The orthographic case is a special case of "Vertical perspective (ortographic case)" with all points on the ellipsoid (height = 0).
An Orthographic file is available on Geotk, but can not be ported as-is in SIS for licensing reason, except the projection derivative formulas and the work on (de)normalization matrices. However we can restart from the formulas given in the EPSG guide. But EPSG gives ellipsoidal formulas instead than spherical ones, so the work is a little bit more complicated.
See §1.3.18 in IOGP Publication 373-7-2 – Geomatics Guidance Note number 7, part 2 – April 2015.