P320: Enumeration of all $r$-rooted $2$-connected triangulations of a planar graph

P320: Enumeration of all $r$-rooted $2$-connected triangulations of a planar graph
Input:
A planar graph $G = (V, E)$ and an integer $r$.
Output:
All $r$-rooted $2$-connected triangulations of $G$.
Complexity:
$O(|V|^2N)$ total time and $O(|V|)$ space.
Comment:
$N$ is the number of solutions.
Reference:
[Avis1996b] (Bibtex)