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.

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"]

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]]]]

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"]

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]]