Plotting Semi-hollow spheres

Question

I wish to create a nice data representation of three nested spherical sections, with a cut away so they can be viewed. As a MWE, something like;

a = SphericalPlot3D[{1}, {θ, 0, Pi}, {ϕ, 0, 4 Pi/2}, 
   PlotStyle -> Directive[Blue, Opacity[0.7], Specularity[White, 20]],
    Mesh -> None, PlotPoints -> 40];

b = SphericalPlot3D[{2}, {θ, 0, Pi}, {ϕ, 0, 3 Pi/2}, 
   PlotStyle -> Directive[Red, Opacity[0.7], Specularity[White, 20]], 
  Mesh -> {{0}, {0}, {0}}, PlotPoints -> 40];

c = SphericalPlot3D[{3}, {θ, 0, Pi}, {ϕ, 0, 3 Pi/2}, 
   PlotStyle -> 
   Directive[Green, Opacity[0.7], Specularity[White, 20]], 
  Mesh -> {{0}, {0}, {0}}, PlotPoints -> 40];

abc = Show[a, b, c, PlotRange -> Automatic]

This gives me the following image, after some rotation for clarity;

Nested spheres

This is kind of the idea, but the problem is that this displays as spherical surfaces at r = 1, r = 2 and r = 3. In reality, there is a thick spherical shell (let's say a red one) for $1 \leq r \leq 2$ and a thick spherical shell (a green one) at $2 \leq r \leq 3$. The spherical core at $r \leq 1$ is solid blue. Is there a nice way to make this image? I was hoping I could somehow modify the $r$ term in the SphericalPlot3D function to do this.

I could also like to add a vertical line running through the sphere centre (z = 0) to make the image clearer. Any ideas?

Thanks

Im not sure how to go about this, as AFAIR Plot3D only takes functions of 2 variables ? I suppose I could rewrite equation of sphere but seems messy.. — DRG, Aug 15 '14 at 13:38
http://rsos.royalsocietypublishing.org/content/1/1.cover-expansion — Dr. belisarius, Sep 24 '14 at 20:14
In light of the post of @belisarius, I wonder if the answers here contributed significantly to your cover image? If so, attribution (which I don't see, but might have missed in the article) would be appropriate. — Mark McClure, Sep 27 '14 at 16:36
If you look below you'll see I thank Eldo for his suggestions, because I used some of his suggestions in the approach I took to fill in regions between the spheres. The data, the concepts and the rendering I had already put together, some (but not all) of which you see in the MWE. I do not think an attribution is appropriate, but thanks most certainly are! — DRG, Sep 28 '14 at 17:51

eldo · Accepted Answer · 2014-08-16T13:50:10.147

12

SetOptions[{SphericalPlot3D, ParametricPlot3D}, Mesh -> None];

fun = {r {0, -Sin[t], Cos[t]}, r {Sin[t], 0, Cos[t]}};

p1 = SphericalPlot3D[{2, 2.5},
   {u, 0, Pi}, {v, 0, 1.5 Pi},
   PlotStyle -> Directive[Green, Opacity[0.7], Specularity[White, 20]]];

p2 = ParametricPlot3D[fun,
   {r, 2, 2.5}, {t, 0, Pi},
   PlotStyle -> Directive[Green, Opacity[0.7], Specularity[White, 20]]];

p3 = SphericalPlot3D[{1.5, 1.99},
   {u, 0, Pi}, {v, 0, 1.5 Pi},
   PlotStyle -> Directive[Red, Opacity[0.7], Specularity[White, 20]]];

p4 = ParametricPlot3D[fun,
   {r, 1.5, 1.99}, {t, 0, Pi},
   PlotStyle -> Directive[Red, Opacity[0.7], Specularity[White, 20]]];

p5 = SphericalPlot3D[{1, 1.48},
   {u, 0, Pi}, {v, 0, 2 Pi},
   PlotStyle -> Directive[Blue, Opacity[0.7], Specularity[White, 20]]];

Show[p1, p2, p3, p4, p5, PlotRange -> All]

enter image description here

Show[p1, p2, p3, p4, p5, PlotRange -> All, ViewPoint -> Front]

enter image description here

Edit

With the new V10 function ClipPlanes you can easily slice your graphics:

Grid[
 {{
   Show[p1, p2, p3, p4, p5, ClipPlanes -> {{-1, 1, 0, 1}}, ImageSize -> 400],
   Show[p1, p2, p3, p4, p5, ClipPlanes -> {{0, 0, -1, 0}}, ImageSize -> 400]
   }}]

enter image description here

edited Aug 16 '14 at 13:50

answered Aug 15 '14 at 14:10

eldo

67,911
5
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@DRG Thanks for acceptance, interesting question :) – eldo Aug 15 '14 at 18:07
Nice use of ClipPlanes! – chris Aug 16 '14 at 13:55
4

This image (or a derivation of it) has made the cover of the first volume of Royal Society Open Science: http://rsos.royalsocietypublishing.org/content/1/1.cover-expansion – dr.blochwave Sep 24 '14 at 12:29
1

@blochwave Wow!, thank you! – eldo Sep 24 '14 at 13:03
Just spotted it! – dr.blochwave Sep 24 '14 at 13:06
Well spotted and cheers again - I used some of the techniques you kind folks outlined here to generate the image from my spheroid data, then just played with the light sources and orientation to make it look pretty as a supplementary addition to the paper! – DRG Sep 26 '14 at 09:58

score 7 · Answer 2 · answered Aug 15 '14 at 13:51

7

regionsandcolors =  Thread[
   {{(x <= 0 || y >= 0) && x^2 + y^2 + z^2 < 1,
     (x <= 0 || y >= 0) &&  1 <= x^2 + y^2 + z^2 < 2,
     (x <= 0 || y >= 0) &&  2 <= x^2 + y^2 + z^2 <= 3}, {Blue, Red, Green}}]; 
plots =  RegionPlot3D[#1, {x, -3, 3}, {y, -3, 3}, {z, -3, 3}, Mesh -> None, 
       PlotStyle -> FaceForm[{Opacity[.9], #2}], 
       PlotRange -> {{-3, 3}, {-3, 3}, {-3, 3}}, PlotPoints -> 100, 
       MaxRecursion -> 10] & @@@ regionsandcolors;
Show[plots]

enter image description here

answered Aug 15 '14 at 13:51

kglr

394,356
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This really had me puzzled. So many simple ways that Mathematica ought to let one do this but doesn't ;-( Great solution with broad application. +1 – Jagra Aug 15 '14 at 13:55
@Jagra, thank you for the upvote. I agree, this seems to fall in the cracks between Mathematica's many xPlot3D functions:) – kglr Aug 15 '14 at 14:11
Very clever - I like this approach too. Thanks so much! – DRG Aug 15 '14 at 16:24

Plotting Semi-hollow spheres

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