O mapeamento de texturas é uma técnica bastante importante para adicionar detalhamento a modelos geométricos. O mapeamento de texturas baseadas em imagens costuma ser a abordagem preferida, mas faz uso de imagens pré-computadas que são mais adequadas à representação de padrões estáticos. Por outro lado, texturas procedurais oferecem uma alternativa que depende de funções para descrever os padrões das texturas. Elas garantem mais flexibilidade na definição dos padrões em cenas dinâmicas, tendo ainda uma representação mais compacta e dando um maior controle da aparência da textura através do ajuste de parâmetros. Quando mapeadas por coordenadas 3D, as texturas procedurais não consideram a forma da superfície domodelo, e com coordenadas 2D torna-se necessária a definição dessas coordenadas de forma coerente, que, em modelos complexos ,não é uma tarefa simples. Neste trabalho nós introduzimos o leitor às texturas procedurais e ao mapeamento de texturas, então apresentamos GeoTextures, uma nova abordagem que faz uso de distâncias geodésicas definidas com base em múltiplos pontos de origem sobre a superfície do modelo. As distâncias geodésicas são passadas como parâmetros que permitem que a textura procedural se adeqüe ao relevo do modelo texturizado. Nós validamos a proposta ao usar alguns exemplos de texturas procedurais aplicadas em tempo real na texturização de superfícies complexas, mudando tanto a textura do modelo como a forma, através do uso de tesselagem em hardware. / Texture mapping is an important technique to add detail to geometric models. Imagebased texture mapping is the preferred approach but employs pre-computed images, which are better suited for static patterns. On the other hand, procedural-based texture mapping offers an alternative that rely on functions to describe texturing patterns. This allows more flexibility to define patterns in dynamic scenes, while also having a more compact representation and more control for parametric adjustments on the texture visual appearance. When mapped with 3D coordinates, the procedural textures do not consider the model surface, and with 2D mapping the coordinates must be defined in a coherent way, which for complex models is not an easy task. In this work we give a introduction to procedural texturing and texture mapping, and introduce GeoTextures, an original approach that uses geodesic distance defined from multiple sources at different locations over the surface of the model. The geodesic distance is passed as a parameter that allows the shape of the model to be considered in the definition of the procedural texture. We validate the proposal using procedural textures that are applied in real-time to complex surfaces, and show examples that change both the shading of the models, as well as their shape using hardware-based tessellation.

O mapeamento de texturas é uma técnica bastante importante para adicionar detalhamento a modelos geométricos. O mapeamento de texturas baseadas em imagens costuma ser a abordagem preferida, mas faz uso de imagens pré-computadas que são mais adequadas à representação de padrões estáticos. Por outro lado, texturas procedurais oferecem uma alternativa que depende de funções para descrever os padrões das texturas. Elas garantem mais flexibilidade na definição dos padrões em cenas dinâmicas, tendo ainda uma representação mais compacta e dando um maior controle da aparência da textura através do ajuste de parâmetros. Quando mapeadas por coordenadas 3D, as texturas procedurais não consideram a forma da superfície domodelo, e com coordenadas 2D torna-se necessária a definição dessas coordenadas de forma coerente, que, em modelos complexos ,não é uma tarefa simples. Neste trabalho nós introduzimos o leitor às texturas procedurais e ao mapeamento de texturas, então apresentamos GeoTextures, uma nova abordagem que faz uso de distâncias geodésicas definidas com base em múltiplos pontos de origem sobre a superfície do modelo. As distâncias geodésicas são passadas como parâmetros que permitem que a textura procedural se adeqüe ao relevo do modelo texturizado. Nós validamos a proposta ao usar alguns exemplos de texturas procedurais aplicadas em tempo real na texturização de superfícies complexas, mudando tanto a textura do modelo como a forma, através do uso de tesselagem em hardware. / Texture mapping is an important technique to add detail to geometric models. Imagebased texture mapping is the preferred approach but employs pre-computed images, which are better suited for static patterns. On the other hand, procedural-based texture mapping offers an alternative that rely on functions to describe texturing patterns. This allows more flexibility to define patterns in dynamic scenes, while also having a more compact representation and more control for parametric adjustments on the texture visual appearance. When mapped with 3D coordinates, the procedural textures do not consider the model surface, and with 2D mapping the coordinates must be defined in a coherent way, which for complex models is not an easy task. In this work we give a introduction to procedural texturing and texture mapping, and introduce GeoTextures, an original approach that uses geodesic distance defined from multiple sources at different locations over the surface of the model. The geodesic distance is passed as a parameter that allows the shape of the model to be considered in the definition of the procedural texture. We validate the proposal using procedural textures that are applied in real-time to complex surfaces, and show examples that change both the shading of the models, as well as their shape using hardware-based tessellation.

