L’analyse de tolérances par des ensembles de contraintes repose sur la détermination de l’accumulation de variations géométriques par des sommes et intersections d’ensembles opérandes 6d. Les degrés de liberté des liaisons et les degrés d’invariance des surfaces génèrent des opérandes non-bornés (polyèdres), posant des problèmes de simulation. En 2014, L. Homria proposé une méthode pour résoudre ce problème, consistant à ajouter des limites artificielles(contraintes bouchon) sur les déplacements non-bornés. Même si cette méthode permet la manipulation d’objets bornés (polytopes), les contraintes bouchon augmentent la complexité des simulations. En réponse à cette difficulté, une méthode dérivée est proposée dans cette thèse.Cette méthode consiste à tracer et simplifier les contraintes bouchon au travers des opérations.Puis une seconde stratégie basée sur la décomposition d’un polyèdre en une somme d’un polytope et de lignes droites (associées aux déplacements non-bornés). Cette stratégie consiste à simuler d’une part les sommes de droites, et d’autre part, à déterminer la somme de polytopes dans un sous-espace de dimension inférieur à 6. Ces trois stratégies sont comparées au travers d’une application industrielle. Cela montre que la traçabilité des contraintes bouchons est un aspect fondamental pour contrôler leur propagation et pour réduire le temps de calcul des simulations. Toutefois, cette méthode exige encore de déterminer les limites des déplacements non-bornés. La deuxième méthode, adaptant systématiquement la dimension de l’espace de calcul, elle permet de diminuer davantage le temps de calcul. Ce travail permet d’envisager la mise en oeuvre de cette méthode selon des formulations statistiques avec la prise en compte des défauts de forme des surfaces. / The cumulative stack-up of geometric variations in mechanical systems can be modelled summing and intersecting sets of constraints. These constraints derive from tolerance zones or from contact restrictions between parts. The degrees of freedom (DOF) of jointsgenerate unbounded sets (i.e. polyhedra) which are difficult to deal with. L. Homri presented in 2014 a solution based on the setting of fictitious limits (called cap constraints) to each DOFto obtain bounded 6D sets (i.e. polytopes). These additional constraints, however, increase the complexity of the models, and therefore, of the computations. In response to this situation,we defined a derived strategy to control the effects of the propagation of the fictitious limits by tracing and simplifying the generated, new cap constraints. We proposed a second strategy based on the decomposition of polyhedra into the sum of a polytope and a set of straight lines.The strategy consists in isolating the straight lines (associated to the DOF) and summing the polytopes in the smallest sub-space. After solving an industrial case, we concluded that tracing caps constraints during the operations allows reducing the models complexity and,consequently, the computational time; however, it still involves working in 6d even in caseswhere this is not necessary. In contrast, the strategy based on the operands decompositionis more efficient due to the dimension reduction. This study allowed us to conclude that the management of mechanisms’ mobility is a crucial aspect in tolerance simulations. The gain on efficiency resulting from the developed strategies opens up the possibility for doing statistical treatment of tolerances and tolerance synthesis.

