Geodesic? How can I create a curve on a surface that is the shortest distance between two points?

Hi all,

I want to create a curve that follows the shortest path between two points.  Mathematically, this is the geodesic ( https://en.wikipedia.org/wiki/Geodesic )

Just doing a "curve on surface" with two points with the default options doesn't look so good (see all the wiggles below).   Any ideas how to get what I want?  I've attached the part (NX10) if you want to try.

.Not so Geodesic curve