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The Frölicher-Nijenhuis bracket and its applications in geometry and calculus of variations
Šramková, Kristína ; Tomáš, Jiří (referee) ; Kureš, Miroslav (advisor)
This Master's thesis clarifies the significance of Frölicher-Nijenhuis bracket and its applications in problems of physics. The basic apparatus for these applications is differential geometry on manifolds, tensor calculus and differential forms, which are contained in the first part of the thesis. The second part summarizes the basic theory of calculus of variations on manifolds and its selected applications in the field of physics. The last part of the thesis is devoted to the applications of Frölicher-Nijenhuis bracket in the derivation of Maxwell's equations and to the description of the geometry of ordinary differential equations.
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Robust feature curve detection in 3D surface models
Hmíra, Peter
Most current algorithms typically lack in robustness to noise or do not handle T-shaped curve joining properly. There is a challenge to not only detect features in the noisy 3D-data obtained from the digital scanners. Moreover, most of the algorithms even when they are robust to noise, they lose the feature information near the T-shaped junctions as the triplet of lines ``confuses'' the algorithm so it treats it as a plane. Powered by TCPDF (www.tcpdf.org)
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Robust feature curve detection in 3D surface models
Hmíra, Peter ; Dupej, Ján (advisor) ; Pelikán, Josef (referee)
Most current algorithms typically lack in robustness to noise or do not handle T-shaped curve joining properly. There is a challenge to not only detect features in the noisy 3D-data obtained from the digital scanners. Moreover, most of the algorithms even when they are robust to noise, they lose the feature information near the T-shaped junctions as the triplet of lines ``confuses'' the algorithm so it treats it as a plane. Powered by TCPDF (www.tcpdf.org)
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Discrete differential geometry and its applications
Vidličková, Eva ; Šír, Zbyněk (advisor) ; Hron, Jaroslav (referee)
In this thesis we present an elementary introduction to the Discrete differen- tial geometry. We will work with both discrete curves and discrete surfaces. Firstly some basic definitions and theorems from classic Differential geometry will be mentioned and then we will translate these concepts to the discrete setting, so that some important global structures are still preserved. At the end we implement mean curvature flow defined on discrete surfaces and run it on two meshes, that show its area-minimizing feature. This can be used for denoising the discrete surfaces. 1
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Design of Centrifugal Pump Using Differential Geometry Methods
Sloupenský, Zdeněk ; Varchola, Michal (referee) ; Melichar, Jan (referee) ; Drábková, Sylva (referee) ; Pochylý, František (advisor)
This thesis deals with a new approach to the design of impeller, blade and spiral of centrifugal pump. The mathematic model of flow inside meridional section of impeller and spiral is based on the instruments of differential geometry applied to Bezier surfaces. This formerly introduced theory is more deeply developed in this thesis and the conclusions are applied to the design of centrifugal pump parts working with fluid. The main thesis output is the mathematic model and on its principles created software determined for the design of impeller, blade and spiral. The received results are exportable into one of the commonly used 3D modeling programs.
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Geodesics
Čambalová, Kateřina ; Tomáš, Jiří (referee) ; Doupovec, Miroslav (advisor)
The goal of the thesis is to create an overivew of geodesics. At the beginning of their study, they were considered shortest paths connecting two points on surfaces. In the thesis we will show more of the complexity of the term and introduced the properties, some uses of the geodesics and methods of their computation. Later, the Clairaut patches and their geodesics will be analysed. Clairaut patches are characterized by a specific property which makes computation of geodesics simpler. 3D plots of some Clairaut patches and their geodesics are also included.
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Geodesic curves and their applications
Orgoník, Svetoslav ; Hrdina, Jaroslav (referee) ; Vašík, Petr (advisor)
The aim of the thesis is to give a survey of basic results from the classical theory of curves. A special attention will be paid to geodesics and their properties. In particular, we treat geodesics on some special surfaces. We treat one application with animations. All examples will be illustrated by pictures, which were drawn by means of mathematical software.
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