# Convex hull for convex polygons

Is there something tricky about that? Or I should use some of the standard convex hull algorithms ?
I mean, I don't see anything different between creating convex hull for a set of points and creating convex hull for non-overlapping convex polygons (2D)?

Creating the convex hull of a finite set of points takes $\Omega(n\log n)$ steps in worst case, which means $n\log n$ is a lower bound for the complexity of every algorithm that solves this problem.
Otherwise you could sort random points (1D) faster that $n\log n$ by calculating the convex hull (2D) of the points $(p_i,p_i^2)$
Construction of the convex hull of a simple polygon is possible in $O(n)$ as shown for example by Preparata and Shamos in 1985: http://cgm.cs.mcgill.ca/~athens/cs601/Preparata.html
Construction of the convex hull of a convex polygon is actually possible in $O(1)$ because the convex hull of a convex polygon is the polygon itself.