Zoning

Hello!
I apologize for my very very bad English.

I beg you to give a solution.
Given: A set of points with an attribute - number area to which this point belongs.
Objective: Break all the space into regions (area). Non areas - whole, discrete numbers.

It seems to be very similar to the interpolation, but this is not it. Or does it :o

The boundaries are not given. Several points can belong to the same district.

Thanks in advance.