Plotting spherical data

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I do not think that you can get all of that directly with sage.

A viable option would be to call mplot3d (plot_surface) from matplotlib, which is easily done in Sage. This way you can get point 1,2,4 even if the axis are displayed in a different way, and I think also point 3, but i am not sure about that. All the references are here.

If you need some kind of interpolation, I suggest you employ scipy.interpolate module. You can get many different types of N dimensional interpolation.

I don't think that you can interactively rotate with mplot3d. I'm not an expert anyway. I would say that mayavi2 experimental package fits your bill anyway. I use mayavi2 (outside of Sage) to produce antenna patterns of high quality and works beautifully.

I guess you should proceed as follows:

1) Install mayavi2 package following the instruction at this page http://www.sagemath.org/doc/numerical...

2) You invoke mayavi2 with something like this (http://www.sagemath.org/doc/numerical...)

import numpy
from mayavi.tools import imv
x=numpy.arange(-8,8,.2)
def f(x,y):
    r=numpy.sqrt(x**2+y**2)+.01
    return numpy.sin(r)/r
imv.surf(x,x,f)

3) The command you want is mesh(). Read the documentation and the examples here and here

hope it helps.

Giovanni

You could do the spherical transformation yourself to do a spherical list plot. See http://sagenb.org/home/pub/3616/ for an example, using the radius, azimuth, inclination convention for spherical coordinates.