Efficient and High-Quality Rendering of Higher-Order Geometric Data Representations

Computer-Aided Design (CAD) bezeichnet den Entwurf industrieller Produkte mit Hilfe von virtuellen 3D Modellen. Ein CAD-Modell besteht aus parametrischen Kurven und Flächen, in den meisten Fällen non-uniform rational B-Splines (NURBS). Diese mathematische Beschreibung wird ebenfalls zur Analyse, Optimierung und Präsentation des Modells verwendet. In jeder dieser Entwicklungsphasen wird eine unterschiedliche visuelle Darstellung benötigt, um den entsprechenden Nutzern ein geeignetes Feedback zu geben. Designer bevorzugen beispielsweise illustrative oder realistische Darstellungen, Ingenieure benötigen eine verständliche Visualisierung der Simulationsergebnisse, während eine immersive 3D Darstellung bei einer Benutzbarkeitsanalyse oder der Designauswahl hilfreich sein kann. Die interaktive Darstellung von NURBS-Modellen und -Simulationsdaten ist jedoch aufgrund des hohen Rechenaufwandes und der eingeschränkten Hardwareunterstützung eine große Herausforderung. Diese Arbeit stellt vier neuartige Verfahren vor, welche sich mit der interaktiven Darstellung von NURBS-Modellen und Simulationensdaten befassen. Die vorgestellten Algorithmen nutzen neue Fähigkeiten aktueller Grafikkarten aus, um den Stand der Technik bezüglich Qualität, Effizienz und Darstellungsgeschwindigkeit zu verbessern. Zwei dieser Verfahren befassen sich mit der direkten Darstellung der parametrischen Beschreibung ohne Approximationen oder zeitaufwändige Vorberechnungen. Die dabei vorgestellten Datenstrukturen und Algorithmen ermöglichen die effiziente Unterteilung, Klassifizierung, Tessellierung und Darstellung getrimmter NURBS-Flächen und einen interaktiven Ray-Casting-Algorithmus für die Isoflächenvisualisierung von NURBSbasierten isogeometrischen Analysen. Die weiteren zwei Verfahren beschreiben zum einen das vielseitige Konzept der programmierbaren Transparenz für illustrative und verständliche Visualisierungen tiefenkomplexer CAD-Modelle und zum anderen eine neue hybride Methode zur Reprojektion halbtransparenter und undurchsichtiger Bildinformation für die Beschleunigung der Erzeugung von stereoskopischen Bildpaaren. Die beiden letztgenannten Ansätze basieren auf rasterisierter Geometrie und sind somit ebenfalls für normale Dreiecksmodelle anwendbar, wodurch die Arbeiten auch einen wichtigen Beitrag in den Bereichen der Computergrafik und der virtuellen Realität darstellen. Die Auswertung der Arbeit wurde mit großen, realen NURBS-Datensätzen durchgeführt. Die Resultate zeigen, dass die direkte Darstellung auf Grundlage der parametrischen Beschreibung mit interaktiven Bildwiederholraten und in subpixelgenauer Qualität möglich ist. Die Einführung programmierbarer Transparenz ermöglicht zudem die Umsetzung kollaborativer 3D Interaktionstechniken für die Exploration der Modelle in virtuellenUmgebungen sowie illustrative und verständliche Visualisierungen tiefenkomplexer CAD-Modelle. Die Erzeugung stereoskopischer Bildpaare für die interaktive Visualisierung auf 3D Displays konnte beschleunigt werden. Diese messbare Verbesserung wurde zudem im Rahmen einer Nutzerstudie als wahrnehmbar und vorteilhaft befunden.In computer-aided design (CAD), industrial products are designed using a virtual 3D model. A CAD model typically consists of curves and surfaces in a parametric representation, in most cases, non-uniform rational B-splines (NURBS). The same representation is also used for the analysis, optimization and presentation of the model. In each phase of this process, different visualizations are required to provide an appropriate user feedback. Designers work with illustrative and realistic renderings, engineers need a comprehensible visualization of the simulation results, and usability studies or product presentations benefit from using a 3D display. However, the interactive visualization of NURBS models and corresponding physical simulations is a challenging task because of the computational complexity and the limited graphics hardware support. This thesis proposes four novel rendering approaches that improve the interactive visualization of CAD models and their analysis. The presented algorithms exploit latest graphics hardware capabilities to advance the state-of-the-art in terms of quality, efficiency and performance. In particular, two approaches describe the direct rendering of the parametric representation without precomputed approximations and timeconsuming pre-processing steps. New data structures and algorithms are presented for the efficient partition, classification, tessellation, and rendering of trimmed NURBS surfaces as well as the first direct isosurface ray-casting approach for NURBS-based isogeometric analysis. The other two approaches introduce the versatile concept of programmable order-independent semi-transparency for the illustrative and comprehensible visualization of depth-complex CAD models, and a novel method for the hybrid reprojection of opaque and semi-transparent image information to accelerate stereoscopic rendering. Both approaches are also applicable to standard polygonal geometry which contributes to the computer graphics and virtual reality research communities. The evaluation is based on real-world NURBS-based models and simulation data. The results show that rendering can be performed directly on the underlying parametric representation with interactive frame rates and subpixel-precise image results. The computational costs of additional visualization effects, such as semi-transparency and stereoscopic rendering, are reduced to maintain interactive frame rates. The benefit of this performance gain was confirmed by quantitative measurements and a pilot user study

