P19: Enumeration of all triangulations

P19: Enumeration of all triangulations
Input:
A set $S$ of $n$ points in the general position in the plane.
Output:
all the triangulations whose vertex set is $S$ and edge set includes the convex hull of $S$.
Complexity:
$O(\log\log n)$ time per triangulation and linear space.
Comment:
Whether there is the algorithm that outputs all triangulations in constant time delay?
Reference:
[Bespamyatnikh2002] (Bibtex)