11. Lattices on simplicial partitionsGašper Jaklič, Jernej Kozak, Marjetka Knez, Vito Vitrih, Emil Žagar, 2010, objavljeni znanstveni prispevek na konferenci Opis: In this paper, a ▫$(d+1)$▫-pencil lattices on a simplex in ▫${\mathbb{R}}^d$▫ are studied. The barycentric approach naturally extends the lattice from a simplex to a simplicial partition, providing a continuous piecewise polynomial interpolant over the extended lattice. The number of degrees of freedom is equal to the number of vertices of the simplicial partition. The constructive proof of thisfact leads to an efficient computer algorithm for the design of a lattice. Ključne besede: numerical analysis, lattice, barycentric coordinates, simplicial partition Objavljeno v RUP: 03.04.2017; Ogledov: 2171; Prenosov: 135 Povezava na celotno besedilo |
12. An approach to geometric interpolation by Pythagorean-hodograph curvesGašper Jaklič, Jernej Kozak, Marjetka Knez, Vito Vitrih, Emil Žagar, 2012, izvirni znanstveni članek Opis: The problem of geometric interpolation by Pythagorean-hodograph (PH) curves of general degree ▫$n$▫ is studied independently of the dimension ▫$d \ge 2$▫. In contrast to classical approaches, where special structures that depend on the dimension are considered (complex numbers, quaternions, etc.), the basic algebraic definition of a PH property together with geometric interpolation conditions is used. The analysis of the resulting system of nonlinear equations exploits techniques such as the cylindrical algebraic decomposition and relies heavily on a computer algebra system. The nonlinear equations are written entirely in terms of geometric data parameters and are independent of the dimension. The analysis of the boundary regions, construction of solutions for particular data and homotopy theory are used to establish the existence and (in some cases) the number of admissible solutions. The general approach is applied to the cubic Hermite and Lagrange type of interpolation. Some known results are extended and numerical examples provided. Ključne besede: mathematics, parametric curve, PH curve, geometric interpolation, Lagrange interpolation, Hermite interpolation, cubic curves, homotopy Objavljeno v RUP: 03.04.2017; Ogledov: 2260; Prenosov: 71 Povezava na celotno besedilo |
13. High order parametric polynomial approximation of quadrics in R [sup] dGašper Jaklič, Jernej Kozak, Marjetka Knez, Vito Vitrih, Emil Žagar, 2012, izvirni znanstveni članek Opis: 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. Ključne besede: mathematics, quadric hypersurface, conic section, polynomial approximation, approximation order, normal distance Objavljeno v RUP: 03.04.2017; Ogledov: 2138; Prenosov: 32 Povezava na celotno besedilo |
14. Lagrange geometric interpolation by rational spatial cubic Bézier curvesGašper Jaklič, Jernej Kozak, Vito Vitrih, Emil Žagar, 2012, izvirni znanstveni članek Opis: 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. Ključne besede: 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 Objavljeno v RUP: 03.04.2017; Ogledov: 2429; Prenosov: 86 Povezava na celotno besedilo |
15. High order parametric polynomial approximation of conic sectionsGašper Jaklič, Jernej Kozak, Marjetka Knez, Vito Vitrih, Emil Žagar, 2013, izvirni znanstveni članek Opis: 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. Ključne besede: matematika, stožnica, parametrična krivulja, implicitna krivulja, aproksimacija, mathematics, conic section, parametric curve, implicit curve, approximation Objavljeno v RUP: 03.04.2017; Ogledov: 2020; Prenosov: 82 Povezava na celotno besedilo |
16. Pythagorean-hodograph cycloidal curvesJernej Kozak, Marjetka Knez, Mladen Rogina, Vito Vitrih, 2015, izvirni znanstveni članek Opis: 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. Ključne besede: pitagorejski hodograf, C-krivulje, trigonometrične funkcije, karakterizacija, Hermiteova interpolacija, asimptotični red aproksimacije, Pythagorean-hodograph, C-curves, trigonometric functions, characterization, Hermite interpolation, asymptotic approximation order Objavljeno v RUP: 08.08.2016; Ogledov: 2732; Prenosov: 198 Povezava na celotno besedilo |
17. "Pod egido ruskega orla" ali orientalistični izleti A. AškercaKrištof Jacek Kozak, 2011, izvirni znanstveni članek Opis: Anton Aškerc, slovenski pesnik s preloma 20. stoletja, je po tem, ko je dvakrat potoval v Rusijo, objavil svoje popotne zapiske. Kljub zagotovilom o objektivnosti je Aškerčev odnos do Rusije zapletalo tudi njegovo panslavistično nagnjenje. Analiza dokaže jasen orientalistični (skladno s terminom E. Saida) predsodek, pri katerem navsezadnje zmaga Zahodna kultura. Ključne besede: slovenska književnost, potopisi, popotni dnevniki, imagologija, Rusija, orientalizem, panslavizem Objavljeno v RUP: 30.12.2015; Ogledov: 3968; Prenosov: 24 Povezava na celotno besedilo |
18. Parametric curves with Pythagorean binormalsJernej Kozak, Marjetka Knez, Vito Vitrih, 2015, izvirni znanstveni članek Opis: In this paper, a class of rational spatial curves that have a rational binormal is introduced . Such curves (called PB curves) play an important role in the derivation of rational rotation-minimizing osculating frames. The PB curve construction proposed is based upon the dual curve representation and the Euler-Rodrigues frame obtained from quaternion polynomials. The construction significantly simplifies if the curve is a polynomial one. Further, polynomial PB curves of the degree % 7 and rational PB curves of the degree % 6 that possess rational rotation-minimizing osculating frames are derived, and it is shown that no lower degree curves, constructed from quadratic quaternion polynomials, with such a property exist. Ključne besede: pitagorejski hodograf, pitagorejska binormala, racionalna krivulja, dualne koordinate, rotacijsko minimizirajoče ogrodje, pitagorejska binormala, racionalna krivulja, dualne koordinate, rotacijsko minimizirajoče ogrodje, Pythagorean-hodograph, Pythagorean-binormal, rational curve, dual coordinates, rotation-minimizing frame, osculating frame Objavljeno v RUP: 15.10.2015; Ogledov: 2675; Prenosov: 124 Povezava na celotno besedilo |
19. Re-Appearance of Tragedy in Contemporary DramaKrištof Jacek Kozak, 2014, objavljeni znanstveni prispevek na konferenci Ključne besede: sodobna tragedija, tragični junak, indivudualni zakon, junak, heroj, grešni kozel, postdramsko gledališče, performans, globalizirani svet, homo sacer Objavljeno v RUP: 14.10.2015; Ogledov: 2553; Prenosov: 71 Povezava na celotno besedilo |
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