Smooth motion of a rigid body in 2D and 3D

Given measurements of the positions of a number of marked points on a rigid body at a sequence of times t/sub i/ (i=0, 1, ..., n), we represent the motion of the body, assuming this motion to be smooth, by means of piecewise-rational curves, one through each sequence of positions, sharing a common denominator and having the property that the distance between these curves always remains constant. We consider in detail the motion in 2D and 3D of a rigid rod marked at each end.