I like the ant anology.
Green path is obviously shorter but wouldnt be shorter still to head for a tangent to the finger rather than heading for it's center then skirting round?
So the question is: How to answer the above question
Here's another one.
Shortest distance will lie on a single plane for this one but I still don't see a way of finding it without iterating/homing in on the plane manually (or mathematically in this simple case).