Skip to main content

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?


Comments

Post a Comment

Popular posts from this blog

front end - keyboard shortcut to invoke Insert new matrix

I frequently need to type in some matrices, and the menu command Insert > Table/Matrix > New... allows matrices with lines drawn between columns and rows, which is very helpful. I would like to make a keyboard shortcut for it, but cannot find the relevant frontend token command (4209405) for it. Since the FullForm[] and InputForm[] of matrices with lines drawn between rows and columns is the same as those without lines, it's hard to do this via 3rd party system-wide text expanders (e.g. autohotkey or atext on mac). How does one assign a keyboard shortcut for the menu item Insert > Table/Matrix > New... , preferably using only mathematica? Thanks! Answer In the MenuSetup.tr (for linux located in the $InstallationDirectory/SystemFiles/FrontEnd/TextResources/X/ directory), I changed the line MenuItem["&New...", "CreateGridBoxDialog"] to read MenuItem["&New...", "CreateGridBoxDialog", MenuKey["m", Modifiers-...
Post a Comment
Read more

How to thread a list

I have data in format data = {{a1, a2}, {b1, b2}, {c1, c2}, {d1, d2}} Tableform: I want to thread it to : tdata = {{{a1, b1}, {a2, b2}}, {{a1, c1}, {a2, c2}}, {{a1, d1}, {a2, d2}}} Tableform: And I would like to do better then pseudofunction[n_] := Transpose[{data2[[1]], data2[[n]]}]; SetAttributes[pseudofunction, Listable]; Range[2, 4] // pseudofunction Here is my benchmark data, where data3 is normal sample of real data. data3 = Drop[ExcelWorkBook[[Column1 ;; Column4]], None, 1]; data2 = {a #, b #, c #, d #} & /@ Range[1, 10^5]; data = RandomReal[{0, 1}, {10^6, 4}]; Here is my benchmark code kptnw[list_] := Transpose[{Table[First@#, {Length@# - 1}], Rest@#}, {3, 1, 2}] &@list kptnw2[list_] := Transpose[{ConstantArray[First@#, Length@# - 1], Rest@#}, {3, 1, 2}] &@list OleksandrR[list_] := Flatten[Outer[List, List@First[list], Rest[list], 1], {{2}, {1, 4}}] paradox2[list_] := Partition[Riffle[list[[1]], #], 2] & /@ Drop[list, 1] RM[list_] := FoldList[Transpose[{First@li...
Post a Comment
Read more

mathematical optimization - Minimizing using indices, error: Part::pkspec1: The expression cannot be used as a part specification

I want to use Minimize where the variables to minimize are indices pointing into an array. Here a MWE that hopefully shows what my problem is. vars = u@# & /@ Range[3]; cons = Flatten@ { Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; Minimize[{Total@((vec1[[#]] - vec2[[u[#]]])^2 & /@ Range[1, 3]), cons}, vars, Integers] The error I get: Part::pkspec1: The expression u[1] cannot be used as a part specification. >> Answer Ok, it seems that one can get around Mathematica trying to evaluate vec2[[u[1]]] too early by using the function Indexed[vec2,u[1]] . The working MWE would then look like the following: vars = u@# & /@ Range[3]; cons = Flatten@{ Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; NMinimize[ {Total@((vec1[[#]] - Indexed[vec2, u[#]])^2 & /@ R...
Post a Comment
Read more