[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.

L'objectif de cette recherche est de construire un modèle réduit de petite dimension pour prévoir les réponses dynamiques dans une bande BF sur les parties rigides d'un véhicule automobile complet. Un tel modèle réduit "léger" est une aide à la phase de conception en "Avant Projet" de ces véhicules qui ont la particularité de présenter de nombreux modes élastiques locaux en BF dues à la présence de nombreuses parties flexibles et d'équipements. Pour la construction du modèle réduit, nous avons introduit une base non usuelle de l'espace admissible des déplacements globaux. La construction de cette base requiert la décomposition en sous-domaines du domaine de la structure qui peut présenter une très grande complexité géométrique et dont les modèles EF font intervenir de très nombreux types d'éléments finis. Cette décomposition en sous-domaines a été réalisée par la Fast Marching Method que nous avons due étendre pour pouvoir traiter la complexité des modèles EF des véhicules automobiles. Puis les équations matricielles du modèle EF sont projetées sur cette base. Afin de prendre en compte les incertitudes sur les paramètres du modèle, les incertitudes de modèle induites par les erreurs de modélisation et enfin les incertitudes liées à la non prise en compte des contributions locales dans le modèle réduit des déplacements globaux, un unique modèle probabiliste non paramétrique de ces trois sources d'incertitude a été implémenté sur le modèle réduit construit avec les vecteurs propres globaux. Les paramètres de dispersion de ce modèle probabiliste ont été identifiés en utilisant le principe du maximum de vraisemblance et des réponses obtenues à l'aide d'un modèle stochastique de référence qui inclut des informations expérimentales résultant de travaux précédents. Le modèle réduit stochastique, pour la prévision des déplacements globaux sur les parties rigides dans la bande BF qui a été développé, a été validé sur un modèle de structure automobile "nue" puis a été appliqué avec succès sur un modèle complet de véhicule automobile / The objective of this research is to construct a reduced-order model to predict the dynamical response, in the LF band, of the stiff parts of a complete automotive vehicle in order to facilitate the draft design. The vehicles under consideration have many elastic modes in LF due to the presence of many flexible parts and equipments. To build such a model, we introduced a non-usual basis of the admissible space of global displacements. The construction of this basis requires the decomposition of the domain of the structure. This subdomain decomposition is performed by using the Fast Marching Method that we have extended to take into account the high complexity of the mesh of an automotive vehicle. Then the matrix equations of the FE model are projected on this basis. To take into account the system parameters uncertainties, the model uncertainties induced by the modeling errors and finally, the uncertainties related to the neglecting of local contributions in the reduced-order model, a nonparametric probabilistic model of the three sources of uncertainties has been implemented on the reduced-order model constructed with the global displacements eigenvectors. The dispersion parameters of the probabilistic model are identified using the maximum likelihood method and the responses obtained from a stochastic reference model which includes experimental data resulting from previous works. This stochastic model which has been designed for the prediction of the global displacements of the rigid parts in the LF band is validated on a simple structure of an automotive model and has been successfully applied on a complete model of automotive vehicle

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.

Em Computação Gráfica, campos vetoriais possuem diversas aplicações desde a síntese e mapeamento de texturas à animações de fluidos, produzindo efeitos amplamente utilizados na indústria do entretenimento. Para produzir tais campos, é preferível o uso de ferramentas de design em vez de simulações numéricas não só devido ao menor custo computacional mas, principalmente, por prover liberdade ao artista ao sintetizar o campo de acordo com a sua necessidade. Atualmente, na literatura, existem bons métodos de design de campos vetoriais em superfícies de objetos tridimensionais porém, o design no interior desses objetos ainda é pouco estudado, principalmente quando o campo de interesse possui propriedades específicas. O objetivo deste trabalho é desenvolver uma técnica para sintetizar campos vetoriais, com características do movimento de fluidos incompressíveis, no interior de domínios. Em uma primeira etapa, o método consiste na interpolação dos vetores de controle, com uma certa propriedade desejada, em todo o domínio. Posteriormente, o campo obtido é modificado para respeitar a geometria do contorno. / Vector fields are important to an wide range of applications on the field of Computer Graphics, from the synthesis and mapping of textures to fluid animation, producing effects widely used on the entertainment industry. To produce such fields, design tools are prefered over numerical simulations not only for its lower computational cost, but mainly by providing freedom to the artist in the creation process. Nowadays, good methods of vector field design over surfaces exist in literature, however there is only a few studies on the synthesis of vector fields of the interior of objects and even fewer when specific properties of the field are required. This work presents a technique to synthesize vector fields with properties of imcompressible fluids motion in the interior of objects. On a first step, the method consists in interpolating control vectors with a certain desired property throughout the whole domain and later the resulting field is modified to properly fit the boundary geometry of the object.

