20.500.12556/RUL-116851 Konstrukcija geometrijsko zveznih parametričnih ploskev magistrsko delo Construction of geometrically continuous parametric surfaces 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. 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. geometrijska zveznost pogoji za $G^n$-zveznost Bézierjeve ploskve CAGD geometric continuity $G^n$-continuity conditions Bézier patches CAGD true false false Slovenski jezik Angleški jezik Magistrsko delo/naloga 2020-06-13 08:15:01 2020-06-13 08:15:04 2024-05-30 10:48:23 0000-00-00 00:00:00 2020 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.6 106503 19411971 1192.pdf 1192.pdf 1 E61914CBD1920568D3CE89A7D44BE51E cda84d622444a6a01b75bba104b2b8befa6cdca50ae0bb8a49d116249a375bd0 059c8be5-a1b9-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=130540 Fakulteta za matematiko in fiziko 0 0 0