How do I figure out if subsets can be plotted in a normal Euler diagram? In some cases, it may be impossible to draw Euler diagrams with overlapping circles to represent all the overlapping subsets in the correct proportions. This type of data then requires using polygons or other figures to represent each set. When dealing with data that describes overlapping subsets, how can I figure out whether a simple Euler diagram is possible?
If you are interested in an empirical solution, you might consider the Venneuler package in R. It provides residuals (percentage difference between input intersection area and fitted intersection area). 

https://www.rforge.net/doc/packages/venneuler/venneuler.html