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Topološka analiza 3D modelov
ID Treven, Marjana (Author), ID Gabrovšek, Boštjan (Mentor) More about this mentor... This link opens in a new window

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Abstract
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.

Language:Slovenian
Keywords:vektorski prostori, simpleksi, simplicialni kompleksi, robne preslikave, verižni kompleksi, homološki vektorski prostori
Work type:Master's thesis/paper
Organization:FS - Faculty of Mechanical Engineering
Place of publishing:Ljubljana
Publisher:[M. Treven]
Year:2023
Number of pages:XVII, 52 str.
PID:20.500.12556/RUL-152433 This link opens in a new window
UDC:512.642:515.142.33(043.2)
COBISS.SI-ID:183202051 This link opens in a new window
Publication date in RUL:24.11.2023
Views:1219
Downloads:64
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Secondary language

Language:English
Title:Topological analysis of 3D models
Abstract:
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.

Keywords:vector spaces, simplices, simplicial complexes, boundary maps, chain complexes, homology vector spaces

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