Construction of G 3 rational motion of degree eight

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.