Kernel Density Mapping?

[Bill Binko]

Hi everyone,

[I've been sidelined recently battling some painful bugs in GDAL, 
Mapserver, and several raster libs, so I've been putting off some more 
general questions I'd love to pose to the list.  This is my first, but 
I'll probably send several tonight (sorry to flood).]

I'm interested in creating "kernel method" density maps using vector point 
data.  I know there is probably a very well known name for these and I 
suspect that there's an open source tool available that can help produce 
them.  However, I'm a computer engineer, not a GIS expert, and I have to 
claim some ignorance on this one.

Here's the description I have of them from a Business Geography book by
Dr. Grant Thrall (from U.F., my alma mater :):

"Describing the Kernel Function.  The kernel is a three-dimentional 
function that moves across a map.  The kernel has a radius referred to as 
a /bandwidth/.  The kernel is said to visit each of [the] mapped customer 
locations and weighs the area surrounding the ccustomer proportioanlly to 
its distance to other customers.  The kernel value for each customer 
within the study regious is threby calculated.  A smoothed surface is then 
produced of those values (Sabel 1998).  The kernel function is a 
measurement of the average proximity of customers to one antoher...."

In this case, he's looking for customer density, but that's irrelavent to 
the technical approach.  The map physically looks like a contour map 
(similar to one generated by gdal_contour or the like).

I would prefer the output of this to be vector-based, but I'm not picky, 
as I can generate a high-resolution version and serve it via GDAL if 
rasters are all I'm going to get.

Any pointers would be greatly appreciated.

Bill