Modelagem geométrica envolvendo objetos implícitos é um tema de intensa pesquisa em Computação Gráfica. Portanto, obter técnicas eficientes para representar esses objetos é de extrema importância. Dois grupos de objetos implícitos relevantes para Computação Gráfica são as curvas implícitas e superfícies implícitas. As técnicas tradicionais para se aproximar curvas e superfícies implícitas envolvem dividir o domínio e buscar em suas partições partes da curva ou da superfície. Neste projeto propomos um novo métodos de poligonização robusta de curvas implícitas usando uma ferramenta numérica auto-validada chamada de Aritmética Afim. O método consiste na poligonização adaptativa de curvas implícitas em malhas triangulares tridimensionais. / Geometric modeling involving implicit objects is a topic of intense research in Computer Graphics. Thus, obtain efficient techniques for representing these objects is of utmost importance. Two groups of relevant implicit objects for Computer Graphics are implicit curves and implicit surfaces. Traditional techniques for approximating implicit curves and surfaces involve splitting the domain and searching for parts of the curve or the surface. In this project we propose a new methods of robust polygonization of implicit curves using the self-validated numerical tool called Affine Arithmetic. The method consists in the adaptive polygonization of implicit curves in three-dimensional triangular meshes.

[pt] Técnicas de visualização científica criam imagens na tentativa de revelar estruturas e fenômenos complexos. Técnicas ilustrativas têm sido incorporadas aos sistemas de visualizacão científica para melhorar a expressividade de tais imagens. A visualização de linhas caracteríticas é uma técnica importante para transmitir uma melhor informacão sobre a forma das superfícies. Neste trabalho, propomos combinar visualização volumétrica de malhas não estruturadas com isosuperfícies ilustradas. Isto é feito estendendo um algoritmo de traçado de raio em GPU para incorporar ilustração com linhas de variação extrema da iluminação(photic extremum lines), um tipo de linha característica que captura mudanças bruscas de luminância, revelando formas de um jeito perceptualmente correto. / [en] Scientic visualization techniques create images attempting to reveal complex structures and phenomena. Illustrative techniques have been incorporated to scientic visualization systems in order to improve the expressiveness of such images. The rendering of feature lines is an important technique for better depicting surface shapes and features. In this thesis, we propose to combine volume visualization of unstructured meshes with illustrative isosurfaces. This is accomplished by extending a GPU-based ray-casting algorithm to incorporate illustration with photic extremum lines, a type of feature lines able to capture sudden changes of luminance, conveying shapes in a perceptually correct way.

This work examines the feasibility of a novel high-order numerical method, which has been termed Flux Correction. It has been given this name because it "corrects" the flux terms of an established numerical method, cancelling various error terms in the fluxes and making the method higher-order. In this work, this change is made to a traditionally second-order finite volume Galerkin method. To accomplish this, higher-order gradients of solution variables, as well as gradients of the fluxes are introduced to the method. Gradients are computed using lagrange interpolations in a fashion reminiscent of Finite Element techniques. For the Euler Equations, Flux Correction is compared against Flux Reconstruction, a derivative of the high-order Discontinuous Galerkin and Spectral Difference methods, both of which are currently popular areas of research in high-order numerical methods. Flux Correction is found to compare favorably in terms of accuracy, and exceeds expectations for convergence rates. For the full Navier-Stokes Equations, the effect of curved elements on Flux Correction are examined. Flux Correction is found to react negatively to curved elements due to the gradient procedure's poor handling of high-aspect ratio elements.

Cílem mé disertační práce je analyzovat a vyvinout parametrizační metodu pro 2D a 3D tvarové optimalizace v kontextu průmyslového aerodynamického návrhu letounu založeném na CFD simulacích. Aerodynamická tvarová optimalizace je efektivní nástroj, který si klade za cíl snížení nákladů na návrh letounů. Nástroj založený na automatickém hledání optimálního tvaru. Klíčovou částí úspěšného optimalizačního procesu je použití vhodné parametrizační metody, metody schopné garantovat možnost dosažení optimálního tvaru. Parametrizační metody obecně používané v oblasti aerodynamické tvarové optimalizace momentálně nejsou připravený na komplikované průmyslové aplikace vyskytující se u moderních dopravních letounů, které mají šípová zalomená křídla s winglety a motorovými gondolami, přechodové prvky spojující např. trup s křídlem atd.. Existuje tedy potřeba nalezení obecné parametrizační metody, která bude aplikovatelná na širokou škálu různých geometrických tvarů. Free-Form Deformation (FFD[1]) parametrizace může, vzhledem ke svým schopnostem při zacházení s geometrií, být odpovědí na tuto potřebu. Adaptivní parametrizace by se měla být schopna automaticky přizpůsobit danému tvaru tak, aby byly její kontrolní body vhodně rozmístěny. Což umožní dostatečnou kontrolu deformací objektu, která zaručí možnost vytvoření optimálního tvaru objektu a splnění geometrických omezení. Primární aplikací takové parametrizační metody je deformace tvaru objektu. Dalším navrhovaným cílem je modifikace FFD parametrizační metody pro současné deformace tvaru objektu a CFD výpočetní sítě, umožnující velké deformace objektu při zachování kvality výpočetní sítě.

Finite element analysis depends greatly upon a high-quality mesh to be able to provide reasonably accurate answers to engineering problems. Models that need to be analyzed using finite element analysis are becoming increasingly more complex, and correspondingly harder to mesh with good quality. Skew is one quality metric which can cause problems with finite element analyses. This thesis explains how skew is calculated, discusses two common sources of skew: multiply-linked surfaces with interval constraints, and biased edge meshes. Two methods of lessening skew in surface meshes are then presented: the skew control algorithm, and the curve morphing algorithm. These algorithms are discussed in detail, with representative graphics. Examples which demonstrate the skew which arises from the above-mentioned sources are presented. These models are then subjected to the algorithms discussed in the thesis, and a comparison of the skew measure for each example is presented. Finally, areas of possible future work are presented and the possible detrimental effects that the skew control algorithm can exert on the quality metrics of aspect ration and mesh size gradation are discussed.

