Dois métodos distintos são descritos e implementados. O primeiro método, proposto por Ruppert, possui garantias teóricas de qualidade quando a fronteira do domínio obedece certas restrições. O segundo método, proposto por Persson, possibilita um maior controle na densidade dos elementos que discretizam o domínio. As vantagens, desvantagens e particularidades de cada um dos métodos são descritas e detalhadas / Two distinct methods are described and implemented. The first method, proposed by Ruppert, has theoretical guarantees on the quality of elements when the domain boundaries respect certain restrictions. The second method, proposed by Persson, makes it possible to have greater control over the density of the elements that make up the domain. The advantages, disadvantages and specific points about each method are described and detailed

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The presented research summarizes (1) the development of a rapid prototyping framework, (2) the application of advance meshing algorithms, data structures, programming languages and libraries toward the field of numerical surface-water modeling (NSWM), (3) the application of (2) in (1), and (4) a real world application. The result of the research was the development of a prototype grid generator tool, the Mesh Generation and Refinement Tool (MGRT). MGRT supports a customizable interface and plug-and-play functionality through the use of plug-ins and incorporates a plug-in based topology/geometry system. A detailed explanation of the data structures, algorithms, and tools used to construct the MGRT are presented. Additionally, the construction of a mesh of Mobile Bay is presented. This represents a real world application of the MGRT. This tool provides many benefits over current tools in NSWM, which include faster meshing and the ability the use any grid generator that can be plugged-in.

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M.Sc (Computer Science) / Facial modelling and animation is considered one of the most challenging areas in the animation world. Since Parke and Waters’s (1996) comprehensive book, no major work encompassing the entire field of facial animation has been published. This thesis covers Parke and Waters’s work, while also providing a survey of the developments in the field since 1996. The thesis describes, analyses, and compares (where applicable) the existing techniques and practices used to produce the facial animation. Where applicable, the related techniques are grouped in the same chapter and described in a chronological fashion, outlining their differences, as well as their advantages and disadvantages. The thesis is concluded by exploratory work towards a talking head for Northern Sotho. Facial animation and lip synchronisation of a fragment of Northern Sotho is done by using software tools primarily designed for English. / Computing

This large body of work is entirely centered around dual-tree algorithms, a class of algorithm based on spatial indexing structures that often provide large amounts of acceleration for various problems. This work focuses on understanding dual-tree algorithms using a new, tree-independent abstraction, and using this abstraction to develop new algorithms. Stated more clearly, the thesis of this entire work is that we may improve and expand the class of dual-tree algorithms by focusing on and providing improvements for each of the three independent components of a dual-tree algorithm: the type of space tree, the type of pruning dual-tree traversal, and the problem-specific BaseCase() and Score() functions. This is demonstrated by expressing many existing dual-tree algorithms in the tree-independent framework, and focusing on improving each of these three pieces. The result is a formidable set of generic components that can be used to assemble dual-tree algorithms, including faster traversals, improved tree theory, and new algorithms to solve the problems of max-kernel search and k-means clustering.

Les modèles virtuels de plantes sont visuellement de plus en plus réalistes dans les applications infographiques. Cependant, dans le contexte de la biologie et l'agronomie, l'acquisition de modèles précis de plantes réelles reste un problème majeur pour la construction de modèles quantitatifs du développement des plantes.Récemment, des scanners laser 3D permettent d'acquérir des images 3D avec pour chaque pixel une profondeur correspondant à la distance entre le scanner et la surface de l'objet visé. Cependant, une plante est généralement un ensemble important de petites surfaces sur lesquelles les méthodes classiques de reconstruction échouent. Dans cette thèse, nous présentons une méthode pour reconstruire des modèles virtuels de plantes à partir de scans laser. Mesurer des plantes avec un scanner laser produit des données avec différents niveaux de précision. Les scans sont généralement denses sur la surface des branches principales mais recouvrent avec peu de points les branches fines. Le cœur de notre méthode est de créer itérativement un squelette de la structure de la plante en fonction de la densité locale de points. Pour cela, une méthode localement adaptative a été développée qui combine une phase de contraction et un algorithme de suivi de points.Nous présentons également une procédure d'évaluation quantitative pour comparer nos reconstructions avec des structures reconstruites par des experts de plantes réelles. Pour cela, nous explorons d'abord l'utilisation d'une distance d'édition entre arborescence. Finalement, nous formalisons la comparaison sous forme d'un problème d'assignation pour trouver le meilleur appariement entre deux structures et quantifier leurs différences.

