[PROJ] Cassini-Soldner ellipsoid form bug ?

[Charles Karney]

A perusal of src/projections/cass.cpp shows that PROJ implements the
formulas for Cassini-Soldner given in Snyder (1987), p. 95.  It would be
worth verifying that the implementation does indeed correspond to the
text.  But note that the caveat in Snyder:

  a series of approximations is given for use in a zone extending 3d to
  4d of longitude from the central meridian

so all bets are off 149d from the central meridian.

Nowadays it would make sense to implement Cassini-Soldner directly in
terms of geodesics (as is done in for the azimuthal equidistance
projection).  I can look into doing this.  Given that Cassini-Soldner is
fairly rarely used, I doubt that anyone would notice if it were a little
slower.

On Thu, Jan 22, 2026 at 9:40 PM Michael Sumner via PROJ
<proj at lists.osgeo.org> wrote:
>
> I'm having trouble with Cassini-Soldner:
>
> # Good point - agreeable coords
> echo "-6 -71" | proj +proj=cass +R=6378137        # spherical  -217097.18 -7914445.72
> echo "-6 -71" | proj +proj=cass +ellps=WGS84      # ellipsoidal -217749.76 -7891343.23
>
> # Bad point - ellipsoidal diverges
> echo "149 45" | proj +proj=cass +R=6378137        # spherical: 2377511.89 14538559.49
> echo "149 45" | proj +proj=cass +ellps=WGS84      # ellipsoidal: -2738664.72 28023005.14 (WRONG)
>
> That second coordinate seems wildly wrong, I've compared with GeographicLib which shows
>
> lon,lat,x,y
> -6.000000,-71.000000,-217749.757184,-7891343.215151
> 149.000000,45.000000,2381489.299010,14528505.93346
>
> I've laid out a longer description exploring this (and includes the C++ wrapper for GeographicLib):
>
> https://github.com/mdsumner/projcassini
>
> I hope that's enough to show the problem, I found this very confusing but the output of GeographicLib makes me more confident.
>
> Cheers, Mike
>
> --
> Michael Sumner
> Research Software Engineer
> Australian Antarctic Division
> Hobart, Australia
> 0438489030
> e-mail: mdsumner at gmail.com
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-- 
Charles Karney <karney at alum.mit.edu>