Cette thèse présente une méthode de détection et de correction des intersections visuelles et singulières entre courbes B-splines adaptée à la généralisation des cartes marines. Dans une première partie, nous nous intéressons à la détection des intersections. La méthode proposée effectue d'abord un partitionnement du plan. Les courbes sont reparties dans les cellules sans calcul numérique. Le partitionnement est donc rapide et robuste. Ensuite, les intersections sont calculées à l'aide de schémas de subdivision. La deuxième partie concerne la correction des conflits par déformation respectant les contraintes cartographiques. Nous présentons une première méthode où le polygone de contrôle est assimilé à un réseau de barres déformé par l'application de forces externes. Une deuxième méthode est ensuite présentée où le déplacement est représenté par un snake soumis a des énergies définies en fonction des conflits. Les paramètres de forme sont réglés automatiquement.

Ferrets are amusing, flexible creatures that have been under represented in computer models. Because their bodies can assume almost any curved shape, splines are the natural tool for modelling ferrets. Surface pasting is a hierarchical method of modelling with spline surfaces, where features are added onto a base surface. Existing surface pasting techniques are limited to modelling rectilinear shapes. Using the task of modelling a ferret as a driving force, I propose a method of pasting cylinders in world space; I looked at methods for reducing distortion of pasted features; and I created a method for pasting trimmed features to allow for features that do not have the rectilinear shape of standard pasting. With my methods, modelling ferrets with surface pasting is easier, and the resulting models are closer to a real ferret.

Ferrets are amusing, flexible creatures that have been under represented in computer models. Because their bodies can assume almost any curved shape, splines are the natural tool for modelling ferrets. Surface pasting is a hierarchical method of modelling with spline surfaces, where features are added onto a base surface. Existing surface pasting techniques are limited to modelling rectilinear shapes. Using the task of modelling a ferret as a driving force, I propose a method of pasting cylinders in world space; I looked at methods for reducing distortion of pasted features; and I created a method for pasting trimmed features to allow for features that do not have the rectilinear shape of standard pasting. With my methods, modelling ferrets with surface pasting is easier, and the resulting models are closer to a real ferret.

The use of B-spline interpolation functions in the finite element method (FEM) is not a new subject. B-splines have been utilized in finite elements for many reasons. One reason is the higher continuity of derivatives and smoothness of B-splines. Another reason is the possibility of reducing the required number of degrees of freedom compared to a conventional finite element analysis. Furthermore, if B-splines are utilized to represent the geometry of a finite element model, interfacing a finite element analysis program with existing computer aided design programs (which make extensive use of B-splines) is possible. While B-splines have been used in finite element analysis due to the aforementioned goals, it is difficult to find resources that describe the process of implementing B-splines into an existing finite element framework. Therefore, it is necessary to document this methodology. This implementation should conform to the structure of conventional finite elements and only require exceptions in methodology where absolutely necessary. One goal is to implement B-spline interpolation functions in a finite element framework such that it appears very similar to conventional finite elements and is easily understandable by those with a finite element background. The use of B-spline functions in finite element analysis has been studied for advantages and disadvantages. Two-dimensional B-spline and standard FEM have been compared. This comparison has addressed the accuracy as well as the computational efficiency of B-spline FEM. Results show that for a given number of degrees of freedom, B-spline FEM can produce solutions with lower error than standard FEM. Furthermore, for a given solution time and total analysis time B-spline FEM will typically produce solutions with lower error than standard FEM. However, due to a more coupled system of equations and larger elemental stiffness matrix, B-spline FEM will take longer per degree of freedom for solution and assembly times than standard FEM. Three-dimensional B-spline FEM has also been validated by the comparison of a three-dimensional model with plane-strain boundary conditions to an equivalent two-dimensional model using plane strain conditions.

Impellers are important components in the field of aerospace, energy technology, and precision machine industries. Considering the high accuracy and structural integrity, impellers might be manufactured by cutting. Due to their complex geometries and high degrees of interference in machining, multi-axis machines are requested to produce impellers. The object of this thesis is to improve 5-axis tool paths for surface quality of impellers by smoothing point cutting tool paths in terms of linear segments and B-Splines and by using flank milling technologies with linear segment and B-Splines tool paths. Experimental results show that the surface quality of impeller blades can be improved by point cutting with smoothed tool paths and by flank milling. Moreover, the required milling time can be reduced by 18 percent and 13percent based on smoothed linear tool paths and smoothed B-Splines tool paths, respectively.

