decomposing an intersecting polygon?

[Richard Kinch]

In comp.graphics.algorithms Jeff Erickson <jeffe at cs.uiuc.edu> wrote:

> Once you have the intersection points, decomposing the self-intersecting
> polygon into simple components is, er, "easy".  Whenever you see an
> intersection point, turn instead of going straight.

What about cases where an intersection consists of more than two edges?
Which edge do you turn on to?