[PROJ] Central longitude & latitude of origin in ISEA projection

[Luí­s Moreira de Sousa]

Hi Jérôme,

I went reading again the ISEA documentation, I arrive at a different interpretation. lat_0 and lon_0 are the latitude/longitude of natural origin, there is no objective assumption of these representing a central point of projection. The document also states that the exact interpretation of these parameters depends on the projection implementation itself.

There are various other projections with more than one central point, at least all those with interruptions. The parameters lat_0 and lon_0 apply in similar fashion to these. Therefore any change in the meaning of these parameters must also apply to those other projections with interruptions. I see no need to treat ISEA as a special case in this context.

On the same logic, I do not agree with the assertion on the user having to guess the origin in the cartesian space. There are also the false easting / false northing parameters to aid in this aspect.
Regards.

--
Luís Moreira de Sousa
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On Sunday, 15 September 2024 at 02:45, Jérôme St-Louis via PROJ <proj at lists.osgeo.org> wrote:

> Dear Even, All,
>
> I am questioning the current meaning of Central longitude & latitude of origin (lat_0, lon_0) in the ISEA projection.
>
> From what I can see in the code, the +lat_0 and +lon_0 are being stored in Q->o_lat, Q->o_lon:
>
> https://github.com/OSGeo/PROJ/blob/master/src/projections/isea.cpp#L1027
>
> However, these values are also used as the coordinates of the first icosahedron vertex, when using the +orient parameter, which really should have absolutely nothing to do with the concepts of central longitude & latitude of origin in my opinion:
>
> https://github.com/OSGeo/PROJ/blob/master/src/projections/isea.cpp#L604
>
> So it seems like currently, +lat_0 and +lon_0 allow to specify an orientation other than the polar or standard orientation that can be selected with +orient.
> Selecting both would have +orient override the +lat_0 and +lon_0 values.
>
> This is really not obvious (I just realized this now), and I would think it is a misuse of the central latitude/longitude of origin concepts.
> The latitude / longitude of origin are normally associated with less distortion, but distortion is worst in ISEA at the icosahedron vertices, and it'd definitely not "central" either.
>
> What would make sense to me as the central longitude & latitude of origin would be which latitude & longitude is projected to the 0, 0 projected coordinates.
>
> This is currently the point at half the height and half the width of the icosahedron triangle containing South Africa, which is exactly in the middle of the [projection](https://maps.gnosis.earth/ogcapi/collections/gebco/map?crs=OGC:1534) if you exclude the bottom-right rhombus (containing part of New Zealand's north island and Hawaii) making the projection horizontally symmetrical.
>
> I think currently the only way to change this is by specifying false easting & northing with +x_0 and +y_0 in projected coordinates.
>
> Would it make sense / be possible to:
>
> - Introduce new parameters allowing to specify a custom coordinate of the first icosahedron vertex e.g, +orient_lat and +orient_lon
> - Change the meaning of +lat_0 and +lon_0 to be the geographic latitude corresponding to 0, 0 in projected coordinates, documenting that the default value is -30.0945296301° N, 11.25 E (authalic latitude)
>
> This would be a breaking change only for cases where +lat_0 and or +lon_0 is currently being used to position the first icosahedron vertex.
> Given that the documentation does not hint at that in any way, I doubt anyone is using these for that purpose.
>
> Once the authalic / geodetic conversion is in place when using an oblate spheroid ellipsoid, I think +orient_lat and +lat_0 would be assumed to be in geodetic coordinates (rather than authalic).
>
> These changes would also help clarify what is 0,0 with the default +proj=isea, which currently is quite a mystery which users need to figure out by themselves.
>
> It would also make it easier to put 0,0 at the vertex West of Alaska as we do for the OGC:1534 CRS that we're trying to define.
>
> Thank you!
>
> Kind regards,
>
> -Jerome
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