本节书摘来自异步社区《Python极客项目编程 》一书中的第2章，第2.4节，作者 [美] Mahesh Venkitachalam，王海鹏 译，更多章节内容可以访问云栖社区“异步社区”公众号查看。

2.4　完整代码

下面是完整的万花尺程序。也可以从https://github.com/electronut/pp/blob/master/ spirograph/spiro.py 下载该项目的代码。

import sys, random, argparse

import numpy as np

import math

import turtle

import random

from PIL import Image

from datetime import datetime

from fractions import gcd

# a class that draws a Spirograph

class Spiro:

# constructor

def __init__(self, xc, yc, col, R, r, l):

# create the turtle object

self.t = turtle.Turtle()

# set the cursor shape

self.t.shape('turtle')

# set the step in degrees

self.step = 5

# set the drawing complete flag

self.drawingComplete = False

# set the parameters

self.setparams(xc, yc, col, R, r, l)

# initialize the drawing

self.restart()

# set the parameters

def setparams(self, xc, yc, col, R, r, l):

# the Spirograph parameters

self.xc = xc

self.yc = yc

self.R = int(R)

self.r = int(r)

self.l = l

self.col = col

# reduce r/R to its smallest form by dividing with the GCD

gcdVal = gcd(self.r, self.R)

self.nRot = self.r//gcdVal

# get ratio of radii

self.k = r/float(R)

# set the color

self.t.color(*col)

# store the current angle

self.a = 0

# restart the drawing

def restart(self):

# set the flag

self.drawingComplete = False

# show the turtle

self.t.showturtle()

# go to the first point

self.t.up()

R, k, l = self.R, self.k, self.l

a = 0.0

x = R*((1-k)*math.cos(a) + l*k*math.cos((1-k)*a/k))

y = R*((1-k)*math.sin(a) - l*k*math.sin((1-k)*a/k))

self.t.setpos(self.xc + x, self.yc + y)

self.t.down()

# draw the whole thing

def draw(self):

# draw the rest of the points

R, k, l = self.R, self.k, self.l

for i in range(0, 360*self.nRot + 1, self.step):

a = math.radians(i)

x = R*((1-k)*math.cos(a) + l*k*math.cos((1-k)*a/k))

y = R*((1-k)*math.sin(a) - l*k*math.sin((1-k)*a/k))

self.t.setpos(self.xc + x, self.yc + y)

# drawing is now done so hide the turtle cursor

self.t.hideturtle()

# update by one step

def update(self):

# skip the rest of the steps if done

if self.drawingComplete:

return

# increment the angle

self.a += self.step

# draw a step

R, k, l = self.R, self.k, self.l

# set the angle

a = math.radians(self.a)

x = self.R*((1-k)*math.cos(a) + l*k*math.cos((1-k)*a/k))

y = self.R*((1-k)*math.sin(a) - l*k*math.sin((1-k)*a/k))

self.t.setpos(self.xc + x, self.yc + y)

# if drawing is complete, set the flag

if self.a >= 360*self.nRot:

self.drawingComplete = True

# drawing is now done so hide the turtle cursor

self.t.hideturtle()

# clear everything

def clear(self):

self.t.clear()

# a class for animating Spirographs

class SpiroAnimator:

# constructor

def __init__(self, N):

# set the timer value in milliseconds

self.deltaT = 10

# get the window dimensions

self.width = turtle.window_width()

self.height = turtle.window_height()

# create the Spiro objects

self.spiros = []

for i in range(N):

# generate random parameters

rparams = self.genRandomParams()

# set the spiro parameters

spiro = Spiro(*rparams)

self.spiros.append(spiro)

# call timer

turtle.ontimer(self.update, self.deltaT)

# restart spiro drawing

def restart(self):

for spiro in self.spiros:

# clear

spiro.clear()

# generate random parameters

rparams = self.genRandomParams()

# set the spiro parameters

spiro.setparams(*rparams)

# restart drawing

spiro.restart()

# generate random parameters

def genRandomParams(self):

width, height = self.width, self.height

R = random.randint(50, min(width, height)//2)

r = random.randint(10, 9*R//10)

l = random.uniform(0.1, 0.9)

xc = random.randint(-width//2, width//2)

yc = random.randint(-height//2, height//2)

col = (random.random(),

random.random(),

random.random())

return (xc, yc, col, R, r, l)

def update(self):

# update all spiros

nComplete = 0

for spiro in self.spiros:

# update

spiro.update()

# count completed spiros

if spiro.drawingComplete:

nComplete += 1

# restart if all spiros are complete

if nComplete == len(self.spiros):

self.restart()

# call the timer

turtle.ontimer(self.update, self.deltaT)

# toggle turtle cursor on and off

def toggleTurtles(self):

for spiro in self.spiros:

if spiro.t.isvisible():

spiro.t.hideturtle()

else:

spiro.t.showturtle()

# save drawings as PNG files

def saveDrawing():

# hide the turtle cursor

turtle.hideturtle()

# generate unique filenames

dateStr = (datetime.now()).strftime("%d%b%Y-%H%M%S")

fileName = 'spiro-' + dateStr

print('saving drawing to %s.eps/png' % fileName)

# get the tkinter canvas

canvas = turtle.getcanvas()

# save the drawing as a postscipt image

canvas.postscript(file = fileName + '.eps')

# use the Pillow module to convert the poscript image file to PNG

img = Image.open(fileName + '.eps')

img.save(fileName + '.png', 'png')

# show the turtle cursor

turtle.showturtle()

# main() function

def main():

# use sys.argv if needed

print('generating spirograph...')

# create parser

descStr = """This program draws Spirographs using the Turtle module.

When run with no arguments, this program draws random Spirographs.

Terminology:

R: radius of outer circle

r: radius of inner circle

l: ratio of hole distance to r

"""

parser = argparse.ArgumentParser(description=descStr)

# add expected arguments

parser.add_argument('--sparams', nargs=3, dest='sparams', required=False,

help="The three arguments in sparams: R, r, l.")

# parse args

args = parser.parse_args()

# set the width of the drawing window to 80 percent of the screen width

turtle.setup(width=0.8)

# set the cursor shape to turtle

turtle.shape('turtle')

# set the title to Spirographs!

turtle.title("Spirographs!")

# add the key handler to save our drawings

turtle.onkey(saveDrawing, "s")

# start listening

turtle.listen()

# hide the main turtle cursor

turtle.hideturtle()

# check for any arguments sent to --sparams and draw the Spirograph

if args.sparams:

params = [float(x) for x in args.sparams]

# draw the Spirograph with the given parameters

col = (0.0, 0.0, 0.0)

spiro = Spiro(0, 0, col, *params)

spiro.draw()

else:

# create the animator object

spiroAnim = SpiroAnimator(4)

# add a key handler to toggle the turtle cursor

turtle.onkey(spiroAnim.toggleTurtles, "t")

# add a key handler to restart the animation

turtle.onkey(spiroAnim.restart, "space")

# start the turtle main loop

turtle.mainloop()

# call main

if __name__ == '__main__':

main()