[R] plot map of areas

[Pascal A. Niklaus]

Hi all,

Given a number of points (x,y) in a plane, I'd like to plot a map of 
polygons, so that

    1) each polygon contains exactly one point
    2) the polygon defines the area for which this specific point is 
closer than any other point.

It's a bit like a map of areas "influenced" by that point, and it's 
obviously a matter of intersecting the perpendicular bisectors between 
adjacent points.

I believe this type of map has a name, but I can't remember how it's 
called.

Is there a function somewhere in a R package that may do this?

Thanks for your help

Pascal