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1.
Parametric curves with Pythagorean binormals
Jernej 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: 2588; Prenosov: 123
URL Povezava na celotno besedilo

2.
Motion design with Euler-Rodrigues frames of quintic Pythagorean-hodograph curves
Marjetka Knez, 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.
Ključne besede: Pythagorean-hodograph, Euler-Rodrigues frame, rotation minimizing frame, motion design, quaternion, Hermite interpolation
Objavljeno v RUP: 15.10.2013; Ogledov: 2756; Prenosov: 98
URL Povezava na celotno besedilo

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