凸包的敏感性分析中空间多边形的重叠百分比

凸包的敏感性分析中，空间多边形的重叠百分比可以通过以下步骤解决：

1. 定义多边形类：首先，我们需要定义一个多边形类，用于表示多边形的顶点和边。

class Polygon:
    def __init__(self, vertices):
        self.vertices = vertices
        self.edges = self.calculate_edges()

    def calculate_edges(self):
        edges = []
        for i in range(len(self.vertices)):
            edges.append((self.vertices[i], self.vertices[(i+1)%len(self.vertices)]))
        return edges

2. 计算两个多边形的重叠面积：接下来，我们需要计算两个多边形的重叠面积。可以使用Sutherland-Hodgman算法来实现，该算法将一个多边形裁剪为与另一个多边形重叠的部分。

def sutherland_hodgman(polygon, clipping_polygon):
    clipped_polygon = polygon
    for edge in clipping_polygon.edges:
        clipped_polygon = clip_polygon(clipped_polygon, edge)
    return clipped_polygon

def clip_polygon(polygon, edge):
    clipped_polygon = []
    for i in range(len(polygon.vertices)):
        current_vertex = polygon.vertices[i]
        next_vertex = polygon.vertices[(i+1)%len(polygon.vertices)]
        if inside(current_vertex, edge):
            if not inside(next_vertex, edge):
                intersection_point = compute_intersection(current_vertex, next_vertex, edge)
                clipped_polygon.append(intersection_point)
            clipped_polygon.append(next_vertex)
        elif inside(next_vertex, edge):
            intersection_point = compute_intersection(current_vertex, next_vertex, edge)
            clipped_polygon.append(intersection_point)
    return Polygon(clipped_polygon)

def inside(vertex, edge):
    return (edge[1][0] - edge[0][0]) * (vertex[1] - edge[0][1]) > (edge[1][1] - edge[0][1]) * (vertex[0] - edge[0][0])

def compute_intersection(vertex1, vertex2, edge):
    dx = vertex2[0] - vertex1[0]
    dy = vertex2[1] - vertex1[1]
    edge_dx = edge[1][0] - edge[0][0]
    edge_dy = edge[1][1] - edge[0][1]
    s = (dx * (edge[0][1] - vertex1[1]) + dy * (vertex1[0] - edge[0][0])) / (edge_dx * dy - edge_dy * dx)
    intersection_x = vertex1[0] + s * edge_dx
    intersection_y = vertex1[1] + s * edge_dy
    return (intersection_x, intersection_y)

3. 计算凸包的敏感性：最后，我们可以使用Monte Carlo方法来计算凸包的敏感性，即在随机生成的多个多边形对中计算重叠百分比的平均值。

import random

def calculate_overlap_percentage(polygon1, polygon2):
    overlapping_area = 0
    for _ in range(1000):  # 生成1000个随机多边形对
        random_polygon1 = generate_random_polygon()
        random_polygon2 = generate_random_polygon()
        clipped_polygon1 = sutherland_hodgman(random_polygon1, polygon1)
        clipped_polygon2 = sutherland_hodgman(random_polygon2, polygon2)
        overlapping_area += calculate_area(clipped_polygon1) + calculate_area(clipped_polygon2)
    total_area = calculate_area(polygon1) + calculate_area(polygon2)
    overlap_percentage = overlapping_area / (total_area * 1000)  # 计算重叠百分比
    return overlap_percentage

def generate_random_polygon():
    # 随机生成一个多边形
    vertices = []
    for _ in range(4):
        x = random.randint(0, 10)
        y = random.randint(0, 10)
        vertices.append((x, y))
    return Polygon(vertices)

def calculate_area(polygon):
    # 计算多边形的面积
    area = 0
    for i in range(len(polygon.vertices)):
        current_vertex = polygon.vertices[i]
        next_vertex = polygon.vertices[(i+1)%len(polygon.vertices)]
        area