At the design stage, column-beam connections of steel structures are assumed as fully rigid or as hinges, and the design is completed with these assumptions. On the other hand, in practice, steel column-beam connections show neither fully rigid nor fully hinge behaviour, and the characteristic behaviour of the connections lies between these two special cases. Performing realistic calculation of these forces and knowing the behaviour of structures close to reality will decrease life and goods losses to the minimum level in a probable of earthquake to be encountered in the future. &nbsp / In this study, seismic performance of 2-D steel frames were evaluated by Capacity Spectrum Method proposed in the ATC 40 document published in 1996. A new computer program was developed in order to define all geometric and loading data and to perform nonlinear analysis of rigid and semi rigid steel frames for which the performances will be evaluated. In case studies, 3-Floor Steel Frames that have different bay numbers were investigated in various forms according to the rigid and different semi rigid connection types. In addition, the performances these frames for various seismic regions and soil conditions were compared. According to the results, it was observed that semi rigidly connected frames are under the effect of smaller ground acceleration have greater displacement values. As a consequence of this ductile and energy dissipative response, it was seen that the stresses in the members of frame become considerably small, relative to the stresses in the rigid frames&rsquo / . Furthermore, the performances of semi-rigid frames can be affected negatively beyond such a low rigidity. Consequently, the most convenient design should be made according to the seismic and soil region where the structure to be constructed by performing the necessary studies on the connection details in order to achieve desired performance, serviceability and optimum member criteria.

This work considers a cracked semi-infinite cylinder and a finite cylinder. Material of the cylinder is linearly elastic and isotropic. One end of the cylinder is bonded to a fixed support while the other end is subject to axial tension. Solution for this problem can be obtained from the solution for an infinite cylinder having a penny-shaped rigid inclusion at z = 0 and two penny-shaped cracks at z = &plusmn / L. General expressions for this problem are obtained by solving Navier equations using Fourier and Hankel transforms. When the radius of the inclusion approaches the radius of the cylinder, the end at z = 0 becomes fixed and when the radius of the cracks approaches the radius of the cylinder, the ends at z = &plusmn / L become cut and subject to uniformly distributed tensile load. Formulation of the problem is reduced to a system of three singular integral equations. By using Gauss-Lobatto and Gauss-Jacobi integration formulas, these three singular integral equations are converted to a system of linear algebraic equations which is solved numerically.

Dans cette thèse nous proposons des algorithmes pour le suivi 3D du mouvement des objects déformables à partir de plusieurs caméras vidéo. Bien qu’une suite de reconstructions tridimensionnelles peut être obtenue par des méthodes de reconstruction statique, celle-ci ne représente pas le mouvement. Nous voulons produire une représentation temporellement cohérente de la suite de formes prises par l’object. Précisément, nous souhaitons représenter l’objet par une surface maillée 3D dont les sommets se déplacent au cours du temps mais dont la topologie reste identique.Contrairement à beaucoup d’approches existantes, nous proposons de représenter le mouvement du volume intérieur des formes, dans le but de mieux représenter la nature volumétrique des objets. Nous traitons de manière volumétrique les problèmes fondamentaux du suivi déformable que sont l’association d’éléments semblables entre deux formes et la modélisation de la déformation. En particulier, nous adaptons au formes volumétriques les modèles d’association EM-ICP non-rigide ansi que l’association par détection par apprentissage automatique.D’autre part, nous abordons la question de la modélisation de l’évolution temporelle de la déformation au cours d’une séquence dans le but de mieux contraindre le problème du suivi temporel. Pour cela, nous modélisons un espace de forme construit autour de propriétés de déformations locales que nous apprenons automatiqument lors du suivi.Nous validons nos algorithmes de suivi sur des séquences vidéo multi-caméras avec vérité terrain (silhouettes et suivi par marqueurs). Nos résultats se révèlent meilleurs ou équivalents à ceux obtenus avec les méthodes de l’état de l’art.Enfin, nous démontrons que le suivi volumétrique et la représentation que nous avons choisie permettent de produire des animations 3D qui combinent l’acquisition et la simulation de mouvement. / In this thesis we propose algorithms for tracking 3D deformable shapes in motion from multiview video. Although series of reconstructed 3D shapes can be obtained by applying a static reconstruction algorithm to each temporal frame independently, such series do not represent motion. Instead, we want to provide a temporally coherent representation of the sequence of shapes resulting from temporal evolutions of a shape. Precisely, we want to represent the observed shape sequence as a 3D surface mesh whose vertices move in time but whose topology is constant.In contrast with most existing approaches, we propose to represent the motion of inner shape volumes, with the aim of better accounting for the volumetric nature of the observed object. We provide a fully volumetric approach to the fundamental problems of deformable shape tracking, which are the association between corresponding shape elements and the deformation model. In particular, we extend to a volumetric shape representation the EM-ICP tracking framework and the association-by-detection strategy.Furthermore, in order to better constrain the shape tracking problem, we propose a model for the temporal evolution of deformation. Our deformation model defines a shape space parametrized by variables that capture local deformation properties of the shape and whose values are automatically learned during the tracking process.We validate our tracking algorithms on several multiview video sequences with ground truth (silhouette and marker-based tracking). Our results are better or comparable to state of the art approaches.Finally, we show that volumetric tracking and the shape representation we choose can be leveraged for producing shape animations which combine captured and simulatated motion.

