User talk:Isaac Euler/sandbox/test3

Intro
 n-vector is a three parameter non-singular horizontal position representation well-suited for replacing latitude and longitude in mathematical calculations and computer algorithms. Geometrically, it is a unit vector normal to the reference ellipsoid. The vector is decomposed in an  Earth centered earth fixed coordinate system. It behaves the same at all Earth positions, and it holds the mathematical one-to-one property.

great circle distance
Finding the great circle distance between two horizontal positions (assuming spherical Earth) by means of latitude and longitude is done using one of three different expressions; the first is based on arccos, the second is based on  arcsin, and the final is based on  arctan. The three expressions are successively more complex to avoid numerical instabilities, are not easy to find, and since they are based on latitude and longitude, the Pole singularities may become a problem. They also contain deltas of latitude and longitude, which should be used with care near the ±180° meridian and Poles. demo (talk) 08:17, 17 June 2010 (UTC)