# 2D-kromme

import numpy as np

ubegin = 0.000000001
ueinde = 1.000000001
aantalstappen = 1000000
stap = (ueinde - ubegin) / aantalstappen

nulpunt = 0.646027717321562
ibegin = nulpunt - 0.02
ieinde = nulpunt + 0.02

phi0 = 0
E = 2.0117769801886
J = 5
K = E
U = 1 - K**2

a = 1
b = -1
c = 1 / J**2
d = - U / J**2

u = ubegin
fu = 1 / np.sqrt (a * u**3 + b * u**2 + c * u + d)
phi = phi0

while u < ueinde:

 if u > ibegin:

  stap = stap / 1000
  ibegin = 2 * ueinde

 if u > ieinde:

  stap = stap * 1000
  ieinde = 2 * ueinde

 u = u + stap

 fuprev = fu
 fu = 1 / np.sqrt (a * u**3 + b * u**2 + c * u + d)
 phi = phi + (fuprev + fu) * stap / 2
 r = 1 / u
 x = r * np.cos (phi)
 y = r * np.sin (phi)

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