With each computer game generation there is always a demand for more visually pleasing environments. This pushes game developers to create more powerful rendering techniques and game artists to create more detailed art. With a visually stunning backdrop also comes the need for high-resolution models. A common issue is that if all models in a scene are high-resolution it would not only require immensely powerful hardware, it would also be wasteful as only the models in the foreground are close enough that we would recognize the increased details. The common solution to this problem has been to load several versions of each model containing varying amounts of detail. However this solution has the drawback that it increases our memory footprints as more models are loaded into the memory. Tessellation offers a more dynamic solution to the problem as it only requires us to load a low-resolution model and higher resolution versions can be generated during run-time on the GPU. With the introduction of DirectX 11 tessellation is now supported in the hardware, however we are still a few years away from seeing DirectX 11 being used as the core of any 3D rendering engine. In a transitional period like this between hardware generations game developers has to tackle the dilemma that the current hardware generation has to be supported when creating games that will also utilize the next generation. This thesis focuses on comparing the performance of a tessellation scheme supported by the current hardware generation, DirectX 10, as opposed to a scheme developed for the next generation, DirectX 11. Two prototypes, one using the Geometry shader that was introduced in DirectX 10 and the other using the fixed function tessellator introduced in DirectX 11, were built to compare the performance of tessellated model rendering. Several different variants of each prototype were tested and the general conclusion is that the tessellator performed better than the Geometry shader.

Multi-agent systems are extensively used in several applications. An important class of applications involves the optimal spatial distribution of a group of mobile robots on a given area, where the optimality refers to the assignment of subregions to the robots, in such a way that a suitable coverage metric is maximized. Typically the coverage metric encodes a risk distribution defined on the area, and a measure of the performance of individual robots with respect to points inside the region of interest. The coverage metric will be maximized when the set of mobile robots configure themselves as the centroids of the Voronoi tessellation dictated by the risk density. In this work we advance on this result by considering a generalized area control problem in which the coverage metric is non-autonomous, that coverage metric is time varying independently of the states of the robots. This generalization is motivated by the study of coverage control problems in which the coordinated motion of a set of mobile robots accounts for the kinematics of objects penetrating from the outside. Asymptotic convergence and optimality of the non-autonmous system are studied by means of Barbalat's Lemma, and connections with the kinematics of the moving intruders is established. Several numerical simulation results are used to illustrate theoretical predictions.

The thesis apply to reliability problems approach of Voronoi tessellation, typically used in the field of samples designs evaluation and for Monte Carlo samples reweighing. It is shown, this general technique estimation converges to that of Importance Sampling method despite it does not rely on Importance Sampling's auxiliary density. Consequently, reliability analysis could be divided into sampling itself and assessment of simulation results. As an extension of this idea, adaptive statistical sampling using QHull library was attempted.

One way of increasing 3D rendering performance is the use of foveated rendering. In this thesis a novel foveated rendering technique called gaze contingent depth of field tessellation (GC DOF tessellation) is proposed. Tessellation is the process of subdividing geometry to increase detail. The technique works by applying tessellation to all objects within the focal plane, gradually decreasing tessellation levels as applied blur increases. As the user moves their gaze the focal plane shifts and objects go from blurry to sharp at the same time as the fidelity of the object increases. This can help hide the pops that occur as objects change shape. The technique was evaluated in a user study with 32 participants. For the evaluated scene the technique helped reduce the number of primitives rendered by around 70 % and frame time by around 9 % compared to using full adaptive tessellation. The user study showed that as the level of blur increased the detection rate for pops decreased, suggesting that the technique could be used to hide pops that occur due to tessellation. However, further research is needed to solidify these findings. / Ett sätt att öka renderingsprestanda i 3D applikationer är att använda foveated rendering. I denna uppsats presenteras en ny foveated rendering-teknik som kallas gaze contingent depth of field tessellering (GC DOF tessellering). Tessellering är när geometri delas i mindre delar för att öka detaljrikedom. Tekniken fungerar genom att applicera tessellering på alla objekt i fokalplanet och gradvis minska tesselleringsnivåer när oskärpan ökar. När användaren flyttar sin blick så flyttas fokalplanet och suddiga objekt blir skarpa samtidigt som detaljrikedomen i objektet ökar. Det kan hjälpa till att dölja de ’pops’ som uppstår när objekt ändrar form. Tekniken utvärderades i en användarstudie med 32 del- tagare. I den utvärderade scenen visade sig tekniken minska antalet renderade primitiver med ca 70 % och minska renderingstiden med ca 9 % jämfört med att använda full adaptiv tessellering. Användarstudien visade att när oskärpa ökade så minskade antalet som sa sig se ’pops’, vilket tyder på att tekniken kan användas för att dölja de ’pops’ som uppstår på grund av tessellering. Det behövs dock ytterligare forskning för att säkerställa dessa fynd.

