Your theta and phi were essentially 1D rather than 2D, so it didn't allow
for 2 degrees of freedom. And you don't need np.outer() for this:
theta = np.linspace(0, np.pi, 500)[:, None]
phi = np.linspace(0, 2*np.pi, 500)[None, :]
r = f(theta, phi)
x = r**2 * np.cos(phi) * np.sin(theta)
y = r**2 * np.sin(phi) * np.sin(theta)
z = r**2 * np.cos(theta)
The use of np.outer() in the original example acted a bit like a creating a
grid of u/v values in a 2D grid. However, your formulation required
computing a 2D grid of radius values in order to work correctly.
Cheers!
Ben Root
On Fri, Jul 10, 2015 at 7:54 AM, Romain Madar <romain.ma...@cern.ch> wrote:
> 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: romain.ma...@cern.ch
> Tel. : +33 (0)4 73 40 71 57
> Off. : 8204-8205
> =========================================================
>
>
>
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