Problem with SphericalPlot3D plotting

Question

I want to plot the real part of the SphericalHarmonicY[1,1,θ,φ]. That is, I want to plot

$$ - \frac{1}{2}\sqrt {\frac{3}{{2\pi }}} \cos[\phi ]\sin[\theta ]$$

To do so, I evaluated the following expression:

SphericalPlot3D[-(1/2) Sqrt[3/(2 π)] Cos[φ] Sin[θ], {θ, 0, π}, {φ, 0, 2 π}]

But the result I got doesn't show the negtive part. What is wrong?

spherical

Possible duplicate: http://mathematica.stackexchange.com/questions/16534/problem-with-coloring-spherical-harmonics — Mr.Wizard, Jan 01 '13 at 14:22
@Mr.Wizard, I don't think it's a duplicate. That question is about colouring the plot; this one is about parts of the desired plot not showing up at all. Unless there's some subtle property of Mathematica I'm missing that makes these the same thing, which, given that Mathematica is sufficiently complicated, is a possibility I won't dismiss... — , Jan 01 '13 at 14:36
@Rahul Someone flagged this post to be closed but didn't post that link. I chose not to close the question myself, but I put the link there for others to decide. — Mr.Wizard, Jan 01 '13 at 14:38

score 12 · Accepted Answer · 2013-01-01T15:08:54.847

12

The negative part is plotted with negative radius, so it's at the opposite position of where you expect it -- it's exactly overlapping the positive part. You'll have to plot its absolute value or its square, as Nasser suggests, and indicate its negativeness using a different colour or something. Here's one way to do it:

f[θ_, φ_] := -(1/2) Sqrt[3/(2 π)] Cos[φ] Sin[θ]
pos[x_] := If[x >= 0, x, Null]
SphericalPlot3D[{pos[f[θ, φ]], pos[-f[θ, φ]]},
 {θ, 0, π}, {φ, 0, 2 π}, 
 PlotStyle -> {Lighter@Lighter@Red, Lighter@Lighter@Blue}, 
 Lighting -> "Neutral"]

enter image description here

edited Jan 01 '13 at 15:08

answered Jan 01 '13 at 14:25

2

Is there an easy way to replace the escaped characters with their Unicode equivalents? I searched on meta but only found rcollyer saying they would do this, but not how to do so. – Jan 01 '13 at 14:27
Oh well, I pasted them in from Character Map. Hope I didn't make a mistake somewhere. – Jan 01 '13 at 15:09
you can type $\phi$ within the editor and then cut an paste the rendered version. – chris Jan 01 '13 at 15:56
+1 and thanks for the concern about rendered chars. I hate having to read \[WhateverCharYouWant] – Dr. belisarius Jan 01 '13 at 17:47
@chris: Unless the editor is different from the notebook interface, that doesn't work for me. Whether it's an input or output cell, whenever I copy a θ it pastes as \[Theta] outside Mathematica. – Jan 01 '13 at 18:01
you need to type $\theta$ in the StackExchange page. – chris Jan 01 '13 at 18:18
@chris: Oh, that. Yeah, that makes sense. Silly me. – Jan 01 '13 at 20:14
2

@RahulNarain Have you seen this: How to “Copy as Unicode” from a Notebook? – Jens Jan 01 '13 at 20:16
negative part is plotted with negative radius, that is the key. why didn't I realize it before? Thank you very much! – matheorem Jan 02 '13 at 00:39
Honestly, I use the $\LaTeX$ interpreter on the site itself. I will input what I need in the edit window, and then copy from the display view below it. It seems to be the simplest method. – rcollyer Jan 06 '13 at 07:51

Problem with SphericalPlot3D plotting

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