R help - Jul 2014 - Calculate depth from regular xyz grid for any coordinate within the grid

Dear R-experts,

I have a regular grid dataframe (here: the first 50 rows) :

# data frame (regular grid) with x, y (UTM-coordinates) and z (depth)
# x=UTM coordinates (easting, zone 32)
# y=UTM coordinates (northing, zone 32)
# z=river-depth (meters)
df <- data.frame(x=c(3454240, 3454240, 3454240, 3454240, 3454240, 
3454250, 3454250, 3454250, 3454250, 3454250, 3454250, 3454250, 3454250, 
3454250, 3454250, 3454250,
                      3454250, 3454250, 3454260, 3454260, 3454260, 
3454260, 3454260, 3454260, 3454260, 3454260, 3454260, 3454260, 3454260, 
3454260, 3454260, 3454260,
                      3454260, 3454260, 3454260, 3454260, 3454260, 
3454260, 3454260, 3454260, 3454270, 3454270, 3454270, 3454270, 3454270, 
3454270, 3454270, 3454270,
                      3454270, 3454270),
                  y=c(5970610, 5970620, 5970630, 5970640, 5970650, 
5970610, 5970620, 5970630, 5970640, 5970650, 5970660, 5970670, 5970680, 
5970690, 5970700, 5970710,
                      5970720, 5970730, 5970610, 5970620, 5970630, 
5970640, 5970650, 5970660, 5970670, 5970680, 5970690, 5970700, 5970710, 
5970720, 5970730, 5970740,
                      5970750, 5970760, 5970770, 5970780, 5970790, 
5970800, 5970810, 5970820, 5970610, 5970620, 5970630, 5970640, 5970650, 
5970660, 5970670, 5970680,
                      5970690, 5970700),
                  z= c(-1.5621, -1.5758, -1.5911, -1.6079, -1.6247, 
-1.5704, -1.5840, -1.5976, -1.6113, -1.6249, -1.6385, -1.6521, -1.6658, 
-1.6794, -1.6930, -1.7067,
                       -1.7216, -1.7384, -1.5786, -1.5922, -1.6059, 
-1.6195, -1.6331, -1.6468, -1.6604, -1.6740, -1.6877, -1.7013, -1.7149, 
-1.7285, -1.7422, -1.7558,
                       -1.7694, -1.7831, -1.7967, -1.8103, -1.8239, 
-1.8376, -1.8522, -1.8690, -1.5869, -1.6005, -1.6141, -1.6278, -1.6414, 
-1.6550, -1.6686, -1.6823,
                       -1.6959, -1.7095))
head(df)
plot(df[,1:2], las=3)   # to show that it's a regular grid

My question: is there a function to calculate the depth of any 
coordinate pair (e.g. x=3454263, y=5970687) within the grid, e.g. by 
bilinear interpolation or any other meaningful method?

Thanks a lot for your help in anticipation

Best wishes

Thomas