Create concave polygon passing through all given points

Question

Given a set of points, I want to create a concave non-intersecting polygon using these points. A convex hull would negate the concave part, while arranging them by x/y coordinates or angles from centre would create spiky artefacts. Is there a simple way to do this?

An example of the kind of polygon I want to create:

Answer 1

If you only have the perimeter vertices and can guarantee that the distance between perimeter vertices will be less than the distance between edges of the perimeter then you could use a minimum spanning tree.

The top example shows where a MST works (with the first and last vertices in the resulting polyline joined)

The bottom example is what happens if edges of the perimeter get too close.