我正在尝试生成Sierpinski Triangle的输出。我想知道如何在2d点类中使用midpt函数来实现此输出？

由 ueaque发布于 2020-05-24 09:16:56

I have to generate the Sierpinski Triangle using a 2d point class and tkinter canvas.The midpt function is essentially going to take input from a randomly chosen vertex and the last plotted midpoint. You can choose any vertices to plot the first midpoint. The points also need to be instances of the 2d point class. I desperately need help because I can't seem to figure this out. Here is what the output is supposed to look like.

到目前为止，这是我所做的，但是并未使用2d点类生成三角形。

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()

x呆子x

2020-05-24 09:16:57

我几天前收到了这个答案，但仍然不确定它是否在2d点类中使用midpt函数来绘制点以生成Sierpinski三角形。

import math
from random import choice
from Tkinter import *         

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):
        return "({},{})".format(float(self.x), float(self.y))

    # Distance Function
    def dist(self, other):    
        return math.sqrt(((self.x - other.x)**2) + ((self.y - other.y)**2))

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

    def __iter__(self):   
        yield self.x
        yield self.y

# the Chaos Game 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=True)

    # Plots the vertices and midpoints
    def plotPoints(self, triangle, NumberPoints):
        for point in triangle:
            self.plot(point, color='red', r=3)

        direction = center
        for i in range(NumberPoints):
            chosen_vertex = choice(triangle)   
            point_to_plot = chosen_vertex.midpoint(direction)   
            self.plot(point_to_plot)
            direction = point_to_plot

    def plot(self, point, color="black", r=1):
        x, y = point
        self.create_oval(x-r, y-r, x+r, y+r, 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 = Point(5, 510)       
B = Point(290, 5)
C = Point(590, 510)
triangle = (A, B, C)
center = Point(WIDTH/2, HEIGHT/2)

# create the window
window = Tk()
window.geometry("{}x{}".format(WIDTH, HEIGHT))
window.title("The Chaos Game")
# 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()

ueaque

这家伙很懒，什么都没留下

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