This is over my head, so I'll just give the link for uv.es pdf:
It concerns Nurbs curves and singularities, but mentions the beziers, and "extends" the (whatever).
At the end it mentions that one nurbs curve can have a singular point. (Which Moi can already do... I guess)

https://scholar.google.com/scholar?hl=en&as_sdt=0%2C48&q=A+Property+on+Singularities+of+NURBS+Curves+Authors%3A++A.+Arnal+%2C++A.+Lluch+%2C++J.+Monterde&btnG=

- Brian