P146: Enumeration of all biconnected plane triangulations with $n$ vertices and $r$ vertices on the outer face

P146: Enumeration of all biconnected plane triangulations with $n$ vertices and $r$ vertices on the outer face
Input:
Integers $n$ and $r$.
Output:
All biconnected based plane triangulations with $n$ vertices and $r$ vertices on the outer face.
Complexity:
$O(r^2n)$ time per based plane triangulation with $O(n)$ space.
Comment:
Reference:
[Nakano2004a] (Bibtex)