Hastebin

import pygame
import math

pygame.init()

screen = pygame.display.set_mode((360,640))
clock = pygame.time.Clock()

RECT_WIDTH, RECT_HEIGHT = 360, 640  # Rectangle size
rectangle = pygame.Surface((RECT_WIDTH, RECT_HEIGHT), pygame.SRCALPHA)
rectangle.fill('green')

# --- Matrix values ---
a, b = 1.414062, -1.414062
c, d = 1.045898, 1.045898
tx, ty = 0, 640  # Translation values
rotation_origin_x, rotation_origin_y = 0, 320  # Rotation and translation origin

# --- Extract scale and rotation ---
scale_x = math.sqrt(a**2 + b**2) if a or b else 1.0  # ≈ 2.0
scale_y = math.sqrt(c**2 + d**2) if c or d else 1.0  # ≈ 1.479
rotate = -math.degrees(math.atan2(b, a)) if a or b else 0  # Negated rotation ≈ 45°

def blitRotate(surf, image, origin, pivot, angle):
    # Compute the offset vector from the center of the image to the pivot on the image:
    image_rect = image.get_rect(topleft = (origin[0] - pivot[0], origin[1]-pivot[1]))
    offset_center_to_pivot = pygame.math.Vector2(origin) - image_rect.center
    # Rotate the offset vector the same angle you want to rotate the image:
    rotated_offset = offset_center_to_pivot.rotate(-angle)
    # Calculate the new center point of the rotated image by subtracting the rotated offset vector from the pivot point in the world:
    rotated_image_center = (origin[0] - rotated_offset.x, origin[1] - rotated_offset.y)
    # Rotate the image and set the center point of the rectangle enclosing the rotated image. Finally blit the image :
    rotated_image = pygame.transform.rotate(image, angle)
    rotated_image_rect = rotated_image.get_rect(center = rotated_image_center)
    surf.blit(rotated_image, rotated_image_rect)

running = True
while running:
    for event in pygame.event.get():
        if event.type == pygame.QUIT:
            running = False

    screen.fill('white')

    scaled_width = int(RECT_WIDTH * scale_x)
    scaled_height = int(RECT_HEIGHT * scale_y)
    scaled_rect = pygame.transform.scale(rectangle, (scaled_width, scaled_height))

    # Offset the origin before rotating
    origin = rotation_origin_x * scale_x, rotation_origin_y * scale_y
    pygame.draw.circle(scaled_rect, 'blue', origin, 10)
    # Calculate where we need to move the shape so the rotation origin is at the translation coordinate
    translation_vector = -origin[0], screen.height - origin[1]
    scaled_rect.get_rect().move_to(topleft=translation_vector)
    blitRotate(screen, scaled_rect, screen.get_rect().center, origin, rotate)

    # Update the display
    pygame.display.flip()
    clock.tick(60)

pygame.quit()