<HTML dir=ltr><HEAD><TITLE>Re: [Proj] The world of ECEF aka geocentric coordinates</TITLE>
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<DIV dir=ltr><FONT face="Times New Roman" color=#000000>I personally find the Wiki stuff useless and misleading. The proper reference is Bomford's <EM>Geodesy</EM> (Editions 1 <EM><STRONG>thru</STRONG></EM> 4), and not the other trivia listed at the end. The term ECEF is new-age baloney. The <STRONG>Geocentric Coordinate System</STRONG> is the original and decades-old terminology recognized in the classical literature. The notation used in the Wiki equations is just more gobbledygook, as Bomford established the proper (and world-wide recognized) notation about 50 years ago. As if Wiki is entitled to ignore </FONT>(<SPAN style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'; mso-fareast-font-family: 'Times New Roman'; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA"><STRONG>η</STRONG></SPAN>) the ellipsoid normal terminated by the semi-minor axis? The term "<U>spheroid</U>" is further glaring evidence of classical geodetic ignorance. That noun is only used with an ellipsoid that has a specific datum with an associated geoid. Applicable to OSGB36 and WGS84, but certainly <STRONG><EM>not</EM></STRONG> to most classical datums found throughout the world.</DIV>
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<DIV dir=ltr>C. Mugnier</DIV>
<DIV dir=ltr>LSU<BR></DIV>
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<DIV dir=ltr><FONT face=Tahoma size=2><B>From:</B> proj-bounces@lists.maptools.org on behalf of Karney, Charles<BR><B>Sent:</B> Fri 30-Jan-09 15:10<BR><B>To:</B> geraldi.evenden@gmail.com; PROJ.4 andgeneral Projections Discussions<BR><B>Subject:</B> Re: [Proj] The world of ECEF aka geocentric coordinates<BR></FONT><BR></DIV></DIV>
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<P><FONT size=2>> From: Gerald I. Evenden [geraldi.evenden@gmail.com]<BR>> Sent: Friday, January 30, 2009 14:30<BR>><BR>> Karney's routine is limited to WGS84 as is all the software in his<BR>> library. 10 lashes with a wet noodle, Karney.<BR><BR>"Up to a point, Lord Copper." The simple ECEFConvert utility I provide<BR>(merely to illustrate the code) is limited to WGS84. The constructor<BR>for ECEF class allows you to specify the ellipsoid.<BR><BR>> Some of these methods may be equivalent but I have not dug that far<BR>> into the details of the morass. I am also sure that there must be<BR>> more versions out there.<BR><BR>There do seem to be an embarrassing number of published papers on a<BR>mathematically trivial topic. Of course, provided that the methods are<BR>correct, they must me equivalent (in a mathematical sense).<BR><BR>The biggest differentiator, in my book, is the domain of applicability.<BR>Many of the methods (direct or iterative) exclude the center of the<BR>earth (and I think some also exclude very distant points). This is<BR>entirely appropriate for GPS units, but seems to be an unnecessary<BR>restriction for a general-purpose library.<BR><BR>Incidentally, many simple iteration schemes (such as the NGS method, I<BR>believe) just have linear convergence. Some iterative schemes are<BR>amenable to Newton's method with much faster (quadratic) convergence.<BR>Presented with such a choice, I would normally go for a slightly more<BR>complicated iteration which converges faster.<BR><BR>Vermeille's method is a relatively simple direct method. It breaks down<BR>near the center of the earth. But fixing this was straightforward.<BR>Finally, I had to make several fixes to avoid loss of accuracy due to<BR>round-off. The errors I am getting (7 nm) are within spitting distance<BR>of the round-off limit (10^7 / 2^53 m = 1.1 nm).<BR><BR>Incidentally benchmarking ECEF methods for accuracy is easy because the<BR>geodetic to ECEF transformation is stable and, if carried out with long<BR>doubles, accurate. This can be used to generate test data for the<BR>reverse transformation. When probing points near the center of the<BR>earth you need to ensure that<BR><BR> h >= - a (1 - e^2) / sqrt(1 - e^2 sin(phi)^2)<BR><BR>so that the ECEF point is in the same hemisphere as phi.<BR><BR>> Lastly, the use of the term ECEF suggested by Wikipedia for geocentric<BR>> seems appropriate. Also, where are our ENU procedures? Tsk, tsk.<BR><BR>ENU is what I call "local Cartesian" (implemented by the LocalCartesian<BR>class -- and this, I confess, does have WGS84 wired in).<BR><BR>--<BR>Charles Karney <ckarney@sarnoff.com><BR>Sarnoff Corporation, Princeton, NJ 08543-5300<BR><BR>URL: <A href="http://charles.karney.info/">http://charles.karney.info</A><BR>Tel: +1 609 734 2312<BR>Fax: +1 609 734 2662<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>