Orientador: Jorge Stolfi [Orientador] / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Computação. / Made available in DSpace on 2018-08-10T07:43:58Z (GMT). No. of bitstreams: 1 Montagner_ArnaldoJovanini_D.pdf: 2204093 bytes, checksum: 4c9c86ca0312f3b5507e1daa8c6553db (MD5) Previous issue date: 2007 / Resumo: Mapas são subdivisões de espaços topológicos em regiões simples, e triangulações são um tipo específico de mapa em que cada elemento é um simplexo (aresta, triângulo, tetraedro, etc). Neste trabalho, tratamos o problema de representação da topologia de triangulações e mapas de dimensão arbitrária. Estudamos a utilização de uma representação baseada em grafos de arestas coloridas, já utilizada como ferramenta teórica, mas nunca empregada em aplicações práticas. A principal limitação desta representação é a relativa inflexibilidade imposta sobre a manipulação da topologia. Há porém grandes vantagens em sua utilização, como a simplicidade de representação e a generalidade. Este trabalho consiste na especificação teórica de uma estrutura de dados baseada nestes grafos coloridos e de operações topológicas para construção e manipulação da estrutura. A utilização desta estrutura é ilustrada através de algoritmos para resolução de problemas em geometria computacional / Abstract: Maps are subdivisions of topological spaces into simple regions, and triangulations are a specific kind of map wherein each element is a simplex (edge, triangle, tetrahedron, etc). In this work, we analyze the problem of representing the topology of triangulations and maps with arbitrary dimension. We study a representation based on edge-colored graphs, already used as theoretical tool, but never employed in practical applications. The main limitation of this representation is the relative inexibility imposed on the manipulation of topology. There are, though, great advantages in its use, as its simplicity and generality. This work consists in the theoretic specification of a data structure based on these colored graphs and of topological operators to build and manipulate the structure.The use of this structure is illustrated by algorithms for computational geometry problems / Doutorado / Computação Grafica / Mestre em Ciência da Computação

Orientador: Wu Shin-Ting / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação / Made available in DSpace on 2018-08-13T23:55:20Z (GMT). No. of bitstreams: 1 Silva_AdlerCardosoGomesda_M.pdf: 2672358 bytes, checksum: 8e9b303b8bebb1d3e1aee1e46e01b4c9 (MD5) Previous issue date: 2007 / Resumo: A simplificação de linha é a operação da generalização cartográfica que remove os detalhes desnecessários de uma linha, preservando os principais aspectos da sua forma. A simplificação consistente de linha preocupa-se tanto em remover estes detalhes, quanto em gerar um mapa que seja consistente.ao original. Um mapa é dito consistente ao original se possuir a mesma topologia que este e conservar espaçamentos entre os seus objetos. Os trabalhos em simplificação consistente presentes na literatura ainda apresentam diversas limitações, das quais se destacam a aplicabilidade restrita a determinados tipos de objetos, a ineficácia na preservação da topologia em certos casos, a ausência da conservação de espaçamentos e o alto custo computacional. Este trabalho propõe uma nova solução para o problema dá simplificação consistente, procurando contornar estas limitações. Do ponto de vista teórico, ele determina um conjunto de condições que se aplicam a todos os tipos de objetos e garantem a consistência do mapa resultante. Do ponto de vista prático, ele apresenta um algoritmo que, com base nestas condições, é capaz de simplificar consistente e eficientemente as linhas de um mapa. O algoritmo proposto tambem apresenta outras características importantes para a simplificação consistente, tais como a capacidade de produzir de mapas independentes de escala e a invariância do mapa resultante em relação à ordem de processamento dos dados de entrada. / Abstract: Line simplification is the cartographic generalization operation that reduces the complexity of a line, while preserving its main shape features. Consistent line simplification involves not only the reduction of the line complexity, but also the consistency between the original and the simplified maps. A map is said to be consistent to the original one, if it preserves the topology and keeps the same proximity relation of the objects. Current works in consistent simplification still present drawbacks, such as the applicability to just certain types of objects, the failure while preserving topology in particular cases, the lack of proximity handling and the high computational cost. To overcome these drawbacks, this work proposes a new way for handling the consistent simplification problem. From the theoretical point of view, it presents a set of conditions applicable to all typesof objects, which guarantees the consistency between the original and simplified maps. From the practical point of view, it presents an algorithm that, based on these conditions, can consistently and efficiently simplify the lines of the original map. The algorithm also presents other important properties to the consistent simplification, such as the capacity of producing scale-independent maps and the ability of yielding the same simplified map for different data arrangements in the original map. / Mestrado / Engenharia de Computação / Mestre em Engenharia Elétrica

