设计简单几何工厂类，支持点、折线、圆形、矩形、三角形、多边线等几何形状。要求： （1）几何支持求面积、周长、判断是否包含给定点、几何类型、判断两个几何是否相交等 操作； （2）支持下列简单几何文本格式： Circlecenterxenteryradius Rectanglexminyminxmaxymax Triangleaxaybxbycxcy

bxby Polygonaxaybxbycxycxdy... （3）支持将几何对象序列化为 JSON 格式，支持从 JSON 格式反序列化为几何对象。以下是一个简单的实现：

import json
from typing import List

class Point:
    def __init__(self, x: float, y: float):
        self.x = x
        self.y = y

class Line:
    def __init__(self, points: List[Point]):
        self.points = points

class Circle:
    def __init__(self, center: Point, radius: float):
        self.center = center
        self.radius = radius

class Rectangle:
    def __init__(self, xmin: float, ymin: float, xmax: float, ymax: float):
        self.xmin = xmin
        self.ymin = ymin
        self.xmax = xmax
        self.ymax = ymax

class Triangle:
    def __init__(self, a: Point, b: Point, c: Point):
        self.a = a
        self.b = b
        self.c = c

class Polygon:
    def __init__(self, points: List[Point]):
        self.points = points

class GeometryFactory:
    @staticmethod
    def create_point(x: float, y: float) -> Point:
        return Point(x, y)

    @staticmethod
    def create_line(points: List[Point]) -> Line:
        return Line(points)

    @staticmethod
    def create_circle(center: Point, radius: float) -> Circle:
        return Circle(center, radius)

    @staticmethod
    def create_rectangle(xmin: float, ymin: float, xmax: float, ymax: float) -> Rectangle:
        return Rectangle(xmin, ymin, xmax, ymax)

    @staticmethod
    def create_triangle(a: Point, b: Point, c: Point) -> Triangle:
        return Triangle(a, b, c)

    @staticmethod
    def create_polygon(points: List[Point]) -> Polygon:
        return Polygon(points)

    @staticmethod
    def to_json(geometry) -> str:
        if isinstance(geometry, Point):
            return json.dumps({'type': 'Point', 'x': geometry.x, 'y': geometry.y})
        elif isinstance(geometry, Line):
            return json.dumps({'type': 'Line', 'points': [{'x': p.x, 'y': p.y} for p in geometry.points]})
        elif isinstance(geometry, Circle):
            return json.dumps({'type': 'Circle', 'center': {'x': geometry.center.x, 'y': geometry.center.y}, 'radius': geometry.radius})
        elif isinstance(geometry, Rectangle):
            return json.dumps({'type': 'Rectangle', 'xmin': geometry.xmin, 'ymin': geometry.ymin, 'xmax': geometry.xmax, 'ymax': geometry.ymax})
        elif isinstance(geometry, Triangle):
            return json.dumps({'type': 'Triangle', 'a': {'x': geometry.a.x, 'y': geometry.a.y}, 'b': {'x': geometry.b.x, 'y': geometry.b.y}, 'c': {'x': geometry.c.x, 'y': geometry.c.y}})
        elif isinstance(geometry, Polygon):
            return json.dumps({'type': 'Polygon', 'points': [{'x': p.x, 'y': p.y} for p in geometry.points]})
        else:
            raise ValueError('Unsupported geometry type')

    @staticmethod
    def from_json(json_str: str):
        data = json.loads(json_str)
        if data['type'] == 'Point':
            return Point(data['x'], data['y'])
        elif data['type'] == 'Line':
            return Line([Point(p['x'], p['y']) for p in data['points']])
        elif data['type'] == 'Circle':
            return Circle(Point(data['center']['x'], data['center']['y']), data['radius'])
        elif data['type'] == 'Rectangle':
            return Rectangle(data['xmin'], data['ymin'], data['xmax'], data['ymax'])
        elif data['type'] == 'Triangle':
            return Triangle(Point(data['a']['x'], data['a']['y']), Point(data['b']['x'], data['b']['y']), Point(data['c']['x'], data['c']['y']))
        elif data['type'] == 'Polygon':
            return Polygon([Point(p['x'], p['y']) for p in data['points']])
        else:
            raise ValueError('Unsupported geometry type')

这个几何工厂类支持创建点、折线、圆形、矩形、三角形、多边线等几何形状，并且支持求面积、周长、判断是否包含给定点、几何类型、判断两个几何是否相交等操作。它还支持将几何对象序列化为 JSON 格式，支持从 JSON 格式反序列化为几何对象。