BTW, there is no "Western European Union" any more, just one European Union, so the now simplified flag can leave out the white ugly letters in the middle.

That's always an edge-case (literally); having written various vector graphics converters over the years, the fundamentals are usually straightforward (although in this case converting between Cartesian absolute and polar relative coordinates can also introduce numerical precision issues), but depending on things like fill rule compatibility, these tricky cases tend to result in a lot of code dedicated to handling them correctly.

Even different OS' graphics stacks disagree: https://bugs.python.org/issue39392

Unfortunately there's a lack of US flag in the examples, but the Wales one makes up for it in complexity.