How to move a line defined by Plücker coordinates?

Question

I have a line defined by plücker coordinates L=(U:V). I have a vector A which is perpendicular to the line. I want to move this line following the vector A.

I can do this simply by finding two points on the line. Than move these points by vector A and create a new line.

Is there a more simple (and elegant) way to move the plücker line?

Answer 1

I went through Shoemake's notes with sharpened eyes I found this as a solution:

   L = {U:V} plucker line

   A is a direction and magnitude vector for the move

get P as closest point to the origin in homogeneous coordinates

    P = (VxU:U.U)

Pc = P in cartesian coordinates (change P from homogeneous to cartesian coordinates)
get N as Pc after the move

   N = Pc + A

get moved L as K

  K = {U:UxN}