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plotting - ListContourPlot and ListContourPlot3D use better interpolation for arrays of values than for lists of tuples (i.e. {{x,y,z,f[x,y,z]}..}


From reading the documentation, it seems that ListContourPlot3D should work equally well on an array versus a list of tuples,


?ListContourPlot3D



ListContourPlot3D[array] generates a contour plot from a three-dimensional array of values. ListContourPlot3D[{{$x_1$,$y_1$,$z_1$,$f_1$},{$x_2$,$y_2$,$z_2$,$f_2$},$\ldots$}] generates a contour plot from values defined at specified points in three-dimensional space.



But below the plot on the left uses the tuples version while the plot on the right uses the array,


dta = Table[{x, y, z, x^3 + y^2 - z^2}, {z, -2, 2, .1}, {y, -2, 
    2, .1}, {x, -2, 2, .1}];
Grid[{{ListContourPlot3D[Flatten[dta, 2], Contours -> {0}, 
    Mesh -> None],
   ListContourPlot3D[dta[[All, All, All, -1]], Contours -> {0}, 
    Mesh -> None, DataRange -> {#, #, #} &@{-2, 2}]}}]


enter image description here


The interpolation used for the array version is clearly superior. Why is this? InterpolationOrder is not an option for ListContourPlot3D (even an undocumented one). Applying the option MaxPlotPoints -> 120 produces this monstrosity


enter image description here


This problem seems to affect the output of ListContourPlot a little bit differently. Without using InterpolationOrder, they give the same output (top row below), but if I do use InterpolationOrder, it only has an effect on the array, not the tuples.


dta = Table[{x, y, x^3 + y^2}, {y, -2, 2, .2}, {x, -2, 2, .2}];
Grid[{{ListContourPlot[Flatten[dta, 1], Contours -> 20],
   ListContourPlot[dta[[All, All, -1]], Contours -> 20]},
  {ListContourPlot[Flatten[dta, 1], Contours -> 20, 
    InterpolationOrder -> 3],
   ListContourPlot[dta[[All, All, -1]], Contours -> 20, 

    InterpolationOrder -> 3]}}]

enter image description here




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