One of my projects required conversion of Earth Centered Earth Fixed coordinates to geodetic latitude, longitude and height (and vice versa). I couldn’t find any native Python libraries, so I decided to create a simple library called pycoordconvert. I decided this was a good opportunity to learn more about Cython.

I created two versions of the code. One with Python and one with Cython extensions. This is the Python version of the code. It uses the built-in Python math libraries and does not use any explicitly declared types.

from math import atan2, sqrt, cos, sin, degrees, radians

earth_radius = 6378.1*1000
a = 6378137
e2 = 6.6943799901E-3

def normal(lat_radians):
    return a/(sqrt(1-e2*pow(sin(lat_radians),2)))

def geodetic_to_ecef(lon,lat,h):
    lon = radians(lon)
    lat = radians(lat)

    x = (normal(lat)+h)*cos(lon)*cos(lat)
    y = (normal(lat)+h)*cos(lon)*sin(lat)
    z = (normal(lat)*(1-e2)+h)*sin(lat)

    return x,y,z

This is the equivalent code in Cython. It uses the C math libraries and static typing.

cdef extern from "math.h":
    double cos(double theta)
    double sin(double theta)
    double acos(double theta)
    double sqrt(double theta)
    double atan2(double y,double x)
    double pow(double x,double y)

cdef double earth_radius = 6378.1*1000
cdef double a = 6378137
cdef double e2 = 6.6943799901E-3
cdef double pi = 3.141592653589793
cdef double degrees_per_radian = 57.2957795
cdef double radians_per_degree = 0.0174532925

cdef double degrees(double theta):
    return degrees_per_radian*theta

cdef double radians(double theta):
    return radians_per_degree*theta

cdef double normal(lat_radians):
    return a/(sqrt(1-e2*pow(sin(lat_radians),2)))

cdef object geodetic_to_ecef(lon,lat,h):
    cdef double lon_rads,lat_rads,x,y,z
    lon_rads = radians(lon)
    lat_rads = radians(lat)

    x = (normal(lat_rads)+h)*cos(lon_rads)*cos(lat_rads)
    y = (normal(lat_rads)+h)*cos(lon_rads)*sin(lat_rads)
    z = (normal(lat_rads)*(1-e2)+h)*sin(lat_rads)

    return (x,y,z)

The reverse transforms can be found in the pycoordconvert repository.

The following setup file enables building of the Cython module.

from distutils.core import setup
from distutils.extension import Extension
from Cython.Distutils import build_ext

    cmdclass = {'build_ext': build_ext},
    ext_modules = [Extension("cython_coordconvert", ["cython_coordconvert.pyx"])]

Build the extensions using the command python build_ext --inplace. A quick comparison of the two approaches shows a significant speedup for a small amount of work.

The ECEF to Geodetic ran in 4.41 usec/pass in Cython and 39.81 in CPython for 9x speedup. The Geodetic to ECEF ran in 1.01 usec/pass in Cython and 4.84 for CPython for a 4.8x speedup.

Overall my first experience with Cython was favorable. It was a lot easier than writing native C code and provided a huge performance improvement.