This work extends a previously developed finite-volume overset-grid fluid flow solver to enable the characterisation of rigid-body-fluid interaction problems. To this end, several essential components have been developed and blended together. The inherent time-dependent nature of fluid-solid interaction problems is captured through the laminar transient incompressible Navier-Stokes equations for the fluid, and the Euler-Newton equations for rigid-body motion. First and second order accurate time discretisation schemes have been implemented for the former, whereas second and third order accurate time discretisation schemes have been made available for the latter. Without doubt the main advantage the overset-grid method offers regarding moving entities is the avoidance of the time consuming grid regeneration step, and the resulting grid distortion that can often cause numerical stability problems in the solution of the flow equations. Instead, body movement is achieved by the relative motion of a body fitted grid over a suitable background mesh. In this case, the governing equations of fluid flow are formulated using a Lagrangian, Eulerian, or hybrid flow description via the Arbitrary Lagrangian-Eulerian method. This entails the need to guarantee that mesh motion shall not disturb the flow field. With this in mind, the space conservation law has been hard-coded. The compliance of the space conservation law has the added benefit of preventing spurious mass sources from appearing due to mesh deformation. In this work, two-way fluid-solid interaction problems are solved via a partitioned approach. Coupling is achieved by implementing a Picard iteration algorithm. This allows for flexible degree of coupling specificationby the user. Furthermore, if strong coupling is desired, three variants of interface under-relaxation can be chosen to mitigate stability issues and to accelerate convergence. These include fixed, or two variants of Aitken’s adaptive under-relaxation factors. The software also allows to solve for one-way fluid-solid interaction problems in which the motion of the solid is prescribed. Verification of the core individual components of the software is carried out through the powerful method of manufactured solutions (MMS). This purely mathematically based exercise provides a picture of the order of accuracy of the implementation, and serves as a filter for coding errors which can be virtually impossible to detect by other means. Three instances of one-way fluid-solid interaction cases are compared with simulation results either from the literature, or from the OpenFOAM package. These include: flow within a piston cylinder assembly, flow induced by two oscillating cylinders, and flow induced by two rectangular plates exhibiting general planar motion. Three cases pertaining to the class of two-way fluid-interaction problems are presented. The flow generated by the free fall of a cylinder under the action of gravity is computed with the aid of an intermediate ‘motion tracking’ grid. The solution is compared with the one obtained using a vorticity based particle solver for validation purposes. Transverse vortex induced vibrations (VIV) of a circular cylinder immersed in a fluid, and subject to a stream are compared with experimental data. Finally, the fluttering motion of a rectangular plate under different scenarios is analysed.

