# How to subtract geometry in pygame?

## Question:

I am trying to make a logic in which i can subtract the geometrical shapes. Lets say i have to subtract a circle from a rectangle.

The idea is to draw each point of the rectangle as a single individual point using win.set_at(). And then when we need to subtract the circle from the rectangle we an simply calculate that the point on which we are drawing and completing our square lies or not in the circle. If it lies then don’t set pixels else draw the pixel. This is my code:

``````
import pygame

WIDTH, HEIGHT = 700, 500

win = pygame.display.set_mode((WIDTH, HEIGHT))

WHITE = (255, 255, 255)
BLACK = (0, 0, 0)

def drawer(window, x, y, radius, s_l, s_w, s_x, s_y):
for i in range(0, HEIGHT):
for j in range(0, WIDTH):
distance = (x - j)**2 + (y - i)**2
if not distance <= radius**2 and i >= s_y and j >= s_x and i <= s_w + s_x and j <= s_l + s_y:
window.set_at((j, i), BLACK)

c_x, c_y = 130, 150
run = True
while run:
for event in pygame.event.get():
if event.type == pygame.QUIT:
run = False

win.fill(WHITE)
drawer(win, c_x, c_y, 30, 100, 100, 100, 100)
pygame.display.flip()

pygame.quit()
``````

But is it is quite slow. Can you suggest a better way (more optimized algorithm) of doing it.

For a good performance I suggest to use `pygame.mask`. Draw the shapes on `pygame.Surface` objects and create masks from the surfaces:

``````mask1 = pygame.mask.from_surface(shape1)
``````

Invert the mask of the second shape and create the overlapping mask. Finally, create a new _Surface: from the overlapping mask:

``````mask2.invert()
subtract_shape = subtract_maks.to_surface(setcolor = "red", unsetcolor=(0, 0, 0, 0))
``````

Minimal example ``````import pygame

pygame.init()
window = pygame.display.set_mode((300, 300))
clock = pygame.time.Clock()

shape1 = pygame.Surface((200, 200), pygame.SRCALPHA)
pygame.draw.circle(shape1, "white", (100, 100), 100)
shape2 = pygame.Surface((200, 200), pygame.SRCALPHA)
pygame.draw.rect(shape2, "white", (25, 50, 150, 100))

subtract_shape = subtract_maks.to_surface(setcolor = "red", unsetcolor=(0, 0, 0, 0))

background = pygame.Surface(window.get_size())
ts, w, h, c1, c2 = 50, *background.get_size(), (128, 128, 128), (64, 64, 64)
tiles = [((x*ts, y*ts, ts, ts), c1 if (x+y) % 2 == 0 else c2) for x in range((w+ts-1)//ts) for y in range((h+ts-1)//ts)]
[pygame.draw.rect(background, color, rect) for rect, color in tiles]
run = True
while run:
clock.tick(60)
for event in pygame.event.get():
if event.type == pygame.QUIT:
run = False
if event.type == pygame.KEYDOWN:
print(pygame.key.name(event.key))

window.blit(background, (0, 0))
window.blit(subtract_shape, (50, 50))
pygame.display.flip()

pygame.quit()
exit()
``````
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