[pt] Os desafios de estudar formas levaram matemáticos a criar abstrações, em particular através da geometria diferencial. Porém, formas simples como cubos não se adequam a ferramentas diferenciáveis. Este trabalho é uma tentativa de usar avanços recentes da análise, no caso a teoria das distribuições, para estender quantidades diferenciáveis a objetos singulares. Como as distribuições generalizam as funções e permitem derivações infinitas, substituição das parametrizações de subvariedades clássicas por distribuições poderia naturalmente generalizar as subvariedades suaves. Isso nos leva a definir D-imersões. Esse trabalho demonstra que essa formulação, de fato, generaliza as imersões suaves. Extensões para outras classes de subvariedades são discutidas através de exemplos e casos particulares. / [en] The challenge of studying shapes has led mathematicians to create powerful abstract concepts, in particular through Differential Geometry. However, differential tools do not apply to simple shapes like cubes. This work is an attempt to use modern advances of the Analysis, namely Distribution Theory, to extend differential quantities to singular objects. Distributions generalize functions, while allowing infinite differentiation. The substitution of classical immersions, which usually serve as submanifold parameterizations, by distributions might thus naturally generalize smooth immersion. This leads to the concept of D-immersion. This work proves that this formulation actually generalizes smooth immersions. Extensions to non-smooth of immersions are discussed through examples and specific cases.

Submitted by Jadson Francisco de Jesus SILVA (jadson@uefs.br) on 2018-02-23T22:02:41Z No. of bitstreams: 1 DISSERTA??O_JEFFERSON_COSTA.pdf: 4871777 bytes, checksum: 5ba189276fba5c2903773fd8a3ad8484 (MD5) / Made available in DSpace on 2018-02-23T22:02:41Z (GMT). No. of bitstreams: 1 DISSERTA??O_JEFFERSON_COSTA.pdf: 4871777 bytes, checksum: 5ba189276fba5c2903773fd8a3ad8484 (MD5) Previous issue date: 2017-02-18 / The decline of the teaching of the design subjects is expressed in the high repetition rates of students who study Technical design in the courses offered by the Instituto Federal da Bahia (IFBA). The fact that disciplines such as Geometric Design and Descriptive Geometry do not appear as compulsory in the curriculum as well as are not required in college entrance examinations makes them less important than Portuguese or Mathematics, for example. In this regard, the constructions of the motor aspects and the three-dimensional perceptual abilities of students are not seen as significant factors. This issue allows students to reach the first year of high school without the necessary basis to study design. This fact aims to demand a greater commitment of Design teachers to students who understand the subjects addressed. Based on this situation, computational programs focused on geometric design and modeling may have a pedagogical role in the development of spatial visualization skills, however, in the state of Bahia, undergraduate programs which train design teachers have not yet reformulated their r?sum?s to include the teaching of new tools for these areas of knowledge. In order to contribute to the learning of the technical design, in the Building Technician course at IFBA, located in Salvador city, the present master's dissertation sought, through the tools of Geometric Modeling, a method that could contribute to the learning of the Technical Design. / A desvaloriza??o do ensino das disciplinas de desenho, no ensino fundamental, se expressa nos altos ?ndices de reprova??o dos alunos que cursam Desenho T?cnico, nos cursos oferecidos pelo Instituto Federal da Bahia (IFBA). O fato de disciplinas como Desenho Geom?trico e Geometria Descritiva n?o constarem como obrigat?rias no curr?culo e n?o serem cobradas em exames de vestibular torna-as menos importantes do que Portugu?s ou Matem?tica, por exemplo. Neste sentido, as constru??es dos aspectos motores e das habilidades perceptivas tridimensionais dos alunos n?o s?o vistas como fatores importantes. Este problema permite que os alunos cheguem ao primeiro ano do ensino m?dio sem as bases necess?rias para cursar Desenho. Tal fato tende a exigir maior empenho dos professores de Desenho para que os alunos compreendam os assuntos abordados. Diante do problema, programas computacionais voltados para o desenho e a modelagem geom?trica podem ter papel pedag?gico no desenvolvimento das habilidades para visualiza??o espacial, por?m, na Bahia, os cursos de gradua??o que formam professores de desenho ainda n?o reformularam os seus curr?culos, incluindo o ensino de novas ferramentas para as referidas ?reas do conhecimento. No intuito de contribuir com a aprendizagem do Desenho T?cnico, no curso T?cnico em Edifica??es do IFBA, campus Salvador, a presente disserta??o procurou, por meio das ferramentas de Modelagem Geom?trica, um m?todo que pudesse ajudar com a aprendizagem do Desenho T?cnico.

