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Construction of G[sup]3 rational motion of degree eightKarla Ferjančič,
Marjetka Knez,
Vito Vitrih, 2015, original scientific article
Abstract: 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.
Keywords: motion design, geometric interpolation, rational spline motion, geometric continuity
Published in RUP: 14.10.2015; Views: 3139; Downloads: 125
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