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Hermite geometric interpolation by rational Bézier spatial curves
Jaklič, Gašper ...
Polinomska geometrijska interpolacija s parametričnimi krivuljami je postala ena od standardnih tehnik za interpolacijo geometrijskih podatkov. Očitna pospločitev je geometrijska interpolacija z ...racionalnimi krivuljami, ki pa je mnogo manj raziskano področje. Namen tega članka je predstaviti splošni pristop za Hermiteovo geometrijsko interpolacijo z racionalnimi Bézierovimi prostorskimi krivuljami. Še posebej želimo analizirati kubično ▫$G^2$▫ interpolacijo in interpolacijo z ▫$G^3$▫ zveznimi krivuljami stopnje štiri. Izpeljemo sisteme nelinearnih enačb v poenostavljeni obliki in študiramo obstoj sprejemljivih rešitev. Za kubični primer izpeljemo geometrijske pogoje za rešljivost sistema nelinearnih enačb. Za oba primera izvedemo asimptotično analizo in dokažemo optimalni red aproksimacije. Podamo numerične primere, ki potrjujejo teoretične izsledke.
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