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This thesis deals with problem of computation of global illumination in real-time. Two methods are described. Namely Reflective Shadow Maps and Light Propagation Volumes. The first of them deals with the problem by using extended Shadow Mapping algorithm. The second one uses scene embedded into a 3D grid together with Spherical harmonics to compute light propagation in the scene. Furthermore this thesis contains results of measurement of the rendering speed of the Light Propagation Volumes algorithm with various settings on several machines. Quality of the resulting output of the algorithm is also evaluated.

Les performances des antennes Ultra Large Bande (ULB) les rendent appropriées pour de nombreuses applications. En radar à pénétration de surface (SPR), application visée de cette thèse, une telle bande passante offre un excellent compromis entre capacité de pénétration et résolution spatiale en imagerie micro-ondes. De plus, il a été démontré que la prise en compte du champ rayonné par l'antenne en présence de la surface améliore considérablement la qualité des images obtenues. Cette thèse aborde la problématique de la quantité de données représentant les antennes ULB. En effet, les descripteurs classiques d'antenne ne suffisent pas à caractériser l’évolution en fréquence de leurs performances. Le développement en harmoniques ou vecteurs sphériques est utilisé pour modéliser le diagramme de rayonnement d’antennes tout en réduisant le volume de données. D'autre part, les méthodes d'expansion en singularités modélisent la réponse en fréquence (ou impulsionnelle) de l'antenne par un ensemble de pôles de résonance. Le but de ce travail de thèse est d'établir un modèle compact qui représente avec précision le rayonnement d'antenne, et permette la connaissance du champ à différentes distances. A cette fin, plusieurs combinaisons des méthodes de caractérisation ont été étudiées. L'approche proposée est validée par la modélisation du diagramme de rayonnement simulé et mesuré d'une antenne Vivaldi (ETSA). Le modèle établi fournit le champ rayonné à différentes distances de l'antenne avec une erreur inférieure à 3% avec un taux de compression de 99%. La dernière partie de cette thèse présente une application de l'approche proposée au rayonnement d’antennes en présence d’interfaces / UWB antennas bandwidth makes them highly suitable for a number of applications. In surface penetrating radar (SPR) applications, which is the focus of our research, such a bandwidth range allows good signal penetration ability and fine space resolution for microwave imaging. In addition, it has been shown that the knowledge of the radiated field by the antenna enhances drastically the quality of the resulting images. The work reported in this thesis deals with the problematic of the huge amount of data representing UWB antennas. Indeed, due to the frequency dependence, the classical antenna parameters are not sufficient to characterize this type of antenna. The scalar or vector spherical wave expansion is widely used to expand the radiation pattern of a radiating antenna and permit a high compression data rate. On the other hand, the Singularity Expansion Methods are used in frequency/time domain to model the antenna response by a set of resonant poles. The purpose of this thesis is to establish a compact model representing accurately the antenna radiation characteristics, which also allows to find the field at various distances. To this end, several ways of combining the aforementioned methods have been investigated. The proposed approach is validated by modeling the simulated and measured radiation pattern of an Exponential Tapered Slot Antenna (ETSA) in free space. Furthermore, we verify that the established compact model provide radiated field at different distances from the antenna with a compression of the initial pattern up to 99% and an error below 3%. The last part of this thesis, present an application of the proposed methodology to SPR context

Every year a higher life expectancy is reported for people living in industrial countries. With increasing age, the risk of getting Alzheimer's Disease increases as well. Alzheimer's Disease is a neurodegenerative disease that is characterised by progressive deterioration of brain tissue. One of the first regions in the brain to be affected is the hippocampus. A common method to quantify the deterioration of the hippocampus is to measure its volume. However, decreasing volume is no specific marker of Alzheimer's Disease, but can be caused by other diseases as well. Thus, the deformation has to be observed in more detail, which can be done using shape analysis. A powerful shape analysis technique is the approximation of the surface by means of spherical harmonics. A process chain computing such an approximation is explained in this thesis. Therefore, the data is triangulated, forming a closed manifold. Afterwards, a homogeneous mapping of the surface to the unit sphere is computed in two steps. First an initial spherical parametrisation is computed, which is optimised afterwards to resemble the properties of the initial surface. The optimisation is mandatory, to allow for inter-subject comparability. The optimised parametrisation defines a function on the sphere, that can be approximated by spherical harmonics, a set of basis functions on the unit sphere. This procedure results in a mathematical description of the surface that can be analysed statistically. The method is applied to data of Alzheimer's Disease patients.

