
Modelling of NURBS curves and surfaces in the projective space
Ondroušková, Jana ; Štarha, Pavel (referee) ; Martišek, Dalibor (advisor)
In the first part I discuss ancestors of NURBS curves and surfaces, rather Ferguson, Beziere, Coons and Bspline curves and surfaces and furthermore Bspline functions. In the second part I devote to NURBS curves and surfaces, their description as a linear combination of Bspline functions in the projective space. I specify conical arcs more detailed, their submit in the projective space and NURBS surfasec given as tensor product of NURBS curves. Last part is devote to describtion programs for modeling conicals and NURBS surface.


Object Speed Measuring Using The Fourier Transform
Zikmund, Tomáš ; Martišek, Karel (referee) ; Štarha, Pavel (advisor)
This work deals with object speed measuring using image analysis method. The reader will become familiar with a mathematical theory upon which the method is based. The mathematical algorithm for obtaining the speed of a given object is illustrated. Furthermore, an original computer program has been developed and the results of real measuring are shown.


Integral transforms and their applications
Béreš, Lukáš ; Štarha, Pavel (referee) ; Franců, Jan (advisor)
This bachelor's thesis deals with integral transforms and their applications. Its aim is to get together basic properties of Laplace and Fourier transforms and then illustrate their application in solving partial dierential equations, by calculating specic tasks with numerical experiments in MATLAB software.


Geometric surface modeling
Adámková, Barbora ; Martišek, Dalibor (referee) ; Štarha, Pavel (advisor)
The Bachelor thesis deals with display geometric surfaces on a computer in parallel projection and central projection. It includes part of mathematical theory which is necessary for definition of given projection. There are couple of important terms defined such as euclidean space, projective space, surfaces and elementary operations. The thesis also includes description of applications development for display geometric surfaces by using the author's own procedures and functions (socalled library) in Delphi 7 and by using OpenGL library. This Bachelor thesis result is the writer's own implementation of described processes by applications development.


The behavior of functions of several variables in terms of extremes
Beseda, Jiří ; Štarha, Pavel (referee) ; Hoderová, Jana (advisor)
Thesis deals with problems of extreme searching in multivariable calculus. Searching maxima/minima of the function can be moreover specified to local extremes, global extremes or strict extremes. Computations are mainly based on first derivations of the function that are set to be zero, in order to obtain the stationary point. Stationary point is point, where maxima or minima of the function is expected.


Mathematical algorithm of telescope control by using dobsonian mount
Malec, Jan ; Martišek, Dalibor (referee) ; Štarha, Pavel (advisor)
This thesis is an analysis of the relationship between the position of the azimuthal telescope assembly and the position of the object in the sky, assuming that the position of the object in the sky is described right ascension and declination. There is also an analysis of the telescope resolution. For this purpose has created a simple program (attached to this thesis) to compute the diffraction patterns in the focal plane from point star. From motion of telescope tracing observed object are also expressed the necessary torque and power generated by controlled drives on mount.


Computeraided method of analytic surfaces modelling
Stodola, Jakub ; Štarha, Pavel (referee) ; Martišek, Dalibor (advisor)
The first part of the thesis deals with projections of points from an Euclidean space into a plane and displaying of the resulted planar points on a computer. The second part focuses on a discretization of analytically specified surfaces. This is an approximation with network points. Due to the previous part, we are able to display them on a computer. The third part is dedicated to various types of coating fillings. Finally, the software solution is added.


Extremes of Single and MultiVariable Functions
Floderová, Hana ; Hoderová, Jana (referee) ; Štarha, Pavel (advisor)
Extremes of single and multivariable functions are problems in which we try to solve maximum or minimum of function. Maximum and minimum of function can be local, global and by the functions of multivariable bounded. For calculation help us derivative of function, which we put equal to zero and we get out a stationary point. The stationary point is a point, in which we suppose existence of maximum or minimum of function.


The Fourier Series and Its Properties
Sladká, Pavla ; Žák, Libor (referee) ; Štarha, Pavel (advisor)
The functional series, and especially the Fourier series, are an important mathematical apparatus exploited in the various technical branches. A very essential group of the functional series are the power series, which are applied because of their simplicity for solving of the many problems. An expansion of the function to the power series, i. e. the Taylor expansion, whose sum is the expanded function. These expansions are suitable for evaluation of operations, such as calculation of functional values, limits, derivatives and integrals. Calculations of these expansions are easier than of the functions theirself. The Fourier series are used for studies of events with periodic character. An advantage of the Fourier series is the fact, that the requirements for convergency are weaker than in case of the Taylor expansions. Likewise, calculation of the coefficients can be more simple than in the Taylor expansions. Expansions of functions to the Fourier series are used especially for solving ordinary and partial differential equations. This method of solving is known as the Fourier method or the Fourier method of variable separation.


Integral Transformations Using Vector Operators
Joch, Lukáš ; Štarha, Pavel (referee) ; Hoderová, Jana (advisor)
This Bachelor`s thesis is devoled to the vector operotrs. The operators plays the big role in the mathematical notation of different physical processes. The main aim od this paper is to show various vector operators and their properties. At the end are the integral theorems presented, concretely GaussOstrogradsky theorem, Green`s theorem and Stokes`s theorem.
