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I have a surface in 3D space which is defined by equation in ContourPlot3D. For simplicity let me use x + y == z surface (in reality I have a transcendental equation). I also have function of the variables (x,y,z) which behaviour I need to study on the surface. I want to show function's values by color, but it's fails even in such simple example:

f[x_, y_, z_] := z^2
ContourPlot3D[x + y == z, {x, -2, 2}, {y, -2, 2}, {z, -2, 2},ColorFunction -> Function[{x, y, z}, Hue[f[x, y, z]]],AxesLabel -> {"x", "y", "z"}] 

enter image description here

Here levels z and -z must be the same color because I use the even function z^2. What did I missed? Thanks!

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