[Proj] Transverse Mercator algorithm

Gerald I. Evenden geraldi.evenden at gmail.com
Sun Sep 7 16:29:16 EDT 2008

On Sunday 07 September 2008 2:53:23 pm Charles Karney wrote:
>  > I will get a 3D plot made sometime today.
> 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.  Iso-error contours are nearly circular with the center at 90,0 
on an equirectangular grid.

Give it a looksee:


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.  With your original loops of 10 points per 
degree I figure maybe:

900*900=810000 points at 2/second gives 6750 minutes or 112 hours or a little 
more than 4 1/2 days.  And that is with my klutzy 3GHz 64 bitter.

A few more points than I have patience for.  ;-)

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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