python - How can I set a minimum distance constraint for generating points with numpy.random.rand?

Question

I am trying to generate an efficient code for generating a number of random position vectors which I then use to calculate a pair correlation function. I am wondering if there is straightforward way to set a constraint on the minimum distance allowed between any two points placed in my box.

My code currently is as follows:

def pointRun(number, dr):
"""
Compute the 3D pair correlation function
for a random distribution of 'number' particles
placed into a 1.0x1.0x1.0 box.
"""
## Create array of distances over which to calculate.   
    r = np.arange(0., 1.0+dr, dr)

## Generate list of arrays to define the positions of all points,
##    and calculate number density.
    a = np.random.rand(number, 3)
    numberDensity = len(a)/1.0**3

## Find reference points within desired region to avoid edge effects. 
    b = [s for s in a if all(s > 0.4) and all(s < 0.6) ]

## Compute pairwise correlation for each reference particle
    dist = scipy.spatial.distance.cdist(a, b, 'euclidean')
    allDists = dist[(dist < np.sqrt(3))]

## Create histogram to generate radial distribution function, (RDF) or R(r)
    Rr, bins = np.histogram(allDists, bins=r, density=False)

## Make empty containers to hold radii and pair density values.
    radii = []
    rhor = []

## Normalize RDF values by distance and shell volume to get pair density.
    for i in range(len(Rr)):
        y = (r[i] + r[i+1])/2.
        radii.append(y)
        x = np.average(Rr[i])/(4./3.*np.pi*(r[i+1]**3 - r[i]**3))
        rhor.append(x)

## Generate normalized pair density function, by total number density
    gr = np.divide(rhor, numberDensity)
    return radii, gr

I have previously tried using a loop that calculated all distances for each point as it was made and then accepted or rejected. This method was very slow if I use a lot of points.

Answer 1

Based on @Samir 's answer, and make it a callable function for your convenience :)

import numpy as np
import matplotlib.pyplot as plt

def generate_points_with_min_distance(n, shape, min_dist):
    # compute grid shape based on number of points
    width_ratio = shape[1] / shape[0]
    num_y = np.int32(np.sqrt(n / width_ratio)) + 1
    num_x = np.int32(n / num_y) + 1

    # create regularly spaced neurons
    x = np.linspace(0., shape[1]-1, num_x, dtype=np.float32)
    y = np.linspace(0., shape[0]-1, num_y, dtype=np.float32)
    coords = np.stack(np.meshgrid(x, y), -1).reshape(-1,2)

    # compute spacing
    init_dist = np.min((x[1]-x[0], y[1]-y[0]))

    # perturb points
    max_movement = (init_dist - min_dist)/2
    noise = np.random.uniform(low=-max_movement,
                                high=max_movement,
                                size=(len(coords), 2))
    coords += noise

    return coords

coords = generate_points_with_min_distance(n=8, shape=(2448,2448), min_dist=256)

# plot
plt.figure(figsize=(10,10))
plt.scatter(coords[:,0], coords[:,1], s=3)
plt.show()