
There was a very useful article in one of the 1989 issues of
Transactions On Graphics. I believe Maureen Stone was one of
the authors. Sorry not to be more specific. I don't have the
reference here with me.

The article actually was more general than this, giving a way to decide
whether a given (cubic) Bezier curve contains cusps, intersection points
or whatever wierdness. The same treatment is also available in SIGGRAPH 89
course notes for the course called "Math for Siggraph" or something like
that.