Les protéines sont des macromolécules participant à d’importants processus biophysiques de la vie des organismes. Or, il a été démontré que des variations de leur structure peuvent conduire à des changements de fonction en lien avec certaines maladies telles que celles associées à des processus neurodégénératifs. Ainsi, tant pour la communauté scientifique que pour l’industrie médicale, il est capital d’avoir une meilleure compréhension de la structure de ces protéines, ainsi que de leurs interactions avec d’autres molécules, ce en vue d’inventer et d’évaluer de nouveaux médicaments.Au cours de ces travaux de thèse, nous nous sommes particulièrement intéressés au développement de nouvelles méthodes de recherche de chemins biologiquement faisables entre deux états connus pour un système composé d’une protéine ou d’une protéine et d’un ligand. Au cours des dernières décennies, une grande quantité d’approches algorithmiques ont été proposées pour faire face à ce problème. Pourtant, les méthodes développées sont encore aujourd’hui confrontées à deux grands défis : d’une part la haute dimension des espaces de recherche, associée au grand nombre d’atomes impliqués, d’autre part la complexité des interactions entre ces atomes.Cette dissertation propose deux nouvelles méthodes pour obtenir de manière efficace des chemins pertinents pour des systèmes moléculaires. Ces méthodes sont rapides et génèrent des solutions qui peuvent ensuite être analysées ou améliorées à l’aide de méthodes d’avantage spécialisées. La première approche proposée produit des chemins d’interpolation pour systèmes biomoléculaires, à l’aide des approches dites aussi-rigides-que-possible, (ARAP) utilisées en animation graphique. Cette méthode est robuste et génère des solutions préservant au mieux la rigidité du système d’origine. Une extension de cette méthode basée sur des critères énergétiques a également été proposée et s’est avérée capable d’améliorer de manière significative les chemins solution. Cependant, pour les scénarios nécessitant de complexes déformations, cette approche géométrique peut conduire à des chemins solution non naturels. Nous avons donc proposé une seconde méthode appelée ART-RRT, qui utilise l’approche ARAP pour réduire la dimensionalité de l’espace et la combine avec les arbres d’exploration RRT (Rapidely-exploring Random Tree) issus de la Robotique, afin d’explorer efficacement les chemins possibles de l’espace.En plus de fournir une variété de solutions en temps raisonnable, cette ART-RRT produit des chemins de faible énergie, sans collision et dont la rigidité est préservée autant que possible. Des versions monodirectionnelles de bidirectionelles de cette méthode ont été proposées et appliquées respectivement à la recherche de chemin d’extraction d’un ligand hors du site actif d’une protéine, ainsi qu’a la recherche de chemin de transition conformationnelle pour protéine seule. Les solutions trouvées se sont avérées être en accord avec les données expérimentales ainsi qu’avec les solutions issues de l’état de l’art. / Proteins are macromolecules participating in important biophysical processes of living organisms. It has been shown that changes in protein structures can lead to changes in their functions and are found linked to some diseases such as those related to neurodegenerative processes. Hence, an understanding of their structures and interactions with other molecules such as ligands is of major concern for the scientific community and the medical industry for inventing and assessing new drugs.In this dissertation, we are particularly interested in developing new methods to find for a system made of a single protein or a protein and a ligand, the pathways that allow changing from one state to another. During past decade, a vast amount of computational methods has been proposed to address this problem. However, these methods still have to face two challenges: the high dimensionality of the representation space, associated to the large number of atoms in these systems, and the complexity of the interactions between these atoms.This dissertation proposes two novel methods to efficiently find relevant pathways for such biomolecular systems. The methods are fast and their solutions can be used, analyzed or improved with more specialized methods. The first proposed method generates interpolation pathways for biomolecular systems using the As-Rigid-As-Possible (ARAP) principle from Computer Graphics. The method is robust and the generated solutions preserve at best the local rigidity of the original system. An energy-based extension of the method is also proposed, which significantly improves the solution paths. However, in scenarios requiring complex deformations, this geometric approach may still generate unnatural paths. Therefore, we propose a second method called ART-RRT, which combines the ARAP principle for reducing the dimensionality, with the Rapidly-exploring Random Trees from Robotics for efficiently exploring possible pathways. This method not only gives a variety of pathways in reasonable time but the pathways are also low-energy and clash-free, with the local rigidity preserved as much as possible. The mono-directional and bi-directional versions of the ART-RRT method were applied for finding ligand-unbinding and protein conformational transition pathways, respectively. The results are found to be in good agreement with experimental data and other state-of-the-art solutions.

