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I'm setting up a data set, and the goal is to make a sphere with a normal distribution along the radial direction, and uniform theta and phi distributions. Despite using uniform distributions for theta and phi, I keep getting regions of very dense points at the poles (symmetrically near +/- radius on the z axis) that have a small but noticeable size. I am also writing to a file and using ROOT to plot my results.

I've tried reducing the range of theta and phi to graph half a sphere, but the problem still persists in both cases. I have also set the radius to a constant to make sure that wasn't interfering with the formation of the poles. The poles still formed.

    #Size is the number of points to generate, and n is the dimension of the problem (n=2 for circle, n=3 for sphere, etc.)
    hs_points = np.zeros((size, n)) 
    for i in range(size):

        hs_point = hs_points[i]
        for j in range(n):
            if j == 0:
                # normal distribution on radius
                coord = np.random.normal(mu, sigma)

            elif j < n-1:
                 coord=round(random.uniform(0,np.pi),15)


            else:
                coord = np.random.rand()*(2*np.pi)
                hs_point[j] = coord
        hs_points[i] = hs_point
    return hs_points


    c_points = np.zeros((size, n))
    # translate each hyperspherical point into a cartesian point
    for i in range(size):   
          hs_point = hs_points[i]
          xCoord=hs_point[0]*np.sin(hs_point[1])*np.cos(hs_point[2])      
          yCoord=hs_point[0]*np.sin(hs_point[1])*np.sin(hs_point[2])
          zCoord=hs_point[0]*np.cos(hs_point[1])

          c_points[i,0]=xCoord
          c_points[i,1]=yCoord
          c_points[i,2]=zCoord

I expect the program to output a "fuzzy" sphere with a normal distribution along the radial direction, but with uniform behavior everywhere else (i.e. no particularly dense regions). Actual behavior is the generation of dense poles with uniform behavior everywhere else.

Young Canadian
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    Perhaps related to [dispersing-n-points-uniformly-on-a-sphere](https://stackoverflow.com/questions/14805583/dispersing-n-points-uniformly-on-a-sphere) ? – John Anderson Jan 27 '19 at 19:39
  • Consider also [Sampling uniformly distributed random points inside a spherical volume](https://stackoverflow.com/questions/5408276/sampling-uniformly-distributed-random-points-inside-a-spherical-volume) – hpaulj Jan 27 '19 at 20:50
  • Per John Anderson: possible duplicate of [Dispersing n points uniformly on a sphere](https://stackoverflow.com/questions/14805583/dispersing-n-points-uniformly-on-a-sphere) – Davis Herring Jan 28 '19 at 05:39
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    Consider the area between the circles of theta=1 degree and 2 degrees (near the pole), and that between 89 and 90 (on the equator). Uniformity in theta implies that each receives the same number of points. – Davis Herring Jan 28 '19 at 05:42
  • I think you may have an indentetion error in the last `else`, i.e. you should remove one indentation for `hs_point[j] = coord` so it stands outside the `if` block – Tarifazo Jan 28 '19 at 13:37

0 Answers0