How can I calculate certain points on the surface of cylinder after I rotate it?

I want to get the positions of two end points( these two end points are fixed) on the surface of the cylinder after I rotate it around itself( the rotate point is the center of the cylinder) in any compination of x y z direction , how can do it? Please help me!

This is rather simple: if v is vector containing coords of the point before transformation and M- transformation matrix then coordinates of v after transformation are M*v.