In this paper we introduce an algorithm for the creation of polyhedral approximations for objects represented as strongly connected sets of voxels in three-dimensional binary images. The algorithm generates the convex hull of a given object and modifies the hull afterwards by recursive repetitions of generating convex hulls of subsets of the given voxel set or subsets of the background voxels. The result of this method is a polyhedron which separates object voxels from background voxels. The objects processed by this algorithm and also the background voxel components inside the convex hull of the objects are restricted to have genus 0. The second aim of this paper is to present some improvements to our convex hull algorithm to reduce computation time.

Made available in DSpace on 2014-06-11T19:24:53Z (GMT). No. of bitstreams: 0 Previous issue date: 2007-04-16Bitstream added on 2014-06-13T19:11:46Z : No. of bitstreams: 1 buske_n_me_rcla.pdf: 2292266 bytes, checksum: 62def68434237e23a32ee13c7d52e395 (MD5) / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / O objetivo desta pesquisa foi analisar como o origami e o caleidoscópio podem contribuir no processo de ensino e aprendizagem de alguns conceitos da Geometria. Este trabalho foi desenvolvido seguindo a proposta metodológica de Romberg, tem abordagem do tipo qualitativa e a coleta de dados se deu, essencialmente, por observação-participante em sala de aula, com a utilização de questionários, gravações de áudio, fotos, anotações e análise documental. Elaboramos uma proposta de ensino com a finalidade de levar os alunos a trabalharem com os problemas utilizando as construções feitas com origami e caleidoscópio. Foram desenvolvidas atividades, via resolução de problemas, com alunos do segundo semestre de um curso de licenciatura em Matemática, e os conteúdos estudados estavam relacionados às construções fundamentais, polígonos e poliedros. No encadeamento dos assuntos são apresentadas as explicações de como se realizar as construções com origami e como se confeccionar o caleidoscópio generalizado, juntamente com os preceitos matemáticos necessários para justificá-los. A execução prática da proposta de ensino por nós sugerida permitiu-nos fazer o levantamento e a análise de diversas possibilidades e limitações do uso do origami e caleidoscópio no estudo de conceitos relacionados à Geometria, mas circunscritos às proposições já citadas. Assim, trazemos sugestões para aperfeiçoar o trabalho e também de como ele pode ser mais bem aproveitado, cônscios de que o assunto aqui não se esgota, podendo surgir novas aplicações aos olhos de um educador interessado em utilizar esses recursos. / The purpose of this research was to analyze how Origami and kaleidoscope may contribute on the teaching and learning process over some Geometry concepts. This work has been developed according to Romberg s methodological proposal, it has a qualitative-type approach and the data collecting was essentially carried out by practical class observation, utilizing questionnaires, audio recordings, pictures, drafts and document analysis. We ve elaborated a teaching proposal aiming to lead students to work with problems by utilizing the constructions made with the Origami and Kaleidoscope. Activities have been developed, via problem solving, with the first-year students in a bachelor math's graduation course, and the researched subjects were related to the fundamental constructions, polygon and polyhedron. Explanations are shown within the subject sequences on how to do the constructions by using the Origami and how to build an average kaleidoscope, according to the mathematical precepts needed to justify them. The practical execution of the teaching proposal suggested by us, allowed ourselves to make the research and analyzes of many kaleidoscope and Origami possibility and limitation use on the Geometry related concepts research, besides circumscription to the already mentioned proposals. Thus, we bring along suggestions to improve the work and also how it could be more developed, aware that the subject here is not over, since applications may appear before an educator's eyes interested in using those resources.

