Construction of low degree rational motions

Construction of rational spline motions is an important issue in robotics, animations and related fields. In this paper a geometric approach to interpolate given sequence of rigid body positions is considered, which, in contrast to standard approaches, is free of choosing parameter values in advance and it enables the lowest possible degree of the motion. A general solution to the problem how to interpolate 2n2n given positions by rational motion of degree 2n2n is presented and two particular cases, motions of degree six and eight, are studied in more detail. This interpolation scheme is further generalized to a method for constructing first order geometric continuous rational spline motions of degree six. Numerical examples are given which confirm the presented theoretical results.