The following code applies the
Jukowsi transformation to various circles on the complex plane.
from pylab import plot,show,axis,subplot
import cmath
from numpy import *
def cplxcircm(radius,center):
"""Returns an array z where every z[i] is a point
on the circle's circumference on the complex plane"""
teta = linspace(0,pi*2,150)
z = []
for a in teta:
# rotating of radius+0j of a radians and translation
zc = (radius+0j)*cmath.exp(complex(0,a)) - center
z.append(zc)
return array( z, dtype=complex )
def jukowsi(z,L):
return z+L/z # asimmetric Jukowski transformation
# let's try the transformation on three different circles
subplot(131)
z = cplxcircm(1,complex(0.5,0)) #1st circle
w = jukowsi(z,1) # applying the trasformation
plot(real(z),imag(z),'b',real(w),imag(w),'r')
axis('equal')
subplot(132)
z = cplxcircm(0.8,complex(0.4,0.3))
w = jukowsi(z,0.188)
plot(real(z),imag(z),'b',real(w),imag(w),'r')
axis('equal')
subplot(133)
z = cplxcircm(1.1,complex(0.1,0.0))
w = jukowsi(z,1)
plot(real(z),imag(z),'b',real(w),imag(w),'r')
axis('equal')
show()
The script shows the following figure. Every subplot shows two curves on the complex plane (x real values, y imaginary values), the blue curve is the starting curve and the red is the transformation.