Orientador: Claudemir Murari / Banca: Ruy Madsen Barbosa / Banca: Miriam Godoy Penteado / Resumo: O objetivo desta pesquisa foi analisar como o origami e o caleidoscópio podem contribuir no processo de ensino e aprendizagem de alguns conceitos da Geometria. Este trabalho foi desenvolvido seguindo a proposta metodológica de Romberg, tem abordagem do tipo qualitativa e a coleta de dados se deu, essencialmente, por observação-participante em sala de aula, com a utilização de questionários, gravações de áudio, fotos, anotações e análise documental. Elaboramos uma proposta de ensino com a finalidade de levar os alunos a trabalharem com os problemas utilizando as construções feitas com origami e caleidoscópio. Foram desenvolvidas atividades, via resolução de problemas, com alunos do segundo semestre de um curso de licenciatura em Matemática, e os conteúdos estudados estavam relacionados às construções fundamentais, polígonos e poliedros. No encadeamento dos assuntos são apresentadas as explicações de como se realizar as construções com origami e como se confeccionar o caleidoscópio generalizado, juntamente com os preceitos matemáticos necessários para justificá-los. A execução prática da proposta de ensino por nós sugerida permitiu-nos fazer o levantamento e a análise de diversas possibilidades e limitações do uso do origami e caleidoscópio no estudo de conceitos relacionados à Geometria, mas circunscritos às proposições já citadas. Assim, trazemos sugestões para aperfeiçoar o trabalho e também de como ele pode ser mais bem aproveitado, cônscios de que o assunto aqui não se esgota, podendo surgir novas aplicações aos olhos de um educador interessado em utilizar esses recursos. / Abstract: The purpose of this research was to analyze how Origami and kaleidoscope may contribute on the teaching and learning process over some Geometry concepts. This work has been developed according to Romberg’s methodological proposal, it has a qualitative-type approach and the data collecting was essentially carried out by practical class observation, utilizing questionnaires, audio recordings, pictures, drafts and document analysis. We’ve elaborated a teaching proposal aiming to lead students to work with problems by utilizing the constructions made with the Origami and Kaleidoscope. Activities have been developed, via problem solving, with the first-year students in a bachelor math's graduation course, and the researched subjects were related to the fundamental constructions, polygon and polyhedron. Explanations are shown within the subject sequences on how to do the constructions by using the Origami and how to build an average kaleidoscope, according to the mathematical precepts needed to justify them. The practical execution of the teaching proposal suggested by us, allowed ourselves to make the research and analyzes of many kaleidoscope and Origami possibility and limitation use on the Geometry related concepts research, besides circumscription to the already mentioned proposals. Thus, we bring along suggestions to improve the work and also how it could be more developed, aware that the subject here is not over, since applications may appear before an educator's eyes interested in using those resources. / Mestre

This dissertation presents an educational software which explores Virtual Reality techniques (VR) through the development of virtual educational environments. 3D Geometry has been taken as a case study. The objective of this work is the extension of the cut for convex and non-convex polyhedron. The virtual environment and the interaction techniques have been developed using the VRML (Virtual Reality Modeling Language) and JavaScript languages. After making the system available to potential users, they were able to do some experiments and confirmed that the techniques proposed are satisfactory and helpful in the learning process and in the visualization of non-convex polyhedron. / Esta dissertação apresenta um software educacional que explora técnicas de Realidade Virtual (RV) através do desenvolvimento de ambientes virtuais educacionais. Utiliza-se a Geometria Espacial como estudo de caso. O objetivo deste trabalho é a extensão do corte para poliedros convexos e não-convexos. O ambiente virtual e as técnicas de interação propostas foram desenvolvidas utilizando-se a linguagem VRML (Virtual Reality Modeling Language) e JavaScript. Após disponibilizar o sistema para potenciais usuários, estes puderam realizar alguns experimentos e identificaram que as técnicas propostas auxiliam, de forma satisfatória, no processo de aprendizado da visualização de poliedros não-convexos, graças ao uso das técnicas de RV propostas. / Mestre em Ciências

Neste trabalho iremos apresentar uma releitura de um resultado clássico da topologia, na visão da topologia algébrica e em sua notação atual. A demonstração deste, apresentada por Cauchy (1813), é comentada de maneira crítica em Lima (1985a) e para esta apresentação destacaremos as definições, teoremas e entes básicos para o seu entendimento. / In this work we will present a rereading of a classic topology result, in the view of the algebraic topology in its current notation. The proof of this, presented by Cauchy (1813), is critically commented on Lima (1985a) for which we will present the definitions, theorems, basic entities for their understanding.

In this paper we introduce an algorithm for the creation of polyhedral approximations for objects represented as strongly connected sets of voxels in three-dimensional binary images. The algorithm generates the convex hull of a given object and modifies the hull afterwards by recursive repetitions of generating convex hulls of subsets of the given voxel set or subsets of the background voxels. The result of this method is a polyhedron which separates object voxels from background voxels. The objects processed by this algorithm and also the background voxel components inside the convex hull of the objects are restricted to have genus 0. The second aim of this paper is to present some improvements to our convex hull algorithm to reduce computation time.

