# 2D-kromme

import numpy as np

def my_arsinh (x):
 y = np.log (x + np.sqrt (x**2 + 1))
 return y

J = 2.5
Rs = 1

h1 = 1 - 3 * Rs**2 / J**2
h2 = np.sqrt (h1)
h3 = np.sqrt (h2)

n2 = (1 + h2) / (3 * Rs)

rbegin = 0.999999 / n2
reinde = 0.999999999
aantalstappen = 4 * 10**8
stap = (reinde - rbegin) / aantalstappen

phi0 = my_arsinh (1)
r = rbegin - stap

while r > reinde:

 r = r + stap
 phi = 2 / h3 * (phi0 - my_arsinh (h3 / np.sqrt (Rs / r - 1 / 3 - h2 / 3)))
 x = r * np.cos (phi)
 y = r * np.sin (phi)

 print ('{:10.5e}'.format (x), '{:10.5e}'.format (y))