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<DIV>Here’s more on the Ellipsoidal Orthographic FYI:</DIV>
<DIV> </DIV>
<DIV><A
title=http://www.hydrometronics.com/downloads/Ellipsoidal%20Orthographic%20Projection.pdf
style='href: "http://www.hydrometronics.com/downloads/Ellipsoidal%20Orthographic%20Projection.pdf"'
href="http://www.hydrometronics.com/downloads/Ellipsoidal%20Orthographic%20Projection.pdf">http://www.hydrometronics.com/downloads/Ellipsoidal%20Orthographic%20Projection.pdf</A></DIV>
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<DIV>Esri refer to this as their Local Cartesian Projection.</DIV>
<DIV> </DIV>
<DIV>No need for authalic latitude in the ellipsoidal case.</DIV>
<DIV> </DIV>
<DIV style="FONT-SIZE: 12pt; FONT-FAMILY: 'Calibri'; COLOR: #000000">Noel Zinn,
Principal, Hydrometronics LLC<BR>+1-832-539-1472 (office), +1-281-221-0051
(cell)<BR>noel.zinn@hydrometronics.com (email)<BR>http://www.hydrometronics.com
(website)<BR></DIV>
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<DIV style="font-color: black"><B>From:</B> <A title=even.rouault@spatialys.com
href="mailto:even.rouault@spatialys.com">Even Rouault</A> </DIV>
<DIV><B>Sent:</B> Thursday, September 24, 2020 4:01 AM</DIV>
<DIV><B>To:</B> <A title=proj@lists.osgeo.org
href="mailto:proj@lists.osgeo.org">proj@lists.osgeo.org</A> </DIV>
<DIV><B>Subject:</B> Re: [PROJ] "Local" projection method?</DIV></DIV></DIV>
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<P
style="MARGIN: 0px; TEXT-INDENT: 0px; -qt-block-indent: 0; -qt-user-state: 0">On
jeudi 24 septembre 2020 05:42:22 CEST Kristian Evers wrote:</P>
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Nyall,</P>
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</P>
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</P>
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> </P>
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> Based on this, would it be appropriate to directly map this projection</P>
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> method across to the "Orthographic" method? Or am I missing something</P>
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> important?…</P>
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</P>
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</P>
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Yes, it would seem so. Be aware though, the current Orthographic projection</P>
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implementation in PROJ is only valid in the spherical case. You would have</P>
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to extend that to the ellipsoidal case for the mapping described by Esri. </P>
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We’ve got an old issue [0] which contains some hints on how to go about</P>
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that.</P>
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style="MARGIN: 0px; TEXT-INDENT: 0px; -qt-block-indent: 0; -qt-paragraph-type: empty"> </P>
<P
style="MARGIN: 0px; TEXT-INDENT: 0px; -qt-block-indent: 0; -qt-user-state: 0">"Recent"
EPSG guidance note 7.2</P>
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style="MARGIN: 0px; TEXT-INDENT: 0px; -qt-block-indent: 0; -qt-paragraph-type: empty"> </P>
<P
style="MARGIN: 0px; TEXT-INDENT: 0px; -qt-block-indent: 0; -qt-user-state: 0">https://drive.tiny.cloud/1/4m326iu12oa8re9cjiadxonharclteqb4mumfxj71zsttwkx/62018e48-9da4-43e7-b598-1202cd96ec9f</P>
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<P
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got from epsg.org)</P>
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<P
style="MARGIN: 0px; TEXT-INDENT: 0px; -qt-block-indent: 0; -qt-user-state: 0">has
the maths for the ellipsoidal formulation of the orthographic projection in
paragraph 3.3.5, page 89</P>
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style="MARGIN: 0px; TEXT-INDENT: 0px; -qt-block-indent: 0; -qt-paragraph-type: empty"> </P>
<P
style="MARGIN: 0px; TEXT-INDENT: 0px; -qt-block-indent: 0; -qt-user-state: 0">I
cannot comment on the full equivalence of the "Local" projection, but hopefully
in the Scale_Factor=1 + Azimuth=0 case, they would match.</P>
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style="MARGIN: 0px; TEXT-INDENT: 0px; -qt-block-indent: 0; -qt-paragraph-type: empty"> </P>
<P
style="MARGIN: 0px; TEXT-INDENT: 0px; -qt-block-indent: 0; -qt-user-state: 0">One
way to check that the theory local = ortho on the sphere is valid would be to
use ArcGIS with a sphere as the ellipsoid and compare results with
+proj=ortho</P>
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style="MARGIN: 0px; TEXT-INDENT: 0px; -qt-block-indent: 0; -qt-paragraph-type: empty"> </P>
<P
style="MARGIN: 0px; TEXT-INDENT: 0px; -qt-block-indent: 0; -qt-user-state: 0">Other
point:</P>
<P
style="MARGIN: 0px; TEXT-INDENT: 0px; -qt-block-indent: 0; -qt-user-state: 0">Looking
at</P>
<P
style="MARGIN: 0px; TEXT-INDENT: 0px; -qt-block-indent: 0; -qt-user-state: 0">https://pro.arcgis.com/en/pro-app/help/mapping/properties/orthographic.htm
,</P>
<P
style="MARGIN: 0px; TEXT-INDENT: 0px; -qt-block-indent: 0; -qt-user-state: 0">there's
the Auxiliary Sphere Type parameter that can be used to change how orthographic
is computed on an ellipsoid, but I'm not sure any of the listed method is
equivalent to the ellipsoidal formulation from EPSG, as the ellipsoidal
formulation from EPSG doesn't seem to use authalic latitude.</P>
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<P
style="MARGIN: 0px; TEXT-INDENT: 0px; -qt-block-indent: 0; -qt-user-state: 0">Even</P>
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<P
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</P>
<P
style="MARGIN: 0px; TEXT-INDENT: 0px; -qt-block-indent: 0; -qt-user-state: 0">Spatialys
- Geospatial professional services</P>
<P
style="MARGIN: 0px; TEXT-INDENT: 0px; -qt-block-indent: 0; -qt-user-state: 0">http://www.spatialys.com</P>
<P>
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