过滤numpy随机选择的结果

Question

I want to filter the results generated by a numpy.random.choice . The problem I want to solve cannot be solved using applying the condition first by using np.where and then making a random choice. In general, I want some property to hold among all the randomly chosen elements.

The particular instance of this problem is that I want to pick n points in a plane at random such that any given pair of points is at least d distance apart. I am not sure if this can be done in polynomial time since this problem looks like the NP-complete clique problem.

If it's not possible to obtain the required number of points, the algorithm is to be repeated using a lower value of d .

Answer 1

A direct approach would be to generate your array point by point and checking that each new point respects your condition. Here is how you could do it :

import math
import random

# We define a distance function
def distance(x1, y1, x2, y2):
    return math.sqrt((x2-x1)**2+(y2-1)**2)

# We define a function that checks if a new point respects the distance condition
def distance_respected(points, dist_max, new_x, new_y):
    distance_respected = True
    for point in points:
        if distance(point[0], point[1], new_x, new_y)>dist_max:
            distance_respected = False
    return distance_respected

# In the following example I decided to just consider part of a plane. More precisely
# [-10,10]*[-10,10]

number_of_points = 5
max_distance = 2
points = []
for point in range(number_of_points):
    # random.uniform() generates a random float between our two numbers
    new_x = random.uniform(-10,10)
    new_y = random.uniform(-10,10)
    while not distance_respected(points, max_distance, new_x, new_y):
        new_x = random.uniform(-10,10)
        new_y = random.uniform(-10,10)
    points.append((new_x, new_y))

---

Output :

[(-3.425486982794177, -5.415726177177236),
 (-4.109629395121301, -0.8693732638893792),
 (-2.2778596980094257, 1.1101779439932162),
 (-3.0579069964130916, 1.2909258679375473),
 (-3.067639560760325, 1.1507562378468599)]

Answer 2

Poisson disc sampling is good for this. The runtime is nothing like NP-complete.

The algorithm is basically "keep a list of hot points and choose other hot points near them. If you can't find one nearby in a few tries, make the point cold forever."

You'll need a quadtree (or similar) to make finding nearby points efficient.