This paper describes an intuitive way of defining geometry design variables for solving structural topology optimization problems using a genetic algorithm (GA). The geometry representation scheme works by defining a skeleton that represents the underlying topology/connectivity of the continuum structure. As the effectiveness of any GA is highly dependent on the chromosome encoding of the design variables, the encoding used here is a directed graph which reflects this underlying topology so that the genetic crossover and mutation operators of the GA can recombine and preserve any desirable geometric characteristics through succeeding generations of the evolutionary process. The overall optimization procedure is tested by solving a simulated topology optimization problem in which a 'target' geometry is pre-defined with the aim of having the design solutions converge towards this target shape. The procedure is also applied to design a straight-line compliant mechanism : a large displacement flexural structure that generates a vertical straight line path at some point when given a horizontal straight line input displacement at another point. / Singapore-MIT Alliance (SMA)

Submitted by Maria Aparecida (cidazen@gmail.com) on 2017-07-17T13:37:47Z No. of bitstreams: 1 Rodinely Mendes.pdf: 747062 bytes, checksum: 8d872de2414320c64b8f55c204d1f3d1 (MD5) / Made available in DSpace on 2017-07-17T13:37:47Z (GMT). No. of bitstreams: 1 Rodinely Mendes.pdf: 747062 bytes, checksum: 8d872de2414320c64b8f55c204d1f3d1 (MD5) Previous issue date: 2016-09-30 / We present a vector approach of the complex numbers, and using its associated geometry, we discuss and solve several problems of the plane analytical geometry. Moreover, we prove and treat the elementary properties of the complex numbers in this context. / Apresentamos uma abordagem vetorial dos números complexos, e usando sua geometria associada, discutimos e resolvemos diversos problemas da geometria analítica plana. Além disso, demonstramos e interpretamos propriedades elementares dos números complexos neste contexto.

Die Durchdringung von Kuben ist in den vergangenen Jahren eines meiner Themen. Ausgehend von platonischen Körpern bildet der Tetraeder die “Stella Octangula“ aus zwei Tetraedern. Den doppelten Kubus habe ich bei der Zirkelkonstruktion der Blume des Lebens entdeckt. Durch abwechselnde Faltung des Zeichenblattes durch den Mittelpunkt, entlang der Linien zu den Ecken des Sechsecks, entfaltet sich ein Stern. Zwei Sterne fügen sich zu zwei Würfeln. Aus einer “BdL“ lassen sich die Pyramide, Ikosaeder, Tetraeder und ein Fünfeck ablesen. Die Verbindung von zwei BdL-Konstruktionen lässt einen Doppelwürfel entstehen. Zwei Würfel beinhalten eine regelmäßige hexagonale Fäche. Die Außenmaße sind in einem Würfel enthalten.

CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / Este trabalho à uma proposta de abordagem de problemas de geometria plana, nas turmas olÃmpicas de matemÃtica no ensino bÃsico, tendo como base o uso de vetores para resolver esses problemas. Os vetores oferecem novas ferramentas de exploraÃÃo da geometria plana e de suas propriedades. Com o uso de vetores, as demonstraÃÃes das proposiÃÃes da geometria tornam-se bem mais simples. O propÃsito à introduzir os vetores nas turmas que estÃo saindo do ensino fundamental, para o ensino mÃdio e mostrar a importÃncia dos vetores para resolver problemas de geometria plana. Usaremos, as diversas formas de representaÃÃo dos vetores e suas propriedades na demonstraÃÃo, de resultados e na resoluÃÃo de problemas de geometria. Um modelo conceitual serà postulado e fundamentado para que os alunos tenham contato com esses instrumentais. Acreditamos que fazendo a articulaÃÃo entre a representaÃÃo geomÃtrica e a representaÃÃo algÃbrica de uma forma mais natural possÃvel, o estudo da geometria plana como uso de vetores facilitarà o nÃvel de aprendizagem dos alunos, uma vez que conhecerà novas ferramentas para resolver problemas. / This work is a proposal of problems in plane geometry Olympic math classes in basic education approach based on the use of vectors to solve these problems. The arrays offer new tools for exploration of plane geometry and its properties. Using vectors demonstrations of the propositions of geometry become much simpler. The purpose is to introduce vectors into classes that are coming out of elementary school to high school and show the importance of vectors to solve problems of plane geometry. We will use various forms of representation of vectors and their properties in the income statement and solving geometry problems. A conceptual model is postulated and substantiated for students to have contact with these instruments. We believe that making the link between the geometric representation and the algebraic representation of a most natural way possible the study of plane geometry using vectors facilitate the learning level of the students, since meet new tools to solve problems.