nÃo hà / Esta dissertaÃÃo descreve quatro mÃtodos implementados para realizar uma quadrilaterizaÃÃo convexa do espaÃo bidimensional que pode conter linhas poligonais ou buracos. Dois destes mÃtodos, ponto mÃdio e ortoquad, utilizam de elementos guia, o baricentro de uma regiÃo ou o locus de cÃrculos mÃximos tangentes e internos a geometria, para produzir uma malha conforme o domÃnio. Os outros dois, triquad e quadrilaterizaÃÃo incremental, utilizam de uma triangulaÃÃo explÃcita e implÃcita combinando elementos aos pares para realizar a geraÃÃo da malha. Todas as tÃcnicas sÃo feitas por decomposiÃÃo de regiÃes o que garante uma quadrilaterizaÃÃo final, jà que o domÃnio à sempre segmentado a cada iteraÃÃo. Estas tÃcnicas sÃo comparadas por um critÃrio de geometria e topologia de forma a tornar evidentes suas vantagens e desvantagens assim como promover melhorias futuras. As tÃcnicas sÃo aplicadas a alguns exemplos, incluindo-se um reservatÃrio natural, a fim de exibir seu funcionamento em um ambiente real ou prÃximo do mesmo, conforme as amostras utilizadas. TambÃm se pretende apresentar ao longo deste trabalho os requisitos necessÃrios, segundo a experiÃncia deste autor com o tema, para o desenvolvimento de uma tÃcnica de geraÃÃo de malha quadrilateral / This work describes four methods implemented to achieve a convex quadrilaterization of the two- -dimensional space that may have polygonal lines or holes. Two of these methods, midpoint and ortoquad make use of guide elements, the centroid of a region or the locus of maximum tangent circles inside a geometry, to produce a mesh for the domain. The other two methods, triquad and incremental quadrilatezation use a implicit and explicit triangulation while combining elements in pairs to generate a mesh. All these methods are made through domain decomposition which assure quadrilaterization at the end, since the domain is always partitioned at each iteration. These techniques are compared by a criterion of geometry and topology in order to make clear its advantages and disadvantages and as means of promoting future improvements. The techniques are applied to some samples, including a natural reservoir, in order to view its operation in a real environment or near reality according to the sample used. Also it intends to present throughout this work the requirements, according to the experience with the theme of this author, to develop a technique for quadrilateral mesh generation

Orientador: Eduardo Candido Xavier / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Computação / Made available in DSpace on 2018-08-23T15:26:56Z (GMT). No. of bitstreams: 1 Silveira_Tiago_M.pdf: 2498154 bytes, checksum: 4bbdff83ad5a399e1c436ffdbeb89a92 (MD5) Previous issue date: 2013 / Resumo: O resumo poderá ser visualizado no texto completo da tese digital / Abstract: The complete abstract is available with the full electronic document / Mestrado / Ciência da Computação / Mestre em Ciência da Computação

Orientador: Pedro Jussieu de Rezende, Cid Carvalho de Souza / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Computação / Made available in DSpace on 2018-08-19T04:48:53Z (GMT). No. of bitstreams: 1 Kunigami_Guilherme_M.pdf: 3383647 bytes, checksum: 88687783446ea3564995daf2b1ecfd79 (MD5) Previous issue date: 2011 / Resumo: Nesta dissertação, realizamos um estudo extensivo de uma classe de problemas envolvendo mapas de símbolos proporcionais, através de programação linear inteira. Mapas de símbolos proporcionais são uma ferramenta cartográfica para a representação de eventos associados 'a intensidade e localização geográfica. Exemplos clássicos desses tipos de mapas são ocorrências de terremotos e populações de cidades. Devido 'a proximidade e ao tamanho dos símbolos, podem haver sobreposições entre eles. Na ocorrência dessas sobreposições, a decisão sobre quais símbolos ficarão por cima de outros, pode afetar a visibilidade dos símbolos em um desenho. Os problemas envolvendo mapas de símbolos proporcionais dos quais tratamos são restritos ao uso de círculos opacos como símbolos e consistem em decidir a ordem em que estes serão dispostos em vista das sobreposições, de forma a maximizar métricas associadas à qualidade visual desses mapas. Tratam-se, portanto, de problemas de otimização combinatória. Em nosso trabalho, apresentamos modelos de programação linear inteira para resolução de dois desses problemas, um deles foi provado pertencer à classe NP-difícil e o outro tem complexidade ainda não conhecida. Obtivemos resultados teóricos de combinatória poliédrica acerca dos modelos, o que resultou em diversas desigualdades definidoras de facetas que foram incorporadas aos modelos. Desenvolvemos ainda técnicas