Tool for measuring extent of shape around a point (like histogram).

Discussion created by jsmyers on Jul 6, 2011
I've got a number of polygons that are associated with a point.  These points are the center in a social science sense, but are by no means the centroid.

I'd like to produce a graph for each polygon that has the following axes:

Y: a percentage of coverage
X: distance from center

I've made a simple map to help me explain:


This is a very arbitrary example of the sort of data that I have.  For this polygon, the graph I'd like will be 100% at a distance of zero, and then start to fall at about 30 miles (where Line 1 exits the polygon).  Line 2 extends to the point of the polygon which is furthest from the center (about 230 miles).  At ~230 miles the graph will be zero, but the Y-values on the graph between 30 and 230 will reflect the percentage of the concentric circle at that distance (x-value) that is within the polygon.  Because of the irregular nature of the shapes, I'd expect that the slop is not necessarily always negative.

The way I visual the math is to make a grid from 0 to 360 degrees on one axis and from 0 to max distance on the other, with binary values in each cell, then integrate relative to the degrees to "count" up the compass points at a given distance that are in the polygon.

I'm not sure I'm explaining my desires very well, but I don't have any idea what spatial analyst tools might help me get this data.  Any ideas?  Any questions to help me clarify what I'm looking to do?  Thank you for some pointers.