以下是一个简单的示例代码，用于检测半圆和矩形之间的碰撞：

import math

def is_collision(circle_x, circle_y, circle_radius, rect_x, rect_y, rect_width, rect_height):
    # 将矩形的中心点转换为相对于半圆的坐标系
    rect_center_x = rect_x + rect_width/2 - circle_x
    rect_center_y = rect_y + rect_height/2 - circle_y

    # 将矩形的中心点坐标旋转回原始坐标系
    angle = math.atan2(rect_center_y, rect_center_x)
    rect_center_x = math.cos(angle) * rect_center_x + math.sin(angle) * rect_center_y
    rect_center_y = -math.sin(angle) * rect_center_x + math.cos(angle) * rect_center_y

    # 检查矩形的中心点是否在半圆的范围内
    if rect_center_x < 0:
        closest_x = 0
    elif rect_center_x > circle_radius:
        closest_x = circle_radius
    else:
        closest_x = rect_center_x

    if rect_center_y < -rect_height/2:
        closest_y = -rect_height/2
    elif rect_center_y > rect_height/2:
        closest_y = rect_height/2
    else:
        closest_y = rect_center_y

    # 计算半圆中心点和矩形中心点之间的距离
    distance_x = rect_center_x - closest_x
    distance_y = rect_center_y - closest_y
    distance = math.sqrt(distance_x**2 + distance_y**2)

    # 如果距离小于等于半圆的半径，则发生碰撞
    if distance <= circle_radius:
        return True
    else:
        return False

# 示例用法
circle_x = 0
circle_y = 0
circle_radius = 5

rect_x = -3
rect_y = -3
rect_width = 6
rect_height = 6

collision = is_collision(circle_x, circle_y, circle_radius, rect_x, rect_y, rect_width, rect_height)
print(collision)  # 输出 True 或 False，表示是否发生碰撞

以上代码通过将矩形的中心点转换为相对于半圆的坐标系，然后将坐标系旋转回原始坐标系，最后检查矩形的中心点是否在半圆的范围内，来判断是否发生碰撞。