Border Mapping of Scatter plot

Question

I have scatter plot and I want to trace the border of that.

for example:

Plot:

and I wanted it traced:

Or at least wanted to know the border points?

Also, is it possible to detect if any point exist on inside or not?

Answer 1

You probably want to look into the literature on Alpha Shapes. They are a generalization of convex hulls and should give you what you want. There's a discussion in this Stack Overflow question about a Python implementation.