Construction of G^1 Hermite rational spline motion of degree six

Geometric interpolation techniques have many advantages, such as automatically chosen parametrization, lower degree of interpolants and optimal approximation order.

In this talk a geometric continuous Hermite rational spline motion of degree six will be presented. The nonlinear equations that determine the spherical part of the motion turn out to have a nice explicit solution. Particular emphasis will be placed on the construction of the translational part of the motion. Since the geometric continuity of the motion is preserved while changing the lengths of the tangent vectors to the center trajectory, additional free parameters are obtained, which affect the shape of the motion significantly. Numerical examples which confirm the theoretical results, will be presented.