P172: Enumeration of all triangulations of a convex polygon of $n$ vertices

P172: Enumeration of all triangulations of a convex polygon of $n$ vertices
Input:
A convex polygon $P$ with $n$ vertices that are not numbered.
Output:
All triangulations of $P$.
Complexity:
$O(n^2)$ time per triangulation and $O(n)$ space.
Comment:
Reference:
[Parvez2009] (Bibtex)