[Proj] Problems with Pittman geodesic??

[Gerald I. Evenden]

On Monday 19 January 2009 1:16:38 pm OvV_HN wrote:
> 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!

I did not find any surprises here because where problems do show up are for 
the near apodal points which Vincenty (and others) usually flunk.

I have more problems with failures with Pittman and some non-apodal points.

> 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.

"double precision" --- "through twenty significant digits." ???  What kind of 
hardware is being used?  "double" on most 64bit systems is about 15 digits 
+-.  With so much significance, why are the following tables showing 12 at 
best?

> 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

Using Gaussian Quadrature is not a big thing as long as one has the integrals 
to evaluate---one does not need to use gsl to do that. ;-)  I am surprised 
that he can get away with just using that method---or does he?

Lastly, the Saito source is apparently available though "Springer -- 
something" that charges $35(presumably US) for a pdf copy of Vincenty that 
you can get for free from NOAA.

-- 
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