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1.
An approach to geometric interpolation by Pythagorean-hodograph curves
Gašper 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: 2083; Prenosov: 71
URL Povezava na celotno besedilo

2.
High order parametric polynomial approximation of conic sections
Gašper 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: 1835; Prenosov: 82
URL Povezava na celotno besedilo

3.
C [sup] 1 Hermite interpolation with spatial Pythagorean-hodograph cubic biarcs
Bohumír Bastl, Michal Bizzarri, Marjetka Knez, Miroslav Lávička, Kristýna Michálkova, Zbiněk Šír, Vito Vitrih, Emil Žagar, 2014, izvirni znanstveni članek

Opis: In this paper the ▫$C^1$▫ Hermite interpolation problem by spatial Pythagorean-hodograph cubic biarcs is presented and a general algorithm to construct such interpolants is described. Each PH cubic segment interpolates ▫$C^1$▫ data at one point and they are then joined together with a ▫$C^1$▫ continuity at some unknown common point sharing some unknown tangent vector. Biarcs are expressed in a closed form with three shape parameters. Two of them are selected based on asymptotic approximation order, while the remaining one can be computed by minimizing the length of the biarc or by minimizing the elastic bending energy. The final interpolating spline curve is globally ▫$C^1$▫ continuous, it can be constructed locally and it exists for arbitrary Hermite data configurations.
Ključne besede: mathematics, parametric curve, PH curve, Pythagorean-hodograph, Hermite interpolation, biarc, cubic curve
Objavljeno v RUP: 03.04.2017; Ogledov: 1981; Prenosov: 39
URL Povezava na celotno besedilo

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