This dissertation proposes to present an extra tool to be worked with high school students as regards the study of conics, and for that we will use the geometric structures that the complex number of numbers o er mainly when the We use it to represent and classify conics in a reduced way, even when they do not have their axes parallel to the axes of the Cartesian plane. We will also do a case study on the teaching of these contents in high school where we will re ect from the di culties experienced by mathematics teachers in high school. / Essa dissertação propõe apresentar uma ferramenta a mais para ser trabalhado com os alunos do ensino médio no tocante ao estudo das cônicas, e para isso usaremos as estruturas geométricas que o conjunto dos números complexos oferecem, principalmente quando o utilizamos para representar e classi car as cônicas de forma reduzida, mesmo quando estas n~ao possuem seus eixos paralelos aos eixos do plano cartesiano. Faremos tamb em um estudo de caso sobre o ensino desses conte udos no ensino m edio onde re etiremos a partir das di culdades vividas pelos professores de matem atica no ensino m edio. / São Cristóvão, SE

This work presents an overview of the simultaneous localisation and mapping (SLAM) problem in the mobile robotics. The Extended Kalman filter (EKF) based algorithm for localisation and mapping is proposed. For EKF algorithm the models of the skid steering mobile robot and the laser scanner are presented. The EKF algortihm is feature based algorithm, therefore the method for the landmark position determination was developed. This segmentation method is based on the clustering of the Radon transform space. Proposed SLAM algorithm was tested with real data measured with UTAR mobile platform. Achievments of the work are summarized in the conclusion of the proposed work and possible improvements of the components are suggested.

This study introduces an innovative approach to address a complex, real-world packing problem experienced at Emerson Rosemount Tank Radar. The objectives of the study are manifold: primarily, the optimization of packing efficiency within specified geometric and box constraints, and secondarily, the fulfillment of specific packing objectives. The proposed approach comprises the creation of a distinct placement policy, termed the "Constraint Placement Policy". This policy integrates elements of greedy, bottom-left, and proximity-based alignment heuristics to proficiently guide the packing process. Furthermore, to augment the search for the most efficient packing configurations, a genetic algorithm is designed. The genetic algorithm leverages a three-layered chromosome representation for item sequence, rotation sequence, and box sequence, enabling a flexible and dynamic optimization process. Additionally, this study provides a comprehensive analysis of various metaheuristics, highlighting their relevance and applicability in resolving packing problems. It also devises an automated method to extract model code indices, thereby aiding the creation of a component database for Emerson's products. Thereafter, the packing problem is formulated, considering geometric constraints, box constraints, and packing objectives, which significantly affect the overall efficiency and safety of the packing process.The performance of the packaging algorithm is critically evaluated against shipping data. This comparison accentuates the efficacy of the custom heuristic placement policy and the genetic algorithm, particularly focusing on the genetic algorithm capacity to adapt and optimize packing configurations. A contrast between the proposed hybrid approach and conventional packing methods is also provided, illuminating the strengths and limitations of the proposed solution. The results of this study have considerable implications for Emerson's packing process. Not only does it enhance current packing efficiency, but it also proffers valuable insights for potential future improvements in the industrial packing domain.

