How do I measure the shortest distance between two points (1 and 2) with respect to a polygon? So the shortest way around the polygon from 1 to 2.
Using the convex-hull of a polygon this is quite easy. First you have to include your two points in the set of points building the polygon. Now build the convex-hull for that point-cloud which is always the shortest path around the polygon.
There is a GP-tool at Data Management called Minimum Bounding Geometry which you may use for this.