I have a set of 3D points that approximately lie on a cylinder. This cylinder is straight and can be oriented in any direction. I would like to compute the minimal enclosing cylinder for the set; that is, I would like to find the cylinder with the smallest radius (I do not care about the height) that encloses all the points.
In the case of enclosing circles and spheres, I have read that there exists a nice efficient algorithm by Emo Welzl ( Smallest enclosing disks(balls and ellipsoids) ). For cylinders I just found the question Smallest enclosing cylinder for an irregular body, where it seems that the cylinder could be obtained using nonlinear optimization tools.
Can this smallest enclosing cylinder problem be solved without using nonlinear optimization, as in the case of balls?
EDIT: What if I have a good initial guess of the axis of the cylinder? I mean, what if I have to obtain the cylinder with its axis close to a given direction?