Bringing fourier transforms to life

This script animates the reconstruction of a random ellipse from its fourier coefficients. It is a lot of fun to watch the reconstruction, especially for large aspect ratio ellipses.

	# Fourier reconstruction of random ellipse
	# Amar Vutha
	# 2014-04-03
	import pylab as plt
	import numpy as np
	from numpy import pi
	import matplotlib.pyplot as plt
	import matplotlib.animation as animation
	# Generate random ellipse
	t = np.arange(0,2*pi,1e-4)
	r = np.zeros(len(t))
	a,b = np.random.random(), np.random.random()
	theta = t.copy()
	r = a*b/np.sqrt( ( a*np.sin(theta) )**2 + ( b*np.cos(theta) )**2 )
	fig = plt.figure()
	ax = plt.subplot(111,polar=True)
	ax.set_rlim(0,1)
	ax.plot(theta,r,'r--',lw=3,alpha=0.5)
	line, = ax.plot(theta,r,lw=2)
	linebg, = ax.plot(theta,np.ones(len(theta)),'g--',lw=3,alpha=0.2)
	### Fourier transform #####
	phi = t.copy()
	Nmax = 20
	A,B = [],[]
	dp = phi[1] - phi[0]
	A_DC = np.sum(r) * dp/(2*pi)
	A,B = np.zeros( (Nmax) ), np.zeros( (Nmax) )
	for n in range(1,Nmax):
	A[n] = np.sum(r*np.cos(n*phi)) * dp/pi
	B[n] = np.sum(r*np.sin(n*phi)) * dp/pi
	### Reconstruction ######
	def reconstruct(M):
	R = A_DC
	for m in range(1,M):
	R += A[m]* np.cos(m*phi) + B[m]* np.sin(m*phi)
	return R
	def animate(i):
	line.set_ydata(reconstruct(i)) # update the data
	linebg.set_ydata(np.cos(i*theta)) # shows the shape corresponding to the fourier coefficient
	return (line,) + (linebg,)
	#Init only required for blitting to give a clean slate.
	def init():
	line.set_ydata(np.ma.array(phi, mask=True))
	linebg.set_ydata(np.ma.array(phi, mask=True))
	return (line,) + (linebg,)
	ani = animation.FuncAnimation(fig, animate, np.arange(1, Nmax), init_func=init,
	interval=500, blit=True)
	plt.show()

view raw fourier-ellipse.py hosted with ❤ by GitHub