<div>With countless problems facing the world, there is an indispensable need for individuals who are able to persist and succeed in generating virtuous actions to meet unsettling eventualities. There have even been successful attempts to deploy specific wisdom-based curricula and then measure the results. Since the possibility for developing wisdom in the classroom exists, teachers’ perceptions of wisdom and the implicit beliefs that influence their ability to cultivate wisdom in their classroom become important to understand. </div><div>The purpose of this study was to develop and validate the Perception of Wisdom Exploratory Rating (POWER) Scale based on the Polyhedron Model of Wisdom (PMW). According to PMW, components that characterize wisdom are knowledge; reflectivity and self-regulation; moral maturity; openness and tolerance; sound judgment; creativity; and dynamic balance and synthesis. A total number of 585 responses from in-service and preservice teachers with no missing data was collected. Inservice and preservice samples were randomly split into two halves for Exploratory Factor Analysis (n = 290) and Confirmatory Factor Analysis (n = 295). In the EFA, the items fit a seven-factor structure, producing the following subscales: knowledge management; self-regulation; altruism and moral maturity; openness; tolerance; sound judgment and decision making; creative thinking. CFA was performed to test the construct validity of the scale. The model did produce a good fit to the data (χ2/df= 1.67, CFI= .92, TLI= .91, RMSEA= .049, and SRMR= .06). With continued testing and revisions, this instrument could be useful for cross-cultural comparison of perceptions of wisdom and identification of barriers to promoting wisdom instruction. It also could be used to identify and compare, across different populations, educators’ perceptions of wisdom and measuring perceptional changes due to designed interventions.</div><div><br></div>

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20657号 / 理博第4322号 / 新制||理||1621(附属図書館) / 京都大学大学院理学研究科化学専攻 / (主査)教授 寺西 利治, 教授 島川 祐一, 教授 小野 輝男 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

The determination of an aircraft's mass properties is critical during its conceptual design phase. Obtaining reliable mass property information early in the design of an aircraft can prevent design mistakes that can be extremely costly further along in the development process. In this thesis, several methods are presented in order to automatically calculate the mass properties of aircraft structural components and fuel stored in tanks. The first method set forth calculates the mass properties of homogenous solids represented by polyhedral surface geometry. A newly developed method for calculating the mass properties of thin shell objects, given the same type of geometric representation, is derived and explained. A methodology for characterizing the mass properties of fuel in tanks has also been developed. While the concepts therein are not completely original, the synthesis of past research from diverse sources has yielded a new comprehensive approach to fuel mass property analysis during conceptual design. All three of these methods apply to polyhedral geometry, which in many cases is used to approximate NURBS (Non-Uniform Rational B-Spline) surface geometry. This type of approximate representation is typically available in design software since this geometric format is conducive to graphically rendering three-dimensional geometry. The accuracy of each method is within 10% of analytical values. The methods are highly precise (only affected by floating point error) and therefore can reliably predict relative differences between models, which is much more important during conceptual design than accuracy. Several relevant and useful applications of the presented methods are explored, including a methodology for creating a CG (Center of Gravity) envelope graph. / Master of Science

O foco central desta tese é o desenvolvimento de algoritmos para o problema de recoloração convexa de caminhos. Neste problema, é dado um caminho cujos vértices estão coloridos arbitrariamente, e o objetivo é recolorir o menor número possível de vértices de modo a obter uma coloração convexa. Dizemos que uma coloração de um grafo é convexa se, para cada cor, o subgrafo induzido pelos vértices dessa cor é conexo. Sabe-se que este problema é NP-difícil. Associamos a este problema um poliedro, e estudamos sua estrutura facial, com vistas ao desenvolvimento de um algoritmo. Mostramos várias inequações válidas para este poliedro, e provamos que várias delas definem facetas. Apresentamos um algoritmo de programação dinâmica que resolve em tempo polinomial o problema da separação para uma classe grande de inequações que definem facetas. Implementamos um algoritmo branch-and-cut baseado nesses resultados, e realizamos testes computacionais com instâncias geradas aleatoriamente. Apresentamos adicionalmente uma heurística baseada numa formulação linear que obtivemos. Estudamos também um caso especial deste problema, no qual as instâncias consistem em caminhos coloridos, onde cada cor ocorre no máximo duas vezes. Apresentamos um algoritmo de 3/2-aproximação para este caso, que é também NP-difícil. Para o caso geral, é conhecido na literatura um algoritmo de 2-aproximação. / The focus of this thesis is the design of algorithms for the convex recoloring problem on paths. In this problem, the instance consists of a path whose vertices are arbitrarily colored, and the objective is to recolor the least number of vertices so as to obtain a convex coloring.Acoloring of a graph is convex if, for each color, the subgraph induced by the vertices of this color is connected. This problem is known to be NP-hard. We associate a polyhedron to this problem and investigate its facial structure. We show various classes of valid inequalities for this polyhedron and prove that many of them define facets.We present a polynomial-time dynamic programming algorithm that solves, in polynomial time, the separation problem for a large class of facet-defining inequalities.We report on the computational experiments with a branch-and-cut algorithm that we propose for the problem. Additionally, we present a heuristic that is based on a linear formulation for the problem. We also study a special case of this problem, restricted to instances consisting of colored paths in which each color occurs at most twice. For this case, which is also NP-hard, we present a 3/2-approximation algorithm. For the general case, it is known a 2-approximation algorithm.