<div style="font-family: Menlo, Consolas, Courier New, Monospace; font-size: 14px;"><span>Hi Jérôme,</span><div><br></div><div><span>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.</span></div><div><br></div><div><span>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. </span></div><div><br></div><div><span>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.</span></div><span></span><br></div><div style="font-family: Menlo, Consolas, Courier New, Monospace; font-size: 14px;">Regards.</div>
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<div><br></div><div>-- <br></div><div>Luís Moreira de Sousa</div><div>Mastodon: <span><a href="https://mastodon.social/@luis_de_sousa" rel="noreferrer nofollow noopener" target="_blank">https://mastodon.social/@luis_de_sousa</a></span><br></div><div>URL: <a href="https://ldesousa.codeberg.page">https://ldesousa.codeberg.page</a></div>
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<div style="font-family: Menlo, Consolas, Courier New, Monospace; font-size: 14px;"><br></div><div class="protonmail_quote">
On Sunday, 15 September 2024 at 02:45, Jérôme St-Louis via PROJ <proj@lists.osgeo.org> wrote:<br>
<blockquote class="protonmail_quote" type="cite">
<p>Dear Even, All,</p>
<p>I am questioning the current meaning of <i>Central longitude
& latitude of origin</i> (<i>lat_0</i>, <i>lon_0</i>) in
the ISEA projection.</p>
<p>From what I can see in the code, the <i>+lat_0</i> and <i>+lon_0</i>
are being stored in <i>Q->o_lat</i>, <i>Q->o_lon</i>:</p>
<p>
<a href="https://github.com/OSGeo/PROJ/blob/master/src/projections/isea.cpp#L1027" class="moz-txt-link-freetext" target="_blank" rel="noreferrer nofollow noopener">https://github.com/OSGeo/PROJ/blob/master/src/projections/isea.cpp#L1027</a></p>
<p>However, these values are also used as the coordinates of the
first icosahedron vertex, when using the <i>+orient</i>
parameter, which really should have absolutely nothing to do with
the concepts of central longitude & latitude of origin in my
opinion:</p>
<p>
<a href="https://github.com/OSGeo/PROJ/blob/master/src/projections/isea.cpp#L604" class="moz-txt-link-freetext" target="_blank" rel="noreferrer nofollow noopener">https://github.com/OSGeo/PROJ/blob/master/src/projections/isea.cpp#L604</a></p>
<p>So it seems like currently, <i>+lat_0</i> and <i>+lon_0</i>
allow to specify an orientation other than the polar or standard
orientation that can be selected with <i>+orient</i>.<br>
Selecting both would have <i>+orient</i> override the <i>+lat_0</i>
and <i>+lon_0</i> values.<br>
<br>
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.<br>
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.<br>
</p>
<p>What would make sense to me as the <i>central longitude &
latitude of origin</i> would be which latitude & longitude
is projected to the 0, 0 projected coordinates.</p>
<p>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 <a href="https://maps.gnosis.earth/ogcapi/collections/gebco/map?crs=OGC:1534" target="_blank" rel="noreferrer nofollow noopener">projection</a>
if you exclude the bottom-right rhombus (containing part of New
Zealand's north island and Hawaii) making the projection
horizontally symmetrical.</p>
<p>I think currently the only way to change this is by specifying
false easting & northing with <i>+x_0</i> and <i>+y_0</i> in
projected coordinates.</p>
<p>Would it make sense / be possible to:</p>
<p>- Introduce new parameters allowing to specify a custom
coordinate of the first icosahedron vertex e.g, <i>+orient_lat</i>
and <i>+orient_lon<br>
- </i>Change the meaning of <i>+lat_0</i> and <i>+lon_0</i>
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)<br>
</p>
This would be a breaking change only for cases where <i>+lat_0</i>
and or <i>+lon_0</i> is currently being used to position the first
icosahedron vertex.<br>
Given that the documentation does not hint at that in any way, I
doubt anyone is using these for that purpose.
<p>Once the authalic / geodetic conversion is in place when using an
oblate spheroid ellipsoid, I think <i>+orient_lat</i> and <i>+lat_0</i>
would be assumed to be in geodetic coordinates (rather than
authalic).<br>
</p>
These changes would also help clarify what is 0,0 with the default <i>+proj=isea</i>,
which currently is quite a mystery which users need to figure out by
themselves.
<p>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.<br>
</p>
<p>Thank you!</p>
<p>Kind regards,</p>
<p>-Jerome<br>
<br>
</p>
</blockquote><br>
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