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Lagrange geometric interpolation by rational spatial cubic Bézier curves
Gašper Jaklič, Jernej Kozak, Vito Vitrih, Emil Žagar, 2012, original scientific article

Abstract: V članku obravnavamo Lagrangeovo geometrijsko interpolacijo s prostorskimi racionalnimi kubičnimi Bézierovimi krivuljami. Pokažemo, da pod določenimi naravnimi omejitvami obstaja enolična rešitev problema. še več, rešitev je podana v preprosti zaključeni obliki in je zato zanimiva za praktične aplikacije. Asimptotična analiza potrdi pričakovani red aproksimacije, namreč 6. Numerični primeri nakažejo možnost uporabe te metode pri obetavni geometrijski nelinearni subdivizijski shemi.
Keywords: numerična analiza, geometrijska Lagrageova interpolacija, racionalna Bézierova krivulja, prostorska krivulja, asimptotična analiza, subdivizija, numerical analysis, geometric Lagrange interpolation, rational Bézier curve, spatial curve, asymptotic analysis, subdivision
Published in RUP: 03.04.2017; Views: 2345; Downloads: 86
URL Link to full text

6.
Pythagorean-hodograph cycloidal curves
Jernej 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: 2622; Downloads: 198
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7.
Asymptotic automorphism groups of Cayley digraphs and graphs of abelian groups of prime-power order
Edward Dobson, 2010, original scientific article

Abstract: We show that almost every Cayley graph ▫$\Gamma$▫ of an abelian group ▫$G$▫ of odd prime-power order has automorphism group as small as possible. Additionally, we show that almost every Cayley (di)graph ▫$\Gamma$▫ of an abelian group ▫$G$▫ of odd prime-power order that does not have automorphism group as small as possible is a normal Cayley (di)graph of ▫$G$▫ (that is, ▫$G_L \triangleleft {\rm Aut}(\Gamma))$▫.
Keywords: mathematics, graph theory, Cayley graph, abelian group, automorphism group, asymptotic, ▫$p$▫-group
Published in RUP: 15.10.2013; Views: 4555; Downloads: 137
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