COMPUTATION ON THE ELLIPSOID
Before proceeding with the computation of ellipsoidal coordinates, it is necessary to consider certain aspects of direction. In plane surveying, for instance, the direction of BA differs from that of AB by exactly 180◦.
where α is the additional correction due to the convergence of the meridians AP and BP. Using the corrected ellipsoidal azimuths and distances, the coordinates are now calculated relative to a selected point of origin.
The basic problems are known as the ‘direct’ and ‘reverse’ problems and are analogous to computing the ‘polar’ and ‘join’ in plane surveying. The simplest computing routine is one that involves ‘mid-latitude’ formulae.
The mid-latitude formulae are generally expressed as:
The above formulae are accurate to 1 ppm for lines up to 100 km in length.