A falta de um membro, devido a doenças, más-formações ou traumas, impacta enormemente na vida de um indivíduo. Para que o mesmo possa realizar Atividades de Vida Diária (AVD), sem drásticas limitações, faz-se necessário o desenvolvimento de próteses e cientes. Para auxiliar no projeto de tais produtos, este trabalho visa criar e solucionar um modelo de sistema dinâmico capaz de simular o comportamento de joelhos prostéticos. A m de alcançar tal objetivo, foi estudada a biomecânica da marcha humana, além dos tipos de amputações existentes e seus impactos na mesma. Buscou-se também estudar os principais componentes de próteses existentes atualmente no mercado, além de suas geometrias básicas. Após de nir-se um modelo simpli cado que representasse os componentes protéticos e as partes remanescentes do corpo, foram buscadas métodos de solução disponíveis para tal sistema. Baseado nos estudos encontrados em uma revisão bibliográ ca, foi de nida uma metodologia de solução numérica de sistemas multi-corpos. Durante o trabalho, surgiu a necessidade de representar forças de contato entre corpos rígidos, e foram incluídas soluções de atuais teorias do assunto. Essas metodologias foram então empregadas para a construção de um algoritmo capaz de solucionar o sistema proposto. Depois de resolvido o sistema, os valores encontrados para as variáveis cinéticas foram comparados com valores obtidos por uma simulação numérica utilizando dois programas computacionais comercias, cujas fundamentações teóricas utilizam diferentes métodos de solução. A comparação das diferenças entre os resultados apontou similaridade entre o algoritmo e os programas utilizados, mas com a necessidade de validação do método através de ensaio mecânico. Ao nal foram sugeridas ideias para trabalhos futuros. / The lack of a member due to diseases, malformations or trauma, greatly impacts the life of an individual. In order to perform Activities of Daily Living (ADL) without drastic limitations, it is necessary to develop e cient prosthetic devices. To assist the design of such products, this work aims to create and solve a dynamic system model to simulate the behavior of prosthetic knees. In order to achieve this goal, the biomechanics of human gait was studied, as well as the existing types of amputation and their impact on human gait. The main components of existing prosthetic devices, currently on the market, were identi ed, as well as its basic geometries. After de ning a simpli ed model able to incorporate the prosthetic components and the individual remaining body parts, an available methodology for the solution of such a system was prospected. Based on the studies found in the currently literature of multibodysystems, a numerical solution methodology for has been set. During the work, the need to represent contact between parts occurred, leading to the implementation of currently theories of contact forces for rigid bodies. These methodologies were then used to construct an algorithm for solving the proposed system. After the system has been solve, the values found for the kinetic variables were compared with those obtained by numerical simulations using two commercial softwares, whose theoretical foundation used di erent solution methodology. Comparing the di erences in results of these simulations, it was revealed a similar behavior between the algorithm and the commercial programs, but with the need of an experimental test, for truly validation of the method. At the end of this work, ideas for future improvement were suggested.

O final da vida útil de pavimentos com bases rígidas se caracteriza pelo aparecimento de trincas de blocos e de fadiga. Neste cenário, a reciclagem das camadas de base e revestimento asfáltico, com adição de cimento, surge como técnica importante para reabilitação dessas estruturas. Além de se tratar de uma solução vantajosa do ponto de vista técnico, é competitiva em termos econômicos, além de sustentável. Entretanto, a escassa normatização nacional dificulta sua aplicação, destacando-se a falta de um procedimento de dosagem. Objetivando contribuir para o desenvolvimento de um método de dosagem de camadas recicladas com cimento, desenvolveu-se um programa experimental, contemplando a caracterização mecânica (resistência e rigidez), a variação volumétrica e a erodibilidade de misturas contendo fresado asfáltico, materiais de bases rígidas (brita graduada tratada com cimento e solo-cimento) e cimento Portland. Foram analisados os efeitos da porcentagem de fresado, do teor de cimento e do tempo de cura, compactando-se os corpos de prova na energia Modificada. Com auxílio de um software estatístico, foi elaborado