I am learning about spatial dataframes. I have created a simple example that uses inverse distance weighting (IDW) to interpolate values across a grid, based on an initial set of points. I would now like to obtain the interpolated value for each of the initial points. I would presume that this should be relatively easy, but struggle to find an elegant way of doing so. Put differently, I would like to find the nearest grid value in "geog2.idw" for each of the 40 points (x,y).

Code

```
#adjusted from example created by Brian J. Knaus
#packages
library(gstat)
require(gstat)
require(lattice)
require(raster)
require(sp)
##### ##### ##### ##### #####
# Generate data.
set.seed(1)
x <- runif(40, -123, -110)
set.seed(2)
y <- runif(40, 40, 48)
set.seed(3)
z <- runif(40, 0, 1)
# Create spatial data.frame.
geog2 <- data.frame(x,y,z)
# Assigning coordinates results in spdataframe.
coordinates(geog2) = ~x+y
#create grid
pixels <- 100
geog.grd <- expand.grid(x=seq(floor(min(coordinates(geog2)[,1])),
ceiling(max(coordinates(geog2)[,1])),
length.out=pixels),
y=seq(floor(min(coordinates(geog2)[,2])),
ceiling(max(coordinates(geog2)[,2])),
length.out=pixels))
#
grd.pts <- SpatialPixels(SpatialPoints((geog.grd)))
grd <- as(grd.pts, "SpatialGrid")
##### ##### ##### ##### #####
# IDW interpolation.
geog2.idw <- idw(z ~ 1, geog2, grd, idp=6)
spplot(geog2.idw["var1.pred"])
##### ##### ##### ##### #####
# Image.
par(mar=c(2,2,1,1))
#
image(geog2.idw, xlim=c(-125, -110), ylim=c(40, 47))
#
contour(geog2.idw, add=T, lwd=0.5)
#
map("state", lwd=1, add=T)
map("county", lty=3, lwd=0.5, add=T)
#
points(x, y, pch=21, bg=c(1:4))
#######
```