#!/usr/bin/env python

from math import sin, cos, pi
from math import asin, atan2

def normcross (v1, v2):
   l = [v1[1] * v2[2] - v1[2] * v2[1],
        v1[2] * v2[0] - v1[0] * v2[2],
        v1[0] * v2[1] - v1[1] * v2[0]]
   length = (l[0]*l[0]+l[1]*l[1]+l[2]*l[2])**0.5
   return (l[0] / length, l[1] / length, l[2] / length)


def co2vec (lat, lon):
   la = lat / 180. * pi
   lo = lon / 180. * pi

   x = cos (lo) * cos (la)
   y = sin (lo) * cos (la)
   z = sin (la)

   return (x, y, z)


def vec2co (v1):
   return (asin (v1[2]) / pi * 180, atan2 (v1[1], v1[0]) / pi * 180)

if __name__ == '__main__':
   london = co2vec (51.505617, -0.075252) # Tower Bridge
   prag   = co2vec (50.087217, 14.406869) # Karlsbruecke

   paris  = co2vec (48.846919,2.33718)    # Jardin du Luxembourg
   paris  = co2vec (48.858285, 2.294469)  # Eiffelturm

   berlin = co2vec (52.520765, 13.409457) # Alex
   berlin = co2vec (52.481761, 13.390274) # Tempelhof
   berlin = co2vec (52.516221, 13.37785)  # Brandenburger Tor

   c1 = normcross (london, prag)
   c2 = normcross (paris, berlin)

   c3 = normcross (c1, c2)

   print "%6f N, %6f E" % vec2co (c3)