Le dessin est la manière la plus courante de communiquer sur les formes.Ainsi, l'utilisation de l'esquisse comme outil dans le processus de modélisation de contenus 3D est une approche attrayante.Cependant, dans le monde des machines, les dessins sont encore difficiles à interpréter comme des représentations de formes 3D.Ce défi a été relevé par de nombreux travaux de recherche, car tirer parti du peu de connaissances que nous possédons sur la perception n’est pas anodin.Ma thèse se concentre sur les limites de ce qui peut être inféré à partir de dessins uniques de formes lisses sans aucune aide de l'utilisateur.Dans un premier temps, nous avons choisi une catégorie de forme, à savoir les animaux et autres créatures pour lesquels une connaissance préalable aide à résoudre le problème.Ensuite, nous avons proposé de généraliser certaines parties de la solution pour aborder le cas des formes organiques libres.Ce manuscrit présente donc les solutions respectives que nous avons développées.La première permet de déduire des modèles 3D plausibles d’animaux à partir d’une seule esquisse de vue latérale en utilisant des principes anatomiques pour interpréter les éléments du dessin et déduire des décalages de profondeur entre les éléments.La seconde est une approche qui consiste à décomposer les représentations de formes lisses avec des points de recouvrement non triviaux en un ensemble de silhouettes de parties structurelles ordonnées en profondeur, qui peuvent être utilisées à des fins d'édition et d'animation.Beaucoup d'idées connexes ont été explorées en parallèle, et celles présentées dans ce manuscrit me donnent confiance en l'avenir de ce domaine de recherche. / Drawing is the most common way to communicate about shapes.Thus, using sketching as a tool in the process of modeling 3D content is an attractive approach.However in the world of machines, drawings are still difficult to interpret as shape depictions.This has been the challenge tackled by many different research works since leveraging the little we know about perception is non trivial.My thesis focuses on pushing the limits of what can be inferred from single drawings of smooth shapes without any help from the user.In a first attempt we chose to select a category of shape namely animals and other creatures for which prior knowledge helps to solve the problem.Then we proposed to generalize parts of the solution to tackle the case of free form organic shapes.This manuscript thus presents the respective solutions we developed. The first one is able to infer plausible 3D models of animals from a single side-view sketch using anatomic principles to both interpret the drawing's elements and infer depth offsets between these elements.The second is an approach to decompose depictions of smooth shapes with non trivial cusp points into a set of structural parts' silhouettes ordered in depth, which can be used for editing and animation purposes.Many related ideas were explored on the way, and the ones presented in this manuscript leaves me confident about the future of this field of research.

L'imagerie médicale est une ressource de données principale pour différents types d'applications. Bien que les images concrétisent beaucoup d'informations sur le cas étudié, toutes les connaissances a priori du médecin restent implicites. Elles jouent cependant un rôle très important dans l'interprétation et l'utilisation des images médicales. Dans cette thèse, des connaissances anatomiques a priori sont intégrées dans deux applications médicales. Nous proposons d'abord une chaîne de traitement automatique qui détecte, quantifie et localise des anévrismes dans un arbre vasculaire segmenté. Des lignes de centre des vaisseaux sont extraites et permettent la détection et la quantification automatique des anévrismes. Pour les localiser, une mise en correspondance est faite entre l'arbre vasculaire du patient et un arbre vasculaire sain. Les connaissances a priori sont fournies sous la forme d'un graphe. Dans le contexte de l'identification des sous-parties d'un organe représenté sous forme de maillage, nous proposons l'utilisation d'une ontologie anatomique, que nous enrichissons avec toutes les informations nécessaires pour accomplir la tâche de segmentation de maillages. Nous proposons ensuite un nouvel algorithme pour cette tâche, qui profite de toutes les connaissances a priori disponibles dans l'ontologie. / Medical imaging is a principal data source for different applications. Even though medical images represent a lot of knowledge concerning the studied case, all the a priori knowledge known by the specialist remains implicit. Nevertheless this a priori knowledge has a major role in the interpretation and the use of the images. In this thesis, anatomical a priori knowledge is integrated in two medical applications. First, an automatic processing pipeline is proposed in order to detect, quantify and localize aneurysms on a segmented cerebrovascular tree. Centerlines of blood vessels are extracted and then used to automatically detect aneurysms and quantify them. To localize aneurysm, a matching is made between the cerebrovascular tree of the patient and a healthy one. The a priori knowledge, in this case, is represented by a graph. In the context of identifying sub-parts of an organ represented by a mesh, we propose the use of an anatomical ontology. This ontology is first enhanced by all information necessary to achieve the task of mesh segmenting. A new algorithm using this ontology to accomplish the segmentation task is then proposed.

