abstract: Quad-dominant (QD) meshes, i.e., three-dimensional, 2-manifold polygonal meshes comprising mostly four-sided faces (i.e., quads), are a popular choice for many applications such as polygonal shape modeling, computer animation, base meshes for spline and subdivision surface, simulation, and architectural design. This thesis investigates the topic of connectivity control, i.e., exploring different choices of mesh connectivity to represent the same 3D shape or surface. One key concept of QD mesh connectivity is the distinction between regular and irregular elements: a vertex with valence 4 is regular; otherwise, it is irregular. In a similar sense, a face with four sides is regular; otherwise, it is irregular. For QD meshes, the placement of irregular elements is especially important since it largely determines the achievable geometric quality of the final mesh. Traditionally, the research on QD meshes focuses on the automatic generation of pure quadrilateral or QD meshes from a given surface. Explicit control of the placement of irregular elements can only be achieved indirectly. To fill this gap, in this thesis, we make the following contributions. First, we formulate the theoretical background about the fundamental combinatorial properties of irregular elements in QD meshes. Second, we develop algorithms for the explicit control of irregular elements and the exhaustive enumeration of QD mesh connectivities. Finally, we demonstrate the importance of connectivity control for QD meshes in a wide range of applications. / Dissertation/Thesis / Doctoral Dissertation Computer Science 2014

Organic Photovoltaic (OPV) solar cells provide a promising alternative for harnessing solar energy. However, the efficient design of OPV materials that achieve better performance requires support by better-tailored visualization tools than are currently available, which is the goal of this thesis. One promising approach in the OPV field is to control the effective material of the OPV device, which is known as the Bulk-Heterojunction (BHJ) morphology. The BHJ morphology has a complex composition. Current BHJ exploration techniques deal with the morphologies as black boxes with no perception of the photoelectric current in the BHJ morphology. Therefore, this method depends on a trial-and-error approach and does not efficiently characterize complex BHJ morphologies. On the other hand, current state-of-the-art methods for assessing the performance of BHJ morphologies are based on the global quantification of morphological features. Accordingly, scientists in OPV research are still lacking a sufficient understanding of the best material design. To remove these limitations, we propose a new approach for knowledge-assisted visual exploration and analysis in the OPV domain. We develop new techniques for enabling efficient OPV charge transport path analysis. We employ, adapt, and develop techniques from scientific visualization, geometric modeling, clustering, and visual interaction to obtain new designs of visualization tools that are specifically tailored for the needs of OPV scientists. At the molecular scale, the user can use semantic rules to define clusters of atoms with certain geometric properties. At the nanoscale, we propose a novel framework for visual characterization and exploration of local structure-performance correlations. We also propose a new approach for correlating structural features to performance bottlenecks. We employ a visual feedback strategy that allows scientists to make intuitive choices about fabrication parameters. We furthermore propose a visual analysis framework to help answer domain science questions through parameter space exploration for local morphology features. This framework is built on the shape-based clustering of local regions (patches), which for the first time enables local analysis of BHJ morphologies. Using our proposed system, domain experts can interactively create and visualize new BHJ structures of interest at both the molecular and nanoscale levels in a relatively short time.

Scales are a visually striking feature that grows on many animals. These small, rigid plates embedded in the skin form an integral part of our description of fish and reptiles, some plants, and many extinct animals. Scales exist in many shapes and sizes, and serve as protection, camouflage, and plumage for animals. The variety of scales and the animals they grow from pose an interesting problem in the field of Computer Graphics. This dissertation presents a method for generating scales and scale-like structures on a polygonal mesh through surface replacement. A triangular mesh was covered with scales and one or more proxy-models were used as the scales shape. A user began scale generation by drawing a lateral line on the model to control the distribution and orientation of scales on the surface. Next, a vector field was created over the surface to control an anisotropic Voronoi tessellation, which represents the region occupied by each scale. Then these regions were replaced by cutting the proxy model to match the boundary of the Voronoi region and deform the cut model onto the surface. The final result is a fully connected 2-manifold that is suitable for subsequent post-processing applications, like surface subdivision.

