title: verify distribution of uniformly distributed 3D coordinates
body: <p>I would like to write a python script to generate a uniformly distributed 3D coordinates (e.g., x, y, z) where x, y, and z are float numbers between 0 and 1. For the moment, z can be fixed, thus what I need is a uniform distributed points in a 2D (x-y) plane. I have written a script to do this job and checked both x, and y are uniform numbers. However, I am not sure if these points are uniformly distributed in (x-y) plane. </p>
  
  <p>My code is</p>
  
  <pre><code>1 import matplotlib.pyplot as plt
  2 import random
  3 import numpy as np
  4 import csv
  5 nk1=300
  6 nk2=300
  7 nk3=10
  8 kx=[]
  9 ky=[]
  10 kz=[]
  11 for i in range(nk1):
  12     for j in range(nk2):
  13         for k in range(nk3):
  14             xkg1=random.random()
  15             xkg2=random.random()
  16             xkg3 = float(k)/nk3
  17             kx.append(xkg1)
  18             ky.append(xkg2)
  19             kz.append(xkg3)
  20 kx=np.array(kx)
  21 count, bins, ignored = plt.hist(kx, normed=True)
  22 plt.plot(bins, np.ones_like(bins), linewidth=2, color='r')
  23 plt.show()
  </code></pre>
  
  <p>The plot shows both "kx", and "ky" are uniformly distributed numbers, however, how can I make sure that x-y are uniformly distributed in the 2D plane?</p>