Convex or concave hull, depending on quad or non quad, why this behavior? Related to this question, I've tried to understand how triangles are interpreted in Blender.

Doing these experiments, the result is a bit surprising and I'd want to know why.

Starting from a quad, I obtain this (see gif below): kind of convex hull is calculated and the faces are overlapping only for first and third vertex in fan point of view:



But if we test that for a polygon with more than 4 vertices, it does not happen anymore:



Surely, I've not tested it for all configurations (all vertex amount), but it seems to be a rule.

Why? And, by the way, how this behavior has a link to my original question?

In hope the title of this new question is good enough, this time, thanks for any information.
I showed a similar example to your first before. The quad is always cut from vert 0 to vert 3, while n-gons are triangulated using a better algorithm, possibly because the possibility of concave faces is more likely.

You will also find that an n-gon is triangulated dynamically as you alter it.



I expect the tri/quad drawing code was left alone when n-gon support was added. Maybe it could be suggested that the work being done for 2.80 could include the use of same drawing algorithm for all faces.