Doctor of Philosophy

dissertationPartial differential equations (PDEs) are widely used in science and engineering to model phenomena such as sound, heat, and electrostatics. In many practical science and engineering applications, the solutions of PDEs require the tessellation of computational domains into unstructured meshes and entail computationally expensive and time-consuming processes. Therefore, efficient and fast PDE solving techniques on unstructured meshes are important in these applications. Relative to CPUs, the faster growth curves in the speed and greater power efficiency of the SIMD streaming processors, such as GPUs, have gained them an increasingly important role in the high-performance computing area. Combining suitable parallel algorithms and these streaming processors, we can develop very efficient numerical solvers of PDEs. The contributions of this dissertation are twofold: proposal of two general strategies to design efficient PDE solvers on GPUs and the specific applications of these strategies to solve different types of PDEs. Specifically, this dissertation consists of four parts. First, we describe the general strategies, the domain decomposition strategy and the hybrid gathering strategy. Next, we introduce a parallel algorithm for solving the eikonal equation on fully unstructured meshes efficiently. Third, we present the algorithms and data structures necessary to move the entire FEM pipeline to the GPU. Fourth, we propose a parallel algorithm for solving the levelset equation on fully unstructured 2D or 3D meshes or manifolds. This algorithm combines a narrowband scheme with domain decomposition for efficient levelset equation solving

Survey of semi-regular multiresolution models for interactive terrain rendering

Rendering high quality digital terrains at interactive rates requires carefully crafted algorithms and data structures able to balance the competing requirements of realism and frame rates, while taking into account the memory and speed limitations of the underlying graphics platform. In this survey, we analyze multiresolution approaches that exploit a certain semi-regularity of the data. These approaches have produced some of the most efficient systems to date. After providing a short background and motivation for the methods, we focus on illustrating models based on tiled blocks and nested regular grids, quadtrees and triangle bin-trees triangulations, as well as cluster-based approaches. We then discuss LOD error metrics and system-level data management aspects of interactive terrain visualization, including dynamic scene management, out-of-core data organization and compression, as well as numerical accurac

Accurate geometry reconstruction of vascular structures using implicit splines

3-D visualization of blood vessel from standard medical datasets (e.g. CT or MRI) play an important role in many clinical situations, including the diagnosis of vessel stenosis, virtual angioscopy, vascular surgery planning and computer aided vascular surgery. However, unlike other human organs, the vasculature system is a very complex network of vessel, which makes it a very challenging task to perform its 3-D visualization. Conventional techniques of medical volume data visualization are in general not well-suited for the above-mentioned tasks. This problem can be solved by reconstructing vascular geometry. Although various methods have been proposed for reconstructing vascular structures, most of these approaches are model-based, and are usually too ideal to correctly represent the actual variation presented by the cross-sections of a vascular structure. In addition, the underlying shape is usually expressed as polygonal meshes or in parametric forms, which is very inconvenient for implementing ramification of branching. As a result, the reconstructed geometries are not suitable for computer aided diagnosis and computer guided minimally invasive vascular surgery. In this research, we develop a set of techniques associated with the geometry reconstruction of vasculatures, including segmentation, modelling, reconstruction, exploration and rendering of vascular structures. The reconstructed geometry can not only help to greatly enhance the visual quality of 3-D vascular structures, but also provide an actual geometric representation of vasculatures, which can provide various benefits. The key findings of this research are as follows: 1. A localized hybrid level-set method of segmentation has been developed to extract the vascular structures from 3-D medical datasets. 2. A skeleton-based implicit modelling technique has been proposed and applied to the reconstruction of vasculatures, which can achieve an accurate geometric reconstruction of the vascular structures as implicit surfaces in an analytical form. 3. An accelerating technique using modern GPU (Graphics Processing Unit) is devised and applied to rendering the implicitly represented vasculatures. 4. The implicitly modelled vasculature is investigated for the application of virtual angioscopy

