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National Repository of Grey Literature 3 records found  Search took 0.00 seconds. 
Rational minimal surfaces
 Bekrová, Martina ; Šír, Zbyněk (advisor) ; Šmíd, Dalibor (referee)
This bachelor thesis deals with rational surfaces with rational offsets and minimal surfaces. We will give a connection between these two classes of surfaces. We will introduce a method of finding all rational surfaces with rational offsets using dual representation of surface as an envelope of its own tangent surfaces. A connection will be established between minimal surfaces and functions of a complex variable. Furthermore, we will derive the known Weierstrass-Enneper representation and its modifications for generating minimal surfaces. By means of these two tools we will show that all rational minimal surfaces obtained from the Weierstrass-Enneper representation also have rational offsets. Powered by TCPDF (www.tcpdf.org)
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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.
Detailed record
Rational minimal surfaces
 Bekrová, Martina ; Šír, Zbyněk (advisor) ; Šmíd, Dalibor (referee)
This bachelor thesis deals with rational surfaces with rational offsets and minimal surfaces. We will give a connection between these two classes of surfaces. We will introduce a method of finding all rational surfaces with rational offsets using dual representation of surface as an envelope of its own tangent surfaces. A connection will be established between minimal surfaces and functions of a complex variable. Furthermore, we will derive the known Weierstrass-Enneper representation and its modifications for generating minimal surfaces. By means of these two tools we will show that all rational minimal surfaces obtained from the Weierstrass-Enneper representation also have rational offsets. Powered by TCPDF (www.tcpdf.org)
Detailed record

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