Extraordinary vertices (why it happen and how to fix)

Hi Community,

When convert subd to brep, there is extraordinary vertex if we have the wrong topologys. I’m hoping to get some insight on where this problem come from:
1 is it the problem with the grasshopper’s implementation? (e.g. need many codings to make it work)
2 Or, is it like a math problem (e.g. no can find perimeter of ellipse, formula just don’t exist)

Many thanks,

So like, maybe there is some math principle that says, in a nurbs/brep world, there has to be a point that’s not curvature continuous? (like the hairy ball theorem for vector direction). I’m not sure