Let me give the simple case to start:

I have sets of (X,Y) data points that were created from chained lines (polylines).At X fixed intervals, the Y location was measured then rounded to 1/16". All vertices are at a measured points.

Is there some simple way to recreate the polylines from the points? In other words, I would specify a tolerance, then draw a few lines at possible that have vertices on a point but pass through all the points of the set within the tolerance.