Calculating weighted polygon centroids in R

Question

I need to calculate the centroids of a set of spatial zones based on a separate population grid dataset. Grateful for a steer on how to achieve this for the example below.<

Answer 1

Another alternative.

I like it for its compactness, but it will likely only make sense if you're fairly familiar with the full family of raster functions:

## Convert polygons to a raster layer
z <- rasterize(polys, dat)

## Compute weighted x and y coordinates within each rasterized region
xx <- zonal(init(dat, v="x")*dat, z) / zonal(dat,z)
yy <- zonal(init(dat, v="y")*dat, z) / zonal(dat,z)

## Combine results in a matrix
res <- cbind(xx[,2],yy[,2])
head(res)
#          [,1]     [,2]
# [1,] 8.816277 14.35309
# [2,] 8.327463 14.02354
# [3,] 8.993655 13.82518
# [4,] 8.467312 13.71929
# [5,] 9.011808 13.28719
# [6,] 9.745000 13.47444