Boundary enclosing a given set of points

Question

I am having a bit of a problem with an algorithm that I am currently using. I wanted it to make a boundary.

Here is an example of the current behavior:

Answer 1

Consider using an Alpha Shape, sometimes called a Concave Hull. https://en.wikipedia.org/wiki/Alpha_shape

It can be built from the Delaunay triangulation, in time O(N log N).