Diamond-based models for scientific visualization

Hierarchical spatial decompositions are a basic modeling tool in a variety of application domains including scientific visualization, finite element analysis and shape modeling and analysis. A popular class of such approaches is based on the regular simplex bisection operator, which bisects simplices (e.g. line segments, triangles, tetrahedra) along the midpoint of a predetermined edge. Regular simplex bisection produces adaptive simplicial meshes of high geometric quality, while simplifying the extraction of crack-free, or conforming, approximations to the original dataset. Efficient multiresolution representations for such models have been achieved in 2D and 3D by clustering sets of simplices sharing the same bisection edge into structures called diamonds. In this thesis, we introduce several diamond-based approaches for scientific visualization. We first formalize the notion of diamonds in arbitrary dimensions in terms of two related simplicial decompositions of hypercubes. This enables us to enumerate the vertices, simplices, parents and children of a diamond. In particular, we identify the number of simplices involved in conforming updates to be factorial in the dimension and group these into a linear number of subclusters of simplices that are generated simultaneously. The latter form the basis for a compact pointerless representation for conforming meshes generated by regular simplex bisection and for efficiently navigating the topological connectivity of these meshes. Secondly, we introduce the supercube as a high-level primitive on such nested meshes based on the atomic units within the underlying triangulation grid. We propose the use of supercubes to associate information with coherent subsets of the full hierarchy and demonstrate the effectiveness of such a representation for modeling multiresolution terrain and volumetric datasets. Next, we introduce Isodiamond Hierarchies, a general framework for spatial access structures on a hierarchy of diamonds that exploits the implicit hierarchical and geometric relationships of the diamond model. We use an isodiamond hierarchy to encode irregular updates to a multiresolution isosurface or interval volume in terms of regular updates to diamonds. Finally, we consider nested hypercubic meshes, such as quadtrees, octrees and their higher dimensional analogues, through the lens of diamond hierarchies. This allows us to determine the relationships involved in generating balanced hypercubic meshes and to propose a compact pointerless representation of such meshes. We also provide a local diamond-based triangulation algorithm to generate high-quality conforming simplicial meshes

Planet-Sized Batched Dynamic Adaptive Meshes (P-BDAM)

This paper describes an efficient technique for out-of-core management and interactive rendering of planet sized textured terrain surfaces. The technique, called planet-sized batched dynamic adaptive meshes (P-BDAM), extends the BDAM approach by using as basic primitive a general triangulation of points on a displaced triangle. The proposed framework introduces several advances with respect to the state of the art: thanks to a batched host-to-graphics communication model, we outperform current adaptive tessellation solutions in terms of rendering speed; we guarantee overall geometric continuity, exploiting programmable graphics hardware to cope with the accuracy issues introduced by single precision floating points; we exploit a compressed out of core representation and speculative prefetching for hiding disk latency during rendering of out-of-core data; we efficiently construct high quality simplified representations with a novel distributed out of core simplification algorithm working on a standard PC network.147-15

Density-equalizing maps for simply-connected open surfaces

In this paper, we are concerned with the problem of creating flattening maps of simply-connected open surfaces in $\mathbb{R}^3$. Using a natural principle of density diffusion in physics, we propose an effective algorithm for computing density-equalizing flattening maps with any prescribed density distribution. By varying the initial density distribution, a large variety of mappings with different properties can be achieved. For instance, area-preserving parameterizations of simply-connected open surfaces can be easily computed. Experimental results are presented to demonstrate the effectiveness of our proposed method. Applications to data visualization and surface remeshing are explored

Development and Application of Computer Graphics Techniques for the Visualization of Large Geo-Related Data-Sets

