Det finns flera olika metoder och tekniker för tredimensionell rendering, alla med olika för- och nackdelar som lämpar sig för olika applikationer. Voxelbaserad rendering har använts flitigt inom vetenskapliga områden, främst inom det medicinska för visualisering av volymetrisk data. Tekniken används nu inom flera olika områden för tredimensionell rendering, t.ex. i datorspel, i matematiska applikationer och vid geologisk rekonstruktion. I den här rapporten kommer voxelbaserad rendering med Marching Cubes-algoritmen undersökas för att se hur den lämpar sig för realtidsapplikationer. Området behandlas dels teoretiskt, men även praktiskt då en implementering av Marching Cubes gjordes för att genomföra några tester för att se hur prestandan påverkades. Av testerna framkom det tydligt att algoritmen lämpar sig väl för realtidsapplikationer och dagens grafikkort. Viss optimering krävs dock för att kunna utnyttjas på bästa sätt. / There are lots of different methods and techniques for three-dimensional rendering, everyone with different advantages and disadvantages that suits different applications. Voxel-based rendering has been used frequently within the scientific area, mainly within medicin for visualization of volumetric data. The technique is now used within many different areas for three-dimensional rendering, e.g. in computer games, in mathematical applications and in geological reconstruction. In this report voxel-based rendering with Marching Cubes algorithm will be researched to see how it suits for real-time applications. The area will partly be dealt with theoretically, but also practically as an implementation of Marching Cubes was done to run some tests to see how the performance was affected. From the tests it appeared cleary that the algorithm is well suited for real-time applications and today's graphics card. Though some optimization is needed to fully take advantage of it.

Volumetric visualization is something that has become more interesting during recent years. It has been something that was not feasible in an interactive environment due to its complexity in the 3D space. However, today's technology and access to the power of the graphics processing unit (GPU) has made it feasible to render volumetric data interactively. This thesis explores the possibilities to create and render large volumetric terrain using an implementation of Marching Cubes on the GPU. With the advent of general-purpose computing on the GPU (GPGPU) it has become far easier to implement tradition CPU tasks on the GPU. By utilizing newly available functions in DirectX it is possible to create an easier implementation on the GPU using global buffers. Three implementations are created inside the Unity game engine using compute shaders. The implementations are then compared based on creation time, render times and memory consumption. Then a deeper analysis of the time distribution is presented which suggests that Unity introduces some overhead since copying buffers from GPU to CPU is time consuming. It did however improve render times due to its culling and optimization techniques. The system could be used in applications such as games or medical visualization. Finally some future improvements for culling and level of detail (LOD) techniques are discussed. / Volumetrisk visualisering är en teknik som har fått mer uppmärksamhet dom senaste åren. Det har varit någonting som inte har varit rimligt att göra i en interaktiv miljö på grund av dess komplexitet i 3D rymden. Med dagens teknik och tillgänglighet till grafikkortet (GPU) är det nu möjligt att rendera volumetrisk data i en interaktiv miljö. Den här uppsatsen utforskar möjligheterna till att skapa och rendera stora terräng landskap genom en implementering av Marching Cubes på GPU:n. Med framkomsten av general-purpose computing på grafikkortet(GPGPU) har det blivit lättare att programmera på GPU:n. Genom att använda nya funktioner tillgängliga i DirectX är det möjligt att skapa en enklare implementering på GPU:n som använder sig av globala buffrar. Tre implementeringar har skapats i spelmotorn Unity som använder compute shaders. Implementeringarna är sedan jämförda baserad på tid för generering av terräng, renderings tid samt minnes konsumption. Detta följs av en djupare analys av tidsdistribueringen för skapandet som pekar på att Unity håller tillbaka systemets hastiget pga kopierande av minne från GPU:n till CPU:n. Renderingstiden blev dock bättre med hjälp av den inbyggda culling-teknikerna och optimerings tekniker. Detta system skulle kunna appliceras inom spel eller medicinsk visualisering. Slutligen diskuteras framtida förbättringar för culling-tekniker och level of detail (LOD) tekniker.

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Les dépendances fonctionnelles fournissent une information sémantique sur les données d’une table en mettant en lumière les liens de corrélation qui les unient. Dans cette thèse, nous traitons du problème de l’extraction de ces dépendances en proposant un contexte unifié permettant la découverte de n’importe quel type de dépendances fonctionnelles (dépendances de clé, dépendances fonctionnelles conditionnelles, que la validité soit complète ou approximative). Notre algorithme, ParaCoDe, s’exécute en parallèle sur les candidats, réduisant ainsi le temps global de calcul. De ce fait, il est très compétitif vis-à-vis des approches séquentielles connues à ce jour. Les dépendances satisfaites sur une table nous servent à résoudre le problème de la matérialisation partielle du cube de données. Nous présentons une caractérisation de la solution optimale dans laquelle le coût de chaque requête est borné par un seuil de performance fixé préalablement et dont la taille est minimale. Cette spécification de la solution donne un cadre unique pour décrire et donc comparer formellement les techniques de résumé de cubes de données. / Functional dependancies provide a semantic information over data from a table to exhibit correlation links. In this thesis, we deal with the dependancy discovery problem by proposing a unified context to extract any type of functional dependencies (key dependencies, conditional functional dependencies, with an exact or an approximate validity). Our algorithm, ParaCoDe, runs in parallel on candidates there by reducing the global time of computations. Hence, it is very competitive comparated to sequential appoaches known today. Satisfied dependencies on a table are used to solve the problem of partial materiali-zation of data cube. We present a characterization of the optimal solution in which the cost of each query is bounded by a before hand fixed performance threshold and its size is minimal. This specification of the solution gives a unique framework to describe and formally compare summarization techniques of data cubes.