The dissertation introduces Sphere Support Vector Machines (SphereSVM) and Minimal Norm Support Vector Machines (MNSVM) as the new fast classification algorithms that use geometrical properties of the underlying classification problems to efficiently obtain models describing training data. SphereSVM is based on combining minimal enclosing ball approach, state of the art nearest point problem solvers and probabilistic techniques. The blending of the three speeds up the training phase of SVMs significantly and reaches similar (i.e., practically the same) accuracy as the other classification models over several big and large real data sets within the strict validation frame of a double (nested) cross-validation (CV). MNSVM is further simplification of SphereSVM algorithm. Here, relatively complex classification task was converted into one of the simplest geometrical problems -- minimal norm problem. This resulted in additional speedup compared to SphereSVM. The results shown are promoting both SphereSVM and MNSVM as outstanding alternatives for handling large and ultra-large datasets in a reasonable time without switching to various parallelization schemes for SVMs algorithms proposed recently. The variants of both algorithms, which work without explicit bias term, are also presented. In addition, other techniques aiming to improve the time efficiency are discussed (such as over-relaxation and improved support vector selection scheme). Finally, the accuracy and performance of all these modifications are carefully analyzed and results based on nested cross-validation procedure are shown.

Dans cette thèse, nous étudions des problèmes algorithmiques dans les complexes CAT(0) planaires et rectangulaires munis d'une m ́etrique intrinsèque l_2. Nous proposons des algorithmes de calcul du plus court chemin dans les complexes CAT(0) planaires et rectangulaires et de construction de l'enveloppe convexe d'un ensemble fini de points dans les complexes CAT(0) planaires. E ́tant donné un complexe CAT(0) rectangulaire 2-dimensionnel K à n sommets, nous proposons un algorithme qui, pour toute paire de points calcule la distance et le plus court chemin en temps sous-lin ́eaire en nombre de sommets de K, en utilisant une structure de données de taille O(n^2). Le deuxième problème étudié est celui du plus court chemin entre un point-source donné et tout autre point dans un complexe CAT(0) planaire K a n sommets. Pour cela, nous proposons un algorithme qui, pour tout point y de K, étant donnée le point source x et la carte géodésique SPM(x), construit le plus court chemin γ(x,y) en temps O(n), en utilisant une structure de données de taille O(n^2). Enfin, nous nous intéressons au calcul de l'enveloppe convexe d'un ensemble de k points dans un complexe CAT(0) planaire à n sommets. Nous proposons un algorithme qui construit l'enveloppe convexe en temps O(n^2 + nk log k) en utilisant une structure de données de taille O(n^2 + k). / In this thesis, we study algorithmic problems in CAT(0) planar and rectangular complexes with an intrinsic l_2−metric. We present algorithms for some algorithmic problems, such as computing the shortest path and the convex hull of a finite set of points in CAT(0) planar and rectangular complexes. We present an efficient algorithm for answering two-point distance queries in a given CAT(0) rectangular complex K with n vertices. Namely, we show that for a CAT(0) rectangular complex K with n vertices, one can construct a data structure of size O(n^2) so that, given any two points in K, the shortest path can be computed in subliniar time of n. The second problem presented is computing shortest path from a single-source to the query point in a CAT(0) planar complex. We propose an algorithm which computes in O(n) time the shortest path between a given point and the query point in a CAT(0) planar complex with n vertices, using a given shortest path map and data structure of size O(n^2). Finally, we study the problem of computing the convex hull of a set of k points in a CAT(0) planar complex with n vertices. We describe an algorithm which computes the convex hull in O(n^2 + nk log k) time, using a data structure of size O(n^2 + k).