11. High order parametric polynomial approximation of quadrics in R [sup] dGašper Jaklič, Jernej Kozak, Marjetka Knez, Vito Vitrih, Emil Žagar, 2012, original scientific article Abstract: In this paper an approximation of implicitly defined quadrics in ▫${\mathbb R}^d$▫ by parametric polynomial hypersurfaces is considered. The construction of the approximants provides the polynomial hypersurface in a closed form, and it is based on the minimization of the error term arising from the implicit equation of a quadric. It is shown that this approach also minimizes the normal distance between the quadric and the polynomial hypersurface. Furthermore, the asymptotic analysis confirms that the distance decreases at least exponentially as the polynomial degree grows. Numerical experiments for spatial quadrics illustrate the obtained theoretical results. Keywords: mathematics, quadric hypersurface, conic section, polynomial approximation, approximation order, normal distance Published in RUP: 03.04.2017; Views: 2127; Downloads: 32 Link to full text |
12. High order parametric polynomial approximation of conic sectionsGašper Jaklič, Jernej Kozak, Marjetka Knez, Vito Vitrih, Emil Žagar, 2013, original scientific article Abstract: V članku je obravnavana parametrična polinomska aproksimacija stožnic, ki ohranja obliko. Pristop je osnovan na parametrični aproksimaciji implicitno definiranih ravninskih krivulj. Polinomski aproksimanti so zapisani v zaključeni obliki in ponujajo najvišji možen red aproksimacije. Keywords: matematika, stožnica, parametrična krivulja, implicitna krivulja, aproksimacija, mathematics, conic section, parametric curve, implicit curve, approximation Published in RUP: 03.04.2017; Views: 2015; Downloads: 82 Link to full text |
13. Pythagorean-hodograph cycloidal curvesJernej Kozak, Marjetka Knez, Mladen Rogina, Vito Vitrih, 2015, original scientific article Abstract: In the paper, Pythagorean-hodograph cycloidal curves as an extension of PH cubics are introduced. Their properties are examined and a constructive geometric characterization is established. Further, PHC curves are applied in the Hermite interpolation, with closed form solutions been determined. The asymptotic approximation order analysis carried out indicates clearly which interpolatory curve solution should be selected in practice. This makes the curves introduced here a useful practical tool, in particular in algorithms that guide CNC machines. Keywords: pitagorejski hodograf, C-krivulje, trigonometrične funkcije, karakterizacija, Hermiteova interpolacija, asimptotični red aproksimacije, Pythagorean-hodograph, C-curves, trigonometric functions, characterization, Hermite interpolation, asymptotic approximation order Published in RUP: 08.08.2016; Views: 2729; Downloads: 198 Link to full text |
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15. Vector connectivity in graphsMartin Milanič, Endre Boros, Ferdinando Cicalese, Pinar Heggernes, Pim Van 't Hof, Romeo Rizzi, 2014, published scientific conference contribution abstract (invited lecture) Keywords: vektorska povezanost, aproksimacijski algoritmi, polinomski algoritmi, NP-poln problem, razcepljeni grafi, kografi, drevesa, vector connectivity, approximation algorithms, poynomial time algorithms, NP-hard problem, split graphs, cographs, trees Published in RUP: 15.10.2015; Views: 3219; Downloads: 250 Link to full text |