Este trabalho apresenta uma técnica para deformação interativa de objetos 3D não estruturados que combina o uso de sketches em 2D e manipulação interativa de curvas. Através de sketches no plano de imagem, o usuário cria curvas paramétricas a serem usadas como manipulares para modificar a malha do objeto. Um conjunto de linhas desenhadas sobre a projeção do modelo pode ser combinado para criar um esqueleto composto de curvas paramétricas, as quais podem ser interativamente manipuladas, deformando assim a superfície associada a elas. Deformações livres são feitas movendo-se interativamente os pontos de controle das curvas. Alguns outros efeitos interessantes, como torção e escalamento, são obtidos operando-se diretamente sobre o campo de sistemas de coordenadas criado ao longo da curva. Um algoritmo para evitar inter-penetrações na malha durante uma sessão de modelagem com a técnica proposta também é apresentado. Esse algoritmo é executado a taxas interativas assim como toda a técnica apresentada neste trabalho. A técnica proposta lida naturalmente com translações e grandes rotações, assim como superfícies não orientáveis, não variedades e malhas compostas de múltiplos componentes. Em todos os casos, a deformação preserva os detalhes locais consistentemente. O uso de curvas esqueleto permite implementar a técnica utilizando uma interface bem intuitiva, e provê ao usuário um controle preciso sobre a deformação. Restrições sobre o esqueleto e deformações sem inter-penetrações são facilmente conseguidos. É demonstrada grande qualidade em torções e dobras nas malhas e os resultados mostram que a técnica apresentada é consideravelmente mais rápida que as abordagens anteriores, obtendo resultados similares. Dado seu relativo baixo custo computacional, esta abordagem pode lidar com malhas compostas por centenas de milhares de vértices a taxas interativas. / This work presents a technique for interactive shape deformation of unstructured 3D models, based on 2D sketches and interactive curve manipulation in 3D. A set of lines sketched on the image plane over the projection of the model can be combined to create a skeleton composed by parametric curves, which can be interactively manipulated, thus deforming the associated surfaces. Free-form deformations are performed by interactively moving around the curves’ control points. Some other interesting effects, such as twisting and scaling, are obtained by operating directly over a frame field defined on the curve. An algorithm for mesh local self-intersection avoidance during model deformation is also presented. This algorithm is executed at interactive rates as is the whole technique presented in this work. The presented technique naturally handles both translations and large rotations, as well as non-orientable and non-manifold surfaces, and meshes comprised of multiple components. In all cases, the deformation preserves local features. The use of skeleton curves allows the technique to be implemented using a very intuitive interface, and giving the user fine control over the deformation. Skeleton constraints and local self-intersection avoidance are easily achieved. High-quality results on twisting and bending meshes are also demonstrated, and the results show that the presented technique is considerably faster than previous approaches for achieving similar results. Given its relatively low computational cost, this approach can handle meshes composed by hundreds of thousand vertices at interactive rates.

Diagnostic ultrasound has become invaluable to healthcare professions for the purpose of imaging soft tissue without the risk of exposure to damaging, ionizing radiation. However, the majority of commercially available transducers have rigid, fixed interfaces that cannot conform to the surface of the human body. Such limitations both introduce a potential air gap (requiring the application of ultrasound gel) and make long-term monitoring impractical. In this work, I propose a novel flexible 2D ultrasound phased array with adaptive phasing that is capable of compensating for the radius of curvature. I describe the phasing algorithm and illustrate the detrimental effect of a lack of phase correction through simulation. I conduct phase detection by using time of arrival (TOA) without additional external hardware. In addition to simulations, I provide details of the fabrication process of a flexible 16 by 16 element array. The manufactured array, with an operating frequency of 1.4MHz and bandwidth of 41.3%, was capable of generating pressures up to 600 kPa. Finally, I conduct an in-vivo human study to demonstrate the functionality of the array on a human humerus. Although visible without phase correction, the location of the bone can easily be tracked in real-time after applying the correction algorithm.

