Les méthodes géophysiques aéroportées sont très utilisées pour la prospection du sous-sol à l'échelle régionale, permettant ainsi de couvrir de grandes surfaces en particulier les zones difficiles d'accès. Le sujet de thèse concerne le développement de techniques d'interprétation des données géophysiques pour le problème des ressources naturelles et de l'environnement. La première partie de cette thèse concerne le développement d'une méthode de calcul direct des composantes des champs gravimétrique et magnétique à partir d'une structure (corps) géologique modélisé(e) par une grille à base de tétraèdres, ce qui permet de représenter des modèles géologiques très complexes particulièrement en présence de zones faillées et hétérogènes avec un nombre d'éléments optimal. Plusieurs techniques d'inversions utilisent des contraintes mathématiques pour la résolution du problème inverse en modélisation. Ces contraintes permettent de réduire le nombre de modèles possibles. Cependant les solutions proposées appelées aussi « le modèle le plus probable » présentent des solutions lisses, ce qui est loin de représenter la réalité géologique. Pour éluder ce problème, les deuxièmes et troisièmes parties de la thèse proposent des améliorations majeures du processus d'inversion par l'utilisation des méthodes géostatistiques telles que la Simulation Gaussienne Séquentielle ou la Co-Simulation dans le cas d'une inversion conjointe afin d'estimer les probabilités a posteriori des modèles simulés. La quatrième partie de ce mémoire présente une alternative à la simulation de plusieurs variables. L'apprentissage du réseau de neurones supervisé par un certain nombre de points permet d'établir une relation entre les différentes variables / In recent years with the technology developments, airborne geophysical methods (gravity, magnetic, and electromagnetic) are widely used in the natural resource exploration at the regional scale. It covers large areas particularly in the areas with difficult access. The first part of this thesis consist on the development of new forward modeling algorithm for the calculation of the components of the gravity and magnetic fields based on a tetrahedron grid. The tetrahedral mesh allows the representation of very complex geological models holding many heterogeneous and faulted zones with an optimal number of elements, this reduces significantly the time calculation. Several inversion techniques use mathematical constraints for the resolution of the inverse problem in order to reduce the number of possible models. However the proposed solutions called also "the most probable model" provide a smooth solutions that cannot represent the geological reality. To circumvent this problem in the second and the third parts of this thesis, we made two major improvements. The first, we integrate Sequential Gaussian Simulation into the inversion procedure to determine a possible distributions of a single property. The second is that we used the Co-Simulation in the case of joint inversion to estimate a posteriori probabilities of the simulated models. The last part of this thesis presents an alternative to the several variables simulation, supervised learning of neural networks allows to establish a relationship between the different variables

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2015-10-22T14:36:33Z No. of bitstreams: 2 Dissertação - Elismar Jose de Araujo - 2015.pdf: 3923576 bytes, checksum: 60a5b973a48070a14372679c6aa08221 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-10-22T14:39:53Z (GMT) No. of bitstreams: 2 Dissertação - Elismar Jose de Araujo - 2015.pdf: 3923576 bytes, checksum: 60a5b973a48070a14372679c6aa08221 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2015-10-22T14:39:53Z (GMT). No. of bitstreams: 2 Dissertação - Elismar Jose de Araujo - 2015.pdf: 3923576 bytes, checksum: 60a5b973a48070a14372679c6aa08221 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2015-06-17 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This work will concentrate on making a rereading of the theories that surround the procedures for calculating the area of a convex polygon, as well as the volume of a pyramid whose base is a polygon convex, with its vertices properly represented in a coordinate system, in the plan or in space, respectively. Addresses some topics on arrays and determinant and some of its applications, in particular the study of polygon area and the volume of the pyramid. Based on applying a decisive factor for the calculation of the area of a triangle with its vertices represented in a coordinate system, presents a new theorem to calculate the area of any polygon convex, as well as, a new formula to calculate the volume of any pyramid with convex basis as