计算椭圆之间的相交面积- python

import math

def calculate_ellipse_intersection_area(a1, b1, a2, b2):
    # 计算椭圆1的面积
    area1 = math.pi * a1 * b1
    # 计算椭圆2的面积
    area2 = math.pi * a2 * b2

    # 计算椭圆1和椭圆2的长轴、短轴之间的距离
    distance = math.sqrt((a1 - a2) ** 2 + (b1 - b2) ** 2)

    # 判断椭圆是否相离
    if distance >= a1 + a2 or distance >= b1 + b2:
        return 0

    # 判断椭圆是否包含
    if a1 >= a2 + distance or a2 >= a1 + distance or b1 >= b2 + distance or b2 >= b1 + distance:
        return min(area1, area2)

    # 计算相交部分的面积
    angle1 = math.acos((a1 ** 2 + distance ** 2 - a2 ** 2) / (2 * a1 * distance))
    angle2 = math.acos((a2 ** 2 + distance ** 2 - a1 ** 2) / (2 * a2 * distance))
    intersection_area = angle1 * a1 * b1 + angle2 * a2 * b2 - 0.5 * (a1 * math.sin(angle1) + a2 * math.sin(angle2)) * distance

    return intersection_area

# 示例使用
a1 = 5
b1 = 3
a2 = 4
b2 = 2
intersection_area = calculate_ellipse_intersection_area(a1, b1, a2, b2)
print("椭圆1和椭圆2的相交面积为:", intersection_area)