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I'm trying to use SphericalPlot3D to create some images of a surface but I get some rough edges on the surface around the boundary. However, after rotating the image slightly these anomalies go away.

I'd like to find a way to create smooth images without rotating the picture manually. There's also a strange spot at my poles which is also problematic but seems more inevitable. I've tried numerous settings and automatically rotating the image but nothing seems to help with these edge distortions.

Here's my code for the top view of this surface:

a = 5;

b = 3;

\[Epsilon] = .75 - .5*Log[a]/Log[10];

freq[n_] = Sqrt[n (n - 1) (n + 2)];

t = \[Pi]/(2*freq[a]);

r1[\[Theta]_, \[Phi]_] = (1 + \[Epsilon]*Sin[t*freq[a]]*
     SphericalHarmonicY[a, b, \[Phi], \[Theta]]);

SphericalPlot3D[
 Re[r1[\[Theta] + \[Pi], \[Phi]]], {\[Phi], -\[Pi]/2, \[Pi]/
   2}, {\[Theta], 0, \[Pi]}, Mesh -> False, 
 ViewPoint -> {0, 0, Infinity}, Boxed -> False, Axes -> False, 
 Lighting -> {{"Spot", {Gray, 
     Specularity[1]}, {{.5, .5, 4}, {.5, .5, 0}}, \[Pi]/
     100}, {"Spot", {Gray, 
     Specularity[1]}, {{.5, .25, 4}, {.5, .25, 0}}, \[Pi]/
     150}, {"Spot", {Gray, 
     Specularity[1]}, {{.25, .5, 4}, {.25, .5, 0}}, \[Pi]/
     150}, {"Directional", Gray, {10, 10, 20}}}, 
 PlotStyle -> Specularity[1], PreserveImageOptions -> False]

Mathematica graphics

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I've added the result I got when ran your code to your question. –  image_doctor Jul 18 '12 at 19:38
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1 Answer

If you do

sp = SphericalPlot3D[...]

AbsoluteOptions@sp

You get

ViewPoint::nlist3: {0,0,[Infinity]} is not a list of three numbers. >>

So, there is a problem with Infinity there. Change it for a big number and the roughness goes away.

enter image description here

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That's great, thanks. I really should have thought to try that myself. –  user1454550 Jul 18 '12 at 20:28
1  
Or use ViewPoint -> Above. –  Brett Champion Jul 18 '12 at 22:46
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