How to extract values from a 3D kernel density plot built in R using 'ks' and 'rgl'

I've been using the 'ks' package along with the 'rgl' package to produce 3D kernel density estimates and 3D plots of these. This first part has worked out fine (brief example below). What I can't figure out is if it's possible to extract the values of the kernels for the given xyz locations used to build the kernels in the first place. In other words, extract the values for points in a 3D plot, akin to the extract command used for 2D surfaces in the 'raster' package. Does anyone have experience doing something like this that can point me in the right direction? Thanks much. -DJ

library("rgl")
library("ks")

# call the plug-in bandwidth estimator
H.pi <- Hpi(b,binned=TRUE) ## b is a matrix of x,y,z points

# calculate the kernel densities
fhat2 <- kde(b, H=H.pi)

#plot the 50% and 95% kernels in gray and blue
plot(fhat2,cont=c(50,95),colors=c("gray","blue"),drawpoints=TRUE
    ,xlab="", ylab="", zlab="",size=2, ptcol="white", add=FALSE, box=TRUE, axes=TRUE) 




#Structure of fhat2. Original df consists of ~6000 points.  

List of 9
 $ x          : num [1:6173, 1:3] -497654 -497654 -497929 -498205 -498205 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : chr [1:6173] "50" "57" "70" "73" ...
  .. ..$ : chr [1:3] "x" "max_dep" "y"

$ eval.points:List of 3
  ..$ : num [1:51] -550880 -546806 -542733 -538659 -534586 ...
  ..$ : num [1:51] -7.9 -4.91 -1.93 1.06 4.05 ...
  ..$ : num [1:51] -376920 -374221 -371522 -368823 -366124 ...

$ estimate   : num [1:51, 1:51, 1:51] 0 0 0 0 0 ...

$ H          : num [1:3, 1:3] 3.93e+07 -2.97e+03 8.95e+06 -2.97e+03 2.63e+01 ...

$ gridtype   : chr [1:3] "linear" "linear" "linear"

$ gridded    : logi TRUE

$ binned     : logi FALSE

$ names      : chr [1:3] "x" "max_dep" "y"

$ w          : num [1:6173] 1 1 1 1 1 1 1 1 1 1 ...
 - attr(*, "class")= chr "kde"

Solution

Try this

## from ?plot.kde
library(ks)
library(MASS)
 data(iris)

 ## trivariate example
 fhat <- kde(x=iris[,1:3])

## this indicates the orientation
image(fhat$eval.points[[1]], fhat$eval.points[[2]], apply(fhat$estimate, 1:2, sum))
points(fhat$x[,1:2])

library(raster)

## convert to RasterBrick from raw array
## with correct orientation relative to that of ?base::image
b <- brick(fhat$estimate[,ncol(fhat$estimate):1,], 
    xmn = min(fhat$eval.points[[1]]), xmx = max(fhat$eval.points[[1]]), ymn = min(fhat$eval.points[[2]]), ymx = max(fhat$eval.points[[2]]), 
    transpose = TRUE)

## check orientation
plot(calc(b, sum))
points(fhat$x[,1:2])

Now we are happy because raster power is good.

plot(b)

## note this is a matrix with nrows = nrow(fhat$x), ncols = nlayers(b)
extract(b, fhat$x[,1:2])