Colors on a sphere to depict values

Question

I have a data set such that for discrete values of theta and phi, I have some value. I want to represent this on a sphere such that at the point on the sphere given by the polar angle theta and the azimuthal angle phi, the color shows that particular value.

How can I do it in python?

Answer 1

I think this spherical harmonics example is what you need.

• Minimal example:

  from mayavi import mlab
  import numpy as np
  
  # Make sphere, choose colors
  phi, theta = np.mgrid[0:np.pi:101j, 0:2*np.pi:101j]
  x, y, z = np.sin(phi) * np.cos(theta), np.sin(phi) * np.sin(theta), np.cos(phi)
  s = x*y  # <-- colors
  
  # Display
  mlab.figure(1, bgcolor=(1, 1, 1), fgcolor=(0, 0, 0), size=(600, 500))
  mlab.mesh(x, y, z, scalars=s, colormap='Spectral')
  mlab.view()
  mlab.show()
  

• You will need python2, not python3. See this thread from 2015.

• In Ubuntu 14.04 I said:

  sudo apt-get install python-vtk python-scipy python-numpy
  sudo pip install mayavi
  python main.py  # After saving the code below as main.py
  

• Here's the full code:

  # Author: Gael Varoquaux <gael.varoquaux@normalesup.org>
  # Copyright (c) 2008, Enthought, Inc.
  # License: BSD Style.
  
  from mayavi import mlab
  import numpy as np
  from scipy.special import sph_harm
  
  # Create a sphere
  r = 0.3
  pi = np.pi
  cos = np.cos
  sin = np.sin
  phi, theta = np.mgrid[0:pi:101j, 0:2 * pi:101j]
  
  x = r * sin(phi) * cos(theta)
  y = r * sin(phi) * sin(theta)
  z = r * cos(phi)
  
  mlab.figure(1, bgcolor=(1, 1, 1), fgcolor=(0, 0, 0), size=(400, 300))
  mlab.clf()
  # Represent spherical harmonics on the surface of the sphere
  for n in range(1, 6):
      for m in range(n):
          s = sph_harm(m, n, theta, phi).real
  
          mlab.mesh(x - m, y - n, z, scalars=s, colormap='jet')
  
          s[s < 0] *= 0.97
  
          s /= s.max()
          mlab.mesh(s * x - m, s * y - n, s * z + 1.3,
                    scalars=s, colormap='Spectral')
  
  mlab.view(90, 70, 6.2, (-1.3, -2.9, 0.25))
  mlab.show()
  

• You can expect about 20 seconds of loading time for this example if you have a slow computer.

• You can use your mouse to rotate and zoom the image.