Construction of G^3 rational motion of degree eight

In this talk we present a construction of a rigid body motion with point trajectories being rational spline curves of degree eight joining together with G^3 smoothness, which means that also the torsion is continuous. 
The motion is determined through the interpolation of positions and derivative data up to order three in the geometric sense. Nonlinearity involved in a spherical part of construction results in a single univariate quartic equation which yields solutions in a closed form. We give some sufficient conditions on the regions for the curvature data, implying the existence of a real admissible solution. The algorithm how to choose appropriate data is presented too. The theoretical results are substantiated with numerical examples.

These results are joint work with Marjeta Krajnc and Vito Vitrih.