# How to make Sphere Transparent using ParametricPlot3D?

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

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.

• Welcome to MSE. Please provide all of the code to reproduce the image. The definitions for R, S, and f are missing. Commented Sep 13, 2021 at 1:59
• 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
– Nok
Commented Sep 13, 2021 at 8:40
• 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]]]  Commented Sep 13, 2021 at 9:03
• 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
– Nok
Commented Sep 13, 2021 at 9:16
• try if PlotStyle -> FaceForm[] gives what you need.
– kglr
Commented Sep 13, 2021 at 16:10

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]]


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]]


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