linear approximation which, although accurate, can affect the quality of the simulation results. To study the influence of the interface reconstruction on the phase tracking procedure, a visualization method is presented that extracts the interfaces by means of the first-order Taylor approximation, and provides several derived quantities that help assess the simulation results in relation to the interface reconstruction quality. The liquid interface is further investigated from the physical standpoint with an approach based on quantities derived from velocity and surface tension gradients. The developed method supports examination of surface tension forces and their impact on the interface instability, as well as detailed analysis of interface deformation characteristics. A line of research important for engineering applications is the analysis of electric fields on droplet interfaces. It is, however, complicated by higher-order elements used in the simulations to preserve field discontinuities. A visualization method has been developed that correctly visualizes these discontinuities at material boundaries. Additionally, the employed space-time representation of the droplet-insulator contact line reveals characteristics of electric field dynamics. The dynamics of droplets are often examined assuming single-phase flow, for instance when the internal material transport is of interest. From the visualization perspective, this allows for adaption of traditional vector field visualization techniques to the investigation of the studied phenomena. As one such concept, dye based visualization is proposed that extends the transport analysis to advection-diffusion problems, therefore revealing true transport behavior. The employed high quality advection preserves fine details of the dye, while the implementation on graphics processing units ensures interactive visualization. Several streamline-based concepts are applied in space-time representation of 2D unsteady flow. By interpreting time as the third spatial dimension, many 3D streamline-based visualization techniques can be applied to investigate 2D unsteady flow. The introduced vortex core ribbons support the examination of vortical flow behavior by revealing rotation near the core lines. For the study of topological structures, a method has been developed that extracts separatrices implicitly as boundaries of regions with different flow behavior, and therefore avoids potentially complicated explicit extraction of various topological structures. All proposed techniques constitute a novel multi-scale approach for visual analysis of two-phase flow. The analysis of droplet interactions is addressed with visualization of the phenomena leading to breakups and with detailed visual inspection of these breakups. On the interface level, techniques for the interface analysis give insights into the simulation quality, mechanisms behind topology changes, as well as the behavior of electrically charged droplets. Further down the scale, the dye-based visualization, streamline-based concepts for space-time analysis, and the implicit extraction of flow topology allow for the investigation of droplet internal transport as well as general single-phase flow scenarios. The applicability of the proposed methods extends, in a varying degree, beyond the use in two-phase flow. Their usability is demonstrated on data from simulations based on Navier-Stokes equations that exemplify practical problems in the research of fluid dynamics.Die numerische Visualisierung ermöglicht Wissenschaftlern und Ingenieuren, Simulationsergebnisse besser zu verstehen und Einblicke in Naturprozesse zu gewinnen. Insbesondere ist die visuelle Darstellung von Ergebnissen numerischer Strömungsmechanik für die Untersuchung physikalischer Phänomene bei Gasen und Flüssigkeiten äußerst wichtig. Die numerische Strömungsmechanik profitiert einerseits von wachsender Rechenleistung handelsüblicher Desktops und Supercomputer, andererseits von den neuen Entwicklungen in der Strömungsforschung. Um eine effektive Analyse von Strömungen zu gewährleisten, müssen sich die Visualisierungstechniken kontinuierlich den Fortschritten in der Strömungsmechanik anpassen. Ein bemerkenswertes Beispiel hierfür ist die Forschung in der Zweiphasenströmung, in der Hochleistungsrechner und effiziente Algorithmen zur Phasenverfolgung hochaufgelöste und physikalisch genaue Simulationen der Flüssigkeitsdynamik ermöglichen. Dennoch ist die Zweiphasenströmung seitens der Visualisierung weitgehend unerforscht geblieben. Insbesondere sehen sich Wissenschaftler und Ingenieure mit verschiedenen Problemen konfrontiert, die mit angepassten Visualisierungstechniken vermieden werden können. Zu den Problemen zählen beispielweise die Verfolgung und Untersuchung der topologischen Ereignisse in Tropfengruppen, hohe Komplexität der Tropfendynamik und die begrenzte Auswahl an interaktiven Methoden zur Untersuchung der Transportphänomene. Demzufolge ist das Ziel dieser Dissertation, die Entwicklung