Cellular structures are present from the atomic level all the way up to patterns found in human skeleton. They are prevailing structures in the nature and known for their excellent mechanical, thermal, and acoustic properties. Two typical types of cellular structures, lightweight structures and compliant mechanisms, are investigated. Lightweight structures are rigid and designed to reduce weight, while increasing strength and stiffness. Compliant mechanisms are designed to transform motions and forces. Most available artificial lightweight structures are patterns of primitives. However, the performance of lightweight structures can be enhanced by using adaptive cellular structures with conformal strut orientations and sizes, like the trabeculae in femoral bone. Bending, torsion, and nonlinear behaviors of compliant mechanisms have not been sufficiently studied. In order to design adaptive cellular structures, a new unit cell, the unit truss is proposed. The unit truss approach facilitates the design of adaptive cellular structures for enhanced mechanical properties via geometric modeling, finite element analysis, shape optimization, and additive fabrication. Four research questions, which address representation, structural analysis, design synthesis, and manufacturing respectively, are raised and answered. Unit truss enables representation and mechanics analysis for adaptive cellular structures. A synthesis method using engineering optimization algorithms is developed to systematically design adaptive cellular structure. Two examples, graded cellular structure for prosthesis and compliant mechanism for morphing wings, are studied to test the unit truss approach.

This study aims to analyze and evaluate the influence of digital technologies on the inter-action of design and manufacturing processes by representing an outlook of digital tech-nologies through developments in modeling capabilities, manufacturing techniques, mate-rial science, and design strategies. The digital era reached by the technological developments in different fields of sci-ence influenced the field of architecture, just like the others. Thus, a new kind of spa-tial and tectonic quality in architecture is emerging with the lately introduced design tools and materials that are novel to the building industry, while redefining the role of architect in this contemporary medium. The evolutionary process of Frank O. Gehry and his office, being a pioneer in using digital design and manufacturing tools in architecture, is represented with realized examples that point out the formerly discussed developments in the realm of architecture and visualize the tectonics of the digitally designed and produced buildings / culminating with the case study of Guggenheim Museum, Bilbao.

[pt] Este trabalho apresenta uma nova abordagem para o balanceamento de seções geológicas baseada em modelagem física e simulação numérica. O objetivo principal é introduzir alguns conceitos da Mecânica do Contínuo no processo de restauração geológica, de forma a considerar as propriedades físicas dos materiais geológicos durante a simulação do movimento de um bloco de rocha sobre uma falha. A estratégia adotada utiliza-se de um algoritmo de Relaxação Dinâmica acoplado ao Método dos Elementos Finitos para resolver sistemas de equações, com condições de contorno específicas para a movimentação do bloco sobre a falha.Foi adotado como ambiente de desenvolvimento um sistema de balanceamento de seções geológicas composto por um conjunto de transformações geométricas comuns na abordagem clássica do problema. O sistema utiliza uma tecnologia de modelagem geométrica baseada em uma estrutura de dados que permite a representação topológica completa de uma subdivisão planar.A simulação numérica do balanceamento de seções geológicas proposta é implementada dentro desse ambiente e integra três módulos distintos: um módulo de pré- processamento no qual os dados requeridos podem ser facilmente gerados, um módulo de análise onde o método de Relaxação Dinâmica foi implementado e, finalmente, um módulo de pósprocessamento em que podem ser visualizados os resultados obtidos da simulação numérica. Considera-se ainda a natureza palinspática do problema de restauração através de uma interface gráfica amigável do ponto de vista do usuário. Neste sentido, foi realizada uma reorganização completa da interface gráfica e das classes de atributos geológicos associados às entidades topológicas (linhas e regiões) da seção geológica. Esta organização teve dois objetivos: o primeiro, implementar um processo gráfico baseado em uma árvore de decisões para o gerenciamento das tarefas do balanceamento, que envolve passos arbitrários de tentativa e erro, e, o segundo, possibilitar a implementação da simulação numérica dentro do processo de balanceamento.As idéias propostas podem ser consideradas como o primeiro passo para o desenvolvimento de um sistema de balanceamento de seções geológicas, cujas medidas de deformação representem de forma mais aproximada o comportamento mecânico das rochas, além de ser mais automatizado, o que sugere futuramente a implementação de um sistema tridimensional, no qual seja menos exigida a interação com o usuário. / [en] This work presents a new approach for the restoration of geological cross-sections that is based on physical modeling and numerical simulation. The main purpose is to introduce Continuum Mechanics concepts into the geological restoration process in order to consider physical properties of the materials during the simulation of the movement of a rock block along a fault. The adopted strategy uses a dynamic relaxation algorithm to solve the equation system that arises from the numerical simulation based on the Finite Element Method, together with some specific boundary conditions to represent the movement of the rock block over the fault.As development environment, a cross-section restoration system was adopted, composed by a group of usual geometric transformations from the classical approach of the problem. This system adopts a geometric modeling technology based on a data structure that is capable of completely representing the topology of a planar subdivision. The proposed numerical simulation is implemented inside this system and integrates with three different modules: a pre-processing module, where the required input data can be easily generated; an analysis module, in which the dynamic relaxation method has been implemented; and a post- processing module, where the results of the numerical simulation can be viewed. The palinspatic nature of the restoration problem is taken into account by means of a user-friendly graphics interface that was specifically designed for the system. The graphics interface and the geological attribute classes were completely re-organized with two purposes. First, to implement a graphical interface based on a decision tree to manage user tasks involved in the restoration process, which includes trial- and-error steps. Second, to provide support for the implementation of numerical simulation in the restoration process.The ideas proposed herein can be considered as a first step towards a complete geological cross-section restoration system in which more consistent deformation measures can be incorporated into the governing equations to better represent the mechanical behavior of the rocks, and is also an expansion of the presented system to a three-dimensional environment, currently under investigation.

