# Is there a special algorithm for computing the convex hull ordering when the candidate points are on the hull?

I'm dealing with a set of points which are already placed on the 2D hull boundary: a convex polygon. I know this for sure. However, the point set is not ordered, and I need the polygon points to be ordered counter-clockwise.

I'm aware of all the 2D algorithms for convex hull generation from the books/literature, but I'm interested if there is a faster, specialized, algorithm for this special case?

Take the mean of all your points as origin and transform to polar coordinates. This gives the desired ordering in $O(n\log n)$ operations.
Since the points are in 2D, you can use Graham's Scan to order the points instead of a sorting algorithm. This will also give you a $\Theta(nlog(n))$ complexity without the need for any transformations.