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This is a quick follow up to my other question which I thought was different enough to warrant a separate post.

My Question

How do you plot a region (such as $f(x,y)>z$) on a 2D surface $g(x,y)=z$ and change the color of the region?

A Simple Example

f[x_, y_] := Sin[x] + Sin[y];
g[x_, y_] := y x Sin[x y];
img = RegionPlot[3/2 > f[x, y] > 1, {x, 0, 2}, {y, 0, 2}, 
  Frame -> False, PlotRangePadding -> None, PlotStyle -> Orange, 
  BoundaryStyle -> Black]
Plot3D[g[x, y], {x, 0, 2}, {y, 0, 2}, PlotStyle -> {Texture[img]}]

enter image description here enter image description here

So I have figured out how to overlay the region plot on the surface, but the only color the region appears is black. This is in spite that I specified the RegionPlot to be Orange. How can I change the region plot on the surface to anything but black.

Notes

  • If you have any questions or need clarification please ask.
  • Again this is a quick follow up on my previous question.
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2 Answers 2

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MeshFunctions + MeshShading

Plot3D[g[x, y], {x, 0, 2}, {y, 0, 2},
 MeshFunctions -> {f[#, #2] &}, 
 Mesh -> {{1, 3/2}}, 
 MeshShading -> {White, Orange}, 
 Lighting -> "Neutral"]

enter image description here

BoundaryDiscretizeGraphics

Get a single polygon from img using BoundaryDiscretizeGraphics and use it as the texture:

img2 = BoundaryDiscretizeGraphics[img, MeshCellStyle -> {2 -> Orange, 1 -> Black}, 
   ImagePadding -> 0, PlotRangePadding -> 0];

Plot3D[g[x, y], {x, 0, 2}, {y, 0, 2}, PlotStyle -> Texture[img2], 
 Mesh -> None, Lighting -> "Neutral"]

enter image description here

Plot3D + RegionFunction

Show[Plot3D[g[x, y], {x, 0, 2}, {y, 0, 2}, PlotStyle -> None, Mesh -> None], 
 Plot3D[g[x, y], {x, 0, 2}, {y, 0, 2}, PlotStyle -> Orange, 
  BoundaryStyle -> Black, Mesh -> None, RegionFunction -> (1 < f[#, #2] < 3/2 &)]]

enter image description here

ImageMultiply

Minimal change in OP's code that gives the desired result is to use Texture[ImageMultiply[img, White]] instead of Texture[img]:

Plot3D[g[x, y], {x, 0, 2}, {y, 0, 2}, 
 PlotStyle -> Texture[ImageMultiply[img, White]],
 Mesh -> None, Lighting -> "Neutral"]

enter image description here

Post-process RegionPlot output into 3D polygons:

You can use PlotStyle -> None in Plot3D and lift the 2D region plot surface to 3D replacing coordinate {x,y} with {x,y, g[x,y]}:

Show[Plot3D[g[x, y], {x, 0, 2}, {y, 0, 2}, PlotStyle -> None, Mesh -> None], 
 Graphics3D[Cases[img, GraphicsComplex[a_, b__] :> 
    GraphicsComplex[{##, g[##]} & @@@ a, b]]], Lighting -> "Neutral"]

enter image description here

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  • $\begingroup$ Thank you. This is an interesting approach, but can you do it with no meshes? $\endgroup$
    – AzJ
    Mar 7, 2020 at 1:59
  • $\begingroup$ @AzJ, please see the update. $\endgroup$
    – kglr
    Mar 7, 2020 at 2:05
  • $\begingroup$ @kglr As you will soon pass me in reputation I am happy to see that you are writing answers I would be proud to call my own. :-) $\endgroup$
    – Mr.Wizard
    Mar 9, 2020 at 10:38
  • $\begingroup$ @Mr.Wizard, thank you for the kind words. A lot of my answers are in fact based on what i have learned from yours. Re passing you in reps, that sounds like you intend to keep the target fixed for a while longer (which, I hope, is not the case btw :). $\endgroup$
    – kglr
    Mar 9, 2020 at 20:43
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You may also try Piecewise: Something similar to this for defining Colorfunction of separate regions.

    colfn = Piecewise[{{Red, 3/2 > f[#, #2] > 1}, {White, True}}] &

    Plot3D[g[x, y], {x, 0, 2}, {y, 0, 2}, 
    PlotPoints -> 200, PlotRange -> All, ColorFunction -> colfn, 
    ColorFunctionScaling -> False, Mesh -> None]

Also, check Exclusions in the plot options.

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