[pt] Malhas são amplamente usadas na discretização de domínios geométricos em aplicações na engenharia, como simulações de fluxo, transmissão de calor e deformação mecânica. O problema de geração de malhas é bem conhecido e estudado, mas a geração automática de malhas para um domínio físico com geometrias complexas, criando elementos que obedeçam a forma do objeto, e de tamanho e qualidade adequados, ainda é um desafio. Neste trabalho, foram estudados e implementados métodos para gerar malhas com restrições arbitrárias. O gerador implementado é do tipo de Delaunay, que constrói malhas Delaunay com restrições, e utiliza as propriedades da malha para inserir novos vértices e melhorar a qualidade dos elementos. / [en] Meshes are widely used in the discretization of geometric domains for engineering applications such as fluid flow simulator, heat transfer simulations and mechanical deformation. The mesh generation problem is well known and studied, nevertheless the automatic generation of meshes to domains with complex geometry, creating elements that conform to the forms, and of adequate size and quality, is still a challenge. In this work, mesh generation methods capable of generation mesh of arbitrary restrictions were studied and implemented. The implemented generator is a Delaunay generator, which constructs constrained Delaunay meshes, and utilizes the properties of the mesh to insert new vertices and improve the quality of the elements.

This paper presents a robust and artist driven method for fracturing a surface polyhedral mesh via fracture maps. A fracture map is an undirected simple graph with nodes representing positions in UV-space and fracture lines along the surface of a mesh. Fracture maps allow artists to concisely and rapidly define, edit, and apply fracture patterns onto the surface of their mesh. The method projects a fracture map onto a polyhedral surface and splits its triangles accordingly. The polyhedral mesh is then segmented based on fracture lines to produce a set of independent surfaces called fracture components, containing the visible surface of each fractured mesh fragment. Subsequently, we utilize a Voronoi-based approximation of the input polyhedral mesh’s medial axis to derive a hidden surface for each fragment. The result is a new watertight polyhedral mesh representing the full fracture component. Results are aquired after a delay sufficiently brief for interactive design. As the size of the input mesh increases, the computation time has shown to grow linearly. A large mesh of 41,000 triangles requires approximately 3.4 seconds to perform a complete fracture of a complex pattern. For a wide variety of practices, the resulting fractures allows users to provide realistic feedback upon the application of extraneous forces.

No / The development and validation of a sensor for extrusion melt temperature field measurement is described. A grid of opposing thermocouple wires was constructed and held in position by a supporting frame. Wires were joined together at crossing points to form thermocouple junctions, which were computer monitored. The mesh was used to monitor melt temperature fields during single screw extrusion at the die entrance. Design and construction of the mesh is described in addition to experimental optimization of wire diameter and junction forming. Calibration of the sensor and potential measurement errors including shear heating effects are discussed. Initial results from single screw extrusion are presented for a commercial grade of low density polyethylene using five- and seven-junction thermocouple meshes. The dependence of melt temperature profile on screw speed is illustrated. At low screw speeds melt temperature profiles were flat in shape and higher than set wall temperatures. At higher screw speeds the profiles became more pointed in shape. Use of higher resolution sensors exposed more complex temperature profiles with shoulder regions.

No / Polymer extrusion is fundamental to the processing of polymeric materials and melt flow temperature homogeneity is a major factor which influences product quality. Undesirable thermal conditions can cause problems such as melt degradation, dimensional instability, weaknesses in mechanical/optical/geometrical properties, and so forth. It has been revealed that melt temperature varies with time and with radial position across the die. However, the majority of polymer processes use only single-point techniques whose thermal measurements are limited to the single point at which they are fixed. Therefore, it is impossible for such techniques to determine thermal homogeneity across the melt flow. In this work, an extensive investigation was carried out into melt flow thermal behavior of the output of a single extruder with different polymers and screw geometries over a wide range of processing conditions. Melt temperature profiles of the process output were observed using a thermocouple mesh placed in the flow and results confirmed that the melt flow thermal behavior is different at different radial positions. The uniformity of temperature across the melt flow deteriorated considerably with increase in screw rotational speed while it was also shown to be dependent on process settings, screw geometry, and material properties. Moreover, it appears that the effects of the material, machine, and process settings on the quantity and quality of the process output are heavily coupled with each other and this may cause the process to be difficult to predict and variable in nature. (C) 2013 Society of Plastics Engineers

No / Polymer extrusion is an energy intensive process, which is often run at less than optimal conditions. The extrusion process consists of gradual melting of solid polymer by thermal conduction and viscous shearing between a rotating screw and a barrel; as such it is highly dependent upon the frictional, thermal and rheological properties of the polymer. Extruder screw geometry and extrusion variables should ideally be tailored to suit the properties of individual polymers, but in practice this is rarely achieved due to the lack of understanding of the process. Here, in-process monitoring techniques have been used to characterise the thermal dynamics of the extrusion process. Novel thermocouple grid sensors have been used to measure melt temperature fields within flowing polymer melts at the entrance to an extruder die in conjunction with infra-red thermometers and real-time quantification of energy consumption. A commercial grade of polyethylene has been examined using three extruder screw geometries at different extrusion operating conditions to understand the process efficiency. Extruder screw geometry, screw rotation speed and set temperature were found to have a significant effect on the thermal homogeneity of the melt and process energy consumed. (C) 2012 Elsevier Ltd. All rights reserved.