Algorithm for detecting closed region on a plane First off, I just want to say that I am not well versed in computational geometry, so if this question has some obvious answer, I apologize.  I tried googling it but I could not find anything.

My question: Given an input of a plane with 1 or more line segments, is there an efficient algorithm for determining if there exists a closed region on this plane?  For example, see the following picture:

benjamindicken.com/closed_region.png

On this plane, there exists one closed region.  I would like the algorithm to return true if a closed region exists, and false if one does not.

At the moment, I only need this algorithm to determine if a closed region exists or not, but I could foresee needing this to return the number of closed regions as well.

Thanks for your help.
Let $S$ be a set of segments with the property that no two segments have an intersection with positive length. The set $S$ bounds a region if and only if the intersection graph of the segments in $S$ has a cycle.