<html><body name="Mail Message Editor"><div>"Gerald I. Evenden" <geraldi.evenden@gmail.com> writes:<br></div><div><span class="Apple-style-span" style="font-family: -webkit-monospace; font-size: 11px; "><span class="Apple-style-span" style="font-family: Helvetica; font-size: 12px;"><br></span>>For the spherical case the situation of parallel lines meeting at infinity <br>>seems reasonable and there seems to be mathematical conditions for this <br>>state. But for the elliptical case there is the currently publically <br>>unsubstatiated position that the end points are at a finite distance from</span></div><div><span class="Apple-style-span" style="font-family: -webkit-monospace; font-size: 11px; ">>the central meridian of the map (the vertical line through the poles).<br></span></div><div><br></div><div><span class="Apple-style-span" style="font-family: -webkit-monospace; font-size: 11px;"><span class="Apple-style-span" style="font-family: Helvetica; font-size: 12px; "><div>Would you please cease this campaign of misinformation? There is no controversy. None. There is no "publicly unsubstantiated position". The fact that you have not personally bothered to check the references or did not understand what you read or have not been able to get your computer to image it does not mean anything with respect to "publicly". All that is nothing but "privately". As I have repeatedly noted on this list, the full mathematics of the ellipsoidal transverse Mercator can be found in</div><div><br></div><div><p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica">L.P. Lee, 1976. "Conformal Projections Based on Elliptic Functions", Cartographica Monograph #16.</p><p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica"><br></p></div><div>along with (gasp) an illustration of the projection in global extent. There have been several other publications over the years that discuss the global extent of the ellipsoidal transverse Mercator, including:</div><div><br></div><div>E.H. Thompson, 1945, as remarked on by Snyder in "Map Projections — A Working Manual", US Geological Survey Professional Paper 1395, p. 48. </div><div>L.P. Lee, 1962. "The Transverse Mercator projection of the entire ellipsoid". Empire Survey Review, 16: 208-217. London. </div><div>J.P. Snyder, as mentioned above.</div><div>Jeff Dozier, 1980. "Improved algorithm for calculation of UTM and geodetic coordinates: NOAA Technical Report NESS 81.</div><div><br></div><div>Interested readers can see an equivalent image here:</div><div><br></div><div><div><p style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 12px/normal Helvetica; ">http://mapthematics.com/Projection%20Images/Cylindrical/Transverse%20Mercator.GIF</p><div><br></div></div></div><div>Regards,</div><div>-- daan Strebe</div><div><br></div></span></span></div><div><span class="Apple-style-span" style="font-family: -webkit-monospace; font-size: 11px;"><br></span></div><div>On Jun 16, 2008, at 7:44:09 PM, "Gerald I. Evenden" <geraldi.evenden@gmail.com> wrote:<br></div><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=""Gerald I. Evenden" <geraldi.evenden@gmail.com>">"Gerald I. Evenden" <geraldi.evenden@gmail.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; ">[Proj] Tmerc status with libproj4 and notes</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>June 16, 2008 7:44:09 PM 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; ">Things on the libproj4-Transvers Mercator front are still progressing with<span class="Apple-converted-space"> </span><br>another TM version finished today: ktmerc for Kruger. Speed wise this fits<span class="Apple-converted-space"> </span><br>beteen etmerc and ftmerc and seems to give reasonable values out to expected<span class="Apple-converted-space"> </span><br>limits. One problem did arise with ftmerc during testing that involved<span class="Apple-converted-space"> </span><br>problems with the inverse operation. This does not look like serious fixing<span class="Apple-converted-space"> </span><br>problem and a new release of libproj4 should be out later this week.<br><br>Speaking of limits, it might be fun to re-explore the extremes of the<span class="Apple-converted-space"> </span><br>Transverse Mercator since we had so much fun with the issue a couple of years<span class="Apple-converted-space"> </span><br>ago. Since then we or at least I have still not seen any code that delivers<span class="Apple-converted-space"> </span><br>finite values for values of, say, 90W-0N. All the versions in libproj4 still<span class="Apple-converted-space"> </span><br>like to deliver stars for this kind of input. Evidence seems permanently<span class="Apple-converted-space"> </span><br>locked in the secret vaults and only available to the special few.<br><br>For those who do not know what a global TM maps looks like draw a vertical<span class="Apple-converted-space"> </span><br>line and place three equally space points on that line. The points, from<span class="Apple-converted-space"> </span><br>bottom to top are the south pole, north pole and the south pole again. Now<span class="Apple-converted-space"> </span><br>draw two horizontal lines midway between the three poles: the equator. Note<span class="Apple-converted-space"> </span><br>that these two lines are part of the same thing yet never connect---kinda<span class="Apple-converted-space"> </span><br>sounds like parallel lines that meet at infinity. Now draw three more<span class="Apple-converted-space"> </span><br>horizontal parallel lines through the three pole points. THese lines are<span class="Apple-converted-space"> </span><br>meridians at +-90 longitude. Note that the right end of all five lines<span class="Apple-converted-space"> </span><br>should meet at a point at 90E0N and similarly the left ends at a point 90W0N.<br><br>For the spherical case the situation of parallel lines meeting at infinity<span class="Apple-converted-space"> </span><br>seems reasonable and there seems to be mathematical conditions for this<span class="Apple-converted-space"> </span><br>state. But for the elliptical case there is the currently publically<span class="Apple-converted-space"> </span><br>unsubstatiated position that the end points are at a finite distance from the<span class="Apple-converted-space"> </span><br>central meridian of the map (the vertical line through the poles).<br><br>This condition is analogous to finite polar extent cylindrical maps like<span class="Apple-converted-space"> </span><br>Millers and flat pole pseudocylindricals. Points at the poles are not points<span class="Apple-converted-space"> </span><br>but a line that borders the top and bottom of the map. In the TM case a<span class="Apple-converted-space"> </span><br>point at 90Ew0N is a line defining the left of right extent of the map.<span class="Apple-converted-space"> </span><br>Regardless of whether there is a singularity at the edge plotting, position<span class="Apple-converted-space"> </span><br>becomes increasingly affected by the precision of the point's coordinates.<span class="Apple-converted-space"> </span><br>It becomes apparent that even if it is possible to extend a TM map to the<span class="Apple-converted-space"> </span><br>extreme edge, limiting the extent of the map in a manner similar to the<span class="Apple-converted-space"> </span><br>standard Mercator is appropriate especially when considering distortion along<span class="Apple-converted-space"> </span><br>the left and right edges.<br><br>Pursuing the issue of determining the real value of 90EW0N seems pointless and<span class="Apple-converted-space"> </span><br>only of interest to the diehard cartophile. Global extent TM maps are easily<span class="Apple-converted-space"> </span><br>and adequately handled by the spherical equations and thus leaves elliptical<span class="Apple-converted-space"> </span><br>usage only to largescale mapping and cadastal applications.<br><br>--<span class="Apple-converted-space"> </span><br>The whole religious complexion of the modern world is due<br>to the absence from Jerusalem of a lunatic asylum.<br>-- Havelock Ellis (1859-1939) British psychologist<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="u6177BEABC2B4405A80DA394075C3685E"><FONT style="color: black; font: normal 10pt ARIAL, SAN-SERIF;"><HR style="MARGIN-TOP: 10px"><A title="http://toolbar.aol.com/moviefone/download.html?ncid=aolcmp00050000000011" href="http://toolbar.aol.com/moviefone/download.html?ncid=aolcmp00050000000011" target="_blank">Get the Moviefone Toolbar</A>. Showtimes, theaters, movie news, & more!</FONT></div></body></html>