I have a grid data of evenly spaced points that gives the number of people with a facebook account within a certain radius (approximately equal to the mid-distance between to points). From that I'd like to draw a smoothed map of my variable density of facebook users.
I read that available interpolation methods for that were :
- natural neighbours
- kriging, or IDW in the simpler way
- rectangular interpolation
1) Kriging seems to be a good idea in any case, still I wonder if rectangular interpolation could be more appropriate and far less complex since I have perfectly evenly spaced values ?
2) Are there any interpolation models that takes also as input the radius around each data point ? From what I understand all of the above methods use only X-Y coordinates and the value of the interest feature, not any radius around X-Y in which the value is the same.
From @Spacedman's comment, I see that I misunderstood my dataset. What I actually have is z values for a set of discs defined by a set of points (X,Y) and a unique radius r*. Which means, at that point I don't have a true grid to interpolate on.
An easy workaround is to assume that the density at each point (let's call them f(X,Y) by contrast with z(X,Y,r*)) is uniform in my disc, so that f(X,Y) = a in disc A. Since I know that z(A) = a*pi*r^2, I know that a = z(A)/(pi*r^2). I know have values for a set of points, which are still consistent with the values of the disc they belong to.
What if the discs overlap ? I can't assume anymore that f(X,Y) = a around a whole disc since I may have different values for a same (X,Y). Would taking the mean be outrageous ?
