第一个计算几何算法的可视化---极点法获取凸包

1. 生成随机的点

2. 使用EP算法得到极点

   • 初始化状态
   • 3重循环遍历三角形
   • 第四重循环判断点
   • intriagle测试里面先要保证三角形的顶点是CCW
   • to-left测试的计算公式

3. 可视化所有的点

4. 完整代码

   import pygame
   import random
   
   # 定义颜色
   RED = (255, 0, 0)
   GREEN = (0, 255, 0)
   BACKGROUND_COLOR = (255, 255, 255)
   
   
   class Point:
       def __init__(self, x, y):
           self.x = x
           self.y = y
           self.extreme = True
   
   def toLeft(p, q, s):
       area = p.x * q.y - p.y * q.x + \
              q.x * s.y - q.y * s.x + \
              s.x * p.y - s.y * p.x
   
       return area > 0
   
   
   
   def InTriangle(p, q, r, s):
       # 这里需要一个函数来检测点s是否在由p, q, r形成的三角形内
       # 返回True如果s在三角形内, 否则返回False
       # NOTE: 这个函数的具体实现需要更多的背景知识来完成，这里我暂时用一个简单的返回值代替
       if not toLeft(p, q, r):
           p, r = r, p
   
       ret1 = toLeft(p, q, s)
       ret2 = toLeft(q, r, s)
       ret3 = toLeft(r, p, s)
       if ret1 and ret2 and ret3:
           return True
       return False
   
   def extremePoint(points):
       n = len(points)
       for s in range(n):
           points[s].extreme = True
   
       for p in range(n):
           for q in range(p + 1, n):
               for r in range(q + 1, n):
                   for s in range(n):
                       if s == p or s == q or s == r or not points[s].extreme:
                           continue
                       if InTriangle(points[p], points[q], points[r], points[s]):
                           points[s].extreme = False
                           break
   
   # 生成随机点
   def generate_random_points(num_points=40, xlim=(0, 700), ylim=(0, 500)):
       return [Point(random.randint(xlim[0], xlim[1]), random.randint(ylim[0], ylim[1])) for _ in range(num_points)]
       # return [Point(0, 0), Point(100, 0), Point(50, 100), Point(50, 50)]
   
   
   def visualize(points, width=800, height=600):
       pygame.init()
       screen = pygame.display.set_mode((width, height))
       pygame.display.set_caption('Visualization of Extreme Points')
       font = pygame.font.SysFont(None, 24)  # 使用默认字体，大小为24
   
       running = True
       while running:
           for event in pygame.event.get():
               if event.type == pygame.QUIT:
                   running = False
   
           screen.fill(BACKGROUND_COLOR)
           index = 0
           for point in points:
               if point.extreme:
                   pygame.draw.circle(screen, GREEN, (point.x, height - point.y), 6)
               else:
                   pygame.draw.circle(screen, RED, (point.x, height - point.y), 3)
   
               label = font.render(str(index), True, (0, 0, 0))  # 使用黑色显示序号
               screen.blit(label, (point.x + 10, height - point.y - 10))
               index += 1
   
           pygame.display.flip()
   
       pygame.quit()
   
   
   # 主程序
   if __name__ == "__main__":
       points = generate_random_points()
       extremePoint(points)
       # for point in points:
       #     if point.extreme:
       #         print(f"极点: ({point.x}, {point.y})")
       visualize(points)
   
   
   

   5. 运行结果

      
      6. 补充一下极边法，其实变化不大，只写一下核心的代码：

    
      
def extremeEdge(points):
    n = len(points)
    for s in range(n):
        points[s].extreme = False

    for p in range(n):
        for q in range(p + 1, n):
            true_count = 0
            false_count = 0
            for target in range(n):
                if target == p or target == q:
                    continue

                if toLeft(points[p], points[q], points[target]):
                    true_count += 1
                else:
                    false_count += 1

            if true_count * false_count == 0:
                points[p].extreme = True
                points[q].extreme = True