Background. Ray tracing can be used to achieve hyper-realistic 3D rendering but it is a computationally heavy task. Since hardware support for real-time ray tracing was released, the game industry has been introducing this feature into games. However, even modern hardware still experience performance issues when implementing common rendering techniques with ray tracing. One of these problematic techniques is alpha testing. Objectives. The thesis will investigate the following: 1) How the texture format of the alpha map and the number of alpha maps affect the rendering times. 2) How tessellation of the alpha tested geometry affects the performance and if tessellation has the potential to fully replace the alpha test from a performance perspective. Methods. A DXR 3D renderer will be implemented capable of rendering alpha tested geometry using an any-hit shader. The renderer was used to conduct a computational performance benchmark of the rendering times while varying texture and geometry data. Two alpha tested tree models were tessellated to various levels and their related textures were converted into multiple formats that could be used for the test scenes. Results & Conclusions. When the texture formats BC7, R(1xfloat32), and BC4 were used for the alpha map, the rendering times decreased in all cases, relative RGBA(4xfloat32). BC4 showed to give the best performance gain, decreasing the rendering times with up to 17% using one alpha map per model and up to 43% using eight alpha maps. When increasing the number of alpha maps used per model the rendering times increased with up to 52% when going from one alpha map to two. A large increase in rendering times was observed when going from three to four alpha maps in all cases. Using alpha testing on the tessellated model versions increased the rendering times in most cases, at most 135%. A decrease of up to 8% was however observed when the models were tessellated a certain amount. Turning off alpha testing gave a significant decrease in rendering allowing higher tessellated versions to be rendered for all models. In one case, while increasing the number of triangles with a factor of 78 the rendering times were still decreased by 30% relative to the original alpha test implementation. This suggests that pre-tessellated models could potentially be used to replace alpha tessellated geometry when performance is highly required. / Bakgrund. Strålspårning(Ray tracing) kan användas för att uppnå hyperrealistisk 3D-rendering, men det är en mycket tung beräkningsuppgift. Sedan hårdvarustöd för att utföra strålspårning i realtid lanserades har spelindustrin introducerat funktionen i spel. Trots modern hårdvara upplevers fortfarande prestandaproblem när vanliga renderingstekniker kombineras med strålspårning. En av dessa problematiska tekniker är alfa-testning(alpha testing). Syfte. Denna avhandling kommer att undersöka följande: 1) Hur texturformatet på alfamasken(alpha map) och hur antalet alfamaskar påverkar renderingstiderna. 2) På vilket sätt tesselering av den alfa-testade geometrin påverkar prestandan och om tesselering har potentialen att ersätta alfa-testet helt ur ett prestandaperspektiv. Metod. En DXR 3D-renderare kommer att implementeras som kan rendera alfatestad geometri med hjälp av en “Any-hit” shader. Renderaren användes för att mäta och jämföra renderingstider givet varierande textur- och geometri-data. Två alfaprövade trädmodeller tesselaterades till olika nivåer och deras relaterade texturer konverterades till fyra format som användes i testscenerna. Resultat & Slutsatser. När texturformaten BC7, R(1xfloat32) och BC4 användes för alfamasken visade alla en minskad renderingstid relativ RGBA (4xfloat32). BC4 gav bästa prestandaökningen och minskade renderingstiden med upp till 17% med en alfamask per modell och upp till 43% med åtta alfamasker. När antalet alfamasker som användes per modell ökade renderingstiderna med upp till 52% när alfamaskerna ökade från en till två. En stor ökning av renderingstiden observerades när alfamaskerna gick från tre till fyra i alla testfall. När alfatestning användes på de tesselerade modellversionerna ökade renderingstiderna i de flesta fall, som högst 135%. En minskning på upp till 8% observerades emellertid när modellerna tesselaterades till en viss grad. Att stänga av alfatestning gav en signifikant ökning av prestandan, vilket tillät högre tesselerade versioner att renderas för alla modeller. Samtidigt som antalet trianglar ökade med en faktor på 78, i ett av fallen, minskades renderingstiden med 30%. Detta antyder att förtesselerade modeller potentiellt kan användas för att ersätta alfatestad geometri när prestanda är ett högt krav.

