<html><head></head><body name="Mail Message Editor"><div><span class="Apple-style-span" style=""><br></span></div><div><span class="Apple-style-span" style="">Charles:<div><span class="Apple-style-span" style=""><br></span></div><div><span class="Apple-style-span" style="">Thank you very much for this reference, which I had not heard of. Now I can be less surprised that the variant has been overlooked! I will add the “complex latitude transverse Mercator” as a synonym in Geocart’s literature and try to acquire a copy of the paper.<div><span class="Apple-style-span" style=""><br></span></div><div><span class="Apple-style-span" style="">Regards,<div><span class="Apple-style-span" style="">— daan Strebe</span></div></span></div></span></div></span></div><div><span class="Apple-style-span" style=""><br></span></div><div><span class="Apple-style-span"><br></span></div><div id="replyPrefaceElement">On Jul 13, 2010, at 2:36:48 PM, "Karney, Charles" <ckarney@Sarnoff.com> wrote:</div><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-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: 0px; font-size: medium; "><div style="width: 749px; "><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: 749px; "><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=""Karney, Charles" <ckarney@Sarnoff.com>">"Karney, Charles" <ckarney@Sarnoff.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; ">Wallis 1 transverse Mercator</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>July 13, 2010 2:36:48 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>,<span class="Apple-converted-space"> </span><span title=""strebe@aol.com" <strebe@aol.com>">"strebe@aol.com" <strebe@aol.com></span></td></tr></tbody></table></div><div id="felix-mail-content-block" style="color: black; background-color: white; width: 749px; "><div style="font-family: monospace; color: black; background-color: white; font-size: 8pt; "><pre>> From: strebe@aol.com
> Sent: Sunday, February 01, 2009 04:23
>
> I've posted here and image of yet another ellipsoidal transverse
> Mercator variation:
> http://www.mapthematics.com/Wallis1TransverseMercator.tif
>
> This one's properties are:
> Conformal (of course)
> Straight central meridian (of course)
> Parallels are equally spaced.
>
> The importance of this last property is that the projection then may
> be squeezed through the rectifying latitude calculation as applied to
> the complex plane, and out pops Gauß-Krüger. I generated the map using
> the same eccentricity in your examples so that the 81st meridian (and
> 99th) will run into the singularities. The graticule is 9°. The
> projection is cropped at a distance of 4 arc seconds around the
> singularities; in point of fact the projection is infinite in extent.
There's a depiction of your "Wallis 1" projection in
R. Koenig and K. H. Weise,
Mathematische Grundlagen der Hoeheren Geodaesie und Kartographie,
(Springer-Verlag, 1951), Vol 1.
See figure 16b on page 88. They call this the "complex latitude plane"
(B-Ebene).
--Charles
--
Charles Karney <ckarney@sarnoff.com>
Sarnoff Corporation, Princeton, NJ 08543-5300
Tel: +1 609 734 2312
Fax: +1 609 734 2662
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