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plotting - Why is my rasterized graphic blank?


Bug introduced in 7.0 or earlier, and persisting through 10.1 or later (OSX 10.10.2)




Consider the following code:


jet[u_?NumericQ] := 
  Blend[{{0, RGBColor[0, 0, 9/16]}, {1/9, Blue}, {23/63, 
      Cyan}, {13/21, Yellow}, {47/63, Orange}, {55/63, Red}, {1, 
      RGBColor[1/2, 0, 0]}}, u] /; 0 <= u <= 1;
(* jet function get from http://stackoverflow.com/a/9321152/1363677*)
caxis[x_, {min_, max_}] := 
  If[x < min, jet[0], If[x > max, jet[1], jet[(x - min)/(max - min)]]];

data1 = Table[

   Sinc[x*y] + RandomReal[{0., 0.2}], {x, -2 Pi, 2 Pi, 0.05}, {y, -2 Pi, 2 Pi, 0.05}];
data2 = Table[
   Sinc[x*y] + RandomReal[{0., 0.2}], {x, -2 Pi, 2 Pi, 0.02}, {y, -2 Pi, 2 Pi, 0.02}];

Row[{Graphics[Raster[data1, ColorFunction -> (caxis[#, {-0.5, 2}] &)],
    ImageSize -> 200],
  Graphics[Raster[data2, ColorFunction -> (caxis[#, {-0.5, 2}] &)], 
   ImageSize -> 200],
  Graphics[Raster[data2, ColorFunction -> "BlueGreenYellow"], 
   ImageSize -> 200]}]


It gives the output:


enter image description here


Why is the second plot blank?


If the dynamic updating is turned off, all of the three are blank.


enter image description here


Why does Mathematica behave like this? I'm using OSX 10.8.4 on a Macbook Air with 1.7 GHz Intel Core i5 and 4GB memory.



Answer



Label this a most bizarre bug -- I can reproduce the problem (v9.0.0.0) -- the fix, change all those integer fractions in Blend to decimals..


This fails:



jet[u_?NumericQ] :=  Blend[{{0, RGBColor[0, 0, 1/9]}, {1, Red}}, u] /; 0 <= u <= 1

This works


jet[u_?NumericQ] := Blend[{{0, RGBColor[0, 0, 0.11111111]}, {1, Red}}, u] /; 0 <= u <= 1

Edit: another curiosity.. this should be the same (I think..) normalising the values before passing to the color function.


Graphics[Raster[data1, Automatic, {-.05, 2}, 
         ColorFunction -> (caxis[#, {0, 1}] &)], ImageSize -> 200]

Although it works, the colors are substantially different.



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