P173: Enumeration of all triangulations of a triconnected plane graph of $n$ vertices

P173: Enumeration of all triangulations of a triconnected plane graph of $n$ vertices
Input:
A triconnected planar graph $G$ with $n$ vertices.
Output:
All triangulations of $G$.
Complexity:
$O(1)$ time per triangulation and $O(n)$ space.
Comment:
Reference:
[Parvez2009] (Bibtex)