eines Ansatzes zur visuellen Analyse von Zweiphasenströmung auf mehreren Skalen mit dem Fokus auf Interaktionen zwischen den Tropfen, Dynamik der Oberfläche und Materialtransport. Um die Analyse hochkomplexer Simulationsdaten der Zweiphasenströmung zu behandeln, wird eine auf Linked-View-Verfahren basierte Visualisierungstechnik präsentiert, in der die Tropfen sowohl in einer 3D Darstellung als auch in einer abstrakten Graph-Repräsentation visualisiert werden. Der interaktive Brushing-and-Linking-Ansatz ermöglicht eine globale Exploration der topologischen Ereignisse sowie eine detaillierte Inspektion der Dynamik im Hinblick auf die Oszillation und Rotation der Tropfen. Eine andere Technik zeigt die Aufteilung des Tropfenvolumens im zeitlichen Verlauf. Somit ermöglicht diese Methode eine ausführliche Untersuchung der Topologiedynamik mit Hilfe einer statischen Visualisierung. Dafür werden Grenzflächen erzeugt, die das ursprüngliche Volumen des Tropfens hinsichtlich der sich entwickelnden Zerfallskomponenten aufzeigen. Zusätzlich werden die zur Verfolgung der Tropfen benutzten Partikel visualisiert, um Einblicke in die Dynamik der Separation zu gewähren. Die Analyse der Oberfläche ist notwendig, um die Wechselwirkung zwischen der Oberflächendynamik und der Dynamik der Tropfeninteraktion besser zu verstehen. Eine häufig angewendete Technik zur Verfolgung der Phasengrenzen im Volume-of-Fluid-Verfahren ist die zellenweise planare Approximation. Obwohl diese einen guten Kompromiss zwischen Genauigkeit und Performanz bietet, kann die Approximation die Qualität der Simulationsergebnisse erheblich beeinflussen. Es wird deshalb eine Visualisierungsmethode präsentiert, die die Oberfläche mit Hilfe der Taylor-Approximation erster Ordnung extrahiert und unter anderem darauf basierte Größen bereitstellt, die die Relation zwischen der Simulationsapproximation und Qualität der Ergebnisse zeigt. Die Tropfenoberfläche wird weiterhin mit einer Visualisierungsmethode analysiert, die von den Geschwindigkeits- und Oberflächenspannungsgradienten abgeleitete Größen verwendet. Die entwickelte Methode unterstützt die Untersuchung der Deformation der Oberfläche sowie die Untersuchung der Oberflächenspannung und deren Auswirkung auf die Oberflächenstabilität. Eine wichtige Forschungsrichtung in der Zweiphasenströmung ist die Analyse elektrischer Felder auf der Tropfenoberfläche. Die in der Simulation angewendeten Elemente höherer Ordnung ermöglichen physikalische Diskontinuitäten, die für die visuelle Analyse eine gesonderte Behandlung benötigen. Im Zuge dessen wird eine Methode präsentiert, welche die Diskontinuitäten visuell korrekt darstellt und zusätzlich eine Raum-Zeit-Darstellung anwendet, um Einblicke in die Phänomene an der Kontaktlinie zwischen den Tropfen und dem untersuchten Isolator zu gewähren. Die Tropfendynamik wird oft mit der Annahme einer Einphasenströmung analysiert, beispielsweise für die Untersuchung der internen Strömung des Tropfens. Dies ermöglicht eine Anpassung und Verwendung traditioneller Visualisierungsmethoden für Vektorfelder. Eine solche Technik ist die ,,Dye-Advection'', die in dieser Dissertation nicht nur zur Analyse der Advektion, sondern auch zur Untersuchung der Diffusion verwendet wird. Die eingesetzte hochqualitative Rekonstruktion des virtuellen Pigments bewahrt feine Details, während die Implementierung auf der Grafikkarte eine interaktive Visualisierung ermöglicht. Überdies werden einige auf Stromlinien basierende Konzepte in Raum-Zeit-Darstellung angewendet, in der die Zeit als die dritte Raumachse interpretiert wird. Demzufolge können diese Methoden zur Analyse der zeitabhängigen zweidimensionalen Strömung verwendet werden. Die eingeführten ,,Vortex Core Ribbons" unterstützen die Analyse der rotierenden Strömung um die Wirbelkernlinien. Für die Analyse der topologischen Strukturen wurde eine Methode entwickelt, die die Separatrizen implizit als Ränder einer Segmentierung des Vektorfeldes extrahiert. Damit wird eine möglicherweise komplexe direkte Extraktion der Separatrizen vermieden. Die präsentierten Visualisierungsmethoden bilden ein neuartiges Multiskalen-Verfahren zur visuellen Analyse von Zweiphasenströmungen. Die Tropfeninteraktionen werden mit Hilfe einer Visualisierung dargestellt, die sich auf die Ursache des Tropfenzerfalls und deren Ablauf konzentriert. Für die Untersuchung der Oberfläche zeigen die vorgeschlagenen Techniken die Qualität der Ergebnisse hinsichtlich der Oberflächenrekonstruktion, die Mechanismen hinter den topologischen Ereignissen, als auch die Dynamik der elektrisch geladenen Tropfen auf. Andererseits werden unter Annahme der Einphasenströmung neue Techniken basierend auf Dye-Advection, Stromlinien-basierte Konzepte, sowie Verfahren zur Extraktion der Topologie untersucht, um einen besseren Einblick in den Materialtransport zu gewinnen. Die Anwendung dieser Methoden wird in dieser Dissertation auf Daten demonstriert, die durch Simulation, basierend auf Navier-Stokes-Gleichungen, erzeugt wurden

