在Python中用变量Theta绘制函数

Question

I'm new to Python, and especially new to plotting graphs using matplotlib. I'm working on an assignment where we have to plot spirographs on a cartesian coordinate system with equations for x and y:

x = (R + r) * math.cos(theta) - d * math.cos((R+r)*theta/r)
y = (R + r) * math.sin(theta) - d * math.sin((R+r)*theta/r)

where we are given the values of R, r, and d.

This produces an error because the variable theta isn't defined. I've seen ways of defining theta using numPy, but we aren't allowed to use that particular library for this assignment. What would be the best way of plotting the spirographs for 0 < theta < 2pi?

Thanks in advance!

Answer 1

If you cannot use numpy, you cannot use matplotlib; because numpy is a dependency of matplotlib. So I'd suggest to solve your problem in the following way:

Prepend a sentence to your solution saying "Because numpy is a dependency of matplotlib, it's technically impossible to solve this task without using numpy. Since I do not want this restriction to prevent me from solving the task, I simply assume that I can use numpy here."

Then go on with the canonical solution,

import matplotlib.pyplot as plt
import numpy as np

theta = np.linspace(0,2*np.pi,301)
R = 8
r = 1
d = 3

x = (R + r) * np.cos(theta) - d * np.cos((R+r)*theta/r)
y = (R + r) * np.sin(theta) - d * np.sin((R+r)*theta/r)

plt.plot(x,y)
plt.axis("equal")
plt.show()

Answer 2

If you can't use numpy, you can do it with functions and loops :

import math
import matplotlib.pyplot as plt

def X(theta,R,r,d) : 
    return (R + r) * math.cos(theta) - d * math.cos((R+r)*theta/r)

def Y(theta,R,r,d) : 
    return (R + r) * math.sin(theta) - d * math.sin((R+r)*theta/r)

nbSamples=100
theta=[]
for i in range (nbSamples) : 
    theta.append(i/(nbSamples-1)*2*math.pi)


x=[]
y=[]    

R=8
r=1
d=3
for th in theta:

    x.append(X(th,R,r,d))
    y.append(Y(th,R,r,d))

plt.plot(x,y)
plt.axis("equal")
plt.show()