[pt] Esta dissertação tem por objetivo estudar um método para aproximação de dados esparços multivariados denominado o método Mínimos Quadrados Móveis por Aproximações Iteradas (Iterated Approximate Moving Least-Square Approximation – IAMLA). Este método é baseado no método de interpolação por funções de base radial (RBF) e no método de aproximação AMLS. Mas diferentemente do método RBF, ele não requer a solução de um sistema de equações lineares. O método IAMLS no limite converge para o interpolante RBF sob certas condições. / [en] The objective of this work is to study an approximation method for multivariate sparse data named Iterated Approximate Moving Least Square Approximation – IAMLS. This method is based on the Radial Basis Functions (RBF) interpolation method and on the AMLS approximation method. Differently from the RBF interpolation method, the IAMLS does not requires to solve a system of linear equations. The IAMLS method converges to the RBF interpolant under some conditions.

[pt] O presente trabalho de pesquisa, apresenta a aplicação de um novo conceito de visualização e interpretação da informação geológica. Os mapas geológicos que, até hoje em dia, são apresentados em papel, agora podem ser vistos, em computador, de forma tridimensional. Esta representação tridimensional é realizada a partir do software GOCAD (Geological Object Computer Aided Draw) (grupo de Ciência da Computação da Escola Nacional de Geologia, Nancy, França, 1989). Este software foi inicialmente desenvolvido para aplicação e representação de bacias sedimentares na indústria do petróleo. O presente trabalho de pesquisa apresenta uma extensão do GOCAD à representação tridimensional de maciços rochosos, como os encontrados na região litorânea do Estado do Rio de Janeiro. Uma área na zona sul da cidade do Rio de Janeiro foi escolhida como área piloto de estudo para a modelagem tridimensional. Esta área, o maciço Dois Irmãos, foi inicialmente caracterizada do ponto de vista da geologia estrutural e as informações coletadas foram utilizadas na modelagem geométrica usando GOCAD. Os resultados obtidos são comentados e são também mostrados o potencial e limitações do software GOCAD para este tipo particular de modelagem geométrica de maciços rochosos. / [en] The present research presents the application of a new concept in visualization and interpretation of geological information. The geological maps that until now are still represented on paper, now can be seen tridimensionally, in computer screen. This 3D representation is accomplished through the software GOCAD (Geological Object Computer Aided Draw), developped by a team of Computer Science of the National School of Geology, Nancy, France. The software was developed originally for application and representation of sedimentary basins basically for use in the petroleum industry. The present research, presents an extension of the GOCAD software to the 3D representation of rock masses found on the coastal region of the state of Rio de Janeiro. An area in the southern area of the city of Rio de Janeiro was chosen to be a pilot study area for the 3D geometrical modelling. This area, the Morro Dois Irmãos massive, was initially characterized from the structural geology point of view and the collected information was used in the 3D geometrical modelling with GOCAD . The obtained results are commented and the potential and limitations of the GOCAD software for this particular type of geometrical modelling of rock masses are discussed. / [es] Este trabajo de investigación presenta la aplicación de un nuevo concepto de visualización e interpretación de la información geológica. Los mapas geológicos que, hasta hoy en día, son presentados en papel, pueden ser vistos ahora en computador, de forma tridimensional. Esta representación tridimensional se realiza a partir del software GOCAD (Geological Object Computer Aided Draw) (grupo de Ciencias de la Computación de la Escuela Nacional de Geología, Nancy, Francia, 1989). Este software fue inicialmente desarrollado para la aplicación y representación de bacias sedimentares en la industria del petróleo. EL presente trabajo de investigación presenta una extensión del GOCAD a la representación tridimensional de macizos rocosos, como los encontrados en la región litoránea del Estado del Rio de Janeiro. Cierta área situada en la zona sul de la ciudad de Rio de Janeiro fue escogida como área piloto de estudio para la modelaje tridimensional. Esta área, el macizo Dois Irmãos, fue inicialmente caracterizada desde el punto de vista de la geología extructural y las informaciones recolectadas fueron utilizadas en el modelo geométrico usando GOCAD. Se comentan los resultados obtenidos y se muestra el potencial y limitaciones del software GOCAD para este tipo particular de modelo geométrico de macizos rocosos.