Improving Filtering for Computer Graphics

When drawing images onto a computer screen, the information in the scene is typically more detailed than can be displayed. Most objects, however, will not be close to the camera, so details have to be filtered out, or anti-aliased, when the objects are drawn on the screen. I describe new methods for filtering images and shapes with high fidelity while using computational resources as efficiently as possible. Vector graphics are everywhere, from drawing 3D polygons to 2D text and maps for navigation software. Because of its numerous applications, having a fast, high-quality rasterizer is important. I developed a method for analytically rasterizing shapes using wavelets. This approach allows me to produce accurate 2D rasterizations of images and 3D voxelizations of objects, which is the first step in 3D printing. I later improved my method to handle more filters. The resulting algorithm creates higher-quality images than commercial software such as Adobe Acrobat and is several times faster than the most highly optimized commercial products. The quality of texture filtering also has a dramatic impact on the quality of a rendered image. Textures are images that are applied to 3D surfaces, which typically cannot be mapped to the 2D space of an image without introducing distortions. For situations in which it is impossible to change the rendering pipeline, I developed a method for precomputing image filters over 3D surfaces. If I can also change the pipeline, I show that it is possible to improve the quality of texture sampling significantly in real-time rendering while using the same memory bandwidth as used in traditional methods

New Techniques for the Modeling, Processing and Visualization of Surfaces and Volumes