On étudie divers problèmes concernant le n-cube. On décrit les exemples connus de (0,2) graphes (bipartis de diamètre 2 ou 3). On présente des constructions de (0,2) graphes. On étudie les (0,2) graphes avec des triangles. On montre comment construire certains des (0,2) graphes comme graphes de Cayley de groupes. On étudie les invariants immédiats du n-cube.

[pt] O Marching Cubes 33 proposto por Chernyaev é um dos primeiros algoritmos de extração de isosuperfície destinados a preservar a topologia do interpolante trilinear. Neste trabalho, abordamos três problemas no algoritmo do Marching Cubes 33, dois dos quais estão relacionados com a sua descrição original. Em particular, resolvemos um problema no procedimento para resolver ambiguidades interiores do Marching Cubes 33, que impede que a isosuperfície seja extraída corretamente para o caso ambíguo 13.5. O algoritmo Marching Cubes é considerado simples, robusto e com baixo custo computacional, características que contribuíram para torná-lo popular entre os algoritmo de extração de isosuperfícies. Porém no que se refere a qualidade da triangulação da malha resultante, não raramente observamos um grande número de triângulos finos (triângulos com ângulos pequenos) e até mesmo degenerados (triângulos com área zero). Buscando unir à coerência topológica uma melhor qualidade na triangulação gerada, propomos uma extensão da tabela de triangulação proposta por Chernyaev, de modo que os vértices da grade passem a fazer parte da triangulação, eliminando assim a possibilidade de geração de triângulos degenerados. Esta nova tabela é utilizada para evitar a criação de triângulos finos, através de pequenas alterações do campo escalar nos vértices da grade. / [en] Chernyaev s Marching Cubes 33 is one of the first isosurface extraction algorithms intended to preserve the topology of the trilinear interpolant. In this work, we address three issues in the Marching Cubes 33 algorithm, two of which are related to its original description. In particular, we solve a problem with the core disambiguation procedure of Marching Cubes 33 that prevents the extraction of topologically correct isosurfaces for the ambiguous configuration 13.5 thus fixing the original formulation of the algorithm. The Marching Cubes algorithm is considered simple, robust and with low computational cost, characteristics that contributed to make it the most popular algorithm for isosurfaces extraction. However, regarding the quality of the resulting mesh, frequently it is possible to observe a large number of badly-shaped triangles (triangles with small angles) and even degenerate (triangles with zero area) ones. Seeking to unite a better triangulation quality of the resulting mesh to the topological consistency, we propose an extension of the triangulation table proposed by Chernyaev, so that the vertices of the grid become part of the triangulation generated, thus eliminating the possibility of generation of degenerate triangles. This new table is used to avoid the creation of badly-shaped triangles via small changes of the scalar field on the vertices of the grid.

We present an implicit approach for constructing smooth isolated or interconnected 3-D inscribed volumes which can be employed for volumetric modeling of various kinds of spongy or porous structures, such as volcanic rocks, pumice stones, Cancellus bones *, liquid or dry foam, radiolarians, cheese, and other similar materials. The inscribed volumes can be represented in their normal or positive forms to model natural pebbles or pearls, or in their inverted or negative forms to be used in porous structures, but regardless of their types, their smoothness and sizes are controlled by the user without losing the consistency of the shapes. We introduce two techniques for blending and creating interconnections between these inscribed volumes to achieve a great flexibility to adapt our approach to different types of porous structures, whether they are regular or irregular. We begin with a set of convex polytopes such as 3-D Voronoi diagram cells and compute inscribed volumes bounded by the cells. The cells can be irregular in shape, scale, and topology, and this irregularity transfers to the inscribed volumes, producing natural-looking spongy structures. Describing the inscribed volumes with implicit functions gives us a freedom to exploit volumetric surface combinations and deformations operations effortlessly / Graduate

