# Make a density plot from a file where the data makes a shape with a hole in it

I have a .dat file and I want to make preferably a density (or surface) plot with it.

ListDensityPlot[f, ColorFunction -> "Rainbow", Axes -> False,
Background -> Black,
PlotLegends ->
Placed[BarLegend[Automatic, LegendMargins -> {{0, 0}, {10, 6}},
LegendMarkerSize -> {15, 300}, LegendLabel -> "F"], After] ,
AspectRatio -> 0.5,  PlotRange -> All]


The data has the shape of a not perfectly round donut seen from above, so there's a hole inside and the density and surface plot commands apply the color of the ColorFunction as if it's 0 to the part in the center that corresponds to the hole. Is there a way that the part in the middle doesn't get colored? Or can I assign specifically black to the values that are "0" (but where in reality there's not data) and still use the Color Function?

You may try the option"RegionFunction" of ListDensityPlot. Here is an example:

dat = Table[t1 = RandomReal[{-1, 1}]; t2 = RandomReal[{-1, 1}];
If[t1^2 + t2^2 < .5, Nothing[], {t1, t2, t1^2 + t2^2}], 1000];
ListDensityPlot[dat, RegionFunction -> ((#1^2 + #2^2 >= .6) &)]


But note, RegionFunction together with ListDensity plot is a bit finicky. It seems that it only works if at least a few points are excluded. E.g. in the above, setting the limit to 0.5:RegionFunction -> ((#1^2 + #2^2 >= .5) &) will not work.

You can design a ColorFunction so that a standard color function is used in most cases, except for some values. Here is a possiblity.

Case 1: The standard "rainbow" function

h = Table[Sin[j^2 + i], {i, 0, Pi, Pi/4}, {j, 0, Pi, Pi/4}];
l1 = ListDensityPlot[h, ColorFunction -> ColorData["Rainbow"],
Axes -> False, Background -> LightGray, AspectRatio -> 0.5,
PlotRange -> All]


Case 2: As Case 1, but returns Black for value 0

h = Table[Sin[j^2 + i], {i, 0, Pi, Pi/4}, {j, 0, Pi, Pi/4}];
col[c_] := Black;
l2 = ListDensityPlot[h,
ColorFunction -> (If[# != 0., ColorData["Rainbow"][#] &, col[#] &]),
Axes -> False, Background -> LightGray, AspectRatio -> 0.5,
PlotRange -> All]


Case 3: As Case 2, but returns Black with Opacity 0 for value 0

h = Table[Sin[j^2 + i], {i, 0, Pi, Pi/4}, {j, 0, Pi, Pi/4}];
col[c_] := {Opacity[0], Black};
l3 = ListDensityPlot[h,
ColorFunction -> (If[# != 0., ColorData["Rainbow"][#] &, col[#] &]),
Axes -> False, Background -> LightGray, AspectRatio -> 0.5,
PlotRange -> All]