Given a set $$$S$$$ containing $$$n \gt 3$$$ points on a 2D-plane. We find a convex hull $$$H_1$$$ of $$$S$$$. If $$$S-H_1$$$ contains $$$\geq 3$$$ points, we find a convex hull $$$H_2$$$ of $$$S-H_1$$$. If $$$S-H_1-H_2$$$ contains $$$\geq 3$$$ points, we then find a convex hull $$$H_3$$$ of $$$S-H_1-H_2$$$...

We need to iterate and continue this process until there are less than $$$3$$$ points remaining. You might assume there are no colinear points.

How to solve this problem efficiently? There are some relevant papers, however I found them rather hard to implement:

Maintenance of configurations in the plane, Journal of Computer and System Sciences, published by Mark H. Overmars, Jan van Leeuwen in 1981. ($$$O(nlog^2n)$$$)

On the convex layers of a planar set, IEEE Transactions on Information Theory, published by B. Chazelle in 1985. ($$$O(nlogn)$$$)

A Simple Convex Layers Algorithm, Arxiv, published by Raimi A. Rufai, Dana S. Richards in 2017. ($$$O(nlogn)$$$)