[Proj] Distance calculations

Duncan Agnew dagnew at ucsd.edu
Wed Oct 15 12:40:39 EDT 2008

The "down-under" paper that Cliff Mugnier refers to is available at


(At least I assume this is the one). The abstract states:

Vincenty’s (1975) formulas for the direct and inverse geodetic problems 
(i.e., in relation to the geodesic) have been verified by comparing 
them with a new formula developed by adapting a fourth-order 
Runge-Kutta scheme for the numerical solution of ordinary differential 
equations, advancing the work presented by Kivioja in 1971. A total of 
3,801 lines of varying distances 10 to 18,000 km and azimuths (0 to 
90°, because of symmetry) were used to compare these two very different 
techniques for computing geodesics. In every case, the geodesic 
distances agreed to within 0.115 mm, and the forward and reverse 
azimuths agreed to within 5 microarcsec, thus verifying Vincenty’s 

They reference Pittman but don't make any comparisons with his work. 
The reference for that work is

Pittman, M. E. (1986). Precision direct and inverse solutions of the
geodesic, Surveying and Mapping 46(1), 47-54.

(which I wish Cliff Mugnier had cited) and for Kivioja is

Kivioja, L. A. (1971). Computation of geodetic direct and indirect prob-
lems by computers accumulating increments from geodetic line elements.
Bull. Geod. 99, 55-63.

This result would seem to settle the question for all practical (and 
impractical) purposes, though a further comparison might be warranted.

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