Hermite G1 rational spline motion of degree six

Applying geometric interpolation techniques to motion construction has many advantages, e.g., the parameterization is chosen automatically and the obtained rational motion is of the lowest possible degree. In this paper a G1 Hermite rational spline motion of degree six is presented. An explicit solution of nonlinear equations that determine the spherical part of the motion is derived. Particular emphasis is placed on the construction of the translational part of the motion. Since the center trajectory is a G1 continuous for an arbitrary choice of lengths of tangent vectors, additional free parameters are obtained, which are used to minimize particular energy functionals. Thenumerical examples provide an evidence that the obtained motions have nice shapes.