[Proj] Re: wrong computation of meridinal distance / pj mlfn.c
Gerald I. Evenden
gerald.evenden at verizon.net
Wed Jul 13 10:50:45 EDT 2005
To the best of my knowledge, there are four ways to compute the
meridinal (or meridianal)
distance: 1) multiple angle series (as given by Snyder and many others),
power series
of sine terms (earlier proj4 and others---better computationally), using
an elliptical integral
form (per current libproj4) and numerical integration.
The main advantage of the reduction to an elliptic integral and use of a
standard
method to evaluate same, is that it is relatively easy to obtain
distance values that
are near machine precision.
Note that in developing various forms of this problem I usually did
testing of the methods
against numerical integration that used extended precision. The kernel
of the integral
is quite well behaved and lends itself readily to numerical integration.
For the math involved see the section in the libproj4 manual (p. 24) on
the web site
http://members.verison.net/~vze2hc4d/proj4
Note that all references to latitude in the manual are to the geodetic
latitude.
Geocentric is only of interest to satellite problems and I can't imagine
that
substituting the geocentric form into the integral would simplify the
solution.
Also note that the meridianal distance procedure in the libproj4 library
is pj_mdist.
Sorry that I did not get into this discussion earlier but by ISP was
down for a couple
of days.
--
_____________________________________________________________
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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