EPSG:9839

Note: These formulas have been transcribed from EPSG Guidance Note #7-2. Users are encouraged to use that document rather than the text which follows as reference because limitations in the transcription will be avoided.

The orthographic vertical perspective is a special case of the vertical perspective with the viewing point (hv) at infinity. Therefore, all projection "rays" are parallel to one another and all are perpendicular to the tangent plane. Since the rays are parallel, coordinates in the tangent-plane are the same in any other parallel mapping plane, i.e. are consistent for any value of ho, which therefore becomes irrelevant to the forward formulas.

The orthographic vertical perspective forward conversion from 3D geographic coordinates latitude, longitude and ellipsoidal height (lat, lon, h) to Easting (E) and Northing (N) is given by:

E = U = limit (U hv / (hv – W), hv -> infinity)
N = V = limit (V hv / (hv – W), hv -> infinity)

where, as in Sections 2.2.3 and 1.3.17.2:

U = (* + h) cos * sin (* – *O)
V = (* + h) [sin * cos *O – cos * sin *O cos (* – *O)] + e2 (*O sin *O – * sin * ) cos *O 

The reverse calculation from E,N to U,V,W and *,*,h is indeterminate.