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Curves hidden in differential equations
Žalobínová, Petra ; Pyrih, Pavel (advisor) ; Bárta, Tomáš (referee)
Bachelor thesis Curves hidden in differential equations is engaged in solving and deriving differential equations, leading to the selected curve, which are cycloid curve and curves described by the hyperbolic functions . The core of the work is outlined into four transparent chapters, where the first of them gives a brief insight into the theory of curves and differential equations. In the following chapters, the work is specifically devoted to two historically significant problems, which are brachistochrone and catenary problems, but also deals with eigen, more modern problem of dynamics of symbiotic populations. The text explains the procedure of deriving differential equations from the considered problems and shows their solutions, by multiple methods. The contribution of this work, apart from the formulation and solution of the problem of symbiotic populations, is processing and making additions to solutions of these problems using a variety of methods from cited literature. The most important addition is relatively new and less known proof of the uniqueness of solutions of brachistochrone problem, which is enhanced by eigen intermediate steps and explanations.
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The construction of curves by Descartes
Fabián, Tomáš ; Kvasz, Ladislav (advisor) ; Zhouf, Jaroslav (referee)
This work studies the construction of algebraic curves by means of mechanical plotting tools designed by René Descartes. The work includes a brief biography of Descartes, an outline of his scientific method and a description of Descartes' views on curves, their construction and use. By means of dynamic geometry several curves established by Descartes are constructed. These include curves constructed by means of a drawing instrument composed of several rulers; a drawing instrument designed for the hyperbola and its different variations, in which the guiding line is replaced by one of conics in a special position. In the final part we present the construction of four ovals, which are usable in catoptric and dioptric that Descartes constructed by a point wise construction. All drawings are made in Cabri Geometry II and are accompanied by a derivation of the equations of the resulting curves. In deriving these equations we used only elementary algebraic methods, which could be used by Descartes himself and which are comprehensible by secondary school students. Keywords: Descartes, ruler device, curve, conchoid, trident, oval
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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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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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Problems of the Expert Analysis of the Vehicle Movement and Braking Action in General Spatial Curve at Speed Higher than 50 km/h
Panáček, Vladimír ; Šachl, Jindřich (referee) ; Drahotský, Ivo (referee) ; Vémola, Aleš (advisor)
The present apparatus for the technical analysis of road accidents has no well-integrated information, recommendations or procedures of how to solve comprehensively the analysis of road accidents involving vehicles equipped with stabilization system of driving dynamics. The problem in the investigation of a vehicle movement in a curve is the ignorance of the contributions of vehicle dynamics intervention of the electronic stability system. Although some of the simulation software used in the analysis of road accidents makes it possible to take into account the modelled vehicle movement impacted by a stabilization system in the examined process, but the experts do not know what parameters should be entered in the numerical models of stabilization system in a computer programme. Therefore, the thesis investigates the issue of the expert analysis of vehicle riding and braking in a general spatial curve at speeds exceeding 50 kph with simultaneous examining the impact of electronic stability system chassis on vehicle driving dynamics. The thesis first deals with the solutions based on classical analytical methods, then dwells on experimental measurements in real conditions on testing grounds and, finally, addresses the use of computer simulation software in expert practice. Nevertheless, it is important to realize that no computer simulation software can be an absolutely unambiguous solver, and it is not enough to generate a computer simulation, but so obtained results should be evaluated and justified technically. Road accident analyst needs to know the impact of vehicle electronic stability control systems on vehicle movement. The thesis investigated the mutual relationship between the vehicle speed limit in a curve specified by analytical calculation and the vehicle speed in a curve experimentally detected by measuring the parameters of driving dynamics of a vehicle equipped with electronic stability system. The impact of selected electronic stability control systems of the chassis on the vehicle movement in the investigated processes in the curve was detected and quantified by driving experiments. Finally, the input values of significant quantities of computational models of the ESP simulation programs were found consistent with the results of experimental measurements in defined curves for the vehicles equipped with electronic stability systems. The results of the thesis can be used both in the expert and in the teaching activities.
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Selected ČSN Road Design Elements Optimization
Stránský, Jakub ; Čepil, Jiří (referee) ; Kosňovský, Michal (advisor)
The master‘s thesis focuses on the optimization of the design values of curves of the horizontal alignments of the roads. It deals with the comparison of values between czech and foreign standards and differences between them. The practical part examines the values of the real speeds of vehicles passing through the curves of various parameters that were measured during measurements of selected curves during 2014. From these data a new design values are derived that could be used for the design of horizontal alignments.
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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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