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Distance calculation

Geometry classes seem to be a long time ago...
Since a couple of days, I am trying to bring at least some logic in a
very simply looking problem:
I want to calculate the distances of points on a 3D regular grid to a
limited, 2D, planar area within the grid.
Mathbooks provide a bunge of solutions for the distance between a
point and a surface or for shortest distances between two lines (all
refering to basic vector algebra..), but none seems to be applicable
to this simple buffer problem I'd like to solve...

As I want to code it in IDL, one of my hopes is, that somebody already
solved this problem - or has heard of sombody who knows somebody
who... - or simply that someone has a good idea for a