Enhancing detailed haptic relief for real-time interaction

The present document exposes a different approach for haptic rendering, defined as the simulation of force interactions to reproduce the sensation of surface relief in dense models. Current research shows open issues in timely haptic interaction involving large meshes, with several problems affecting performance and fidelity, and without a dominant technique to treat these issues properly. Relying in pure geometric collisions when rendering highly dense mesh models (hundreds of thousands of triangles) sensibly degrades haptic rates due to the sheer number of collisions that must be tracked between the mesh's faces and a haptic probe. Several bottlenecks were identified in order to enhance haptic performance: software architecture and data structures, collision detection, and accurate rendering of surface relief. To account for overall software architecture and data structures, it was derived a complete component framework for transforming standalone VR applications into full-fledged multi-threaded Collaborative Virtual Reality Environments (CVREs), after characterizing existing implementations into a feature-rich superset. Enhancements include: a scalable arbitrated peer-to-peer topology for scene sharing; multi-threaded components for graphics rendering, user interaction and network communications; a collaborative user interface model for session handling; and interchangeable user roles with multi-camera perspectives, avatar awareness and shared annotations. We validate the framework by converting the existing ALICE VR Navigator into a complete CVRE, showing good performance in collaborative manipulation of complex models. To specifically address collision detection computation, we derive a conformal algebra treatment for collisions among points, segments, areas, and volumes, based on collision detection in conformal R{4,1} (5D) space, and implemented in GPU for faster parallel queries. Results show orders of magnitude time reductions in collisions computations, allowing interactive rates. Finally, the main core of the research is the haptic rendering of surface mesostructure in large meshes. Initially, a method for surface haptic rendering was proposed, using image-based Hybrid Rugosity Mesostructures (HRMs) of per-face heightfield displacements and normalmaps layered on top of a simpler mesh, adding greater surface detail than actually present. Haptic perception is achieved modulating the haptic probe's force response using the HRM coat. A usability testbed framework was built to measure experimental performance with a common set tests, meshes and HRMs. Trial results show the goodness of the proposed technique, rendering accurate 3D surface detail at high sampling rates. This local per-face method is extended into a fast global approach for haptic rendering, building a mesostructure-based atlas of depth/normal textures (HyRMA), computed out of surface differences of the same mesh object at two different resolutions: original and simplified. For each triangle in the simplified mesh, an irregular prism is considered defined by the triangle's vertices and their normals. This prism completely covers the original mesh relief over the triangle. Depth distances and surfaces normals within each prism are warped from object volume space to orthogonal tangent space, by means of a novel and fast method for computing barycentric coordinates at the prism, and storing normals and relief in a sorted atlas. Haptic rendering is effected by colliding the probe against the atlas, and effecting a modulated force response at the haptic probe. The method is validated numerically, statistically and perceptually in user testing controlled trials, achieving accurate haptic sensation of large meshes' fine features at interactive rendering rates, with some minute loss of mesostructure detail.En aquesta tesi es presenta un novedós enfocament per a la percepció hàptica del relleu de models virtuals complexes mitjançant la simulació de les forces d'interacció entre la superfície i un element de contacte. La proposta contribueix a l'estat de l'art de la recerca en aquesta àrea incrementant l'eficiència i la fidelitat de la interacció hàptica amb grans malles de triangles. La detecció de col·lisions amb malles denses (centenars de milers de triangles) limita la velocitat de resposta hàptica degut al gran nombre d'avaluacions d'intersecció cara-dispositiu hàptic que s'han de realitzar. Es van identificar diferents alternatives per a incrementar el rendiment hàptic: arquitectures de software i estructures de dades específiques, algorismes de detecció de col·lisions i reproducció hàptica de relleu superficial. En aquesta tesi es presenten contribucions en alguns d'aquests aspectes. S'ha proposat una estructura completa de components per a transformar aplicacions de Realitat Virtual en Ambients Col·laboratius de Realitat Virtual (CRVEs) multithread en xarxa. L'arquitectura proposada inclou: una topologia escalable punt a punt per a compartir escenes; components multithread per a visualització gràfica, interacció amb usuaris i comunicació en xarxa; un model d'interfície d'usuari col·laboratiu per a la gestió de sessions; i rols intercanviables de l'usuari amb perspectives de múltiples càmeres, presència d'avatars i anotacions compartides. L'estructura s'ha validat convertint el navegador ALICE en un CVRE completament funcional, mostrant un bon rendiment en la manipulació col·laborativa de models complexes. Per a incrementar l'eficiència del càlcul de col·lisions, s'ha proposat un algorisme que treballa en un espai conforme R{4,1} (5D) que permet detectar col·lisions entre punts, segments, triangles i volums. Aquest algorisme s'ha implementat en GPU per obtenir una execució paral·lela més ràpida. Els resultats mostren reduccions en el temps de càlcul de col·lisions permetent interactivitat. Per a la percepció hàptica de malles complexes que modelen