National Repository of Grey Literature 45 records found  1 - 10nextend  jump to record: Search took 0.01 seconds. 
Factorization of quaternion and dual quaternion polynomials
Molnár, Michal ; Šír, Zbyněk (advisor) ; Vršek, Jan (referee)
In this thesis we provide basic algorithms for factorization of polynomials over quater- nions and dual quaternions. In the case of quaternions, we translate the art of finding roots of given polynomial into factorization. In the case of dual quaternions, we analyse the case of motion polynomials. We show when it is possible to find a factorization of such polynomial into linear terms and give a workaround if it is not. All of this is supplied with geometric interpretations. More specifically, we use the factorizations to construct mechanical linkages. 1
Space curves with Pythagorean Hodograph
Schneider, Petr ; Šír, Zbyněk (advisor) ; Bizzarri, Michal (referee)
The works discusses the basics of motions along curves in 3D space and especially those that are both rational and whose frames have the least rotation during their movement. These rotation minimizing rational frames open up avenues in both computer modelling and adjecent fields. We also introduce an alternative way of defining what a Pythagorean hodograph is, which could allow a new path for research. 1
Tessellation of trimmed NURBS surfaces.
Safko, Martin ; Šír, Zbyněk (advisor) ; Pelikán, Josef (referee)
Tessellation of trimmed NURBS surfaces is classical problem in CAD/CAM, with long history and huge amount of research developed so far. We present and describe a tessellation algorithm suitable for visualization purposes in either offline or online setting and present our results. We also provide pointers to litera- ture and to tessellation algorithms for simulation. We discuss relevant definitions and procedures necessary to work with CAD data and try to familiarize it for people outside the industry. 1
Tessellation of trimmed NURBS surfaces.
Safko, Martin ; Šír, Zbyněk (advisor) ; Pelikán, Josef (referee)
Tessellation of trimmed NURBS surfaces is classical problem in CAD/CAM, with long history and huge amount of research developed so far. We present and describe a tessellation algorithm suitable for visualization purposes in either offline or online setting and present our results. We also provide pointers to litera- ture and to tessellation algorithms for simulation. We discuss relevant definitions and procedures necessary to work with CAD data and try to familiarize it for people outside the industry. 1
Subdivision curves and their convergence
Molnár, Michal ; Šír, Zbyněk (advisor) ; Surynková, Petra (referee)
In this thesis we summarize the basic terms of subdivision and accompany them with examples of widely used schemes. We also show our own implementations of those schemes. In further parts we define the so-called Exponential scheme, which will be a subject of our research, and we illustrate it's behavior using our own images. We focus on properties of curves this scheme produces. As we will see, those curves are C1 -continuous. We also sum up the terms necessary for our research of subdivision curves, which will form the basis of our proof justifying said property of Exponential scheme. 1
Selected problems in differential geometry
Paclt, Jan ; Slavík, Antonín (advisor) ; Šír, Zbyněk (referee)
This thesis covers an overview and solution to selected problems in the differential geometry of plane curves. It focuses mainly on calculating areas of regions bounded by plane curves and also on evolutes, involutes and related trochoids and their properties. The work also provides a self-contained theoretical introduction to the differential geome- try of plane curves. Some ideas and mathematical derivations obtained from the original publications were further expanded and generalized by the author. All derivations men- tioned in the work are given in a uniform convention, which should make it easier for the reader to orientate and find relations between the topics discussed. The thesis can be used as a study support for students of bachelor's courses in geometry or specifically for students with a focus on descriptive geometry. 1
Important theorems of affine geometry
Kundratová, Lucie ; Šír, Zbyněk (advisor) ; Halas, Zdeněk (referee)
V této práci se seznámíme s pojmy a nástroji afinní geometrie. To jsou zejména barycentrické souřadnice, afinní zobrazení a dělicí poměr. Ty pak použijeme k dokázání afinních vět. K Menelaově větě uvidíme vícero důkazů. Dále ukážeme Menelaovu větu z Cevovy a naopak. Uvedeme projektivní tvrzení, ze kterých obě věty plynou. Nakonec se budeme zabývat překladem Menelaových Sférik z latiny a spletitou historií Menelaovy věty. 1
Websites for teaching of geometric transformations at secondary school
Dobiášová, Kateřina ; Robová, Jarmila (advisor) ; Šír, Zbyněk (referee)
As a part of this thesis existing web pages about planar geometrical transformations were evaluated and new web pages were created. Pages in Czech and in English language were evaluated shortly verbally. There is a table summarizing findings about existing web pages at the end of this part. The second part of this thesis contains newly created web pages. Scope of subject matter of created web pages overreaches common secondary school curriculum. There are Java applets used for illustrating findings about geometrical transformations as an integral part of web pages. Solving of exercises is accompanied by step-by-step operation. Web pages contain definitions, theorems with proofs and explanations of constructions.

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