Arbitrary topology meshes in geometric design and vector graphics

Meshes are a powerful means to represent objects and shapes both in 2D and 3D, but the techniques based on meshes can only be used in certain regular settings and restrict their usage. Meshes with an arbitrary topology have many interesting applications in geometric design and (vector) graphics, and can give designers more freedom in designing complex objects. In the first part of the thesis we look at how these meshes can be used in computer aided design to represent objects that consist of multiple regular meshes that are constructed together. Then we extend the B-spline surface technique from the regular setting to work on extraordinary regions in meshes so that multisided B-spline patches are created. In addition, we show how to render multisided objects efficiently, through using the GPU and tessellation. In the second part of the thesis we look at how the gradient mesh vector graphics primitives can be combined with procedural noise functions to create expressive but sparsely defined vector graphic images. We also look at how the gradient mesh can be extended to arbitrary topology variants. Here, we compare existing work with two new formulations of a polygonal gradient mesh. Finally we show how we can turn any image into a vector graphics image in an efficient manner. This vectorisation process automatically extracts important image features and constructs a mesh around it. This automatic pipeline is very efficient and even facilitates interactive image vectorisation

A novel parallel algorithm for surface editing and its FPGA implementation

A thesis submitted to the University of Bedfordshire in partial fulfilment of the requirements for the degree of Doctor of PhilosophySurface modelling and editing is one of important subjects in computer graphics. Decades of research in computer graphics has been carried out on both low-level, hardware-related algorithms and high-level, abstract software. Success of computer graphics has been seen in many application areas, such as multimedia, visualisation, virtual reality and the Internet. However, the hardware realisation of OpenGL architecture based on FPGA (field programmable gate array) is beyond the scope of most of computer graphics researches. It is an uncultivated research area where the OpenGL pipeline, from hardware through the whole embedded system (ES) up to applications, is implemented in an FPGA chip. This research proposes a hybrid approach to investigating both software and hardware methods. It aims at bridging the gap between methods of software and hardware, and enhancing the overall performance for computer graphics. It consists of four parts, the construction of an FPGA-based ES, Mesa-OpenGL implementation for FPGA-based ESs, parallel processing, and a novel algorithm for surface modelling and editing. The FPGA-based ES is built up. In addition to the Nios II soft processor and DDR SDRAM memory, it consists of the LCD display device, frame buffers, video pipeline, and algorithm-specified module to support the graphics processing. Since there is no implementation of OpenGL ES available for FPGA-based ESs, a specific OpenGL implementation based on Mesa is carried out. Because of the limited FPGA resources, the implementation adopts the fixed-point arithmetic, which can offer faster computing and lower storage than the floating point arithmetic, and the accuracy satisfying the needs of 3D rendering. Moreover, the implementation includes Bézier-spline curve and surface algorithms to support surface modelling and editing. The pipelined parallelism and co-processors are used to accelerate graphics processing in this research. These two parallelism methods extend the traditional computation parallelism in fine-grained parallel tasks in the FPGA-base ESs. The novel algorithm for surface modelling and editing, called Progressive and Mixing Algorithm (PAMA), is proposed and implemented on FPGA-based ES’s. Compared with two main surface editing methods, subdivision and deformation, the PAMA can eliminate the large storage requirement and computing cost of intermediated processes. With four independent shape parameters, the PAMA can be used to model and edit freely the shape of an open or closed surface that keeps globally the zero-order geometric continuity. The PAMA can be applied independently not only FPGA-based ESs but also other platforms. With the parallel processing, small size, and low costs of computing, storage and power, the FPGA-based ES provides an effective hybrid solution to surface modelling and editing