de pré-processamento que decompuseram as instâncias de entrada em um grande número de componentes de menor tamanho. Essas técnicas permitiram resolver de maneira ótima, pela primeira vez, diversas instâncias criadas a partir de dados reais. Ademais, descrevemos um trabalho que aborda um desses problemas através de uma heurística GRASP, ao qual também contribuímos / Abstract: In this dissertation, we present an extensive study of a class of problems involving proportional symbol maps, through integer linear programming. Proportional symbol maps are a cartographic tool to represent events associated to specified values and geographical coordinates. Classic examples of these maps include representation of earthquakes and city populations. Due to the size and proximity of the symbols, there may be overlap among them. In such case, deciding which symbols will be placed above others may result in maps with different visibility information. The problems dealing with proportional symbol maps we address restrict symbols to be opaque disks and consist of deciding the order of their placement in view of overlaps, so as to maximize metrics related to the visual quality of such maps. Therefore, these amount essentially to combinatorial optimization problems. In our work, we designed integer linear programming models to solve two of these problems, one proven to be NP-hard and the other of complexity yet unknown. We obtained theoretical results concerning these models, through polyhedral combinatorics, which allowed us to include several facet defining inequalities into these models. We also developed preprocessing techniques that successfully broke down the input instances into a large number of smaller components. These techniques lead, for the first time, to optimal solutions of several test instances created from real-world data. Furthermore, we describe work on a heuristic approach to one of these problems using GRASP, to which we also contributed / Mestrado / Ciência da Computação / Mestre em Ciência da Computação

Orientador: Cid Carvalho de Souza / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Computação / Made available in DSpace on 2018-08-20T15:20:18Z (GMT). No. of bitstreams: 1 Oliveira_Lucasde_M.pdf: 1308997 bytes, checksum: cc147cd3d3c9f50c61a48d83579b6c49 (MD5) Previous issue date: 2012 / Resumo: Esta dissertação tem como foco a investigação experimental de algoritmos exatos, aproximativos e heurísticos aplicados na resolução do chamado problema do corredor de comprimento mínimo (PCCM). No PCCM recebemos um polígono retilinear P e um conjunto de polígonos retilineares menores formando uma subdivisão S planar conexa de P. Uma solução para este problema, também chamada de corredor, é formada por um conjunto conexo de arestas de S, e tal que cada face interna em S possui pelo menos um ponto em sua borda que pertence a alguma aresta deste conjunto. O objetivo então é encontrar um corredor tal que a soma total dos comprimentos das arestas seja a menor possível. Trata-se de um problema NP-difícil com aplicações em áreas diversas, tais como telecomunicações, engenharia civil e projeto de circuitos VLSI. O PCCM pode ser reduzido polinomialmente a um problema em grafos denominado problema da árvore de Steiner com grupos (PASG). Considerando esta transformação, estudamos e implementamos dois métodos aproximativos, um método exato de branch-and-cut, e um método heurístico baseado na metaheurística GRASP combinada com um evolutionary path relinking (GRASP+EPR). Além disso, propomos três heurísticas de busca local que visam melhorar a qualidade de soluções do PASG. Instâncias do PCCM foram geradas aleatoriamente, nas quais aplicamos os métodos implementados. Analisamos os resultados, e apresentamos as situações onde é interessante utilizar cada método. Verificamos que o método branch-and-cut foi capaz de encontrar soluções ótimas para instâncias que julgamos ser de grande porte em tempos computacionalmente aceitáveis. O melhor algoritmo aproximativo obteve corredores que na média têm comprimento 17% maior que o comprimento ótimo. Se combinarmos este algoritmo com as heurísticas de melhoria propostas este percentual cai para a média de 3,5%. Finalmente, o GRASP+EPR consome mais tempo que este algoritmo aproximativo, entretanto, o comprimento dos corredores obtidos por ele é em média 0,9% maior que o comprimento ótimo / Abstract: This dissertation focuses on the experimental investigation of exact, approximation and heuristic algorithms applied to solve the so-called minimum length corridor problem (MLCP). In the MLCP we receive a rectilinear polygon P and a set of minor rectilinear polygons forming a connected planar subdivision S of P. A solution for this problem, also called corridor, is formed by a set of connected edges of S, and such that each inner face of S has at least one point on its your border which belongs to an edge in this set. The goal is to find a corridor such that the sum of lengths of the edges is as small as possible. This is an NP-hard problem with applications in several areas such as