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<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 class="pl-smi">y</span> = P-><span class="pl-smi">k0</span>
* (<span class="pl-c1">....</span> - Q-><span class="pl-smi">ml0</span>
+ ....... )</p>
<p>(the false northing value is added in generic PROJ code)<br>
</p>
<p>where</p>
<p>Q->ml0 = <span class="pl-c1">pj_mlfn</span>(P-><span
class="pl-smi">phi0</span>, <span class="pl-c1">sin</span>(P-><span
class="pl-smi">phi0</span>), <span class="pl-c1">cos</span>(P-><span
class="pl-smi">phi0</span>), Q-><span class="pl-smi">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 class="moz-txt-link-freetext" href="https://en.wikipedia.org/wiki/Transverse_Mercator_projection#Coordinates,_grids,_eastings_and_northings">https://en.wikipedia.org/wiki/Transverse_Mercator_projection#Coordinates,_grids,_eastings_and_northings</a><br>
</p>
<p>Even<br>
</p>
<div class="moz-cite-prefix">Le 13/01/2023 à 15:28, Javier Jimenez
Shaw a écrit :<br>
</div>
<blockquote type="cite"
cite="mid:CADRrdKsGvXkwBtWagy9k6+scb8A+Y2dXApXjNsdid46GQYzR_w@mail.gmail.com">
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<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" class="gmail_signature"
data-smartmail="gmail_signature">.___ ._ ..._ .. . ._.
.___ .. __ . _. . __.. ... .... ._ .__<br>
Entre dos pensamientos racionales <br>
hay infinitos pensamientos irracionales.<br>
<br>
</div>
</div>
</div>
</div>
<br>
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