Modéliser avec des squelettes est une alternative très séduisante aux "points de contrôle" souvent placés à l'extérieur des formes : cette approches, analogue à un fil de fer dans une forme modelée, permet de créer des modèles de toutes géométries et topologies. Pour cela, il faut que les formes définies par chacun des squelettes soient capable de se mélanger de manière lisse. Introduites en informatique graphique dans les années 90, les surfaces implicites sont la principale solution à ce problème. Elles constituent un modèle puissant à la fois pour la modélisation d'objets tridimensionnels et pour leur animation : leur construction par squelette et leurs capacités de mélange par sommation des champs potentiels qui les définissent permettent en effet la conception progressive et le stockage compact d'objets volumiques, ainsi que l'animation de déformations pouvant comprendre des changements de topologie. Les surfaces implicites, et plus particulièrement les surfaces de convolution, forment donc un modèle particulièrement adapté à la modélisation par squelette. Toutefois, elles présentent un certain nombre de défaut qui les ont rendu inutilisable en pratique. Cette thèse propose de nouveaux modèles implicites à squelettes, s'inspirant de la convolution mais basés aussi sur des déformations de l'espace. Ils permettent : – une génération plus aisée de forme le long de squelettes formés de courbes (des arc d'hélices), – un meilleur contrôle des formes tant au niveau de leur épaisseur que de leur mélange, notamment nos modèles sont invariant par homothétie ce qui les rend plus intuitif, – la génération de surfaces ayant une topologie plus proche de celle des squelettes, – la génération de détail fins engendrés par un bruit procédural, les détails se comportant de manière cohérentes avec la surface (et les squelettes) sous-jacente. / Modeling with skeleton is an attractive alternative to "control points" usually placed outside a shape in order to model it : this paradigm, similar to a wire inside the modeled shape, enables to create model of arbitrary geometry and topology. In order to do so, shapes defined by skeletons should be able to smoothly blend together. Introduced in computer graphics in the 90's, implicit surfaces are one of the main solution to this problem. They are powerful both for the modeling of 3D models and their animations : their construction from a skeleton and their blending capacity by simply summing their scalar field provide an easy way to incrementally create shapes and store them in a compact way, it also ease the animation containing changes in topology. Implicit surfaces, and more specifically Convolution surfaces, are therefore particularly well adapted to skeleton-based modeling. However, they present a number of drawback that make them unusable in practice. This thesis propose new skeleton-based implicit models, inspired not only by convolution but also from space deformations. They enable : – an easier generation of shape along curve skeletons (arcs of helix), – a better control of generated shape both in term of thickness and blending, in particular our model are scale-invariant that make them more intuitive, – the generation of shape which topology better reflects the topology of its skeleton, – the generation of small scale details from a procedural texture, the details behave in a coherent way with the underlying surface (and its skeleton).

