如何编写基于距中心的距离和边数在油漆中绘制规则图形的功能？

Question

我正在研究一个函数，该函数接受距常规图形中心的像素长度和边数。 例如：

draw_figure(r=200, side_count=4) : It would draw quadrilateral
draw_figure(r=100, side_count=8) : It would draw an octagon

我试图列出所有距中心半径相同的坐标，获取一个随机坐标，并根据长度获取其余坐标，但是我无法弄清楚。

from time import sleep
import subprocess
import pyautogui
from math import cos, radians, sqrt
from random import choice

def draw_figure(side_count, r):
    # Open mspaint and move the cursorto the center.
    subprocess.Popen("mspaint", shell=True) 
    sleep(1)
    x, y = pyautogui.size()
    pyautogui.moveTo(x/2, y/2)


    # Define cos of alpha value in center and side_len of figure
    a = 360/side_count
    cos_a = cos(radians(a))
    side_len = round(sqrt(2*(r**2) - 2*r*cos_a), 3)


    # Get every x/y pair on screen inside a set
    all_points = set()
    for x_cord in list(range(x)):
        for y_cord in list(range(y)):
            all_points.add((x_cord, y_cord))


    # Create points list with all x/y tuples that all are at same 
        # distance from center by r count of pixels 
    points = []
    for point in all_points:
        try:
            R = round(sqrt((point[0] - x/2)**2 + (point[1] - 
                        y/2)**2), 3)
            if R == r:
                points.append(point)
        except ValueError:
            pass


    # Pick a random coordinate and find x/y of side points
    r_point = choice(points)
    square_vectors = []
    pyautogui.moveTo(r_point)

    for point in points:
        try:
            test_len = round(sqrt((r_point[0] - point[0])**2 + 
                        (r_point[1] - point[1])**2), 3)
            if test_len == side_len:
                vector = tuple([point[0] - r_point[0], 
                                point[1] - r_point[1]])
                square_vectors.append(vector)
        except ValueError:
            pass
    for vector in square_vectors:
        pyautogui.dragRel(vector)
    return square_vectors

示例：

A________B     O is center of square       
 |  \   |      OA = r
 | O \  |           
D|___ \_|C