um planejamento experimental para definição das misturas analisadas, contemplando-se diversos níveis para as variáveis independentes (teores de cimento entre 1% e 7%, e porcentagens de fresado variando entre 8% e 92%, aproximadamente). Os tempos de cura considerados foram extrínsecos ao planejamento e variaram de acordo com o ensaio, sendo de 3, 7 e 14 dias para os ensaios de comportamento mecânico e de 7 dias para os demais ensaios. Obtiveram-se modelos com efeitos estatisticamente significativos, com exceção da expansão. Os demais modelos apresentaram coeficientes de determinação de médios a elevados, tendo em vista a heterogeneidade dos materiais estudados, além do tamanho amostral considerável. Foi verificado que todas as variáveis afetam as propriedades analisadas, sendo que o teor de cimento demonstrou maior efeito, sendo que sua adição melhora consideravelmente o comportamento das misturas empregadas, frente à ação do tráfego e da água. Foram alcançados resultados bastante elevados de resistência à compressão simples (1,00 MPa a 6,49 MPa) e resistência à tração na compressão diametral (0,17 MPa a 1,22 MPa); já a rigidez das misturas apresentou uma ampla variação de resultados (484 MPa a 20.031 MPa). Com relação aos materiais de base empregados (brita graduada tratada com cimento e solo-cimento), não se observou uma tendência única; as misturas com solo-cimento apresentaram maior resistência, entretanto, com comportamento ligeiramente inferior quanto à variação volumétrica e à erodibilidade. Na análise da rigidez, os materiais de base mostraram comportamento bastante similar. Para concluir, foi verificado que o procedimento proposto por Fedrigo (2015) também é satisfatório para a dosagem de misturas recicladas constituídas por antigas bases cimentadas e fresado asfáltico, restando ainda quantificar a possível retração por secagem das misturas estudadas. / The end of the useful life of pavements with rigid bases characterizes by the appearance of block and fatigue cracking. The full-depth reclamation with cement (FDR-C) of this layer combined with the asphalt layer seem to be a good choice for the rehabilitation of the pavement structure. Besides being an advantageous solution from a technical point of view, it is competitive in economic terms, besides being sustainable. However, the Brazilian standards are scarce thus limiting its application, highlighting the lack of an appropriated mix design method to this technique. In order to contribute for the development of an FDR-C mix design method, an experimental program was developed aiming to test the mechanical characterization (strength and stiffness), volumetric variation and the erodibility of mixtures made of reclaimed asphalt pavement (RAP), rigid base materials (cement treated crushed stone and soil-cement) and Portland cement. There were analyzed the effects of the RAP percentage, the cement content and the curing time of the specimens. For that, the compaction effort used was the Brazilian Modified one. Through a statistic software, an experimental planning was prepared for mixtures determination, with several levels for the independent variables (cement content between 1% and 7%, and RAP percentage varying by 8% up to 92%, approximately). The curing time analyzed was outward of experimental planning and it varied according to the kind of test. The specimens of mechanical performance were cured for 3, 7 and 14 days, and the other tests were examined at the 7th day of curing time. Models with statically significant effects were obtained, except the swell one. The others had medium and high coefficients of determination, given the heterogeneity of the studied materials, in addition to considerable sample size. It was found that all variables affect the analyzed properties, and the cement content proved to be with the greatest effect among the analyzed factors. Cement addition improves considerably the behavior of the mixtures for the traffic and water actions. Moreover, higher results were achieved for UCS (1.00 MPa up to 6.49 MPa) and ITS (0.17 MPa up to 1.22 MPa) tests. While the mixtures stiffness presented a wide range of results (484 MPa up to 20,031 MPa). Regarding the studied materials, it was observed that they do not have a single trend. The mixtures with soil-cement presented stronger, but with slightly lower behavior for volumetric variation and erodibility. At the stiffness analysis, different materials showed very similar behavior. All in all, it was found that the mix design method proposed by Fedrigo (2015) is also suitable for employment in semi-rigid FDR-C, still remaining to measure the possible drying shrinkage of specimens.

