how to order vertices in a simple, non-convex polygon

Question

I have a problem where I have a series of points for a simple, non-convex polygon (I hope I have the terminology correct). But the points are not necessarily in order (ie,

Answer 1

Well, you're not going to like it, but it's not possible. If you think about removing all the lines in your demonstration polygon, you could connect them in a different way and still have a valid non-convex polygon, so how's a sort supposed to know which way to go? That's what sucks about non-convex polygons.