What's the best way to draw lines on a surface like this:



if I haven't been careful about orienting the cylinder and sphere relative to each other?



In other words, if isocurves on the sphere can't match up with those on the cylinder, how do I draw lines that smoothly flow from one face to another? I tried both a cline and a curve > line along the axis of the cylinder hoping that I could snap to the intersection between the cylinder axis and the surface of the sphere, but snapping to that point didn't pan out.