[PROJ] Relevant descrepancies between Sinusoidal and Homolosine

[Luí­s Moreira de Sousa]

Hi Even,

I have not yet checked the formulas from that source, but regarding the current Homolosine implementation, its outputs are the expected. So perhaps it is applying the spherical Sinusoidal and the ellipsoidal Mollweide?

--
Luís

‐‐‐‐‐‐‐ Original Message ‐‐‐‐‐‐‐
On Tuesday, March 10, 2020 1:21 PM, Even Rouault <even.rouault at spatialys.com> wrote:

> Luí­s,
>
> > after some more trials I can only but conclude that Daan is correct: the
> > current implementation of the SInusoidal projection in PROJ does not match
> > the historical equal-area projection associated with cartographers like
> > Cossin, Sanson, Flamsteed or Mercator. I confirmed in Snyder's "Flattening
> > the Earth" (pag. 113) the expressions for this projection, the relationship
> > between latitude and northing is the identity (btw, Wikipaedia currently
> > claims the same).
>
> For the sphere, yes.
> But for the ellipsoid, if I trust https://pubs.usgs.gov/pp/1395/report.pdf,
> Snyder's "MAP PROJECTIONS-A WORKING MANUAL ", at page 148, equations (30-9)
> and (3-21) show the northing is not the identity of latitude. And while I've
> not checked in depth, I believe that the M expression must hopefully match the
> pj_mlfn() function.
>
> > Whomever implemented the Homolosine projection must had thus to implement
> > the real Sinusoidal internally, otherwise the scale would not match the
> > Mollweide projection at the prescribed latitude (~ 40.75 º). Whether with
> > the sphere or the ellipsoid, this implementation respects the expected
> > relationship with latitude (and Pi).
>
> I believe I found what is wrong with igh. igh implementation is only meant to
> work on the sphere, as there is a P->es = 0 in it. Mollweide implementation is
> only meant to work on the sphere. But Sinusoidal has a separate spherical and
> ellipsoidal implementation. The issue was that igh was forcing P->es = 0 too
>
> late, that is after the sinusoidal has been instanciated. Thus if using igh
> with an ellipsoid, you got the ellipsoidal sinusoidal and the spherical
> mollweide.
> I've submitted https://github.com/OSGeo/PROJ/pull/2042, to make sure the
> spherical shape is force early so that spherical sinusoidal is used, which I
> believe is how igh should be fixed.
>
> Even
>
> ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
>
> Spatialys - Geospatial professional services
> http://www.spatialys.com