[Proj] Distance calculations

OvV_HN ovv at hetnet.nl
Thu Oct 16 03:07:13 EDT 2008

Let's throw in Saito.
He investigated this matter rather thoroughly in two papers. Sadly his first 
paper contains subtle but serious errors, but his second paper is nearly a 
dream. He sets up the integrals leading to distance and azimuth of the 
geodesic and he solves them with Gaussian quadrature. This can be done with 
nearly arbitrary precision. However, he gives several procedures - 
especially in his first paper - to get more accuracy in difficult regions if 
you've got only a handful of bits computer precision, like IEEE 754.

Tsutomu Saito, The computation of long geodesics on the ellipsoid through 
Gaussian quadrature, Bull. Geod. 53 (1979), pp. 165-177

First paper: The computation of long geodesics on the ellipsoid by 
non-series expanding procedure, Journal of geodesy, vol. 44, no. 4, Dec. 

Sadly, these papers are not on-line for free.
Somebody has put a probably not legal copy on an educational web site. Let's 
not publish the url...

Oscar van Vlijmen

----- Original Message ----- 
From: "Irwin Scollar" <al001 at uni-koeln.de>
To: <proj at lists.maptools.org>
Sent: Wednesday, October 15, 2008 3:10 PM
Subject: [Proj] Distance calculations

> Karl Swartz wrote:
> How does this compare to Thomas Vincenty's algorithm (which can be found
> at http://www.ngs.noaa.gov/PUBS_LIB/inverse.pdf)?
> and Gerald Evenden wrote:
> I second the request as I considered it the gold standard and besides full
> documentation and source code are available at NGS as well as online
> computational services.
> An on-line source with a derivation of the Zhang Xue-Lian distance 
> calculations can be found in
> http://kom.aau.dk/~borre/masters/frames/notes.pdf
> pages 18 ff.
> I have not found  on-line sources for the Pittman paper or critiques noted 
> by Cliff Mugnier.
> It would indeed be helpful if the three methods can be compared for 
> accuracy.
> Irwin Scollar
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