O escoamento entre o poço marítimo e a unidade flutuante é realizado através de dutos definidos como risers. Os risers flexíveis são compostos por camadas intercaladas de diferentes materiais, como aço e polietileno, o qual cada camada possui uma função. Os mecanismos de falha mais reportados são referentes a danos na camada externa polimérica, o que leva à exposição de suas armaduras metálicas ao meio externo. Os risers rígidos são dutos fabricados normalmente em aço, formados por segmentos de dutos unidos por soldas, onde a causa de dano mais frequente é a corrosão. Tem-se como objetivo nesta dissertação, o projeto e desenvolvimento de uma ferramenta e de um método para operações submarinas em risers. A ferramenta deverá ser capaz de aplicar de forma automática, um clamp bipartido no reparo da camada externa polimérica de risers flexíveis, ou acoplar sistemas de monitoramento em risers rígidos. Já o método, deverá permitir a sua aplicação tanto no reparo quanto na proteção do sistema de monitoramento. Para isto, realizou-se uma revisão bibliográfica a fim de obter uma melhor compreensão sobre o tema estudado. Desenvolveu-se o projeto do método e da ferramenta, e, posteriormente, construiu-se o protótipo para a realização de testes de funcionamento em um duto rígido Por último, através de ensaios hidrostáticos de pressão interna e externa, realizaram-se ensaios para avaliação do comportamento do método aplicado em um duto rígido. Os ensaios comprovaram a eficácia do clamp quando aplicado em ambientes submarinos em grandes profundidades, porém apresentou vazamentos nos ensaios de pressão interna e externa. A resina epóxi utilizada não garantiu a estanqueidade, possivelmente devido a sua alta rigidez, aderência ineficaz em superfícies metálicas, ou presença de vazios ou porosidades. O ensaio de pressão interna indicou que as deformações não ultrapassaram o regime elástico tanto do duto quanto do clamp até aproximadamente 182 bar de pressão. No regime elástico, o ensaio apresentou deformações menores no clamp em relação ao duto, possivelmente porque a resina acabou absorvendo as deformações. O método demonstrou ser eficiente como recipiente para a resina, e também permitiu a montagem e fixação de um colar de sensores no seu interior. Os testes de funcionamento mostraram que a ferramenta projetada e construída mostrou-se adequada para a aplicação automática de um clamp bipartido em risers, e o método mostrou-se adequado para sua aplicação em risers, tanto no reparo quanto na proteção do sistema de monitoramento. / The drain between the maritime oil well and the floating unit is made trough pipes, which is defined as risers. The flexible risers are composed by alternate layers from different materials as steel and polyethylene, each layer has its function. The failure mechanisms more reported are referent to the damage in the external polymeric layer which leads to the exposition of the metal armature to the outside. The rigid risers are pipes usually fabricated in steel made by ducts segments connect by spot welding, where the most common damage is corrosion. This essay aims to project and create a tool and a method for submarine operations in risers. The tool must be able to apply, in an automatic way, a bipartite clamp in the repair of the flexible rises in external polymeric layer or to attach monitoring systems to the rigid risers. The method must allow its application in the repair as much as the monitoring system protection. For this, it was made a bibliographic review to obtain a better comprehension from the studied theme. A project from the method and a tool were developed, later a prototype was built to make the operation tests in a rigid pipe. At last, by internal and external pressure hydrostatic trials, were made tests to evaluate the behavior of the method applied in a rigid pipe The trials proved the efficiency of the clamps when applied in submarine environments and in depth; however there were leaks in the internal and external pressure tests. The Epóxi resin did not guarantee the leak-tightness, possible due to its hardness, ineffective adherence in metal surfaces or presence of gaps and porosities. The internal pressure trial indicated that the deformations did not exceed the elastic regime in the pipe as in the clamp until, about 182 pressure bar. In the elastic regime, the trial presented minor deformation in the clamps related to the pipe possibly, because the resin absorbed the deformation. The method has proven efficient as recipient for the resin and also allowed the assembly and fixation of a sensor collar in its interior. The operation tests showed that the designed and built tool is proper for an automatic bipartite clamp application in risers and the method has proven proper for its application in risers in repair as much as monitoring system protection.