La fissuration à chaud est un défaut majeur rencontré en solidification des alliages d'aluminium. Elle est liée à l'incapacité du liquide de s'écouler dans les zones où des porosités sont présentes, ne permettant pas de les refermer avant qu'elles gagnent en volume. Pour comprendre la fissuration à chaud, il est crucial de développer nos connaissances du comportement mécanique de la zone pâteuse. Pour cela, il est très utile d'effectuer des expériences de microtomographie aux rayons X et des simulations mécaniques sur des volumes élémentaires représentatifs. Dans cette thèse, nous proposons de coupler les deux approches en initialisant une simulation par éléments finis grâce à des données de microtomographie issues d'un test de traction isotherme d'un alliage d'aluminium-cuivre à l'état pâteux. Cette approche originale nous donne directement accès à la réalité expérimentale et permet des comparaisons des évolutions numérique et expérimentale de l'éprouvette. Nous expliquons dans un premier temps comment obtenir la représentation numérique à l'aide de l'algorithme des marching cubes et de la méthode d'immersion de volume. Nous présentons ensuite notre modèle numérique qui s'appuie sur une résolution monolithique des équations de Stokes. Une fois le champ de vitesse obtenu dans l'ensemble des phases solide, liquide et gazeuse, nous utilisons une méthode level set dans un formalisme eulérien afin de faire évoluer la morphologie de notre échantillon numérique. Malgré la simplicité du modèle, les résultats expérimentaux et numériques montrent un accord raisonnable en ce qui concerne la propagation de l'air à l'intérieur de l'échantillon. / Hot tearing is a major defect arising during solidification of aluminium alloys. This defect is associated with the inability of liquid to feed areas where voids have started to appear, not allowing to heal small defects before they grow bigger. To understand hot tearing, it is mandatory to develop a good knowledge of the semi-solid mechanical behaviour. It is thus very useful to carry out X-ray microtomographies experiments and mechanical simulations on representative elementary volumes. In this work, we couple the both approaches by initialising a finite element simulation with the help of microtomography data obtained during an isothermal tensile testing of an aluminium-copper alloy in the mushy state. This innovative approach gives a direct access to the experimental reality and allows comparisons of numerical and experimental evolutions of the sample. We explain in a first time how to get the numerical representation thanks to a marching cubes algorithm and the immersed volume method. Then, we present our numerical model for which we solve the Stokes equations in a monolithic way. Once the velocity computed in all the solid, liquid and gaseous phases, we use a level set method in a Eulerian formalism to obtain the morphological evolution of our numerical sample. Despite the model simplicity, numerical and experimental results show a reasonable agreement concerning the air propagation inside the sample.

This thesis focuses on work with reading cubes and with game named Story Cubes. It deals with possibilities how to use it to support reading literacy, understanding of text and speech development of pre-school children. The theoretical part first introduces characteristics of preschool children and describes reading literacy development in preschool age. Then it deals with principles of work with reading cubes and Story Cubes and with possibilities to use it in kindergarten. The thesis also includes a practical part which suggests other usage options for reading cubes. There are created specific lessons with reading cubes for preschool children, which follow the rules and recommendations mentioned in the theoretical part. These lessons were repeatedly implemented at kindergarten to be able to observe reading literacy development of each child in time. The hypothesis that preschool children can use selected reading strategies while working with reading cubes, and at the same time, these readership activities support the interest of children in books and related activities, proved to be correct. These children also expanded their vocabulary and improved expressing abilities through Story Cubes activities. KEYWORDS reading pre-literacy, reading cubes, Story Cubes, pre-school education, kindergarten

The project evaluates how well a haptic device can be used to interact with a visualization of volumetric data. Since the interface to the haptic device require explicit surface descriptions, triangles had to be constructed from the volumetric data. The algorithm used to extract these triangles is marching cubes. The triangles produced by marching cubes are then transmitted to the haptic device to enable the force feedback. Marching cubes was suitable for parallelization and it was executed using OpenCL. Graphs in the report shows how this parallelization ran almost 70 times faster than the sequential CPU counterpart of the same algorithm. Further development of the project would give medical students the opportunity to practice difficult procedures on a simulation instead of a real patient. This would give a realistic and accurate simulation to practice on. / Projektet går ut på att utvärdera hur väl en haptisk utrustning går att använda för att interagera med en visualisering av volumetrisk data. Eftersom haptikutrustningen krävde explicit beskrivna ytor, krävdes först en triangelgenerering utifrån den volymetriska datan. Algoritmen som används till detta är marching cubes. Trianglarna som producerades med hjälp av marching cubes skickas sedan vidare till den haptiska utrustningen för att kunna få gensvar i form av krafter för att utnyttja sig av känsel och inte bara syn. Eftersom marching cubes lämpas för en parallelisering användes OpenCL för att snabba upp algoritmen. Grafer i projektet visar hur denna algoritm exekveras upp emot 70 gånger snabbare när algoritmen körs som en kernel i OpenCL istället för ekvensiellt på CPUn. Tanken är att när vidareutveckling av projektet har gjorts i god mån, kan detta användas av läkarstuderande där övning av svåra snitt kan ske i en verklighetstrogen simulering innan samma ingrepp utförs på en individ.