Alors que les surfaces géométriques sont essentiellement représentées à l'aide de maillages triangulaires dans le domaine de la géométrie numérique, les structures permettant d'interagir avec ces géométries sont variées et adaptées aux différents traitements visés par l'utilisateur. Cette thèse présente des travaux réalisés sur des structures de dimension et de représentation géométrique variées, allant de l'étude des structures internes comme les squelettes analytiques pour la modélisation géométrique, passant par les structures surfaciques pour la sélection automatiques de poignées de déformation, jusqu'aux structures externes de contrôle d'objet de type "cage" offrant une représentation haut niveau de séquences animées d'objets issues de systèmes de performance capture. Sont présentés également les résultats obtenus sur les coordonnées aux valeurs moyennes offrant une solution au problème de l'interpolation de conditions de Dirichlet, pour lesquelles les formules analytiques des gradients et Hessiens sont fournies, et les fonctions biharmoniques pour lesquelles une base d'éléments finis est formulée pour la résolution du problème de Laplace biharmonique avec conditions mixtes Dirichlet/Neumann, ainsi que leurs applications à la déformation de formes 3D. / While 3D surfaces are essentially represented using triangle meshes in the domain of digital geometry, the structures that allow to interact with those are various and adapted to the different geometry processing tasks that are targetted by the user.This thesis presents results on structures of various dimension and various geometrical representations, going from internal structures like analytical curve skeletons for shape modeling, to on-surface structures allowing automatic selection of feature handles for shape deformation, and external control structures known as “cages” offering a high-level representation of animated 3D data stemming from performance capture. Results on spatial functions are also presented, in particular for the Mean-Value Coordinates, for which the analytical formulae of the gradients and the Hessians are provided, and biharmonic functions, for which a finite elements basis is given for the resolution of the biharmonic Laplace problem with mixed Dirichlet/Neumann boundary conditions, as well as their applications to 3D shapes deformation.

No description available.

Gradient echo (GRE) imaging, a magnetic resonance imaging (MRI) technique that is sensitive to changes in the magnetic susceptibility property of tissues, has recently revealed significant signal heterogeneity in white matter (WM) at high magnetic field B0 ≥ 3T. Various aspects of the underlying white matter microstructure have been linked to the observed contrast between white matter regions. This thesis investigates the origins of the observed differences in GRE signal behaviour. We proposed an explicit multi-compartmental model of WM that incorporates realistic representation of the geometry and magnetic susceptibility of the underlying microstructure that can be used to study the effects of WM microstructural changes on GRE signal characteristics. In particular, we looked at the apparent transverse relaxation rate (R2*) and the resonance frequency, as well as their respective deviations from mono-exponential decay and linear phase evolution. Next, we investigated the effect of WM fiber orientation on GRE signal using healthy human volunteers at 3T by correlating the GRE signal from different WM regions with WM fiber orientation information. Using literature-based parameters, we demonstrated that the geometric model predicted similar trends. Lastly, we studied the effect of myelin on GRE signal using a cuprizone mouse model at 7T . An ex vivo study was used to correlate GRE signal in fixed mouse brain with normalized myelin stain intensity. Simulated GRE signal from hypothetical scenarios of demyelination were then compared with the experimental results. R2* and resonance frequency were then used in an in vivo longitudinal study to track myelin changes during demyelination and subsequent remyelination.

This dissertation delivers a new computational framework for the automatic generation of geometric feature patterns for industrial design and architectural facades on free-form surfaces. Such patterns include holes in a speaker grill, showerhead holes, protrusions on ceramics or bumpy textures on a panel. These patterns play a key role in making a designed object aesthetically pleasing as well as functional. Computer Aided Design (CAD) systems currently offer tools for generating simple patterns, such as uniformly spaced rectangular or radial patterns. However, they are not applicable to more general cases required in industrial design, including arbitrarily shaped target geometry and graded feature sizes. These tools are limited in several ways: (1) They cannot be applied to free-form geometries used in industrial design, (2) Patterning of these features happens within a single working plane and is not applicable to highly curved surfaces, and (3) Created features lack anisotropy and spatial variations, such as changes in the size and orientation of geometric features within a given region. This thesis proposes a new method of taking input for a target region along with sizing metrics. It will generate feature patterns automatically in three steps: (1) packing isotropic or anisotropic cells tightly in a target region, (2) scaling features according to the specified sizing metrics, and (3) adding features on the base geometry. This approach automatically generates complex patterns that conform to the boundary of any specified region. User input of a small number of geometric features (called “seed features”) of desired size and orientation in preferred locations also can be specified within the target domain. These geometric seed features are then transformed into tensors and used as boundary conditions to generate a Riemannian metric tensor field. A form of the Laplace heat equation is used to generate the field over the target domain, subject to specified boundary conditions. The field represents the anisotropic pattern of the geometric features. The system is implemented as a plugin module in a commercial CAD package to add geometric features to the target region of the model using two set operations, union and subtraction. This method facilitates the creation of a complex pattern of hundreds of geometric features in minutes. All the features are accessible from the CAD system and can be manipulated individually if required by the user. This allows the industrial designer or architect to explore more alternatives by avoiding the tedious and time-consuming manual generation of these geometric patterns.

