Animated reconstruction of a random ellipse from fourier coefficients

fourier-ellipse.py

# 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()