Fast and improved 2D Convex Hull algorithm and its implementation in O(n log h)

This article is about a relatively new and unknown Convex Hull algorithm and its implementation. This new algorithm has great performance and this article present many implementation variations and/or optimizations of it. This article contains detailed explanation, code and benchmark in order for the reader to easily understand and compare results with most regarded and popular actual convex hull algorithms and their implementation. You will find real working and tested code here. This article combines: code, algorithms and mathematical. It is a little bit specialized, but I hope you will find something interesting here.