At my work, I've been doing some maintenance on internal software that claims to implement a Stereographic projection whose formulas were copied from an old system a long time ago.
From what I've seen, it seems to implement the "Oblique and Equatorial Stereographic" from EPSG (code 9809). But there is one step that I was not able to identify. The "R" value used in our code is calculated with the following parameters:
(phi_n, lambda_n) - null distortion coordinates (PHI_nc, LAMBDA_nc) - conformal null distortion coordinates (PHI_o, LAMBDA_o) - conformal projection origin coordinates e - eccenttricity r_eq - earth radius at equator
Given this, the formula to get R is:
a = 1 + cos(PHI_nc) * cos(PHI_o) * cos(LAMBDA_nc - LAMBA_o) b = sin(PHI_nc) * sin(PHI_o) c = 2 * cos(PHI_nc) * [1 - (sin(phi_n) * e/2) ^ 2] ^ 1/2 R = r_eq * cos(phi_n) * (a + b) / c
Does anyone know what is going on here? I've been searching and reading about stereographic projections, but I wasn't able to find anything like that. In fact, I've not seen any projections that use this "null distortion coordinate."