What is the center line of a complex polygon? Routing as the solution

I’ve had a series of posts (including this one) on finding the center line of a complex polygon– especially with an interest in finding the center line of streams and river bodies.  We have to give credit to my colleague Tom Kraft for solving the polygon centerline problem.  Tom struck upon the very elegant solution– derive the medial axis, and then use a few end points to route between to extract just the important features.  It’s not fully automated, but the amount of user input is so nominal as to be as close to automatic as I care about.  So far, we have this implemented in a mix of ArcGIS and PostGIS, but I can easily picture a pretty simple web interface with a PostGIS back end for extracting the centerlines of polygons in a nominally interactive way.  As a teaser, a non-stream example:

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