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Računanje ukrivljenosti na prostorskih triangulacijah : magistrsko delo
ID Reberc, Petra Ivana (Author), ID Knez, Marjetka (Mentor) More about this mentor... This link opens in a new window

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Abstract
V delu so obravnavane različne metode za ocenjevanje ukrivljenosti na dani prostorski triangulaciji. Opisan je postopek aproksimacije triangulacije po metodi najmanjših kvadratov z Bézierjevimi ploskvami iz tenzorskega produkta in z B-zlepki, na katerih lahko uporabimo standardne analitične formule za izračun ukrivljenosti. Predstavljena je še metoda prostorskih povprečij, s katero izpeljemo računsko nezahtevne in elegantne formule za direkten izračun ukrivljenosti v ogliščih triangulacije, pri čemer se upošteva bližnjo okolico izbranega oglišča.

Language:Slovenian
Keywords:ocena ukrivljenosti, prostorska triangulacija, metoda prostorskih povprečij, aproksimacija, Bézierjeva ploskev, ploskev iz B-zlepkov
Work type:Master's thesis/paper
Organization:FMF - Faculty of Mathematics and Physics
Year:2021
PID:20.500.12556/RUL-128486 This link opens in a new window
UDC:519.6
COBISS.SI-ID:70092803 This link opens in a new window
Publication date in RUL:15.07.2021
Views:778
Downloads:82
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Secondary language

Language:English
Title:Curvature computation on triangle meshes
Abstract:
The master thesis proposes various methods for estimating the curvature on triangle meshes in a 3D space. We describe the approximation of the triangle mesh with tensor product Bézier surfaces and B-spline surfaces, using the least squares method. We can then use standard formulas to compute curvature on the approximating surface. Furthermore the method of spatial averages is presented, which offers computationally effective and elegant formulas for calculating the curvature at a given vertex in regard to its surroundings.

Keywords:curvature estimation, triangle mesh, method of spatial averages, approximation, Bézier surface, B-spline surface

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