Geometric trimming of surfaces results in a new mathematical description of the matching surface. This matching surface is required to closely resemble the remaining portion of the original surface. Typically, the approximation error in such cases is measured with a view to minimize it. The data associated with the error between two matching surfaces is large and needs to be filtered into meaningful information.This research looks at suitable norms for achieving this data reduction or abstraction with a view to provide quantitative feedback about the approximation error. Also, the differences between geometric shapes are easily discerned by the human eye but are difficult to characterize or describe. Error visualization tools have been developed to provide effective visual inputs that the designer can interpret into meaningful information. / Master of Science

The contributions of this dissertation can be divided into three primary foci: input waveform optimization, the modeling and optimization of fish-like robots, and experiments on a flapping wing robot. Novel contributions were made in every focus. The first focus was on input waveform optimization. This goal of this research was to develop a means by which the optimal input waveforms can be selected to vibrationally stabilize a system. Vibrational stabilization is the use of high-frequency, high-amplitude periodic waveforms to stabilize a system about a desired state. The contributions presented herein develop a technique to choose the ``best" input waveform and a discussion of how the ``best" input waveform changes with the definition of ``best." The next focus was the optimization of a fish-like robot. In order to optimize such robots, a new model for fish-like locomotion is developed. An optimization technique that uses numerous simulations of fish-like locomotion was used to determine the best gaits for traveling at various speeds. Based on these results, trends were found that can determine the optimal gait using a couple relatively simple functions. The final focus was experimentation on a flapping wing robot in a wind tunnel. These experiments determined the performance of the flapping wing robot at a variety of flight conditions. The results of this research were presented in manner that is accessible to the larger aircraft design community rather than only to those specializing in flapping flight. / Ph. D.

Given a set of n points on a plane, in the Minimum Weight Triangulation problem, we wish to find a triangulation that minimizes the sum of Euclidean lengths of its edges. The problem has been studied for more than four decades and is known to be incredibly challenging. In fact, the complexity status of this problem remained open until recently when it was shown to be NP-Hard. We present a novel polynomial-time algorithm that computes a 16-approximation of the minimum weight triangulation---a constant that is significantly smaller than what has been previously known. To construct our candidate solution, our algorithm uses grids to partition edges into levels by increasing weights, so that edges with similar weights appear in the same level. We incrementally triangulate the point set by constructing a growing partial triangulation for each level, introducing edges in increasing order of level. At each level, we use a variant of the ring heuristic followed by a greedy heuristic to add edges, finally resulting in a complete triangulation of the point set. In our analysis, we reduce the problem of comparing the weight of the candidate and the optimal solutions to a comparison between the cardinality of the two underlying graphs. We develop a new technique to compare the cardinality of planar straight-line graphs, and in combination with properties due to the imposed grid structure, we bound the approximation ratio. / Master of Science

There is frequently a need for algorithms capable of automatic modification of geometric models in response to manufacturing process constraints. Designers typically initiate product models using ideal, exact geometry; however, several non-traditional manufacturing processes frequently require slight modifications to the ideal model to accommodate various manufacturing process constraints. These modifications can be difficult, complex, and tedious to compute. For instance, metal-ceramic brazing requires adjustments to the part geometry primarily to accommodate thermal expansion and to allow for the insertion of a narrow braze-filler gap. These adjustments depend on the particular geometry, material properties, and processing parameters. Any modification to these product model parameters necessitates extensive recomputation to reestablish a manufacturable part geometry. This thesis demonstrates in part the integration of geometry into the overall product model by having the non-geometric parts of the product model provide feedback to the geometry by means of automatically modifying its shape. The methodology is demonstrated in a prototype model which introduces the concept of auxiliary geometric structures. In particular, the auxiliary geometric structures provide a mapping between the designer's intent and the part geometry described in the solid model. The designer's intent is represented in a rule base for metal-ceramic brazing that is controlled by fuzzy logic. This rule base aids the user in quantifying and generating from the auxiliary geometric structures the geometric modifications needed to conform with a complex set of rules derived from both analytic and empirical work in metal-ceramic brazing / Master of Science

