Custom MeshFunctions in SphericalPlot3D

Questions
1

Hello,

Whenever I try to modify the MeshFunctions which SphericalPlot3D uses, Mathematica plots an additional mesh line in the xz-plane. For example

x := Sin[\[Phi]]*Cos[\[Theta]]
y := Sin[\[Phi]]*Sin[\[Theta]]
z := Cos[\[Phi]]
SphericalPlot3D[
5*x^2 + 10*y^2 + 3*z^2, {\[Phi], 0, 2 \[Pi]}, {\[Theta], 0, \[Pi]},
ColorFunction -> (ColorData["TemperatureMap"][#6] &),
MeshFunctions -> {#6 &},
Mesh -> {8}
]

results in

Minimalbeispiel.bmp (375 KB)

Does anyone know what’s causing this behaviour and how to stop it? I’m using Mathematica 10.0.1.0 Student Edition.

Thank you!

2

What you are seeing is the boundary of the parametric surface, at theta=0 and theta=Pi. To get rid of the boundary use BoundaryStyle:

With[{x = Sin[\[Phi]]*Cos[\[Theta]], y = Sin[\[Phi]]*Sin[\[Theta]], 
  z = Cos[\[Phi]]},
 SphericalPlot3D[
  5*x^2 + 10*y^2 + 3*z^2, {\[Phi], 0, 2 \[Pi]}, {\[Theta], 0, \[Pi]},
   ColorFunction -> (ColorData["TemperatureMap"][#6] &), 
  MeshFunctions -> {#6 &}, Mesh -> {8}, BoundaryStyle -> None]]
3

Thank you very much! This completely resolves the issue.