P144: Enumeration of all based plane triangulations with $n$ vertices

P144: Enumeration of all based plane triangulations with $n$ vertices
Input:
An integer $n$.
Output:
All based plane triangulations.
Complexity:
$O(1)$ time per based plane triangulation with $O(n)$ space.
Comment:
A \textit{based plane triangulation} is a plane triangulation with one designated edge on the outer face. The algorithm does not output entire solution but output the difference from the previous solution.
Reference:
[Nakano2004a] (Bibtex)