Reinforced concrete (RC) shear wall buildings constitute a significant portion of the building inventory in many earthquake-prone regions. A similar type of structural system is fully-grouted reinforced masonry (RM) shear wall structures. The accurate determination of the nonlinear response of reinforced concrete and reinforced masonry (RC/RM) walls subjected to lateral loading is of uttermost importance for ensuring the safety of the built environment. Analytical models provide a cost efficient and comprehensive tool to study the nonlinear response of RC/RM structures, as compared to experimental tests. Predictive models should capture nonlinear material behavior as well as the geometrically nonlinear response of RC/RM shear wall structures during major seismic events. This thesis outlines the formulation and validation of a nonlinear shell element for the simulation of RC/RM structures. The proposed shell element enhances an existing formulation of a four-node Discrete Kirchhoff shell element through the inclusion of a corotational approach to account for geometric nonlinearities and of nonlinear material models to capture the effect of cracking and crushing in concrete or masonry and the nonlinear hysteretic behavior of reinforcing steel. The analytical results obtained from multiple linear and nonlinear analyses are compared against theoretical solutions and experimental test data. These comparative validation studies show the enhanced shell element can satisfactorily capture the salient features of the response of nonlinear reinforced concrete/masonry shear wall structures including axial-shear-flexure interaction, damage patterns, and in-plane and out-of-plane loading. / Master of Science

Many problems in geometric measure theory are centered around finding conditions and structures on a set to guarantee that its distance set must be large. Two notions of structure that are of importance in this work are Hausdorff dimension and thickness. Recent progress has been made on generalizing the notion of thickness so part of this work also generalizes previous results using this new upgraded version of thickness. We also show why a famous conjecture about distance sets does not hold on the real line and thus, why this conjecture needs to happen in higher dimensions. Furthermore, we give explicit distance set and thickness calculations for a special class of self-similar sets. / Master of Science / Part of the study of geometric measure theory is centered around creating interesting structures to place on a set and determining what sort of threshold on that structure allows you to guarantee that some interesting geometric property exists for that set. An example of this is determining when you can guarantee that a set contains many unique distances between elements in that set. This work presents various types of structures that help to investigate the problem of when you can guarantee that a set has the previously mentioned geometric property.

This study investigated perceptual and cognitive issues relating to manipulations in geometric field-of-view (GFOV) in perspective displays and the effects of incorporating virtual environment enhancements in the interface based on visual momentum (VM) techniques. Geometric field-of view determines the field-of-view (FOV) for perspective displays. Systematic errors in size and distance have been shown to occur in perspective displays as the result of changes in the GFOV. Furthermore, as humans' normal FOV becomes restricted, their ability to acquire spatial information is reduced resulting in a incomplete formulation and representation of the visual world. The magnitude of the resulting biases increase as task difficulty increases. It was predicted that as VM increases in the interface, the ability to overcome problems associated with restricted FOVs will also increase. Sixty participants who were pre-tested for spatial ability were required to navigate through a virtual office building while estimating space dimensions and performing spatial orientation and representation tasks. A 3 x 2 x 2 mixed-subjects design compared three levels of GFOV, two levels of VM, and two levels of Difficulty. The results support the hypothesis that 60° is the optimum GFOV for perspective displays. VM increased accuracy for space dimension estimates, reduced direction judgment errors, improved distance estimates when task difficulty was increased, improved participants' cognitive maps, and reduced the error for reconstructing the spatial layout of objects in a virtual space. The results also support the hypothesis that wider FOVs are needed to accurately perform spatial orientation and representation tasks in virtual environments. Spatial ability was also shown to influence performance on some of the tasks in this experiment. This study effectively demonstrates that the spatial characteristics of architectural representations in perspective displays are not always accurately perceived. There is a clear tradeoff for setting GFOV in perspective displays: A 60° GFOV is necessary for perceiving the basic characteristics of space accurately; however, if spatial orientation and representation are important, a 90° FOV or larger is required. To balance this tradeoff if symbolic enhancements are included in the virtual environment, such as VM techniques, larger FOVs are less of a concern. / Master of Science

