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<div class="elementToProof"><span style="font-family: "Times New Roman", Times, serif; font-size: 10pt; color: rgb(0, 0, 0); background-color: rgb(255, 255, 255);" class="elementToProof">Mathematically correct is not necessarily LEGALLY correct. For instance
with regard to France and to many French colonies, the French Army Lambert Truncated Cubic Conic is only partially conformal, but is a perfectly LEGAL projection for computing cadastral boundaries BEFORE 1948. After 1948, the French Legislature changed the
Law to require the perfectly conformal mathematical equations for France, and many French colonies followed suit - except for Algeria.</span></div>
<div class="elementToProof"><span style="font-family: "Times New Roman", Times, serif; font-size: 10pt; color: rgb(0, 0, 0); background-color: rgb(255, 255, 255);" class="elementToProof"><br>
</span></div>
<div class="elementToProof"><span style="font-family: "Times New Roman", Times, serif; font-size: 10pt; color: rgb(0, 0, 0); background-color: rgb(255, 255, 255);" class="elementToProof">Mathematical elegance is nice but not always correct under the Law for
a particular place. The EPSG tries to pay attention to that; I am not so sure about ESRI.</span></div>
<div class="elementToProof"><span style="font-family: "Times New Roman", Times, serif; font-size: 10pt; color: rgb(0, 0, 0); background-color: rgb(255, 255, 255);" class="elementToProof"><br>
</span></div>
<div class="elementToProof"><span style="font-family: "Times New Roman", Times, serif; font-size: 10pt; color: rgb(0, 0, 0); background-color: rgb(255, 255, 255);" class="elementToProof">Same goes for the many various truncations of the Transverse Mercator.
It depends on <u>where and when for what equations.</u></span></div>
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<div style="font-family: "Times New Roman", Times, serif; font-size: 10pt; color: rgb(0, 0, 0);" class="elementToProof">
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<p><font face="Copperplate Gothic Bold">Clifford J. Mugnier, c.p., c.m.s.</font></p>
<p><font face="Copperplate Gothic Bold">Chief of Geodesy, <i style="text-align:start;background-color:rgb(255, 255, 255)"><span> </span>(Emeritus)</i></font></p>
<p><font face="Copperplate Gothic Bold">LSU Center for GeoInformatics (ERAD 266)</font></p>
<p><font face="Copperplate Gothic Bold">Dept. of Civil Engineering </font></p>
<p><font face="Copperplate Gothic Bold"><b>LOUISIANA STATE UNIVERSITY</b></font></p>
<p><font face="Copperplate Gothic Bold">Baton Rouge, LA 70803</font></p>
<p><font face="Copperplate Gothic Bold">Research: (225) 578-4578</font></p>
<p><font face="Copperplate Gothic Bold">Cell: (225) 328-8975</font></p>
<p><font face="Copperplate Gothic Bold">honorary lifetime member, lsps</font></p>
<p><font face="Copperplate Gothic Bold">fellow emeritus, asprs</font></p>
<p><font face="Copperplate Gothic Bold">member, apsg</font></p>
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<div id="divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" style="font-size:11pt" color="#000000"><b>From:</b> PROJ <proj-bounces@lists.osgeo.org> on behalf of Even Rouault <even.rouault@spatialys.com><br>
<b>Sent:</b> Wednesday, December 28, 2022 3:43 PM<br>
<b>To:</b> charles@karney.com <charles@karney.com>; proj <PROJ@lists.osgeo.org><br>
<b>Subject:</b> Re: [PROJ] Ellipsoidal version of the gnomonic projection</font>
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<div class="PlainText">I'm favorable to this improvement. This isn't the first time we add an
<br>
ellipsoidal formulation to a projection method that had only a spherical <br>
one (last time was for orthographic). As I mentioned in the PR, it would <br>
be great if we know how to deal with CRS definitions under the Esri <br>
authority that use gnomonic to hopefully be consistent with what they <br>
do, at least on CRS under their authority, as Esri has several flavors <br>
of gnomonic. Hopefully we'll get some input from Esri people. I'll try <br>
to reach with them.<br>
<br>
Even<br>
<br>
Le 28/12/2022 à 22:01, Charles Karney a écrit :<br>
> I've submitted a pull request (PR)<br>
><br>
> <a href="https://nam04.safelinks.protection.outlook.com/?url=https%3A%2F%2Fgithub.com%2FOSGeo%2FPROJ%2Fpull%2F3522&data=05%7C01%7Ccjmce%40lsu.edu%7Ccd3df9623f73492cd90808dae91c9044%7C2d4dad3f50ae47d983a09ae2b1f466f8%7C0%7C0%7C638078606138115575%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=KQ9%2FVZ4BQb1XKztml3zCOeYSWMlK%2FyAfY0NaIkyCWHU%3D&reserved=0">
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><br>
> for PROJ to implement an ellipsoidal generalization of the gnomonic<br>
> projection.<br>
><br>
> The spherical gnomonic projection has the property that geodesics map to<br>
> straight lines.<br>
><br>
> There's no projection with the same property for the ellipsoid.<br>
> However, the spherical gnomonic projection is also the limit of a double<br>
> azimuthal projection, a projection which preserves the azimuths from two<br>
> points, in the limit that the two points coalesce. This property<br>
> carries over to the ellipsoidal version of the projection implemented by<br>
> this PR. For earth ellipsoids, geodesics which pass within a few<br>
> hundred km of the center of the projection are very nearly straight.<br>
> For details and for a derivation of the projection, see Sec. 8 of my<br>
> 2013 paper<br>
><br>
> Algorithms for geodesics<br>
> <a href="https://nam04.safelinks.protection.outlook.com/?url=https%3A%2F%2Fdoi.org%2F10.1007%2Fs00190-012-0578-z&data=05%7C01%7Ccjmce%40lsu.edu%7Ccd3df9623f73492cd90808dae91c9044%7C2d4dad3f50ae47d983a09ae2b1f466f8%7C0%7C0%7C638078606138115575%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=D1Q2L9O6vA9mRVwlzX%2FWzmhfdLl5RHuIMU%2FdpU%2Fjels%3D&reserved=0">
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><br>
> Merging this PR will result in a minor incompatibility: With the<br>
> gnomonic projection in current version of PROJ, an ellipsoid is treated<br>
> (inconsistently!) as a sphere whose radius matches the equatorial radius<br>
> of the ellipsoid. After the merge, the ellipsoidal gnomonic projection<br>
> will be used (and you will get somewhat different results). To retain<br>
> the previous behavior you'll need to set the flattening of the ellipsoid<br>
> to zero, +f=0.<br>
><br>
> Comments are welcome...<br>
><br>
-- <br>
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My software is free, but my time generally not.<br>
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