Ray Tracing Gems

This book is a must-have for anyone serious about rendering in real time. With the announcement of new ray tracing APIs and hardware to support them, developers can easily create real-time applications with ray tracing as a core component. As ray tracing on the GPU becomes faster, it will play a more central role in real-time rendering. Ray Tracing Gems provides key building blocks for developers of games, architectural applications, visualizations, and more. Experts in rendering share their knowledge by explaining everything from nitty-gritty techniques that will improve any ray tracer to mastery of the new capabilities of current and future hardware. What you'll learn: The latest ray tracing techniques for developing real-time applications in multiple domains Guidance, advice, and best practices for rendering applications with Microsoft DirectX Raytracing (DXR) How to implement high-performance graphics for interactive visualizations, games, simulations, and more Who this book is for: Developers who are looking to leverage the latest APIs and GPU technology for real-time rendering and ray tracing Students looking to learn about best practices in these areas Enthusiasts who want to understand and experiment with their new GPU

Characterization of multiphase flows integrating X-ray imaging and virtual reality

Multiphase flows are used in a wide variety of industries, from energy production to pharmaceutical manufacturing. However, because of the complexity of the flows and difficulty measuring them, it is challenging to characterize the phenomena inside a multiphase flow. To help overcome this challenge, researchers have used numerous types of noninvasive measurement techniques to record the phenomena that occur inside the flow. One technique that has shown much success is X-ray imaging. While capable of high spatial resolutions, X-ray imaging generally has poor temporal resolution. This research improves the characterization of multiphase flows in three ways. First, an X-ray image intensifier is modified to use a high-speed camera to push the temporal limits of what is possible with current tube source X-ray imaging technology. Using this system, sample flows were imaged at 1000 frames per second without a reduction in spatial resolution. Next, the sensitivity of X-ray computed tomography (CT) measurements to changes in acquisition parameters is analyzed. While in theory CT measurements should be stable over a range of acquisition parameters, previous research has indicated otherwise. The analysis of this sensitivity shows that, while raw CT values are strongly affected by changes to acquisition parameters, if proper calibration techniques are used, acquisition parameters do not significantly influence the results for multiphase flow imaging. Finally, two algorithms are analyzed for their suitability to reconstruct an approximate tomographic slice from only two X-ray projections. These algorithms increase the spatial error in the measurement, as compared to traditional CT; however, they allow for very high temporal resolutions for 3D imaging. The only limit on the speed of this measurement technique is the image intensifier-camera setup, which was shown to be capable of imaging at a rate of at least 1000 FPS. While advances in measurement techniques for multiphase flows are one part of improving multiphase flow characterization, the challenge extends beyond measurement techniques. For improved measurement techniques to be useful, the data must be accessible to scientists in a way that maximizes the comprehension of the phenomena. To this end, this work also presents a system for using the Microsoft Kinect sensor to provide natural, non-contact interaction with multiphase flow data. Furthermore, this system is constructed so that it is trivial to add natural, non-contact interaction to immersive visualization applications. Therefore, multiple visualization applications can be built that are optimized to specific types of data, but all leverage the same natural interaction. Finally, the research is concluded by proposing a system that integrates the improved X-ray measurements, with the Kinect interaction system, and a CAVE automatic virtual environment (CAVE) to present scientists with the multiphase flow measurements in an intuitive and inherently three-dimensional manner