telecommunications, civil engineering and design of VLSI circuits. The MLCP can be polynomially reduced to a graph problem known as group Steiner tree problem (GSTP). Based on this transformation, we studied and implemented two approximation methods, an exact branch-and-cut method, and a heuristic method based on the metaheuristic GRASP combined with an evolutionary path relinking (GRASP+EPR). Furthermore, we propose three local search heuristics to improve the quality of GSTP solutions. MLCP instances were randomly generated, in which we apply the methods implemented. We analyzed the results, and present situations where it is interesting to use each method. We found that the branch-and-cut has been able to find optimal solutions for instances that we consider to be large in acceptable computational times. The best approximation algorithm obtained corridors having average length 17% higher than the optimum length. If we combine this algorithm with the improvement heuristics proposed this percentage drops to an average of 3.5%. Finally, the GRASP+EPR spent more time than this approximation algorithm, however, the length of the corridors obtained by the method is, on average, 0.9% higher than the optimum length / Mestrado / Ciência da Computação / Mestre em Ciência da Computação

A range space (P, S) consists of a set P of n elements and a collection S = {S1,...,Sm} of subsets of P , referred to as ranges. A hitting set for this range space refers to a subset H of P such that every Si in S contains at least one element of H. The hitting set problem is studied for many geometric range spaces where P is a set of n points in Rd and the ranges are defined by the intersection of geometric objects with P . The algorithmic question of finding the minimum-sized hitting set for a given range space is well studied and is NP-Complete even for geometric range spaces defined by unit disks. The dual of the hitting set problem is the equally well studied set cover problem. A set cover is a sub-collection C⊆S such that every element in P is contained in at least one range in C. A classic problem which is related to the minimum set cover problem is the maximum coverage problem. In this problem, given a range space (P, S) and an integer k, we have to find k ranges from S such that the number of elements in P that are covered by these k ranges are maximized. In this thesis, we study combinatorial questions on a similar variant of hitting set problem for specific geometric range spaces where the size of the hitting set is fixed as a small constant. We study the small hitting set problem mainly for two broad classes of range spaces. We first consider the Dense range space (P, S) where P is a set of n points in Rd and S is defined by “dense” geometric objects i.e, geometric objects that contain more than a constant fraction, say �, of points from P . We fix the size of the hitting set as a small constant k and investigate bounds on the value of � such that all ranges that contain more than �n points from P are hit. Next we consider the Induced range space (P, I) where P isa setof n points in R2 and the ranges are all geometric objects that are induced(spanned) by P i.e., the ranges are defined by geometric objects that have a distinct tuple of points from P on its boundary. For Induced range spaces, we prove bounds on the maximum number of ranges that can be hit using a single point. We also prove combinatorial bounds on the size of the hitting set for various families of induced objects. Now, we describe the problems that we study in this thesis and summarize the results obtained. 1. Strong centerpoints: Here we study the small hitting set question for dense range spaces when the size of hitting set is one. This is related to a classic result in geometry called Centerpoint Theorem. A point x ∈ Rd is said to be the centerpoint of P if x is contained in all convex objects that contain more than dn points from P . Centerpoint Theorem states d+1 that a centerpoint always exists for any point set P . A centerpoint need not be an input point. A natural question to ask is the following: Does there exist a strong centerpoint? i.e., is it true that for any given point set P there exists a point p ∈ P such that p is contained in every convex object that contains more than a constant fraction, say �, of points of P ? It can be easily seen that a strong centerpoint does not exist even for geometric range spaces defined by half spaces. We study the existence and the corresponding bounds for strong centerpoints for some range spaces. In particular, we prove the existence of strong centerpoint and show tight bounds for the following range spaces. Convex polytopes defined by a fixed set of orientations : Geometric range spaces like those induced by axis-parallel boxes, skylines and downward facing equilateral triangles belong to this family of convex polytopes. Hyperplanes in Rd Range spaces with discrete intersection 2. Small Strong Epsilon Nets: This can be considered as an extension of strong centerpoints. This question is related to a well studied area called �-nets. N ⊂ P is called a (strong) �-net of P with respect to S if N ∩ S =�∅ for all objects S ∈S that contain more than �n points of P . We study the following question. Let �S∈ [0, 1] represent the smallest real number such that, for any given point set P , there exists Q ⊂ P of size i which is an �S-net with respect to S. Thus a strong centerpoint will be an �S1 -net. We prove bounds on �Si for small values of i where S is the family of axis-parallel rectangles, halfspaces and disks. 