Interactive volume ray tracing

Die Visualisierung von volumetrischen Daten ist eine der interessantesten, aber sicherlich auch schwierigsten Anwendungsgebiete innerhalb der wissenschaftlichen Visualisierung. Im Gegensatz zu Oberflächenmodellen, repräsentieren solche Daten ein semi-transparentes Medium in einem 3D-Feld. Anwendungen reichen von medizinischen Untersuchungen, Simulation physikalischer Prozesse bis hin zur visuellen Kunst. Viele dieser Anwendungen verlangen Interaktivität hinsichtlich Darstellungs- und Visualisierungsparameter. Der Ray-Tracing- (Stahlverfolgungs-) Algorithmus wurde dabei, obwohl er inhärent die Interaktion mit einem solchen Medium simulieren kann, immer als zu langsam angesehen. Die meisten Forscher konzentrierten sich vielmehr auf Rasterisierungsansätze, da diese besser für Grafikkarten geeignet sind. Dabei leiden diese Ansätze entweder unter einer ungenügenden Qualität respektive Flexibilität. Die andere Alternative besteht darin, den Ray-Tracing-Algorithmus so zu beschleunigen, dass er sinnvoll für Visualisierungsanwendungen benutzt werden kann. Seit der Verfügbarkeit moderner Grafikkarten hat die Forschung auf diesem Gebiet nachgelassen, obwohl selbst moderne GPUs immer noch Limitierungen, wie beispielsweise der begrenzte Grafikkartenspeicher oder das umständliche Programmiermodell, enthalten. Die beiden in dieser Arbeit vorgestellten Methoden sind deshalb vollständig softwarebasiert, da es sinnvoller erscheint, möglichst viele Optimierungen in Software zu realisieren, bevor eine Portierung auf Hardware erfolgt. Die erste Methode wird impliziter Kd-Baum genannt, eine hierarchische und räumliche Beschleunigungstruktur, die ursprünglich für die Generierung von Isoflächen reguläre Gitterdatensätze entwickelt wurde. In der Zwischenzeit unterstützt sie auch die semi-transparente Darstellung, die Darstellung von zeitabhängigen Datensätzen und wurde erfolgreich für andere Anwendungen eingesetzt. Der zweite Algorithmus benutzt so genannte Plücker-Koordinaten, welche die Implementierung eines schnellen inkrementellen Traversierers für Datensätze erlauben, deren Primitive Tetraeder beziehungsweise Hexaeder sind. Beide Algorithmen wurden wesentlich optimiert, um eine interaktive Bildgenerierung volumetrischer Daten zu ermöglichen und stellen deshalb einen wichtigen Beitrag hin zu einem flexiblen und interaktiven Volumen-Ray-Tracing-System dar.Volume rendering is one of the most demanding and interesting topics among scientific visualization. Applications include medical examinations, simulation of physical processes, and visual art. Most of these applications demand interactivity with respect to the viewing and visualization parameters. The ray tracing algorithm, although inherently simulating light interaction with participating media, was always considered too slow. Instead, most researchers followed object-order algorithms better suited for graphics adapters, although such approaches often suffer either from low quality or lack of flexibility. Another alternative is to speed up the ray tracing algorithm to make it competitive for volumetric visualization tasks. Since the advent of modern graphic adapters, research in this area had somehow ceased, although some limitations of GPUs, e.g. limited graphics board memory and tedious programming model, are still a problem. The two methods discussed in this thesis are therefore purely software-based since it is believed that software implementations allow for a far better optimization process before porting algorithms to hardware. The first method is called implicit kd-tree, which is a hierarchical spatial acceleration structure originally developed for iso-surface rendering of regular data sets that now supports semi-transparent rendering, time-dependent data visualization, and is even used in non volume-rendering applications. The second algorithm uses so-called Plücker coordinates, providing a fast incremental traversal for data sets consisting of tetrahedral or hexahedral primitives. Both algorithms are highly optimized to support interactive rendering of volumetric data sets and are therefore major contributions towards a flexible and interactive volume ray tracing framework

Fast Visualization by Shear-Warp using Spline Models for Data Reconstruction

This work concerns oneself with the rendering of huge three-dimensional data sets. The target thereby is the development of fast algorithms by also applying recent and accurate volume reconstruction models to obtain at most artifact-free data visualizations. In part I a comprehensive overview on the state of the art in volume rendering is given. Part II is devoted to the recently developed trivariate (linear,) quadratic and cubic spline models defined on symmetric tetrahedral partitions directly obtained by slicing volumetric partitions of a three-dimensional domain. This spline models define piecewise polynomials of total degree (one,) two and three with respect to a tetrahedron, i.e. the local splines have the lowest possible total degree and are adequate for efficient and accurate volume visualization. The following part III depicts in a step by step manner a fast software-based rendering algorithm, called shear-warp. This algorithm is prominent for its ability to generate projections of volume data at real time. It attains the high rendering speed by using elaborate data structures and extensive pre-computation, but at the expense of data redundancy and visual quality of the finally obtained rendering results. However, to circumvent these disadvantages a further development is specified, where new techniques and sophisticated data structures allow combining the fast shear-warp with the accurate ray-casting approach. This strategy and the new data structures not only grant a unification of the benefits of both methods, they even easily admit for adjustments to trade-off between rendering speed and precision. With this further development also the 3-fold data redundancy known from the original shear-warp approach is removed, allowing the rendering of even larger three-dimensional data sets more quickly. Additionally, real trivariate data reconstruction models, as discussed in part II, are applied together with the new ideas to onward the precision of the new volume rendering method, which also lead to a one order of magnitude faster algorithm compared to traditional approaches using similar reconstruction models. In part IV, a hierarchy-based rendering method is developed which utilizes a wavelet decomposition of the volume data, an octree structure to represent the sparse data set, the splines from part II and a new shear-warp visualization algorithm similar to that presented in part III. This thesis is concluded by the results centralized in part V