20.500.12556/RUL-105133 Kubični Clough-Tocherjevi zlepki magistrsko delo Cubic Clough-Tocher splines V nalogi opišemo prostor kubičnih Clough-Tocherjevih zlepkov nad triangulacijo domene, pri čemer vsak trikotnik iz triangulacije z izbiro delilne točke razdelimo na tri manjše. Nad vsakim trikotnikom želimo dobiti kubični polinom, nad celotno triangulacijo pa ${\cal C}^1$ zlepek. Zanimal nas bo poseben podprostor tega prostora, prostor zreduciranih Clough-Tocherjevih zlepkov, za katerega lahko konstruiramo normalizirano bazo. Bazni zlepki imajo lokalni nosilec, so nenegativni in tvorijo particijo enote. Iskanje baze lahko prevedemo na geometrijski problem iskanja množice trikotnikov, ki morajo vsebovati določen nabor točk. To nas pripelje do strukture kontrolnih trikotnikov in stabilnega računanja zreduciranih Clough-Tocherjevih zlepkov. In this thesis we present the Clough-Tocher space of cubic splines on a triangulation, where we make a refinement of the triangulation by splitting each triangle on three smaller ones. The spline is composed of cubic polynomials over each triangle and it is ${\cal C}^1$ over the whole triangulation. We focus on a special subspace - the reduced Clough-Tocher spline space and construct a normalized basis for it. The basis splines have a local support, they are nonnegative and they form a partition of unity. Geometrically, the basis construction problem is converted to a problem of finding a set of triangles that contain specific points. This leads us to control triangles and a stable way of computing with Clough-Tocher splines. Clough-Tocherjevi zlepki B-zlepki makro-elementi določitvene množice Clough-Tocher splines B-splines macro-elements determining sets true false false Slovenski jezik Angleški jezik Magistrsko delo/naloga 2018-10-28 07:45:20 2018-10-28 07:45:24 2022-10-11 12:23:04 0000-00-00 00:00:00 2018 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.6 93836 18474329 528.pdf 528.pdf 1 BB0388A539B1AC76DC89389E7F9CF777 50a201c99f2e8f255ada21b0b8074bac66bed1b62875db363b1295e90934135c 1f0cae0c-a1b6-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=115728 Fakulteta za matematiko in fiziko 0 0 0