If we have functions to clothe the framed vectors with images of the vertebrae, then we could re-create their image from the framed vectors that have just been computed. For instance, if the image were a ring, it might be written as follows.
This expression states to move to the centerof the K’th object and then rotate a vector of length about that center in the plane perpendicular to the third element of the vertebra’s orientation frame of reference through an angular excursion of radians. The rotating vector traces out a circle centered upon the center of the K’th object.
If we want it to be a torus, then we can draw a series of circles about the curve that has just been defined.