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color - A better "VisibleSpectrum" function?


Since ColorData["VisibleSpectrum"] is wrong, I would like to have a more accurate function to use.
Can this information be extracted from Mathematica itself?



Answer



Notice:



Simon Woods did just this months ago for an answer I missed:




It seems that it can. By spelunking ChromaticityPlot I found:


Image`ColorOperationsDump`$wavelengths

Image`ColorOperationsDump`tris

These are a list of wavelengths and their corresponding XYZ color values used by this plot command:


ChromaticityPlot["sRGB", Appearance -> {"VisibleSpectrum", "Wavelengths" -> True}]


enter image description here


We can therefore use them to generate a new color function:


ChromaticityPlot;  (* pre-load internals *)

newVisibleSpectrum =
  With[
    {colors =
      {Image`ColorOperationsDump`$wavelengths,
       XYZColor @@@ Image`ColorOperationsDump`tris}\[Transpose]},

    Blend[colors, #] &
  ];

A comparison with the old function:


ArrayPlot[
 {Range[385, 745]},
 ImageSize -> 400,
 AspectRatio -> 0.1,
 ColorFunctionScaling -> False,
 ColorFunction -> #

] & /@
  {"VisibleSpectrum", newVisibleSpectrum} // Column

enter image description here


589nm is now the bright sodium yellow that it should be:


Graphics[{newVisibleSpectrum @ 589, Disk[]}]

enter image description here


If you wish to integrate this into ColorData see:





As requested by J.M. red-green-blue plots for each function:


old = List @@@ Array[ColorData["VisibleSpectrum"], 361, 385];

new = List @@@ ColorConvert[Array[newVisibleSpectrum, 361, 385], "RGB"];

ListLinePlot[Transpose @ #,
   PlotStyle -> {Red, Green, Blue},
   DataRange -> {385, 745}
] & /@ {old, new}


enter image description here


Clipping occurs during conversion to screen RGB; the newVisibleSpectrum function actually produces unclipped XYZColor data. For example projected over gray:


newVSgray = 
  With[{colors = 
     Array[{#, Blend[{newVisibleSpectrum@#, ColorConvert[GrayLevel[.66], "XYZ"]}, 
         0.715]} &, 361, 385]}, Blend[colors, #] &];

ListLinePlot[
 List @@@ ColorConvert[Array[newVSgray, 361, 385], "RGB"] // Transpose, 

 PlotStyle -> {Red, Green, Blue}, DataRange -> {385, 745}, ImageSize -> 400]

enter image description here


Which corresponds to the plot:


ArrayPlot[{Range[385, 745]}, ImageSize -> 400, AspectRatio -> 0.1, 
 ColorFunctionScaling -> False, ColorFunction -> newVSgray, 
 Background -> GrayLevel[0.567]]

enter image description here


cf. "VisibleSpectrum" similarly over gray blended in XYZColor and RGBColor respectively:



enter image description here
enter image description here


Note that neither rendering of this spectrum has the vibrancy of newVisibleSpectrum.


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