[R-sig-Geo] Polygon width

[Paulo Flores Ribeiro]

Hello,

I have a shapefile with ca. 25000 polygons. Each polygon has an average 
of 40 vertices (nodes). I would like to extract, for each polygon, the 
distance separating the two most distant vertices (aka "polygon 
diagonal" or "maximum polygon width"). It is not important whether the 
polygon is convex or concave, so the lines connecting the vertices can 
be inside or outside the polygon. The desired result would be a 
two-column array, with a number of rows equal to the number of polygons, 
and where the first column is the id of the polygons, and the second the 
"maximum width" of the corresponding polygon.

What would be the best way to do this, considering that the calculation 
will probably require frequent updates (e.g. due to changes in the shape 
of the polygons)?

Thanks in advance,

PauloFR