[PROJ] Relevant descrepancies between Sinusoidal and Homolosine

[strebe at aol.com]

Caveat: I don’t know much about PROJ specifically.
The formulæ given here for sinusoidal are wrong:https://proj.org/operations/projections/sinu.html
There is no parameterization of these formulæ attributed to “MacBryde” (presumably McBride) and Thomas whereby you arrive at the sinusoidal. I haven’t looked at the source code to see if that’s actually how they’re implemented.

Also, the datum you specify is ellipsoidal, but the formulæ operate against the sphere. This results in not-quite-equal-area, at least theoretically. Again,  don’t know anything about the implementation. That would be a problem for all three of the equal-area projections you list, though.

— daan
 
 
-----Original Message-----
From: Luí­s Moreira de Sousa <luis.de.sousa at protonmail.ch>
To: proj at lists.osgeo.org <proj at lists.osgeo.org>
Sent: Wed, Jan 22, 2020 6:06 am
Subject: [PROJ] Relevant descrepancies between Sinusoidal and Homolosine

Dear all,

the past couple of weeks I have been struggling with visible differences between the Sinusoidal and the Homolosine. Between 40º S and 40º N the northing coordinates in the both projections should be the same - the interruptions in the Homolosine only affect easting. However this is not case, and the further away from the Equator the worse it is. By parallel 40 the difference is well past 20 km. One of the two computations must be incorrect.

While trying to identify the cause I found out that the Sinusoidal as implemented by PROJ is not actually equal area. The further away from the Equator, the smaller areas become. Whereas other equal-area projections like the Homolosine, Eckert IV or Mollweide all agree closely in their full co-domain. I am attaching a small CSV that digests some of these computations.

Before digging further into this issue, I would like to ask you to verify these discrepancies. Can you replicate, or am I seeing this wrong?

My set up:
- Ubuntu 18.04
- UbuntuGIS-Unstable PPA
- PROJ 5.2.0

The PROJ strings I am using:
+proj=sinu +lat_0=0 +lon_0=0 +datum=WGS84 +units=m +no_defs
+proj=moll +lat_0=0 +lon_0=0 +datum=WGS84 +units=m +no_defs
+proj=igh +lat_0=0 +lon_0=0 +datum=WGS84 +units=m +no_defs
+proj=latlong +datum=WGS84

Thank you.

--
Luís
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