Abstract: We discuss the following problem, which arises in computer animation and robot motion planning: given are N positions or keyframes Σ(t_i) of a moving body Σ⊂R³ at time instances t_i. Compute a smooth rigid body motion Σ(t) that interpolates or approximates the given positions Σ(t_i) such that chosen feature points of the moving system run on smooth paths. We present an algorithm that can be considered as a transfer principle from curve design algorithms to motion design. The algorithm relies on known curve design algorithms and on registration techniques from computer vision. We prove that the motion generated in this way is of the same smoothness as the curve design algorithm employed.