a direct application of the volume of the tetrahedron with its vertices represented in an orthogonal system. For both, it was essential to the concept of coordinates in the plane and in space, vectors in the plane and in space, and some of its properties, being essential for the demonstrate the volume of the tetrahedron and the area of the triangle, using determinant. Keywords: Volume. Area. Convex polygon. Pyramid. Triangle. Tetrahedron / O presente trabalho versar a em fazer uma releitura das teorias que circundam os procedimentos de c alculo da area de um pol gono convexo, assim como, do volume de uma pir^amide cuja base e um pol gono convexo, com seus v ertices devidamente representados em um sistema de coordenadas, no plano ou no espa co, respectivamente. Aborda alguns t opicos sobre matrizes e determinante e algumas de suas aplica c~oes, em especial o estudo de area de pol gonos e o volume de pir^amide. Baseado na aplica c~ao de determinante para o c alculo da area de um tri^angulo com seus v ertices representados em um sistema de coordenadas, apresenta um novo teorema para o c alculo da area de qualquer pol gono convexo, assim como, uma nova f ormula para calcular o volume de qualquer pir^amide com base convexa como uma aplica c~ao direta do volume do tetraedro com seus v ertices representados em um sistema ortogonal. Para tanto, foi imprescind vel abordar o conceito de coordenadas no plano e no espa co, vetores no plano e no espa co e algumas de suas propriedades, sendo fundamentais para a demonstrar o volume do tetraedro e a area do tri^angulo, usando determinante.

Nous étudions, dans la première partie de notre thèse, les polysimplexes d’un espace euclidien de dimension quelconque, c’est-à-dire les objets consistant en une juxtaposition de simplexes réguliers (de tétraèdres si la dimension est 3) accolés le long de leurs faces. Nous étudions principalement le groupe des symétries de ces polysimplexes. Nous présentons une façon de représenter un polysimplexe à l’aide d’un diagramme. Ceci fournit une classification complète des polysimplexes à similitude près. De plus, le groupe des symétries se déduit du groupe des automorphismes du diagramme. Il découle en particulier de notre étude qu’en dimension supérieure à 2, une telle structure ne possède jamais deux faces parallèles et ne contient jamais de circuit fermé de simplexes.<p><p>Dans la seconde partie de notre thèse, nous abordons un problème classique de combinatoire :l’énumération des pavages d’un rectangle mxn à l’aide de dominos. Klarner et Pollack ont montré qu’en fixant m la suite obtenue vérifie une relation de récurrence linéaire à coefficients constants. Nous établissons une nouvelle méthode nous permettant d’obtenir la fonction génératrice correspondante et la calculons pour m <= 16, alors qu’elle n’était connue que pour m <= 10.<p> / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

[pt] A reconstrução de superfícies é um problema que recebe bastante atenção em Computação Gráfica dada a importância de suas aplicações. Uma solução comum é representar essas superfícies por malhas triangulares. Neste trabalho é proposta uma estrutura de tetraedros com cúbicas definidas em seu interior que são utilizadas para aproximar a superfície. Essas cúbicas, chamadas de TetraQuads, são superfícies implícitas de grau 3 definidas como interpolação de quádricas posicionadas nos vértices dos tetraedros. Esses elementos foram idealizados de forma que seja rápido o processamento para visualização dessa estrutura pelo hardware gráfico. Os objetos definidos dessa maneira carregam mais informações do ponto de vista da geometria diferencial que uma malha triangular. Por esse motivo, têm uma modelagem mais complexa a ser resolvida. Esse problema é discutido ao apresentar os passos para reconstrução de superfícies por TetraQuads a partir de nuvens de pontos. / [en] Surface reconstruction is a problem that receives a lot of attention in Computer Graphics due to the importance and the number of its applications. A common solution is to represent these surfaces through triangular meshes. This work introduces an alternative structure of tetrahedrons with cubics defined in its interior, which are used to approximate the surface. Those cubics, called TetraQuads, are third-degree implicit surfaces defined as an interpolation of quadrics positioned at the tetrahedrons vertices. These elements are constructed for an efficient visualization by the graphics hardware. Objects defined in this manner contain more information from the differential geometry point of view than a triangle mesh, which entails a more complex modeling problem. This problem is discussed throughout the steps of surface reconstruction from point clouds through TetraQuads.

