我不確定爭論的目的degree是什么，也許是為了限制遞歸深度？
這是一個基于您的問題的示例，使用遞歸 sierpinski 函數：
import pygame
def draw_triangle(p1, p2, p3, color, line_width, screen):
pygame.draw.polygon(screen, color, [p1, p2, p3], line_width)
def midpoint(p1, p2):
""" Return the mid-point on the line p1 to p2 """
x1, y1 = p1
x2, y2 = p2
x_mid = (x1 + x2) // 2
y_mid = (y1 + y2) // 2
return (x_mid, y_mid)
def sierpinski(degree, p1, p2, p3, color, line_width, screen):
# p1 → bottom left, p2 → bottom right, p3 → top
# recursive function so check for exit condition first
if abs(p1[0] - p2[0]) <= 2 and abs(p2[0] - p3[0]) <= 2 and abs(p1[0] - p3[0]) <= 2:
return
draw_triangle(p1, p2, p3, color, line_width, screen)
a = midpoint(p1, p2)
b = midpoint(p1, p3)
c = midpoint(p2, p3)
# skip the centre triangle
sierpinski(degree, p1, a, b, color, line_width, screen)
sierpinski(degree, p2, a, c, color, line_width, screen)
sierpinski(degree, p3, b, c, color, line_width, screen)
height = 640
width = 640
pygame.init()
screen = pygame.display.set_mode((width, height), pygame.RESIZABLE)
pygame.display.set_caption("Sierpiński")
clock = pygame.time.Clock()
update_screen = True
running = True
while running:
for event in pygame.event.get():
if event.type == pygame.QUIT:
running = False
elif event.type == pygame.VIDEORESIZE:
width, height = event.dict["size"]
screen = pygame.display.set_mode((width, height), pygame.RESIZABLE)
update_screen = True
if update_screen:
# only draw the screen when required
screen.fill(pygame.color.Color("white"))
# determine initial points based on window size
p1 = [5, height - 5]
p2 = [(width - 10) // 2, 5]
p3 = [width - 5, height - 5]
sierpinski(None, p1, p2, p3, pygame.color.Color("black"), 1, screen)
pygame.display.update()
update_screen = False
# limit framerate
clock.tick(30)
pygame.quit()
為了簡潔起見，我刪除了顏色處理，而是使用pygame.color.Color接受其構造函數的字符串參數。我還使用整數除法//來代替round(…).
根據遞歸函數的深度或復雜性，您可以重新繪制每一幀，但我想展示一個限制示例，以防函數復雜性增加。最后，我最近一直在調整屏幕大小，這似乎與一次繪制有關，所以我也將其包括在內。
編輯：我修改了該sierpinski函數以支持degree指定遞歸 dep 的參數
def sierpinski(degree, p1, p2, p3, color, line_width, screen):
# p1 → bottom left, p2 → bottom right, p3 → top
# recursive function so check for exit condition first
if degree is None:
if abs(p1[0] - p2[0]) <= 2 and abs(p2[0] - p3[0]) <= 2 and abs(p1[0] - p3[0]) <= 2:
return
else:
if degree == 0:
return
else:
degree -= 1
…
然后我添加了一些事件處理，以便可以使用鼠標滾輪來增加和減少度數，這顯示在標題欄上：
elif event.type == pygame.MOUSEBUTTONUP:
if event.button == 4: # wheel up
if degree is None:
degree = 8
else:
degree += 1
if degree > maximum_degree:
degree = maximum_degree
update_screen = True
elif event.button == 5: # wheel down
if degree is None:
degree = 3
else:
degree -= 1
if degree < minimum_degree:
degree = minimum_degree
update_screen = True
…
