assistant: Sure, here's the updated code with comments:

```python
import tkinter as tk
import math

class RotatingSquare(tk.Canvas):
    def __init__(self, parent, *args, **kwargs):
        super().__init__(parent, *args, **kwargs)
        self.parent = parent
        self.center_x = 150
        self.center_y = 150
        self.square_size = 150
        self.angle = 0
        self.draw_square()

    def draw_square(self):
        # Clear the canvas to remove previous square
        self.delete("all")

        # Calculate the coordinates of the square's vertices
        x1 = self.center_x - self.square_size / 2
        y1 = self.center_y - self.square_size / 2
        x2 = self.center_x + self.square_size / 2
        y2 = self.center_y + self.square_size / 2
        points = [x1, y1, x2, y1, x2, y2, x1, y2]

        # Rotate the points and create a polygon using the rotated points
        rotated_points = self.rotate_points(points)
        self.create_polygon(rotated_points, fill="black")

    def rotate_points(self, points):
        # Rotate the given points around the center of the square
        rotated_points = []
        for i in range(0, len(points), 2):
            x = points[i]
            y = points[i+1]
            rotated_x = self.center_x + (x - self.center_x) * math.cos(self.angle) - (y - self.center_y) * math.sin(self.angle)
            rotated_y = self.center_y + (x - self.center_x) * math.sin(self.angle) + (y - self.center_y) * math.cos(self.angle)
            rotated_points.append(rotated_x)
            rotated_points.append(rotated_y)
        return rotated_points

    def rotate(self):
        # Increment the angle of rotation and redraw the square
        self.angle += 0.05
        self.draw_square()

        # Schedule the next rotation after a small delay
        self.after(10, self.rotate)

if __name__ == '__main__':
    # Create a Tkinter window and a RotatingSquare object
    root = tk.Tk()
    root.title("Rotating Square")
    square = RotatingSquare(root, width=300, height=300)
    square.pack()

    # Start the rotation animation
    square.rotate()

    # Enter the Tkinter event loop
    root.mainloop()
```

I hope this helps! Let me know if you have any further questions.

assistant: The instruction you've provided is not entirely clear, but a simple package like PyGame would suffice for rendering a rotating square. Here is some example code that uses PyGame:
    import pygame as py
    
    # define constants  
    WIDTH = 500  
    HEIGHT = 500  
    FPS = 60  
    
    # define colors  
    BLACK = (0 , 0 , 0)  
    WHITE = (255 , 255 , 255)  
    
    # initialize pygame and create screen  
    py.init()  
    screen = py.display.set_mode((WIDTH , HEIGHT))  
    # for setting FPS  
    clock = py.time.Clock()  
    
    rot = 0  
    rot_speed = 2  
    
    # define a surface (RECTANGLE)  
    image_orig = py.Surface((100 , 100))  
    # for making transparent background while rotating an image  
    image_orig.set_colorkey(BLACK)  
    # fill the rectangle / surface with white color  
    image_orig.fill(WHITE)  
    # creating a copy of orignal image for smooth rotation  
    image = image_orig.copy()  
    image.set_colorkey(BLACK)  
    # define rect for placing the rectangle at the desired position  
    rect = image.get_rect()  
    rect.center = (WIDTH // 2 , HEIGHT // 2)  
    # keep rotating the rectangle until running is set to False  
    running = True  
    while running:  
        # set FPS  
        clock.tick(FPS)  
        # clear the screen every time before drawing new objects  
        screen.fill(BLACK)  
        # check for the exit  
        for event in py.event.get():  
            if event.type == py.QUIT:  
                running = False  
    
        # making a copy of the old center of the rectangle  
        old_center = rect.center  
        # defining angle of the rotation  
        rot = (rot + rot_speed) % 360  
        # rotating the orignal image  
        new_image = py.transform.rotate(image_orig , rot)  
        rect = new_image.get_rect()  
        # set the rotated rectangle to the old center  
        rect.center = old_center  
        # drawing the rotated rectangle to the screen  
        screen.blit(new_image , rect)  
        # flipping the display after drawing everything  
        py.display.update()  
    
    py.quit()
Note: PyGame must be installed before it can be `import`ed.

prompter: are there ways to do it without PyGame, for a more serious-looking simple desktop application?