Modeling of the ionosphere has been a highly interesting subject within the scientific community due to its effects on the propagation of electromagnetic waves. The development of the Global Positioning System (GPS) and creation of extensive ground-based GPS networks started a new period in observation of the ionosphere, which resulted in several studies on GPS-based modeling of the ionosphere. However, software studies on the subject that are open to the scientific community have not progressed in a similar manner and the options for the research community to reach ionospheric modeling results are still limited. Being aware of this need, a new MATLAB&reg / based ionosphere modeling software, i.e. TECmapper is developed within the study. The software uses three different algorithms for the modeling of the Vertical Total Electron Content (VTEC) of the ionosphere, namely, 2D B-spline, 3D B-spline and spherical harmonic models. The study includes modifications for the original forms of the B-spline and the spherical harmonic approaches. In order to decrease the effect of outliers in the data a robust regression algorithm is utilized as an alternative to the least squares estimation. Besides, two regularization methods are employed to stabilize the ill-conditioned problems in parameter estimation stage. The software and models are tested on a real data set from ground-based GPS receivers over Turkey. Results indicate that the B-spline models are more successful for the local or regional modeling of the VTEC. However, spherical harmonics should be preferred for global applications since the B-spline approach is based on Euclidean theory.

<p>Paper A: In this paper, the development and implementation of a contact algorithm based on C2-continuous surface representations is discussed. In 3D contact simulations involving models with arbitrarily curved surfaces (as in the case of vessel walls), the discretization of the contact surfaces by means of facet-based techniques could lead to numerical instabilities and finally loss of quadratic convergence. These instabilities arise mainly due to the sliding of contractor (slave) nodes over the boundaries of target (master) contact facets, where jumps of the normal vector are experienced. The paper addresses successfully this problem, by discretization of the target surfaces by means of C2-continuous parameterization schemes. Initially, the uniform cubic B-spline surfaces are introduced. Next, in an attempt for more accurate representations of the geometric models of the contact surfaces, a new parameterization based on the expression of cubic B-splines is developed. The two approaches are implemented into a finite element framework and more specifically, into the multipurpose finite element analysis program FEAP. The special merits of the developed algorithms and the advantages of the smooth surfaces over facet-based approaches are exhibited through a classical contact mechanics problem, considering incompressibility, finite deformations and large slidings. Next, a simulation of balloon angioplasty with stenting is presented, where the contact between both medical devices (balloon and stent) with the arterial wall is modeled. The arterial wall is modeled in this first approach, as hyperelastic, homogeneous, isotropic, while a cylindrically orthotropic model is developed to capture the nonlinear, anisotropic behavior of the balloon catheter under pressure. Two stents with the same geometry but different strut thickness, are studied. Both are considered elasto-plastic. The performed simulations point out the outcome of the balloon angioplasty and stenting in terms of luminal gain and mechanical strains. Finally, a comparison between the two stent configurations is presented.</p><p>Paper B: The second paper makes use of the contact tool developed in Paper A and focuses on the changes of the mechanical environment of the arterial wall due to stenting, as a function of a set of stent design parameters. In particular, Paper B presents a detailed geometric and material model of a postmortem human iliac artery, composed by distinct tissue components, each associated with specific mechanical properties. The constitutive formulation for the artery considers anisotropic, highly nonlinear mechanical characteristics under supraphysiological loadings. The material and structural parameters of the arterial model are obtained through uniaxial tensile tests on stripes extracted from the several arterial tissues that form the stenosis, axially and circumferentially oriented. Through cooperation with a well-established stent manufacturing company, an iliac stent was acquired. The dimensions of the stent are measured under a reflected-light microscope, while it is parameterized in such a way as to enable new designs to be simply generated through variations of its geometric parameters. The 3D balloon-stent-artery interaction is simulated by making use of the smooth contact surfaces with C2-continuity, as previously mentioned. Next, scalar quantities attempt to characterize the arterial wall changes after stenting, in form of contact forces induced by the stent struts, stresses within the individual components and luminal change. These numerically derived quantities allow the determination of the most appropriate stent configuration for an individual stenosis. Therefore, the proposed methodology has the potential to provide a scientific basis for optimizing treatment procedures, stent material and geometries on a patient-specific level.</p>