Fast Volume Rendering and Deformation Algorithms

Volume rendering is a technique for simultaneous visualization of surfaces and inner structures of objects. However, the huge number of volume primitives (voxels) in a volume, leads to high computational cost. In this dissertation I developed two algorithms for the acceleration of volume rendering and volume deformation. The first algorithm accelerates the ray casting of volume. Previous ray casting acceleration techniques like space-leaping and early-ray-termination are only efficient when most voxels in a volume are either opaque or transparent. When many voxels are semi-transparent, the rendering time will increase considerably. Our new algorithm improves the performance of ray casting of semi-transparently mapped volumes by exploiting the opacity coherency in object space, leading to a speedup factor between 1.90 and 3.49 in rendering semi-transparent volumes. The acceleration is realized with the help of pre-computed coherency distances. We developed an efficient algorithm to encode the coherency information, which requires less than 12 seconds for data sets with about 8 million voxels. The second algorithm is for volume deformation. Unlike the traditional methods, our method incorporates the two stages of volume deformation, i.e. deformation and rendering, into a unified process. Instead to deform each voxel to generate an intermediate deformed volume, the algorithm follows inversely deformed rays to generate the desired deformation. The calculations and memory for generating the intermediate volume are thus saved. The deformation continuity is achieved by adaptive ray division which matches the amplitude of local deformation. We proposed approaches for shading and opacit adjustment which guarantee the visual plausibility of deformation results. We achieve an additional deformation speedup factor of 2.34~6.58 by incorporating early-ray-termination, space-leaping and the coherency acceleration technique in the new deformation algorithm

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

Innovative mathematical and numerical models for studying the deformation of shells during industrial forming processes with the Finite Element Method

