According to this source, an optimal projection for small, roughly square areas is the stereographic projection. The wikipedia page of the stereographic projection shows how to convert from spherical coordinates to polar or xy coordinates. However, I would like to convert WGS84 data (latitude and longitude) to xy coordinates and WGS84 uses an ellipsoidal model of Earth instead of a sphere.
My questions is:
What are the formulae for a stereographic projection on an ellipsoid centred at
lat0,lon0 (point tangent to the plane) projected from the antipode of
1) What is the inverse transformation?
2) Is this projection still conformal?
I have read section 18.104.22.168 of the Geomatics Guidance Note 7, part 2 "Coordinate Conversions & Transformations including Formulas" (March 2019) and while I believe it may contain the answers to questions (1) and (3), I'm not sure what does it mean by "For the ellipsoid the parameters defining the conformal sphere at the tangent point as origin are first derived". Does it first compute the parameters for a sphere tangent to
lat0,lon0? Then uses the antipode of
lat0,lon0 in that sphere instead of the ellipsoid? If so, why does it do it that way? To preserve conformality? If this is true then would there be any advantage in projecting stereographically from the antipode on the ellipsoid instead of projecting from the antipode in the conformal sphere?