[Proj] Wallis 1 transverse Mercator

Karney, Charles ckarney at Sarnoff.com
Tue Jul 13 16:36:48 EST 2010

> 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"


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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