The ShortPath command creates the shortest possible curve (geodesic) between two points on a surface.
A true shortest path exists, and if this path does not run along a surface boundary, it is a geodesic.
Not all geodesic curves are shortest paths between their end points. For instance, a great circle on a sphere is a closed geodesic, it does not have endpoints. An arc of a great circle on a sphere containing more than 180 degrees is a geodesic, but it is not the shortest path between the end points.
However, geodesics are locally shortest paths. This means that if you take a sufficiently small piece of a geodesic curve, it will be the shortest path between its endpoints.
Create curves from other objects