How can I plot a sublevel set?

I wish to create a 2d plot which includes the sublevel set of a two variable function. The plot would also include other single variable functions. I am able to plot the region from a saved splot of the two variable function as points, but I have not been able to figure out how to just have the sublevel set as a shaded region. Thank you for any suggestions.

set table 'sublevel.dat'
splot f(x,y)
unset table

plot g(x), sublevel.dat using 1:($3\< value ? $2 : 1/0)

with points # works but not really just shading

with filledcurves (various other stuff none satisfactory)

set table 'sublevel.dat'
set contour ; set cntrparam levels discrete value
unset surface ; set view map
splot f(x,y)
unset table

plot g(x), sublevel.dat using 1:($3\< value ? $2 : 1/0)

with filledcurves xy=clever_x,clever_y # sometimes works but definitely not always

Solution

The following probably doesn't fully answer your exact question, but maybe helps to find a solution. If you want to fill a contour line up to (or from) a certain level you could simply set the color palette accordingly, e.g.

set palette defined (zmin c1, z0 c1, z0 c0, zmax c0)

where zmin, zmax, z0 are the minimum, maximum and desired level and c0 and c1 the desired colors.

First you plot your function into a table using set contour and set cntrparam level discrete z0 which will put the z-data into the first block (index 0) and the contour line(s) in following blocks (here: just one contour line in index 1). Plot this data ... index 0 with image and ... index 1 with lines.

When using a function, the higher you set samples and isosamples (here: 250), the more precise/smoother the border will get, but it takes longer.

Although I don't know how to plot your special function, but if you have your data already in a file or table x y z=f(x,y), you could use the same procedure.

Script:

### fill contour above/below certain level
reset session

f(x,y) = sin(1.3*x)*cos(.9*y)+cos(.8*x)*sin(1.9*y)+cos(y*.2*x)

z0 = 0
set contour
set cntrparam levels discrete z0
set table $Data
    set samples    250
    set isosamples 250
    splot sample [x=-7:7][y=-7:7] '++' u 1:2:(f(x,y))
unset table
stats $Data u 3 nooutput   # get zmin,zmax
zmin = STATS_min
zmax = STATS_max
set xrange noextend
set yrange noextend
set tics out
set key out noautotitle
set cbrange[zmin:zmax]
set style fill solid border lt -1
unset colorbox

c0 = "0xffffff"   # fillcolor 0
c1 = "0xffcccc"   # fillcolor 1
set palette defined (zmin c1, z0 c1, z0 c0, zmax c0)

plot $Data index 0 u 1:2:3 w image, \
        keyentry w boxes fc rgb c1 ti "z < ".z0, \
        '' index 1 u 1:2 w l lc "black" ti "z = ".z0, \
        keyentry w boxes fc rgb c0 ti "z > ".z0
### end of script

Result: (output from wxt terminal)

Addition: (transparent "fill")

As far as I know, you cannot set a transparent fillcolor (at least not in gnuplot 5.4), but you can use the ternary operator (check help ternary) and set the values z>0 to NaN. If you then use, e.g. the terminal pngcairo with option transparent you will get a PNG with transparent areas and background.

You need to change the first plotting line to

plot $Data index 0 u 1:2:($3>z0 ? NaN : $3) w image

and add the following lines at the end:

set term pngcairo transparent
set output "SO79103168.png"
    replot
set output

Output: (Screenshot of generated PNG imported into Inkscape with checkerboard background)