Os métodos de controle de movimento em animação baseados em Física, e utilizados em Computação Gráfica, tem como objetivo simular o comportamento de objetos de acordo com as leis físicas que governam o mundo virtual adotado. Este trabalho utiliza a dinâmica de corpos rígidos como método de controle de movimento em animação por computador aplicada a movimentos e colisões de corpos rígidos não-articulados. O trabalho também apresenta uma metodologia para projeto e implementação de simulações gráficas com o objetivo de estabelecer relações entre modos de interação e os mecanismos de abstração necessários em ambientes de simulação. A principal vantagem da utilização da Mecânica newtoniana esta no fato de que ela garante o realismo dos movimentos e colisões. Associados a cada objeto devem estar os seguintes atributos físicos: centro de massa, massa total, momento de inércia e, eventualmente, a elasticidade do material. A partir de um estado inicial (velocidade linear, posição, velocidade angular e orientação) e de estímulos iniciais sobre os objetos (forças e torques), o sistema determina a evolução do estado dinâmico inicial ao longo de um dado intervalo de tempo. Para produzir o movimento dos corpos, são resolvidos sistemas de equações diferenciais de primeira ordem utilizando métodos numéricos. O tratamento de colisões de corpos rígidos envolve a detecção da colisão e contato entre objetos e a determinação das forças de contato entre os mesmos. A estratégia utilizada para a colisão considera que num determinado instante de tempo existe apenas um ponto de contato entre dois objetos. As superfícies dos objetos são representadas por uma grade de pontos conectados para formar polígonos. Existem dois tipos de estratégias para se detectar o ponto de contato entre dois objetos: o ponto de contato resultante da intersecção do vértice das arestas de um objeto com a face poligonal de outro objeto e o resultante da intersecção da aresta de um objeto com a face poligonal de um outro objeto. A análise de impacto, para resolver a dinâmica, utiliza um método analítico que preserva os momentos linear e angular durante a colisão e resulta em novas velocidades linear e angular para cada corpo rígido. Este tratamento de colisões permite ao sistema de animação realizar, em tempo de simulação, um controle automático da restrição de que dois corpos rígidos, ao colidirem, não podem se interpenetrar. Tal tratamento automático, em geral, não realizado pelos sistemas de animação por computador atualmente existentes. O trabalho apresenta o protótipo desenvolvido para validar as soluções dadas aos problemas de determinação do movimento e detecção de colisões, assim como sua aplicação na produção de suas seqüência animadas. São comentadas, também, as extensões do presente trabalho, decorrentes da abordagem dada ao problema da simulação do comportamento fundamental de corpos rígidos num dado mundo virtual a qual permite a incorporação de outras características aos objetos: elasticidade, para modelagem de deformações, e articulações, para produção de movimentos articulados com diferentes graus de liberdade. / The goal of the motion control methods used in Computer Graphics for physically based animation is to simulate the behavior of objects according to physical laws that govern a certain virtual world. This work uses rigid body dynamics as a motion control method for animation applied to motions and collisions of non-articulated rigid bodies. In addition, the work presents a methodology for the design and implementation of graphical simulation systems with the aim of providing relationships among interaction modes and abstraction mechanisms for a variety of applications. The principal advantage in using Newtonian Mechanics is that it keeps the realism of motions and collisions. Physical attributes must be associated with objects: center of mass, mass, moment of inertia, and sometimes, elasticity of the materials. Given an initial state (linear velocity, position, angular velocity, and orientation) and initial stimuli applied to the objects (forces and torques), the system determines the evolution of the dynamic state along a determinate time interval. The motion description is obtained using numerical solutions of sets of first order differential equations. The treatment of collisions of rigid bodies involves detecting collision and contact between objects and determining the contact forces present between contacting objects. The strategy used to treat collisions takes into account that there is just one contact point between two objects. The surfaces of objects are represented by a grid of connecting points forming polygons. There are two kinds of strategies to detect the contact point between two objects: the contact point resulting of intersecting the vertices of the edges of an object with the polygonal face of another one and that resulting of intersecting the edges of an object with the polygonal face of another one. The analysis of impact, to resolve the dynamic, uses an analytical method that preserves the linear and angular moments during the collision, finding a new linear and angular velocity for each rigid body. This treatment of collision allows the animation system to provide, at simulation time, an automatic control of the restriction that there is no interpenetration between two rigid bodies when they colide. This automatic treatment in general is not provided by existing computer animation systems. The work presents the prototype developed for validating the solutions given to the problems of motion control and collisions treatment, as well as its application in the production of animated sequences. The text ends with comments on extension of the present work from the approach given to the problem of simulating the behavior of objects in a certain virtual world allowing the incorporation of other characteristics to the objects: elasticity, to model deformations, and articulations, for the production of articulated movements with different degrees of freedom.

