Given 2 points P1= (x1, y1, z1) and P2= (x2, y2, z2), how can we describe a cylinder around the line formed?

I was thinking of finding a parallel line segment and rotating it at distance r around the line segment defined by P1 and P2, but i'm not sure how to define these.

I don't want to find just the surface area, per se, but the actual points that the cylinder would go through.

thanks. if that's not clear enough, please let me know.