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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 B-spline curves and surfaces and furthermore B-spline functions. In the second part I devote to NURBS curves and surfaces, their description as a linear combination of B-spline 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.
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Modifikace obálky řečového spektra
Přibilová, Anna
The paper is aimed at speech spectrum envelope modification for voice conversion. Spline interpolation using digital filtering techniques with cubic B-splines is applied to speech spectrum envelope determination. Modification of the determined spectrum envelope is performed as the formant shift by a constant factor corresponding to the mean formant shift between male and female voices. Together with pitch modification by a constant factor, voice conversion from male to female and vice versa is performed.
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Detailed analysis of POD method applied on turbulent flow
Kellnerová, Radka ; Kukačka, Libor ; Uruba, Václav ; Jurčáková, Klára ; Jaňour, Zbyněk
Proper orthogonal decomposition (POD) on very turbulent flow inside the street canyon is performed. The energy contribution of each mode is yielded up. Also, physical meaning of the POD method is clarified. Particular modes of POD are assigned to the particular flow events like sweep event, vortex behind the roof or vor- tex at the bottom of street. Test of POD sensitivity on the length of data recording is done when the acquisition time increases up to its triple value. Test with decreasing sample frequency is executed. Further, interpola- tion of POD expansion coefficient is attempted in order to test possible increase in sample frequency and get new information about flow from the POD analysis. We tested linear and spline sort of interpolation and the linear one brought slightly better results.
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Methods for construction of zero-coupon yield curve from the Czech coupon bond market
Hladíková, Hana ; Radová, Jarmila (advisor) ; Pelikán, Jan (referee) ; Onder, Štěpán (referee)
The zero coupon yield curve is one of the most fundamental tools in finance and is essential in the pricing of various fixed-income securities. Zero coupon rates are not observable in the market for a range of maturities. Therefore, an estimation methodology is required to derive the zero coupon yield curves from observable data. If we deal with approximations of empirical data to create yield curves it is necessary to choose suitable mathematical functions. We discuss the following methods: the methods based on cubic spline functions, methods employing linear combination of the Fourier or exponential basis functions and the parametric model of Nelson and Siegel. The current mathematical apparatus employed for this kind of approximation is outlined. In order to find parameters of the models we employ the least squares minimization of computed and observed prices. The theoretical background is applied to an estimation of the zero-coupon yield curves derived from the Czech coupon bond market. Application of proper smoothing functions and weights of bonds is crucial if we want to select a method which performs best according to given criteria. The best performance is obtained for Bspline models with smoothing.
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Interpolace hladkých funkcí pomocí kvadratických a kubických splinů
Eckstein, Jiří ; Kučera, Václav (advisor) ; Dolejší, Vít (referee)
In this thesis, we study properties of cubic and quadratic spline interpolation. First, we define the notions of spline and interpolation. We then merge them to study cubic and quadratic spline interpolations. We go through the individual spline interpolation types, show an algorithm for constructing selected types and sum up their basic properties. We then present a computer program based on the provided algorithms. We use it to construct spline interpolations of some sample functions and we calculate errors of these interpolation and compare them with theoretical estimates.
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Spline inerpolation and smoothing.
Ullrichová, Martina ; Kofroň, Josef (referee) ; Najzar, Karel (advisor)
Nazcv prace: fnterpolace a zhlazovam pomoci spliuu Autor: Martina Ullricliova Katedra (ustav): Katedry numericke niatcinatiky Vedoucf ba.kalafsko prace: Doc. RNDr. Ka.rcl Najzar, CSc. e-mail vedoucilio: knaj^karlin.mff.cuni.cz Abstrakt: V pfedlozene praci json definovany obccnc abstraktm spliny na Hilbertovych prostorech. Nejprve json definovany spliny interpolacm. Dale json odvozcny podminky jcjicli existence a jednoznacnoHti, je popsana je- jich konstrukce a sestaven algoritnms pro jejich nalezcni. Pote JHOU zav(?- deny spliny zhlaznjicf. Opet json urcony podininky jejich existence a jedno- znacnosti, ]nx)vcde se srovnani intcrpolacni'ch a zhlaznjicich splinu s ohlcdem na zhlazuji'ci ])aranietr. Je nkazan algoritnins konstrukce zhlazujicfch splinii pro dany /hla/iijici parainctr, ale- ta.kc algoritnuis pro nalezeni vhodneho zhlazuji'cilio parainetru. Nakonec yena ukazkovcin pffklade dane typy splinu zkonstruuji a. porovnaji. Klicova ylova: inlerpolace. zhlazovani, spline Title: Spline incrpolation and smoothing. Author: Martina Ullrichova Department: Department of Numerical Mathematics Supervisor: Doc. RNDr. Karel Najzar. CSc. Supervisor's e-mail address: knaj'&'karlin.inff.cuni.cz Abstract: In the submitted work there are defined generally abstract splines on a Hilbert. space. At first there arc defined...
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Numerical solution of boundary equations by splines.
Stašek, Petr ; Knobloch, Petr (referee) ; Najzar, Karel (advisor)
Nazcv praee: Aplikace splinu k muncrickemu fcscni okrajovych uloh Autor: Petr Stasek Katcdra (nsta,v): Katedra nnmericke inateniatiky Vetlouci bakalafske prace: Doe. RNDr. Karel Najzar, CSc (vnia.il vedoun'ho: Karel.NajzarKihiiff. euni.cz Abstrakt: V pfedlozeric praci ncjprve delinujeme spliny a uvadime jejich zakladni vlast- uosti a take konstrukci kubickeho splinu, potom so xabyvame intcrpolaci .spliny, uvadime jeji druliy a odvozujeme jakych ehyb se dupustime pfi pouziti interpolaee kubickym splinein. Vc druhe kapitolc se zabyvamc aplikaci splinu k fescni obyccjnych difcrcncialnieh rovnic, nejprve uvadime diferencialni rovnice .s pocatecni podminkou, ktere fesimc za pomoei kolokacc, potom se zabyvame diferencialniini ulohy s okrajovyini podniinkami v daneui tvaru, ktere fesimc Galerkinovou metodou za pomoci B-y])linu. Ca.stccne se take vcmvjcine stabilite metod. Na zaver uvadirn dva pfiklady jako konkretni aplikaei. Title: Numerical solution of boundary equations by splines Author: Petr Sta.sek Department: Department of Numerical Mathematics Supervisor: Doc. RNDr. Karel Najzar, CSc Supervisor's e-mail address: Karel.NajzarQmff.cuni.cz Abstract: In the present work first we define splines and report their basic properties and construction of cubic spline, then we study interpolation by splines and report...
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Contour lines to heightfield conversion
Klimeš, Jonáš ; Pelikán, Josef (advisor) ; Dupej, Ján (referee)
Title: Contour lines to heightfield conversion Author: Jonáš Klimeš Department: Department of Software and Computer Science Education Supervisor: RNDr. Josef Pelikán, Department of Software and Computer Science Education Abstract: The task of this project is to design and test algorithms for semiautomatic contour lines conversion to height field. This work tries to solve following problems: automatic connection of disconnected contour lines, adjacent paths finding, semiautomatic ordering of contour lines with user assistance, creating of terrain height field using Catmull-Rom splines or radial basis functions. A part of this thesis is an experimental application, which implements these algorithms and displays the process of conversion. Program input are in form of contour lines in SVG vector format. Output 3D meshes are in Wavefront OBJ format. Keywords: contour lines, height field, terrain
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