The doctoral thesis "Innovative mathematical and numerical models for studying the deformation of shells during industrial forming processes with the Finite Element Method" aims to contribute to the development of finite element methods for the analysis of stamping processes, a problematic area with a clear industrial application. To achieve the proposed objectives, the first part of this thesis covers the solid-shell elements. This type of element is attractive for the simulation of forming processes, since any type of three-dimensional constitutive law can be formulated without the need to consider any additional conjecture. Additionally, the contact of both sides can be easily treated. This work first presents the development of a triangular prismatic solid-sheet element, for the analysis of thick and thin sheets with capacity for large deformations. This element is in total Lagrangian formulation, and uses neighboring elements to compute a field of quadratic displacements. In the original formulation, a modified right Cauchy tensor was obtained; however, in this work, the formulation is extended obtaining a modified strain gradient, which allows the concepts of push-forward and pull-back to be used. These concepts provide a mathematically consistent method for the definition of temporary derivatives of tensors and, therefore, can be used, for example, to work with elasto-plasticity. This work continues with the development of the contact formulation used, a methodology found in the bibliography on computational contact mechanics for implicit simulations. This formulation consists of an exact integration of the contact interface using mortar methods, which allows obtaining the most consistent integration possible between the integration domains, as well as the most exact possible solution. The most notable contribution of this work is the consideration of dual augmented Lagrange multipliers as an optimization method. To solve the system of equations, a semi-smooth Newton method is considered, which consists of an active set strategy, also extensible in the case of friction problems. The formulation is functional for both frictionless and friction problems, which is essential for simulating stamping processes. This frictional formulation is framed in traditional friction models, such as Coulomb friction, but the development presented can be extended to any type of friction model. The remaining necessary component for the simulation of industrial processes are the constitutive models. In this work, this is materialized in the formulation of plasticity considered. These constitutive models will be considered plasticity models for large deformations, with an arbitrary combination of creep surfaces and plastic potentials: the so-called non-associative models. To calculate the tangent tensor corresponding to these general laws, numerical implementations based on perturbation methods have been considered. Another fundamental contribution of this work is the development of techniques for adaptive remeshing, of which different approaches will be presented. On the one hand, metric-based techniques, including the level-set and Hessian approaches. These techniques are general-purpose and can be considered in both structural problems and fluid mechanics problems. On the other hand, the SPR error estimation method, more conventional than the previous ones, is presented. In this area, the contribution of this work consists in the estimation of error using the Hessian and SPR techniques for the application to numerical contact problems.La tesis doctoral "Modelos matemáticos y numéricos innovadores para el estudio de la deformación de láminas durante los procesos de conformado industrial por el Método de los Elementos Finitos" pretende contribuir al desarrollo de métodos de elementos finitos para el análisis de procesos de estampado, un área problemática con una clara aplicación industrial. De hecho, este tipo de problemas multidisciplinares requieren el conocimiento de múltiples disciplinas, como la mecánica de medios continuos, la plasticidad, la termodinámica y los problemas de contacto, entre otros. Para alcanzar los objetivos propuestos, la primera parte de esta tesis abarca los elementos de sólido lámina. Este tipo de elemento resulta atractivo para la simulación de procesos de conformado, dado que cualquier tipo de ley constitutiva tridimensional puede ser formulada sin necesidad de considerar ninguna conjetura adicional. Además, este tipo de elementos permite realizar una descripción tridimensional del cuerpo deformable, por tanto, el contacto de ambas caras puede ser tratado fácilmente. Este trabajo presenta en primer lugar el desarrollo de un elemento de sólido-lámina prismático triangular, para el análisis de láminas gruesas y delgadas con capacidad para grandes deformaciones. Este elemento figura en formulación Lagrangiana total, y emplea los elementos vecinos para poder computar un campo de desplazamientos cuadráticos. En la formulación original, se obtenía un tensor de Cauchy derecho modificado (¯C); sin embargo, en este trabajo, la formulación se extiende obteniendo un gradiente de deformación modificado (¯F), que permite emplear los conceptos de push-forward y pull-back. Dichos conceptos proveen de un método matemáticamente consistente para la definición de derivadas temporales de tensores y, por tanto, puede ser usado, por ejemplo, para trabajar con elasto-plasticidad. El elemento se basa en tres modificaciones: (a) una aproximación clásica de deformaciones transversales de corte mixtas impuestas; (b) una aproximación de deformaciones impuestas para las Componentes en el plano tangente de la lámina; y (c) una aproximación de deformaciones impuestas mejoradas en la dirección normal a través del espesor, mediante la consideración de un grado de libertad adicional. Los objetivos son poder utilizar el elemento para la simulación de láminas sin bloquear por cortante, mejorar el comportamiento membranal del elemento en el plano tangente, eliminar el bloqueo por efecto Poisson y poder tratar materiales elasto-plásticos con un flujo plástico incompresible, así como materiales elásticos cuasi-incompresibles o materiales con flujo plástico isocórico. El elemento considera un único punto de Gauss en el plano, mientras que permite