Bezier curve is one of the most fundamental primitives for the modeling of fonts and two-dimensional (2D) computer graphics objects. How to efficiently render the Bezier curve becomes an important task for many embedded applications. This thesis first proposed a novel adaptive curve-rendering algorithm which can determine the coordinates of all the crossing points of the curve and scan-lines with the required accuracy for the graphics fill operation. Next, for the rendering of stroked Bezier curves, this thesis proposed several possible rendering circuit architectures. The performance and gate count of these architectures have been estimated, and compared in this thesis. It has been found that the design based on the table-lookup normal vector calculator can lead to the fastest circuit, while the design based on the Cordic operator represents the most economic design. A basic Bezier curve rendering circuit has been implemented in this thesis, and used to accelerate a prototype OpenVG embedded systems.

Die Geometrie eines Druckbehälters wird unter Zuhilfenahme parametrischer Bezierkurven und durch die Integration einer externen Mathcad-Analyse in Creo hinsichtlich einer harmonischen, meridianen Spannungsverteilung optimiert.

[Truncated abstract] This thesis is concerned with geometrically-defined curves that can be used for interpolation in Riemannian or, more generally, semi-Riemannian manifolds. As in much of the existing literature on such curves, emphasis is placed on manifolds which are important in computer graphics and engineering applications, namely the unit 3-sphere S3 and the closely related rotation group SO(3), as well as other Lie groups and spheres of arbitrary dimension. All geometrically-defined curves investigated in the thesis are either higher order variational curves, namely critical points of cost functionals depending on (covariant) derivatives of order greater than 1, or defined by geometrical algorithms, namely generalisations to manifolds of algorithms from the field of computer aided geometric design. Such curves are needed, especially in the aforementioned applications, since interpolation methods based on applying techniques of classical approximation theory in coordinate charts often produce unnatural interpolants. However, mathematical properties of higher order variational curves and curves defined by geometrical algorithms are in need of substantial further investigation: higher order variational curves are solutions of complicated nonlinear differential equations whose properties are not well-understood; it is usually unclear how to impose endpoint derivative conditions on, or smoothly piece together, curves defined by geometrical algorithms. This thesis addresses these difficulties for several classes of curves. ... The geometrical algorithms investigated in this thesis are generalisations of the de Casteljau and Cox-de Boor algorithms, which define, respectively, polynomial B'ezier and piecewise-polynomial B-spline curves by dividing, in certain ratios and for a finite number of iterations, piecewise-linear control polygons corresponding to finite sequences of control points. We show how the control points of curves produced by the generalised de Casteljau algorithm in an (almost) arbitrary connected finite-dimensional Riemannian manifold M should be chosen in order to impose desired endpoint velocities and (covariant) accelerations and, thereby, piece the curves together in a C2 fashion. A special case of the latter construction simplifies when M is a symmetric space. For the generalised Cox-de Boor algorithm, we analyse in detail the failure of a fundamental property of B-spline curves, namely C2 continuity at (certain) knots, to carry over to M.

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Die Geometrie eines Druckbehälters wird unter Zuhilfenahme parametrischer Bezierkurven und durch die Integration einer externen Mathcad-Analyse in Creo hinsichtlich einer harmonischen, meridianen Spannungsverteilung optimiert.

This work deals with the creation of several interactive web applets for education of vector graphics. Described is the image signal, his discretization, vector and bitmap types of image record. Further they describe selected vector curves, their properties, algorithms for their construction and usage. The principles of rasterization of basic vector objects are explained. Using the Figma tool, graphical user interfaces for each applet are designed. These applets are implemented using HTML and Javascript. The implemented applets are placed on web pages that are used in computer graphics education.

Les recherches présentées dans ce mémoire s’inscrivent dans le cadre des réseaux decapteurs périodiques. Elles portent sur l’étude et la mise en oeuvre d’algorithmes et de protocolesdistribués dédiés à la gestion de données volumineuses, en particulier : la collecte, l’agrégation etla fouille de données. L’approche de la collecte de données permet à chaque noeud d’adapter sontaux d’échantillonnage à l’évolution dynamique de l’environnement. Par ce modèle le suréchantillonnageest réduit et par conséquent la quantité d’énergie consommée. Elle est basée surl’étude de la dépendance de la variance de mesures captées pendant une même période voirpendant plusieurs périodes différentes. Ensuite, pour sauvegarder plus de l’énergie, un modèled’adpatation de vitesse de collecte de données est étudié. Ce modèle est basé sur les courbes debézier en tenant compte des exigences des applications. Dans un second lieu, nous étudions unetechnique pour la réduction de la taille de données massive qui est l’agrégation de données. Lebut est d’identifier tous les noeuds voisins qui génèrent des séries de données similaires. Cetteméthode est basée sur les fonctions de similarité entre les ensembles de mesures et un modèle defiltrage par fréquence. La troisième partie est consacrée à la fouille de données. Nous proposonsune adaptation de l’approche k-means clustering pour classifier les données en clusters similaires,d’une manière à l’appliquer juste sur les préfixes des séries de mesures au lieu de l’appliquer auxséries complètes. Enfin, toutes les approches proposées ont fait l’objet d’études de performancesapprofondies au travers de simulation (OMNeT++) et comparées aux approches existantes dans lalittérature. / This thesis proposes novel big data management techniques for periodic sensor networksembracing the limitations imposed by wsn and the nature of sensor data. First, we proposed anadaptive sampling approach for periodic data collection allowing each sensor node to adapt itssampling rates to the physical changing dynamics. It is based on the dependence of conditionalvariance of measurements over time. Then, we propose a multiple level activity model that usesbehavioral functions modeled by modified Bezier curves to define application classes and allowfor sampling adaptive rate. Moving forward, we shift gears to address the periodic dataaggregation on the level of sensor node data. For this purpose, we introduced two tree-based bilevelperiodic data aggregation techniques for periodic sensor networks. The first one look on aperiodic basis at each data measured at the first tier then, clean it periodically while conservingthe number of occurrences of each measure captured. Secondly, data aggregation is performedbetween groups of nodes on the level of the aggregator while preserving the quality of theinformation. We proposed a new data aggregation approach aiming to identify near duplicatenodes that generate similar sets of collected data in periodic applications. We suggested the prefixfiltering approach to optimize the computation of similarity values and we defined a new filteringtechnique based on the quality of information to overcome the data latency challenge. Last butnot least, we propose a new data mining method depending on the existing K-means clusteringalgorithm to mine the aggregated data and overcome the high computational cost. We developeda new multilevel optimized version of « k-means » based on prefix filtering technique. At the end,all the proposed approaches for data management in periodic sensor networks are validatedthrough simulation results based on real data generated by periodic wireless sensor network.