[PROJ] "Local" projection method?

[Noel Zinn (cc)]

Here’s more on the Ellipsoidal Orthographic FYI:

http://www.hydrometronics.com/downloads/Ellipsoidal%20Orthographic%20Projection.pdf

Esri refer to this as their Local Cartesian Projection.

No need for authalic latitude in the ellipsoidal case.

Noel Zinn, Principal, Hydrometronics LLC
+1-832-539-1472 (office), +1-281-221-0051 (cell)
noel.zinn at hydrometronics.com (email)
http://www.hydrometronics.com (website)


From: Even Rouault 
Sent: Thursday, September 24, 2020 4:01 AM
To: proj at lists.osgeo.org 
Subject: Re: [PROJ] "Local" projection method?

On jeudi 24 septembre 2020 05:42:22 CEST Kristian Evers wrote:

> Nyall,

> 

> 

> > 

> > Based on this, would it be appropriate to directly map this projection

> > method across to the "Orthographic" method? Or am I missing something

> > important?…

> 

> 

> Yes, it would seem so. Be aware though, the current Orthographic projection

> implementation in PROJ is only valid in the spherical case. You would have

> to extend that to the ellipsoidal case for the mapping described by Esri. 

> We’ve got an old issue [0] which contains some hints on how to go about

> that.



"Recent" EPSG guidance note 7.2



https://drive.tiny.cloud/1/4m326iu12oa8re9cjiadxonharclteqb4mumfxj71zsttwkx/62018e48-9da4-43e7-b598-1202cd96ec9f



(link got from epsg.org)



has the maths for the ellipsoidal formulation of the orthographic projection in paragraph 3.3.5, page 89



I cannot comment on the full equivalence of the "Local" projection, but hopefully in the Scale_Factor=1 + Azimuth=0 case, they would match.



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



Other point:

Looking at

https://pro.arcgis.com/en/pro-app/help/mapping/properties/orthographic.htm ,

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.





Even



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