Este trabalho apresenta um estudo para aerogerador de pequeno porte projetado inicialmente para uso residencial. A ênfase está na modelagem e simulação virtual da estrutura das pás em compósito de fibra de vidro. A modelagem geométrica foi feita com software para desenho assistido por computador (CAD 3D). Para o projeto, foi escolhido o perfil MH110 que apresenta boa relação entre coeficiente de sustentação e coeficiente de arrasto e facilidade de fabricação. Os parâmetros como o diâmetro do rotor, a corda e a torção da pá, as relações entre velocidades e a aplicação de cargas na estrutura do material utilizado foram definidos segundo bibliografia específica, software para análise de perfil aerodinâmico e simulações pelo método dos elementos finitos. Procurou-se buscar sempre a maior eficiência, segurança e economia. O material considerado para o projeto das pás foi projetado para resistir às tensões decorrentes de operação em condições consideradas normais e para rajadas de vento. A simulação pelo método dos elementos finitos foi conduzida com ferramenta computacional e levou em conta os limites de falha do material utilizado. A geometria foi simulada sem reforço interno e apresentou baixo deslocamento quando submetida às cargas aerodinâmicas de empuxo e rotacional. Ao realizar simulação com critério de falha, foi possível determinar a espessura mais adequada para o material compósito e verificar seu comportamento de acordo com diferentes velocidades de vento. / This work presents a study for small wind generator designed for residential usage. The emphasis is modeling and virtual simulation of the blade structure made in composite material (fiberglass). Geometric modeling was performed by computer aided design (CAD 3D) software. The MH110 profile was chosen for design because it presents good ratio of lift coefficient and drag coefficient, and manufacturing facility. Parameters such as rotor diameter, chord and blade twist, the relationship between the blade speeds, and the application of loads on the material used were defined according to specific bibliography, software for airfoil analysis and simulations by finite element method. It tried to always seek most efficiency, safety and economy. The material was designed to withstand the stresses arising from operation under conditions considered normal and wind gusts. The simulation by finite element method was conducted by computational tool and took into account the material failure criterion. The geometry was simulated without internal reinforcement and presented low displacement when subjected to aerodynamic loads of thrust and rotational forces. When performing simulation with the failure criterion, it was possible to determine the most appropriate thickness for the composite material and verify its behavior under different wind speeds.

Este trabalho apresenta um estudo para aerogerador de pequeno porte projetado inicialmente para uso residencial. A ênfase está na modelagem e simulação virtual da estrutura das pás em compósito de fibra de vidro. A modelagem geométrica foi feita com software para desenho assistido por computador (CAD 3D). Para o projeto, foi escolhido o perfil MH110 que apresenta boa relação entre coeficiente de sustentação e coeficiente de arrasto e facilidade de fabricação. Os parâmetros como o diâmetro do rotor, a corda e a torção da pá, as relações entre velocidades e a aplicação de cargas na estrutura do material utilizado foram definidos segundo bibliografia específica, software para análise de perfil aerodinâmico e simulações pelo método dos elementos finitos. Procurou-se buscar sempre a maior eficiência, segurança e economia. O material considerado para o projeto das pás foi projetado para resistir às tensões decorrentes de operação em condições consideradas normais e para rajadas de vento. A simulação pelo método dos elementos finitos foi conduzida com ferramenta computacional e levou em conta os limites de falha do material utilizado. A geometria foi simulada sem reforço interno e apresentou baixo deslocamento quando submetida às cargas aerodinâmicas de empuxo e rotacional. Ao realizar simulação com critério de falha, foi possível determinar a espessura mais adequada para o material compósito e verificar seu comportamento de acordo com diferentes velocidades de vento. / This work presents a study for small wind generator designed for residential usage. The emphasis is modeling and virtual simulation of the blade structure made in composite material (fiberglass). Geometric modeling was performed by computer aided design (CAD 3D) software. The MH110 profile was chosen for design because it presents good ratio of lift coefficient and drag coefficient, and manufacturing facility. Parameters such as rotor diameter, chord and blade twist, the relationship between the blade speeds, and the application of loads on the material used were defined according to specific bibliography, software for airfoil analysis and simulations by finite element method. It tried to always seek most efficiency, safety and economy. The material was designed to withstand the stresses arising from operation under conditions considered normal and wind gusts. The simulation by finite element method was conducted by computational tool and took into account the material failure criterion. The geometry was simulated without internal reinforcement and presented low displacement when subjected to aerodynamic loads of thrust and rotational forces. When performing simulation with the failure criterion, it was possible to determine the most appropriate thickness for the composite material and verify its behavior under different wind speeds.