How to show no data (white background) with ListDensityPlot instead of copying exteme values of data?

Question

I have a list of experimental (x,y,f) data, e.g. I can generate similar data with this:

Fitness[{x_, y_}] := (x - 1)^2 + 10 (x^2 - y)^2;
ListDensityPlot[Flatten[#, 1] &@ Table[{x, y, Fitness[{x, y}]}, {x, -1, 1.5, 0.1}, {y, -1, 1.5, 
    0.1}], InterpolationOrder -> 0]

How to show more range in this ListDensityPlot to illustrate absence of data (of course with white backgroung style)? I mean that if you just try to increase range with PlotRange -> {{-5, 5}, Automatic, Automatic}, you will see smth like this

This picture illustrates that WM instead of showing white background in regions without data interpolates data or, idk, tries to copy extreme values of data and shows this values in no data regions.

How to show white background in regions where I don't have experimental data?

Answer 1

You can use RegionFunction to limit where the data is plotted. For example, to plot just for x values between -1 and 1.5:

ListDensityPlot[Flatten[#, 1] &@
   Table[{x, y, Fitness[{x, y}]}, {x, -1, 1.5, 0.1}, {y, -1, 1.5, 
0.1}], InterpolationOrder -> 0, 
 PlotRange -> {{-5, 5}, Automatic, Automatic}, 
 RegionFunction -> Function[{x, y, f}, -1 <= x <= 1.5]]

If you want the full range of your function for x from -1 to 1.5, change the PlotRange to {{-5, 5}, Automatic, All}

Answer 2

I think the easiest way would be to use PlotPaddingRange inside Show just like this:

Show[ListDensityPlot[
  Flatten[#, 1] &@
   Table[{x, y, Fitness[{x, y}]}, {x, -1, 1.5, 0.1}, {y, -1, 1.5, 
     0.1}], InterpolationOrder -> 0],
 PlotRangePadding -> {{4, 3.5}, {0, 0}}]

And the result (please, do not mind small white artifacts) would be: