[pt] Neste trabalho apresentamos uma proposta para auxiliar o estudo de funções polinomiais no ensino médio por intermédio das Curvas de Bézier. Para isto introduzimos as curvas de Bézier utilizando o algoritmo de De Casteljau e discutimos suas propriedades. Em seguida aplicamos a formulação das curvas de Bézier não paramétricas para representar funções polinomiais e discutimos alguns resultados observados em sala de aula. / [en] In this work we present a proposal to assist the study of polynomial functions in high school through the Bezier curves. For this we introduce the Bezier curves using the De Casteljau algorithm and discuss its properties. Then apply the formulation of Bezier curves non-parametric to represent polynomial functions and discuss some results observed in the classroom.

Ce travail s'inscrit dans le cadre de la géométrie de la CAO. Il traite d'un point de vue algorithmique des coniques et de leurs faisceaux. Ces courbes rationnelles sont ici décrites par une liste de trois vecteurs massiques linéairement indépendants appelée forme (BR) de la conique. Un vecteur massique est soit un vecteur pur, soit un point pondéré de l'espace dans lequel sont plongées ces courbes rationnelles ainsi que l'ont défini Fiorot et Jeannin en 1986. Le chapitre 1 rappelle les principaux résultats concernant les courbes Bézier-de Casteljau et les courbes (BR). Le chapitre 2 établit toutes les formes d'une conique définie par un foyer, la directrice associée et l'excentricité. Les différentes formes (BR) d'une conique sont obtenues par des changements de paramètre homographique. Réciproquement, à partir de trois vec-teurs massiques linéairement indépendants et à l'aide de changements de paramètre homographique appropriés, une forme (BR) particulière de la conique est obtenue. Celle-ci donne directement les éléments géométriques remarquables de la conique. Les chapitres suivants traitent de la représentation (BR) des faisceaux de coniques. Chaque type de faisceau se caractérise par une liste de trois vecteurs massiques. Un de ces vecteurs sert à définir le paramètrage du faisceau. Le chapitre 3 donne deux formes (BR) du faisceau de coniques bitangentes. Le chapitre 4 donne une forme (BR) du faisceau des coniques passant par trois points et tangente en un des points à une droite donnée. La forme (BR) d'un faisceau de coniques passant par quatre points du plan est traitée dans le chapitre 5. Les chapitres 6 et 7 traitent respectivement des faisceaux (BR) de coniques osculatrices et surosculatrices. Notons enfin que, pour les coniques comme pour leurs faisceaux, les formes (BR) présentent dans la plupart des cas un ou deux vecteurs purs décrivant les points à l'infini de la conique et les rendant aisément exploitables dans le domaine de la CAO.

Splines are a common mixed-initiative technique for road generation. A designer draws the shape of the curve but the mesh can be procedurally generated along the spline. This relationship improves the workflow of building roads in virtual environments and video games without taking away all of the control of the designer. Whilst this technique is useful when building single roads such as race tracks, it unfortunately struggles when dealing with more complex road networks that feature intersections. These intersections struggle with overlapping meshes and flickering textures without a straightforward solution. This problem significantly limits the usefulness of spline tools when generating roads. This paper aims to solve part of this problem by suggesting a method for detecting intersections in splines that support procedural mesh generation.

This diploma thesis deals with the creation of interactive tools for 3D computer graphics. The introduction of the thesis focuses on general theory of curves and surfaces and its mathematical description. The topics of Geometric transformation, Perspective projection and Parametric description of 3-dimensional surface are analysed in more detail. The successive chapter deals with the subject of visualisation of spatial objects in Java platform interface. The practical part describes the implementation of individual applets. JAVA programming language, which uses the library functions JOGL, was employed for the very realization of the interactive tools. The goal of the diploma thesis is the creation of a set of interactive applets in the field of computer graphics. These applets will be placed on the website of the faculty and they will serve students of VUT in Brno to improve the quality of education.

In this master’s thesis we focus on the basic properties of computer curves and their practical applicability. We explain how the curve can be understood in general, what are polynomial curves and their composing possibilities. Then we focus on the description of Bezier curves, especially the Bezier cubic. We discuss in more detail some of fundamental algorithms that are used for modelling these curves on computers and then we will show their practical interpretation. Then we explain non uniform rational B-spline curves and De Boor algorithm. In the end we discuss topic rasterization of segment, thick line, circle and ellipse. The aim of master’s thesis is the creation of the set of interactive applets, simulating some of the methods and algorithm we discussed in theoretical part. This applets will help facilitate understanding and will make the teaching more effective.

This thesis deals with basic methods of root mean square and peak value measurement of a digital acoustic signal, algotithms to measure audio programme loudness and true-peak audio level according to recommendation ITU-R BS.1770-1 and digital systems for control of signal dynamic range. It shows achieved results of root mean square and peak value measurement and results of implementation of dynamic processor with general piecewise linear non-decreasing static curve and algorithms according to recommendation ITU-R BS.1770-1.

In this master’s thesis we focus on the basic properties of computer curves and their practical applicability. We explain how the curve can be understood in general, what are polynomial curves and their composing possibilities. Then we focus on the description of Bezier curves, especially the Bezier cubic. We discuss in more detail some of fundamental algorithms that are used for modelling these curves on computers and then we will show their practical interpretation. Then we explain non uniform rational B-spline curves and De Boor algorithm. In the end we discuss topic rasterization of segment, thick line, circle and ellipse. The aim of master’s thesis is the creation of the set of interactive applets, simulating some of the methods and algorithm we discussed in theoretical part. This applets will help facilitate understanding and will make the teaching more effective.