I have created a grid of 1Km2 over some census zones. Now, for each cell of the grid, I need to provide some characterization of it: population, socio-econ, etc. coming from the census zones.

So, some cells will be completely inside some census zone, some others will cover two or more zones, etc. (see figure).

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How can I interpolate the data from the zones to the grid in the best (mathematical) way?

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