objectes rugosos, s'han proposat diferents algorismes i estructures de dades. Les denominades Mesoestructures Híbrides de Rugositat (HRM) permeten substituir els detalls geomètrics d'una cara (rugositats) per dues textures: de normals i d'alçades. La percepció hàptica s'aconsegueix modulant la força de resposta entre el dispositiu hàptic i la HRM. Els tests per avaluar experimentalment l'eficiència del càlcul de col·lisions i la percepció hàptica utilitzant HRM respecte a modelar les rugositats amb geometria, van mostrar que la tècnica proposada va ser encertada, permetent percebre detalls 3D correctes a altes tases de mostreig. El mètode es va estendre per a representar rugositats d'objectes. Es proposa substituir l'objecte per un model simplificat i un atles de mesoestructures en el que s'usen textures de normals i de relleus (HyRMA). Aquest atles s'obté a partir de la diferència en el detall de la superfície entre dos malles del mateix objecte: l'original i la simplificada. A partir d'un triangle de la malla simplificada es construeix un prisma, definit pels vèrtexs del triangle i les seves normals, que engloba el relleu de la malla original sobre el triangle. Les alçades i normals dins del prisma es transformen des de l'espai de volum a l'espai ortogonal tangent, amb mètode novedós i eficient que calcula les coordenades baricèntriques relatives al prisma, per a guardar el mapa de textures transformat en un atles ordenat. La percepció hàptica s'assoleix detectant les col·lisions entre el dispositiu hàptic i l'atles, i modulant la força de resposta d'acord al resultat de la col·lisió. El mètode s'ha validat numèricament, estadística i perceptual en tests amb usuaris, aconseguint una correcta i interactiva sensació tàctil dels objectes simulats mitjançant la mesoestructura de les mallesEn esta tesis se presenta un enfoque novedoso para la percepción háptica del relieve de modelos virtuales complejos mediante la simulación de las fuerzas de interacción entre la superficie y un elemento de contacto. La propuesta contribuye al estado del arte de investigación en este área incrementando la eficiencia y fidelidad de interacción háptica con grandes mallas de triángulos. La detección de colisiones con mallas geométricas densas (cientos de miles de triángulos) limita la velocidad de respuesta háptica debido al elevado número de evaluaciones de intersección cara-dispositivo háptico que deben realizarse. Se identificaron diferentes alternativas para incrementar el rendimiento háptico: arquitecturas de software y estructuras de datos específicas, algoritmos de detección de colisiones y reproducción háptica de relieve superficial. En esta tesis se presentan contribuciones en algunos de estos aspectos. Se ha propuesto una estructura completa de componentes para transformar aplicaciones aisladas de Realidad Virtual en Ambientes Colaborativos de Realidad Virtual (CRVEs) multithread en red. La arquitectura propuesta incluye: una topología escalable punto a punto para compartir escenas; componentes multithread para visualización gráfica, interacción con usuarios y comunicación en red; un modelo de interfaz de usuario colaborativo para la gestión de sesiones; y roles intercambiables del usuario con perspectivas de múltiples cámaras, presencia de avatares y anotaciones compartidas. La estructura se ha validado convirtiendo el navegador ALICE en un CVRE completamente funcional, mostrando un buen rendimiento en la manipulación colaborativa de modelos complejos. Para incrementar la eficiencia del cálculo de colisiones, se ha propuesto un algoritmo que trabaja en un espacio conforme R4,1 (5D) que permite detectar colisiones entre puntos, segmentos, triángulos y volúmenes. Este algoritmo se ha implementado en GPU a efectos de obtener una ejecución paralelamás rápida. Los resultadosmuestran reducciones en el tiempo de cálculo de colisiones permitiendo respuesta interactiva. Para la percepción háptica de mallas complejas que modelan objetos rugosos, se han propuesto diferentes algoritmos y estructuras de datos. Las denominadasMesoestructuras Híbridas de Rugosidad (HRM) permiten substituir los detalles geométricos de una cara (rugosidades) por una textura de normales y otra de alturas. La percepción háptica se consigue modulando la fuerza de respuesta entre el dispositivo háptico y la HRM. Los tests realizados para evaluar experimentalmente la eficiencia del cálculo de colisiones y la percepción háptica utilizando HRM respecto a modelar las rugosidades con geometría, mostraron que la técnica propuesta fue acertada, permitiendo percibir detalles 3D correctos a altas tasas de muestreo. Este método anterior es extendido a un procedimiento global para representar rugosidades de objetos. Para hacerlo se propone sustituir el objeto por un modelo simplificado y un atlas de mesostructuras usando texturas de normales y relieves (HyRMA). Este atlas se obtiene de la diferencia en detalle de superficie entre dos mallas del mismo objeto: la original y la simplificada. A partir de un triángulo de la malla simplificada se construye un prisma definido por los vértices del triángulo a lo largo de sus normales, que engloba completamente el relieve de la malla original sobre este triángulo. Las alturas y normales dentro de cada prisma se transforman del espacio de volumen al espacio ortoganal tangente, usando un método novedoso y eficiente que calcula las coordenadas baricéntricas relativas a cada prisma para guardar el mapa de texturas transformado en un atlas ordenado. La percepción háptica se consigue detectando directamente las colisiones entre el dispositivo háptico y el atlas, y modulando la fuerza de respuesta de acuerdo al resultado de la colisión. El procedmiento se ha validado numérica, estadística y perceptualmente en ensayos con usuarios, consiguiendo a tasas interactivas la correcta sensación táctil de los objetos simulados mediante la mesoestructura de las mallas, con alguna pérdida muy puntual de detall

