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Fast Implementation of Geometric Algorithms
Krba, Martin ; Jošth, Radovan (referee) ; Havel, Jiří (advisor)
One of the most often used calculations in computer graphics is detection of collision between ray of light and triangle on the surface of object in 3D space. This frequent usage is motivation to search for the best methods for this calculations. This thesis contains explanation of basics of this topic and also testing of methods with real input data to better and accurate comparison.
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Presentation Software - Triangle Basic Facts
Kašparová, Šárka ; Švub, Miroslav (referee) ; Štancl, Vít (advisor)
This bachelor's thesis is about development of presentation software supporting teaching of mathematics - triangle basic geometrical facts. It suggests basic knowledge about education and triangles. The second part is about analysis and implementation of the program and tools that were applied in its development.
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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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Visualization of Large Data Sets
Mokroš, Petr ; Chudý, Peter (referee) ; Přibyl, Jaroslav (advisor)
Work is focused on visualization of large data sets, especially on high resolution terrain models. Thus the goal of this work is to design a library which can divide large models to small regular parts for fast render of whole scene using level of detail techniques. Further goal is theoretical analysis how the library for fast and smooth visualization of large scenes in real time can be used.
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Fast Ray-Triangle Intersection
Horák, František ; Navrátil, Jan (referee) ; Havel, Jiří (advisor)
This work contains a few basic terms of analytical geometry. We mention some of ray-triangle intersection computation algorithms and present some use-case examples. We discuss capabilities of CUDA, optimization techniques of this architecture and implementation with focus on given issues. Algorithms of ray-triangle intersection are tested and results are discussed.
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Fast Ray-Triangle Intersection
Havel, Jiří ; Zemčík, Pavel (referee) ; Herout, Adam (advisor)
Triangle is the mostly used primitive in computer graphics. Calculation of its intersection with a ray has many applications and is often a bottleneck of a program. This work focuses on its usage and various methods of calculation. It tries to combine these techniques to achieve high performance on modern processors.
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Use of paper folding techniques in teaching mathematics
MRÁZ, Luděk
The target of the Bachelor's thesis "Use of paper folding techniques in teaching mathematics" is to highlight the importance of origami in mathematics and its subsequent use as a suitable tool in lessons of mathematics in primary or in secondary schools. Most of the work is devoted to practical problems. It means constructions of planar and spatial figures and solving interesting or problematic tasks which are accompanied by graphics solutions and proofs.
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Selected topics for teaching mathematics in school with the interactive whiteboard - planimetry
BABKA, Jan
The diploma thesis covers points, line segments, lines and half-lines, angles, circles, triangles and their teaching through computers and interactive whiteboards. It is divided into two parts, theoretical and practical. The first one covers motivation for learning, constructivism, evaluation of teaching materials and interactivity in school environment. The practical part contains worksheets for teaching with an interactive whiteboard created by the author of the thesis and their use in Year Six of primary and lower-secondary schools. In the conclusion the author mentions his observations gained during his own teaching practice.
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Construction of a triangle - interactive aid
KRATOCHVÍL, Daniel
This dissertation informs readers about self-made interactive aid, enabling to understand the problematic of the construction of the triangle. The basic information about this aid, it´s preference and usage is illustrated on some several cases of the solution to tasks of the construction of the triangle. The interactive aid is appropriate for teaching, but also for consesutive usage about the solution of concrete tasks.
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Using of the Riemannian integral for mathematical and physical calculus
MAREČEK, Ondřej
The theoretical part of the thesis includes introduction of Riemann integral and its qualities, introduction of function of more variables, introduction of double and triple Riemann integral and physical applications of integral. The practical part includes derivation of general area formulas for different shapes and volume formulas for different solids, in some examples there are shown different ways of solution. The practical part also includes the use of Riemann integral for the determination of centre of mass, of statical moments and moments of inertia of objects.
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