Cette thèse s'intéresse à la génération, à l'utilisation et à l'évaluation des maillages hex-dominants, composés d'hexaèdres et de tétraèdres, dans la cadre de la simulation numérique par la méthode des éléments finis. Les éléments finis hexaédriques sont souvent préférés aux éléments tétraédriques car ils offrent un meilleur ratio entre précision et temps de calcul dans un certain nombre de situations. Cependant, si la génération automatique de maillages tétraédriques est aujourd'hui un domaine bien maîtrisé, ce n'est pas le cas de la génération de maillages hexaédriques alignés avec le bord, qui reste un problème largement ouvert. En l'absence de progrès significatifs, les approches actuelles se contentent de maillages hex-dominants afin de tirer parti des performances supérieures des hexaèdres et de la flexibilité géométrique des tétraèdres, qui rend possible le maillage automatique. Dans une première partie, nous développons des algorithmes robustes pour la génération de maillages hex-dominants à partir de champs de directions, notamment pour l'isolement et le remplissage des régions difficiles à mailler (singularités et autres dégénérescences). Dans la seconde partie, nous essayons de déterminer dans quelles situations et dans quelle mesure les maillages hexaédriques, et hex-dominants générés précédemment, sont plus intéressants que les maillages tétraédriques. Ceci implique spécifiquement d'étudier plusieurs manières d'effectuer des simulations par éléments finis avec les maillages hybrides, dont une approche où nous utilisons des contraintes de continuité pour maillages non-conformes. Pour mesurer l'influence du maillage sur l'approximation des solutions, nous proposons une nouvelle méthode d'échantillonnage pour calculer très efficacement des distances globales entre solutions éléments finis définies sur des domaines compliqués / This thesis focuses on generation, usage and evaluation of hex-dominant meshes, which are made of hexaehedra and tetrahedra, in the context of the finite element method. Hexahedron finite elements are often preferred to tetrahedron elements because they offer a better compromise between accuracy and computation time in certain situations. However, if tetrahedral meshing is a well mastered subject, it is not the case of hexahedral meshing. Generating hexahedral meshes with elements aligned to the borders is still an open and difficult problem. Meanwhile, current automated approaches can use hex-dominant meshes in order to take advantage of both hexahedron accuracy and geometrical flexibility of tetrahedra. In the first part, we develop robust algorithms for the generation of hex-dominant meshes with elements aligned with the borders. Specifically, we propose a method to extract and fill the areas where hexahedral meshing is difficult (singularities and degeneracies). In the second part, we try to identify and to quantify the advantages of hexahedral and hex-dominant meshes over tetrehedral ones. This requires to study various ways to apply the finite element method on hybrid meshes, including one in which we propose to use continuity constraints on hexahedral-tetrahedral non-conforming meshes. To measure the impact of meshes on the finite element accuracy, we develop a new sampling method which allows to compute efficiently global distances between finite element solutions defined on complicated 3D domains