Este trabalho visa resgatar a importância do ensino do desenho geométrico em especial dos Métodos dos Lugares Geométricos, aplicado à resolução de problemas de construção geométrica plana. A abordagem apresentada é tradicional, com o uso da régua e do compasso. Nesse sentido, o trabalho é composto da apresentação(conceito e construção), de vários Lugares Geométricos que podem ser considerados fundamentais para a resolução de problemas elementares de Desenho Geométrico, e a apresentação de construções das cônicas como algo mais elaborado destes lugares geométricos considerados fundamentais. Para a fixação dos conceitos, cada Lugar Geométrico (L.G.) contará com alguns exemplos de aplicação e, ao final dos capítulos, serão apresentados alguns exercícios propostos (para o leitor que se interessar em praticar os conceitos e as construções abordadas). Finalizando será feito um breve comentário das origens do desenho geométrico, bem como seu ensino no Brasil, evidenciando a resolução de problemas como método eficaz para o ensino da geometria. / This study reviews the importance of education in special geometric design of the \"Methods of Geometric Places\", applied to the resolution of flat geometric construction problems. The presented approach is traditional, using ruler and compass. In this sense, the work consists of the presentation (concept and construction), several Geometric places that may be considered fundamental to solving elementary geometric design problems, and the presentation of conical constructions as something more elaborate of these loci considered fundamental. For fixing the concepts, each geometric place will feature some application examples and at the end of chapters, some proposed exercises will be presented ( to the reader who is interested iun practing the concepts and addressed buildings). Finalizing will be a brief review of the origins of geometric design and its teaching in Brazil, emphasizing problem solving as an effective method for teaching geometry.

Neste estudo é proposto um método para resolução de problemas de tangências, especificamente para o décimo caso do problema de Apolônio. Este método é baseado na transformação geométrica inversão e no uso do conceito de feixes de circunferências. Além de permitir a resolução de todas as configurações do problema, ele é aplicável também à resolução de outros problemas. Através do trabalho indicamos a importância do tema Desenho Geométrico no ensino de Desenho que há muito tempo enfatiza apenas o desenvolvimento da visualização espacial. Destacamos ao longo do texto como o ensino de Desenho Geométrico pode ser utilizado eficazmente para fomentar o raciocínio lógico-dedutivo dos estudantes através da prática de demonstrações. / A new method to solve the tenth case of Appolonius problem is presented in this study. This method is based on the geometric transformation called inversion and the concept of coaxal circumferences. Besides allowing the resolution of all configurations of the problem, it can also be used to solve other problems. We indicate the importance of the subject about geometric constructions in teaching Drawing, which, since a long time ago has given attention only to the development of the spatial visualization ability. We detach along the text how the teaching of geometric construction can be used efficiently to foment the deductive logical reasoning of the students through the practice of demonstrations.

Submitted by Jean Medeiros (jeanletras@uepb.edu.br) on 2016-04-20T11:50:55Z No. of bitstreams: 1 PDF - Sérgio da Silva Minzé.pdf: 2924730 bytes, checksum: 91c88e23d644d6880c14d62c4d7cfd74 (MD5) / Approved for entry into archive by Secta BC (secta.csu.bc@uepb.edu.br) on 2016-07-22T20:26:16Z (GMT) No. of bitstreams: 1 PDF - Sérgio da Silva Minzé.pdf: 2924730 bytes, checksum: 91c88e23d644d6880c14d62c4d7cfd74 (MD5) / Approved for entry into archive by Secta BC (secta.csu.bc@uepb.edu.br) on 2016-07-22T20:26:23Z (GMT) No. of bitstreams: 1 PDF - Sérgio da Silva Minzé.pdf: 2924730 bytes, checksum: 91c88e23d644d6880c14d62c4d7cfd74 (MD5) / Made available in DSpace on 2016-07-22T20:26:23Z (GMT). No. of bitstreams: 1 PDF - Sérgio da Silva Minzé.pdf: 2924730 bytes, checksum: 91c88e23d644d6880c14d62c4d7cfd74 (MD5) Previous issue date: 2015-05-29 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This work aims to develop a didatic sequence for the student can learn inductively the notion of convergent geometric series. The proposal was applied and developed in a class of 9th grade ofelementary school and the results obtainedwere very satisfactory. The work also contains a historical review of the concepts of sequences and geometric series. / Este trabalho tem como objetivo desenvolver uma sequência didática para que o aluno consiga aprender de forma indutiva a noção de série geométrica convergente. A o proposta foi aplicada e desenvolvida em uma turma do 9 ano do ensino fundamental e os resultados obtidos foram muito satisfatórios. O trabalho também contém uma resenha histórica dos conceitos de sequências e séries geométricas.