第一个计算几何算法的可视化---极点法获取凸包

生成随机的点
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
可视化所有的点

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)

运行结果
1. 补充一下极边法，其实变化不大，只写一下核心的代码：

python 复制代码

    
      
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