[Proj] Troubles with Newton-Raphson inverse projections
Gerald I. Evenden
geraldi.evenden at gmail.com
Sat Oct 18 11:48:39 EDT 2008
I finished the basics of the Newton-Raphson general inverse projection method
(as described in the Turkish paper) about a week ago.
One additional problem with the Turkish paper is that they understated the
problem of making an appropriate initial estimation of the lon/lat solution.
If the estimate is sufficiently poor, the looping process can follow the
wrong path to a solution or simply fail to converge. Also, the poorer the
estimation, more loops are required to converge to a solution. At the moment
I am pursuing developing a low degree polynomial estimation function which
will hopefully improve the initial estimate process.
Secondly, finding the root may also be difficult when the precision of the
derivatives start to fail. This is the case near the poles of both the
Hammer and Aitoff projections. At a latitude greater than 89° the method
fails for both these projections. One also gets suspicious that this will
occur when the nature of the curve flattens out like the top of a sine curve.
I have not tried the flat pole Winkel Triplel yet.
This is just an alert to the readership that the Turkish method *is not* a
cureall for determining the inverse projection.
--
The whole religious complexion of the modern world is due
to the absence from Jerusalem of a lunatic asylum.
-- Havelock Ellis (1859-1939) British psychologist
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