[Proj] Poor example in general inverse procedure

Gerald I. Evenden geraldi.evenden at gmail.com
Sun Sep 21 12:22:50 EDT 2008

Something kept bothering me with the last example in the Ipbuker-Bildirici 
paper "A general algolrith for the inverse ... " using the 3x3 Jacobian for 
the Newton-Raphson solution for the inverse of the Mollweide projection on 
pages 180, 181.  Then it finally struck me:

You do not need an iterative process at all.  First, determine
	t=asin(Y/sqrt(2))  (from eqn. 33)
Then you get
	lambda (longitude) = X /(2*sqrt(2)*cos(t)/Pi)  (from eqn. 32)
and finally:
	phi (latitude) = asin(sin(2*t)  + 2*t)/Pi.  (from eqn. 34)

The only iterative process required is in the forward projection to solve eqn 
34 for t;

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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