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11.

Construction of G[sup]3 rational motion of degree eight
Karla Ferjančič, Marjetka Knez, Vito Vitrih, 2015, izvirni znanstveni članek

Opis: The paper presents a construction of a rigid body motion with point trajectories being rational spline curves of degree eight joining together with ▫$G^3$▫ smoothness. The motion is determined through interpolation of positions and derivative data up to order three in the geometric sense. Nonlinearity in the spherical part of construction results in a single univariate quartic equation which yields solutions in a closed form. Sufficient conditions on the regions for the curvature data are derived, implying the existence of a real admissible solution. The algorithm how to choose appropriate data is proposed too. The theoretical results are substantiated with numerical examples.
Ključne besede: motion design, geometric interpolation, rational spline motion, geometric continuity
Objavljeno v RUP: 15.10.2015; Ogledov: 2862; Prenosov: 124
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12.

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: 2860; Prenosov: 98
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