Os métodos de controle de movimento em animação baseados em Física, e utilizados em Computação Gráfica, tem como objetivo simular o comportamento de objetos de acordo com as leis físicas que governam o mundo virtual adotado. Este trabalho utiliza a dinâmica de corpos rígidos como método de controle de movimento em animação por computador aplicada a movimentos e colisões de corpos rígidos não-articulados. O trabalho também apresenta uma metodologia para projeto e implementação de simulações gráficas com o objetivo de estabelecer relações entre modos de interação e os mecanismos de abstração necessários em ambientes de simulação. A principal vantagem da utilização da Mecânica newtoniana esta no fato de que ela garante o realismo dos movimentos e colisões. Associados a cada objeto devem estar os seguintes atributos físicos: centro de massa, massa total, momento de inércia e, eventualmente, a elasticidade do material. A partir de um estado inicial (velocidade linear, posição, velocidade angular e orientação) e de estímulos iniciais sobre os objetos (forças e torques), o sistema determina a evolução do estado dinâmico inicial ao longo de um dado intervalo de tempo. Para produzir o movimento dos corpos, são resolvidos sistemas de equações diferenciais de primeira ordem utilizando métodos numéricos. O tratamento de colisões de corpos rígidos envolve a detecção da colisão e contato entre objetos e a determinação das forças de contato entre os mesmos. A estratégia utilizada para a colisão considera que num determinado instante de tempo existe apenas um ponto de contato entre dois objetos. As superfícies dos objetos são representadas por uma grade de pontos conectados para formar polígonos. Existem dois tipos de estratégias para se detectar o ponto de contato entre dois objetos: o ponto de contato resultante da intersecção do vértice das arestas de um objeto com a face poligonal de outro objeto e o resultante da intersecção da aresta de um objeto com a face poligonal de um outro objeto. A análise de impacto, para resolver a dinâmica, utiliza um método analítico que preserva os momentos linear e angular durante a colisão e resulta em novas velocidades linear e angular para cada corpo rígido. Este tratamento de colisões permite ao sistema de animação realizar, em tempo de simulação, um controle automático da restrição de que dois corpos rígidos, ao colidirem, não podem se interpenetrar. Tal tratamento automático, em geral, não realizado pelos sistemas de animação por computador atualmente existentes. O trabalho apresenta o protótipo desenvolvido para validar as soluções dadas aos problemas de determinação do movimento e detecção de colisões, assim como sua aplicação na produção de suas seqüência animadas. São comentadas, também, as extensões do presente trabalho, decorrentes da abordagem dada ao problema da simulação do comportamento fundamental de corpos rígidos num dado mundo virtual a qual permite a incorporação de outras características aos objetos: elasticidade, para modelagem de deformações, e articulações, para produção de movimentos articulados com diferentes graus de liberdade. / The goal of the motion control methods used in Computer Graphics for physically based animation is to simulate the behavior of objects according to physical laws that govern a certain virtual world. This work uses rigid body dynamics as a motion control method for animation applied to motions and collisions of non-articulated rigid bodies. In addition, the work presents a methodology for the design and implementation of graphical simulation systems with the aim of providing relationships among interaction modes and abstraction mechanisms for a variety of applications. The principal advantage in using Newtonian Mechanics is that it keeps the realism of motions and collisions. Physical attributes must be associated with objects: center of mass, mass, moment of inertia, and sometimes, elasticity of the materials. Given an initial state (linear velocity, position, angular velocity, and orientation) and initial stimuli applied to the objects (forces and torques), the system determines the evolution of the dynamic state along a determinate time interval. The motion description is obtained using numerical solutions of sets of first order differential equations. The treatment of collisions of rigid bodies involves detecting collision and contact between objects and determining the contact forces present between contacting objects. The strategy used to treat collisions takes into account that there is just one contact point between two objects. The surfaces of objects are represented by a grid of connecting points forming polygons. There are two kinds of strategies to detect the contact point between two objects: the contact point resulting of intersecting the vertices of the edges of an object with the polygonal face of another one and that resulting of intersecting the edges of an object with the polygonal face of another one. The analysis of impact, to resolve the dynamic, uses an analytical method that preserves the linear and angular moments during the collision, finding a new linear and angular velocity for each rigid body. This treatment of collision allows the animation system to provide, at simulation time, an automatic control of the restriction that there is no interpenetration between two rigid bodies when they colide. This automatic treatment in general is not provided by existing computer animation systems. The work presents the prototype developed for validating the solutions given to the problems of motion control and collisions treatment, as well as its application in the production of animated sequences. The text ends with comments on extension of the present work from the approach given to the problem of simulating the behavior of objects in a certain virtual world allowing the incorporation of other characteristics to the objects: elasticity, to model deformations, and articulations, for the production of articulated movements with different degrees of freedom.