We consider the distribution of the zero and typical cells of a (homogeneous) Poisson hyperplane tessellation. We give a direct proof adapted to our setting of the well known Complementary Theorem. We provide sharp bounds for the tail distribution of the number of facets. We also improve existing bounds for the tail distribution of size measurements of the cells, such as the volume or the mean width. We improve known results about the generalised D.G. Kendall's problem, which asks about the shape of large cells. We also show that cells with many facets cannot be close to a lower dimensional convex body. We tacle the much less study problem of the number of facets and the shape of small cells. In order to obtain the results above we also develop some purely geometric tools, in particular we give new results concerning the polytopal approximation of an elongated convex body.

Une mosaïque de Poisson-Voronoï est une partition aléatoire de l'espace euclidien en polyèdres, appelés cellules, obtenue à partir d'un ensemble aléatoire discret de points appelés germes. A chaque germe correspond une cellule, qui est l'ensemble des points de l'espace qui sont plus proches de ce germes que des autres germes. Ces modèles sont souvent utilisées dans divers domaines tels que la biologie, les télécommunications, l'astronomie, etc. Les caractéristiques de ces mosaïques et des cellules associées ont été largement étudiées dans l'espace euclidien mais les travaux sur les mosaïques de Voronoï dans un cadre non-euclidien sont rares.Dans cette thèse, on étend la définition de mosaïque de Voronoï à une variétériemannienne de dimension finie et on s'intéresse aux caractéristiques des cellules associées. Plus précisément, on mesure dans un premier temps l'influence que peut avoir la géométrie locale de la variété, c'est-à-dire les courbures sur les caractéristiques moyennes d'une cellule, comme son volume ou son nombre de sommets, en calculant des développements asymptotiques des ces caractéristiques moyennes à grande intensité. Dans un deuxième temps, on s'interroge sur la possibilité de retrouver la géométrie locale de la variété à partir des caractéristiques combinatoires de la mosaïque sur la variété. En particulier, on établit desthéorèmes limites, quand l'intensité du processus des germes tend vers l'infini, pour le nombre de sommets de la mosaïque dans une fenêtre, ce qui permet de construire un estimateur de la courbure et d'en donner quelques propriétés.Les principaux résultats de cette thèse reposent sur la combinaison de méthodesprobabilistes et de techniques issues de la géométrie différentielle. / A Poisson-Voronoi tessellation is a random partition of the Euclidean space intopolytopes, called cells, obtained from a discrete set of points called germs. To each germ corresponds a cell which is the set of the points of the space which are closer to this germ than to the other germs. These models are often used in several domains such as biology, telecommunication, astronomy, etc. The caracteristics of these tessellations and cells have been widely studied in the Euclidean space but only a few works concerns non-Euclidean Voronoi tessellation. In this thesis, we extend the definition of Poisson-Voronoi tessellation to a Riemannian manifold with finite dimension and we study the caracteristics of the associated cells. More precisely, we first measure the influence of the local geometry of the manifold, namely the curvatures, on the caracteristics of the cells, e.g. the mean volume or the mean number of vertices. Second, we aim to recover the local geometry of the manifold from the combinatorial properties of the tessellation on the manifolds. In particular, we establish limit theorems for the number of vertices of the tessellation, when the intensity of the process of the germs tends to infinity. This leads to the construction of an estimator of the curvature of the manifold and makes it possible to derive some properties of it. The main results of this thesis relies on the combination of stochastic methods and techniques from the differential geometry theory.

No description available.