I have a polygon and a layer of many points. How many more points would be captured if I expanded the polygon by x meters? I want to end up with values for x = 1 mile, 5 miles, 10 miles, and maybe a few more. My instinct is to plug it into GIS, calculate a buffer, cut out the original polygon, and count point features, but it may not be feasible when I get more points: I will eventually be using a layer of tens of millions of points.
Is there a faster way to do this, maybe outside of a GIS?