[PROJ] Relevant descrepancies between Sinusoidal and Homolosine

[Luí­s Moreira de Sousa]

Dear all,

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).

In the spreadsheet attached you can verify that the current Sinusoidal implementation only respects this northing relationship for the sphere. With a very exaggerated ellipsoid it becomes clear that a linear relationship between northing and Pi no longer exists.

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 would recommend re-naming the current implementation to something else (perhaps MacBryde, but in truth I do not know this projection). And in tandem raise the internal implementation in the Homolosine to a stand-alone class named as Sinusoidal. Should issues be opened on this?

There is always a chance I am mistaken somehow. Please let me know if this makes sense.

Thank you.

--
Luís
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