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1.
Motion design with Euler-Rodrigues frames of quintic Pythagorean-hodograph curves
Marjetka Krajnc, Vito Vitrih, 2012, izvirni znanstveni članek

Opis: The paper presents an interpolation scheme for ▫$G^{1}$▫ Hermite motion data, i.e., interpolation of data points and rotations at the points, with spatial quintic Pythagorean-hodograph curves so that the Euler-Rodrigues frame of the curve coincides with the rotations at the points. The interpolant is expressed in a closed form with three free parameters, which are computed based on minimizing the rotations of the normal plane vectors around the tangent and on controlling the length of the curve. The proposed choice of parameters is supported with the asymptotic analysis. The approximation error is of order four and the Euler-Rodrigues frame differs from the ideal rotation minimizing frame with the order three. The scheme is used for rigid body motions and swept surface construction.
Najdeno v: ključnih besedah
Povzetek najdenega: ...paper presents an interpolation scheme for ▫$G^{1}$▫ Hermite motion data, i.e., interpolation of data points...
Ključne besede: Pythagorean-hodograph, Euler-Rodrigues frame, rotation minimizing frame, motion design, quaternion, Hermite interpolation
Objavljeno: 15.10.2013; Ogledov: 1159; Prenosov: 58
URL Polno besedilo (0,00 KB)

2.
An approach to geometric interpolation by Pythagorean-hodograph curves
Vito Vitrih, Marjetka Krajnc, Emil Žagar, Jernej Kozak, Gašper Jaklič, 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.
Najdeno v: ključnih besedah
Povzetek najdenega: ...general approach is applied to the cubic Hermite and Lagrange type of interpolation. Some known...
Ključne besede: mathematics, parametric curve, PH curve, geometric interpolation, Lagrange interpolation, Hermite interpolation, cubic curves, homotopy
Objavljeno: 03.04.2017; Ogledov: 667; Prenosov: 41
URL Polno besedilo (0,00 KB)

3.
C [sup] 1 Hermite interpolation with spatial Pythagorean-hodograph cubic biarcs
Miroslav Lávička, Zbiněk Šír, Vito Vitrih, Marjetka Krajnc, Bohumír Bastl, Michal Bizzarri, Emil Žagar, Kristýna Michálkova, 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.
Najdeno v: ključnih besedah
Ključne besede: mathematics, parametric curve, PH curve, Pythagorean-hodograph, Hermite interpolation, biarc, cubic curve
Objavljeno: 03.04.2017; Ogledov: 626; Prenosov: 12
URL Polno besedilo (0,00 KB)

4.
Pythagorean-hodograph cycloidal curves
Jernej Kozak, Marjetka Krajnc, 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.
Najdeno v: ključnih besedah
Povzetek najdenega: ...Further, PHC curves are applied in the Hermite interpolation, with closed form solutions been determined....
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: 08.08.2016; Ogledov: 1127; Prenosov: 126
URL Polno besedilo (0,00 KB)

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