20.500.12556/RUL-172125 Bézierjeve diagonale magistrsko delo Bézier diagonals V delu so predstavljene Bézierjeve krivulje in ploskve - definicije in osnovne lastnosti skupaj s primeri. Podani so natančni pogoji na kontrolne točke, pri katerih je zlepek dveh Bézierjevih krivulj (ploskev) zvezen oziroma geometrijsko odvedljiv. Osrednji cilj naloge je študij diagonal na Bézierjevih ploskvah. Najprej se pokaže, da so diagonale same tudi Bézierjeve krivulje - določiti se dà njihovo stopnjo in kontrolne točke. V nadaljevanju je izpeljano, kdaj sta dve poljubni krivulji diagonali Bézierjeve ploskve. Na koncu je določen še razred ploskev z enakima diagonalama in kako se ta razred spreminja, če pogoju na diagonale dodamo še kakšen pogoj na rob ploskve. The thesis presents Bézier curves and surfaces - their definitions, fundamental properties, and examples. It also provides precise conditions on the control points under which the join of two Bézier curves (or surfaces) is continuous or geometrically diferentiable. The central aim of the thesis is the study of diagonals on Bézier surfaces. It is first shown that the diagonals themselves are Bézier curves and how to determine their degree and control points. The thesis then derives the conditions under which two arbitrary curves can be diagonals of a Bézier surface. Finally, the class of surfaces with identical diagonals is characterized, and the way this class changes when additional boundary constraints are imposed. Bézierjeva krivulja ploskev in diagonala kontrolne točke Bézier curve surface and diagonal control points true false false Slovenski jezik Angleški jezik Magistrsko delo/naloga 2025-09-06 08:15:05 2025-09-06 08:15:07 2025-10-06 03:48:59 0000-00-00 00:00:00 2025 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.6 152689 247884547 18725.pdf 18725.pdf 1 3DB072E86E6B13392FB41DA0D69CCE79 afa0d0fc58077fc5411a5c95f315cbcb0ec3293b3f5077b67d88275b6948430c af1eb217-8ae8-11f0-9328-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=215925 Fakulteta za matematiko in fiziko 0 0 0