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plotting - Mark an 2d-area on a 3dPlot (ListPlot3d)



I have a list {(IC,s,FK)}, which I use to generate a 3d-plot with the help of the command ListPlot3D. IC and s go from 0 to 1.


enter image description here


There is an area (lets say 0.11 < IC < 0.3, 0.1 < s < 0.4) which is specially important, because this is the physical range. For some reason I want to plot the whole parameter space, but highlight (for example with a red rectangle) this physical range. It would be great to frame the physical range with a red rectangle on the surface of the 3d-Plot. (In the end, this 2d-rectangle should look similar to these mesh lines, but it should frame the range, defined above).


Do you have any idea?



Answer



With


 data = Table[{x = RandomReal[{-1, 1}], y = RandomReal[{-1, 1}], x^2 - y^2}, {300}];

Three possible methods are




  1. using ColorFunction

  2. using a combination of Mesh, MeshFunctions and MeshShading, (or, and better yet, just Mesh and MeshShading as in @Brett's answer)

  3. produce two plots using different RegionFunction settings and combine them using Show.


Using ColorFunction:


 ListPlot3D[data, BoxRatios -> Automatic, Mesh -> None, 
  ColorFunction -> Function[{x, y, z}, If[-.5 < x < .5 && -.3 < y < .1, Red, White]],
  ColorFunctionScaling -> False, BoxRatios -> Automatic, 
   MaxPlotPoints -> 100, Lighting -> "Neutral"]


enter image description here


or with a different setting for the ColorFunction, say:


 ColorFunction -> Function[{x, y, z}, If[-.5 < x < .5 && -.3 < y < .1,
    ColorData["DeepSeaColors", (1 + x)/2], Directive[Opacity[.7], Hue[(1 + z)/2]]]]

enter image description here


Using Mesh, MeshFunctions and MeshShading:


 ListPlot3D[data,
  MeshFunctions -> {Boole[-.5 < #1 < .5 && -.2 < #2 < .75] &}, 
  Mesh -> {{1}},  MeshShading -> {White, Red}, 

  BoxRatios -> Automatic,  MaxPlotPoints -> 100, Lighting -> "Neutral"]

enter image description here


Using RegionFunction and Show:


lp1 = ListPlot3D[data,
    RegionFunction -> (! (-.5 < #1 < .5 && -.2 < #2 < .75) &),
    Mesh -> None, BoxRatios -> 1,
    MaxPlotPoints -> 100, Lighting -> "Neutral",
    ColorFunction -> (Directive[Opacity[.9], Hue[#1]] &), 
    Lighting -> "Neutral",   ImageSize -> 300];

lp2 = ListPlot3D[data,
    RegionFunction -> ((-.5 < #1 < .5 && -.2 < #2 < .75) &),
    Mesh -> None, BoxRatios -> 1,
    MaxPlotPoints -> 100, Lighting -> "Neutral",
    ColorFunction -> (Red &), Lighting -> "Neutral",
    ImageSize -> 300];
    Panel@Row[{lp1, lp2, Show[{lp1, lp2}]}, Spacer[5]]

enter image description here


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