20.500.12556/RUL-152433 Topološka analiza 3D modelov Topological analysis of 3D models V magistrskem delu je predstavljena homologija poljubnega telesa ali ploskve. Homologija nam pomaga prepoznati, šteti in meriti različne vrste ”lukenj” v prostoru, kot so vrzeli, zanke in votline. V delu se posebej osredotočamo na teoretično ozadje in samo definicijo homologije, ki jo definiramo preko vektorskih prostorov. Sledi nekaj primerov izračunov homologije ter predstavitev programske kode, ki za poljubno triangulirano telo ali ploskev izračuna dimenzije homoloških vektorskih prostorov. V zadnjem delu magistrske naloge so predstavljene aplikacije, kjer se uporabljajo homološke metode. S pomočjo homologije lahko na primer odkrivamo luknje v brezžičnih omrežjih, pomaga pa nam tudi pri odkrivanju rakastih tkiv. In the master's thesis we present the homology of a body or surface. Homology helps us recognize, count and measure different types of "holes" in space, such as gaps, loops or cavities. The main focus of the work is on the theoretical background and on the definition of homology which is defined through vector spaces. We presented a few examples of homology calculations and wrote a program code that calculates the dimension of homology vector spaces for any triangulated body or surface. The final part of the thesis presents applications where homological methods are used. For example, with the help of homology, we can detect holes in wireless networks, and it also aids us in the detection of cancerous tissues. vektorski prostori simpleksi simplicialni kompleksi robne preslikave verižni kompleksi homološki vektorski prostori vector spaces simplices simplicial complexes boundary maps chain complexes homology vector spaces true false false [M. Treven] Slovenski jezik Angleški jezik Magistrsko delo/naloga 2023-11-24 09:52:28 2023-11-24 09:52:30 2024-01-31 12:48:14 0000-00-00 00:00:00 2023 0 Ljubljana 0 XVII, 52 str. 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 1970-01-01 512.642:515.142.33(043.2) 259633 183202051 32564.pdf 32564.pdf 1 AABAB7E2C9F782E50AC0EBD6AC2E5280 22f2c8c47f923ddbc63d62fa4d4d893333ed79c32d4131be124e9ef201d8d8d5 cd5e81cf-8aa6-11ee-8840-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=177950 Fakulteta za strojništvo 0 0 0