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Non-Euclidean Raytracer
Kostelník, Martin ; Vlnas, Michal (referee) ; Starka, Tomáš (advisor)
This bachelor's thesis deals with the real-time ray tracing algorithm enhanced by non-euclidean spaces. The goal is to design and implement an interactive application, which allows the user to move around in a 3D scene. All computations are performed by the CPU. In total, four non-euclidean elements are implemented. These include portals, warped tunnels, shrinking and rotation tunnels. The result of this project is an interactive application consisting of eight sample scenes demonstrating the non-euclidean elements.
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Non-Euclidean Raytracer
Kostelník, Martin ; Vlnas, Michal (referee) ; Starka, Tomáš (advisor)
This bachelor's thesis deals with the real-time ray tracing algorithm enhanced by non-euclidean spaces. The goal is to design and implement an interactive application, which allows the user to move around in a 3D scene. All computations are performed by the CPU. In total, four non-euclidean elements are implemented. These include portals, warped tunnels, shrinking and rotation tunnels. The result of this project is an interactive application consisting of eight sample scenes demonstrating the non-euclidean elements.
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Contribution of János Bolyai to the elements of non-euclidean geometry
Dvořáková, Tereza ; Krump, Lukáš (advisor) ; Žádník, Vojtěch (referee)
The work is dedicated to the only publication of János Bolyai called briefly Appendix, where János Bolyai presented his research about parallels and about dividing geometry into two parts according to the truth or falsity of Euclid's parallel postulate. The aim of the work is to demonstrate, how Bolyai invented new geometry, to approach which proofs he used and at the same time to show the connection between results of Bolyai and today's knowledge about non-Euclidian geometry. Moreover there are two types of pictures in the work. One type corresponds with Bolyai's idea about new geometry, the other type describes geometric situations in Beltrami-Klein's model, which is often used for describing hyperbolic geometry nowadays.
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