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FFD methods
Novák, Jiří ; Martišek, Karel (referee) ; Procházková, Jana (advisor)
The diploma thesis deals with the topic of free-form deformations. The main goal of this work were elaboration of theoretical knowledge about this issue and the programming of selected methods od free-form deformations. The first part describes the required spline theory, matrix calculus and free-form deformations. The resulting version shows three programs. The first program compares the selected free-form deformation methods to the example of the 4x4 control point grid. The second program serves as a generalization for the general case of grid of control points. The last program is based on direct manipulation of arbitrary surface point and following recomputation of the control points to obtain demanded shape.
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Dynamic model for estimation of radon concentration in buildings
Vaňková, Barbora ; Brabec, Marek (advisor) ; Komárek, Arnošt (referee)
Title: Dynamic model for estimation of radon concentration in buildings Author: Barbora Vaňková Department: Department of probability and mathematical statistics Supervisor: Ing. Marek Brabec, Ph.D. Supervisor's e-mail address: mbrabec@cs.cas.cz Abstract: In the present work there is described the method for estimation of functi- onal data from discrete values and basic methods of functional data analysis. 1
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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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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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Movement correction in thoracic dynamic contrast CT data
Jakubíček, Roman ; Malínský, Miloš (referee) ; Walek, Petr (advisor)
This thesis deals with a nonrigid image registration for movement correction in thoracic dynamic contrast CT data. The deformation field is initialized by the analysis of disparities based on nonlinear matched filter, which defines local movement deformation. The values of control points are optimized by the Nelder-Mead method. The transformation model is based on a 4D (3D + time) free-form B-spline deformation for feature of movement distortion. The first part of the thesis briefly discusses the theory of image registration. Knowledge of this theory is necessary for understanding the remaining chapters, which describe the proposed method and its realization. The large part of this thesis is devoted to the geometrical image transformations, that is very important for the image registration. The thesis also describes a simplex method for function minimization. Three publicated methods of registration of medical 4D CT data are given. In the following chapter are individual parts of the purposed nonrigid registration including possible problems and their solution described.
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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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Functional data analysis and modeling age-specific mortality and age-specific fertility
Bezchlebová, Daniela ; Bašta, Milan (advisor) ; Dotlačilová, Petra (referee)
The aim of this thesis is to analyze two major indicators representing the processes of natural changes in population, which are not influenced by age structure -- age specific fertility rate and age specific mortality rate and to introduce functional data analysis, which has recently become increasingly applied in many scientific fields. The functional data analysis is introduced on the Czech demographic data set for more than last sixty years. The thesis briefly describes historical development of mortality and fertility and also describes selected methods of functional data analysis by using statistical program R. Functional data analysis provides a wide variety of graphics tools to explore the data which we called functional and help us to explore all typical and atypical features, identify outliers etc.
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SIGA 2011
Kolman, Radek ; Linkeová, I. ; Okrouhlík, Miloslav ; Pařík, Petr
The conference SIGA 2011 aimed to bring together mathematicians, physicists, computer designers and engineers dealing with splines who are using them for the numerical solutions of partial differential equations of various problems in mechanics and physics. In computational mechanics, it is isogeometric analysis (IGA) which is being dynamically developed. This numerical method employs shape functions based on different types of splines (B-splines, NURBS, T-splines and many others), and the fields of unknown quantities are consequently described the same way as the geometry of the studied domain. In addition, this approach provides a higher degree of continuity than that offered by the classical finite element (FE) method based on Lagrangian polynomials. Isogeometric analysis aims to integrate FE ideas in CAD systems without necessity to regenerate mesh. The conference intends to create a forum for further discussion in multidisciplinary scientific areas involving mathematics, computer graphics, geometry, physics, engineering and software engineering, respectively.
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