How can I include hexagonal meshing on a Plot3D such as this?
Plot3D[Sin[x], {z, -3, 3}, {x, -4 \[Pi], 4 \[Pi]}]
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$\begingroup$ You may be able to use the answers from here: mathematica.stackexchange.com/q/39879/9490 $\endgroup$– Jason B.Commented Jan 23, 2018 at 18:37
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$\begingroup$ I saw that, but I couldn't use that because that was used for graphic plot 3d and my plot is not graphic plot $\endgroup$– someCommented Jan 23, 2018 at 18:49
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$\begingroup$ I think its fair to say there is not a straightforward way to do this for a general function. $\endgroup$– george2079Commented Jan 23, 2018 at 20:48
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$\begingroup$ This is a step in the right direction: pastebin.com/raw/NtSmn50x , based off the answer here: mathematica.stackexchange.com/q/77312/9490 $\endgroup$– Jason B.Commented Jan 23, 2018 at 20:59
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1 Answer
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Using rm-rf's hextile yet again
hexTile[n_, m_] := With[{hex = Polygon[Table[{Cos[2 Pi k/6] + #, Sin[2 Pi k/6] + #2},
{k, 6}]] &}, Table[hex[3 i + 3 ((-1)^j + 1)/4, Sqrt[3]/2 j], {i, n}, {j, m}] /.
{x_?NumericQ, y_?NumericQ} :> 2 π {x/(3 m), 2 y/(n Sqrt[3])}
ClearAll[plot3DwHexMesh]
plot3DwHexMesh[f_, n_: 20, m_: 20, s_: Yellow, o : OptionsPattern[]] :=
Graphics3D[hexTile[n, m] /. Polygon[l_] :>
{s, Polygon[l], Polygon[{Pi/5, 0} + {-1, 1} # & /@ l]} /.
Polygon[l_List] :> Polygon[{#, #2, f[#, #2]} & @@@ l], o,
Axes -> False, PlotRange -> All, Lighting -> "Neutral"]
Examples:
plot3DwHexMesh[Sin[#] &]
plot3DwHexMesh[Sin[# + #2] &, 20, 20,
Directive[Orange, Opacity[0.8], Specularity[White, 30]], Boxed -> False]
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$\begingroup$ The problem with this, and every variant I tried using
hexTile, is that I couldn't find a way to respect the originalPlotRange.plot3DwHexMeshshould, ultimately, take thexandyrange into consideration, and show theAxeswith the correct values. $\endgroup$– Jason B.Commented Jan 23, 2018 at 21:32 -
$\begingroup$ @JasonB, right; I was puzzling over exactly those challenges. Not easy. Hence
Falseas the default option value forAxes:) $\endgroup$– kglrCommented Jan 23, 2018 at 21:40