Distance from a point to a polygon

Question

I am trying to determine the distance from a point to a polygon in 2D space. The point can be inside or outside the polygon; The polygon can be convex or concave.

If

Answer 1

I do not know about the difference in performance with respect to the rest of answers, but in boost C++ libraries there is an generic implementation called distance. It has information about complexity in every case and in your problem case it is linear.

I was also looking for solutions to this problem some days ago and I want to share this finding. Hope it helps to someone.