plotting - can the color in MeshStyle be specified by a ColorFunction, such as "SunsetColors" for example. If so, what is the correct syntax?

This is an example given in Help:

Plot3D[Sin[x y], {x, 0, 3}, {y, 0, 3}, MeshStyle -> Gray]

Could this be changed to something like

Plot3D[Sin[x y], {x, 0, 3}, {y, 0, 3}, MeshStyle -> "SunsetColors"]

The above line does not work, but is there a way to modify syntax so that "SunsetColors" can be used?

Answer

Here is the method you posted as an answer yourself, condensed by exploiting repetitious code.

Module[{a, d, t, p, kx, ky, func, cf, plot1, plot2},

 a = 1.42;   d = a Sqrt[3];   t = 2.8;   p = 25;

 func := t Sqrt[3 + 2 Cos[a kx] + 4 Cos[a/2 kx] Cos[d/2 ky]];

 cf[1] = ColorData["SunsetColors", #3] &;
 cf[-1] = ColorData["SunsetColors", 1 - #3] &;

 plot1 = Plot3D[#3 func, {#, -2 Pi / a, 2 Pi / a}, {#2, -2 Pi / a, 2 Pi / a},
    ColorFunction -> cf[#3], BoundaryStyle -> None, Mesh -> None, PlotPoints -> p] &;


 plot2 = ParametricPlot3D[
    Table[{kx, ky, #3 func}, {#2, -2 Pi / a, 2 Pi / a, 1/2}],
    {#, -2 Pi / a, 2 Pi / a}, ColorFunction -> cf[#3], 
    PlotStyle -> Directive[Thickness[0.002]], PlotPoints -> p] &;

 Show[
  plot1[kx, ky, #] & /@ {1, -1},
  plot2[kx, ky, #] & /@ {1, -1},
  plot2[ky, kx, #] & /@ {1, -1},


  PlotRange -> All,
  BoxRatios -> {1, 0.75, 0.75},
  AxesLabel -> 
   Map[Style[#, Large, Bold] &, {Subscript[k, x], Subscript[k, y], Ε[OverVector[k]]}],
  ImageSize -> {800, 800},
  ViewPoint -> {-3, -2, 0}
 ]
]

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