#!/usr/bin/python3

import numpy as np
import matplotlib.pyplot as plt

def x(rho, phi):
    return rho*np.cos(phi)

def y(rho, phi):
    return rho*np.sin(phi)

a = 2
v = 1

t = np.linspace(0, a/v, 1000000)
rho = a/np.sqrt(2) - v*t/np.sqrt(2)
phi = np.log(a/(a - v*t))

fig, ax = plt.subplots()

for phi0 in (np.pi/2)*np.linspace(1, 4, 4) + np.pi/4:
    ax.plot(x(rho, phi0+phi), y(rho, phi0+phi))

ax.set_aspect('equal')
plt.show()
# fig.savefig('z5.pdf')
plt.close(fig)