Method to populate a disk with points in python

I have an application that requires a disk populated with 'n' points in a quasi-random fashion. I want the points to be somewhat random, but still have a more or less regular density over the disk.

My current method is to place a point, check if it's inside the disk, and then check if it is also far enough away from all other points already kept. My code is below:

import os
import random
import math

# ------------------------------------------------ #
# geometric constants
center_x = -1188.2
center_y = -576.9
center_z = -3638.3

disk_distance = 2.0*5465.6
disk_diam = 5465.6

# ------------------------------------------------ #

pts_per_disk = 256
closeness_criteria = 200.0
min_closeness_criteria = disk_diam/closeness_criteria

disk_center = [(center_x-disk_distance),center_y,center_z]
pts_in_disk = []
while len(pts_in_disk) < (pts_per_disk):
    potential_pt_x = disk_center[0]
    potential_pt_dy = random.uniform(-disk_diam/2.0, disk_diam/2.0)
    potential_pt_y = disk_center[1]+potential_pt_dy
    potential_pt_dz = random.uniform(-disk_diam/2.0, disk_diam/2.0)
    potential_pt_z = disk_center[2]+potential_pt_dz
    potential_pt_rad = math.sqrt((potential_pt_dy)**2+(potential_pt_dz)**2)

    if potential_pt_rad < (disk_diam/2.0):
        far_enough_away = True
        for pt in pts_in_disk:
            if math.sqrt((potential_pt_x - pt[0])**2+(potential_pt_y - pt[1])**2+(potential_pt_z - pt[2])**2) > min_closeness_criteria:
                pass
            else:
                far_enough_away = False
                break
        if far_enough_away:
            pts_in_disk.append([potential_pt_x,potential_pt_y,potential_pt_z])

outfile_name = "pt_locs_x_lo_"+str(pts_per_disk)+"_pts.txt"
outfile = open(outfile_name,'w')
for pt in pts_in_disk:
    outfile.write(" ".join([("%.5f" % (pt[0]/1000.0)),("%.5f" % (pt[1]/1000.0)),("%.5f" % (pt[2]/1000.0))])+'\n')
outfile.close()

In order to get the most even point density, what I do is basically iteratively run this script using another script, with the 'closeness' criteria reduced for each successive iteration. At some point, the script can not finish, and I just use the points of the last successful iteration.

So my question is rather broad: is there a better way to do this? My method is ok for now, but my gut says that there is a better way to generate such a field of points.

An illustration of the output is graphed below, one with a high closeness criteria, and another with a 'lowest found' closeness criteria (what I want).