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I've had the same effect in Mathematica 9 and 10.

I'm trying to color a 3D Plot with another function, let's call it colorFun ( it should highlight the areas where the colorFun is above a certain threshold), but ColorFunction seems to use the wrong coordinates.

Horribly colored minimal example

colorFun := Function[{x, y},If[x < y, Red, Blue]]
Plot3D[Evaluate[x^2+y^2],{x,0,1},{y,0,2},ColorFunction->colorFun]

Holy cow it's ugly!

Note that x and y have different intervals plotted, so the divide should not be through the middle. Similar things happen if you change the colorFun to something like y<0.5 . It seems that the ColorFunction is not using the same coordinates as the function, but rather a kind of normalized version, always going from 0 to 1.

Is this a bug, or is Mathematica beating my ability to understand computers again?

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  • 1
    $\begingroup$ You actually essentially answered your own questions: the values passed to ColorFunction are in fact scaled to [0,1] by default. To avoid that, use ColorFunctionScaling -> False. $\endgroup$
    – MarcoB
    Jul 15, 2015 at 14:57
  • $\begingroup$ Possible duplicates: (6741), (6986), (14758) $\endgroup$
    – Mr.Wizard
    Jul 15, 2015 at 15:05
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    $\begingroup$ Please pardon the reopen but I was just about to post an answer when it closed. If you would still like to close this as a duplicate let me know. Either way I hope my answer is useful to you. $\endgroup$
    – Mr.Wizard
    Jul 15, 2015 at 15:20
  • $\begingroup$ I'm fine with keeping it open, if others agree to my impression that your answer help show a new facet of the problem, as compared to the old answers. $\endgroup$
    – GeckoGeorge
    Jul 15, 2015 at 15:36

2 Answers 2

Reset to default
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You'll get a much crisper output if you use Mesh functionality instead:

Plot3D[x^2 + y^2, {x, 0, 1}, {y, 0, 2},
  MeshFunctions -> {#/#2 &},
  Mesh -> {{1}}, 
  MeshShading -> {Red, Blue}
]

enter image description here

Or with additional grid lines:

Plot3D[x^2 + y^2, {x, 0, 1}, {y, 0, 2},
  MeshFunctions -> {#/#2 &, # &, #2 &}, 
  Mesh -> {{1}, 12, 12},
  MeshShading -> {{{Red, Blue}}}
]

enter image description here

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  • $\begingroup$ It does look a lot better. Thanks for teaching cool new stuff! $\endgroup$
    – GeckoGeorge
    Jul 15, 2015 at 15:34
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And immediately after submitting, I find the answer here:

Using ColorFunctionScaling->False

Plot3D[Evaluate[x^2+y^2],{x,0,1},{y,0,2},ColorFunction->colorFun,ColorFunctionScaling->False]

Gives the correct coloring. Sorry to bother you all, and thanks for listening!

Decided to keep the question and answer it myself for other who might do the same searches I did, since finding the answer was kinda random for me.

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