Construction of G3 rational motion of degree eight

Karla Ferjančič, Marjeta Krajnc and Vito Vitrih

Applied Mathematics and Computation, 2016, vol. 272, issue P1, 127-138

Abstract: The paper presents a construction of a rigid body motion with point trajectories being rational spline curves of degree eight joining together with G3 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.

Keywords: Motion design; Geometric interpolation; Rational spline motion; Geometric continuity (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:272:y:2016:i:p1:p:127-138

DOI: 10.1016/j.amc.2015.08.073

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