[Proj] Transverse Mercator algorithm
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
Tel: +1 609 734 2312
Fax: +1 609 734 2662
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