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3D Triangles Polygonal Mesh Conversion on 3D Spline Surfaces
Jahn, Zdeněk ; Španěl, Michal (referee) ; Kršek, Přemysl (advisor)
This bachelor's thesis deals with the problem of the remeshing of unstructured triangular 3D meshes to more suitable representations ( quadrilateral meshes or spline surfaces ). It explains the basic problems related with the unstructured meshes and the reasons for its solution. It classifies the usable methods, describes the most suitable candidates briefly. It follows the chosen method in detail - both the theoretical matter and the specific implementation.
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Spline interpolation in CNC milling
Soukupová, Veronika ; Píška, Miroslav (referee) ; Ohnišťová, Petra (advisor)
Tato práce se zaměřuje na využití různých typů splinové interpolace pro obrábění na číslicově řízených strojích. Cílem této práce je teoreticky popsat využití splinových interpolací při CNC frézování a následně stanovit a zhodnotit limity využití různých typů splinových interpolací na základně daného objemu vstupních dat. Součástí práce je vytvoření programu pro generaci různého počtu uzlových bodů na analyticky známé křivce. Následuje vložení uzlových bodů do vytvořeného CNC programu pětiosého obráběcího centra a poté jeho verifikace. Pro stejné uzlové body jsou aplikovány různé druhy interpolace pro následné porovnání metod a stanovení minimálního počtu bodů na délku křivky pro dosažené vyhovující přesnosti při použití dané interpolační metody.
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Application for 2D Curves Demonstration
Opletal, Pavel ; Švub, Miroslav (referee) ; Venera, Jiří (advisor)
This Bachelor's Thesis deals with planar curves used in computer graphics. It sums up general ideas of these curves and deals with particular methods for computing planar curves. It describes methods used for computing Ferguson cubic curves, Kochanek-Bartels spline, Cardinal spline, Catmull-Rom spline, Bézier curves and their modifications, Coons cubic curves, Coons cubic B-spline curves and NURBS. Practical part of this project deals with concept and impementation of tutorial, which demonstrates chosen curves.
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Interpolating and approximating spline curves
Jelínek, Daniel ; Štarha, Pavel (referee) ; Procházková, Jana (advisor)
This bachelor’s thesis deals with properties and algorithms of smooth curves calculation, specifically the calculation of B-spline curves. These curves can be applied in computer graphics. Since their calculation is defined recurrently, it is almost a necessity to use computers with programmed algorithms to obtain these curves. As for the practical part of this work, three programs for the calculation of approximating B-spline curves, interpolating B-spline curves and NURBS curves were created.
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FFD methods
Novák, Jiří ; Martišek, Karel (referee) ; Procházková, Jana (advisor)
The diploma thesis deals with the topic of free-form deformations. The main goal of this work were elaboration of theoretical knowledge about this issue and the programming of selected methods od free-form deformations. The first part describes the required spline theory, matrix calculus and free-form deformations. The resulting version shows three programs. The first program compares the selected free-form deformation methods to the example of the 4x4 control point grid. The second program serves as a generalization for the general case of grid of control points. The last program is based on direct manipulation of arbitrary surface point and following recomputation of the control points to obtain demanded shape.
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3D Triangles Polygonal Mesh Conversion on 3D Spline Surfaces
Jahn, Zdeněk ; Šiler, Ondřej (referee) ; Kršek, Přemysl (advisor)
In computer graphics we can handle unstructured triangular 3D meshes which are not too usable for processing through their irregularity. In these situations it occurs need of conversion that 3D mesh to more suitable representation. Some kind of 3D spline surface can be proper alternative because it institutes regularity in the form of control points grid and that's why it is more suitable for next processing. During conversion, which is described in this thesis, quadrilateral 3D mesh is constructed at first. This mesh has regular structure but mainly the structure corresponds to structure of control points grid of resulting 3D spline surface. Created quadrilateral 3D mesh can be saved and consequently used in specific modeling applications for T-spline surface creation.
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Effective User Interface for Editing Parametric Curves
Ondruch, Milan ; Sumec, Stanislav (referee) ; Herout, Adam (advisor)
At present, the standard method of accessing a curve is using a polygon composed of control points. When dealing with complex curves, the result becomes lost in a clutter of lines comprising this polygon. This bachelor thesis proposes an algorithm for curve editing without the use of control points. The output is a tool that modifies the curve in an intuitive way reminiscent of work with plastic material. A sample program is implemented in C++ language with a graphic output by means of OpenGL library and OpenGLUT window toolkit.
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Mathematical description of vehicle motion trajectory
Lorenczyk, Jiří ; Popela, Pavel (referee) ; Porteš, Petr (advisor)
The goal of this thesis is to nd types of curves which would allow for the construction of a path that could be traversed by a vehicle. It seems that a minimal constraint for such a path is the continuity of curve's curvature. This leads to a closer look at the three types of curves: Clothoids, which are able to smoothly connect straights with arcs of a constant curvature, interpolation quintic splines, which are C2 smooth in the interpolation nodes and -splines, these belong to the family of quintic polynomial curves too, however, they are characterised by the vector of parameters which modies the shape of the curve. The thesis is accompanied by an application allowing for manual construction of the path composed of spline curves.
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