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Acceleration of Graphics Operations by Means FPGA
Čapka, Ladislav ; Šimek, Václav (referee) ; Vašíček, Zdeněk (advisor)
This term project is aimed on analysis of graphic pipeline which can rasterize required picture. Document is specialized to drawing algorithms that are used in rasterization block. Major aim of this project is describing of rasterization algorithms that can be implemented on hardware. Type of aimed hardware is field-programmable gate array FPGA.
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NURBS surfaces of revolution
Sekáč, Ondřej ; Martišek, Dalibor (referee) ; Procházková, Jana (advisor)
The goal of this bachelor’s thesis is to give an overview of NURBS surfaces of revolution. NURBS surfaces are rational B-spline surfaces, which allows for construction of conics, hence anuloid, sphere and other surfaces of revolution. The thesis also contains an application that can create NURBS surfaces of revolution and description of algorithms used.
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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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Proposal of 3D Electronic Catologue
Špaček, Ondřej ; Dvořák,, Jiří (referee) ; Dvořák, Jiří (advisor)
This Bachelor's thesis deals proposal of 3D electronic catalogue solution of private company. The work affords theoretic base of 3D modeling and methods 3D modeling uses. There is account of some options for display 3D graphics by 2D display devices. The work describes basic axiom of HTML, CSS and PHP languages too.
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Teaching aids for 2D computer graphics
Malina, Jakub ; Průša, Zdeněk (referee) ; Rajmic, Pavel (advisor)
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.
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Mathematical description of vehicle motion trajectory
Lorenczyk, Jiří ; Popela, Pavel (referee) ; Porteš, Petr (advisor)
The goal of this thesis is to nd types of curves which would allow for the construction of a path that could be traversed by a vehicle. It seems that a minimal constraint for such a path is the continuity of curve's curvature. This leads to a closer look at the three types of curves: Clothoids, which are able to smoothly connect straights with arcs of a constant curvature, interpolation quintic splines, which are C2 smooth in the interpolation nodes and -splines, these belong to the family of quintic polynomial curves too, however, they are characterised by the vector of parameters which modies the shape of the curve. The thesis is accompanied by an application allowing for manual construction of the path composed of spline curves.
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Interpolating and approximating spline curves
Jelínek, Daniel ; Štarha, Pavel (referee) ; Procházková, Jana (advisor)
This bachelor’s thesis deals with properties and algorithms of smooth curves calculation, specifically the calculation of B-spline curves. These curves can be applied in computer graphics. Since their calculation is defined recurrently, it is almost a necessity to use computers with programmed algorithms to obtain these curves. As for the practical part of this work, three programs for the calculation of approximating B-spline curves, interpolating B-spline curves and NURBS curves were created.
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NURBS surfaces of revolution
Sekáč, Ondřej ; Martišek, Dalibor (referee) ; Procházková, Jana (advisor)
The goal of this bachelor’s thesis is to give an overview of NURBS surfaces of revolution. NURBS surfaces are rational B-spline surfaces, which allows for construction of conics, hence anuloid, sphere and other surfaces of revolution. The thesis also contains an application that can create NURBS surfaces of revolution and description of algorithms used.
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Spline interpolation in CNC milling
Soukupová, Veronika ; Píška, Miroslav (referee) ; Ohnišťová, Petra (advisor)
Tato práce se zaměřuje na využití různých typů splinové interpolace pro obrábění na číslicově řízených strojích. Cílem této práce je teoreticky popsat využití splinových interpolací při CNC frézování a následně stanovit a zhodnotit limity využití různých typů splinových interpolací na základně daného objemu vstupních dat. Součástí práce je vytvoření programu pro generaci různého počtu uzlových bodů na analyticky známé křivce. Následuje vložení uzlových bodů do vytvořeného CNC programu pětiosého obráběcího centra a poté jeho verifikace. Pro stejné uzlové body jsou aplikovány různé druhy interpolace pro následné porovnání metod a stanovení minimálního počtu bodů na délku křivky pro dosažené vyhovující přesnosti při použití dané interpolační metody.
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Isogeometric analysis in applications
Bekrová, Martina ; Šír, Zbyněk (advisor) ; Hron, Jaroslav (referee)
Isogeometric analysis (IGA) is a numerical method for solving partial differential equations (PDE). In this master thesis we explain a concept of IGA with special emphasis on problems on closed domains created by a single NURBS patch. For them we show a process how to modify the NURBS basis to ensure the highest possible continuity of the function space. Then we solve the minimal surface problem using two different Newton type methods. The first one is based on the classical approach using PDE, in the second one we use unique advantages of IGA to directly minimize the area functional.
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