Konstrukcija geometrijsko zveznih parametričnih ploskev : magistrsko delo

Černe, Katarina (author), Knez, Marjetka (mentor)

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.

• Language: Slovenian
• Keywords: geometrijska zveznost, pogoji za $G^n$-zveznost, Bézierjeve ploskve, CAGD
• Work type: Master's thesis/paper
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2020
• PID: 20.500.12556/RUL-116851
• UDC: 519.6
• COBISS.SI-ID: 19411971
• Publication date in RUL: 13.06.2020

Secondary language

• Language: English
• Title: Construction of geometrically continuous parametric surfaces

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.

• Keywords: geometric continuity, $G^n$-continuity conditions, Bézier patches, CAGD