[Proj] Wallis 1 transverse Mercator

[strebe]

Charles:

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.

Regards,
— daan Strebe


On Jul 13, 2010, at 2:36:48 PM, "Karney, Charles" <ckarney at Sarnoff.com> wrote:

From:   "Karney, Charles" <ckarney at Sarnoff.com>
Subject:    Wallis 1 transverse Mercator
Date:   July 13, 2010 2:36:48 PM PDT
To: "PROJ.4 and general Projections Discussions" <proj at lists.maptools.org>, "strebe at aol.com" <strebe at aol.com>
> From: strebe at 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 at sarnoff.com>
Sarnoff Corporation, Princeton, NJ 08543-5300

Tel: +1 609 734 2312
Fax: +1 609 734 2662
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