Plot ellipse in Python using matplotlib
Published:
To plot ellipse in Python you can use the polar form of the ellipse which is
\[x = u + a cos(t) ; y = v + b sin(t)\]of the ellipse having center at (u,v):
\[\frac{(x-u)^2}{a^2} + \frac{(y-v)^2}{b^2} = 1\]First we define the x and y coordinates of the ellipse (curve), then, we plot all the points.
Example:
import numpy as np
from matplotlib import pyplot as plt
u=0 #abcissa of center
v=0 #ordinate of center
a=2 # major axis 2a
b=1 # minor axis 2b
t = np.linspace(0, 2*np.pi, 100)
plt.plot( u+a*np.cos(t) , v+b*np.sin(t) )
plt.grid()
plt.show()
Output:
You can also rotate the ellipse in the anticlocwise direction by multiplying the array of coordinates with the rotation matrix.
Example:
import numpy as np
from matplotlib import pyplot as plt
u=0 #abcissa of center
v=0 #ordinate of center
a=2 # major axis 2a
b=1 # minor axis 2b
t_rot=pi/4 #rotation angle
t = np.linspace(0, 2*np.pi, 100)
# Coordinates of the ellipse
Ell = np.array([a*np.cos(t) , b*np.sin(t)])
# Rotation matrix
R_rot = np.array([[np.cos(t_rot), -np.sin(t_rot)], [np.sin(t_rot), np.cos(t_rot)]])
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_rot[0,:] , v+Ell_rot[1,:])
plt.grid()
plt.show()
Output:
