Venn diagram with 4 sets or more unable to display all intersections

[jklaise]

E.g. for 4 sets there are $2^4-1=15$ distinct intersections, but since the diagrams are only drawn using circles, it's impossible to show them all. In particular, the example on the Readme with 4 sets is misleading, as all 15 subsets are defined, but the visualisation can only show 13 (the A+C and B+D intersections are missing).

I think there should be a warning to the user that the corresponding set intersections are non-empty but could not be displayed.

[paulbrodersen]

a) Thanks for the heads up, and b) ouch, that is a big oversight.

E.g. for 4 sets there are 2 4 − 1 = 15 distinct intersections, but since the diagrams are only drawn using circles, it's impossible to show them all.

Do you know how to work out the maximum number of intersections that can exist for a given number of circles?

I think there should be a warning to the user that the corresponding set intersections are non-empty but could not be displayed.

Well, at the very least.

[jklaise]

Do you know how to work out the maximum number of intersections that can exist for a given number of circles?

I just looked it up, it seems that this number is $i(n)=n^2-n+2$ (including the empty exterior), so for $n=4$ it gives 14 (13 interior ones as you can count in your example diagram +1 exterior one). There's a reference here.

We could use this number (-1 for the exterior) to issue a warning to the user that there are more non-empty intersections than can be displayed by the circle diagram.

[paulbrodersen]

I just looked it up, it seems that this number is i ( n ) = n 2 − n + 2 (including the empty exterior), so for n = 4 it gives 14 (13 interior ones as you can count in your example diagram +1 exterior one). There's a reference here.

Thanks for finding a good reference / list of references.

We could use this number (-1 for the exterior) to issue a warning to the user that there are more non-empty intersections than can be displayed by the circle diagram.

Yeah, but that assumes that the optimization does as well as it possibly could. For the time being, I am simply checking each non-empty subset, if the associated shapely geometry has a non-zero area.

[paulbrodersen]

We could use this number (-1 for the exterior) to issue a warning to the user that there are more non-empty intersections than can be displayed by the circle diagram.

I added another warning if the theoretical maximum is exceeded.

[paulbrodersen]

Alright, this is about as much as I can do short of writing a new layout engine that uses some shape other than circles.
Again, thanks for the heads-up, and thanks for the help!