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<p>Hi Luis,</p>
<p>Thanks for the input.<br>
</p>
<p>
<blockquote type="cite"><span>lat_0 and lon_0 are the
latitude/longitude of natural origin,</span></blockquote>
</p>
<p>
<blockquote type="cite"><span>The document also states that the
exact interpretation of these parameters depends on the
projection implementation itself.</span></blockquote>
</p>
<p>I understand that, but the current interpretation for the ISEA
projection is a very specific meaning which in my opinion has
nothing to do with the use of <i>lat_0</i> or <i>lon_0</i> in
any other projections.</p>
<p>Specifically, the current interpretation is related to the
placement of the first vertex of the icosahedron.<br>
</p>
<p>Could you point out one of these projection with interruptions
where you think the interpretation is similar?</p>
<p>For these classic interrupted projection:<br>
<br>
<a class="moz-txt-link-freetext" href="https://proj.org/en/stable/operations/projections/imoll.html">https://proj.org/en/stable/operations/projections/imoll.html</a><br>
<br>
<a class="moz-txt-link-freetext" href="https://proj.org/en/9.4/operations/projections/igh.html">https://proj.org/en/9.4/operations/projections/igh.html</a></p>
<p><i>lon_0</i> is the central meridian in the middle of the map.<br>
</p>
<p>Furthermore, this interpretation clashes with the <i>+orient</i>
parameter, and the documentation is not clear at all about what it
does or about the relationship between <i>+lat_0</i> <i>+lon_0</i>
and <i>+orient</i>.<br>
This is why I propose to rename these <i>+orient_lat</i> and <i>+orient_lon</i>,
where the overlap would be obvious.<br>
</p>
<p>
<blockquote type="cite"><span>Therefore any change in the meaning
of these parameters must also apply to those other projections
with interruptions. <br>
</span></blockquote>
In my opinion, from analyzing the code (not the documentation that
just uses the generic description of lat_0 and lon_0), the current
interpretation has nothing to do with the use of <i>lat_0</i> and
<i>lon_0</i> in any other projection in PROJ.</p>
<p>Happy to get together virtually to try to explain better in case
I am not being clear.</p>
<p>In the vast majority of cases, lat_0, lon_0 correspond to the
center of the projection. In OGC API maps, these are generally
mapped to the <i>crs-proj-center</i> query parameter, except if <i>lat_ts</i>
is defined in which case that takes priority<br>
(see <a
href="https://docs.ogc.org/is/20-058/20-058.html#_d71deb2d-553e-4302-bd6e-a1eeea248581">Custom
Projection CRS 18.2.3</a>).<br>
</p>
<p>
<blockquote type="cite">
<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>
</blockquote>
Yes, +x_0 and +y_0 allows to shift the origin, but these need to
be specified in projected coordinates, which is more complicated
than specifying the geodetic coordinates.</p>
<p>You can of course use the forward transformation of the geodetic
coordinate, then use the negated output of that as the false
easting / northing, but this is a 2-step process, and if the
accuracy of the projection implementation is improved, the easting
/ northing obtained earlier are no longer accurate.<br>
</p>
<p>Kind regards,</p>
<p>-Jerome</p>
<div class="moz-cite-prefix">On 9/16/24 7:18 AM, Luí s Moreira de
Sousa wrote:<br>
</div>
<blockquote type="cite"
cite="mid:zcANJnvE4HE2lCRaB_ak-5oUBEQszHGhsD_w9X2j-2h3ERNzBtR1eEB6RNehvJi731zGlKG0ZCan0YB0EjD4rIPCLxT_BgefcO50lvYfMsw=@protonmail.ch">
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<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>
<div class="protonmail_signature_block"
style="font-family: Menlo, Consolas, Courier New, Monospace; font-size: 14px;">
<div class="protonmail_signature_block-user">
<div><br>
</div>
<div>-- <br>
</div>
<div>Luís Moreira de Sousa</div>
<div>Mastodon: <span><a
href="https://mastodon.social/@luis_de_sousa"
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moz-do-not-send="true" class="moz-txt-link-freetext">https://mastodon.social/@luis_de_sousa</a></span><br>
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moz-do-not-send="true" class="moz-txt-link-freetext">https://ldesousa.codeberg.page</a></div>
</div>
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<div class="protonmail_quote"> On Sunday, 15 September 2024 at
02:45, Jérôme St-Louis via PROJ <a class="moz-txt-link-rfc2396E" href="mailto:proj@lists.osgeo.org"><proj@lists.osgeo.org></a>
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" moz-do-not-send="true">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" moz-do-not-send="true">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"
moz-do-not-send="true">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>
</div>
</blockquote>
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