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Modeli hiperbolične geometrije in njihova vizualizacija : magistrsko delo
ID Albreht, Katja (Avtor), ID Bauer, Andrej (Mentor) Več o mentorju... Povezava se odpre v novem oknu, ID Podpečan, Vid (Komentor)

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Izvleček
Magistrsko delo v prvem delu vsebuje predstavitev osnovnih lastnosti hiperbolične geometrije. Predstavljeni so vsi trije njeni glavni modeli in osnovne geometrijske značilnosti posameznega modela. Delo obravnava tudi vrste tlakovanj, nato pa na kratko povzema tlakovanje Poincaréjevega diska in opisuje izpeljavo tlakovanja polsfernega modela hiperbolične geometrije. V nadaljevanju pa je predstavljen potek modeliranja in tiskanja 3D modelov, od pravilnih poliedrov do tlakovane hiperbolične polsfere. Dodane so izpeljave predpisov projekcij, ki izvirajo iz senčenja tiskanega 3D modela tlakovane polsfere.

Jezik:Slovenski jezik
Ključne besede:geometrija, hiperbolična geometrija, 3D model, vizualizacija
Vrsta gradiva:Magistrsko delo/naloga
Tipologija:2.09 - Magistrsko delo
Organizacija:FMF - Fakulteta za matematiko in fiziko
Leto izida:2024
PID:20.500.12556/RUL-153457 Povezava se odpre v novem oknu
COBISS.SI-ID:179957251 Povezava se odpre v novem oknu
Datum objave v RUL:07.01.2024
Število ogledov:650
Število prenosov:111
Metapodatki:XML DC-XML DC-RDF
:
ALBREHT, Katja, 2024, Modeli hiperbolične geometrije in njihova vizualizacija : magistrsko delo [na spletu]. Magistrsko delo. [Dostopano 9 april 2025]. Pridobljeno s: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=slv&id=153457
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Sekundarni jezik

Jezik:Angleški jezik
Naslov:Models of hyperbolic geometry and their visualisation
Izvleček:
The first part of the master's thesis includes the presentation of the basic characteristics of the hyperbolic geometry including all three main models and basic geometry characteristics of each model. The thesis also covers the types of tessellations and then briefly summarises tessellation of Poincare’s discus and describes the derivationof semispheric model tessellation of the hyperbolic geometry. Furthermore the course of modelling and 3D model printing is presented, spanning from regular polyhedra to tesselled hyperbolic semisphere. The derivation of projection regulations are added, which derive from shadowing of the 3D model of a tessellated semisphere.

Ključne besede:geometry, hyperbolic geometry, 3D model, visualisation

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