Le réalisme des images en infographie exige de créer des objets (ou des scènes) de plus en plus complexes, ce qui entraîne des coûts considérables. La modélisation procédurale peut aider à automatiser le processus de création, à simplifier le processus de modification ou à générer de multiples variantes d'une instance d'objet. Cependant même si plusieurs méthodes procédurales existent, aucune méthode unique permet de créer tous les types d'objets complexes, dont en particulier un édifice complet. Les travaux réalisés dans le cadre de cette thèse proposent deux solutions au problème de la modélisation procédurale: une solution au niveau de la géométrie de base, et l’autre sous forme d'un système général adapté à la modélisation des objets complexes. Premièrement, nous présentons le bloc, une nouvelle primitive de modélisation simple et générale, basée sur une forme cubique généralisée. Les blocs sont disposés et connectés entre eux pour constituer la forme de base des objets, à partir de laquelle est extrait un maillage de contrôle pouvant produire des arêtes lisses et vives. La nature volumétrique des blocs permet une spécification simple de la topologie, ainsi que le support des opérations de CSG entre les blocs. La paramétrisation de la surface, héritée des faces des blocs, fournit un soutien pour les textures et les fonctions de déplacements afin d'appliquer des détails de surface. Une variété d'exemples illustrent la généralité des blocs dans des contextes de modélisation à la fois interactive et procédurale. Deuxièmement, nous présentons un nouveau système de modélisation procédurale qui unifie diverses techniques dans un cadre commun. Notre système repose sur le concept de composants pour définir spatialement et sémantiquement divers éléments. À travers une série de déclarations successives exécutées sur un sous-ensemble de composants obtenus à l'aide de requêtes, nous créons un arbre de composants définissant ultimement un objet dont la géométrie est générée à l'aide des blocs. Nous avons appliqué notre concept de modélisation par composants à la génération d'édifices complets, avec intérieurs et extérieurs cohérents. Ce nouveau système s'avère général et bien adapté pour le partionnement des espaces, l'insertion d'ouvertures (portes et fenêtres), l'intégration d'escaliers, la décoration de façades et de murs, l'agencement de meubles, et diverses autres opérations nécessaires lors de la construction d'un édifice complet. / The realism of computer graphics images requires the creation of objects (or scenes) of increasing complexity, which leads to considerable costs. Procedural modeling can help to automate the creation process, to simplify the modification process or to generate multiple variations of an object instance. However although several procedural methods exist, no single method allows the creation of all types of complex objects, including in particular a complete building. This thesis proposes two solutions to the problem of procedural modeling: one solution addressing the geometry level, and the other introducing a general system suitable for complex object modeling. First, we present a simple and general modeling primitive, called a block, based on a generalized cuboid shape. Blocks are laid out and connected together to constitute the base shape of complex objects, from which is extracted a control mesh that can contain both smooth and sharp edges. The volumetric nature of the blocks allows for easy topology specification, as well as CSG operations between blocks. The surface parameterization inherited from the block faces provides support for texturing and displacement functions to apply surface details. A variety of examples illustrate the generality of our blocks in both interactive and procedural modeling contexts. Second, we present a novel procedural modeling system which unifies some techniques into a common framework. Our system relies on the concept of components to spatially and semantically define various elements. Through a series of successive statements executed on a subset of queried components, we grow a tree of components ultimately defining an object whose geometry is made from blocks. We applied our concept and representation of components to the generation of complete buildings, with coherent interiors and exteriors. It proves general and well adapted to support partitioning of spaces, insertion of openings (doors and windows), embedding of staircases, decoration of façades and walls, layout of furniture, and various other operations required when constructing a complete building.

