<HTML dir=ltr><HEAD><TITLE>Re: [Proj] Distance calculations</TITLE>
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<DIV dir=ltr><FONT face="Times New Roman" color=#000000 size=2>The "down-under" paper I was referring to is:</FONT></DIV>
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<DIV dir=ltr><FONT size=2><STRONG><EM>Geodesics on an Ellipsoid</EM></STRONG>, </FONT></DIV>
<DIV dir=ltr><FONT size=2>by R.E.Deakin and M.N.Hunter, </FONT></DIV>
<DIV dir=ltr><FONT size=2>School of Mathematical and Geospatial Sciences, </FONT></DIV>
<DIV dir=ltr><FONT size=2>RMIT University, </FONT></DIV>
<DIV dir=ltr><FONT size=2>GPO Box 2476V, </FONT></DIV>
<DIV dir=ltr><FONT size=2>Melbourne, VIC 3001.</FONT></DIV>
<DIV dir=ltr><FONT size=2></FONT> </DIV>
<DIV dir=ltr><FONT size=2>Cliff Mugnier</FONT></DIV>
<DIV dir=ltr><FONT size=2>LSU</FONT></DIV></DIV>
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<FONT face=Tahoma size=2><B>From:</B> proj-bounces@lists.maptools.org on behalf of Duncan Agnew<BR><B>Sent:</B> Wed 15-Oct-08 11:40<BR><B>To:</B> PROJ.4 and general Projections Discussions<BR><B>Subject:</B> Re: [Proj] Distance calculations<BR></FONT><BR></DIV>
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<P><FONT size=2>The "down-under" paper that Cliff Mugnier refers to is available at<BR><BR><A href="http://www.cage.curtin.edu.au/~will/thomas-featherstone.pdf">http://www.cage.curtin.edu.au/~will/thomas-featherstone.pdf</A><BR><BR>(At least I assume this is the one). The abstract states:<BR><BR>Vincenty’s (1975) formulas for the direct and inverse geodetic problems<BR>(i.e., in relation to the geodesic) have been verified by comparing<BR>them with a new formula developed by adapting a fourth-order<BR>Runge-Kutta scheme for the numerical solution of ordinary differential<BR>equations, advancing the work presented by Kivioja in 1971. A total of<BR>3,801 lines of varying distances 10 to 18,000 km and azimuths (0 to<BR>90°, because of symmetry) were used to compare these two very different<BR>techniques for computing geodesics. In every case, the geodesic<BR>distances agreed to within 0.115 mm, and the forward and reverse<BR>azimuths agreed to within 5 microarcsec, thus verifying Vincenty’s<BR>formula.<BR><BR>They reference Pittman but don't make any comparisons with his work.<BR>The reference for that work is<BR><BR>Pittman, M. E. (1986). Precision direct and inverse solutions of the<BR>geodesic, Surveying and Mapping 46(1), 47-54.<BR><BR>(which I wish Cliff Mugnier had cited) and for Kivioja is<BR><BR>Kivioja, L. A. (1971). Computation of geodetic direct and indirect prob-<BR>lems by computers accumulating increments from geodetic line elements.<BR>Bull. Geod. 99, 55-63.<BR><BR>This result would seem to settle the question for all practical (and<BR>impractical) purposes, though a further comparison might be warranted.<BR><BR><BR><BR>_______________________________________________<BR>Proj mailing list<BR>Proj@lists.maptools.org<BR><A href="http://lists.maptools.org/mailman/listinfo/proj">http://lists.maptools.org/mailman/listinfo/proj</A><BR></FONT></P></DIV></BODY></HTML>