Ziel dieser Arbeit war es, Algorithmen zu entwickeln und zu verbessern, die es gestatten, grosse geographische und andere geo-bezogene Datensätze mithilfe computergraphischer Techniken visualisieren zu können. Ein Schwerpunkt war dabei die Entwicklung neuer kamera-adaptiver Datenstrukturen für digitale Höhenmodelle und Rasterbilder. In der Arbeit wird zunächst ein neuartiges Multiresolutionmodell für Höhenfelder definiert. Dieses Modell braucht nur sehr wenig zusätzlichen Speicherplatz und ist geeignet, interaktive Anpassungsraten zu gewährleisten. Weiterhin werden Ansätze zur schnellen Bestimmung sichtbarer und verdeckter Teile einer computergraphischen Szene diskutiert, um die Bewegung in grossen und ausgedehnten Szenen wie Stadtmodellen oder Gebäuden zu beschleunigen. Im Anschluss daran werden einige Problemstellungen im Zusammenhang mit Texture Mapping erörtert, so werden zum Beispiel eine neue beobachterabhängige Datenstruktur für Texturdaten und ein neuer Ansatz zur Texturfilterung vorgestellt. Die meisten dieser Algorithmen und Verfahren wurden in ein interaktives System zur Geländevisualisierung integriert, das den Projektnamen 'FlyAway' hat und im letzten Kapitel der Arbeit beschrieben wird

Festschrift zum 60. Geburtstag von Wolfgang Strasser

Die vorliegende Festschrift ist Prof. Dr.-Ing. Dr.-Ing. E.h. Wolfgang Straßer zu seinem 60. Geburtstag gewidmet. Eine Reihe von Wissenschaftlern auf dem Gebiet der Computergraphik, die alle aus der "Tübinger Schule" stammen, haben - zum Teil zusammen mit ihren Schülern - Aufsätze zu dieser Schrift beigetragen. Die Beiträge reichen von der Objektrekonstruktion aus Bildmerkmalen über die physikalische Simulation bis hin zum Rendering und der Visualisierung, vom theoretisch ausgerichteten Aufsatz bis zur praktischen gegenwärtigen und zukünftigen Anwendung. Diese thematische Buntheit verdeutlicht auf anschauliche Weise die Breite und Vielfalt der Wissenschaft von der Computergraphik, wie sie am Lehrstuhl Straßer in Tübingen betrieben wird. Schon allein an der Tatsache, daß im Bereich der Computergraphik zehn Professoren an Universitäten und Fachhochschulen aus Tübingen kommen, zeigt sich der prägende Einfluß Professor Straßers auf die Computergraphiklandschaft in Deutschland. Daß sich darunter mehrere Physiker und Mathematiker befinden, die in Tübingen für dieses Fach gewonnen werden konnten, ist vor allem seinem Engagement und seiner Ausstrahlung zu verdanken. Neben der Hochachtung vor den wissenschaftlichen Leistungen von Professor Straßer hat sicherlich seine Persönlichkeit einen entscheidenden Anteil an der spontanten Bereischaft der Autoren, zu dieser Festschrift beizutragen. Mit außergewöhnlich großem persönlichen Einsatz fördert er Studenten, Doktoranden und Habilitanden, vermittelt aus seinen reichen internationalen Beziehungen Forschungskontakte und schafft so außerordentlich gute Voraussetzungen für selbständige wissenschafliche Arbeit. Die Autoren wollen mit ihrem Beitrag Wolfgang Straßer eine Freude bereiten und verbinden mit ihrem Dank den Wunsch, auch weiterhin an seinem fachlich wie menschlich reichen und bereichernden Wirken teilhaben zu dürfen

Multi-scale data storage schemes for spatial information systems

This thesis documents a research project that has led to the design and prototype implementation of several data storage schemes suited to the efficient multi-scale representation of integrated spatial data. Spatial information systems will benefit from having data models which allow for data to be viewed and analysed at various levels of detail, while the integration of data from different sources will lead to a more accurate representation of reality. The work has addressed two specific problems. The first concerns the design of an integrated multi-scale data model suited for use within Geographical Information Systems. This has led to the development of two data models, each of which allow for the integration of terrain data and topographic data at multiple levels of detail. The models are based on a combination of adapted versions of three previous data structures, namely, the constrained Delaunay pyramid, the line generalisation tree and the fixed grid. The second specific problem addressed in this thesis has been the development of an integrated multi-scale 3-D geological data model, for use within a Geoscientific Information System. This has resulted in a data storage scheme which enables the integration of terrain data, geological outcrop data and borehole data at various levels of detail. The thesis also presents details of prototype database implementations of each of the new data storage schemes. These implementations have served to demonstrate the feasibility and benefits of an integrated multi-scale approach. The research has also brought to light some areas that will need further research before fully functional systems are produced. The final chapter contains, in addition to conclusions made as a result of the research to date, a summary of some of these areas that require future work