[Proj] Finally: geodesic-1.0 is available

Charles Karney ckarney at sarnoff.com
Thu Jan 8 18:45:50 EST 2009

Gerald I. Evenden wrote:
>> On the last point:
>> Does anyone know of a large set of test data?  The papers on the
>> geodesic paper typically present a handful of cases.  Instead I'm
>> thinking of a large test set mostly with randomly chosen points but
>> with some significant fraction of "hard" examples (near antipodal,
>> points near the poles, etc.).  I'm thinking that these could be
>> produced by doing the forward calculation to high precision (using as
>> many terms in the expansion of the integral to get to 1 nm precision
>> or better on the WGS84 ellipsoid).  The result data could be used to
>> test both forward and reverse geodesic calculations.
> I know that the antipod is a problem and that is what seems to attract
> the interest, but, for the life of me, I cannot see what the fuss is
> about.  Sorry, that's just my attitude about it.

Undoubtedly the issue if partly philosophical: I see a well-defined
mathematical problem, and I want to see a complete solution to it.

As a practical matter, having a reasonably comprehensive set of test
data is very important when developing approximate numerical algorithms.
You saw this, I believe, in the tests you did on various transverse
Mercator projections.  Generating a set of test data for the geodesic
would seem to be similarly helpful.  (Wouldn't it be nice to say: the
error is < 1mm provided the distance is less than x km?  I believe that
such statements belong on all numerical software.)

Having such a set of data would also let you quickly evaluate competing
algorithms.  Someone's claim to do substantially better than Vincenty
can be confirmed or dismissed, thereby leading to a much less noise on
the proj.4 mailing list!

If I don't hear of a good geodesic test set, I'm tempted to construct
one myself (no promises, though).

On the subject of the transverse Mercator projection, I'm about 2 weeks
away from posting a new version of my "exact" TM program with much more
exhaustive testing (see above), a more careful treatment of singular
points, etc.  Stay tuned.

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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