With the advent of powerful 3D acquisition technology, there is a growing demand for the modeling, processing, and visualization of surfaces and volumes. The proposed methods must be efficient and robust, and they must be able to extract the essential structure of the data and to easily and quickly convey the most significant information to a human observer. Independent of the specific nature of the data, the following fundamental problems can be identified: shape reconstruction from discrete samples, data analysis, and data compression. This thesis presents several novel solutions to these problems for surfaces (Part I) and volumes (Part II). For surfaces, we adopt the well-known triangle mesh representation and develop new algorithms for discrete curvature estimation,detection of feature lines, and line-art rendering (Chapter 3), for connectivity encoding (Chapter 4), and for topology preserving compression of 2D vector fields (Chapter 5). For volumes, that are often given as discrete samples, we base our approach for reconstruction and visualization on the use of new trivariate spline spaces on a certain tetrahedral partition. We study the properties of the new spline spaces (Chapter 7) and present efficient algorithms for reconstruction and visualization by iso-surface rendering for both, regularly (Chapter 8) and irregularly (Chapter 9) distributed data samples

Interactive visualization tools for topological exploration

Thesis (Ph.D.) - Indiana University, Computer Science, 1992This thesis concerns using computer graphics methods to visualize mathematical objects. Abstract mathematical concepts are extremely difficult to visualize, particularly when higher dimensions are involved; I therefore concentrate on subject areas such as the topology and geometry of four dimensions which provide a very challenging domain for visualization techniques. In the first stage of this research, I applied existing three-dimensional computer graphics techniques to visualize projected four-dimensional mathematical objects in an interactive manner. I carried out experiments with direct object manipulation and constraint-based interaction and implemented tools for visualizing mathematical transformations. As an application, I applied these techniques to visualizing the conjecture known as Fermat's Last Theorem. Four-dimensional objects would best be perceived through four-dimensional eyes. Even though we do not have four-dimensional eyes, we can use computer graphics techniques to simulate the effect of a virtual four-dimensional camera viewing a scene where four-dimensional objects are being illuminated by four-dimensional light sources. I extended standard three-dimensional lighting and shading methods to work in the fourth dimension. This involved replacing the standard "z-buffer" algorithm by a "w-buffer" algorithm for handling occlusion, and replacing the standard "scan-line" conversion method by a new "scan-plane" conversion method. Furthermore, I implemented a new "thickening" technique that made it possible to illuminate surfaces correctly in four dimensions. Our new techniques generate smoothly shaded, highlighted view-volume images of mathematical objects as they would appear from a four-dimensional viewpoint. These images reveal fascinating structures of mathematical objects that could not be seen with standard 3D computer graphics techniques. As applications, we generated still images and animation sequences for mathematical objects such as the Steiner surface, the four-dimensional torus, and a knotted 2-sphere. The images of surfaces embedded in 4D that have been generated using our methods are unique in the history of mathematical visualization. Finally, I adapted these techniques to visualize volumetric data (3D scalar fields) generated by other scientific applications. Compared to other volume visualization techniques, this method provides a new approach that researchers can use to look at and manipulate certain classes of volume data

Doctor of Philosophy

dissertationThe medial axis of an object is a shape descriptor that intuitively presents the morphology or structure of the object as well as intrinsic geometric properties of the object’s shape. These properties have made the medial axis a vital ingredient for shape analysis applications, and therefore the computation of which is a fundamental problem in computational geometry. This dissertation presents new methods for accurately computing the 2D medial axis of planar objects bounded by B-spline curves, and the 3D medial axis of objects bounded by B-spline surfaces. The proposed methods for the 3D case are the first techniques that automatically compute the complete medial axis along with its topological structure directly from smooth boundary representations. Our approach is based on the eikonal (grassfire) flow where the boundary is offset along the inward normal direction. As the boundary deforms, different regions start intersecting with each other to create the medial axis. In the generic situation, the (self-) intersection set is born at certain creation-type transition points, then grows and undergoes intermediate transitions at special isolated points, and finally ends at annihilation-type transition points. The intersection set evolves smoothly in between transition points. Our approach first computes and classifies all types of transition points. The medial axis is then computed as a time trace of the evolving intersection set of the boundary using theoretically derived evolution vector fields. This dynamic approach enables accurate tracking of elements of the medial axis as they evolve and thus also enables computation of topological structure of the solution. Accurate computation of geometry and topology of 3D medial axes enables a new graph-theoretic method for shape analysis of objects represented with B-spline surfaces. Structural components are computed via the cycle basis of the graph representing the 1-complex of a 3D medial axis. This enables medial axis based surface segmentation, and structure based surface region selection and modification. We also present a new approach for structural analysis of 3D objects based on scalar functions defined on their surfaces. This approach is enabled by accurate computation of geometry and structure of 2D medial axes of level sets of the scalar functions. Edge curves of the 3D medial axis correspond to a subset of ridges on the bounding surfaces. Ridges are extremal curves of principal curvatures on a surface indicating salient intrinsic features of its shape, and hence are of particular interest as tools for shape analysis. This dissertation presents a new algorithm for accurately extracting all ridges directly from B-spline surfaces. The proposed technique is also extended to accurately extract ridges from isosurfaces of volumetric data using smooth implicit B-spline representations. Accurate ridge curves enable new higher-order methods for surface analysis. We present a new definition of salient regions in order to capture geometrically significant surface regions in the neighborhood of ridges as well as to identify salient segments of ridges

