我想生成一个Sierpinski Triangle的输出。我想知道如何使用二维点类中的midpt函数来实现这个输出？

Question

我必须使用二维点类和 tkinter 画布来生成 Sierpinski 三角形.midpt 函数本质上是要从随机选择的顶点和最后绘制的中点中获取输入。你可以选择任何顶点来绘制第一个中点。这些点也需要是二维点类的实例。我非常需要帮助，因为我似乎无法理解这个问题。下面是输出结果的样子。

这是我目前所做的，但它不是使用2d点类来生成三角形。

import math
from fractions import Fraction
from random import randrange
from Tkinter import *
# the 2D point class
class Point(object):
    def __init__(self, x=0, y=0):
        self.x = x
        self.y = y

    # Mutators and Accessors
    @property
    def x(self):
        return self._x

    @x.setter
    def x(self, value):
        self._x = value

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

    @y.setter
    def y(self, value):
        self._y = value

    # String function
    def __str__(self):
        floatX = float(str(self.x))
        floatY = float(str(self.y))
        return "({},{})".format(floatX, floatY)

    # Distance function
    def dist(self, other):
        distance = math.sqrt(((self.x - other.x)**2)+((self.y - other.y)**2))
        return "{}".format(distance)

    # Midpoint function
    def midpt(self, other):
        x0 = float(str(((self.x + other.x))))/2
        y0 = float(str(((self.y + other.y)/2)))
        return Point(x0, y0)

# the coordinate system class: (0,0) is in the top-left corner
# inherits from the Canvas class of Tkinter
class ChaosGame(Canvas):
    def __init__(self, master):
        Canvas.__init__(self, master, bg = "white")
        self.pack(fill = BOTH, expand = 1)

    def plotPoints(self, triangle, NumberPoints):
        x0, y0 = WIDTH / 2, HEIGHT / 2
        direction = center
        for i in range(NumberPoints):
            point = randrange(len(triangle))
            direction = triangle[point]
            x0 = (direction[0] + x0) / 2
            y0 = (direction[1] + y0) / 2
            color = direction[1]
            self.plot(x0, y0)
        self.plotV(5, 510)
        self.plotV(290, 5)
        self.plotV(590, 510)

    def plot(self, x, y):
        POINT_COLORS=["black"]
        RADIUS = 0
        color = POINT_COLORS
        self.create_oval(x, y, x+2, y+2, outline = color, fill = color)

    def plotV(self, x, y):
        POINT_COLORS=["red"]
        RADIUS = 3
        color = POINT_COLORS
        self.create_oval(x, y, x+RADIUS*2, y+RADIUS*2, outline = color, fill = color)

##########################################################
# ***DO NOT MODIFY OR REMOVE ANYTHING BELOW THIS POINT!***
# the default size of the canvas is 600x520
WIDTH = 600
HEIGHT = 520
# the number of points to plot
NumberPoints = 50000

# the vertices
A = (5, 510)
B = (290, 5)
C = (590, 510)
triangle = (A, B, C)
center = (WIDTH/2, HEIGHT/2)

# create the window
window = Tk()
window.geometry("{}x{}".format(WIDTH, HEIGHT))
window.title("2D Points...Plotted")
# create the chaos game as a Tkinter canvas inside the window
s = ChaosGame(window)
# plot some random points
s.plotPoints(triangle, NumberPoints)
# wait for the window to close
window.mainloop()

Answer 1

问题是你重复了基于点的代码。midpt() 在你的 plotPoints() 方法，但是对于元组而不是点。 由于三角形是以元组列表的形式交给我们的，我们将其转换为点的列表，并修改我们的 plot() 方法来接受一个Point，并运行整个 plotPoints() 法，以Points为单位。

from random import choice
from Tkinter import *

class Point(object):
    ''' a 2D point class '''

    def __init__(self, x=0, y=0):
        self.x = float(x)
        self.y = float(y)

    # Mutators and Accessors
    @property
    def x(self):
        return self._x

    @x.setter
    def x(self, value):
        self._x = float(value)

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

    @y.setter
    def y(self, value):
        self._y = float(value)

    # String function
    def __str__(self):
        return "({},{})".format(self.x, self.y)

    # Midpoint function
    def midpt(self, other):
        x0 = (self.x + other.x) / 2
        y0 = (self.y + other.y) / 2
        return Point(x0, y0)

class ChaosGame(Canvas):
    ''' Plotting class that inherits from Canvas class of Tkinter '''

    VERTEX_RADIUS = 3
    VERTEX_COLORS = ["red"]

    POINT_RADIUS = 1
    POINT_COLORS = ["black"]

    def __init__(self, master):
        Canvas.__init__(self, master, bg="white")
        self.pack(fill=BOTH, expand=1)

    def plotPoints(self, triangle, NumberPoints):
        point = Point(WIDTH / 2, HEIGHT / 2)

        deltoid = [Point(x, y) for x, y in triangle]  # tuples -> Points

        for _ in range(NumberPoints):
            point = point.midpt(choice(deltoid))
            self.plot(point)

        for vertex in deltoid:
            self.plotV(vertex)

    def plot(self, point):
        radius = self.POINT_RADIUS
        color = self.POINT_COLORS
        x, y = point.x, point.y

        self.create_oval(x, y, x + radius*2, y + radius*2, outline=color, fill=color)

    def plotV(self, vertex):
        radius = self.VERTEX_RADIUS
        color = self.VERTEX_COLORS
        x, y = vertex.x, vertex.y

        self.create_oval(x, y, x + radius*2, y + radius*2, outline=color, fill=color)

超越的东西。

##########################################################
# ***DO NOT MODIFY OR REMOVE ANYTHING BELOW THIS POINT!***

不在此赘述。 我还处理了你的Points方法中的一些怪癖，他们坚持把数字转换为字符串，再转换为数字，例如：。

x0 = float(str(((self.x + other.x))))/2

例如：

x0 = (self.x + other.x) / 2

而不是... self.x 拟做 float 当 Point 是创建。