Elevers inflytande på matematikundervisningen är önskvärd men föga undersökt. Syftet med examensarbetet var således att undersöka elevers upplevelse av att ha digitala läroböcker i matematikundervisningen. Undersökningen genomfördes med hjälp av fokusgruppsintervjuer med elever på gymnasiet. Tre klasser på teknikprogrammet intervjuades. Intervjuerna bearbetades med hjälp av innehållsanalys. Resultatet analyserades utifrån den didaktiska tetraedern med den digitala läroboken som artefakt. Resultatet visade att elever anser att läroböcker ska hjälpa dem lösa och förstå matematikuppgifter. Digitala läroböcker upplevdes ha goda förutsättningar att förklara matematik genom exempelvis anpassade förklaringar, ledtrådar och återkoppling. Däremot upplevdes digitala läroböcker ha sämre förutsättningar att lösa uppgifter eftersom risken att distraheras av annat på datorn var stor, svarsinmatningen var bristfällig, läroboken kunde vara oåtkomlig eller att förklaringar och uppgifter inte nödvändigtvis matchade varandra. För att ge elever inflytande på matematikundervisningen bör dessa aspekter beaktas vid val av läromedel genom övervägande av den digitala lärobokens utformning, implementering samt när en tryckt lärobok är att föredra. / Students’ influence on mathematics teaching is desirable but not extensively researched. The purpose of the thesis was therefore to investigate students' experience of using digital textbooks in mathematics education. The study was carried out using focus group interviews with Swedish upper secondary school students. Three classes from the technology program were interviewed. The interviews were processed using content analysis. The results were analysed using the didactic tetrahedron with the digital textbook as the artifact. The results showed that students believe that textbooks should help them solve and understand mathematics exercises. Digital textbooks were perceived to be well suited to explain mathematics by, for example, customized explanation, clues, and feedback. On the other hand, digital textbooks were felt to provide a worse environment for solving exercises. Reasons given include the risk of being distracted by other things on the computer was high, the ability to input answers was inadequate, the textbook could be inaccessible or that explanations and tasks did not necessarily match each other. To give students an influence on mathematics teaching, these aspects should be factors to consider when choosing teaching materials in terms of the digital textbook's design, implementation and when a printed textbook is preferable.

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TITLE Spatial generalizations of the properties of the triangle AUTHOR Jirˇı' Sřubarˇ SUPERVISOR Prof. RNDr. Adolf Karger, DrSc. DEPARTMENT Department of mathematics education ABSTRACT The present thesis describes various interesting properties of a triangle. The aim is to find and prove similar properties of its spatial generalization - a tetrahedron. Even though both synthetic and computational methods are used for proving spatial relations, synthetic approach is preferred whenever possible. The thesis is divided into two parts. In the first part, the properties of the tetrahedron analogous to the centroid and the orthocenter of the triangle are described. Also, conditions on the existence of the orthocenter of the tetrahedron are derived. Moreover, for tetrahedrons without an orthocenter, the so-called Monge point is introduced as its generalization. In the second part of the thesis, some further properties of the triangle are studied - - the Simson line, the de Longchamps point, the nine-point circle, the Euler line, the Lemoine point, the isodynamic points, the Lemoine axis and the Brocard axis. As the main contribution of the present thesis we define and prove the existence of spatial analogues of the above mentioned properties for the tetrahedron - the de Longchamps point, the twelve-point and...

This thesis deals with blobs modeling and visualizing (iso-surfaces, implicit-surfaces). It includes implementation of full-featured editor of these objects. It provides real-time operations over surfaces. The work also contains its motivation - where this modeling technique comes from, required equations and computations needed for surface rendering and algorithms used for blobs visualization.

