<html><body name="Mail Message Editor"><div>Frank:</div><div><br></div><div>I reviewed a promising paper on this topic two years ago. The author took the novel approach of leaving the series development on the complex plane instead of teasing apart the real and imaginary portions. This resulted in a much simpler expression of the series, including inverse. This leaves room for more terms without becoming unwieldy. Unfortunately the paper came with some important problems and did not see publication in that form. I do not know who the author was, or authors were, and I have not heard any more about it. </div><div><br></div><div>You might contact Elisabeth Nelson of CaGIS about manuscript MS06916, "The Formulation of Gauss Projection by Complex Numbers". It may be that the author has published by now, or that "he" would be willing to share details anyway.</div><div><br></div><div>Regards,</div><div>-- daan Strebe</div><div><br></div><br>On May 27, 2008, at 8:52:08 AM, "Frank Warmerdam" <warmerdam@pobox.com> wrote:<br><blockquote style="padding-left: 5px; margin-left: 5px; border-left-width: 2px; border-left-style: solid; border-left-color: blue; color: blue; "><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0; "><div style="width: 100%; "><div id="felix-mail-header-block" style="color: black; background-color: white; border-bottom-width: 1px; border-bottom-style: solid; border-bottom-color: silver; padding-bottom: 1em; margin-bottom: 1em; width: 100%; "><table border="0" cellpadding="1" cellspacing="1" width="100%"><tbody><tr><td width="70px" style="font-family: 'Lucida Grande'; font-size: 8pt; color: gray; text-align: right; vertical-align: top; font-weight: bold; "><span>From:</span></td><td style="font-family: 'Lucida Grande'; font-size: 8pt; color: black; text-align: left; vertical-align: top; padding-left: 5px; "><span title=""Frank Warmerdam" <warmerdam@pobox.com>">"Frank Warmerdam" <warmerdam@pobox.com></span></td></tr><tr><td width="70px" style="font-family: 'Lucida Grande'; font-size: 8pt; color: gray; text-align: right; vertical-align: top; font-weight: bold; "><span>Subject:</span></td><td style="font-family: 'Lucida Grande'; font-size: 8pt; color: black; text-align: left; vertical-align: top; padding-left: 5px; "><span style="font-weight: bold; ">Re: [Proj] Transverse Mercator algorithm</span></td></tr><tr><td width="70px" style="font-family: 'Lucida Grande'; font-size: 8pt; color: gray; text-align: right; vertical-align: top; font-weight: bold; "><span>Date:</span></td><td style="font-family: 'Lucida Grande'; font-size: 8pt; color: black; text-align: left; vertical-align: top; padding-left: 5px; "><span>May 27, 2008 8:52:08 AM PDT</span></td></tr><tr><td width="70px" style="font-family: 'Lucida Grande'; font-size: 8pt; color: gray; text-align: right; vertical-align: top; font-weight: bold; "><span>To:</span></td><td style="font-family: 'Lucida Grande'; font-size: 8pt; color: black; text-align: left; vertical-align: top; padding-left: 5px; "><span title=""PROJ.4 and general Projections Discussions" <proj@lists.maptools.org>">"PROJ.4 and general Projections Discussions" <proj@lists.maptools.org></span></td></tr></tbody></table></div><div id="felix-mail-content-block" style="color: black; background-color: white; width: 100%; "><div style="font-family: monospace; color: black; background-color: white; font-size: 8pt; ">Oscar van Vlijmen wrote:<br>> In my opinion, there are 2 possibilities:<br>><span class="Apple-converted-space"> </span><br>> * High accuracy.<br>> * Speed.<br><br>Folks,<br><br>To state the obvious, computers are pretty fast now, so for many purposes<br>a TM variant that is quite a bit slower would be acceptable.<br><br>I would like to see a TM version that is very reversable well outside the<br>typical six degree swath around the central meridian.<br><br>Mostly I wish I could have a highly reversable TM variant that was exactly<br>the same as the existing TM approximation in at least one direction. It is<br>the failure to reverse that is a nightmare for me.<br><br>Best regards,<br>--<span class="Apple-converted-space"> </span><br>---------------------------------------+--------------------------------------<br>I set the clouds in motion - turn up | Frank Warmerdam, warmerdam@pobox.com<br>light and sound - activate the windows | http://pobox.com/~warmerdam<br>and watch the world go round - Rush | President OSGeo, http://osgeo.org<br><br>_______________________________________________<br>Proj mailing list<br>Proj@lists.maptools.org<br>http://lists.maptools.org/mailman/listinfo/proj<br><br></div></div></div></span></blockquote><br><div><br></div><div class="aol_ad_footer" id="u8020F1B7A0944DC79DA55788D015893F"><FONT style="color: black; font: normal 10pt ARIAL, SAN-SERIF;"><HR style="MARGIN-TOP: 10px">Stay informed, get connected and more <A title="http://mobile.aol.com/productOverview.jsp?productOverview=aol-mobile-overview&?ncid=aolmbd00030000000139" href="http://mobile.aol.com/productOverview.jsp?productOverview=aol-mobile-overview&?ncid=aolmbd00030000000139" target="_blank">with AOL on your phone</A>.</FONT></div></body></html>