Puzzling behaviour of ListContoutPlot3D

*To*: mathgroup at smc.vnet.net*Subject*: [mg122139] Puzzling behaviour of ListContoutPlot3D*From*: "Tony Harker" <a.harker at ucl.ac.uk>*Date*: Sun, 16 Oct 2011 07:06:47 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

Having struggled to understand why a real-world application was giving me puzzling output from ListContourPlot3D, I boiled the problem down to the following reduced cases. First, a simple spherically symmetrical cases in the interval -1 to 1 in each dimension, with data given either as a grid of values or as a list of {x,y,z,f} values: fn[{x_, y_, z_}] := Sqrt[x^2 + y^2 + z^2] grid = Table[{x, y, z}, {x, -1, 1, .2}, {y, -1, 1, .2}, {z, -1, 1, .2}]; ListContourPlot3D[Map[fn, grid, {3}], Contours -> {.5}] ListContourPlot3D[Map[Flatten[{#, fn[#]}] &, Flatten[grid, 2]], Contours -> {.5}] Both plots give closed surfaces, but although the underlying values are the same the first plot is nearer to spherical than the second. Why the difference? Then I tried a different range of values: fn[{x_, y_, z_}] := Sqrt[(x - 6)^2 + (y - 6)^2 + (z - 6)^2] grid = Table[{x, y, z}, {x, 1, 11}, {y, 1, 11}, {z, 1, 11}]; ListContourPlot3D[Map[fn, grid, {3}], Contours -> {5}] ListContourPlot3D[Map[Flatten[{#, fn[#]}] &, Flatten[grid, 2]], Contours -> {5}] Again, the first plot was nice and spherical. This time, though, the second plot did not even produce a closed surface. In the real problem I was originally tackling, half the surface octants were missing and half were present, but here the amount of surface that shows is not so neatly classifiable. What's happening? In[473]:= $Version Out[473]= "8.0 for Microsoft Windows (64-bit) (February 23, 2011)" Tony A.H. Harker Department of Physics and Astronomy University College London Gower Street London WC1E 6BT Tel: (within UK) 020 7679 3404 (overseas ) +44 20 7679 3404 E: a.harker at ucl.ac.uk