Question

I am trying to generate a set of points that do not fall within the range of each other in a fixed area. My approach is given below:

import collections
from random import uniform

X = 100.0
Y = 100.0
points = 10
radius = 10

def in_circle(c_x, c_y, radius, x, y):
    dist_squared = (c_x - x)**2 + (c_y - y)**2
    return dist_squared <= radius ** 2

current = collections.defaultdict(lambda: [])

threshold = 0    

for point in range(1, points+1):
    cX = uniform(1.0, X)
    cY = uniform(1.0, Y)

    for cur in current:
        while in_circle(current[cur][0], current[cur][1], 2*radius, cX, cY):
          cX = uniform(1.0, X)
          cY = uniform(1.0, X)

          threshold += 1
          if threshold >= 1e+05:
              print "Cannot satisfy constraints"
              sys.exit(1)

    threshold = 0

    current[point] = [cX, cY]
    print cX, cY

Is there a good way to terminate this algorithm without making it enter an infinite loop? I do have a threshold check but are there better ways to do this?

Answer 1

This article about poisson disk sampling may be interesting to you. The author explains a strategy for selecting points that aren’t too close to each other, and even provides sample code in a few languages, including Python.

The problem with the strategy you outlined is, as you noted, that if you want to select a lot of points, or you want the points to be quite far apart, the performance can become atrocious. The poisson disk scheme has better performance characteristics, I believe.