Plot Ellipse with matplotlib.pyplot (Python)

The matplotlib ellipse demo is nice. But I could not implement it in my code without a for loop. I was getting an axes figure error. Here is what I did instead, where of course the xy center are my own coordinates with respective width and height based on the image over which I plotted the ellipse.

from matplotlib.patches import Ellipse

plt.figure()
ax = plt.gca()

ellipse = Ellipse(xy=(157.18, 68.4705), width=0.036, height=0.012, 
                        edgecolor='r', fc='None', lw=2)
ax.add_patch(ellipse)

This code is based partially on the very first code box on this page. See Chris's response above for a link to matplotlib.patches.Ellipse.

Have you seen the matplotlib ellipse demo? Here they use matplotlib.patches.Ellipse.

If you do not want to use a patch, you can use the parametric equation of an ellipse:

x = u + a cos(t) ; y = v + b sin(t)

import numpy as np
from matplotlib import pyplot as plt
from math import pi

u=1.     #x-position of the center
v=0.5    #y-position of the center
a=2.     #radius on the x-axis
b=1.5    #radius on the y-axis

t = np.linspace(0, 2*pi, 100)
plt.plot( u+a*np.cos(t) , v+b*np.sin(t) )
plt.grid(color='lightgray',linestyle='--')
plt.show()

Which gives:

The ellipse can be rotated thanks to a 2D-rotation matrix :

import numpy as np
from matplotlib import pyplot as plt
from math import pi, cos, sin

u=1.       #x-position of the center
v=0.5      #y-position of the center
a=2.       #radius on the x-axis
b=1.5      #radius on the y-axis
t_rot=pi/4 #rotation angle

t = np.linspace(0, 2*pi, 100)
Ell = np.array([a*np.cos(t) , b*np.sin(t)])  
     #u,v removed to keep the same center location
R_rot = np.array([[cos(t_rot) , -sin(t_rot)],[sin(t_rot) , cos(t_rot)]])  
     #2-D rotation matrix

Ell_rot = np.zeros((2,Ell.shape[1]))
for i in range(Ell.shape[1]):
    Ell_rot[:,i] = np.dot(R_rot,Ell[:,i])

plt.plot( u+Ell[0,:] , v+Ell[1,:] )     #initial ellipse
plt.plot( u+Ell_rot[0,:] , v+Ell_rot[1,:],'darkorange' )    #rotated ellipse
plt.grid(color='lightgray',linestyle='--')
plt.show()

Returns: