<div dir="ltr"><div>Thanks Even.</div><div>I also reached the article in the Wikipedia, but I couldn't find the meaning of "m" in "m(phi0)</div><div>Then I went to PROJ code. In the simplified version it was kind of clear that they were equivalent, but got very confused with the notation, and didn't know what is pj_mlfn (thanks for the tip). I downloaded "map projections a working manual" from USGS, and the formulas are a bit different, that confused me even more (I hope they are equivalent ;)</div><div>That pushed me to ask here.</div><div><br></div><div>Cheers.<br> </div><div><div><div dir="ltr" class="gmail_signature" data-smartmail="gmail_signature">.___ ._ ..._ .. . ._. .___ .. __ . _. . __.. ... .... ._ .__<br>Entre dos pensamientos racionales <br>hay infinitos pensamientos irracionales.<br><br></div></div><br></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Fri, 13 Jan 2023 at 16:13, Even Rouault <<a href="mailto:even.rouault@spatialys.com">even.rouault@spatialys.com</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
<div>
<p>Hi Javier,</p>
<p>interesting. Quick numerical experimentation seems to confirm
that they are "equivalent", as well as looking at the drawing of
how the projection is built.<br>
</p>
<p>And looking at the maths of the approximate ellipsoidal forward
method in src/projections/tmerc.cpp, one can see:</p>
<p>xy.<span>y</span> = P-><span>k0</span>
* (<span>....</span> - Q-><span>ml0</span>
+ ....... )</p>
<p>(the false northing value is added in generic PROJ code)<br>
</p>
<p>where</p>
<p>Q->ml0 = <span>pj_mlfn</span>(P-><span>phi0</span>, <span>sin</span>(P-><span>phi0</span>), <span>cos</span>(P-><span>phi0</span>), Q-><span>en</span>);</p>
<p>where pj_mlfn() computes the meridional distance (formula in
src/mlfn.cpp)<br>
</p>
<p>So - P->k0 * Q->ml0 should be the value of the false
northing equivalent to the effect of phi0. (I believe :-))</p>
<p>Also confirmed by the formula N=N0 +y(lam,phi) - k0 * m(phi0) of
<a href="https://en.wikipedia.org/wiki/Transverse_Mercator_projection#Coordinates,_grids,_eastings_and_northings" target="_blank">https://en.wikipedia.org/wiki/Transverse_Mercator_projection#Coordinates,_grids,_eastings_and_northings</a><br>
</p>
<p>Even<br>
</p>
<div>Le 13/01/2023 à 15:28, Javier Jimenez
Shaw a écrit :<br>
</div>
<blockquote type="cite">
<div dir="ltr">
<div>Hi</div>
<div><br>
</div>
<div>I have a question about Transverse Mercator.</div>
<div>What is the impact of the parameter "<span style="color:rgb(48,48,48);font-family:Arial,Helvetica,sans-serif;font-size:13px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;display:inline;float:none">Latitude
of natural origin", compared with the "False Northing"?
(apart from the fact that one is in degrees and the other in
meters)<br>
</span></div>
<div><span style="color:rgb(48,48,48);font-family:Arial,Helvetica,sans-serif;font-size:13px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;display:inline;float:none">Is
there any difference on using a <span style="color:rgb(48,48,48);font-family:Arial,Helvetica,sans-serif;font-size:13px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;display:inline;float:none">Latitude
of natural origin of, let's say, 40 degrees, or compute
the equivalent False Northing?<br>
</span></span></div>
<div><span style="color:rgb(48,48,48);font-family:Arial,Helvetica,sans-serif;font-size:13px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;display:inline;float:none"><span style="color:rgb(48,48,48);font-family:Arial,Helvetica,sans-serif;font-size:13px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;display:inline;float:none"><br>
</span></span></div>
<div><span style="color:rgb(48,48,48);font-family:Arial,Helvetica,sans-serif;font-size:13px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;display:inline;float:none"><span style="color:rgb(48,48,48);font-family:Arial,Helvetica,sans-serif;font-size:13px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;display:inline;float:none">Thanks.</span></span></div>
<div><span style="color:rgb(48,48,48);font-family:Arial,Helvetica,sans-serif;font-size:13px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;display:inline;float:none"><span style="color:rgb(48,48,48);font-family:Arial,Helvetica,sans-serif;font-size:13px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;display:inline;float:none">Javier<br>
</span></span></div>
<div>
<div>
<div dir="ltr">.___ ._ ..._ .. . ._.
.___ .. __ . _. . __.. ... .... ._ .__<br>
Entre dos pensamientos racionales <br>
hay infinitos pensamientos irracionales.<br>
<br>
</div>
</div>
</div>
</div>
<br>
<fieldset></fieldset>
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