Plot a function on a 2D surface

ColorFunction

Consider:

Plot3D[g[x, y], {x, 0, 2}, {y, 0, 2}, 
 ColorFunction -> 
  Function[{x, y, z}, ColorData["RustTones"][f[x, y]/4.5]], 
 ColorFunctionScaling -> False]

enter image description here

Replace "RustTones" with your favorite value from ColorData["Gradients"] (I do not know how to mimic the original DensityPlot color scheme).

The DensityPlot output + PlotStyle

Alternatively, use the original DensityPlot as a texture:

img = DensityPlot[f[x, y], {x, 0, 2}, {y, 0, 2}, Frame -> False, 
  PlotRangePadding -> None]
Plot3D[g[x, y], {x, 0, 2}, {y, 0, 2}, PlotStyle -> Texture[img]]

enter image description here


You can also use a custom color function using your function f and the default color function for DensityPlot (which is "M10DefaultDensityGradient") as follows:

minmax = Through[{NMinValue, NMaxValue}[{f[x, y], 0 <= x <= 2 && 0 <= y <= 2}, {x, y}]];

cF1 = ColorData["M10DefaultDensityGradient"][Rescale[f[#, #2], minmax]] &;

Plot3D[g[x, y], {x, 0, 2}, {y, 0, 2}, ColorFunction -> cF1,
 ColorFunctionScaling -> False, Lighting -> "Ambient", ViewPoint -> {1.5, -.5, 3}]

enter image description here

Use a different gradient color scheme, say "CMYKColors", instead of "M10DefaultDensityGradient" to get:

enter image description here

Tags:

Plotting

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