Cassini-Soldner easting difference

[eriksorngard]

Hello,

While stress testing our forward Cassini-Soldner projection, implemented from EPSG documentation and not dependend on PROJ, I notice an increasing difference between PROJ's easting output and ours, with increasing longitudal distance.

The only other software I know that allows me to configure an arbitrary Cassini-Soldner independently of PROJ and project arbitrary coordinates is SurvCE, which yields the same results as our software.

I can recreate PROJ's results by adapting line 45 and 46 in cass.cpp to build with our source code:

    xy.x = nu * A * (1. - A2 * T *
        (C1 - (8. - T + 8. * C) * A2 * C2));

Optimizing EPSG's expression for calculating E (which appears to be the same as Snyder's 13-7) to match PROJ's implementation, i notice a different sign after C1:

    xy.x = nu * A * (1. - A2 * T *
        (C1 + (8. - T + 8. * C) * A2 * C2));

Test results

cs2cs -I -f "%.5f" +proj=cass +lat_0=57 +lon_0=18 +x_0=0 +y_0=0 +ellps=GRS80

		PROJ	PROJ	"EPSG"	"EPSG"	Difference	Difference
Latitude	Longitude	Easting	Northing	Easting	Northing	Easting	Northing
57	18	0	0	0	0	0	0
57	15	-182257.97503	4003.72144	-182257.94813	4003.72144	0.02690	0
60	18	0	334158.93324	0	334158.93334	0	0.00010

Should the sign in cass.cpp be flipped?

Best regards,
Erik

Environment Information

• PROJ version (9.1.0)
• Ubuntu 22.04, running under Windows 11

Installation method

• Built from source

[rouault]

totally agree with your diagnostic (good spotting!). Fix in #3433