Self-adaptive isogeometric spatial discretisations of the first and second-order forms of the neutron transport equation with dual-weighted residual error measures and diffusion acceleration

As implemented in a new modern-Fortran code, NURBS-based isogeometric analysis (IGA) spatial discretisations and self-adaptive mesh refinement (AMR) algorithms are developed in the application to the first-order and second-order forms of the neutron transport equation (NTE). These AMR algorithms are shown to be computationally efficient and numerically accurate when compared to standard approaches. IGA methods are very competitive and offer certain unique advantages over standard finite element methods (FEM), not least of all because the numerical analysis is performed over an exact representation of the underlying geometry, which is generally available in some computer-aided design (CAD) software description. Furthermore, mesh refinement can be performed within the analysis program at run-time, without the need to revisit any ancillary mesh generator. Two error measures are described for the IGA-based AMR algorithms, both of which can be employed in conjunction with energy-dependent meshes. The first heuristically minimises any local contributions to the global discretisation error, as per some appropriate user-prescribed norm. The second employs duality arguments to minimise important local contributions to the error as measured in some quantity of interest; this is commonly known as a dual-weighted residual (DWR) error measure and it demands the solution to both the forward (primal) and the adjoint (dual) NTE. Finally, convergent and stable diffusion acceleration and generalised minimal residual (GMRes) algorithms, compatible with the aforementioned AMR algorithms, are introduced to accelerate the convergence of the within-group self-scattering sources for scattering-dominated problems for the first and second-order forms of the NTE. A variety of verification benchmark problems are analysed to demonstrate the computational performance and efficiency of these acceleration techniques.Open Acces

A freeform shape optimization of complex structures represented by arbitrary polygonal or polyhedral meshes

In this paper we propose a new scheme for freeform shape optimization on arbitrary polygonal or polyhedral meshes. The approach consists of three main steps: (1) surface partitioning of polygonal meshes into different patches; (2) a new freeform perturbation scheme of using the Cox–de Boor basis function over arbitrary polygonal meshes, which supports multi-resolution shape optimization and does not require CAD information; (3) freeform shape optimization of arbitrary polygonal or polyhedral meshes. Numerical experiments indicate the effectiveness of the proposed approach. Copyright © 2004 John Wiley & Sons, Ltd.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/34540/1/1050_ftp.pd

Towards Predictive Rendering in Virtual Reality

The strive for generating predictive images, i.e., images representing radiometrically correct renditions of reality, has been a longstanding problem in computer graphics. The exactness of such images is extremely important for Virtual Reality applications like Virtual Prototyping, where users need to make decisions impacting large investments based on the simulated images. Unfortunately, generation of predictive imagery is still an unsolved problem due to manifold reasons, especially if real-time restrictions apply. First, existing scenes used for rendering are not modeled accurately enough to create predictive images. Second, even with huge computational efforts existing rendering algorithms are not able to produce radiometrically correct images. Third, current display devices need to convert rendered images into some low-dimensional color space, which prohibits display of radiometrically correct images. Overcoming these limitations is the focus of current state-of-the-art research. This thesis also contributes to this task. First, it briefly introduces the necessary background and identifies the steps required for real-time predictive image generation. Then, existing techniques targeting these steps are presented and their limitations are pointed out. To solve some of the remaining problems, novel techniques are proposed. They cover various steps in the predictive image generation process, ranging from accurate scene modeling over efficient data representation to high-quality, real-time rendering. A special focus of this thesis lays on real-time generation of predictive images using bidirectional texture functions (BTFs), i.e., very accurate representations for spatially varying surface materials. The techniques proposed by this thesis enable efficient handling of BTFs by compressing the huge amount of data contained in this material representation, applying them to geometric surfaces using texture and BTF synthesis techniques, and rendering BTF covered objects in real-time. Further approaches proposed in this thesis target inclusion of real-time global illumination effects or more efficient rendering using novel level-of-detail representations for geometric objects. Finally, this thesis assesses the rendering quality achievable with BTF materials, indicating a significant increase in realism but also confirming the remainder of problems to be solved to achieve truly predictive image generation