Faster numpy cartesian to spherical coordinate conversion?

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This is similar to Justin Peel’s answer, but using just numpy and taking advantage of its built-in vectorization:

import numpy as np

def appendSpherical_np(xyz):
    ptsnew = np.hstack((xyz, np.zeros(xyz.shape)))
    xy = xyz[:,0]**2 + xyz[:,1]**2
    ptsnew[:,3] = np.sqrt(xy + xyz[:,2]**2)
    ptsnew[:,4] = np.arctan2(np.sqrt(xy), xyz[:,2]) # for elevation angle defined from Z-axis down
    #ptsnew[:,4] = np.arctan2(xyz[:,2], np.sqrt(xy)) # for elevation angle defined from XY-plane up
    ptsnew[:,5] = np.arctan2(xyz[:,1], xyz[:,0])
    return ptsnew

Note that, as suggested in the comments, I’ve changed the definition of elevation angle from your original function. On my machine, testing with pts = np.random.rand(3000000, 3), the time went from 76 seconds to 3.3 seconds. I don’t have Cython so I wasn’t able to compare the timing with that solution.

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