complex test case to find outer planar graph face

[adamhosticka]

Finding outer face in a more complex graphs doesn't work.

[adamant-pwn]

Hi, thanks for the pull request! But I'm a bit confused, so you mean that the current implementation is incorrect? Is it possible for you to also add a fix for it in such a case?

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[adamhosticka]

Yes, I believe there is an error. Unfortunately I do not have the time right now create a fix in cpp. I am coding in Python and managed to create a workaround, but I am not even sure it is correct. All I can provide right now is the comment I have added to my code 2 weeks ago:

The sourced algorithm contains an error when finding the outer face. It cannot be just found by checking the orientation
of the vertices. Therefore, I changed the logic.
First we find the outer face candidates - these are the faces containing all the vertices.
The outer face is then the face with the least vertices.
Proof by dispute:
The face with more vertices f1 must contain at least one extra vertex v.
This vertex lies inside the face with fewer vertices f2.
If we create a new face f3 by splitting any edge (a,b) of the f2 into (a,v)&(v,b),
then the edge (a,b) won't lie in the new face f3.
Therefore, the extra vertex v is not a part of the outer face.
Repeat for all extra vertices.