[Matplotlib-users] question on spherical coordinate plots

[Romain M. <rom...@ce...>]

Dear experts,

I am trying to plot spherical harmonics with matplotlib and I have some 
troubles. I am starting from the example 
http://matplotlib.org/examples/mplot3d/surface3d_demo2.html where I 
change the factor 10 in a function of r=f(theta,phi) (or r=f(u,v) as 
they are named in the example). I observe very strange behaviours:

(1) (x,y,z) = (r cos(phi) sin(theta) , r sin(phi) sin(theta) , r 
cos(theta)). But np.outer(a,b) is not commutative while the 
multiplication is. So how to choose the order in the np.outer() product? 
In fact, different order gives very different results.

(2) It's seem impossible to reproduce the well known Ylm(theta,phi) 
plots. Using for example this document 
http://www.cs.dartmouth.edu/~wjarosz/publications/dissertation/appendixB.pdf 
:





I don't know if I am doing something wrong or so, but I don't understand 
... My full code is bellow.

Thanks a lot in advance !
Cheers,
Romain


PS:

import math
import numpy as np
import pylab as p
from mpl_toolkits.mplot3d import Axes3D

def f(theta,phi):
     return np.sin(phi)*np.cos(phi)*np.sin(theta)**2

fig = p.figure()
ax = fig.add_subplot(111, projection='3d')

theta = np.linspace(0,   np.pi, 500)
phi   = np.linspace(0, 2*np.pi, 500)

r = f(theta,phi)
x = r**2 * np.outer( np.cos(phi) , np.sin(theta) )
y = r**2 * np.outer( np.sin(phi) , np.sin(theta) )
z = r**2 * np.outer(np.ones(phi.shape), np.cos(theta))

#x = r**2 * np.outer( np.sin(theta) , np.cos(phi) )
#y = r**2 * np.outer( np.sin(theta) , np.sin(phi) )
#z = r**2 * np.outer( np.cos(theta), np.ones(theta.shape) )

ax.plot_surface(x,y,z)
ax.set_xlabel("X")
ax.set_ylabel("Y")
ax.set_zlabel("Z")

p.show()


-- 
=========================================================
	Romain Madar

Laboratoire de Physique Corpusculaire de Clermont-Ferrand
   Campus Universitaire des Cézeaux
   4 avenue Blaise Pascal
   TSA 60026, CS 60026
   63178 Aubière cedex, FRANCE

Email: rom...@ce...
Tel. : +33 (0)4 73 40 71 57
Off. : 8204-8205
=========================================================