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Computation of compression force on surface
Stejskal, Jiří ; Habán, Vladimír (referee) ; Čermák, Libor (advisor)
In technical computing we often need to find the resulting load on surface caused by the compression force. The aim of this thesis is to suggest one of the possible approaches to do so if the surface is given explicitly or by the coordinates of some of it's points. In the first section, the mathematical definition of the surface with some of it's important properties is mentioned. There is a basic theory of Bézier surfaces, which form the main part of this thesis in the second part. Further on, some results from the theory of surface integrals are mentioned. The last section describes the whole algorithm of computing the resulting load together with the MATLAB program which is added to this thesis. Three examples are given at the end.
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Modification of Navier_Stokes equations asuming the quasi-potential flow
Navrátil, Dušan ; Pochylý, František (referee) ; Fialová, Simona (advisor)
The master's thesis deals with Navier-Stokes equations in curvilinear coordinates and their solution for quasi-potential flow. The emphasis is on detailed description of curvilinear space and its expression using Bézier curves, Bézier surfaces and Bézier bodies. Further, fundamental concepts of hydromechanics are defined, including potential and quasi-potential flow. Cauchy equations are derived as a result of the law of momentum conservation and continuity equation is derived as a result of principle of mass conservation. Navier-Stokes equations are then derived as a special case of Cauchy equations using Cauchy stress tensor of Newtonian compressible fluid. Further transformation into curvilinear coordinates is accomplished through differential operators in curvilinear coordinates and by using curvature vector of space curve. In the last section we use results from previous chapters to solve boundary value problem of quasi-potential flow, which was solved by finite difference method using Matlab environment.
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Computer-aided 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.
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Automatic Verification of Product Assembling Correctness
Doležal, Petr ; Šmirg, Ondřej (referee) ; Říha, Kamil (advisor)
This diploma evaluates methods for verification of key characteristics of a product using digital image processing techniques. At first, reasons why this work has been done are described followed by a list of all methods that were used in this diploma such as Hough Circle Transform and Flood Fill (Seed Fill) algorithm. Also, a new approach how to compensate non regularly illuminated scene, which is based on surface modeling with Bézier Surfaces, was developed. Moreover, the algorithm was implemented in the C++ programming language and some of the parts were also simulated using the MATLAB environment. The algorithm was evaluated based on the percentage level of recognition of the required parameters. Efficiency of the implementation is also important for the author.
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Modification of Navier_Stokes equations asuming the quasi-potential flow
Navrátil, Dušan ; Pochylý, František (referee) ; Fialová, Simona (advisor)
The master's thesis deals with Navier-Stokes equations in curvilinear coordinates and their solution for quasi-potential flow. The emphasis is on detailed description of curvilinear space and its expression using Bézier curves, Bézier surfaces and Bézier bodies. Further, fundamental concepts of hydromechanics are defined, including potential and quasi-potential flow. Cauchy equations are derived as a result of the law of momentum conservation and continuity equation is derived as a result of principle of mass conservation. Navier-Stokes equations are then derived as a special case of Cauchy equations using Cauchy stress tensor of Newtonian compressible fluid. Further transformation into curvilinear coordinates is accomplished through differential operators in curvilinear coordinates and by using curvature vector of space curve. In the last section we use results from previous chapters to solve boundary value problem of quasi-potential flow, which was solved by finite difference method using Matlab environment.
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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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Automatic Verification of Product Assembling Correctness
Doležal, Petr ; Šmirg, Ondřej (referee) ; Říha, Kamil (advisor)
This diploma evaluates methods for verification of key characteristics of a product using digital image processing techniques. At first, reasons why this work has been done are described followed by a list of all methods that were used in this diploma such as Hough Circle Transform and Flood Fill (Seed Fill) algorithm. Also, a new approach how to compensate non regularly illuminated scene, which is based on surface modeling with Bézier Surfaces, was developed. Moreover, the algorithm was implemented in the C++ programming language and some of the parts were also simulated using the MATLAB environment. The algorithm was evaluated based on the percentage level of recognition of the required parameters. Efficiency of the implementation is also important for the author.
|
|
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Computer-aided 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.
|
|
|
Computation of compression force on surface
Stejskal, Jiří ; Habán, Vladimír (referee) ; Čermák, Libor (advisor)
In technical computing we often need to find the resulting load on surface caused by the compression force. The aim of this thesis is to suggest one of the possible approaches to do so if the surface is given explicitly or by the coordinates of some of it's points. In the first section, the mathematical definition of the surface with some of it's important properties is mentioned. There is a basic theory of Bézier surfaces, which form the main part of this thesis in the second part. Further on, some results from the theory of surface integrals are mentioned. The last section describes the whole algorithm of computing the resulting load together with the MATLAB program which is added to this thesis. Three examples are given at the end.
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