Historically 3D game environments have almost always been immutable. Mutable environments are a technical challenge that will affect performance. For games of the future to continue approaching realism, mutable environments are an essential step. Popularized by the game title Minecraft (2009), the use of voxel engines in games has become increasingly common. However, by the nature of the discrete position of voxels, the method is limited in representing arbitrary polyhedral shapes like angled slopes. It also prohibits smooth mutations including proper movement and rotation of objects within the voxelization. This is generally mitigable with more voxels. However, this paper proposes a more precise solution to the problem. A tetrahedral mesh engine (tetra engine). By altering tetrahedral topology, vertex positions, and material of individual tetrahedrons, tetras are intended to solve the issue of arbitrary polyhedral shapes for voxels. Additionally, the tetrahedral mesh shows other promises such as providing a robust collision detection method and as an acceleration structure for e.g. raycasting. The research question can be summarized as investigating the feasibility of a tetra engine as a mutable game environment. 3 sub-research questions are given: The first regarding performance, the second regarding robustness, and the third different types mutations. The research questions are addressed along with a proof of concept (POC). The POC intends to investigate a proposal for the most efficient robust solution possible for the most basic mutation type known as edits. Because of time constraints, it does not cover all parts of the research questions but works as a bottom-up approach to understand what is required to realize a full-fledged tetra engine. Thus, a large part of the research question is answered theoretically both hypothetically with grounds from the POC and through previous work. The result shows a much more critical robustness consideration than expected and suggests relying on slower but more robust algorithms that are known to work. In conclusion, nothing suggests that a scalable future-proof tetra engine is impossible, but the algorithms required are much less efficient than those for voxels and robustness is an issue to overcome. However, numerous hypothetical advantages particularly regarding deformation and fluid simulation are still recognized and it is not obvious that future mutable environments would not benefit from a tetra engine rather than voxels. / Historiskt sätt har 3D-datorspelmiljöer nästan uteslutande varit oföränderliga. Det finns goda anledningar till detta. Föränderliga miljöer är en teknisk utmaning som påverkar speleffektiviteten. Om man däremot vill fortsätta utveckla mer realistiska datorspel är föränderliga spelmiljöer ett naturligt steg. Spelet Minecraft (2009) populariserade användandet av voxlar i datorspel vars material kan ändras för att förändra miljön. Sedan dess har voxlar i datorspel blivit mer och mer populära. Dock, på grund av voxlars diskreta positioner har de begränsningar i dess förmåga att representera godtyckliga polyedriska former så som arbiträrt vinklade plan. Detta omöjliggör även mjuka rörelser inklusive rörelse och rotering inom voxeliseringen. Det här problemet kan generellt dämpas med hjälp av mindre och fler voxlar. Men, för att lösa problemet ordentligt föreslår den här rapporten en annan lösning, nämligen en tetrahedrisk-mesh-motor (tetramotor). Genom att ändra tetraedrisk topologi, hörn positioner, samt material av individuella tetraedrar ska tetrorna kunna forma arbiträra polyedriska former och lösa problemet med voxlar. Utöver detta visar en tetraedrisk mesh andra intressanta möjligheter likt en metod för robust kollisions hantering och som en accelereringsstruktur för till exempel ray-casting. Forskningsfrågan kan sammanfattas som att utforska tillämpbarheten av en tetramotor för föränderliga datorspelsmiljöer. Tre underfrågor ges: Den första handlar om beräkningseffektivitet, den andra angående robusthet och den tredje oliky typer av mutationer. Forskningsfrågorna angrips med hjälp av en proof of concept lösning (POC). POC:en är menad att utforska ett förslag på en effektiv och robust metod för direkta förändringar. På grund av tidsbegränsningar så täcker inte POC:en alla delar av frågeställningarna men är menad som en botten upp lösning för att inse och förstå kraven för en komplett tetramotor. På grund av detta är en stor del av forskningsfrågorna svarade teoretiskt, både hypotetiskt baserat på insikterna från POC:en och med grund från tidigare forskning. Resultatet visar en mycket mer kritisk hänsyn till robusthet än förväntat och föreslår att man använder sig av långsammare men fungerande existerande lösningar. Slutsatsen är att inget tyder på att en skalbar framtidssäker tetramotor är en omöjlighet, men att algoritmerna är mycket långsammare än de som krävs för voxlar. Däremot finns potentieally fördelar med en tetra motor, främst med hänsyn till deformering och flödessimulering. Det är därför inte självklart att framtida muterbara spelmijöer inte skulle ha fördelar av en tetramotor istället för voxlar.