Subdivision surfaces are capable of modeling and representing complex shapes of arbi-trary topology. However, methods on how to build the control mesh of a complex surfaceare not studied much. Currently, most meshes of complicated objects come from trian-gulation and simplification of raster scanned data points, like the Stanford 3D ScanningRepository. This approach is costly and leads to very dense meshes.Subdivision surface based one-piece representation means to represent the final objectin a design process with only one subdivision surface, no matter how complicated theobject's topology or shape. Hence the number of parts in the final representation isalways one.In this dissertation we present necessary mathematical theories and geometric algo-rithms to support subdivision surface based one-piece representation. First, an explicitparametrization method is presented for exact evaluation of Catmull-Clark subdivisionsurfaces. Based on it, two approaches are proposed for constructing the one-piece rep-resentation of a given object with arbitrary topology. One approach is to construct theone-piece representation by using the interpolation technique. Interpolation is a naturalway to build models, but the fairness of the interpolating surface is a big concern inprevious methods. With similarity based interpolation technique, we can obtain bet-ter modeling results with less undesired artifacts and undulations. Another approachis through performing Boolean operations. Up to this point, accurate Boolean oper-ations over subdivision surfaces are not approached yet in the literature. We presenta robust and error controllable Boolean operation method which results in a one-piecerepresentation. Because one-piece representations resulting from the above two methodsare usually dense, error controllable simplification of one-piece representations is needed.Two methods are presented for this purpose: adaptive tessellation and multiresolutionanalysis. Both methods can significantly reduce the complexity of a one-piece represen-tation and while having accurate error estimation.A system that performs subdivision surface based one-piece representation was im-plemented and a lot of examples have been tested. All the examples show that our ap-proaches can obtain very good subdivision based one-piece representation results. Eventhough our methods are based on Catmull-Clark subdivision scheme, we believe they canbe adapted to other subdivision schemes as well with small modifications.

[pt] Num modelador de sólidos, uma das ferramentas mais poderosas para a criação de objetos tridimensionais de qualquer nível de complexidade geométrica é a aplicação das operações booleanas. Elas são formas intuitivas e populares de combinar sólidos, baseadas nas operações aplicadas a conjuntos. Os tipos principais de operações booleanas comumente aplicadas a sólidos são: união, interseção e diferença. Havendo interesse prático, para garantir que os objetos resultantes possuam a mesma dimensão dos objetos originais, sem partes soltas ou pendentes, o processo de regularização é aplicado. Regularizar significa restringir o resultado de tal forma que apenas volumes preenchíveis possam existir. Na prática, a regularização é realizada classificando-se os elementos topológicos e eliminando-se estruturas de dimensão inferior. A proposta deste trabalho é o desenvolvimento de um algoritmo genérico que permita a aplicação do conjunto de operações booleanas em um ambiente de modelagem geométrica aplicada à análise por elementos finitos e que agregue as seguintes funcionalidades: trabalhar com um número indefinido de entidades topológicas (conceito de Grupo), trabalhar com objetos de dimensões diferentes, trabalhar com objetos non-manifold, trabalhar com objetos não necessariamente poliedrais ou planos e garantir a eficiência, robustez e aplicabilidade em qualquer ambiente de modelagem baseado em representação B-Rep. Neste contexto, apresenta-se a implementação do algoritmo num modelador geométrico pré- existente, denominado MG, seguindo o conceito de programação orientada a objetos e mantendo a interface com o usuário simples e eficiente. / [en] In a solid modeler, one of the most powerful tools to create threedimensional objects with any level of geometric complexity is the application of the Boolean set operations. They are intuitive and popular ways to combine solids, based on the operations applied to sets. The main types of Boolean operations commonly applied to solids are: union, intersection and difference. If there is practical interest, in order to assure that the resulting objects have the same dimension of the original objects, without loose or dangling parts, the regularization process is applied. To regularize means to restrict the result in a way that only filling volumes are allowed. In practice, the regularization is performed classifying the topological elements and removing the lower dimensional structures. The objective of this work is the development of a generic algorithm that allows the application of the Boolean set operations in a geometric modeling environment applied to finite element analysis, which aggregates the following functionalities: working with an undefined number of topological entities (Group concept), working with objects of different dimensions, working with nonmanifold objects, working with objects not necessarily plane or polyhedrical and assuring the efficiency, robustness and applicability in any modeling environment based on B-Rep representation. In this context, the implementation of the algorithm in a pre-existing geometric modeler named MG is presented, using the concept of object oriented programming and keeping the user interface simple and efficient.

[pt] Operações booleanas em modelagem 3D são usadas para criar novos modelos ou para modificá-los. Na maioria dos tipos de representação de objetos 3D, estas operações são bastante complexas. Nos últimos anos tem sido muito explorado um novo tipo de modelagem, a modelagem por pontos, que apresenta muitas vantagens em relação às outras representações como maior simplicidade e eficiência. Dois trabalhos exploram as operações booleanas na modelagem por pontos, o trabalho de Adams e Dutré e o trabalho de Pauly et. al. Dada a grande importância deste novo tipo de modelagem e do uso de operações booleanas, esta dissertação apresenta uma introdução à modelagem por pontos, implementa o algoritmo proposto em Adams e Dutré com algumas melhorias e o compara com o método de Pauly et. al. / [en] Boolean operations are used to create or modify models. These operations in the majority of 3D object representations are very complex. In the last years a significant trend in computer graphics has been the shift towards point sampled 3D models due to their advantages over other representations, such as simplicity and efficiency. Two recent works present algorithms to perform interactive boolean operations on point-based models: the work by Adams and Dutré and the work by Pauly et. Al.. Due to great importance of this novel representation and of the use of boolean operations, the present work makes an introduction to point-based representation, implements the algorithm proposed by Adams and Dutré with some improvements, and compares this implementation with the work by Pauly et. al..

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.

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.