[Proj] Local Projection Selection

Gerald I. Evenden gerald.evenden at verizon.net
Sun Aug 7 21:06:04 EDT 2005

On Sun, 2005-08-07 at 21:47 +0200, Patrick Mézard wrote:

> Ok, and how do I compute the "real" scale factor? By comparing the 
> "projected" and geodesic distance of two points ? It would make sense 
> and given the geodesic functions in PROJ.4, I could generate the k_0 
> from any defined limit radius with some kind of minimization heuristic. 
> But you are right, I will stay with k_0=1.0 for now.

I would pick a scale factor that works for  the 50km case and apply it
to all computation.

To figure an appropriate scale factor use the -V option which shows
scale error.
For example:

[l]proj -I -proj=sterea +ellps=whatever lat_0=45 lon_0=0 k_0=1. -V

which is the inverse projection.  Give some xy values like 0 50000 or
50000 0
and see what the scale error is.  From this select a value of k_0 which
this error by half.

For Clarke '66 50km shows a scale error of 1.00001536.  Take the
fractional part
and divide by two and subtract that from 1 to get 0.99999232 for k_0.
The scale
error is now 0.99999232 at the center and 1.00000768 at 50km.  The scale
error is about 1 at 37km from the center.

Changing the ellipsoid won't make that much difference for k_0 so one
use the above value for all ellipsoids.

One might want to do the above experiment at various latitudes to check
on that effect.

To see true error between hypotenuse of Cartesian triangle and geodesic,
with program 'geod' distributed with the old PROJ.4 package or use
Vincenti's FORTRAN
program available from NGS.


Jerry and the Low Riders: Daisy Mae and Joshua
"The most certain test by which we judge whether a country is
really free is the amount of security enjoyed by minorities"
---Lord Acton, 1907 
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