De nos jours, les objets virtuels sont devenus omniprésents. On les trouve dans de nombreux domaines comme le divertissement (cinéma, jeux vidéo, etc.), la conception assistée par ordinateur ou encore la réalité virtuelle. Nous nous intéressons en particulier à la modélisation d'objets 3D dans le domaine de la création artistique. Ici, la création d'images riches nécessite de faire appel à des modèles très détaillés et donc extrêmement complexes. Les surfaces de subdivision, traditionnellement utilisées dans ces domaines, voient leur complexité croître rapidement lorsqu'on ajoute des détails, et la gestion de la connectivité du maillage de contrôle devient trop contraignante. Une approche standard pour gérer la complexité de tels modèles est d'utiliser des représentations différentes pour la forme générale de la surface et les détails. Cependant, ces détails sont représentés par des cartes matricielles qui ne possèdent pas la plupart des avantages des représentations vectorielles, et cela complexifie certaines tâches, comme par exemple l'animation. Dans cette thèse, nous proposons deux nouvelles représentations vectorielles, la première pour les surfaces de base, la deuxième pour les détails. Nous utilisons pour cette dernière une représentation vectorielle appelée images de diffusion permettant de créer des variations lisses à l'aide d'un ensemble réduit de contraintes. Cela nous permet de représenter aussi bien la géométrie que la couleur ou d'autres paramètres nécessaires au rendu de façon purement vectoriel, en conservant des contrôles de haut niveau.Notre première contribution est une représentation de surfaces, baptisée LS3, issue de la combinaison entre surfaces de subdivision et -point set surfaces. Cette approche réduit notablement les artefacts des surfaces de subdivision aux alentours de sommets dits extraordinaires, qui sont connus pour poser problème. Nous présentons une analyse numérique des propriétés de ces surfaces, qui tend à montrer que du point de vue de la continuité elles se comportent au moins aussi bien que les schémas de subdivision linéaires traditionnels. Notre deuxième contribution est un solveur pour les images de diffusion dont le principal avantage est de produire en sortie une autre représentation vectorielle légère et très rapide à évaluer. Nous illustrons la force de note solveur sur de nombreux exemples difficiles ou impossibles à réaliser avec les méthodes précédentes. Pour conclure, nous montrons comment combiner nos deux contributions pour obtenir une représentation de surface entièrement vectorielle capable de représenter des détails sans avoir à manipuler la connectivité d'un maillage. / Nowadays, virtual objects have become omnipresent. We can find them in various domains such as entertainment (movies, video games, etc.), computer-aided design or virtual reality. Our main focus in this document is the modeling of 3D objects in the domain of artistic creation, where rich images creation requires highly detailed and complex models.Subdivision surfaces, the most used surface representation in this domain, quickly become very dense as the user add details, and manual handling of the connectivity becomes too cumbersome. A standard approach to handle the complexity of such models is to separate the overall shape of the surface and the details. Although, these detail maps are often stored in bitmap images that does not provide the advantages of vectorial representation, which complicate some tasks, like animation.In this document, we present two new vectorial representations: the first one for the base surface, the second one for the detail maps. For the later, we use a vectorial representation called diffusion images that allow to create smooth or sharp variations from a small set of constraints. This enables us to represent geometry as well as color or any other parameter required for rendering, while keeping high-level controls.Our first contribution is a surface representation, called LS3, based on the combination of subdivision surfaces and point set surfaces. This approach reduces notably artifacts that subdivision surfaces produce around so called extraordinary vertices. We also present a numerical analysis of the mathematical properties of these surfaces, that show that they behave at least as well as classical subdivision schemes.Our second contribution is a solver for diffusion images that has the particularity to produce as output a denser vectorial representation which is light and fast to evaluate. We show the advantages of this approach on several examples that would be hard or impossible to produce with former methods.To conclude, we show how these two contributions can be used together to obtain a fully vectorial surface representation able to produce detailed surfaces without needing to deal with complex connectivity.