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This is the code I used Edit: This is the full code to create this image

R[r_, s_] := {r, s, 0};
S[r_, s_] := {2 r/(r^2 + s^2 + 1), 2 s/(r^2 + s^2 + 1), (r^2 + s^2 - 1)/(r^2 + s^2 + 1)};
f[t_] = Tan[(Pi/2) * t];



Show[ParametricPlot3D[R[r, s], {r, -3, 3}, {s, -3, 3}, ImageSize -> 600, 
  Epilog -> Inset[Style[" 710178 ", FontSize -> 84, Red, Opacity[0.1]]]],
 ParametricPlot3D[S[f[r], f[s]], {r, -3, 3}, {s, -3, 3},PlotStyle -> Transparent]]

And this is my output enter image description here

The reason I'm trying to make it transparent is because I have to plot curves on the sphere and currently when I do plot, I can't see the curves.

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    $\begingroup$ Welcome to MSE. Please provide all of the code to reproduce the image. The definitions for R, S, and f are missing. $\endgroup$
    – Rohit Namjoshi
    Commented Sep 13, 2021 at 1:59
  • $\begingroup$ My apologies, I was unaware that the full code was required, however I have added it. Just for further information, I tried to plot the sphere S first, instead of the plane R and that still made no difference $\endgroup$
    – Nok
    Commented Sep 13, 2021 at 8:40
  • $\begingroup$ How about Show[ParametricPlot3D[R[r, s], {r, -3, 3}, {s, -3, 3}, ImageSize -> 600, PlotStyle -> Opacity[0.2], Epilog -> Inset[Style[" 710178 ", FontSize -> 84, Red, Opacity[0.1]]]], ParametricPlot3D[S[f[r], f[s]], {r, -3, 3}, {s, -3, 3}, PlotStyle -> Opacity[0.1]]] $\endgroup$
    – chris
    Commented Sep 13, 2021 at 9:03
  • $\begingroup$ The circle just becomes a light orange when I change opacity. I also tried PlotStyle-> Directive[Orange, Opacity[0.1]], but that didn't do anything $\endgroup$
    – Nok
    Commented Sep 13, 2021 at 9:16
  • $\begingroup$ try if PlotStyle -> FaceForm[] gives what you need. $\endgroup$
    – kglr
    Commented Sep 13, 2021 at 16:10

1 Answer 1

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I think this is a version problem. In MMA 12.3 I get:

Show[ParametricPlot3D[R[r, s], {r, -3, 3}, {s, -3, 3}, 
  ImageSize -> 600, 
  Epilog -> 
   Inset[Style[" 710178 ", FontSize -> 84, Red, Opacity[0.1]]]], 
 ParametricPlot3D[S[f[r], f[s]], {r, -3, 3}, {s, -3, 3}, 
  PlotStyle -> Transparent]]

enter image description here

Update

To make the plane translucent, you could write:

Show[ParametricPlot3D[R[r, s], {r, -3, 3}, {s, -3, 3}, 
  ImageSize -> 600, PlotStyle -> Opacity[0.3], 
  Epilog -> 
   Inset[Style[" 710178 ", FontSize -> 84, Red, Opacity[0.1]]]], 
 ParametricPlot3D[S[f[r], f[s]], {r, -3, 3}, {s, -3, 3}, 
  PlotStyle -> Transparent]]

enter image description here

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  • $\begingroup$ Output in Mathematica 13.0 appears to be the same as that from 12.3 you show. $\endgroup$
    – murray
    Commented Dec 24, 2021 at 17:25

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