# Plot a revolution surface, with two cross sections to show its shape

I'm having trouble plotting a revolution surface with intersections. What I have done is shown in the figure, with the help of SphericalPlot3D: .

But I can't plot the two cross-sections to make it an enclosed surface. And the final style I like to achieve is like the figure below: i.e., I'd like to have enclosed surface, with different types of meshes if possible, moreover, I wonder if I can plot something without color of the surface, just like the desired style?

Below are the code I used to generate figure 1:

r = -16/(5 π) (θ - 0.5 π)^2 + π;
s1 = SphericalPlot3D[{r},
{θ, 0, Pi}, {ϕ, 0, 3.2 π/2},
PlotStyle -> Directive[White, Opacity],
PlotPoints -> 30,
Boxed -> False,
AxesOrigin -> {0, 0, 0},
TicksStyle -> Directive[FontOpacity -> 0, FontSize -> 0],
AxesStyle -> Directive[Black, 12],
Mesh -> {Range[-π, π, 0.04 π], Range[0, 2 π, 2 π], {}},
ImageSize -> 1000,
PlotRange -> {{-1.5 π, 1.5 π}, {-1.5 π, 1.5 π}, {-1 π, 1 π}}
]


Thanks a lot!

• Try Lighting -> "Neutral" – J. M.'s ennui Mar 29 '16 at 17:00
• Hi @J.M., this does work for the color issue, btw, do you have any idea how to enclosing the surface? Thanks a lot! – larry Mar 29 '16 at 17:58

## 1 Answer

With addition to your SphericalPlot3D you can trnsform the equation and plot the boudary with ParametricPlot3D.

Show[ (*your plot with fixed lighting*)
SphericalPlot3D[{-16/(5 \[Pi]) (\[Theta] - 0.5 \[Pi])^2 + \[Pi]},
{\[Theta], 0, Pi}, {\[Phi], 0, 3.2 \[Pi]/2},
PlotStyle -> Directive[White, Opacity],
PlotPoints -> 30, Boxed -> False, AxesOrigin -> {0, 0, 0},
TicksStyle -> Directive[FontOpacity -> 0, FontSize -> 0],
AxesStyle -> Directive[Black, 12],
Mesh -> {Range[-\[Pi], \[Pi], 0.04 \[Pi]], Range[0, 2 \[Pi], 2 \[Pi]], {}},
ImageSize -> 1000, Lighting -> {{"Ambient", White}}
],
ParametricPlot3D[ (*boundaries*)
Evaluate[ CoordinateTransform[
"Spherical" -> "Cartesian",
{(-16/(5 \[Pi]) (\[Theta] - 0.5 \[Pi])^2 + \[Pi]) rr, \[Theta], #}]],
{\[Theta], 0, Pi}, {rr, 0, 1},
PlotStyle -> White,
MeshFunctions -> {# &, #2 &, #3 &},
Lighting -> {{"Ambient", White}}
] & /@ {-.4 \[Pi], 0}
] • Thanks a lot, this is exactly what I want! – larry Apr 20 '16 at 20:48