[R] projecting onto 2d *integer* grid?

[haettulegur]

I have a bunch of data points in R^2 (Euclidean plane). But I want to project
these onto a 2d integer grid -- that is, there's at most one data point for
each integer (x, y) coordinate, and points near each other in the integer
grid should also be near each other in the original R^2 space.
Is there some method to do this? I'm not necessarily looking for an R
function (though that would be nice).

For example, I tried a kind of simulated annealing approach (basically, I
threw all the data points onto a rectangular integer grid, and tried to
minimize the distances between points), but is there any other method?
I'm not too familiar with self-organizing maps, but would using an SOM with
# of clusters = # of original data points give me what I want?
Any pointers are appreciated!
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