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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);">Absolutely correct. My point was philosophical rather than pointed to the gnomonic.</span></div>
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Happy New Year!</div>
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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> Charles Karney <charles.karney@gmail.com><br>
<b>Sent:</b> Wednesday, December 28, 2022 5:44 PM<br>
<b>To:</b> Clifford J Mugnier <cjmce@lsu.edu>; Even Rouault <even.rouault@spatialys.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">Clifford: point taken. But would this comment apply to the gnomonic<br>
projection? Historically this has been a spherical-only projection and<br>
so extending it (in some reasonable way) to an ellipsoid won't tread on<br>
anyone's toes.<br>
<br>
--Charles<br>
<br>
On 12/28/22 16:59, Clifford J Mugnier wrote:<br>
> Mathematically correct is not necessarily LEGALLY correct. For instance <br>
> with regard to France and to many French colonies, the French Army <br>
> Lambert Truncated Cubic Conic is only partially conformal, but is a <br>
> perfectly LEGAL projection for computing cadastral boundaries BEFORE <br>
> 1948. After 1948, the French Legislature changed the Law to require the <br>
> perfectly conformal mathematical equations for France, and many French <br>
> colonies followed suit - except for Algeria.<br>
> <br>
> Mathematical elegance is nice but not always correct under the Law for a <br>
> particular place. The EPSG tries to pay attention to that; I am not so <br>
> sure about ESRI.<br>
> <br>
> Same goes for the many various truncations of the Transverse Mercator. <br>
> It depends on _where and when for what equations._<br>
> <br>
> Clifford J. Mugnier, c.p., c.m.s.<br>
> <br>
> Chief of Geodesy, /(Emeritus)/<br>
> <br>
> LSU Center for GeoInformatics (ERAD 266)<br>
> <br>
> Dept. of Civil Engineering<br>
> <br>
> *LOUISIANA STATE UNIVERSITY*<br>
> <br>
> Baton Rouge, LA 70803<br>
> <br>
> Research: (225) 578-4578<br>
> <br>
> Cell: (225) 328-8975<br>
> <br>
> honorary lifetime member, lsps<br>
> <br>
> fellow emeritus, asprs<br>
> <br>
> member, apsg<br>
> <br>
> ------------------------------------------------------------------------<br>
> *From:* PROJ <proj-bounces@lists.osgeo.org> on behalf of Even Rouault <br>
> <even.rouault@spatialys.com><br>
> *Sent:* Wednesday, December 28, 2022 3:43 PM<br>
> *To:* charles@karney.com <charles@karney.com>; proj <PROJ@lists.osgeo.org><br>
> *Subject:* Re: [PROJ] Ellipsoidal version of the gnomonic projection<br>
> 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%7C5ac61fc0ab1d47f591cb08dae92d6fb3%7C2d4dad3f50ae47d983a09ae2b1f466f8%7C0%7C0%7C638078678623357214%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=IV2T6kvB3QNcpAyfsl8gClLPN7KgM%2BvB%2B%2Fi0i8RUOPs%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%7C5ac61fc0ab1d47f591cb08dae92d6fb3%7C2d4dad3f50ae47d983a09ae2b1f466f8%7C0%7C0%7C638078678623357214%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=2at6dReqm6CDJxlETPt9xCHD9k6HziY5lXSo%2Fxa6t9g%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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