The Geocentric Mercator Projection: A Fast and Accurate Approximation of the Ellipsoidal Mercator Projection

The spherical Mercator projection on geocentric latitudes is orders of magnitude closer to the ellipsoidal Mercator projection compared to the spherical Mercator projection on geographic latitudes (aka Web Mercator), which is often found in software applications (e.g. Google Maps and Bing Maps). For the WGS 84 ellipsoid, the maximum deviation of courses decreases from 6' (arc minutes) to 0.6" (arc seconds), and the maximum deviation between spherical and ellipsoidal Mercator coordinates decreases from over 21 km to under 16 m. Since the computational cost and formula complexity increase only slightly, this map projection can be used almost anywhere where the simplicity of the spherical Mercator projection is preferred over the ellipsoidal one.