Ellipse

python code

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

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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

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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

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

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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()