considerar un número cualquiera de puntos de integración en su eje, con el objetivo de poder considerar problemas con una significativa no linealidad en cuanto a plasticidad. Este trabajo continúa con el desarrollo de la formulación de contacto empleada, una metodología que se encuentra en la bibliografía sobre la mecánica de contacto computacional para simulaciones implícitas. Dicha formulación consiste en una integración exacta de la interfaz de contacto mediante métodos de mortero, lo que permite obtener la integración más consistente posible entre los dominios de integración, así como la solución más exacta posible. La implementación también considera varios algoritmos de optimización, como la optimización mediante penalización. La contribución más notable de este trabajo es la consideración de multiplicadores de Lagrange aumentados duales como método de optimización. Estos permiten condensar estáticamente el sistema de ecuaciones, lo que permite eliminar los multiplicadores de Lagrange de la resolución y, por lo tanto, permite la consideración de solvers iterativos. Además, la formulación ha sido adecuadamente linealizada, asegurando la convergencia cuadrática del problema. Para resolver el sistema de ecuaciones, se considera un método de Newton semi-smooth, que consiste en una estrategia de set activo, extensible también en el caso de problemas friccionales. La formulación es funcional tanto para problemas sin fricción como para problemas friccionales, lo que es esencial para la simulación de procesos de estampado. Esta formulación friccional se enmarca en los modelos de fricción tradicionales, como la fricción de Coulomb, pero el desarrollo presentado puede extenderse a cualquier tipo de modelo de fricción. Esta formulación de contacto es totalmente compatible con el elemento sólido-lámina introducido en este trabajo. El componente necesario restante para la simulación de procesos industriales son los modelos constitutivos. En este trabajo, esto se ve materializado en la formulación de plasticidad considerada. Estos modelos constitutivos se considerarán modelos de plasticidad para grandes deformaciones, con una combinación arbitraria de superficies de fluencia y potenciales plásticos: los llamados modelos no asociados. Para calcular el tensor tangente correspondiente a estas leyes generales, se han considerado implementaciones numéricas basadas en métodos de perturbación. Otra contribución fundamental de este trabajo es el desarrollo de técnicas para el remallado adaptativo, de las que se presentarán distintos enfoques. Por un lado, las técnicas basadas en métricas, incluyendo los enfoques level-set y Hessiano. Estas técnicas son de propósito general y pueden considerarse tanto en la aplicación de problemas estructurales como en problemas de mecánica de fluidos. Por otro lado, se presenta el método de estimación de errores SPR, más convencional que los anteriores. En este ámbito, la contribución de este trabajo consiste en la estimación de error mediante las técnicas de Hessiano y SPR para la aplicación a problemas de contacto numérico. Con los desarrollos previamente introducidos, estaremos en disposición de introducir los casos de aplicación centrados en el contexto de procesos de estampado. Es relevante destacar que estos ejemplos son comparados con las soluciones de referencia disponibles en la bibliografía como forma de validar los desarrollos presentados hasta este punto. El presente documento está organizado de la siguiente manera. El primer capítulo establece los objetivos y revisa la bibliografía acerca de los temas clave de este trabajo. El segundo capítulo hace una introducción de la mecánica de medios continuos y los conceptos relativos al Método de los Elementos Finitos (MEF), necesarios en los desarrollos que se presentarán en los capítulos siguientes. El tercer capítulo aborda la formulación del elemento sólido-lámina, así como del elemento de lámina sin grados de libertad de rotación que inspira el sólido-lámina desarrollado. Esta parte muestra varios ejemplos académicos que son comúnmente empleados en la bibliografía como problemas de referencia de láminas. El cuarto capítulo presenta la formulación desarrollada para la resolución de problemas de contacto numérico, consistente en una formulación implícita de integración exacta mediante métodos mortero y multiplicadores de Lagrange aumentados duales. Este capítulo incluye, asimismo, varios ejemplos comúnmente encontrados en la bibliografía, que generalmente son considerados para su validación. El quinto capítulo presenta la formulación de plasticidad empleada, incluyendo algunos detalles técnicos desde el punto de vista de la implementación, así como varios ejemplos de validación. El sexto capítulo muestra los algoritmos de remallado adaptativo desarrollados en el contexto de este trabajo, y presenta varios ejemplos, que incluyen no solo casos estructurales, sino también de mecánica de fluidos. El séptimo capítulo encapsula algunos casos de validación y aplicación para procesos de estampado. El capítulo final comprende las conclusiones, así como los trabajos que podrían continuar el presente estudio.Postprint (published version

Robust and numerically stable Bézier clipping method for ray tracing NURBS surfaces

Raytracing has become a popular method for generating realistic images and movies. The progress in hardware development shows that the real time raytracing on a single PC might be possible in the ongoing future. Obviously, that new generation of raytracing based applications will require more visualization precision and flexibility. Most of the modern raytracing based applications only deal with triangles as basic primitives, which brings limitations to an application and may cause visual artifacts to appear. NURBS surface representation is common for most of 3D modeling tools because of its compactness and useful geometric properties of NURBS surfaces. Using the direct raytracing NURBS surfaces, one can achieve better quality of rendered images. Although, many such approaches have already been presented, almost all of them suffer from numerical problems or do not work in some special cases. This paper presents a modified Bézier clipping method for finding ray - NURBS surface intersection points, which is fast, robust, and numerically stable