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}]}}] 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 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]}}] • According to the ListContourPlot/3D docs, there is a Method option which seems to deal with that problem ("the method to use for interpolation and data reduction") but no examples are available at all in the Options section ! I couldn't make it work, setting it with various def. – SquareOne Oct 29 '15 at 11:19
• Interesting, looks like Szabolcs made a post about that, but got no answer yet. Also, anyone else find that Wolfram Community website has been insanely slow lately? Unusable sometimes. – Jason B. Oct 29 '15 at 11:25