3. Strong First Selection Lemma: Here we consider the hitting question for induced range spaces when the size of the hitting set is one. In other words, given an induced range space, we prove bounds on the maximum number of ranges that can be hit using a single input point. Such questions are referred to as First Selection Lemma and are well studied. We consider the strong version of the First Selection Lemma where the “heavily covered” point is required to be an input point. We study the strong first selection lemma for induced rectangles, induced special rectangles and induced disks. We prove an exact result for the strong variant of the first selection lemma for axis-parallel rectangles. We also prove exact results for the strong variant of the first selection lemma for some subclasses of axis-parallel rectangles like orthants and slabs. We prove strong first selection lemma with almost tight bounds for skylines, another sub-class of axis-parallel rectangles. We prove bounds for first selection lemma for disks in the plane and exact results for a special case when the discs are induced by a centrally symmetric point set. 2 Hitting all Induced Objects: Here we discuss and prove combinatorial bounds on the size of the minimum hitting set for induced range spaces. We prove tight bounds on the hitting set size when induced objects are special rectangles, disks and downward facing equilateral triangles.

Neste trabalho estudamos problemas relacionados com a busca de pontos e segmentos em janelas retangulares com os lados paralelos aos eixos. É dado um conjunto de segmentos (ou pontos) no plano. Em uma primeira fase estes segmentos são organizados em estruturas de dados de tal forma a tornar buscas por aqueles que estão contidos em janelas retangulares mais eficiente. Na segunda fase são dadas as janelas de maneira online. Várias destas estruturas de dados são baseadas em árvores balanceadas, tais como, árvore limite, árvore de busca com prioridade, árvore de intervalos e árvore de segmentos. Na dissertação mostramos detalhadamente estas estruturas de dados e os algoritmos para resolver este problema para conjuntos de pontos (versão unidimensional do problema) e para segmentos no plano, tanto horizontais e verticais como com qualquer orientação (sem cruzamentos). Os algoritmos são analisados de forma rigorosa quanto ao seu uso de espaço e de tempo. Implementamos também os vários algoritmos estudados, construindo uma biblioteca destas estruturas de dados. Apresentamos, finalmente os resultados de experimentos computacionais com instâncias do problema. / In this work we study problems about point and segment query in rectangular windows whose edges are parallel to the axis. Given a set of segments (or points) in the plane. In a first phase these segments are organized in data structures such that queries for segments in windows are done more efficiently. In the second phase windows are given online. The data structures are balanced trees as range tree, priority search tree, interval tree and segment tree. In this master\'s thesis we show in details data structures and algorithms for solving windowing queries to sets of points (unidimensional version of the problem) and of segments in the plane, as horizontal and vertical as any orientation (without crossings). The algorithms are analysed rigorously regarding their space and time used. We implement the algorithms studied, building a library of these data structures. Finally, we present, the results of computational experiments with instances of the problem.

We explore the problem of transforming plane triangulations using simultaneous diagonal flips. Wagner showed that any n-vertex plane triangulation can be transformed to any other plane triangulation on equal number of vertices using a finite sequence of diagonal flips. Later on it has been established that O(n) individual flips suffice to complete this transformation. Bose et al. showed that the transformation can also be done in 4 × ( 2 / log 54/53 + 2 / log 6/5 ) logn + 2 ≈ 327.1 log n simultaneous flips. This bound is asymptotically tight. We present two algorithms to improve the leading coefficient of this bound for transforming any plane triangulation into any other. The first of the two algorithms lowers this bound down to 4 × ( 2 / log 12/11 + 2 / log 9/7 ) logn + 2 ≈ 85.8 log n. By processing and preprocessing the interior and exterior of the triangulation’s Hamiltonian cycle parallelly in an interlaced fashion, we make further improvement of the algorithm from ≈ 327.1 log n down to 12 / log 6/5 logn + 2 ≈ 45.6 log n.