Konstrukcija geometrijsko zveznih parametričnih ploskev

magistrsko delo

Katarina Černe (Author), Marjetka Krajnc (Mentor)

Abstract

V magistrskem delu je predstavljen pojem geometrijske zveznosti parametrično podanih ploskev. Opisani so potrebni in zadostni pogoji za $G^n$-zveznost dveh ploskev vzdolž skupne krivulje ter geometrijska interpretacija $G^1$-zveznosti. V nadaljevanju so predstavljene polinomske Bézierjeve ploskve iz tenzorskega produkta in trikotne Bézierjeve krpe ter njihove lastnosti. Pomemben rezultat tega dela je izpeljava potrebnih in zadostnih pogojev za $G^n$-zveznost med dvema Bézierjevima ploskvama. Dobljeni pogoji so nato uporabljeni na nekaj primerih konstrukcije $G^1$ in $G^2$-zveznih Bézierjevih ploskev nizkih stopenj, dodana pa je tudi primerjava s pogoji za $C^1$ in $C^2$-zveznost. Izpeljani so tudi kompatibilnostni pogoji za $G^1$-zveznost med $N$ ploskvami, ki se stikajo v skupni točki.

Keywords

matematika;geometrijska zveznost;pogoji Gn-zveznost;Bézierjeve ploskve;CAGD;

Data

Language:	Slovenian
Year of publishing:	2020
Typology:	2.09 - Master's Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[K. Černe]
UDC:	519.6
COBISS:	19411971
Views:	1372
Downloads:	180
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Construction of geometrically continuous parametric surfaces
Secondary abstract:	This thesis presents the notion of geometric continuity between adjacent parametric surfaces. It describes the necessary and sufficient conditions for two adjacent surfaces joining $G^n$-continuously and geometric interpretation of $G^1$-continuity. Triangular and tensor product polynomial Bézier patches are introduced and their properties are given. An important result of this work is a derivation of necessary and sufficient conditions for $G^n$-continuity between two adjacent tensor product Bézier surfaces. Those conditions, expressed with control points, are then used in examples of $G^1$ and $G^2$-continuous Bézier surfaces. The comparison with $C^1$ and $C^2$-continuity conditions is given too. The obtained results are applied to derive the compatibility conditions for $N$ surfaces joining $G^1$-continuously at the common vertex.
Secondary keywords:	geometric continuity;Gn-continuity conditions;Bézier patches;computer aided geometric design;
Type (COBISS):	Master's thesis/paper
Study programme:	0
Embargo end date (OpenAIRE):	1970-01-01
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Matematika - 2. stopnja
Pages:	IX, 61 str.
ID:	11828941