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I would like to use the thermometer color gradient in Graphics3D. Taking an example, I have the following:

Graphics3D[{Hue[1], 
Polygon[{{1/2, 0, 0}, {1, 0, 0}, {5/4, Sqrt[3]/4, 0}, {1, Sqrt[3]/2,
  0}, {1/2, Sqrt[3]/2, 0}, {1/4, Sqrt[3]/4, 0}}]}]

Mathematica graphics

which gives a red hexagon as desired. However, I would like to use the thermometer colors, so that lower numbers correspond to the bluer spectrum of the color gradient. However, when I attempt to copy the code given here: https://reference.wolfram.com/language/ref/ColorData.html using

Graphics3D[{ColorFunction -> (ColorData["TemperatureMap"][1] &), 
Polygon[{{1/2, 0, 0}, {1, 0, 0}, {5/4, Sqrt[3]/4, 0}, {1, Sqrt[3]/2,
  0}, {1/2, Sqrt[3]/2, 0}, {1/4, Sqrt[3]/4, 0}}]}]

it outputs a colorless hexagon. How should I fix this, provided I want to plot data with colors accordingly on the thermometer gradient given values in the interval [-1,1]?

Thanks!

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  • $\begingroup$ ColorFunction isn't an option of Graphics3D. You could use VertexColors. $\endgroup$ – Sjoerd C. de Vries Sep 16 '15 at 14:49
  • $\begingroup$ BTW What do you mean by "lower numbers correspond to the bluer spectrum of the color gradient"? $\endgroup$ – Sjoerd C. de Vries Sep 16 '15 at 14:57
  • $\begingroup$ As in, the temperature gradient ranges from blue to red. If I assign a higher number to a hexagon, I would like it to color the hexagon red.If I assign a lower number to the hexagon, then I would like it to be a bluer color. This is not the case for hue, which takes on a wide range of colors $\endgroup$ – user238194 Sep 16 '15 at 15:05
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Something like this?

pol = {{1/2, 0, 0}, {1, 0, 0}, {5/4, Sqrt[3]/4, 0}, {1, Sqrt[3]/2, 0}, 
       {1/2, Sqrt[3]/2, 0}, {1/4, Sqrt[3]/4, 0}}; 
Graphics3D[{
   Polygon[ pol, 
           VertexColors -> (ColorData["TemperatureMap"] /@ Rescale[pol[[All, 1]]])
   ]}
]

Mathematica graphics

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  • $\begingroup$ Not exactly. This hexagon is one unit cell in my lattice. So say I assign a number .5 to one hexagon. Then I would like it to correspond to a specific color on the temperature gradient spectrum. Then on the next hexagon in the lattice, it might have a different number, say -.5. Then its color should be blue. Sorry, if I was not clear. So basically, I want, for each hexagon, to have a solid color representing its value. $\endgroup$ – user238194 Sep 16 '15 at 15:04
  • 1
    $\begingroup$ Well, in that case instead of the Hue[1] you used in your first example simply use ColorData["TemperatureMap"][Rescale[val, {valMin, valMax}]], with val the value you want to represent and valMin and valMax the minimum and maximum values present in your data set. $\endgroup$ – Sjoerd C. de Vries Sep 16 '15 at 15:10
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zmin = -1;
zmax = 1;

Manipulate[
 Row[{
   Graphics3D[{
     ColorData["TemperatureMap"][
      (z - zmin)/(zmax - zmin)],
     Polygon[{
       {1/2, 0, z},
       {1, 0, z},
       {5/4, Sqrt[3]/4, z},
       {1, Sqrt[3]/2, z},
       {1/2, Sqrt[3]/2, z},
       {1/4, Sqrt[3]/4, z}}]},
    PlotRange -> {zmin, zmax},
    ImageSize -> 300,
    BoxRatios -> {1, 1, 1}],
   BarLegend[{"TemperatureMap", {zmin, zmax}}]}],
 {{z, (zmax+zmin)/2}, zmin, zmax, .1, Appearance -> "Labeled"}]

enter image description here

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