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What is a curve?
Koudela, Libor ; Veselý, Jiří (advisor) ; Pyrih, Pavel (referee) ; Bobok, Jozef (referee)
The notion of a curve played important role in the history of mathematical thought. This dissertation is focused on the conception of a curve in analysis, point set theory and topology. The rectification of curves and the notion of arc length are considered in connection with the history of analysis from antiquity to the beginning of the 20th century. "Measurement of curves" is also discussed from the measure-theoretic viewpoint and various definitions of linear measure and fractional dimension are described. Historically, there are two main approaches to understanding curves. Jordan defined a curve as a continuous image of a closed interval. However, his definition appeared to be too wide, since it was met by objects such as the Peano curve. In the point set theory, a curve is considered to be a one-dimensional continuum. The development of the dimension theory and the continuum theory, starting with the pioneering work of Bolzano, was motivated by the search for rigorous topological definition of a curve, a surface etc. Among "pathological" curves, that were often introduced as counterexamples in the development of modern analysis, we can find early examples of fractals. The fractal theory motivated further study of mathematical properties of these curves in the late 20th century, such as self-similarity and...
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Working with vector graphics in .NET
Růžička, Filip ; Brožek, Jiří (advisor) ; Hanzlík, Petr (referee)
Current version of the Microsoft .NET Framework (4.6) provides access to the basic functionality of GDI+ (Graphical Device Interface) with more than fifty of code elements (classes, interfaces, structures, enumerated types, and delegates) contained in the System.Drawing namespace. Many advanced functions are then offered in other three nested namespaces, namely Drawing2D, Imaging and Text. This work demonstrates on a complex example using of a selected set of these library functions and compares their output, time and memory requirements with its own parameterizable implementation of the corresponding planar geometric shapes, antialiasing techniques and filling closed areas. The goal of this work is to create an application - a simple SVG format (Scalable Vector Graphics) viewer - which will be able to interpret SVG file commands in a graphical user interface by both of the above methods and for each of them to provide information about the computational complexity, on the basis of which we can show the appropriateness of using one or the other approach, library functions or user-defined functions with the possibility of further optimization.
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Spirometric measurement in LabVIEW
Hastík, Matěj ; Slávik, Vladimír (referee) ; Harabiš, Vratislav (advisor)
This bachelor thesis deals with a detailed description of functional examination of lungs. Predominant part of this thesis is focused on spirometry method and evaluation with spirometry curve. It also deals with study of Vernier LabPro, properties of spirometry probe Vernier and proposal of the structure of software in LabVIEW environment, which will serve for basic spirometry examination. The second part is devoted to the design of the program in LabVIEW, description of its features and capabilities and its actual runtime. The program is further enhanced with a feature that allows the processing, evaluation and archiving of measured spirometric curves. The program also includes a temperature compensation of breath in and breath out air.
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Curves in Computer Graphics
Míchal, Luboš ; Zuzaňák, Jiří (referee) ; Venera, Jiří (advisor)
This work deal with proposal and implementation demonstrational application, that will be instrumental towards demonstration curves used in computer graphic. Application is created in language C++ in environment Visual Studio 2005. By the help of those application can be individual steps of calculation watch and set control point. After it is possible watch differences among single used algorithms. Aim work is put near individual curves potential interested person about this theme.
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Interpolation with NURBS curves
Škvarenina, Ľubomír ; Rajmic, Pavel (referee) ; Zátyik, Ján (advisor)
Diploma thesis deals with image interpolation. The aim of this work is to study theoretically and then describe the nature of the various methods of image interpolation and some of them implemented in the program MATLAB. The introductory part of this work theoretically closer to important terms that are closely related to this topic of digital image processing sufficient to understand the principle. In the following of the thesis will be discussed all of today's commonly used method of image interpolation. Will hear all about the method of image interpolation using nearest neightbor interpolation and image help of polynimals such as (bi)linear, (bi)quadratic and (bi)kubic method. Then work theoretically analyzes the theory of individual species curves and splines. More specifically, coming to their most frequently used variants of B-spline curves and ther generalizations called NURBS, with addressing the problem of interpolating these curves. The final chapter consists of the results achieved in the program MATLAB.
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Live typeface
Jiříček, Milan ; Špiřík, Jan (referee) ; Rajmic, Pavel (advisor)
The work describes the theoretical foundations of modern methods of creating new fonts, that is, using information technology, specifically vector programs. It also marginally shows the history of the font, Roman writing, the basic division of its compositions and describes its individual elements. The next part of the project focuses on creating digital fonts and continues with bringing it to live using algorithms and methods that can easily be processed in Matlab programming language. The method of implementation of the bringing the typeface to live is described and presentation of the generated results are then shown in few examples. Attention is also paid to the coordinates system, which is very important to solve geometric transformations, and two-dimensional vector graphics, which are widely used in the design and to render the fonts. Bézier curves and cubic Bézier curves are described in further detail along with vector graphics rasterization. One part of this text describes very important de Casteljau algorithm. The last chapter focuses on implementation in Matlab programming language, the creation of curves, that means single font characters, and the ways of how the algorithm works with transformations. Some sample images showing transformations using different input arguments are displayed in this section as well. There is evaluation of the contribution of this application and the possibilities of further expansion at the end.
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Software support of education in cryptography area based on elliptic curves
Szturc, Jakub ; Sobotka, Jiří (referee) ; Burda, Karel (advisor)
The master‘s thesis is focusing on cryptography based on elliptical curves consists of four main parts. The first part provides an overview of the basic cryptographic and mathematical concepts. A key element of this work is the second part which are described in detail the mechanisms of counting two points on elliptic curve and counting point to themselves over the various fields. On this mechanism is based almost the entire issue. In the third section provides the best-known algorithms and protocols for key exchange, encryption and digital signature. The goal of this paper is to devise software to support teaching. This material is created as a web presentation, which described the theoretical foundations and the main characteristics of cryptosystems based on elliptical curves. The whole issue is supported by practical examples of calculations examples, there are also examples for independent work. Additionally, java applets are prepared that allow an interactive opportunity to try the basic parameters of curves, or verify the calculations.
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Vývoj poptávky po vybraných komoditách na základě sekundárních dat
Řičař, Michal ; Soukup, Jindřich (advisor) ; Nováček, Jan (referee)
Poptávka, jakožto determinující faktor vyráběných statků z dlouhodobého hlediska, je natolik důležitý činitel dění v ekonomickém světě, že je potřebné důkladné zkoumání všech příčin a souvislostí, které ji mohou ovlivňovat. Pokud se podaří eliminovat jednotlivé, dříve zvažované, prvky, pak lze postupně získat takové ukazatele, které jednoznačně na poptávku působí. Sekundární data poslouží k náležitému rozlišení a následné dedukce pomohou k osvětlení nejužších souvislostí. Je zřejmé, že k takovýmto závěrům je třeba relevantních softwarových nástrojů, bez kterých by v dnešní době nebylo možno dostatečně adekvátně reagovat na turbulentní prostředí.
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