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plotting - How to scale values for ColorFunction in SliceContourPlot3D?


Trying to help out in the question, Finite Elements 3D, I came across this behavior of SliceContourPlot3D:


op = -Laplacian[u[x, y, z], {x, y, z}] - 2;
uif = NDSolveValue[{op == 0, DirichletCondition[u[x, y, z] == 0, True}, 
   u, {x, y, z} ∈ Ball[{0, 0, 0}]];

SliceContourPlot3D[
 uif[x, y, z], "CenterPlanes", {x, y, z} ∈ MeshRegion@uif["ElementMesh"], 
 ColorFunction -> "Rainbow"]


Mathematica graphics


The range of colors does not go all the way down to violet/indigo. I expected the range of colors to be something like this:


With[{sel = Positive[uif["Grid"].{0.3, -0.4, -1}]},
 With[{pts = Pick[uif["Grid"], sel]},
  Graphics3D[
   GraphicsComplex[
    pts,
    {Point[Range@Length@pts, 
      VertexColors -> (ColorData["Rainbow"] /@ Rescale[Pick[uif["ValuesOnGrid"], sel]])

      ]}
    ]]
  ]]

Mathematica graphics


Is this a bug in SliceContourPlot3D? (Perhaps it's due to extrapolation from sampling outside the domain?) Is there a way to get it to rescale the colors the way I expected?


I'm using V10.3.0, Mac OSX.



Answer



It seems SliceContourPlot3D makes an initial sample, that is not quite right - i.e. outside of the region. Using


op = -Laplacian[u[x, y, z], {x, y, z}] - 2;

uif = NDSolveValue[{op == 0, 
    DirichletCondition[u[x, y, z] == 0, True]}, 
   u, {x, y, z} \[Element] Ball[{0, 0, 0}], 
   "ExtrapolationHandler" -> {(Indeterminate &),
              "WarningMessage" -> False}];

SliceContourPlot3D[
 uif[x, y, z], "CenterPlanes", {x, y, z} \[Element] 
  MeshRegion@uif["ElementMesh"], ColorFunction -> "Rainbow"]


enter image description here


On a related note, I am wondering if for FEM this ExtrapolationHandler should be the default - what do you think?


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