写一个路径数组的自交叉检测函数

创建一个自交叉检测函数通常用于图形处理或路径分析场景，例如在计算机图形学中检查一条二维线条是否与其他线条发生自相交。这种算法的基本思路通常是通过计算两条线段的交点来判断。这里是一个简单的Python示例，使用了向量几何：

import numpy as np

def is_self_intersection(path):
    # 将路径转换为一系列线段
    segments = [(path[i], path[i+1]) for i in range(len(path) - 1)]
    
    def line_intersection(line1, line2):
        xdiff = (line1[0][0] - line1[1][0], line2[0][0] - line2[1][0])
        ydiff = (line1[0][1] - line1[1][1], line2[0][1] - line2[1][1])

        def det(a, b):
            return a[0] * b[1] - a[1] * b[0]

        div = det(xdiff, ydiff)
        if div == 0:  # Parallel lines have no intersection
            return None

        d = (det(*line1), det(*line2))
        x = det(d, xdiff) / div
        y = det(d, ydiff) / div
        return [x, y]
        
    intersections = [line_intersection(s1, s2) for s1, s2 in zip(segments[:-1], segments[1:]) if line_intersection(s1, s2)]

    # 检查是否有两个交点之间的距离小于某个阈值（避免误报），通常这个阈值取决于线宽
    min_dist_threshold = 1e-6  # 例如像素级别
    closest_intersections = sorted(intersections, key=lambda p: np.linalg.norm(p))

    for i, inter in enumerate(closest_intersections):
        if i > 0 and np.linalg.norm(inter - closest_intersections[i-1]) < min_dist_threshold:
            return True  # 如果找到一对接近的交点，则说明有自交叉

    return False

# 使用示例
path = [[0, 0], [1, 1], [2, 0], [3, 1]]  # 假设这是你要检查的一条路径
if is_self_intersection(path):
    print("路径存在自交叉")
else:
    print("路径无自交叉")