以下是使用AABB分离轴定理来寻找重叠深度的示例代码：

class AABB:
    def __init__(self, x, y, width, height):
        self.x = x
        self.y = y
        self.width = width
        self.height = height

def get_overlap_depth(box1, box2, axis):
    # 计算两个AABB在给定轴上的重叠深度
    box1_min = box1.x - box1.width/2
    box1_max = box1.x + box1.width/2
    box2_min = box2.x - box2.width/2
    box2_max = box2.x + box2.width/2

    if box1_min > box2_max or box2_min > box1_max:
        # 没有重叠，返回0
        return 0
    
    depth = min(box1_max, box2_max) - max(box1_min, box2_min)

    return depth

def check_collision(box1, box2):
    overlap_x = get_overlap_depth(box1, box2, "x")
    overlap_y = get_overlap_depth(box1, box2, "y")

    if overlap_x > 0 and overlap_y > 0:
        # 发生碰撞，返回重叠的深度
        return max(overlap_x, overlap_y)
    
    # 没有碰撞
    return 0

# 示例用法
box1 = AABB(0, 0, 4, 4)
box2 = AABB(2, 2, 4, 4)
overlap_depth = check_collision(box1, box2)
print("重叠深度:", overlap_depth)

以上代码定义了一个AABB类来表示矩形框，并实现了get_overlap_depth函数用于计算在给定轴上的重叠深度。check_collision函数使用AABB分离轴定理来检测两个矩形框是否发生碰撞，并返回重叠的深度。在示例中，我们创建了两个矩形框box1和box2，并使用check_collision函数来计算它们的重叠深度。最后，打印出重叠的深度。