La nécessité de protéger les véhicules de rentrée atmosphérique a conduit à la sélection des matériaux carbonés pour les applications les plus extrêmes [1, 2]. Au vu du coût prohibitif des essais en conditions réelles [1], la simulation permet de prédire et comprendre le comportement du matériau lors de la rentrée atmosphérique. Les modèles de l’ablation du carbone n’ont cessé de se complexifier [1, 3, 4, 5, 6]. Cependant, ils ne donnent pas de descriptions fines de la surface du matériau. C’est pour remédier à cela que plusieurs études ont été lancées au Laboratoire des Composites Thermostructuraux (LCTS) [7, 8]. Le Plasmatron du VKI est le moyen à haut flux de chaleur et à haute vitesse utilisé pour cette thèse [9, 10]. Dans cette étude, des échantillons sont testés sous des flux de chaleur allant jusqu’à 2800 kW/m2. Ces essais sur le composite 3D carbone/carbone (Cf/C) ont mené à des résultats très intéressants sur la morphologie du composite lors de l’ablation. Le four à image d’arc est le moyen à très haut flux de chaleur et à convection nulle utilisé au cours de cette thèse. Des flux de chaleurs de 10 MW m-2 ont pu être appliqués à des échantillons de 3D Cf/C. Les observations MEB couplées à la reconstruction numérique du four ont permis de noter les différences entre l’oxydation et la sublimation du composite. Un code de diffusion/ablation est développé depuis plusieurs années au LCTS [7, 11, 12, 13, 14] : AMA. Il permet de simuler l’ablation d’un matériau en carbone. Ce code a été validé par J. Lachaud sans prise en compte de l’écoulement [7]. Un nouveau couplage avec le code Open-Foam [15] a été développé et validé. Le code AMA a été utilisé afin de déterminer les paramètres influençant la rugosité du 3D Cf/C sous un écoulement laminaire. / Carbonaceous materials have been selected to protect atmospheric re-entry vehicles under the most extremes conditions [1, 2]. Because real flight experiments are very expensive [1], simulation is an important means to predict and understand the material behaviour during atmospheric re-entry. The models of carbonaceous materials ablation have become more and more complex [1, 3, 4, 5, 6]. However, they are not accurate to describe finely the material surface. To find a solution to this problem, several studies have been conducted at the Laboratoire des Composites Thermostructuraux (LCTS) [7, 8]. The Plasmatron of the VKI is the experimental means which has been used in this doctoral thesis. It can reach moderately high heat flux under high speed flow [9, 10]. In this study, several samples have been tested under an heat flux up to 2800 kW/m2. These tests on the 3D carbon/carbon (Cf/C) composite have given very interesting results about the material morphology during ablation. An arc image furnace, which can reach very high heat flux but without important flow field, has been used during this doctoral study. 3D Cf/C samples have been ablated under heat flux up to 10 MW m-2. SEM observations with the help of a numerical simulation of the furnace, have put the differences between oxidation and sublimation forward. A diffusion/ablation code has been developed at LCTS for several years [7, 11, 12, 13, 14] : AMA. This piece of software is designed to simulate the ablation of a carbonaceous material. It has been validated without flow field by J. Lachaud [7]. A new coupling method between AMA and Open-Foam [15] has been developed and validated. Finally, AMA has been used to point out the parameters which drive the 3D Cf/C surface recession under laminar flow field.

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.