The design of curves and surfaces in C.A.D. systems has many applications in car, plane or ship industry. Because they offer more flexibility, rational functions are often preferred to polynomial functions to modelize curves and surfaces. In this work, several methods to generate rational Bezier curves and surfaces which minimize some functionals are proposed. The functionals measure a technical smoothness of the curves and surfaces, and are related to the energy of beams and plates in the sense of the elasticity theory.

Les environnements CAO fournissent des outils puissants pour la programmation graphique et la manipulation d’entités géométriques complexes. Dans cette thèse, nous proposons d’exploiter ce potentiel dans le domaine de la conception de robots parallèles. Ces robots sont considérés comme une alternative intéressante vis-à-vis de leurs homologues sériels dans différentes applications comme le « pick and place » et l’usinage. Cependant, leur utilisation industrielle est encore restreinte en raison d’un espace de travail limité, de modèles géométriques difficiles à résoudre et l’existence de configurations singulières délimitant leur domaine d’exploitation. L’analyse et la caractérisation de l’espace de travail jouent alors un rôle fondamental dans la phase de conception de robots manipulateurs parallèles. Dans ce travail de thèse, nous proposons des approches géométriques originales donnant lieu à un ensemble de méthodes et techniques basées CAO pour l’analyse et la caractérisation de l’espace de travail de robots parallèles plans et spatiaux. L’espace de travail est généré comme un solide dans l’environnement CAO à partir d’un paramétrage géométrique, d’esquisses et d’opérations élémentaires telles que le balayage hélicoïdal et l’intersection. Nous avons montré que ces méthodes constituent des outils pertinents et efficaces d’aide à la conception des mécanismes parallèles. Ils permettent également la résolution du problème géométrique direct et la génération de trajectoires libres de singularités. Plusieurs types de manipulateurs ont été considérés dans ce travail pour mettre en avant et illustrer les techniques CAO / Géométriques proposées : robots parallèles plans à 3 degrés de mobilité de type 3-RPR, 3-RRR, 3-PPR et 3-PRR, robots parallèles spatiaux à 6 degrés de mobilité de type ou 3-CRS ou 3-PRRS. / CAD environments provide very powerful tools for graphical programming and manipulation of complex geometric entities. In this thesis, we propose to exploit such potential in the design of parallel robots. These robots are considered an attractive and important alternative towards their serials counterparts in various applications, like “pick and place” and machining. However, their industrial applications are restricted due to limited workspace, complexity related to resolution of the direct geometric model, and in addition the existence of the singular configurations which bound their application field. The analysis and the characterization of the workspace therefore play an essential role in the design phase of parallel robotic manipulators. In this thesis, we suggest original geometric approaches giving rise to a set of methodologies and techniques based on the use of CAD in order to analyze and characterize the workspace of planar and spatial parallel robotic manipulators. Workspace is generated as a solid in CAD environment by using a parametric geometric model, sketches, and elementary operations such as helical scanning and performing then Boolean intersection operation. We have shown in this thesis, that the proposed methodologies represent relevant and efficient tools which assist designers of parallel mechanisms. Moreover, they allow us to solve the direct geometric problem and to plan singularity-free trajectories. Several types of robotic manipulators have been considered in this work to highlight and illustrate the proposed CAD / Geometric techniques : planar parallel manipulators having three degree of freedom such as 3-RPR, 3-RRR, 3-PPR, and 3-PRR, and spatial parallel robotic manipulators having six degree of freedom 3-CRS-type.

In the first part I discuss ancestors of NURBS curves and surfaces, rather Ferguson, Beziere, Coons and B-spline curves and surfaces and furthermore B-spline functions. In the second part I devote to NURBS curves and surfaces, their description as a linear combination of B-spline functions in the projective space. I specify conical arcs more detailed, their submit in the projective space and NURBS surfasec given as tensor product of NURBS curves. Last part is devote to describtion programs for modeling conicals and NURBS surface.