Thanks for reaching out. I think this is probably a bit too specialized to get its own function in the library; on the other hand, I suppose a lot of people might make use of something like that. So to strike a balance, one could opt for providing this as an example in the gallery.
Let's see what others think.

From the code perspective I'm wondering if using a matplotlib.patches.Arc wouldn't be better suited? I also think one would usually desire this arc to be at a fixed distance/radius to the intersecting point, independent on the axis limits or zoom level, and also have it appear circular even with unequal aspect. An example showing this would definitely be useful.
I haven't thought this through, so I don't know if there is a good solution possible only with transforms or whether one would need to write a callback for this.

@ImportanceOfBeingErnest

I agree about having the arc appear circular for any aspect ratio; that's something I can look into. I disagree about the fixed radius, however, as I found it useful to be able to increase or decrease the radius for my diagrams, so why not have that as an optional argument?

Of course the radius should be a parameter to be set programmatically. By "fixed" I mean if you zoom in and out, the radius on screen should be the same. I.e the radius is fixed in screen coordinates, not fixed in data coordinates.

The join-style idea is interesting, except I don't see how one can equip this with different linestyle, color etc. In addition the usual use case does not necessarily contain a single line, but probably several, or some polygon shapes. So the limit might be to create a single object of same color, linestyle etc.

Here everything that's black would be the line with the "funny" joint-style. Is that the idea?

Ah, my mistake, I misunderstood. I'll see if I can put together something more robust over the next few weeks. I think you're right that this may work better as a submission to the example gallery, so should I update here or is there a better place for this exchange?

Yes, we can discuss here. Or, once you have something ready, you can submit a pull request with the example (examples are in matplotlib/examples/, though I don't currently know which category this would best fit into).