Given two points laying on the surface of a cylinder, is there a simple equation for the arclength of the geodesic that connects those two points?
In my use case, the cylinder is oriented axially coincident with the x axis. I have two points for which I know their (x,y,z) locations, and I understand that I can convert these coordinates to cylindrical coordinates by the transformation x=x, y=rcos(theta), z=rsin(theta). Beyond that, I am not sure is there is a simple equation for calculating the geodesic length of between these two points without "unrolling" the cylinder into a plane and using the distance formula.
Can someone confirm for me if it is simply: L=SQRT(r^2θ^2+x^2), where x ix the axial distance which separates the points in my example? Is it this easy?