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I have a problem with limitation in a 3DPlot. In the following, you can see some constraints where should be satisfied for eta and mu. By RegionPlot, one can see an area that is not the same as the area appears in the 3DPlot in z=0. Is it a meaningful expectation?!

-0.1 + 2420.57 (0.000504756 \[Eta] - 0.0000756665 \[Mu])<0

-3.27589 + \[Mu]<0

0.000504756 \[Eta] - 0.0000756665 \[Mu]>0

0.0551428 \[Eta] + 0.0101754 \[Mu]>0

Abs[(-56.5585 \[Eta]^2 Sqrt[\[Mu]] - 
7.66021 \[Eta]^(3/2) Sqrt[33.354 \[Eta] - 5. \[Mu]] Sqrt[\[Mu]] - 
52.0236 \[Eta] \[Mu]^(3/2) + 1.33815 \[Mu]^(5/2) + 
1. \[Eta] Sqrt[27.0963 \[Eta] + 5. \[Mu]])/(\[Eta] Sqrt[
27.0963 \[Eta] + 5. \[Mu]])] < 1

The range of each parameter is:

{\[Mu], 0, 0.113}, {\[Eta], 0, 0.09}

The region from RegionPlot

The region from 3DPlot

The original code to generate the first figure is:

RegionPlot[{ -0.1 + 2420.57 (0.000504756 \[Eta] - 0.0000756665 \[Mu])<0 && 
-3.27589 + \[Mu]<0 && 0.000504756 \[Eta] - 0.0000756665 \[Mu]>0 && 0.0551428 
\[Eta] + 0.0101754 \[Mu]>0 && 
Abs[(-56.5585 \[Eta]^2 Sqrt[\[Mu]] - 
7.66021 \[Eta]^(3/2) Sqrt[33.354 \[Eta] - 5. \[Mu]] Sqrt[\[Mu]] - 
52.0236 \[Eta] \[Mu]^(3/2) + 1.33815 \[Mu]^(5/2) + 
1. \[Eta] Sqrt[27.0963 \[Eta] + 5. \[Mu]])/(\[Eta] Sqrt[
27.0963 \[Eta] + 5. \[Mu]])] < 1}, {\[Mu], 0, 0.113}, {\[Eta], 0, 0.09}, 
BoundaryStyle -> {Green}, PlotStyle -> {None}, 
FrameLabel -> Automatic]

and the second:

Plot3D[0, {\[Mu], 0, 0.113}, {\[Eta], 0, 0.09}, 
PlotLegends -> {0, "PNTC", "NTC"}, AxesLabel -> Automatic, 
RegionFunction -> 
Function[{\[Eta], \[Mu]}, 
 -0.1 + 2420.57 (0.000504756 
\[Eta] - 0.0000756665 \[Mu])<0 && 
-3.27589 + \[Mu]<0 && 0.000504756 \[Eta] - 0.0000756665 \[Mu]>0 && 0.0551428 
\[Eta] + 0.0101754 \[Mu]>0 && 
Abs[(-56.5585 \[Eta]^2 Sqrt[\[Mu]] - 
7.66021 \[Eta]^(3/2) Sqrt[33.354 \[Eta] - 5. \[Mu]] Sqrt[\[Mu]] - 
52.0236 \[Eta] \[Mu]^(3/2) + 1.33815 \[Mu]^(5/2) + 
1. \[Eta] Sqrt[27.0963 \[Eta] + 5. \[Mu]])/(\[Eta] Sqrt[
27.0963 \[Eta] + 5. \[Mu]])] < 1], PlotStyle -> Red]

Thanks for your useful answers.

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  • $\begingroup$ please show the full code used to generate those figures. There is no 3DPlot so its not obvious what that means.. $\endgroup$
    – george2079
    Mar 9 '18 at 17:13
  • $\begingroup$ You need to switch the arg order in the region function: Function[{\[Mu], \[Eta]} $\endgroup$
    – george2079
    Mar 9 '18 at 17:43
  • $\begingroup$ I this questions somehow related to your earlier post? If yes, you should merge them maybe (e.g. delete one of them). $\endgroup$
    – gwr
    Mar 9 '18 at 19:38
  • $\begingroup$ Maybe. But I think there is also another useful thing here $\endgroup$ Mar 9 '18 at 19:59
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for sake of closing this out here's what you get with the correct ordering of the region function arguments.

Plot3D[0, {\[Mu], 0, 0.113}, {\[Eta], 0, 0.09}, 
 PlotLegends -> {0, "PNTC", "NTC"}, AxesLabel -> Automatic, 
 RegionFunction -> 
  Function[{\[Mu], \[Eta]}, -0.1 + 
      2420.57 (0.000504756 \[Eta] - 0.0000756665 \[Mu]) < 
     0 && -3.27589 + \[Mu] < 0 && 
    0.000504756 \[Eta] - 0.0000756665 \[Mu] > 0 && 
    0.0551428 \[Eta] + 0.0101754 \[Mu] > 0 && 
    Abs[(-56.5585 \[Eta]^2 Sqrt[\[Mu]] - 
         7.66021 \[Eta]^(3/2) Sqrt[
           33.354 \[Eta] - 5. \[Mu]] Sqrt[\[Mu]] - 
         52.0236 \[Eta] \[Mu]^(3/2) + 1.33815 \[Mu]^(5/2) + 
         1. \[Eta] Sqrt[27.0963 \[Eta] + 5. \[Mu]])/(\[Eta] Sqrt[
          27.0963 \[Eta] + 5. \[Mu]])] < 1], PlotStyle -> Red]

enter image description here

note that Function doesn't know or care that you used the same symbol names \[Eta], \[Mu] for the Plot3D iterators, so by transposing you transpose the region.

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