How-to control color range assignment in ListContourPlot

Question

I haven't been using Mathematica for some time. So, I got a bit stuck, and I would appreciate some help :).

I would like to...

• Assign specific colors to the grid cells
• Generate a legend, based on the above
• Overlay a set of contours where value of f is lower than a set of pre-defined values e.g. {.25, .5, .75}

Following is the code I am working with just now

ListContourPlot[
  Outer[{#1, #2*10^2, #1*#2*10^2} &, #, #] & @ Range[0, 1, .02] // 
  Flatten[#, 1] &
 , Mesh -> 4
 , MeshFunctions -> {#1 &, #2 &}
 , Contours -> 3
 , ContourStyle -> Black
 , ContourLabels -> True
 , PlotLegends -> Automatic
 , ContourShading -> {Green, Yellow, Orange, Red}
 ]

Output of the above code can be seen below

Desired output would be something like this

Answer 1

maybe something like:

data1 = Outer[{#1, #2*10^2, #1*#2*10^2} &, #, #] &@Range[0, 1, .02] //
    Flatten[#, 1] &;

data2 = Outer[{#1, #2*10^2, Ceiling[#1/.2]*Ceiling[#2 10^2/20]} &, #, #] &@
    Range[0, 1, .02] // Flatten[#, 1] &;

intF = Interpolation[data2, InterpolationOrder -> 0];

cp = ContourPlot[intF[x, y], {x, 0, 1}, {y, 0, 100}, Contours -> 3, 
   PlotPoints -> 60, ContourShading -> {Green, Yellow, Orange, Red}];

Show[cp, lcp]

DensityHistogram

Alternatively, use DensityHistogram with an input array of color codes:

mat = {{2, 3, 3, 4, 4}, {2, 2, 3, 3, 4}, {1, 2, 2, 3, 3}, {1, 1, 2, 2, 3}};

colorFunc = Blend[{{1, Green}, {2, Yellow}, {3, Orange}, {4, Red}}, #1] &;

binspecs = {Subdivide[##]} & @@@ (Flatten /@ 
     Thread[{PlotRange[lcp], Dimensions[mat]}]);

heightspecs = Reverse @ mat &;

dh = DensityHistogram[{{1, 1}}, binspecs, heightspecs, 
   ColorFunction -> colorFunc, ColorFunctionScaling -> False, Mesh -> All];

Show[dh, lcp]

ListDensityPlot

You can also pad mat and use it with ListDensityPlot

paddedmat = ArrayPad[Reverse /@ Transpose@mat, {{0, 1}, {0, 1}}, "Fixed"];


ldp = ListDensityPlot[paddedmat, Mesh -> All, 
  InterpolationOrder -> 0, DataRange -> {{0, 1}, {0, 100}}, 
  ColorFunction -> colorFunc, ColorFunctionScaling -> False];

Show[ldp, lcp]

EventHandler + DensityHistogram

Specify the bin colors interactively using mouse clicks:

dims = {4, 5};
DynamicModule[{m = ConstantArray[1, dims], 
  nc = Length[colorFunc[[1, 1]]], 
  binspecs = {Subdivide[##]} & @@@ (Flatten /@ Thread[{PlotRange[lcp], dims}]), 
  sc = PlotRange[lcp][[All, 2]]/dims}, 
 EventHandler[Dynamic@Show[
    DensityHistogram[{{1, 1}}, binspecs, Reverse @ m &, 
     ImageSize -> Large, AspectRatio -> 1, ColorFunction -> colorFunc,
      ColorFunctionScaling -> False, Mesh -> All, MeshStyle -> Gray, 
     ImageSize -> Large, PerformanceGoal -> "Speed"], 
    lcp], 
 {{"MouseClicked", 1} :> With[{p = {1 + dims[[1]] - #, #2} & @@ 
        Ceiling[(MousePosition["Graphics"])/sc]}, m[[## & @@ p]] =
      Mod[m[[## & @@ p]] + 1, nc, 1]], 
 {"MouseClicked", 2} :> With[{p = {1 + dims[[1]] - #, #2} & @@ 
        Ceiling[(MousePosition["Graphics"])/sc]}, 
     m[[## & @@ p]] = Mod[m[[## & @@ p]] - 1, nc, 1]]}]]