<p>У оквиру дисертације истражен је утицај геометријске репрезентације<br />простора на развој савремене архитектуре. Показано је на који начин су<br />различите идеје о простору и инструментализација путем медијумa,<br />техникa и алатa утицали на нове развоје архитектуре. Резултати<br />истраживања сугеришу репозиционирање улоге репрезентације<br />простора у процесу архитектонског пројектовања. Посебна пажња<br />посвећена је утицају дигиталних медијума и алата репрезентације, где<br />је уочен прелаз од традиционалних геометријских ка новим,<br />алгоритамским, моделима.</p> / <p>U okviru disertacije istražen je uticaj geometrijske reprezentacije<br />prostora na razvoj savremene arhitekture. Pokazano je na koji način su<br />različite ideje o prostoru i instrumentalizacija putem medijuma,<br />tehnika i alata uticali na nove razvoje arhitekture. Rezultati<br />istraživanja sugerišu repozicioniranje uloge reprezentacije<br />prostora u procesu arhitektonskog projektovanja. Posebna pažnja<br />posvećena je uticaju digitalnih medijuma i alata reprezentacije, gde<br />je uočen prelaz od tradicionalnih geometrijskih ka novim,<br />algoritamskim, modelima.</p> / <p> Presented research explores the influence of geometric representation of<br /> space on modern architecture. Relation between new concepts of space as<br /> well as media, techniques and tools of representation and new movements in<br /> architecture are shown in this work. Notion of the crucial moments of<br /> developments in contemporary architecture suggests repositioning of the role<br /> of space representation in the process of architectural design. Special<br /> attention was made to the role of digital media and tools of representation<br /> that is recognized as a threshold towards new algorithmic models of<br /> representation.</p>

Made available in DSpace on 2016-04-27T16:58:48Z (GMT). No. of bitstreams: 1 Marcelo Cordeiro da Silva.pdf: 1895701 bytes, checksum: b76c020e24ea7c9012d0e9cd221384e6 (MD5) Previous issue date: 2008-11-27 / Secretaria da Educação do Estado de São Paulo / This present study aimed to introduce the rational numbers concept on Elementary School. This study is about semiotic approach education, based on representation s register theory by Raymond Duval (1993, 1995, 2005), found on article by French research Adjiage and Pluvinage (2000). In this article has proposed to consider the graduated straight line as a register of semiotic representation of rationals numbers, it indicates good results to education comparing to use of geometric figures dimension size 2, as chocolate bars, for example. Two questions guided this study: if the introduction of graduated straight line as a semiotic register to rationals numbers extends the possibility in opposition of difficulties to learn rationals numbers, and if it setups as element to help on Brazilian education. The dates for this analyze were Parâmetros Curriculares Nacionais para o Ensino Fundamental (PCN) to 2nd cycle (3rd and 4th grades) and 3rd cycle (5th and 6th grades) and the volumes of a didactic books' collection to these grades. We could check that the graduated straight line's or geometric s register has potential that could to promote education because it designs as a true semiotic register with a lot of signs and adaptable to development of a set of skills. This approach isn't recommendation by PCN and it doesn't act in didactics books, in this case, we can infer that if it could be introduced among us it can be a element to help on Brazilian education / O presente trabalho tem por foco a introdução do conceito de número racional no Ensino Fundamental. Trata-se de um estudo sobre uma abordagem semiótica de ensino, fundamentada na teoria dos registros de representação de Raymond Duval (1993, 1995, 2005), apresentada num artigo dos pesquisadores franceses Adjiage e Pluvinage (2000). Nela é proposto que se considere a reta graduada como um registro de representação semiótica dos racionais, indicando ganhos para a aprendizagem comparativamente ao uso de figuras geométricas de dimensão 2, como as barras de chocolate, num papel figurativo. Duas questões nortearam este trabalho: se a introdução da reta graduada como um registro semiótico para os racionais de fato amplia a possibilidade de enfrentamento das dificuldades consagradas da aprendizagem dos racionais e se ela se configura como um elemento de auxílio para o ensino brasileiro. Os dados para a análise foram buscados nos Parâmetros Curriculares Nacionais de Matemática para o Ensino Fundamental (PCN) do ciclo II (3ª e 4ª séries) e do ciclo III (5ª e 6ª séries) e nos volumes de duas coleções de livros didáticos referentes a essas séries. Pudemos concluir que o registro da reta graduada ou geométrico de dimensão 1 tem potencialidades que podem favorecer a aprendizagem, pois ela se configura como um verdadeiro registro semiótico rico em signos e mais adaptado ao desenvolvimento de um conjunto de competências. Essa abordagem não é recomendada nos PCN e nem aparece nos livros didáticos, levando-nos a inferir que se introduzida entre nós, pode se configurar como um elemento de auxílio para o ensino brasileiro