Dans les industries agro-alimentaires ainsi que dans d'autres secteurs d'activités, l'analyse sensorielle est la clé pour répondre aux attentes des consommateurs. Cette discipline est le plus souvent basée sur l'établissement de profils sensoriels à partir de notes attribuées par des juges entraînés selon une liste de descripteurs (variables sensorielles). Dans ce type d'étude, il importe d'étudier la performance des juges et d'en tenir compte dans l'établissement des profils sensoriels. Dans cette perspective, nous proposons une démarche qui permet de procurer des indicateurs de performance du jury et de chacun des juges et de tenir compte de cette performance pour une détermination d'un tableau moyen. Des tests d'hypothèses pour évaluer la significativité de la contribution des juges à la détermination du compromis sont également proposés.<br />Depuis une vingtaine d'années, les courbes temps-intensité (TI) qui permettent de décrire l'évolution d'une sensation au cours de l'expérience sont de plus en plus populaires parmi les praticiens de l'analyse sensorielle. La difficulté majeure pour l'analyse des courbes TI provient d'un effet juge important qui se traduit par la présence d'une signature propre à chaque juge. Nous proposons une approche fonctionnelle basée sur les fonctions B-splines qui permet de réduire l'effet juge en utilisant une procédure d'alignement de courbes.<br />D'autres données sensorielles au cours du temps existent telles que le suivi de la dégradation organoleptique de produits alimentaires. Pour les étudier, nous proposons la modélisation par des chaînes de Markov cachées, de manière à pouvoir ensuite visualiser graphiquement la suivi de la dégradation.

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<p>Interfaces play a dominant role in governing the response of many biological systems and they pose many challenges to traditional finite element. For sharp-interface model, traditional finite element methods necessitate the finite element mesh to align with surfaces of discontinuities. Diffuse-interface model replaces the sharp interface with continuous variations of an order parameter resulting in significant computational effort. To overcome these difficulties, we focus on developing a computationally efficient spline-based finite element method for interface problems.</p><p>A key challenge while employing B-spline basis functions in finite-element methods is the robust imposition of Dirichlet boundary conditions. We begin by examining weak enforcement of such conditions for B-spline basis functions, with application to both second- and fourth-order problems based on Nitsche's approach. The use of spline-based finite elements is further examined along with a Nitsche technique for enforcing constraints on an embedded interface. We show that how the choice of weights and stabilization parameters in the Nitsche consistency terms has a great influence on the accuracy and robustness of the method. In the presence of curved interface, to obtain optimal rates of convergence we employ a hierarchical local refinement approach to improve the geometrical representation of interface. </p><p>In multiple dimensions, a spline basis is obtained as a tensor product of the one-dimensional basis. This necessitates a rectangular grid that cannot be refined locally in regions of embedded interfaces. To address this issue, we develop an adaptive spline-based finite element method that employs hierarchical refinement and coarsening techniques. The process of refinement and coarsening guarantees linear independence and remains the regularity of the basis functions. We further propose an efficient data transfer algorithm during both refinement and coarsening which yields to accurate results.</p><p>The adaptive approach is applied to vesicle modeling which allows three-dimensional simulation to proceed efficiently. In this work, we employ a continuum approach to model the evolution of microdomains on the surface of Giant Unilamellar Vesicles. The chemical energy is described by a Cahn-Hilliard type density functional that characterizes the line energy between domains of different species. The generalized Canham-Helfrich-Evans model provides a description of the mechanical energy of the vesicle membrane. This coupled model is cast in a diffuse-interface form using the phase-field framework. The effect of coupling is seen through several numerical examples of domain formation coupled to vesicle shape changes.</p> / Dissertation