Fans are often used in equipment such as home appliances andelectronic equipment where the margin of profit is small butcustomers demands on a low noise level are high. Therefore,methods for predicting the noise emitted by an applicationincluding one or several fans are desirable in order toimprove, accelerate and reduce the cost of low-noise design.The Noise Shaping Technology (NST) has been developed withinthe EC-project NABUCCO in order to fulfil the aboverequirements on a prediction method. According to NST, thenoise source (not necessary a fan) is described by one orseveral noise descriptors, CSSs, and the correspondingtransmission paths through the structure described by one orseveral transfer functions, ACFs. In this thesis, theapplicability of NST is evaluated on a cabinet for electronicequipment where small axial cooling fans constitute the primarysources of the airborne sound. As an axial fan is a complex source of sound,simplifications are necessary when modelling its acousticproperties. Therefore, the sound radiation of an axial fan infree space was examined by expanding the generated soundpressure field into spherical harmonics. The conclusion on asource model for the cabinet example, where the fans are moreor less In-duct mounted, is a modified single axial dipole. Themodel is expected to be valid in the entire frequency range ofinterest except in the mid-frequency range where the modaldensity is low. In order to improve the source model in thisfrequency range, a future model based on a rotating dipole isproposed. The sound power of a small axial fan is measured in an ISO10302 test-rig. In order to take account of flow conditions,acoustically transparent ducts have been developed. These shallbe attached to the test-rig when measuring the sound power ofthe fan. A simple but practical method of how to correct thesound power for the baffling effect of the test-rig has alsobeen developed. Finally, the sound power can be converted intodipole force, which is the airborne CSS corresponding to thesingle axial dipole model. The corresponding airborne transfer function (ACF), i.e.,from dipole force at the source point to sound pressure at thereceiver point, is measured reciprocally by taking use ofLyamshevs reciprocity relation. From multiplication of the CSS and the ACF, the soundpressure can be predicted. The prediction shows quite goodagreement with the measured values. <b>Keywords:</b>axial fan, airborne sound, sourcecharacterisation, transmission path analysis, In-duct,spherical harmonics, rotating dipole, installation effects, ISO10302, flow conditions, baffling effect, acousticallytransparent ducts, Lyamshevs reciprocity relation, reciprocity,CSS, ACF, GSM, NST. / NR 20140805

Through Spherical Harmonics, one can describe complex gravitational fields. However as the order and degree of the spherical harmonics increases, the computation speed rises exponentially. In addition, for onboard applications of spherical harmonics, the processors are radiation hardened in order to mitigate negative effects of the space environment on electronics. But, those processors have outdated processing speeds, resulting in a slower onboard spherical harmonic program. This thesis examines a partial solution to the slow computation speed of spherical harmonics programs. The partial solution was to supplant the gravity models in the flight software. The spherical harmonics gravity model can be replaced by a hybrid model, a mass concentrations model and a secondary (lesser degree or order) spherical harmonics model. That hybrid model can lead to greater processing speeds while maintaining the same level of accuracy. To compute the mass values for the mass concentration model, a potential estimation scheme was selected. In that scheme, mass values were computed by minimizing the integral of the difference between the correct and the estimated potential. The best hybrid model for the 8 degree and 8 order, 15 degree and 15 order, and 30 degree and 30 order lunar potential fields is developed following three different approaches: potential zeros method, gravitational anomalies method, and iterative method. Afterwards, the accuracy and computation time of the models are measured and compared to the primary spherical harmonic lunar model. In the aftermath, while the best hybrid model for all three cases was able to run faster than the primary spherical harmonic model, it was unable to be sufficiently accurate to replace the primary spherical harmonic model. The mass estimation scheme is severely hindered by the condition number and convergence issues resulting in inaccurate estimates for the mass values for a given distribution. It is recommended to alleviate the condition number error by eliminating the inverse in the mass estimation scheme. Other recommendations include fixing the convergence error, investing in software and hardware development, and focusing on other hybrid research objectives.

Background. Global illumination is not trivial to compute in real-time computer graphics. One approximate solution is to distribute virtual light sources from a primary light, to then apply direct light calculations to said virtual lights. This can effectively estimate two-bounce illumination. To mitigate artifacts, virtual lights make use of a spherical shape and utilize spherical harmonics to allow for efficient light integration. These indirect light sources are referred to as "harmonics virtual lights" (HVLs). Objectives. The objectives of this thesis are to analyze the data structures, calculations and performance of an HVL implementation in different 3D scenes. Methods. HVLs are implemented using the Vulkan API. Experiments are then performed to evaluate and optimize execution times. Furthermore, different measures are taken to ensure correctness and minimize errors wherever possible. Results. The GPU pass responsible for gathering indirect light contributions from HVLs turned into a heavy bottleneck. A number of different optimization techniques were applied to said pass and analyzed. Seven techniques were found to have a positive effect on performance, each with varying degrees of impact on timings. No optimization compromised on input parameters, visual results or mathematical correctness. Additionally, three techniques were instead worsening performance of the implementation, despite having initial motivations for possible improvements. Conclusions. All optimization techniques with positive effects working in conjunction led to a total speedup of 46.9x in a specific use case of our implementation. There is room for further potential improvements, and a number of different techniques for future work are explained. The final source code for the implementation can be viewed in a public GitHub repository.

No / We address the problem of recognition and growth of ice nuclei in simulation of supercooled bulk water. Bond orientation order parameters based on the spherical harmonics analysis are shown to be ineffective when applied to ice nucleation. Here we present an alternative method which robustly differentiates between hexagonal and cubic ice forms. The method is based on accumulation of the maximum projection of bond orientations onto a set of predetermined vectors, where different terms can contribute with opposite signs with the result that the irrelevant or incompatible molecular arrangements are damped out. We also introduce an effective cluster size by assigning a quality weight to each molecule in an ice-like cluster. We employ our cluster analysis in Monte Carlo simulation of homogeneous ice formation. Replica-exchange umbrella sampling is used for biasing the growth of the largest cluster and calculating the associated free energy barrier. Our results suggest that the ice formation can be seen as a two-stage process. Initially, short tetrahedrally arranged threads and rings are present; these become correlated and form a diffuse ice-genic network. Later, hydrogen bond arrangements within the amorphous ice-like structure gradually settle down and simultaneously `tune-up¿ nearby water molecules. As a result, a well-shaped ice core emerges and spreads throughout the system. The process is very slow and diverse owing to the rough energetic landscape and sluggish molecular motion in supercooled water, while large configurational fluctuations are needed for crystallization to occur. In the small systems studied so far the highly cooperative molecular rearrangements eventually lead to a relatively fast percolation of the forming ice structure through the periodic boundaries, which inevitably affects the simulation results. / EPSRC