Self intersecting boundaries about cdt

[LeoPizzo1]

Here you can find two tests, ne very easy (but exaggerated by intention), where a "butterfly" is created.
The other one, on the contrary, is the "real life" case.
I know I can fix the problem adding a vertex at the intersection and splitting the edges accordingly, but it takes time...
My idea is that it is not to obtain a correct tessellation, but to obtain the triangles up to the edges, even if the resulting tessellation is not "well formed" and self intersecting.
To display it would be enough.

real_life_test.txt
test_exagerated.txt

[artem-ogre]

Could you provide a small (preferably) example of the input you are talking about?

[LeoPizzo1]

Here, for your info, the real life working case:
real_life_working.txt

[artem-ogre]

The proper fix is as you pointed out: split edges at intersection position.
Maybe at some point functionality for that will be added to CDT.

Another fix is to modify boundary edges in a way that they don't intersect.

Otherwise the triangulation topology is inconsistent and I have no good idea how triangle-removal algorithm can be modified to work with intersecting edges.