def point_maker(pre_point):
    if isinstance(pre_point, Point):
        return pre_point
    elif isinstance(pre_point, tuple):
        return Point(pre_point[0], pre_point[1])
    else:
        raise ValueError("Invalid input for Point")


class ShapeBase(object):
    def __init__(self):
        pass

    def show(self):
        pass

    def move(self, dx, dy):
        pass

    def set_color(self, color):
        pass

    def get_color(self):
        pass


class Shape2D(ShapeBase):
    def __init__(self, **kwargs):
        super(Shape2D, self).__init__()
        self.color = kwargs.get("color", "white")
        self.fill = kwargs.get("fill", False)
        self.width = kwargs.get("width", 1)


class Point(Shape2D):
    def __init__(self, x, y):
        super(Point, self).__init__()
        self._x = x
        self._y = y

    @property
    def x(self):
        return self._x

    @property
    def y(self):
        return self._y


class Line(Shape2D):
    def __init__(self, point1, point2, **kwargs):
        super(Line, self).__init__(**kwargs)
        self.point1 = point_maker(point1)
        self.point2 = point_maker(point2)

    def contains(self, point, allow_on_extended=False):
        """判断点`point`是否在线段上

        Args:
            point (Point or tuple): 需要判断的点
            allow_on_extended (bool, optional): 是否允许点在线段的延长线上. Defaults to False.

        Returns:
            _type_: boolean
        """        
        point = point_maker(point)
        f = self.function()
        if allow_on_extended:
            return f(point.x) == point.y
        else:
            return f(point.x) == point.y and (
                (point.x >= min(self.point1.x, self.point2.x) and point.x <= max(self.point1.x, self.point2.x)))

    # 通过关键字`in`判断点是否在线段上
    def __contains__(self, point):
        return self.contains(point)

    # 该线段所在直线的纵截距
    def y_intercept(self):
        if self.point1.x == self.point2.x:
            return 0
        return ((self.point1.y * self.point2.x) \
            - (self.point1.x * self.point2.y)) \
                / (self.point2.x - self.point1.x) 

    # 该线段的斜率
    def slope(self):
        if self.point1.x - self.point2.x == 0:
            return float("inf")
        else:
            return (self.point1.y - self.point2.y) / (self.point1.x - self.point2.x)

    # 该线段所在直线的函数方程
    def function(self):
        a = self.slope()
        b = self.y_intercept()
        return lambda x: a * x + b
    
    # 该线段的函数式
    def equation(self):
        if self.point1.x - self.point2.x == 0:
            return "y = " + str(self.point1.y)
        else:
            a = self.slope()
            b = self.y_intercept()
            return f"y = {a}x{' + ' if b != 0 else ''}{b if b != 0 else ''}"

    # 该线段的长度
    def length(self):
        return (
            (self.point1.x - self.point2.x) ** 2 + (self.point1.y - self.point2.y) ** 2
        ) ** 0.5

    # 该线段与另一线段的交点
    def intersection(self, other):
        if isinstance(other, Line):
            if self.slope() == other.slope():
                return None
            else:
                x = (
                    self.slope() * other.point1.x
                    - self.point1.y
                    + other.slope() * self.point1.x
                    - other.point1.y
                ) / (self.slope() - other.slope())
                y = self.slope() * (x - self.point1.x) + self.point1.y
                return Point(x, y)
        else:
            raise ValueError("Invalid input for Line")


class Rectangle(Shape2D):
    def __init__(self, point1, point2):
        super(Rectangle, self).__init__()
        if isinstance(point1, Point) and isinstance(point2, Point):
            self.point1 = point1
            self.point2 = point2
        elif isinstance(point1, tuple) and isinstance(point2, tuple):
            self.point1 = Point(point1[0], point1[1])
            self.point2 = Point(point2[0], point2[1])
        else:
            raise ValueError("Invalid input for Rectangle")