GPU data structures for graphics and vision

Graphics hardware has in recent years become increasingly programmable, and its programming APIs use the stream processor model to expose massive parallelization to the programmer. Unfortunately, the inherent restrictions of the stream processor model, used by the GPU in order to maintain high performance, often pose a problem in porting CPU algorithms for both video and volume processing to graphics hardware. Serial data dependencies which accelerate CPU processing are counterproductive for the data-parallel GPU. This thesis demonstrates new ways for tackling well-known problems of large scale video/volume analysis. In some instances, we enable processing on the restricted hardware model by re-introducing algorithms from early computer graphics research. On other occasions, we use newly discovered, hierarchical data structures to circumvent the random-access read/fixed write restriction that had previously kept sophisticated analysis algorithms from running solely on graphics hardware. For 3D processing, we apply known game graphics concepts such as mip-maps, projective texturing, and dependent texture lookups to show how video/volume processing can benefit algorithmically from being implemented in a graphics API. The novel GPU data structures provide drastically increased processing speed, and lift processing heavy operations to real-time performance levels, paving the way for new and interactive vision/graphics applications.Graphikhardware wurde in den letzen Jahren immer weiter programmierbar. Ihre APIs verwenden das Streamprozessor-Modell, um die massive Parallelisierung auch für den Programmierer verfügbar zu machen. Leider folgen aus dem strikten Streamprozessor-Modell, welches die GPU für ihre hohe Rechenleistung benötigt, auch Hindernisse in der Portierung von CPU-Algorithmen zur Video- und Volumenverarbeitung auf die GPU. Serielle Datenabhängigkeiten beschleunigen zwar CPU-Verarbeitung, sind aber für die daten-parallele GPU kontraproduktiv . Diese Arbeit präsentiert neue Herangehensweisen für bekannte Probleme der Video- und Volumensverarbeitung. Teilweise wird die Verarbeitung mit Hilfe von modifizierten Algorithmen aus der frühen Computergraphik-Forschung an das beschränkte Hardwaremodell angepasst. Anderswo helfen neu entdeckte, hierarchische Datenstrukturen beim Umgang mit den Schreibzugriff-Restriktionen die lange die Portierung von komplexeren Bildanalyseverfahren verhindert hatten. In der 3D-Verarbeitung nutzen wir bekannte Konzepte aus der Computerspielegraphik wie Mipmaps, projektive Texturierung, oder verkettete Texturzugriffe, und zeigen auf welche Vorteile die Video- und Volumenverarbeitung aus hardwarebeschleunigter Graphik-API-Implementation ziehen kann. Die präsentierten GPU-Datenstrukturen bieten drastisch schnellere Verarbeitung und heben rechenintensive Operationen auf Echtzeit-Niveau. Damit werden neue, interaktive Bildverarbeitungs- und Graphik-Anwendungen möglich