Noel,
The projection you describe, a central projection the ellipsoid onto a
plane, Method 1, is the ellipsoidal generalization of the gnomonic
projection suggested in 2 papers from 1997:
B. R. Bowring,
The central projection of the spheroid and surface lines
https://doi.org/10.1179/sre.1997.34.265.163
R. Williams,
Gnomonic projection of the surface of an ellipsoid
https://doi.org/10.1017/S0373463300023936
Much earlier, Letoval'tsev proposed a different generalization, Method
2:
I. G. Letoval'tsev,
Generalization of the gnomonic projection for a spheroid and the
principal geodetic problems involved in the alignment of surface
routes,
Geodesy and Aerophotography, 5, 271-274 (1963),
translation of Geodeziya i Aerofotos'emka 5, 61-68 (1963).
Let's call my method (the limit of a double azimuthal projection),
Method 3.
In my 2013 paper, I compared all three methods finding the maximum
deviation, h, of straight line segments in the gnomonic projection from
the geodesic where the endpoints lie within a radius r of the center of
projection. I found that h/r scaled as
r/a for Method 1
(r/a)^2 for Method 2
(r/a)^3 for Method 3
where a is the equatorial radius of the ellipsoid. If the straightness
of geodesics is the desired property of the projection (as it is for
seismic work and for radio direction finding), then Method 3 (the method
implemented in the proposed PR) is the best choice.
On 12/28/22 17:30, Noel Zinn wrote:
The following is a link to a derivation of an ellipsoidal gnomonic via
ECEF that I did 12 years ago:
http://www.hydrometronics.com/downloads/Ellipsoidal%20Gnomonic%20Projection.pdf
Being thoroughly retired now, and having donated my entire technical
library to a university, I’m not in a position to test this ellipsoidal
version against the criteria stated by Charles, namely “The spherical
gnomonic projection has the property that geodesics map to straight
lines”. That may, or may not, be true for this ellipsoidal version. But
does that matter if this “ellipsoidal gnomonic is a direct perspective
from the geocenter through the ellipsoid onto the tangential plane”, the
same method of derivation of the spherical version?
Noel
On 12/28/2022 3:59 PM, Clifford J Mugnier wrote:
The spherical gnomonic projection has the property that geodesics map to
> straight lines.
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