Calculate the shortest distance across a polygon.

[RoryHall]

Hi all,
I appologise in advance here as I am flying a bit blind.
I am trying to find a method to calculate the shortest distance across a polygon. My line of thought is to get access to the points that make up the segments between vertices and shoot out a line perpendicular until it reaches the opposite side of the polygon measure that line and find the shortest.
What I need to know is how Arc manages the geometry for polygons and how to get access to that for the calcs. I am assuming the topology is managed using something like a polygons can is either be on the right or left side of a shared line. How do I access this data and the points data?
There are two outcomes I hope to acheive here is, can someone point me to to a "doc" describing how Arc manages polygons especially topology, and to actually acheive the task.
This is one of those "Are you able to do....." requests, and I am sure you can but don't really know where to start.

Thanks in advance for anyone help
Cheers ~ Rory

[DanPatterson_Retired]

The shortest distance across a polygon could conceivably be at one of its points with a distance of 0 (consider a diamond polygon oriented NS, the bottom or top point would meet your current criteria)
Can you clarify your criteria a bit

[ChrisSnyder]

Rory,

Perhaps if you specified that the "shortest distance line" must pass through the polygon's centroid point (center of gravity), it would be a better description of what you are trying to do?

Also, you might have better luck getting a vector-based way to do this if you posted it in the Geoprocessing forum: http://forums.arcgis.com/forums/31-Geoprocessing. Contrary to the name, the "Spatial Analyst" forum is dedicated to raster-based data analysis (not vector-based) using the ESRI "Spatial Analyst" application extension software.

The Python-based geoprocessing API gives very easy access to a polygon's constituent vertices (ArcObjects API does as well, but is more complicated to program).