Em Computação Gráfica, campos vetoriais possuem diversas aplicações desde a síntese e mapeamento de texturas à animações de fluidos, produzindo efeitos amplamente utilizados na indústria do entretenimento. Para produzir tais campos, é preferível o uso de ferramentas de design em vez de simulações numéricas não só devido ao menor custo computacional mas, principalmente, por prover liberdade ao artista ao sintetizar o campo de acordo com a sua necessidade. Atualmente, na literatura, existem bons métodos de design de campos vetoriais em superfícies de objetos tridimensionais porém, o design no interior desses objetos ainda é pouco estudado, principalmente quando o campo de interesse possui propriedades específicas. O objetivo deste trabalho é desenvolver uma técnica para sintetizar campos vetoriais, com características do movimento de fluidos incompressíveis, no interior de domínios. Em uma primeira etapa, o método consiste na interpolação dos vetores de controle, com uma certa propriedade desejada, em todo o domínio. Posteriormente, o campo obtido é modificado para respeitar a geometria do contorno. / Vector fields are important to an wide range of applications on the field of Computer Graphics, from the synthesis and mapping of textures to fluid animation, producing effects widely used on the entertainment industry. To produce such fields, design tools are prefered over numerical simulations not only for its lower computational cost, but mainly by providing freedom to the artist in the creation process. Nowadays, good methods of vector field design over surfaces exist in literature, however there is only a few studies on the synthesis of vector fields of the interior of objects and even fewer when specific properties of the field are required. This work presents a technique to synthesize vector fields with properties of imcompressible fluids motion in the interior of objects. On a first step, the method consists in interpolating control vectors with a certain desired property throughout the whole domain and later the resulting field is modified to properly fit the boundary geometry of the object.

Volumetric clouds are often used in video games in order to improve the realism or graphical quality of the game. However, in order to achieve real-time rendered clouds, optimizations have to be implemented as part of the rendering algorithm. These kinds of optimizations improve the performance, but can also have a negative impact on the visual quality of the clouds. This thesis investigates the use of bilinear interpolation for the purpose of improving the performance of a volumetric cloud renderer, while trying to avoid any substantial reduction in visual quality. This is extended by looking at the effect of adaptively sampling the pixel colors. The renderer itself is created in Unity3D using a ray marching algorithm. As part of the literature study, this research also explores different ways of measuring visual quality within real-time rendering. As a result of this, the thesis uses the Structural Similarity Index Measure to measure the visual quality. The research found that utilizing bilinear interpolation to ray march every eighth pixel results in a performance gain of 45%. However, it also reduces the visual quality of the volumetric clouds. This is counteracted by using adaptive sampling to interpolate only where the standard deviation of pixel colors is below a threshold. We cannot, however, determine the optimal value of this parameter, since it depends on the requirements of the renderer. Instead, it has to be determined on a case-by-case basis. / Volymetriska moln används i spel för att uppnå realism och förbättra den grafiska kvaliteten. Men för att uppnå realtidsrendering så måste optimeringar göras. Dessa typer av optimeringar förbättrar prestandan av programmet, men kan också försämra den visuella kvalteten. Den här studien undersöker hur en optimering baserad på bilinjär interpolering kan användas för att förbättra prestandan av volymetriska moln, utan att försämra den visuella kvaliteten i någon större utsträckning. Studien tittar även på hur adaptiv sampling av pixlarna påverkar optimeringen. För att utföra detta renderas molnen i Unity3D med hjälp av en ray marching-algoritm. Som del av litteraturstudien utforskas även olika sätt att evaluera visuell kvalitet inom realtidsrendering. Utifrån denna använder studien måttet Structural Similarity Index Measure för att mäta visuell kvalitet. Studien fann att den bilinjära interpoleringen resulterade i att prestandan ökade med 45% när endast var åttonde pixel är beräknad med ray marching, och resten interpoleras. Dock reduceras även den visuella kvaliteten av molnen. Detta kan motverkas med hjälp av adaptiv sampling. Då interpoleras endast pixlar där standardavvikelsen av de kringliggande pixlarna är under ett fördefinierat värde. Vi kan däremot inte definiera ett universiellt optimalt värde på detta värde. Det beror på att det optimala värdet beror på kraven vi har på programmet. Dessa kan variera från program till program. Därför måste detta bestämmas individuellt för varje program.