I need to interpolate values from points to polygons.
I have a point shapefile and a shapefile of adjacent polygons. Some polygons get several points falling inside, some have nothing. I thought about interpolating values for polygon centroids only, but this is rather crude. I would like to take into account whole polygon areas.
I was going to produce a grid in ArcGIS with very small cells and then calculate average values of cells falling inside each polygon (by zonal statistics), but this way is very time and memory consuming (I have a lot of points and polygons and a large area).
Also I found in ArcGIS for a geostatistical layer: Predicting values for specified point locations. I can set there polygons as my specific locations and have the output with predicted values for each polygon in the attribute table. But I have no idea how ArcGIS calculates values for polygons there (they appear different from the values for the point centers of the polygons).
I appreciate your advices!