[Proj] Transverse Mercator algorithm

Charles Karney ckarney at sarnoff.com
Sun Sep 7 18:49:30 EDT 2008

 >> There's a good chance that this will look messy because of the
 >> oscillatory behavior of the error with latitude and the fact that
 >> round-off errors dominate for small x.
 > On the contrary.  The error well out of the lon,lat=90,0 zone is
 > simply a frothy quantum like noise around 10^-9 meters due to float
 > precision limits.  As one approaches 90,0 the surface is a remarkable
 > smooth---totally without undulations.

You're quite right.  I guess dx and dy are both oscillatory, but
sqrt(dx^2 + dy^2) is not.

 > Iso-error contours are nearly circular with the center at 90,0 on an
 > equirectangular grid.

It might therefore be useful to display your results as

     error vs mu

with mu = asin(sin(lon) * cos(lat)).  This might allow you to report the
results more succinctly (and compare to the error table I sent

 > As to generating a zillion test points, I had a gaming break while
 > waiting for just 2116 or so points.  It takes nearly a second per
 > point for starters and more as one nears upper limits.

You could download the dataset I created.  Of course these are random
points and I don't know whether your analysis tools let you use such

Charles Karney <ckarney at sarnoff.com>
Sarnoff Corporation, Princeton, NJ 08543-5300

URL: http://charles.karney.info
Tel: +1 609 734 2312
Fax: +1 609 734 2662

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