Python Turtle Graphics，如何在一定间隔内绘制函数？

Question

I need to plot a function over a specified interval. The function is f1, which is shown below in the code, and the interval is [-7, -3]; [-1, 1]; [3, 7] with a step of .01. When I execute the program, nothing is drawn. Any ideas?

import turtle
from math import sqrt

wn = turtle.Screen()
wn.bgcolor("white")
wn.title("Plotting")
mypen = turtle.Turtle()
mypen.shape("classic")
mypen.color("black")
mypen.speed(10)

while True:
try:
    def f1(x):
        return 2 * sqrt((-abs(abs(x)-1)) * abs(3 - abs(x))/((abs(x)-1)*(3-abs(x)))) * \
(1 + abs(abs(x)-3)/(abs(x)-3))*sqrt(1-(x/7)**2)+(5+0.97*(abs(x-0.5)+abs(x+0.5))-\
3*(abs(x-0.75)+abs(x+0.75)))*(1+abs(1-abs(x))/(1-abs(x)))

    mypen.penup()

    step=.01
    startf11=-7
    stopf11=-3
    startf12=-1
    stopf12=1
    startf13=3
    stopf13=7
    def f11 (startf11,stopf11,step):
        rc=[]
        y = f1(startf11)
        while y<=stopf11:
            rc.append(startf11)
            #y+=step
            mypen.setpos(f1(startf11)*25,y*25)
            mypen.dot()
    def f12 (startf12,stopf12,step):
        rc=[]
        y = f1(startf12)
        while y<=stopf12:
            rc.append(startf12)
            #y+=step
            mypen.setpos(f1(startf12)*25, y*25)
            mypen.dot()
    def f13 (startf13,stopf13,step):
        rc=[]
        y = f1(startf13)
        while y<=stopf13:
            rc.append(startf13)
            #y+=step
            mypen.setpos(f1(startf13)*25, y*25)
            mypen.dot()

    f11(startf11,stopf11,step)
    f12(startf12,stopf12,step)
    f13(startf13,stopf13,step)

except ZeroDivisionError:
    continue

Answer 1

I think because f1 returns an imaginary value. I literally just started learning python like 15 minutes ago and i'm starting with the turtle. So i might not completely understand and be off...but in general i understand code...

But yeah when you defined it; this bit; your second term.

sqrt((-abs(abs(x)-1))

you're trying to get the squareroot of a negative number. That's not on the cartesian plane. No idea how math interprets that and no idea how turtle interprets it either but that's my first guess...

Answer 2

You're trying to plot a buggy function using buggy plotting code. You need to debug them separately, not together. Let's start with the function. If we look at the starts of the three intervals in question, -7, -1, and 3 and call f1() on them, we get:

-7 -> 0.0
-1 -> division by zero
 3 -> division by zero

In the first, ploting never starts as f1(startf11) is > stopf11 aka -3 before the loop begins:

y = f1(startf11)
while y <= stopf11:

In the other two cases, there is no y due to the divide by zero as the

except ZeroDivisionError:
    continue

doesn't fix that problem. So no plots. Which probably doesn't matter as the plotting code itself doesn't work. All three f1* functions (which are identical BTW which makes no sense) do:

while y <= stop:

but y never changes so it's an infinite loop. The commented out y += step would help, but in a different position in the code. Also, it attempts to plot 100 values for every individual screen pixel! That can be accomodated by changing the coordinate system but I won't go into that here, just reduce this to 10 values for every screen pixel to speed up the result.

Let's start over with the plotting code using a simpler test function:

def f1(x):
    return x

And get that to plot that successfully. Here's my rework of the plotting code:

from turtle import Turtle, Screen

def f1(x):
    return x  # dummy test plot

wn = Screen()

mypen = Turtle(visible=False)
mypen.speed('fastest')
mypen.penup()

def f11(start, stop, step):

    y = f1(start)

    while y <= stop:

        try:
            mypen.setpos(f1(start) * 25, y * 25)
            mypen.dot()
            y += step

        except ZeroDivisionError:
            continue

step = 0.1  # increased from 0.01 for debugging/speed

startf11 = -7
stopf11 = -3

f11(startf11, stopf11, step)

startf12 = -1
stopf12 = 1

f11(startf12, stopf12, step)

startf13 = 3
stopf13 = 7

f11(startf13, stopf13, step)

wn.exitonclick()

Which gives us the test result:

Which seems reasonable for our test function. Now you're in a postion to change the coordinate system for a higher resolution plot and/or debug your f1() function using a working plotter.