20.500.12556/RUL-174322 Rektifikacijski poligon krivulj s pitagorejskim hodografom v ravnini in prostoru magistrsko delo Rectifying control polygon for Pythagorean hodograph curves in the plane and in the space Krivulja s pitagorejskim hodografom (PH krivulja) je parametrično podana krivulja, katere enotska tangenta je podana racionalno. Takšne krivulje imajo številne uporabne lastnosti, kot so enostavno računanje dolžine loka krivulje, racionalno podane krivulje odmika ter numerično enostavno reparametrizacijo na naravni parameter. Bézierjev kontrolni poligon PH krivulje sicer povsem določa krivuljo, vendar že premik ene njegove točke navadno uniči pitagorejsko lastnost, zato ni primeren za opis takih krivulj. V ta namen bomo uvedli rektifikacijski poligon, ki ima enako število prostih parametrov kot sama PH krivulja. Podrobneje bomo obravnavali primere PH krivulj stopenj 3, 5 in 7. A Pythagorean hodograph curve (PH curve) is a parametrically defined curve whose unit tangent vector has a rational representation. Such curves possess several useful properties, including straightforward arc length computation, rationally defined offset curves, and numerically simple reparametrization with respect to the arc-length parameter. Although the Bézier control polygon of a PH curve uniquely determines the curve, moving even a single control point typically destroys the Pythagorean property, which makes it unsuitable for describing such curves. To address this, we introduce the rectifying polygon, which has exactly the same number of free parameters as the PH curve itself. In particular, we examine the cases of PH curves of degrees 3, 5, and 7. krivulja s pitagorejskim hodografom Bézierjev kontrolni poligon rektifikacijski poligon Gauss-Legendrejeve uteži in vozli kvaternionska reprezentacija Pythagorean hodograph curve Bézier control polygon rectifying control polygon Gauss-Legendre nodes and weights quaternion representation true false false Slovenski jezik Angleški jezik Magistrsko delo/naloga 2025-10-01 08:15:55 2025-10-01 08:15:57 2025-11-20 03:51:39 0000-00-00 00:00:00 2025 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 155101 251334915 20066.pdf 20066.pdf 1 011CDA88CBB426BCE83305737457D846 7fc3ab8b60988fbf986060d635bab2b57c682b4046c04e0f79060ad396497dd8 e35ab5b6-9e8d-11f0-9328-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=219111 Fakulteta za matematiko in fiziko 0 0 0