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ggplot2 - R plot filled.contour() output in ggpplot2

I want to plot this figure created with filled.contour(), but in ggplot2, how do I do this?

I want to use ggplot2 because the graphing conventions are easier. The reason I want to use filled.contour() is because I tried geom_tile() and image.plot() and they both created very tile like outputs, and I need an output similar to filled.contour().

This is my figure:

enter image description here

Code:

library(akima)

df <-read.table("Petra_phytoplankton+POM_xydata_minusNAs_noduplicates.txt",header=T)
attach(df)
names(df)
fld <- with(df, interp(x = longitude, y = latitude, z = d13C))

filled.contour.ungeoreferenced <- 
  (filled.contour(x = fld$x,
                  y = fld$y,
                  z = fld$z,
                  color.palette =
                    colorRampPalette(c("blue", "green", "yellow",
                                       "orange", "red")),
                  xlab = "Longitude",
                  ylab = "Latitude",
                  key.title = title(main = "d13C", 
                                    cex.main = 1)))

Snippet of data:

latitude    longitude   d13C
-65 -70 -27.7
-61 150 -32.2
-61 150 -28.3
-60 116 -26.8
-60 116 -24.7
-47 38  -24.8
-38 150 -20.5
19  -65.7   -19.9
19  -65.5   -18.5
18  -60.7   -20
18  -58.5   -18.2
18  -57.8   -19
17  -55.4   -18.6
17  -50.8   -18
17  -47.1   -18.3
17  -45.5   -19.4
16  -43.3   -17.9
15  -40.7   -18.5
14  -39.3   -19.9
12  -36.7   -19.9
12  -36.2   -19.9
11  -34.4   -19.2
10  -32 -18.5
9   -30.3   -19.3
8   -29.2   -19.4
7   -26.6   -18.2
7   -25.5   -19.3
6   23.9    -20
3   -21.3   -20.4
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You can tweak the colors as you need:

gdat <- interp2xyz(fld, data.frame=TRUE)

ggplot(gdat) + 
  aes(x = x, y = y, z = z, fill = z) + 
  geom_tile() + 
  coord_equal() +
  geom_contour(color = "white", alpha = 0.5) + 
  scale_fill_distiller(palette="Spectral", na.value="white") + 
  theme_bw()

enter image description here

You can reduce the pixelation at the cost of some processing time by increasing the density of the interpolation:

fld <- with(df, interp(x = longitude, 
                       y = latitude, 
                       z = d13C,
                       xo = seq(min(longitude), max(longitude), length=400),
                       duplicate="mean"))

and also reducing the bin width:

ggplot(gdat) + 
  aes(x = x, y = y, z = z) + 
  geom_tile(aes(fill=z)) + 
  coord_equal() +
  stat_contour(aes(fill=..level..), geom="polygon", binwidth=0.005) + 
  geom_contour(color="white", alpha=0.5) +
  scale_fill_distiller(palette="Spectral", na.value="white") + 
  theme_bw()

enter image description here

NOTE: that is going to crunch for a noticeable few seconds on a decent desktop system. On my fairly beefy MacBook Pro it was:

   user  system elapsed 
  6.931   0.655   8.153 

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