make_unit_disk_plot.py

#!/usr/bin/python3

import sys
import random
import math
import matplotlib.pyplot as plt


class Vec3:
    __slots__ = (
        'x',
        'y',
        'z'
    )

    def __init__(self, x, y, z):
        self.x = x
        self.y = y
        self.z = z

    def length_squared(self):
        return (self.x * self.x) + \
               (self.y * self.y) + \
               (self.z * self.z)


def main():
    if len(sys.argv) < 2:
        print('Please provide an integer for how many points to sample (e.g. 1000)')
        sys.exit(0)

    # seed the random
    random.seed('asdf')

    # number of points to sample
    n = int(sys.argv[1])
    points = []

    for _ in range(0, n):
        # Make sure we get a valid vector
        while True:
            # cartesian
            x = random.uniform(-1, 1)
            y = random.uniform(-1, 1)

            # polar
#            r = random.uniform(0, 1)
#            th = random.uniform(0, 2 * math.pi)
#
#            x = r * math.cos(th)
#            y = r * math.sin(th)

            v = Vec3(x, y, 0)
            if v.length_squared() <= 1:
                break

        points.append(v)

    # Transform it into a pyplot friendly format
    x = [p.x for p in points]
    y = [p.y for p in points]

    plt.scatter(x, y)
    plt.show()


if __name__ == '__main__':
    main()

Cartesian produces this:

This is polar: