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On Sun, 2005-08-07 at 21:47 +0200, Patrick Mézard wrote:<BR>
...
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<FONT COLOR="#000000">Ok, and how do I compute the "real" scale factor? By comparing the </FONT>
<FONT COLOR="#000000">"projected" and geodesic distance of two points ? It would make sense </FONT>
<FONT COLOR="#000000">and given the geodesic functions in PROJ.4, I could generate the k_0 </FONT>
<FONT COLOR="#000000">from any defined limit radius with some kind of minimization heuristic. </FONT>
<FONT COLOR="#000000">But you are right, I will stay with k_0=1.0 for now.</FONT>
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I would pick a scale factor that works for the 50km case and apply it to all computation.<BR>
<BR>
To figure an appropriate scale factor use the -V option which shows scale error.<BR>
For example:<BR>
<BR>
[l]proj -I -proj=sterea +ellps=whatever lat_0=45 lon_0=0 k_0=1. -V<BR>
<BR>
which is the inverse projection. Give some xy values like 0 50000 or 50000 0<BR>
and see what the scale error is. From this select a value of k_0 which reduces<BR>
this error by half.<BR>
<BR>
For Clarke '66 50km shows a scale error of 1.00001536. Take the fractional part<BR>
and divide by two and subtract that from 1 to get 0.99999232 for k_0. The scale<BR>
error is now 0.99999232 at the center and 1.00000768 at 50km. The scale<BR>
error is about 1 at 37km from the center.<BR>
<BR>
Changing the ellipsoid won't make that much difference for k_0 so one could<BR>
use the above value for all ellipsoids.<BR>
<BR>
One might want to do the above experiment at various latitudes to check<BR>
on that effect.<BR>
<BR>
To see true error between hypotenuse of Cartesian triangle and geodesic, compare<BR>
with program 'geod' distributed with the old PROJ.4 package or use Vincenti's FORTRAN<BR>
program available from NGS.<BR>
<BR>
...<BR>
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