[Proj] Problems with Pittman geodesic??

[OvV_HN]

Some time ago I referred to 2 articles by Saito.
He computes the geodesic problems by numerical integration. There are some 
errors in the formulae, but his second article gives correct results for 
'normal' values. Saito attends much detail to borderline situations, but 
there are probably some errors in his descriptions.
Anyhow, he gives a couple of test points which everybody with geodesics code 
definitively should try to replicate. You might be surprised!

Saito article 2 examples.

Using the formulas and the procedure described in the article, with an 
equatorial radius of 6378388 meters and an inverse flattening of 297, the 
following results were obtained. The computation was made in double 
precision arithmetic - through twenty significant digits.

Line lat1                lat2               delta lon
1. 37d 19' 54.95367"   26d 07' 42.83946"  041d 28' 35.50729"
2. 35  16  11.24862    67  22  14.77638   137  47  28.31435
3. 01  00  00.00000   -00  59  53.83076   179  17  48.02997
4. 01  00  00.00000    01  01  15.18952   179  46  17.84244
5. 41  41  45.88000    41  41  46.20000   000  00  00.56000
6. 30  00  00.00000    37  53  32.46584   116  19  16.68843
7. 30  19  54.95367   -30  11  50.15681   179  58  17.84244
8. 00  39  49.12586   -00  45  14.13112   179  58  17.84244
9. 00  00  54.95367    00  00  42.83946   179  28  17.84244

Line  dist.           azim.                back azim.
1.  4085966.7026 m   095d 27' 59.630899"  118d 05' 58.961609"
2.  8084823.8383     015  44  23.748498   114  55  39.921473
3. 19959999.9998     088  59  59.998971   091  00  06.118356
4. 19780006.5588     004  59  59.999957   174  59  59.884800
5.       16.2839751  052  40  39.390671   052  40  39.763172
6. 10002499.9999     045  00  00.000004   129  08  12.326009
7. 19989590.5480     002  23  52.108130   177  36  19.670109
8. 19994529.4446     177  39  39.010104   002  20  21.153036
9. 19977290.7711     054  08  27.731619   125  51  32.272327

From:
THE COMPUTATION OF LONG GEODESICS ON THE ELLIPSOID
THROUGH GAUSSlAN QUADRATURE
Tsutomu SAITO
Construction College,
Kodaira-shi Tokyo, 187 Japan.


Oscar van Vlijmen


----- Original Message ----- 
From: "Gerald I. Evenden" <geraldi.evenden at gmail.com>
To: "PROJ.4 and general Projections Discussions" <proj at lists.maptools.org>
Sent: Monday, January 19, 2009 2:57 AM
Subject: [Proj] Problems with Pittman geodesic??


> While checking out the accuracy of Vincenty vs. Pittman
> I was fairly consistently getting agreement to micron or
> better.
>
> BUT not always!!!
>
> I would appreciate anyone who has a Pittman geodesic routine
> to test the following inverse (WGS84 ellipsoid):
>

.....